its_morren_20061113.
Johan Morren
ISBN: 90-811085-1-4
Grid support by power electronic
converters of Distributed Generation units
The introduction of Distributed Generation (DG) causes several problems, which are mainly
related to the differences between DG units and conventional generators. A large part of the
DG units are connected to the grid via power electronic converters. The main task of these
converters is to convert the power that is available from the prime source to the characteristic
voltage and frequency of the grid. The flexibility of the converters offers the possibility to
configure them in such a way that, in addition to their main task, they can support the grid. Four
issues have been considered in this thesis: damping of harmonics, voltage control, the behaviour
of DG units during grid faults, and frequency control. The different control strategies that are
required to achieve the grid support can all be implemented simultaneously in the control of a
DG unit. In this way a multi-functional DG unit is obtained that can autonomously support the
grid in several ways.
Johan Morren
Grid support by power
electronic converters
of Distributed
Generation units
Uitnodiging
Graag wil ik u uitnodigen om
aanwezig te zijn bij de openbare
verdediging van mijn proefschrift
Grid support by power
electronic converters
of Distributed
Generation units
Op D.V. maandag 13 november om
12:30 uur in de Aula van de Technische Universiteit Delft, Mekelweg 5
te Delft.
Voorafgaand geef ik om 12:00 uur
een korte samenvatting van het
onderzoek.
Na afloop van de promotieplechtigheid bent u van harte welkom op de
receptie die op dezelfde locatie zal
plaatsvinden.
Johan Morren
St. Antonielaan 328
6821 GP Arnhem
[email protected]
Grid support by power electronic
converters of Distributed Generation
units
Grid support by power electronic
converters of Distributed Generation
units
PROEFSCHRIFT
ter verkrijging van de graad van doctor
aan de Technische Universiteit Delft,
op gezag van de Rector Magnificus prof. dr. ir. J.T. Fokkema,
voorzitter van het College voor Promoties,
in het openbaar te verdedigen op maandag 13 november 2006 om 12.30 uur
door
Johannes MORREN
elektrotechnisch ingenieur
geboren te Ede
Dit proefschrift is goedgekeurd door de promotor:
Prof. dr. J.A. Ferreira
Toegevoegd promotor:
Ir. S.W.H. de Haan
Samenstelling promotiecommissie:
Rector Magnificus, voorzitter
Prof. dr. J.A. Ferreira, Technische Universiteit Delft, promotor
Ir. S.W.H. de Haan, Technische Universiteit Delft, toegevoegd promotor
Prof. ir. W.L. Kling, Technische Universiteit Delft
Prof. ir. L. van der Sluis, Technische Universiteit Delft
Prof. dr. ir. J.H. Blom, Technische Universiteit Eindhoven
Prof. dr. ir. J. Driesen, Katholieke Universiteit Leuven
Prof. ir. M. Antal, Technische Universiteit Eindhoven (emeritus)
The research was supported financially by SenterNovem in the framework of the
‘Innovatiegerichte OnderzoeksProgramma ElektroMagnetische VermogensTechniek’
(IOP-EMVT).
Cover design by Hans Teerds
Cover pictures: ABB, Capstone, Hans Teerds
Printed by: Gildeprint B.V., Enschede, The Netherlands
ISBN: 90-811085-1-4
Copyright © 2006 by Johan Morren
All rights reserved.
Summary
Grid support by power electronic converters of
Distributed Generation units
Johan Morren
For several reasons an increasing number of small Distributed Generation (DG) units
are connected to the grid. Most DG units are relatively small and connected to the
distribution network. The introduction of DG causes several problems, which are
mainly related to the differences between DG units and conventional generators: they
are located at other places in the network, they are operated in another way, they use
other technologies, and they can not always control their power. Four problems have
been considered in this thesis: damping of harmonics, voltage control, the behaviour of
DG units during grid faults, and frequency control.
A large part of the DG units are connected to the grid via power electronic
converters. The main task of the converters is to convert the power that is available from
the prime source to the correct voltage and frequency of the grid. The flexibility of the
converters offers the possibility however to configure them in such a way that, in
addition to their main task, they can avoid or solve some of the problems they cause.
The general objective of this thesis is to investigate how the power electronic
converters can support the grid and solve some problems.
An increasing number of power electronic interfaced DG units will result in an increase
of the capacitance in the grid, as most converters have a capacitor in their output filter.
This capacitance can resonate with the network reactance. An active damping controller
is defined in chapter 3, which can easily be implemented in the DG unit control. With
this damping controller the DG unit converter can significantly increase the contribution
to damping and reduce the harmonics in the network. Conditions are derived for which
the converter works and it is analysed how large its contribution can be.
The connection of DG units to the network will result in a change in voltage. The
maximum allowable voltage change is limited by regulations and standards. They limit
the maximum percentage of DG that can be connected to a network. The DG units can
consume reactive power to limit the voltage increase they cause by supplying active
power to the grid. Especially in networks that have a high X/R ratio a significantly
higher penetration of DG can be allowed in this way. Most networks are rather resistive
however. By applying converter overrating, generation curtailment, or the use of a
variable inductance, also in these networks the maximum penetration level can be
increased considerably. An approach has been presented to determine the maximum
allowable DG unit penetration.
Most grid operators require the disconnection of DG units when faults like shortcircuits and voltage dips occur in the network. An important reason for this requirement
is that the grid operators fear that DG units disturb the classical protection schemes that
are applied. Chapter 5 shows that power electronic interfaced DG units do not
necessarily disturb the protection schemes however, as they do not supply large shortcircuit currents. Thus, disconnection of these DG units is not necessary. The units can
then be used to support the grid (voltage) during the fault.
Most types of DG unit can remain connected to the network in case of a grid fault.
Appropriate control strategies have been presented. For one type of DG unit, namely a
wind turbine with a doubly-fed induction generator, ride-through is more difficult.
Some special measures have been proposed to protect this type of turbine. The key of
the technique is to limit the high currents in the rotor circuit with a set of shunt resistors,
without disconnecting the converter. In this way the turbine remains synchronised and it
can supply (reactive) power to the grid during and immediately after a voltage dip.
Nowadays the grid frequency is stabilised by the conventional power plants. The
goal of the frequency control is to maintain the power balance and the synchronism
between the synchronous generators in the system. Most DG units do not participate in
the frequency control. An increasing DG penetration level can therefore result in larger
frequency fluctuations after disturbances. A method has been developed to let DG units
participate in frequency control. For most individual DG units this is not possible,
because they can not control their power source or because they are too slow. With a
combination of different types of DG unit it is possible to support the frequency control
however. Requirements are derived which can be used to determine the percentage of
each of the DG unit types that is required to obtain a good overall response. Controllers
have been presented that implement the frequency control on the DG units.
The different control strategies that have been defined in this thesis can all be
implemented simultaneously in the control of a DG unit. A state diagram is derived that
can be used to achieve the appropriate control in each situation. The control operates
autonomously. Only the grid voltage at the DG unit terminal needs to be measured. In
this way a multi-functional DG unit is obtained that can autonomously support the grid
in several ways. Implementation of the grid support controller requires in most cases
only adaptation of the control software. It can thus be implemented at low cost.
Samenvatting
Netondersteuning door vermogenselektronische
omvormers van decentrale opwekeenheden
Johan Morren
Om diverse redenen neemt het aantal kleine decentrale opwek (Distributed Generation,
DG) eenheden toe. De meeste DG eenheden zijn relatief klein en aan het distributienet
gekoppeld. De introductie van DG leidt tot diverse problemen, welke hoofdzakelijk
gerelateerd zijn aan de verschillen tussen DG eenheden en conventionele opwekkers: ze
bevinden zich op andere plaatsen in het netwerk, worden op een andere manier
bedreven, gebruiken andere technologieën en kunnen niet altijd hun vermogen regelen.
Vier problemen zijn beschouwd in dit proefschrift: demping van harmonischen,
spanningsregeling, het gedrag van DG eenheden bij netfouten en frequentieregeling.
Een groot gedeelte van de DG eenheden is via vermogenselektronische omvormers
aan het net gekoppeld. De belangrijkste taak van deze omvormers is om het vermogen
dat de primaire bron levert om te zetten naar de juiste spanning en frequentie van het
net. De flexibiliteit van de omvormers biedt echter de mogelijkheid om ze zodanig te
configureren dat ze, in aanvulling op hun eigenlijke taak, sommige problemen die ze
zelf veroorzaken kunnen vermijden of oplossen.
Het doel van dit proefschrift is te onderzoeken hoe de vermogenselektronische
omvormers het net kunnen ondersteunen en sommige problemen kunnen oplossen.
Een toenemend aantal vermogenselektronisch gekoppelde DG eenheden zal leiden tot
een toename van de capaciteit in het net, aangezien de meeste omvormers een
condensator in hun uitgangsfilter hebben. Deze capaciteit kan resoneren met de
netwerkinductiviteit. In hoofdstuk 3 is een ‘active damping controller’ gedefinieerd die
eenvoudig geïmplementeerd kan worden in de regeling van de DG eenheid. Met deze
regeling kan de omvormer van de DG eenheid de bijdrage aan de demping aanzienlijk
verhogen en de harmonischen in het net reduceren. Voorwaarden waarvoor waarvoor de
omvormer werkt zijn afgeleid en de grootte van zijn bijdrage is geanalyseerd.
De koppeling van DG eenheden aan het net zal een verandering in spanning
veroorzaken. De maximaal toegestane spanningsverandering wordt beperkt door regels
en standaarden. Ze beperken het maximum DG percentage dat aan een net gekoppeld
IV
kan worden. De DG eenheden kunnen reactief vermogen opnemen om de
spanningstoename, die ze veroorzaken door actief vermogen aan het net te leveren, te
beperken. Speciaal in netwerken die een hoge X/R verhouding hebben kan op deze
manier een significant hogere DG penetratie toegestaan worden. De meeste netwerken
hebben echter een veel lagere X/R verhouding. Door overbelasting van de converter of
beperking van de opwek, of door een variabele inductiviteit te gebruiken, kan ook in
deze netwerken een hogere DG penetratie toegestaan worden. Een aanpak om de
maximaal toegestane DG eenheid penetratie te bepalen is gepresenteerd.
De meeste netbeheerders eisen de afkoppeling van DG eenheden wanneer fouten
zoals kortsluitingen en spanningsdips plaatsvinden in het netwerk. Een belangrijke
reden voor deze eis is dat ze vrezen dat DG eenheden de klassieke beveilingsconcepten
verstoren. Hoofdstuk 5 laat zien dat vermogenselektronisch gekoppelde DG eenheden
niet noodzakelijkerwijs de beveiliging verstoren, aangezien ze geen grote kortsluitstroom leveren. Daarom is afkoppeling van deze DG eenheden niet nodig. De eenheden
kunnen dan gebruikt worden om gedurende de fout het net te ondersteunen.
De meeste typen DG eenheid kunnen dus aan het net gekoppeld blijven in het geval
van een fout. Regelstrategieën om dit mogelijk te maken zijn gepresenteerd. Voor één
type DG eenheid, namelijk een wind turbine met dubbelgevoede inductiegenerator, is
het moeilijker om tijdens een fout netgekoppeld te blijven. Speciale maatregelen zijn
voorgesteld om dit type wind turbine te beveiligen. De kern van de techniek is om de
hoge stromen in het rotorcircuit te beperken met een set parallelweerstanden, zonder de
omvormer af te koppelen. Op deze manier kan de turbine gesynchroniseerd blijven en
kan ze gedurende en direct na de spanningsdip (reactief) vermogen aan het net leveren
Vandaag de dag wordt de netfrequentie gestabiliseerd door de conventionele
centrales. Het doel van de frequentieregeling is om de vermogensbalans en het
synchronisme tussen de synchrone generators in het net te handhaven. De meeste DG
eenheden participeren niet in de frequentieregeling. Een toenemende DG penetratie kan
daarom resulteren in grotere frequentiefluctuaties na verstoringen. Een methode om DG
eenheden te laten participeren in frequentieregeling is ontwikkeld. Voor de meeste
individuele DG eenheden is dit niet mogelijk, omdat ze hun vermogensbron niet (snel
genoeg) kunnen regelen. Met een combinatie van verschillende typen DG eenheid is het
echter mogelijk frequentieregeling te ondersteuen. Er zijn vereisten afgeleid die
gebruikt kunnen worden om het percentage te bepalen van elk type DG eenheid (of
groep van typen) dat nodig is om een goede totaalreponsie te behalen. Regelaars zijn
gepresenteerd die de frequentieregeling implementeren in de DG eenheden.
De verschillende regelstrategieën die gedefinieerd zijn in dit proefschrift kunnen
allemaal gelijktijdig geïmplementeerd worden in de regeling van een DG eenheid. Er is
Samenvatting
V
een toestandsdiagram ontworpen dat in elke situatie de geschikte regeling bepaald. Deze
regeling werkt autonoom. Alleen de netspanning aan de klemmen van de DG eenheid
behoeft gemeten te worden. Op deze manier is een multi-functionele DG eenheid
verkregen die autonoom op verschillende manieren het net kan ondersteunen. De
implementatie van de regelingen vereist in de meeste geval alleen maar een aanpassing
van de regelsoftware. De regelingen kunnen dus meestal tegen weinig kosten
geïmplementeerd worden.
VI
Contents
Summary
I
Samenvatting
III
Contents
VII
Chapter 1. Introduction
1.1 Background
1.2 Problem definition
1.3 Objective and research questions
1.4 Approach
1.5 Outline
1.6 Intelligent power systems research project
Chapter 2. Distributed Generation and Power
Electronics
2.1 The conventional electricity network
2.2 Distributed Generation: drivers and definitions
2.3 Distributed Generation Technologies
2.3.1 Fuel cells
2.3.2 Micro turbines
2.3.3 Wind turbines
2.4 Power Electronic Converters
1
1
2
3
5
6
8
11
11
12
13
13
15
16
17
VIII
2.4.1 Basic principles
2.4.2 Control
2.4.3 Voltage and current source converters
2.5 Literature review
2.5.1 Introduction
2.5.3 Distribution Generation
2.5.4 Grid support by DG units
2.5.5 Microgrids
Chapter 3. Harmonic damping contribution of
DG unit Converters
3.1. Introduction
3.2. Incremental impedance
3.3. Frequency domain analysis of power electronic converters
3.3.1 Converter description
3.3.2 Basic building blocks
3.3.3 Model comparison
3.4 Damping capability of converter
3.4.1 Converter output impedance
3.4.2 Damping contribution in grid
3.5 Active damping
3.5.1 Introduction
3.5.2 Damping controller operation principles
3.5.3 Influence of type and location of the harmonic source
3.5.4 Value of emulated damping conductance
3.5.5 Limitations and operation range
3.6 Case studies
3.7 Concluding remarks
18
20
20
22
22
22
23
24
25
25
26
30
30
31
34
32
32
34
35
35
36
38
39
41
42
44
Chapter 4. Voltage control contribution of DG units 47
4.1 Introduction
4.2 Reactive power control
4.2.1 Basic theory
47
49
49
Contents
4.2.2 Effect of X/R ratio on voltage deviation and voltage control
possibilities
4.2.3 Overrating and generation curtailment
4.3 Variable Inductance
4.3.1 Variable Inductance value
4.3.2 Implementation
4.4 Maximum DG penetration
4.4.1 Introduction
4.4.2 DG only
4.4.3 Overrating and curtailment
4.4.4 Variable inductance
4.4.5 Discussion
4.5 Cases
4.5.1 Case 1
4.5.2 Case 2
4.5.3 Discussion and conclusion
4.6 Summary and discussion
Chapter 5. Ride-through and grid support during
faults
5.1 Introduction
5.2 Fault response of DG units
5.3 Disturbance of protection during faults
IX
50
52
55
55
56
58
58
58
59
60
61
62
62
64
65
66
67
67
68
70
5.3.1 Introduction
5.3.2 Blinding of protection
5.3.3 False tripping
5.3.4 Failure of reclosing
5.3.5 Islanding
70
70
71
71
72
5.4 Grid support during dips
72
5.4.1 Introduction
5.4.2 Voltage control with (re-)active power
5.4.3 Variable inductance
5.4.4 Example
5.5 DG Unit ride-through during voltage dips
5.5.1 Introduction
72
73
75
76
77
77
X
5.5.2 Variable speed wind turbine with full converter
5.5.3 Fuel cell and micro turbine
5.6 Doubly-fed Induction Generator
5.6.1 Introduction
5.6.2 Fault response and protection of doubly-fed induction generator
5.6.3 Short-circuit current and by-pass resistor value
5.6.4 Simulation results
5.7 Conclusion
Chapter 6. Frequency-control contribution of
DG units
6.1 Introduction
6.2 Classical power-frequency control
6.2.1 Introduction
6.2.2 Inertial response
6.2.3 Primary control
6.2.4 Secondary control
6.3 Effect of DG units on frequency response
6.4 Method
6.4.1 Primary control
6.4.2 Inertial response
6.4.3 Mix Requirements (or: ‘Equivalent power plants’)
6.5 DG unit contribution to inertia and primary frequency control
6.5.1 Wind turbines
6.5.2 Micro turbines
6.5.3 Fuel cell
6.5.4. Summary: Primary control reserve, deployment time and inertia
6.6 Case studies
6.6.1 Simulation setup
6.6.2 Parameters
6.6.3 Case study: Frequency control with fuel cells and wind turbines
6.6.4 Discussion
6.7 Summary and conclusions
77
82
82
82
83
85
88
90
93
93
94
94
94
95
96
97
99
99
103
107
110
110
112
113
114
115
116
118
119
121
121
Contents
Chapter 7. Implementation of grid support control
7.1 Introduction
7.2 Controller implementation
7.3 Case study
7.3.1 Setup
7.3.2 Models
7.3.3 Parameters
7.3.4 Results case 1
7.3.5 Results case 2
7.4 Discussion and conclusion
Chapter 8. Conclusions and recommendations
8.1 Conclusions
8.2 Recommendations
XI
123
123
123
126
126
127
127
128
131
131
133
133
137
References
139
Appendix A: Network model description
145
A.1 Urban network
A.2 Rural network
A.3 Low-voltage network
Appendix B: Converter model description
B.1 Single-phase full-bridge converter
B.2 Three-phase full-bridge converter
B.3 Three-phase back-to-back converter
Appendix C: DG unit model description
145
146
147
149
149
150
153
155
XII
C.1 Fuel cell
C.2 Micro turbine
C.3 Wind turbine with doubly-fed induction generator
C.4 Wind turbine with synchronous machine and full converter
155
158
160
164
Appendix D: Short-circuit response of induction
machine
165
Appendix E: Park transformation
171
Appendix F: On the use of reduced converter models 175
F.1 Switching function concept
F.2 Fourier analysis theory
F.3 Harmonic spectrum of triangular carrier modulation
F.4 Harmonic voltages in a half-bridge converter
F.5 Discussion and conclusion
175
176
177
179
179
List of symbols
181
Dankwoord
185
List of publications
187
Curriculum Vitae
191
Chapter 1
Introduction
1.1. Background
Over the last years an increasing number of Distributed Generation (DG) units are
connected to the grid. This development is driven by governmental policy to reduce
greenhouse gas emissions and conserve fossil fuels, as agreed in the Kyoto protocol, by
economical developments such as the liberalisation and deregulation of the electricity
markets, and by technical developments. Most DG units are relatively small and
connected to the distribution network (DN). A large percentage of the sources are
connected to the grid via power electronic converters.
The introduction of DG results in a different operation of the electrical power
system. The conventional power system is characterised by a power flow from a
relatively small number of large power plants to a large number of dispersed end-users.
Electrical networks transport the electrical energy using a hierarchical structure of
transmission and distribution networks. In a limited number of control centres the
system is continuously monitored and controlled. [Bla 04], [Don 02]
The changes due to the introduction of DG are mainly caused by the differences in
location and operation principle between the DG units and the conventional generators
and loads. The most important differences are:
• The DG units are mostly connected to the DN; this introduces generators in the DN,
which historically only contained loads [Bar 00], [Had 04].
• A large percentage of the DG units are connected to the grid via power electronic
converters, which have a behaviour that is fundamentally different from the
behaviour of the conventional synchronous machine based generators [Jóo 00], [Kna
04].
• Several types of DG unit are based on renewable energy sources like sun and wind,
which are uncontrollable and have an intermittent character [Ack 02], [Püt 03].
• Most DG units behave as ‘negative loads’ and do not participate in the conventional
control of the network [Jen 00].
2
1.2 Problem definition
The introduction of DG causes several problems. The four problems that will be
investigated in this thesis are described in this section. They are all caused by the
differences in location and operation principle between DG units and the conventional
generators and loads, described in the previous section. First three problems with a local
impact are considered. The fourth issue has a global impact, meaning that the system as
a whole is affected [Slo 03b].
Damping of harmonics – An increasing number of power electronic interfaced DG units
will result in an increase of the capacitance in the grid, as most converters have a
capacitor in their output filter [Lis 06]. Manufacturers try to decrease filter inductors to
make the inverter more cost-effective. At the same time the capacitance has to be
increased to let the cut-off frequency of the filter remain the same [Ens 04]. The output
capacitance can form a resonance circuit with the network reactance. In conventional
grids the amount of capacitance is low, implying high resonance frequencies and a
limited chance that the resonance circuits are excited. With an increasing amount of
capacitance the resonance frequency will decrease and may be more easily excited by
harmonics. As a result there is an increasing risk for resonances, oscillatory responses,
and a high level of harmonic distortion [Ens 04]. How large the amplitude of the
harmonic voltages and currents will be, depends on the damping in the network.
Voltage control - The objective of voltage control is to maintain the RMS value of the
voltage within specified limits, independent of the generation and consumption [Mil 82],
[Kun 94]. Conventional voltage control in the high-voltage transmission network is
mainly performed by the large power plants. In DNs voltage control is done by tap
changers on distribution transformers. This control is relatively slow and compensates
for the current-depending voltage drop along the line, based on the assumption that only
loads are connected to the network. Introduction of DG units in the DN will change the
power flow in a part of the network. In addition some DG units have a primary energy
source that fluctuates [Jen 00], especially those that are based on renewable energy
sources such as wind and sun. As a result the DG unit power may fluctuate. The
changes in magnitude and direction of the power will result in changing voltages, due to
the current-depending voltage drop along the line, which has a relatively high
impedance in the low-voltage and medium-voltage grid [Jen 00], [Str 02]. The voltage
fluctuations can range from slow (hours) to fast (milliseconds). It may become difficult
to keep the voltage within the specified limits and to meet requirements regarding
flicker [Bar 00], [Tan 04].
1. Introduction
3
Fault behaviour - In power systems many types of fault can occur, such as for example
voltage dips and short-circuits [Bol 00]. Fault behaviour concerns the response of the DG
units to these faults. The introduction of DG units in the DN can disturb the classical
protection schemes that are applied [Kum 04]. This holds especially for DG units that are
based on synchronous machines. The response of power electronic interfaced DG units
to a fault will depend on the control implementation. Most grid operators require that
DG units are disconnected from the grid during faults [Nav 05]. This minimises the risk
that the grid protection schemes are disturbed. Disconnection may become undesirable
however, when the percentage of DG in a network is increasing. It can result in a large
power generation deficit and will require a larger power reserve of other generators.
Frequency control - Nowadays the grid frequency is stabilised by the conventional
power plants. The goal of the frequency control is to maintain the power balance and the
synchronism between the synchronous generators in the system [Kun 94]. The inertia of
the synchronous machines plays an important role in maintaining the stability of the
power system during a transient situation, e.g. during and after a disturbance. The more
rotational mass the synchronous generator has, the less the generator rotor will respond
to an accelerating or decelerating tendency due to a disturbance [Kun 94]. The large
amount of rotating mass in the present interconnected power systems tends to keep the
system stable following a disturbance. With an increasing penetration level of DG this
stabilising task can become increasingly difficult because of the decreasing level of
inertia in the grid [Kna 04]. Most DG units are connected to the grid by power electronic
converters, and therefore the direct relation between power and frequency is lost [Jóo 00].
As a result, disturbances might result in larger frequency deviations.
1.3. Objective and research questions
Most of the problems discussed in the previous section occur in the medium and low
voltage networks, where generally no control is available. Although several types of DG
unit employ electric generators that are coupled directly to the grid, the trend is to use a
power electronic interface [Jóo 00]. The main task of these power electronic converters is
to transfer the active power to the grid. The flexibility of the converters offers the
possibility to configure them such that, in addition to their main task, they support the
grid and solve or mitigate some of the mentioned problems. The general objective of
this thesis is based on these observations and is defined as:
4
Investigate if and how the power electronic converters of the DG units can be
used to solve some of the problems caused by the introduction of DG, taking
into account the requirements that are imposed by the network and the DG unit
itself.
Based on this objective and the problem definition given above, four main research
questions have been defined:
a) Damping of harmonics: How and to what extent can the power electronic
converters contribute to the damping in the grid?
b) Voltage control: How and under which conditions can the power electronic
converters of the DG units contribute to steady-state voltage control and how
large can this contribution be?
c) Fault behaviour: How should the power electronic converters of the DG units
react to short-circuits and voltage dips in order to avoid disturbance of the
grid protection, to support the grid, and to protect the DG unit from
malfunctioning?
d) Frequency control: How and to what extent can power electronic interfaced
DG units contribute to primary frequency control and the inertia of the
system?
Voltage
control
Damping of
harmonics
Frequency
control
Fault
behaviour
Power Electronics
Knowledge
base
Research
topics
The main differences between the four research items are the grid parameters that
are controlled (frequency, power, voltage) and the time scale of the phenomena. In
power systems three time scales are generally distinguished, namely steady state,
dynamic, and transient. Fig. 1.1 shows the time scales in which the phenomena fit.
Electro-mechanics
Power Systems
Steady state
Dynamic
Transient
Fig. 1.1. Time scales in which the different problems occur and that are covered by the DG unit connection
technologies
1. Introduction
5
For these research items several knowledge bases play a role, namely power
systems, electro-mechanics and power electronics. These three knowledge bases cover
all time frames, as shown in Fig. 1.1. In this thesis the problems are considered from the
point of view of the power electronics knowledge base, which all power electronic
interfaced DG units have in common.
1.4. Approach
The goal of this thesis is to investigate how DG unit converters can support the grid and
how they can solve the problems mentioned in the previous section. The approach for
each of the topics is more or less the same.
Simplified models of the network and the DG units are derived. They are used to
give a mathematical description of the problem. Based on this description mathematical
analyses are done to quantify for which combination of parameters problems occur and
how large the problems are. In the same way it is investigated how large the support can
be. The results of the analyses are presented in a number of graphs. The values in these
graphs are mostly in per unit to keep the results as general applicable as possible.
In the next step it is investigated how the grid support can be achieved by DG units.
In this stage controller implementations and control strategies are derived. For some of
the topics it is obvious how the control should be implemented. For the other topics
appropriate control schemes, which can be implemented as additional control, will be
described. The performance of the controllers is demonstrated with (time-domain) case
study simulations.
Three types of DG unit will be considered in this thesis. They represent the three
different groups of DG units that are important with respect to frequency control: fuel
cells (static, controllable power source), micro-turbines (rotating, controllable power
source), and wind turbines (rotating, uncontrollable power source). The models that are
used are described in appendix C. The models of the converters that the DG units use
are described in appendix B.
For each of the topics one or more realistic cases are studied to investigate the
performance of the proposed controllers. They are performed on a number of case study
networks, which are simplifications of some Dutch MV and LV networks. The three
networks are described below. More information is given in appendix A.
Urban network - The ‘Testnet’ in Lelystad is a 10 kV cable distribution network in a
residential area. It consists of a HV/MV distribution substation with a number of radial
feeders. Three wind turbines with a total installed capacity of about 1.5 MW and a CHP
6
plant of about 2.5 MW are connected to this network. The network is rather lightly
loaded and can be considered as a ‘strong’ network.
Rural network - The second network is an extensive rural 10 kV cable network in the
north of the Netherlands. Some small wind turbines are connected to a feeder of the
network. The feeder has a relative high impedance, which in some cases results in large
voltage changes. The feeder can be considered as a ‘weak’ network.
Low-voltage network - The network in Vroonermeer-Zuid is a typical 400 V lowvoltage network. It is of special interest because it contains a large penetration of solar
cell inverters. One network, with a peak solar generation capacity of 235 kW and an
average load of 26 kW, is considered. The network is of particular interest because
severe problems with harmonic distortion and resonances have been noted.
All case study simulations are done in Matlab Simulink. Several models that are
used are in the dq0 reference frame. The advantage of using this reference frame is that
all signals are constant in steady state, resulting in a large increase in simulation speed.
The basic principles of deriving models in the dq0 reference frame are presented in
appendix E. For the models in this thesis only the d- and the q-axis are modelled, as
only symmetrical situations are considered.
1.5 Outline
This section presents an outline of the thesis.
Chapter 2 – Chapter 2 gives a review of the relevant basics of power systems,
Distributed Generation, and power electronics. This information can be helpful to
understand the remaining part of the thesis.
Chapter 3 – In chapter 3 is investigated how power electronic converters can improve
the relative damping in the grid. Relative damping is a function of frequency and
therefore the analyses are done in the frequency domain. As a first step, transfer
functions of power electronic converters are obtained. They are used to determine the
damping contribution of the converter, by looking at the location (in the real-imaginary
plane) of the resonant poles of the system. The influence of the converter is shown to be
small, and therefore an active damping controller is proposed to increase the
contribution to damping. Conditions are derived for which the active damping controller
1. Introduction
7
works, and it is analysed how large its contribution can be. With some case studies the
capabilities of the proposed damping controller are shown.
Chapter 4 - The voltage change caused by DG units depends on a number of parameters
such as the short-circuit power of the network and the ratio between the inductance and
the resistance (X/R ratio) of the grid. Chapter 4 starts with deriving relations between
these parameters. The analyses show that voltage control possibilities with reactive
power are limited, due to the low X/R ratio of (cable) distribution networks. The chapter
describes a number of solutions to improve the possibilities for voltage control. It then
continues with deriving equations that can be used to determine the maximum DG
penetration that is possible when the voltage change caused by the DG units should stay
below a certain limit. With some cases it is demonstrated how the relations derived in
the chapter can be used to determine the maximum DG penetration level in practical
situations.
Chapter 5 – Synchronous machines and power electronic converters have a completely
different response to faults. Chapter 5 starts with comparing the responses. To a certain
extent the converter response can be freely chosen, in contrast with a machine that has
an inherent response. The flexibility of the converter control enables minimisation of
the influence on the classical protection, as will be shown. When DG units do not
disturb the protection they can stay connected during a fault and support the grid. The
effectiveness of this support is investigated. To enable fault ride-through some measures
have to be taken for some DG units. These measures will be presented. A special case
during short-circuits is a wind turbine with a doubly-fed induction generator. It is
analysed at the end of chapter 5.
Chapter 6 - Chapter 6 investigates how and to which extent power electronic interfaced
DG units can contribute to frequency control. It starts with a description of the response
of a conventional power system to load unbalances and frequency deviations. The
response depends mainly on the inertia of the systems and the ability of the generators
to increase their output power. For the most important DG unit types it will be
investigated whether they can increase their output power and whether they have inertia
or that a ‘virtual inertia’ can be emulated. With a good mix of types of DG units
frequency control support is possible. A method to determine such a mix will be
derived. The method is used to derive a number of figures that show the minimum and
maximum allowable penetrations levels of different combinations of conventional
generation and different types of DG. Time-domain simulation of a case study shows
that frequency control is possible with the proposed mix.
8
Chapter 7 – The different grid support strategies and controllers are discussed in
separate chapters. Chapter 7 investigates how the different support strategies can be
implemented in one converter. The chapter develops a state diagram that can be
implemented in the DG unit control.
Chapter 8 – General conclusions and recommendations for further research are given in
chapter 8.
1.6 Intelligent power systems research project
The research presented in this thesis was performed within the framework of the
‘Intelligent Power Systems’ project. The project is part of the IOP-EMVT program
(Innovation Oriented research Program – Electro-Magnetic Power Technology), which
is financially supported by SenterNovem, an agency of the Dutch Ministry of
Economical Affairs. The ‘Intelligent Power Systems’ project is initiated by the
Electrical Power Systems and Electrical Power Processing groups of the Delft
University of Technology and the Electrical Power Systems and Control Systems
groups of the Eindhoven University of Technology. In total 10 PhD students, who work
closely together, are involved in the project.
The research focuses on the effects of the structural changes in generation and
consumption which are taking place, like for instance the large-scale introduction of
distributed (renewable) generators [Rez 03].
Such a large-scale implementation of distributed generators leads to a gradual
transition from the current ‘vertically-operated power system’, which is supported
mainly by several big centralised generators, into a future ‘horizontally-operated power
system’, having also a large number of small to medium-sized distributed (renewable)
generators. The project consists of four parts, as illustrated in Fig. 1.2.
The first part investigates the influence of decentralised generation without centralised
control on the stability and dynamic behaviour of the transmission network. As a
consequence of the transition in the generation, fewer centralised plants will be
connected to the transmission network as more generation takes place in the distribution
networks, close to the loads, or in neighbouring systems. Solutions that are investigated
include the control of centralised and decentralised generation, the application of power
electronic interfaces and monitoring of the stability of the system.
1. Introduction
9
The second part focuses on the distribution network, which becomes ‘active’. There is a
need for technologies that can operate the distribution network in different modes and
support the operation and robustness of the network. The project investigates how the
power electronic converters of decentralised generators or power electronic interfaces
between network parts can be used to support the grid. Also the stability of the
distribution network and the effect of the stochastic behaviour of decentralised
generators on the voltage level are investigated. The research presented in this thesis has
been performed in this part of the project
In the third part autonomous networks are considered. When the amount of power
generated in a part of the distribution network is sufficient to supply the local loads, the
network can be operated autonomously but as a matter of fact remains connected to the
rest of the grid for reliability reasons. The project investigates the control functions
needed to operate the autonomous networks in an optimal and reliable way.
The interaction between the grid and the connected appliances has a large influence on
the power quality. The last part of the project analyses all aspects of the power quality.
The goal is to support the discussion between the polluter and the grid operator who is
responsible for compliance with the standards. The realisation of a power quality test
lab is an integral part of this part of the project.
1
Inherently
stable
transmission
system
4
2
Optimal
power
quality
Manageable
distribution
networks
3
Selfcontrolling
autonomous
networks
Fig. 1.2. The four parts of intelligent power systems research project
10
Chapter 2
Distributed Generation and Power
Electronics
Over the last years an increasing number of small, Distributed Generation (DG) units
are connected to the grid. Power electronics plays an important role in the connection of
these DG units to the grid. This chapter discusses some important aspects related to DG,
power electronics and the conventional power system, which might help to understand
this thesis.
2.1 The conventional electricity network
Over the past century the electrical power systems have evolved to the concept that
large power plants provide the optimal cost-effective generation of electricity. The
electrical energy is transported from these sources to the end-user using a hierarchical
structure of high-voltage transmission networks and medium-voltage and low-voltage
distribution networks (DNs), as shown in Fig. 2.1. To ensure both a high security and
availability, most of the networks have been meshed, to provide alternative routing in
case of faults. They are protected from critical failures and natural phenomena, such as
lightning strikes, with mechanical and electronic protection schemes. The networks are
characterised by a power flow from a relatively small number of large power plants to a
large number of dispersed end-users [Don 02].
The conventional arrangement of the power system offers a number of advantages.
Large generating units can be made energy efficient and can be operated with a
relatively small crew. The interconnected high-voltage transmission network allows
generator reserve requirements to be minimised and the most efficient generating plant
to be used at any time [Slo 03b].
Due to a number of developments an increasing number of DG units are connected
to the power system. The introduction of DG results in differences in the operation of
the power system. Most DG units are relatively small and connected to the distribution
network. This results in an increase in the number of generators and it can result in a
12
change in the direction of the power flow. In addition, several DG unit types are based
on renewable energy sources like sun and wind, which are uncontrollable, and have an
intermittent character. This can result in unpredictable and fluctuating power flows in
the network. Unlike the conventional generators, most DG units do not participate in the
control of the network [Jen 00].
Generation
Power plant
Transmission
Distribution
Substation
End-user
Fig. 2.1. Schematic representation of an electrical power system
2.2 Distributed Generation: drivers and definitions
The increasing interest in and application of DG is driven by political, environmental,
economical and technical developments.
The current political intent to reduce greenhouse gas emissions and conserve fossil
fuels, as agreed in the Kyoto protocol, has resulted in a drive to clean and renewable
energy [Sco 02]. Governments started programmes to support the exploitation of
renewable energy sources such as wind and solar power.
The world-wide move to liberalisation of the electricity markets is considered to
have a positive influence on the increase of DG. A deregulated environment and open
access to the DN is likely to provide better opportunities for DG units [Jen 00]. They
require lower capital costs and shorter construction times. Besides this, it is becoming
increasingly difficult to find sites and permissions for the construction of new large
power plants and transmission facilities as high-voltage overhead lines [Püt 03]. As DG
units are mostly connected to the DN, extension of the transmission network might not
be necessary.
Besides this, DG is being increasingly applied just to help to provide for the everexpanding demand for electric power. Benefits of generating power close to the loads
include the use of waste heat for heating or cooling (combined heat and power (CHP),
co-generation) and the availability of standby power for critical loads during periods
when electricity from the utility is unavailable [Wal 01]. Another important reason is just
2. Distributed Generation and Power Electronics
13
that a number of DG technologies have reached a development stage which allows for
large-scale implementation within the existing electric utility systems [Püt 03].
No general accepted definition of Distributed Generation exists and there are even a
number of other names for DG, such as ‘embedded generation’, ‘dispersed generation’,
‘decentralised generation’, and ‘distributed energy resources’ [Ack 01], [Don 02], [Pep 05].
Although all the definitions are more or less the same, there are some small differences.
Distributed Generation is grid-connected, whereas dispersed generation can be standalone. The term decentralised generation stresses the geographical distribution, whereas
the term embedded generation stresses the fact that the generated power is used locally
[Ack 01]. Distributed resources also incorporate storage devices. In this thesis the term
‘Distributed Generation’ (abbreviated as ‘DG’) is used. For a single generator the term
‘Distributed Generation unit’ (‘DG unit’) is used.
Generally, Distributed Generation units can be defined as generation units that are
connected to the distribution network and that have a relatively small capacity [Püt 03].
This definition implies a wide range of different possible generation schemes. At one
side there are large industrial-site generating plants rated at tens of MW capacity,
whereas at the other side there are small units of a few kW, typical of domestic DG
installations. Distributed Generation should not be confused with renewable generation.
DG technologies include renewable energy sources but are not limited to these sources.
The renewable technologies include photovoltaic systems, wind turbines, small hydro
generators and wave energy generators. Non-renewable technologies include combined
heat and power (CHP, co-generation), internal combustion engines, fuel cells and
micro-turbines [Jen 01], [Püt 03].
2.3 Distributed Generation technologies
This section describes the three types of DG unit that are considered throughout the
thesis: fuel cells, micro turbines, and wind turbines. These three types are representative
for the three main groups of DG units (see section 1.4). They will be described as far as
is necessary to understand their use in this thesis. A description of the model
implementation is given in appendix C.
2.3.1 Fuel cells
Fuel cells are electrochemical devices. A fuel cell system generally consist of three
main parts, as shown in Fig. 2.2; a fuel processor (reformer) which converts fuels such
as natural gas to hydrogen, the fuel cell itself, where the electrochemical processes take
14
place and the power is generated and the power conditioner, which converts the DC
voltage to AC and enables grid-connection.
Grid
Valve
Gas
Reformer
H2
Fuel
Cell
Converter
Pset
Fig. 2.2. Fuel cell system
Fuel cell basics - Fig. 2.3 shows the basic diagram of a fuel cell itself, consisting of a
positive (anode) and a negative (cathode) electrode and an electrolyte. The fuel is
electrochemically oxidised on the anode, while the oxidant is electrochemically reduced
on the cathode. The ions created by the electrochemical reactions flow between the
anode and the cathode through the electrolyte, while the electrons resulting from the
oxidation at the anode flow through an external circuit to the cathode, completing the
electric circuit [Bor 01].
2e-
Load
Fuel in
Oxidant in
H2
Positive
ions
½O2
or
H 2O
Negative
ions
H 2O
Exhaust
Exhaust
Electrolyte
Anode
Cathode
Fig. 2.3. Basic fuel cell diagram
Most fuel cells use gaseous fuels and oxidants. Mostly hydrogen and oxygen are
used. The electrolyte of the fuel cell serves as ion conductor. Single fuel cells produce
only about 1 V. Therefore a large number of fuel cells are used in series and parallel to
form a stack with a considerable output power.
The fuel cells that exist nowadays can be classified by the electrolyte they use:
alkaline fuel cell (AFC), molten carbonate fuel cell (MCFC), phosphoric acid fuel cell
(PAFC), proton exchange membrane fuel cell (PEMFC) and solid oxide fuel cell
(SOFC). The last two types are the most widely used. The PEMFC has an electrolyte
that is a layer of solid polymer (usually a sulfonic acid polymer) that allows protons to
be transmitted from one face to the other. Because of the limitations imposed by the
thermal properties of the membrane, PEM fuel cells operate at a temperature that is
2. Distributed Generation and Power Electronics
15
much lower than that of other fuel cells (~ 90 οC). SOFCs operate at temperatures of
650 to 1000 οC. This allows more flexibility in the choice of fuels. Solid oxide fuel cells
have a non-porous metal oxide electrolyte material. Ionic conduction is accomplished
by oxygen ions.
Characteristics and interface - Most fuel cells have a reformer which converts the fuel
(mostly natural gas) to the hydrogen that is necessary for the electrochemical processes.
The processes in the reformer change rather slow, because of the time that is needed to
change the chemical reaction parameters after a change in the flow of reactants. This
will limit the speed with which fuel cells can change their output power. Typically the
response time is several tens of seconds.
Voltage and current depend on parameters such as the number of stacked fuel cells
and the kind of fuel used. For grid-connected fuel cells an inverter is needed to convert
the DC voltage to AC voltage.
2.3.2 Micro turbines
Micro turbines are small gas turbines with power levels up to several hundreds of
kilowatts. Essentially micro turbines can be considered as small versions of
conventional gas-fuelled generators. The important differences are that they run at much
higher speeds and are connected to the grid with a power electronic converter (PEC).
Micro turbine basics - There are basically two micro turbine types. The one that will be
considered in this thesis is a high-speed single-shaft unit with the electrical generator on
the same shaft as the compressor and turbine. The speed of the turbine is mainly in the
range of 50,000 – 120,000 rpm [Zhu 02]. It needs a frequency converter for connection to
the grid.
A micro-turbine system consists of several parts, which are shown in Fig. 2.4. The
first is a compressor in which air is compressed. The compressed air, together with the
fuel, is fed to the combustor. The output of the combustor is used to drive the gas
turbine. The gas turbine drives the electrical generator, which operates at high speed,
ranging from 1500 to 4000 Hz. To match this with the grid frequency a back-to-back
frequency converter is used. The electrical generator is mostly a permanent magnet
synchronous machine.
Characteristics and interface – The gas turbine and permanent magnet generator are
completely decoupled from the grid by the PEC. The characteristics of the micro turbine
are therefore mainly determined by the converter. The response of the system to
changes in the power setpoint depends on the gas turbine properties.
16
Compressor
Turbine
Air
Fuel
Generator
PM
Grid
Converter
Combustor
Speed
control
Fig. 2.4. Micro turbine system
2.3.3 Wind turbines
Wind turbines convert aerodynamic power into electrical energy. In a wind turbine two
conversion processes take place. The first converts the aerodynamic power that is
available in the wind into mechanical power. The next one converts the mechanical
power into electrical power. Wind turbines can be either constant speed or variable
speed. In this thesis only variable speed wind turbines will be considered.
Wind turbine basics - The mechanical power produced by a wind turbine is proportional
to the cube of the wind speed. The rotational speed of the wind turbine for which
maximum power is obtained is different for different wind speeds. Therefore variable
speed operation is necessary to maximise the energy yield.
Variable speed turbines are connected to the grid via a PEC that decouples the
rotational speed of the wind turbine from the grid frequency, enabling variable speed
operation. Two basic concepts exist for variable speed turbines. The first concept has an
electric generator with a converter connected between the stator windings and the grid,
see Fig. 2.5a. The converter has to be designed for the rated power of the turbine. The
generator is mostly a (permanent magnet) synchronous machine. Some types do not
have a gearbox: the direct-drive concept. An alternative concept is a wind turbine with a
doubly-fed induction generator (DFIG), which has a converter connected to the rotor
windings of the wound-rotor induction machine, see Fig. 2.5b. This converter can be
designed for a fraction (~ 30%) of the rated power.
Wind turbine control - Since electrical and mechanical dynamics in a wind turbine are
of different time scales (i.e. the electrical dynamics are much faster than the mechanical
dynamics), the whole system has two hierarchical control levels [Han 04]. The lower
level controls the electrical generator (small time constants). It has the goal to control
the active and reactive power of the wind turbine. The higher level controls the wind
turbine (large time constants) and consists of the pitch and speed control.
2. Distributed Generation and Power Electronics
17
Converter
gear
box
SM
Grid
gear
box
ASM
Grid
Converter
Control
Control
(a)
(b)
Fig. 2.5. Variable speed wind turbines: (a) with full-size converter; (b) with doubly-fed induction generator
The task of the speed controller is to maintain the optimal tip speed ratio λ over
different wind speeds, by adapting the generator speed. The control is based on a predetermined power-speed curve, as shown in
Fig. 2.6. Based on the measured rotational speed of the turbine, the optimal power
and torque are determined. The error between the actual and the reference torque is sent
to a PI controller. This gives a setpoint for the current controller of the turbine, which
controls the torque to achieve the required speed.
ωmeas
Pref
P
Tref
ΔΤ
PI
iref
ω
ωmeas
Τmeas
Fig. 2.6. Speed controller of variable speed wind turbine
Characteristics and interface –The output power of the wind turbine is not controllable.
Due to the large inertia of the wind turbine blades, the output power of the turbine will
vary slowly. In case of wind turbines with a full converter the response to grid events is
mainly determined by the PEC. In case of a turbine with a DFIG the response is a mix
of the induction machine response and the converter response.
2.4 Power Electronic Converters
Power electronic converters play an increasingly important role in modern electrical
engineering. They are an essential part for the integration of DG units into the grid. The
voltage generated by most DG units cannot be connected to the grid directly. The power
electronic interfaces are necessary to match both the voltage level and frequency of the
18
DG unit and the grid [Bla 04]. This section first explains the basic operation principle of
an IGBT-based voltage source converter (VSC), which is the PEC that is used by most
DG units. Afterwards it discusses under which conditions the operation of another
converter topology (a current source converter) is similar to that of a VSC.
2.4.1 Basic principle
In the early days of power electronics most systems were based on thyristor technology.
The introduction of newer types of switches, such as IGBTs, largely increased the
control possibilities and thus the number of applications for PECs. Thyristors only have
turn-on capability. To turn them off, one has to wait until the next zero crossing of the
current. This limits their application. IGBTs can be turned on and off at will and at
much higher frequencies than a thyristor. In this way complete control over current and
voltage can be obtained. Most modern converters that are used to connect DG units to
the grid will be based on IGBT technology or similar technologies such as Mosfets.
As an example to explain the operation of PECs the single-phase half-bridge shown
in Fig. 2.7 is considered. This one-leg converter is nowadays the basic block for other
converters, such as single-phase full-bridge and three-phase full-bridge converters. The
description is based on [Moh 95]. For ease of explanation it is assumed that the midpoint
‘o’ of the DC input voltage is available, although this is not always the case.
Vdc
2
T+
io
a
0
Vdc
Vdc
2
D-
D+
T-
van
n
Fig. 2.7. Half-bridge converter
The converter switches T+ and T- are controlled by a Pulse Width Modulation
(PWM) circuit. The objective of the modulation circuit is to have the inverter output
sinusoidal with magnitude and frequency controllable. In order to produce a sinusoidal
output waveform at a desired frequency, a sinusoidal control signal at the desired
frequency is compared with a triangular waveform with amplitude vtri, as shown by yhe
signals in Fig. 2.8a. The frequency of the triangular waveform establishes the inverter
switching frequency fs. The reference signal vref is used to modulate the switch duty
ratio and has a frequency f1, which is the desired fundamental frequency of the inverter
output voltage.
2. Distributed Generation and Power Electronics
19
(a)
(b)
Fig. 2.8. Pulse Width Modulation signals; (a) comparison of Vref and Vtri, (b) converter output voltage Va0 and
its fundamental frequency component Va0,1
The switches T+ and T- shown in Fig. 2.7 are controlled based on the comparison of
vref and vtri. When vref > vtri T+ is turned on and va0 = ½Vdc. When vref < vtri T- is turned
on and va0 = -½Vdc. Since the two switches are never on or off simultaneously, the
output voltage va0 switches between ½Vdc and -½Vdc. The voltage va0 and its
fundamental frequency component are shown in Fig. 2.8b. It can be seen that the
inverter output voltage is not a perfect sine wave and contains voltage components at
harmonic frequencies of f1. The harmonics appear at sidebands around the switching
frequency and its multiples (see appendix F). A filter is generally connected between the
inverter and the grid, to reduce the harmonics.
The amplitude of the fundamental frequency component is vˆa 0,1 = ma ⋅ 1 2Vd and can
be controlled independently from the grid voltage, by controlling the amplitude
modulation ratio ma which is defined as ma = v con vtri .
For the simulations in this thesis mostly reduced models of PECs are used, in which
the switching of the individual switches is not modelled. The switches are replaced by
controlled voltage sources which are directly controlled by the reference waveforms.
Generally, in the modulation circuit the reference waveforms are compared with the
carrier waveform to control the semiconductor switches. Appendix F shows that in the
lower frequency range, the frequency components in the reference waveform and the
generated voltage waveform are equal, provided that the switching frequency is high
enough. Therefore in the frequency range from zero up to half the switching frequency
the reduced model can be used.
20
2.4.2 Control
Usually the VSC is connected to the grid through a filter. The filter forms a high
impedance for the harmonic voltages that are present in va0 and it enables current
control. The filter can be implemented in different ways, but will always contain at least
one inductor. The inverter bridge can then be considered as a controlled voltage source
behind an inductor, as shown in Fig. 2.9, with the voltage va0 a replica of vref. By
changing vref it can control the current injected into the grid or absorbed from the grid.
Most converters control the current in a feedback loop. For frequencies far enough
below the bandwidth of the controller, the converter can then be considered as a
controlled current source.
Lf
va0
Fig. 2.9. Voltage source converter as controlled voltage source behind filter impedance
In the previous subsection the reference signal vref was assumed to be pure
sinusoidal. This is not necessary true however. It is possible, for example, to introduce
certain harmonic components in vref. These harmonics will also appear in va0 then, if the
switching frequency is high enough. In this way the converter can be used for harmonic
compensation.
A schematic diagram of a current-controlled VSC is shown in Fig. 2.10. The inverter
bridge with the power electronic switches is separated from the grid by a filter, which
contains at least an inductor, but mostly also a capacitor. The current injected into the
grid is controlled by the current controller. The reference value for the current controller
is mostly obtained from a higher-level controller, which either controls the output power
or the DC-link voltage. Besides this, the controller can perform other tasks, such as for
example reactive power control and harmonic compensation.
2.4.3 Voltage and current source converters
The converter described in the previous subsections is a voltage source converter
(VSC). This type of converter generates a voltage v that is a replica of vref. In open loop
it behaves as a voltage source. Also a current source converter (CSC) can be used.
These converters generate a current i, which is a replica of the reference current iref. In
open loop they behave as a current source. By applying feedback control a VSC can be
controlled as a current source and a CSC as a voltage source.
The operation and control of a CSC are dual to that of a VSC. The DC-link of the
CSC behaves as a current source instead of voltage source and normally consists of an
2. Distributed Generation and Power Electronics
21
inductance. The filter of a CSC contains at least a capacitor, which provides a small
parallel impedance for the current harmonics in i.
DC
Voltage
Source
Filter
Grid
Modulation
Measurement
Current control
Iref
Fig. 2.10. Schematic diagram of current controlled voltage source inverter
The VSC is the preferred topology nowadays. This is because of switch technology,
which favours switches with a reverse conduction diode and the cost, weight and size,
which favour capacitors over inductors [Jóo 00]. In the thesis it is assumed that the DG
units are connected to the grid with a VSC. The results are also valid for a CSC
however. This subsection will show under which conditions the operation of a CSC can
considered to be the same as that of a VSC.
When the filter consists of a capacitor and an inductor, the CSC can be controlled
such that it behaves as a voltage source inverter. A schematic diagram of the CSC is
shown in Fig. 2.11. A voltage control loop is implemented on the converter. It controls
the voltage across the filter capacitance. When this voltage control loop is fast enough
the converter can be considered as a controlled voltage source behind an inductance, as
is shown in Fig. 2.9 for the VSC.
DC
Current
Source
Filter
Grid
Modulation
Measurement
Voltage control
Vc,meas
Vref
Fig. 2.11. Schematic diagram of voltage controlled current source converter
In a second control loop a current controller can be implemented that generates the input
for the voltage control loop that controls the capacitor current. As long as the bandwidth
of the voltage control loop is significantly larger than the bandwidth of the current
control loop, the behaviour of the CSC is equal to that of the VSC.
22
2.5 Literature review
2.5.1 Introduction
This section discusses the most important literature on the introduction of DG in the
power system, with emphasis on DG and power electronics. The last years showed a
large increase in the literature on DG, but only some important publications that are
related to the content of this thesis will be discussed. In this section a more general
overview will be presented. Later, in each chapter, more specific literature related to the
respective chapter will be discussed.
The paragraph consists of three subsections. In subsection 2.5.2 general publications
on DG are discussed. Subsection 2.5.3 will discuss publications concerning grid support
by DG units. Subsection 2.5.4 will discuss literature on ‘microgrids’. The concept of
‘microgrids’ is introduced for island networks that are completely based on PECs.
2.5.2 Distributed Generation
This section gives a limited overview of the literature on DG. One of the first books on
DG is [Jen 00]. It focuses mainly on the interaction between DG units and the grid and
concludes that interconnection issues for a single generator are well understood but that
the effect of many generators requires more research. A significant penetration of DG
changes the nature of a distribution network but also affects the transmission network.
At present most DG is considered as negative load over which the distribution utility
has no control. This should change to achieve a more reliable system. Another book is
[Bor 01] in which an extensive description is given of several DG unit types. With respect
to the interconnection issues it is concluded that it is especially important to bring all
concerned parties to a common understanding.
A large number of papers and reports on DG have been written. For this thesis only
the publications that treat the electrical aspects of DG units and their interaction with the
grid are important. An extensive overview is presented in [Don 02]. It investigates the
interaction of DG with a typical urban network. Some of the most important
conclusions are:
• The voltage rise caused by a single unit is a function of DG power and short circuit
power of the grid at the point of connection.
• The short-circuit power in the grid rises because of the DG short-circuit current
contribution. This can result in unacceptable short circuit levels in some cases and
settings in distance relays, over-current relays, short-circuit current indicators, etc.
may have to be changed.
• DG units with a PEC can have a positive impact on the voltage profile.
2. Distributed Generation and Power Electronics
23
•
Network reliability can be improved. DG will support the grid and may prevent
blackouts in times of supply shortages.
Another discussion of the impact of DG on DN operation is given in [Ack 02]. The
paper compares different DG technologies and investigates a number of operation issues
such as the impact on losses, voltage, power quality, short-circuit power and reliability.
It is concluded that the impact of DG on the operational aspects of the distribution
network depends on the DG penetration level as well as on the DG technology. Critical
issues, such as for example the impact of DG on the protection system, can be solved by
using the right technology and detailed studies on beforehand.
In [Tra 03] the impact of DG on LV networks is investigated. It is concluded that the
main constraints are related to the steady-state operation: the voltage profile and the
currents in the branches. No significant fault current contribution of the DG units is
expected, and therefore no major changes in the grid protection is required.
2.5.3 Grid support by DG units
This thesis investigates how DG unit converters can support the grid. This subsection
summarises other publications that propose grid support by DG unit converters.
One of the first papers that discussed the issue appeared in 2000 [Jóo 00]. It proposed
the provision of ‘ancillary services’ by the DG unit converters. Ancillary services are
defined as services provided in addition to real power generation [Jóo 00]. They include,
amongst others, reactive power control, provision of spinning reserve, frequency
control, and power quality improvement. The paper proposes to configure the DG unit
converters such that they can behave as a STATCOM, a Dynamic Voltage Restorer, and
an Active Filter. The first two devices are mainly used for voltage control, while the
third is used for harmonic compensation. The paper only presents some ideas. It does
not go into detail on implementation and effectiveness.
Another concept is that of Flexible Distributed Generation, which is proposed in [Mar
02], [Mar 04]. It is similar to the concept of ancillary services and proposes the use of DG
unit converters to mitigate unbalance, flicker and harmonics. The focus of the papers is
on the use of fuzzy logic controllers and adaptive linear neuron structures for parameter
tracking and estimation.
Using DG units for voltage control has been proposed in a number of other papers.
In [Bar 02] it is concluded that the voltage control should be implemented as a droop
controller. This enables operation without any communication. In [Mog 04] a voltage
control algorithm is proposed that is based on active power curtailment and reactive
power control. A control algorithm is proposed to switch between the two control
modes. Voltage control in weak, rural lines is investigated in [Kas 05]. It is concluded
that a significant distance should be maintained between DG units to avoid dynamic
24
interaction. Proper coordination between multiple DG units can be obtained by a proper
definition of upper and lower thresholds and time delays with which the controllers start
operating. In [Bol 05] analytical expressions are derived for the voltage along a line with
uniformly distributed DG applying voltage control.
2.5.4 Microgrids
The concept of ‘microgrids’ has received considerable interest last years [Hat 06].
Microgrids are small low-voltage networks that can be connected to the main power
network or can be operated autonomously. When they are not connected to the main
power system they are operated in a similar way as the power system of physical
islands. In essence a microgrid consists of a combination of generation sources, loads
and energy storage, which are generally connected to the network with PECs.
Microgrids have been studied in several research projects. A key issue is the control of
the power flow and the network voltage by the PECs. Most controllers that have been
proposed are based on droop lines [Aru 04], [Eng 05].
A key challenge for microgrids is to ensure stable operation during faults and
various network disturbances. Transitions from a situation in which a microgrid is
connected to the main network to a situation in which it is islanded are likely to cause
large mismatches between generation and loads, posing a severe frequency and voltage
control problem [Hat 06]. Several protection techniques and control strategies have been
proposed to ensure a stable operation and to protect the generators [Kat 05], [Peç 05].
There are a number of important differences between the control applied in
microgrids and the grid support by DG units considered in this thesis. The main
difference is that the DG units in this thesis are assumed to be connected to a
conventional power system. They only have to support the control that is performed by
the conventional generators, tap changers and so on. They do not have to control the
whole network. A main issue of this thesis is to investigate how large the support of the
DG units can be. This question is generally not considered in the microgrid
publications. Another difference is that most microgrids use some kind of a centralised
controller to control the interaction between a microgrid and the main network, while
the DG units in this thesis operate autonomously.
Chapter 3
Harmonic damping contribution of DG
unit converters
3.1. Introduction
Power electronic converters (PECs) have an output filter to reduce the harmonic
distortion and EMI. The connection of power electronic interfaced DG units to the
distribution grid will result in an increase of the capacitance in the grid, as most output
filters contain a capacitor. Manufacturers try to decrease filter inductors to make the
inverter cost-effective. This requires an increase in capacitance to keep the cut-off
frequency of the filter the same. The capacitance can resonate with the network
reactance [Ens 04]. In conventional grids the total capacitance was low, and the resonance
frequency was high. In most cases it was much higher than the dominant harmonics in
the grid and thus the chance that these resonance circuits were excited was small. An
increasing amount of capacitance results in a decreasing resonance frequency however.
It may get values in a range that is more easily excited by harmonics.
To avoid resonances, oscillatory responses, and a high level of harmonic distortion,
there should be enough damping in the grid. In passive grids the damping is obtained
from the resistance of the loads and lines. The main goal of this chapter is to investigate
how PECs (can) contribute to the damping. The output impedance of converters can be
represented as a complex number. The real part of this frequency-dependent complex
output impedance represents the resistance and thus the damping contribution of the
converter. For some converter types it can have a negative value, meaning that
harmonics and resonances are amplified instead of attenuated. In the ultimate case the
negative damping can become larger than the positive damping in the network, which
results in instability.
From constant power loads it is known that they can cause stability problems [Ema 04]. A
short review of this instability will be given in section 3.2, as it lays down some basic
principles that will be valuable in understanding this chapter. The need for damping is
not limited to the quasi-stationary case however, it is important at all frequencies.
26
Therefore the analyses will be done in the frequency domain. As a first step, frequency
domain models of PECs are obtained in section 3.3. Only a limited number of converter
types can be discussed in this chapter. A more in debt investigation of the operation of
PECs shows that they consist of a limited number of functional blocks. Most blocks can
be characterised by their transfer function. It will become clear then, that there are only
a few types of converter. In section 3.4 the transfer functions are used to determine the
frequency-dependent output impedance of the most-used converter types and to see how
these converters influence the damping in the grid. Section 3.5 proposes an active
damping controller that can be implemented as an additional controller on DG unit
converters. The section first describes the control and its implementation, followed by
an investigation of possible limitations on the contribution. In section 3.6 the results of
some case studies are presented to demonstrate the functionalities of the active damping
controller. Only single-phase converters will be considered in this chapter.
3.2. Incremental impedance
Power electronic loads that are tightly regulated can sink a constant power from the
grid. This implies that they have a negative incremental impedance characteristic, which
can cause instability, as is known [Ema 04], [Mid 76], [Sud 00], [Wil 95]. As an introduction to
this chapter this type of instability is shortly revised. Understanding the quasi-stationary
case may be helpful in understanding the remaining part of the chapter which concerns
the, more general, frequency-dependent case.
Consider a load (or source) as shown in Fig. 3.1a. It is assumed to work at power
factor one. The incremental impedance is defined as the small-signal deviation of the
voltage over that of the current:
R' =
Δv
Δi
(3.1)
Three types of devices are distinguished here: a resistive load (constant impedance
load), a constant power load and a constant power source, as shown in Fig. 3.1b – d.
Fig. 3.1c shows that a constant power load has negative incremental impedance. This
may result in stability problems. The constant impedance load and the constant power
load both have positive incremental impedance and no stability problems are expected.
Historically most loads in the electricity network are constant impedance loads,
which means that their impedance is independent of the voltage. These loads have
positive incremental impedance. PECs can be programmed as constant power loads in
quasi-stationary situations, which implies negative incremental impedance.
3. Harmonic damping contribution of DG unit converter
27
V
I
V
R’
R’
V
I
I
R’
(a)
(b)
(c)
(d)
Fig. 3.1. Definition of voltage and current direction (a) and incremental impedance of: constant impedance
load (b), constant power load (c), and constant power source (d)
The problems caused by constant power loads can be explained with the network
model shown in Fig. 3.2. It shows a grid with a constant power load RCPL’ and a
constant impedance load Rl. The grid is modelled by a voltage source Vg, a resistance
Rg, an inductance Lg, and a capacitance Cg.
ig
Vg
Rg
Lg
Cg
Vl
R’CPL
Rl
Fig. 3.2. Model of network with constant power load RCPL’ and constant impedance load Rl
As the constant power load is a nonlinear device, small-signal variations around an
operation point have to be considered. The average power consumed by the load is:
PCPL = Vl ,0 I l ,0
(3.2)
When a small-signal perturbation is applied to the voltage, the power becomes:
PCPL = (Vl ,0 + ΔVl )(I l ,0 + ΔI l )
(3.3)
By neglecting the second-order term it can be obtained that [Ema 04]:
Vl , 0
ΔVl
'
=−
= RCPL
ΔI l
I l ,0
(3.4)
where Vl,0 and Il,0 give the load voltage and current in the operation point. They are
assumed to be in phase with each other, meaning that the load only draws active power
from the grid. From (3.4) it can be noted that, with the sign convention of Fig. 3.1a, a
small decrease in voltage results in a small increase in current. As a result of this
increasing current the voltage drops further: an unstable situation. When the overall
equivalent resistance of the grid becomes negative the system becomes unstable.
That constant power loads can cause stability problems is well-known. It is however
less known that also power electronic sources can have negative incremental
impedance. Most single-phase inverters need a sinusoidal reference waveform for their
28
current control. This waveform can be internally generated, but it is also possible to use
a copy of the grid voltage. The converter current is then:
i (t ) = −k ⋅ v(t )
(3.5)
where the value for the constant k is determined by the average power that should be
supplied to the grid. This constant is adapted relatively slow. The incremental
impedance for this constant power source is thus:
'
RCPS
=−
V
1
=− 0
k
I0
(3.6)
This type of converter also has a negative incremental impedance. It depends on the
total resistance of the grid whether the network will become unstable.
3.3. Frequency domain analysis of power electronic converters
The goal of this chapter is to investigate whether PECs can contribute to the damping in
the grid. As both the converter behaviour and the damping are frequency-dependent,
frequency domain analyses will be done. This section describes how linear frequency
domain models for the converters can be obtained by determining their transfer
functions. The frequency-dependent converter output impedance can be obtained by
determining the transfer function from the output current to the output voltage of the
converter. Using transfer functions will make analysis easier. As will be shown in this
section, it is possible to reduce a large number of converter types to a small number of
transfer functions.
3.3.1 Converter description
PECs exist in a wide variety of topologies, with different components, and with all
types of control. Only grid-connected voltage source converters will be investigated in
this thesis as they are used by a large majority of the DG units. A general description of
such a converter is given in section 2.4. The converter is assumed to be single-phase.
The converter generally has two control levels. The output impedance of the
converter is mainly determined by the low-level current control, as its bandwidth is
much higher than that of the high-level control. The phenomena considered in this
chapter are normally at higher frequencies and therefore it will be enough to consider
only the low-level current control.
Converters can be considered to be built up from a number of basic blocks. These
blocks are shown in Fig. 3.3:
3. Harmonic damping contribution of DG unit converter
•
•
•
•
•
29
The core of the converter is formed by the power electronic switches.
The switches are connected to the grid through a filter, which consists of
capacitor(s) and/or inductor(s) and/or resistor(s). It has the task to suppress the
higher harmonics that are produced by the power electronic switches.
The firing of the switches is controlled by the modulator, which transforms the
signals from the controller, to the control signals for the semiconductor switches.
In order to be able to operate, the converter requires knowledge about the actual
current and voltage. So, measurements are necessary. Often only the RMS value is
known. Therefore a sine-wave has to be created in some way.
The sine wave reference can be generated internally and then synchronised with the
grid or it can be a copy of the grid voltage.
Converter
,
filter
v
i
Measurement
vmeas
Controller
Modu
lation
Iref
Sine wave
reference
imeas
Fig. 3.3. Block diagram of voltage source converter with current controller
3.3.2 Basic building blocks
Fig. 3.3 shows the most important blocks that are needed in a converter. This subsection
gives possible implementations of these blocks, together with their transfer functions.
Modulator – The modulator is a device that converts continuous signals to on/off
signals for the switches. The first type that is often used derives its on/off signals from
vref, for instance by comparison of a triangular carrier with vref. The second type derives
its on/off signals from iref, for instance by hysteresis control. The block diagrams for
these two modulation types are shown in Fig. 3.4a and b respectively. As long as the
frequency of the input waveform is much smaller than the frequency of the modulator
(and the switching frequency), the transfer of the modulator is approximately ideal.
Phenomena with a frequency much higher than the modulating frequency are not
transferred through the modulator. Frequencies between these two borders are
transmitted partly. The approximate transfer functions of the modulators are shown in
Fig. 3.4c and d respectively.
30
vref
vo
PWM
iref
io
Hysteresis
(a)
(b)
io(ω)
iref(ω)
vo(ω)
vref(ω)
fs/10
ω
fs/10
ω
(c)
(d)
Fig. 3.4. Modulator block diagrams and transfer functions; (a) and (c): Pulse Width Modulation; (b) and (d)
Hysteresis modulation
Controller - Two basic principles are used as controller in a single-phase converter, the
Proportional-Integral (PI) controller and the Proportional-Resonant controller (PR). PIcontrollers are the most classical controllers. When the reference signal is constant, zero
steady-state error is achieved by the integral term of the controller. When the reference
current is a sinusoidal signal however, straightforward use of the PI controller would
lead to steady-state error due to the finite gain at the operating frequency. For these
situations PR-controllers are proposed, which have infinite gain at a specified
frequency. With this type of control it is possible to realise a zero steady-state error at
the operating frequency (50Hz). The transfer function for a PI controller is:
G PI (s ) =
sK p + K i
(3.7)
s
whereas the transfer function for a PR controller is:
G PR (s ) = K p +
Kr s
(3.8)
s + ω 02
2
Fig. 3.5 shows the transfer functions of the two controllers.
out
in
out
in
Kp
Kp
ω=Kp
ω=Ki ω
fo
ω
(a)
(b)
Fig. 3.5. Controller transfer functions; (a) Proportional-Integral (PI) controller; (b) Proportional-Resonant
(PR) controller
3. Harmonic damping contribution of DG unit converter
31
Sine wave reference - Both for the modulation and the controller a reference sine wave
can be needed. There are basically two categories of reference generators. The reference
can be a copy of the grid voltage or the converter controller can have an internal,
predefined sine wave that is synchronised to the grid with a phase-locked loop (PLL).
Some inverters combine the reference source and the synchronisation with the grid
voltage by using the waveform of the grid voltage as the basis for the reference
waveform that is used by the modulator. The advantage of this technique is its
simplicity. The disadvantage is that if the grid voltage is distorted, also the current is
distorted. The schematic diagram of this type of sine reference is shown in Fig. 3.6a,
and its transfer function in Fig. 3.6c. The schematic diagram for a sine wave reference
based on a PLL is shown in Fig. 3.6b, whereas Fig. 3.6d shows its transfer function.
Iref
Iref
i(t)
k
i(t)
PLL
vg(t)
vg(t)
(a)
(b)
i
i
Iref
Iref
ω
fo
ω
(c)
(d)
Fig. 3.6. Sine wave reference block diagrams and transfer functions; (a) and (c): reference based on grid
voltage; (b) and (d) internally generated reference synchronised with PLL
Measurement - In order to enable feedback control, but also to obtain a reference for the
sine wave, measurement of the grid voltage and grid current is necessary. In order to
avoid high-frequency noise, the measured signals are filtered first. After this filtering
the signal is sampled with a certain sampling rate. In general the bandwidth of the
measurement system is determined by the bandwidth of its filter.
Converter and filter - The transfer function of the converter is mainly determined by its
filter. This filter is designed to avoid that higher harmonics created by the power
electronic switches are injected in the grid. Therefore the filter cut-off frequency has to
be lower than the switching frequency of the converter and the cut-off frequency of the
overall transfer is determined by the filter. The transfer function is similar to those given
in Fig. 3.4, with a cut-off frequency determined by the filter.
32
0.12
0.12
0.1
0.1
0.08
0.08
Gc [S]
Gc [S]
3.3.3 Model comparison
In this chapter transfer functions in the Laplace domain are proposed as a method to
investigate the behaviour of PECs. It should be investigated whether the models based
on transfer functions correctly represent the behaviour of a real converter. Especially the
fact that modulation and switching are neglected requires attention.
As a base case for comparison the single-phase full-bridge converter described in
appendix B.1 is used. In this model the pulse-width modulation and the switching of the
IGBTs is taken into account. The output conductance up to the 31st harmonic is
determined for the full converter and for the converter model based on transfer
functions. The fundamental grid voltage is perturbed with a small harmonic voltage
with a fixed frequency and amplitude. The response of the output current of the
converter model to this perturbing voltage is determined and from this the output
conductance is determined. The results are shown in Fig. 3.7a.
For the full model the results are disturbed by the fact that the converter itself also
produces harmonic currents, independent from the harmonic voltages with which it is
perturbed. Subtracting these harmonics from the results of Fig. 3.7a gives Fig. 3.7b. The
maximum deviation between the results of the full model and the transfer function
model is less than 5%. This shows that the model based on transfer function gives a
good representation of the full model.
0.06
0.04
0.04
0.02
0
0
0.06
full model with IGBTs
transfer function
5
10
15
20
harmonic number
25
30
0.02
0
0
full model with IGBTs
transfer function
5
10
15
20
harmonic number
25
30
(a)
(b)
Fig. 3.7. Output conductance of full model (*) and model based on transfer functions (o); (a) uncompensated
model; (b) model compensated for harmonic distortion of converter itself
3.4 Damping capability of converter
3.4.1 Converter output impedance
This subsection analyses the output impedance of PECs, to see the damping capability
of the converter. The output admittance of a converter can be obtained by determining
3. Harmonic damping contribution of DG unit converter
33
the transfer function from grid voltage to converter output current. The real part of this
frequency-dependent complex value gives the output conductance of the converter as a
function of frequency. The value of the conductance determines the damping
contribution of the converter and will plays a role in the damping of harmonics and
resonances in the grid. For ease of explanation a converter operating at power factor one
is analysed. The results are also valid for other power factors however.
By combining blocks from the groups defined in the previous section, basic
converter models can be constructed. Two important converter models are considered.
The first one, shown in Fig. 3.8a, uses PWM modulation and has a PR controller and a
sine wave reference based on the grid voltage. The second one, shown in Fig. 3.8b, is
the same except the sine wave reference, which is obtained from a PLL. Both converters
have an LCL-filter. A description of the converter and its parameters are given in
appendix B.1.
Converter
Converter
,
filter
v
,
i
filter
Measurement
v
i
Measurement
vmeas
Controller
k
PWM
PR
ϕ
Controller
X
vmeas
Iref
PLL
PWM
PR
X
sin
Iref
imeas
imeas
Converter A
Converter B
Fig. 3.8. Converter model with reference current as a function of the grid voltage (a) and with reference
current based on PLL (b)
The bode diagrams for the transfer function from output voltage to output current,
io(s)/vo(s), of both converters are determined for three different values of Kp (the
proportional constant of the PR controller). This parameter showed to have the largest
effect on the magnitude and angle of the output conductance. Fig. 3.9 shows the bode
diagrams for the two converters. They give the frequency-dependent output
conductance of the converter. For a phase value in the range -90º – 90º (± 360º) the
incremental conductance has a negative value. Fig. 3.9a shows that the incremental
output conductance of converter ‘A’ is thus negative for a large frequency range
(approximately 5 – 400 Hz). For a large value of Kp it is even negative up to ~ 10 kHz.
For converter type ‘B’ the phase angle is always outside the range -90º – 90º. So this
converter will always have a positive influence on damping.
34
Magnitude [dB]
50
20
0
−20
−40 0
10
1
10
2
10
Frequency [Hz]
3
10
Phase [deg]
Neg.
−200
Pos.
1
10
2
10
Frequency [Hz]
3
10
4
2
10
Frequency [Hz]
3
10
4
10
Pos.
400
Neg.
200
0 0
10
10
1
10
600
Pos.
0
−400 0
10
−50
−100 0
10
4
10
200
0
Phase [deg]
Magnitude [dB]
40
Pos.
1
2
10
10
Frequency [Hz]
3
10
4
10
(a)
(b)
Fig. 3.9. Bode diagram for output conductance of converter A (a) and converter B (b) for Kp = 2 (dotted),
Kp = 10 (solid) and Kp = 50 (dashed) (Kr = 10000, Lfc = 0.2 mH, Lfg = 0.8 mH, Cf = 2 μF)
3.4.2 Damping contribution in the grid
The real part of the frequency-dependent complex-valued output admittance of a
converter can be considered as its conductance. The previous subsection investigated
how the value of this conductance depends on the converter type and control. This
section considers the contribution of the converter output conductance to the damping in
the network.
The network of Fig. 3.10 is used for the analysis. It gives the lumped representation
of a real existing 230 V network [Ens 02]. In this network problems were noticed with a
high harmonic distortion, which could be explained from the negative incremental
impedance of solar cell converters. The line impedance of the network is modelled by
Rg and Lg. The resistance Rl represents the load and Cl consists of the capacitance of the
load and other converters. The resonance frequency of the network is a function of Lg
and Cl. It gives a complex-conjugate pole-pair in the real-imaginary plane. The
influence of the converter on the relative damping of these poles will be investigated.
The model of the network is described in appendix A.3 and the converter model in
appendix B.1.
Rg
Vg
Lg
io
Cl
RL
vo
Converter
Fig. 3.10. Network model with converter
The influence of several converter (controller) parameters on the damping of the
resonant poles was investigated. In each analysis the root-locus of the resonant poles
was determined as a function of the parameter under investigation. Parameters that were
varied are the control parameters Kp and Kr, the rated power of the converter and filter
3. Harmonic damping contribution of DG unit converter
35
parameters. As an example Fig. 3.11 shows the root-locus for varying Kp for both
converters. This parameter showed to have the largest influence on the relative
damping. Note that even for this parameter the influence is limited.
The only parameter with a larger influence on the location of the poles is the rated
power of converter A. The system becomes even unstable for large values of the rated
power. This is because the negative damping of the converter becomes larger than the
positive damping in the grid. The network of appendix A.3 for example becomes
unstable when a ~100 kW converter with negative incremental impedance is connected
to it. The short-circuit power of the network is ~500 kW.
K =1
p
1000
Kp=1
1000
Kp=50
K =50
p
Kp=10
Imaginary axis
Imaginary axis
500
0
−500
K =10
p
500
0
−500
Kp=10
Kp=10
Kp=50
Kp=50
−1000
−1000
−1000
K =1
p
−800
−600
−400
Real axis
−200
0
−1000
Kp=1
−800
−600
−400
Real axis
−200
0
(a)
(b)
Fig. 3.11. Stability network with converter A (a) and converter B (b) for changing Kp
3.5 Active damping
3.5.1 Introduction
The previous sections showed that in the most favourable case PECs have a slightly
positive influence on the damping in the grid. In order to have a robust grid which is not
sensitive to disturbances, a much higher damping is required. This section proposes an
additional control loop on PECs, which gives the output impedance of the converter a
resistive behaviour. The ‘emulated resistance’ will increase the damping of the grid,
making it less sensitive to harmonics and oscillations.
The type of control presented in this section is different from the active filters that
have been investigated extensively. These active filters, which can be implemented as
specific devices (for example [Aka 97]), or as a secondary function on power electronic
generators or loads (for example [Mac 04]), are used to compensate for specific
harmonics. The parameters of the power system and the sources of pollution are often
unknown however and can be time-varying, making this type of control difficult.
Contrary, the controller presented in this section presents a damping resistor for a large
36
harmonic spectrum and can be implemented easily. Complete compensation of
harmonics will not be possible with the proposed controller, but generally this will not
be needed.
The control strategy proposed in this chapter is comparable to those presented in [Tak
03], [Ryc 06a], and [Ryc 06b]. In [Tak 03] the control is implemented on a three-phase
converter however. Their control is difficult to implement on single-phase converters, as
it is based on the dq-transformation. The control strategy proposed in this chapter is
more similar to the one in [Ryc 06a] and [Ryc 06b]. In these publications also a single-phase
converter is considered. The publications present experimental verifications of the
operation of the active damping controller. The mentioned publications focus mainly on
the implementation however, while this section extensively investigates how large the
contribution of the damping controller can be in a practical network.
3.5.2 Damping controller operation principles
This subsection gives a description of the controller that emulates a resistive output
impedance for the converter. The controller is additional to the controllers that perform
the primary task of the converter: transferring the DG unit power to the grid. The
transfer of power is done at the fundamental frequency. The additional damping
controller should thus not affect the fundamental frequency.
For the analysis a DG unit converter is assumed to be connected to the grid at a
point of common coupling with voltage vn, as shown in Fig. 3.12. The DG unit
converter is represented as a voltage source, with voltage vdg, behind the filter
impedance. The voltage vn is assumed to be distorted by harmonics. It can be split up in
its fundamental frequency part vn,f and a part containing the other harmonics, vn,h(s):
v n (s ) = v n, f + v n,h (s )
vn
vg
Zg
idg
Zf
(3.9)
vdg
DG
Load
Fig. 3.12. DG unit converter connected to point of common coupling with voltage vn
In order to obtain a resistive behaviour for the harmonic frequencies, the converter
should inject a harmonic current into the grid which is 180° out of phase with the grid
voltage. This gives for the total converter current:
3. Harmonic damping contribution of DG unit converter
37
i dg (s ) = i dg , f + i dg ,h (s )
(3.10)
= G f v n, f − Gd v n,h (s )
The variable Gf determines the active power that is supplied to the grid and Gd is the
damping conductance for the non-fundamental components. It is assumed that the
converter works at power factor one, but this is not necessary.
The active damping controller injects a harmonic current idg,h(s) to obtain a
conductance Gd at the converter terminal. It superimposes a harmonic voltage on the
converter voltage vdg, such that the required harmonic current is obtained. The current
has to flow through the filter of the converter and depends on the voltage difference
between the voltage created by the PEC vdg,h(s) and the node voltage vn,h(s):
i dg ,h (s ) =
v dg ,h (s ) − v n,h (s )
(3.11)
Z f (s )
with Zf(s) the filter impedance. From this equation the voltage vdg,h(s) that is needed to
obtain a certain output conductance can be determined:
(
)
v dg ,h (s ) = 1 − Gd Z f (s ) v n,h (s )
(3.12)
Fig. 3.13 shows a schematic diagram of the complete converter control. The middle part
shows the conventional current control which uses a PR controller. It controls the
fundamental component of the voltage and current.
PWM
Filter
i
v
Measurement
Converter
Current
Control
iref
Regular control
Gd
RMS
1-GdZf
PLL
Active damping
Sin
Fig. 3.13. Block diagram of converter, current control and active damping controller
The active damping controller is shown at the bottom. It consists of two loops. The
first one, which is similar to the control presented in [Ryc 06], subtracts a term Gd⋅vn,h
from the reference current. This implies that in case of an ideal controller the output
current is given by:
38
i dg (s ) = i ref − Gd v n,h (s )
(3.13)
i.e., a resistive behaviour for the non-fundamental components. The PR-controller that
is used has infinite gain for 50Hz, but the gain drops quickly for higher frequencies.
That implies that the controller is less effective for these frequencies. Therefore a
second (feed-forward) control loop is implemented that also works for higher
frequencies. As the damping controller should not influence the fundamental
component of the converter current and voltage, this component is first subtracted from
the measured voltage. The fundamental component is obtained from a predefined sinewave which is synchronised with the grid via a PLL.
The poles that are related to the resonance circuit of Lg and Cl in the network of Fig.
3.10 are shown in Fig. 3.14 for different values of Gd. Fig. 3.14a shows the root-locus of
the poles when the damping controller is implemented on a converter of type ‘A’ and
Fig. 3.14b when it is implemented on converter of type ‘B’. In both cases the damping
constant has a significant influence on the location of the poles. For increasing value of
Gd the poles move to the left, further from the imaginary axis and closer to the real axis,
implying increasing relative damping.
1000
1000
Gd=20
0
Gd=20
−500
−1000
−5000
−3000
−2000
Real axis
−1000
Gd=20
0
Gd=20
−500
Gd=0
−4000
d
500
Imaginary axis
Imaginary axis
G =0
Gd=0
500
0
−1000
−5000
Gd=0
−4000
−3000
−2000
Real axis
−1000
0
(a)
(b)
Fig. 3.14. Resonant poles in the grid for different values of damping conductance Gd: converter type ‘A’ (a)
and converter type ‘B’ (b)
3.5.3 Influence of type and location of the harmonic source
From the point of view of a DG unit harmonics can have two different origins. In the
first one, shown in Fig. 3.15a, the harmonic voltages are caused by closely located
harmonic sources such as a load that draws harmonic current from the grid. In the
second one, shown in Fig. 3.15b, the harmonic voltages are caused by background
harmonic distortion, originating from remote harmonic source. They can be modelled as
a harmonic voltage source in series with the substation voltage. The resonance circuit
that is ‘seen’ by the harmonics is different for the two cases. The first case can be
3. Harmonic damping contribution of DG unit converter
39
modelled by a harmonic current source and a parallel resonance circuit formed by the
capacitance Cl (formed by other loads and DG units) and the grid inductance Lg (formed
by cable and transformer inductance). Fig. 3.16a shows the resonance circuit and the
corresponding impedance (as a function of frequency). The circuit has a high impedance
at its resonance frequency. Background harmonic distortion, the second case, can be
modelled as a harmonic voltage source and a series resonant network formed by Lg and
Cl, see Fig. 3.16b. In this case, the circuit has a low impedance at the resonance
frequency.
The damping controller on the DG unit can also be considered as a (compensating)
harmonic current source. For this case always the parallel resonance circuit of Fig. 3.16a
is valid. This implies that the converter can compensate harmonics most easily when
they are close to the resonance frequency.
vn
vg
Zf
vdg
vn
DG
Zg
il,h
vg
vg,h
Zf
vdg
DG
Zg
Zl
Zl
Load
Load
(a)
(b)
Fig. 3.15. Harmonic source locations
Rg
Lg
ih
Cl
ih
Vh
Rg
Lg
Cl
(a)
(b)
Fig. 3.16. Parallel (a) and series (b) resonance circuits and resonance impedances as a function of frequency
3.5.4 Value of emulated damping conductance
The emulated damping conductance of the converter will determine how large the
damping of resonances and harmonics is. This subsection will lay down a relation
between Gd and the damping that is obtained in a certain network.
40
The voltage vn depends on the value of the damping conductance Gd. The ratio
between the grid current in case of damping, ig,d and without damping, ig,0 and between
the voltage with damping, vn,d and without damping, vn,0 is given by:
ig , d (s )
ig ,0 (s )
=
vn, d (s )
vn,0 (s )
s 2Cl Lg + sRg Cl + 1
=
(
)
(3.14)
s 2Cl Lg + s Rg Cl + Gd Lg + 1 + Gd Rg
At the resonance frequency fr, the term s2ClLg+1 is zero. The equation reduces then to:
ig , d
=
i g ,0
vn , d
vn , 0
=
1
(
1 + Gd Lg Rg Cl
)
(3.15)
These equations indicate how large the value of Gd should be to obtain a certain
reduction of harmonics in the grid voltage. Fig. 3.17 shows some relations for a typical
example. For different frequencies it is shown how the harmonic currents (a) and
voltages (b) can be attenuated as a function of the emulated damping conductance Gd.
The figure shows that for harmonics at the resonance frequency of the grid a much
smaller Gd is required to obtain a certain reduction. For harmonics below and above the
resonance frequency a much larger value of Gd is required. For lower frequencies a
slightly larger Gd is required than for higher frequencies. The parameters that have been
used to obtain Fig. 3.17 are given in table 3.1 and appendix A.3
1
1
f = fr / 3
f=f
r
f=f *3
0.8
vg,d / vg,0 [−]
r
0.6
i
g,d
/i
g,0
[−]
0.8
0.4
0.2
0 −3
10
f = fr / 3
f=f
r
f=f *3
r
0.6
0.4
0.2
−2
10
−1
10
Gd [pu]
0
10
0 −3
10
1
10
−2
10
−1
10
Gd [pu]
0
10
1
10
(a)
(b)
Fig. 3.17. Reduction in harmonic voltages as a function of emulated damping conductance Gd: damping of
harmonic currents (a) and damping of harmonic voltages (b)
Table 3.1 Parameters of network and DG unit converter
Parameter
Value [p.u.]
Parameter
Value [p.u.]
Parameter
Value [p.u.]
Lg
Rg
Cl
Rl
0.44
0.91
105
200
fr
Lf
Pdg,nom
Gf
777
2.9
0.01
0.01
vg,h
il,h
0.07
0.008
3. Harmonic damping contribution of DG unit converter
41
3.5.5 Limitations and operation range
In order to determine the feasibility of the proposed solution it is important to determine
the limiting factors. Possible limitations are:
• Converter current
• (dc-link) voltage of converter
• switching frequency of converter
Current - To compensate the harmonic voltages, the converter has to draw a certain
harmonic current from the grid, which is given as:
i dg ,h (s ) = −Gd v n,h (s )
(3.16)
From this equation and (3.14) the current idg,h can be calculated as a function of the
attenuation of the voltage and current harmonics. The results are shown in Fig. 3.18.
The nominal converter current is used as base value. The harmonic current has to be
added to the fundamental frequency current. The graphs can be used in combination
with the graphs of Fig. 3.17. Fig. 3.17 gives the reduction for a certain emulated
damping conductance, while Fig. 3.18 gives idg,h for this reduction. The figure shows
that high currents may be required to obtain a significant damping.
2
1
f = fr / 3
f = fr
f=f *3
r
r
1.5
dg,h
[pu]
0.6
0.4
1
i
i
dg,h
[pu]
0.8
f=f /3
r
f=f
r
f=f *3
0.5
0.2
0
0
0.2
0.4
i /i
g,d
(a)
g,0
0.6
[−]
0.8
1
0
0
0.2
0.4
v /v
g,d
g,0
0.6
[−]
0.8
1
(b)
Fig. 3.18. Harmonic current that should be created by converter as function of reduction in harmonic current
(a) and voltage (b) that should be achieved (in per unit with nominal converter current and voltage as base
values)
Voltage - The damping controller superimposes a harmonic voltage on the voltage that
has to be supplied by the converter. Equation (3.12) shows that the required harmonic
voltage depends on the frequency. For frequencies far below the resonance frequency of
the filter, the filter can be considered as the sum of its inductances. The filter impedance
and thus the voltage drop across the filter increase linearly with the frequency. The
voltage that can be supplied is limited by the dc-link voltage of the converter. This will
42
limit the maximum damping that can be achieved. The voltage vdg,h as a function of the
attenuation of the voltage and current harmonics can be calculated by combining (3.12)
and (3.14). The results are shown in Fig. 3.19.
0.4
0.35
f = fr / 3
f=f
r
f=f *3
0.35
0.25
0.25
vdg,h [pu]
[pu]
dg,h
v
0.3
r
0.3
0.2
0.15
0.2
0.15
0.1
0.05
0
0
0.2
0.4
0.6
ig,d / ig,0 [−]
(a)
0.8
1
0.1
f = fr / 3
f=f
r
f = fr * 3
0.05
0
0.2
0.4
0.6
vn,d / vn,0 [−]
0.8
1
(b)
Fig. 3.19. Harmonic voltage that should be created by converter as function of reduction in harmonic current
(a) and voltage (b) that should be achieved (in per unit with nominal converter current and voltage as base
values)
The graphs can be used in combination with the graphs of Fig. 3.17. Those graphs give
the reduction that can be obtained for a certain emulated damping conductance, while
Fig. 3.19 gives vdg,h for this reduction. In case of distortion at the resonance frequency of
the network, the voltage vdg,h has a minimum for a reduction of ~ 50%. For other
frequencies the voltage increases for increasing reduction.
Frequency – The frequency range in which the damping control can operate is limited
by the maximum switching frequency of the converter. The switching frequency should
be at least twice as high as the harmonic component to be damped, to be able to
modulate the required harmonic voltages. In case of low-power converters this will
generally pose no problems as they have a high switching frequency.
3.6 Case studies
The damping controller proposed in the previous section reduces the harmonic
distortion in the network. It does not only damp specific harmonics, such as active
filters do, but it influences the whole harmonic spectrum of the network. This implies
that it also reduces possible oscillations that can occur during transient phenomena such
as voltage dips. This section presents the results of some case studies. They show the
positive influence of converters with emulated damping resistance on the quality of the
3. Harmonic damping contribution of DG unit converter
43
grid voltage and current. The model of Fig. 3.20 is used for the case studies. It consists
of a Thévenin equivalent of the network, a load that is modelled by a capacitor and a
constant power source and a converter. For the converter the reduced model is used,
which is described in appendix B. The parameters are given in table 3.1 and B.1. The
constant power load consumes 8 kW. The emulated output conductance of the converter
is 0.5 S.
Rg
Lg
Vg
Cl
PCPL
Converter
Fig. 3.20. Case study network with constant power load PCPL and converter
The first case shows that the converter can damp harmonic voltages and currents in the
grid. The voltage in case of background harmonic distortion in the network is shown in
Fig. 3.21a. In first instance the damping controller does not work, but at time t = 1 s it is
put into operation, resulting in a large reduction in harmonic distortion. In the second
case the load draws harmonic current from the network. The voltage for this case is
shown in Fig. 3.21b. Again a large reduction in harmonic distortion is obtained.
Damping controller turned on
Damping controller turned on
500
150
400
100
300
50
100
Current [A]
Voltage [V]
200
0
−100
0
−50
−200
−300
−100
−400
−500
0.9
0.95
1
time [s]
1.05
1.1
−150
0.9
0.95
1
time [s]
1.05
1.1
(a)
(b)
Fig. 3.21. Damping of harmonic voltage (a) and current (b) (at t = 1 s the active damping controller is
activated)
The second case shows that the damping controller also can be used to avoid negative
impedance instability. At time t = 1 s the power consumed by the constant power load
increases to 24 kW. As a result the grid impedance plus the converter output impedance
is smaller than the negative incremental impedance of the constant power load. This
results in the oscillations in the converter terminal voltage shown in Fig. 3.22. At time t
= 1.05 s the active damping controller is turned on and the system stabilises again.
44
Damping controller turned on
500
400
300
Voltage [V]
200
100
0
−100
−200
−300
−400
−500
0.9
0.95
1
time [s]
1.05
1.1
Fig. 3.22. Avoidance of instability: converter terminal voltage (at t = 1 s the load is reduced, resulting in a
negative damping and oscillating voltage, at t = 1.05 s the active damping controller is activated)
The third case analyses the response to a voltage dip. The dip is modelled as a 50% drop
in the voltage vg that lasts from t = 0.95 s to t = 1.05 s. The resulting converter terminal
voltage is shown in Fig. 3.23b. Due to the dip oscillations will occur in the resonance
circuit formed by Lg and Cl. At the time that the voltage drops the damping controller is
not inserted, and some oscillation in the voltage can be noted. During the dip, at time t =
1 s the controller is put into operation. As a result, there are no oscillations in the
voltage at the moment that the dip is cleared.
Damping controller turned on
500
400
300
Voltage [V]
200
100
0
−100
−200
−300
−400
−500
0.9
0.95
1
time [s]
1.05
1.1
Fig. 3.23. Converter terminal voltage during voltage dip (A voltage dip occurs at t = 0.95 s, resulting in some
oscillations in the voltage. The dip clears at t = 1.05 s without oscillations, as the damping controller is turned
on at t = 1 s.)
3.7 Concluding remarks
The increasing number of DG units results in an increasing number of PECs in the grid.
Due to the output capacitance of these and other converters there is a chance on the
occurrence of harmonics, badly damped transients and oscillations. This chapter
3. Harmonic damping contribution of DG unit converter
45
investigated whether the DG unit converters can contribute to the damping in the grid.
The contribution of converters with conventional control showed to be limited.
Converters that use a sine wave reference that is a copy of the grid voltage can even
have a negative influence.
An additional control loop can be implemented on the DG unit converter to give the
output impedance of the converter a resistive behaviour for a large frequency range. In
this way the damping in the network is increased. With this controller, harmonics can be
mitigated, negative impedance instability can be avoided, and oscillatory responses due
to for example voltage dips can be avoided. Due to the active damping controller the
voltage and current of the converter will increase. This will limit the maximum damping
contribution of the converter. Harmonics at the resonance frequency of the grid can be
compensated easily. A 90% reduction requires only a ~10% increase in current and
voltage (for a converter with a rated power of 1% of the short-circuit power of the grid).
Harmonics at three times the resonance frequency require a ~80% increase in current
and a ~180% increase in voltage however, to obtain a reduction of 90%.
46
Chapter 4
Voltage control contribution of DG units
4.1. Introduction
In conventional power systems the generators are generally connected to the highvoltage transmission network, whereas the loads are connected to the medium- and lowvoltage distribution networks (DNs). This results in a power flow from a higher to a
lower voltage level. Due to the line impedance the voltage decreases from the substation
to the end of the feeder [Mas 02]. To compensate for this voltage drop, the voltage is
stepped up at the HV/MV and MV/LV substation, as is shown in Fig. 4.1. The voltage
in the DN can be controlled continuously by the automatic tap changers on the HV/MV
distribution transformer, whereas the MV/LV transformers normally have manual offload tap changers with a fixed value.
Power plant
HV
MV
LV
Customers
Low load - DG
Vmax
Vmin
High load - No DG
Fig. 4.1. Voltage profile from power plant to customer with all voltages expressed relative to their nominal
value
When DG units are connected to the MV or LV network, the voltage profile in the
line will change [Bon 01], [Con 01], [Dug 02], [Lie 02], [Mas 02], [Soe 05], [Vu 06]. The voltage
might even increase in low load situations [Bon 01], as is shown by the dashed line in Fig.
4.1. In principle the automatic tap changer at the HV/MV transformer can lower the
voltage. However, also feeders without DG can be connected to the same substation and
48
it may become difficult to keep the voltage in all feeders within the allowable range. In
general, too large voltage fluctuations at the MV network make it difficult to keep the
voltage in the LV network within specified limits [Pro 05], as the tap changers on the
MV/LV transformer generally have fixed settings. Therefore, although the official
voltage limits for a 10kV DN are mostly +/- 10%, in practice they are mostly more
stringent. The total voltage fluctuation at the MV/LV transformer is usually required to
be smaller than 5%. In several countries the maximal allowed voltage rise caused by a
single DG unit is maximum 2% or 3% [Nav 05].
The impact of DG units on the voltage profile has widely been considered as a
serious drawback and limitation for the maximum amount of DG that can be connected
to the grid. In most publications on this topic it is concluded that above a certain DG
penetration level the voltage changes become too large [Koj 02], [Dai 03], [Ing 03], [Bol 05],
[Vu 05]. Several publications conclude that voltage control by reactive compensation is
difficult, as the X/R ratio in DNs is low [Sco 02], [Str 02], [Pro 05].
Several solutions have been proposed to limit the voltage change caused by DG.
Some of the solutions are based on coordinated control between the DG units and the
tap changers and line drop compensators at the substation [Str 02], [Cal 05]. Other papers
focus on the use of DG units for voltage control [Woy 03], [Sun 04b], [Tan 04]. These papers
mainly concentrate on the implementation of appropriate controllers and the interaction
and communication between several DG units that contribute to voltage control [Mar 04],
[Mog 04]. Also power electronics based solutions such as a Distribution STATic
COMpensator (D-STATCOM) or a Dynamic Voltage Restorer (DVR) have been
proposed [Saa 98], [Gru 00], [Sun 04a].
Summarizing, most publications conclude that a problem can occur, they determine
how large the voltage change will be and they propose solutions to limit the voltage
change. It is not determined however, what the maximum allowable penetration level of
DG units is, with respect to the voltage change they cause.
The goal of this chapter is to determine the maximum (with respect to the voltage
change they cause) allowable penetration level of DG units, assuming that the DG units
compensate (a part of) the voltage change they cause. Several techniques to increase the
amount of reactive power that the DG unit can compensate are considered and it is
investigated how they can be used to increase the maximum penetration level of DG.
The chapter starts in section 4.2 with discussing some basic theory and proposing
several voltage control techniques. For each of the techniques it is investigated how
effective it is in compensating the voltage deviations caused by the DG units, depending
on the X/R ratio of the line impedance. Section 4.3 presents a device that can be used to
increase the inductance of the grid. Section 4.4 presents a procedure to determine the
4. Voltage control contribution of DG units
49
maximum penetration level of DG (with respect to the voltage change they cause). In
this section the theory and techniques of section 4.2 are used. In section 4.5 the theory is
applied to some practical cases.
4.2 Reactive power control
Power electronic converters can supply or absorb reactive power to control the grid
voltage. In this section first the basic theory on reactive compensation is summarised,
followed by an analysis of the effectiveness of reactive power for voltage control.
Reactive power compensation will not always be enough to keep the voltage within the
allowed borders. Solutions are proposed to improve the possibilities for voltage control.
4.2.1 Basic theory
This subsection investigates the influence of active and reactive power on the grid
voltage. Fig. 4.2 shows a simplified network. The grid is modelled by a voltage source
Vs and a short-circuit impedance Zsc. A constant current load and a DG unit are
connected to the network. The voltage at their terminals is Vdg. The voltage Vdg without
DG unit connected is chosen as the reference voltage. All equations and results in this
chapter are in per unit with the short-circuit power Ssc = 100 MVA and the supply
voltage Vs = 10 kV as the base values (unless otherwise stated).
Vs
Zsc
Supply
Vdg Idg
Load
DG
Fig. 4.2. Network diagram with Thévenin equivalent of grid, load, and DG unit
When the DG unit supplies current to the network the voltage Vdg will change to
Vdg,new. The difference between the two voltages is:
ΔV dg = Z sc I dg
(4.1)
This voltage change has a component ΔVdg,r in phase with Vdg and a component ΔVdg,x
perpendicular to Vdg. According to [Mil 82], and neglecting the load, the two components
can be approximated by:
ΔVdg ,r
1
≈
Pdg cos ϕ sc + Qdg sin ϕ sc
(4.2)
Vdg
S sc
[
]
50
ΔVdg , x
Vdg
≈
[
1
Pdg sin ϕ sc − Qdg cos ϕ sc
S sc
]
(4.3)
with Pdg and Qdg the active and reactive power supplied by the DG unit, and with:
tan ϕ sc =
X sc
Rsc
(4.4)
The voltage Vdg,new is obtained by adding (4.2) and (4.3) to Vdg:
(
)
V dg ,new = Vdg + ΔVdg ,r + j ⋅ ΔVdg , x
(4.5)
The phasor diagram is shown in Fig. 4.3, for a specific situation in which the voltage
without DG unit is below the lower voltage limit. When the DG unit is connected the
voltage increases to a value between the two limits.
Lower voltage
limit
ΔVdg
0
Vdg
Upper voltage
limit
Vdg,new
ΔVdg,x
ΔVdg,r
Fig. 4.3. Phasor diagram of voltage change due to DG unit power
Under the assumption that Vdg ≅ Vs, the following approximation holds [Mil 82]:
ΔVdg
Vdg
≅
S dg
S sc
(4.6)
The equations (4.2) - (4.6) are very useful, as they are expressed in terms of quantities
that describe the characteristics of the network; short-circuit power Ssc and X/R ratio (i.e.
tanϕsc) of the network, and the active and reactive power Pdg and Qdg of the DG unit.
4.2.2 Effect of X/R ratio on voltage deviation and voltage control possibilities
The equations in the previous subsection show that the voltage change due to the active
and reactive power of the DG unit depends on:
• the X/R ratio of the short-circuit impedance (given by tan ϕ sc = X sc Rsc )
•
the ratio between the rated DG unit power Sdg and the short-circuit power at the
point of connection Ssc,
Voltage control with reactive power is traditionally applied in the high-voltage
transmission grid. The impedance is dominated by the reactance of the overhead lines
4. Voltage control contribution of DG units
51
and the transformers, offering good possibilities for reactive compensation. At lower
voltage levels voltage control with reactive power is more difficult because the line
impedance is mainly resistive. In addition the voltage increase due to the active power
of a DG unit is relatively large because of the relatively high resistance. Fig. 4.4a shows
the voltage change due to the DG unit in the network of Fig. 4.2 for 3 different X/R
ratios. The impedance is 1 p.u. in all three cases. The DG unit has a rated power of 0.2
p.u. and operates at 90%. The margin in power (and current) is used to consume reactive
power to reduce the voltage. The figure shows that for X/R = 1/3 and 1 the voltage is
higher than the upper voltage limit. Only for X/R = 3 the voltage stays below the limit.
The whole range of voltages that can be achieved is shown by the circle and ellipses in
Fig. 4.4b. The figure shows that in case of a large X/R ratio the voltage never exceeds
the voltage limits, whereas for a low X/R ratio the voltage is too large in most cases.
3
X/R=
Lower
voltage limit
ΔVdg
Vdg,new
ΔVdg
3
1/
R=
/
X
Vdg
X/R=3
Upper voltage
limit
Upper voltage
limit
X/R=1
X/R
=1
ΔVdg
ΔVdg,x
Vdg
Lower voltage
limit
X/R=1/3
ΔVdg,r
(a)
(b)
Fig. 4.4. Phasor diagrams: (a) Voltage change caused by DG unit for different X/R ratios (Vdg = 1 p.u., Zsc = 1
p.u., Sdg = 0.2 p.u., Pdg = 0.18 p.u., Qdg = 0.087 p.u.); (b) Range of ΔVdg for different X/R ratios (Vdg = 1 p.u., Zsc
= 1 p.u., Sdg = 0.2 p.u.)
Especially cable networks have a low X/R ratio. The voltage range that can be
realised has been analysed for two distribution cable networks in the Netherlands: one
rural network and one urban network. The parameter values are summarized in table
4.1. More information on the networks can be found in Appendix A. For three different
nodes in the network the short-circuit power, the X/R ratio and the distance between the
node and the substation are given. Node 1 is at the substation, node 3 is at the end of a
feeder, and node 2 halfway the feeder. Both the short-circuit power and the X/R ratio of
the grid decrease for increasing distance to the substation.
When a DG unit is connected to node 1, its active power causes only a small voltage
increase, because of the high short-circuit power and the high X/R ratio, which are
mainly determined by the transformer impedance. Due to the high X/R ratio the DG unit
can easily control the voltage by absorbing a small amount of reactive power, as is
52
shown by the solid line in Fig. 4.5a and b for the urban and the rural DN respectively.
Node 2 is located further from the substation. Due to the cable between node and
substation both the short-circuit power and the X/R ratio are lower. The reactive power
required for compensation (dashed line) is approximately equal to the active power. For
node 3, which has a low short-circuit power and a low X/R ratio the required reactive
power is larger than the active power (dotted line).
Table 4.1. Parameters of a two typical Dutch cable networks
Node
Urban network
Ssc
Xsc/Rsc
[MVA]
Distance
[km]
Node
Rural network
Ssc
Xsc/Rsc
[MVA]
Distance
[km]
1
2
3
233
105
60
0
5
10
1
2
3
153
103
21
0
7
14
16
1.25
0.75
10
10
Node 1
Node 2
Node 3
8
Reactive power [MW]
Reactive power [MW]
8
6
4
2
0
0
41
2.2
0.35
Node 1
Node 2
Node 3
6
4
2
2
4
6
Active power [MW]
8
10
0
0
2
4
6
Active power [MW]
8
10
(a)
(b)
Fig. 4.5. Reactive power that is required to compensate the voltage change that is caused by active power at a
certain node: (a) urban network; (b) rural network
From the analysis, which is representative for most cable DNs, some conclusions can be
drawn: DG unit connected at locations close to the substation (node 1) can easily
perform voltage control (high X/R ratio) but it is hardly necessary as the voltage
deviations are small due to the high short-circuit power. Further from the substation the
short-circuit power is lower and voltage control may be necessary, but is more difficult
because of the low X/R ratio. The larger the distance from the substation, the more
voltage control is needed and the more difficult it is, because of the low X/R ratio.
4.2.3 Overrating and generation curtailment
The DG unit will not always be able to supply the reactive power that is necessary for
compensation, because its converter current is limited. Problems are most likely to
4. Voltage control contribution of DG units
53
occur in low-load / high-generation situations. When the DG unit supplies a large
power, there is a chance that the upper voltage limit is exceeded. As the DG unit
supplies a large active power, the margin for reactive power consumption is limited or
even zero. The maximum amount of reactive power that can be consumed is:
Qdg ,max =
(Vdg I dg ,max )2 − Pdg2
(4.7)
with the maximal converter current defined as:
I dg ,max =
S dg ,nom
(4.8)
Vdg ,nom
A possibility to improve the voltage control capability is to increase the maximum
current (Idg,max) that is allowed for the DG unit converter. The basic principle is shown
in Fig. 4.6a. The phasor diagram shows a voltage increase Vp due to the active power
and a compensating voltage VQ (solid line) due to the reactive power. The compensating
term is limited to the maximum current times the grid impedance (represented by the
circle) and therefore it can not bring the voltage below the upper limit of Vdg. When the
maximum current is increased also VQ (dotted line) can be increased, such that Vdg,new is
below the limit. Fig. 4.7a shows for three ratios of X/R how large the overrating of the
converter should be to obtain a certain voltage compensation. Fig. 4.7c shows the
overrating for a converter with higher rated power.
Upper voltage limit
Upper voltage limit
Vdg,new
VQ
VQ
Vdg,new
VP
VP
Vdg
Vdg
Idg,max
Idg,max
1.25Idg,max
(a)
(b)
Fig. 4.6. Phasor diagrams showing strategies to improve the voltage control capabilities of converters; (a)
converter overrating; (b) active power reduction
Another possibility is to lower the amount of active power that is supplied by the
DG unit when the upper voltage limit is exceeded (generation curtailment). As the
active current decreases the reactive power that can be consumed increases, as can be
54
seen from (4.7). The phasor diagram in Fig. 4.6b shows the principle of generation
curtailment. Due to the reduction in active power VP will decrease and the margin for
reactive power will be larger, resulting in a larger VQ. Fig. 4.7b and d show how far the
active power should be reduced to obtain a certain reduction in voltage (due to decrease
of VP and the increase of VQ). The likelihood of the coincidence of low load and high
generation determines the total energy that is lost when curtailment is applied. As the
price of electricity is primarily driven by load demand, and curtailment occurs typically
during periods of low load, the value of the curtailed energy is likely to be low [Str 02].
50
40
Power reduction [%]
Overrating [%]
40
50
X/R= 3
X/R= 1
X / R = 1/3
30
20
10
0
0
X/R= 3
X/R= 1
X / R = 1/3
30
20
10
2
4
ΔV [%]
6
8
0
0
10
2
4
(a)
X/R= 3
X/R= 1
X / R = 1/3
20
Power reduction [%]
Overrating [%]
8
10
6
8
10
25
15
10
5
0
0
6
(b)
25
20
ΔV [%]
X/R= 3
X/R= 1
X / R = 1/3
15
10
5
2
4
ΔV [%]
6
8
10
0
0
2
4
ΔV [%]
(c)
(d)
Fig. 4.7. Measures to improve the voltage control capabilities of converters as a function of the required
voltage change: (a) converter overrating (Sdg,nom = 0.1 p.u.); (b) active power reduction (Sdg,nom = 0.1 p.u.); (c)
converter overrating (Sdg,nom = 0.4 p.u.); (d) active power reduction (Sdg,nom = 0.4 p.u.);
The graphs in Fig. 4.7 show that the overrating that is needed to obtain a certain
voltage change strongly depends on the X/R ratio and the rated power of the converter.
The required curtailment is less dependent on the X/R ratio, but it depends strongly on
the rated power of the converter. The figure shows further that, especially for converters
with a high rated power, only a small percentage of overrating or curtailment is needed
to achieve a significant voltage change.
4. Voltage control contribution of DG units
55
4.3 Variable inductance
The limited effect of reactive power compensation in cable networks is mainly due to
the low inductance of the cables. Increasing the inductance will increase the
effectiveness of reactive compensation. A higher inductance can be undesirable in
normal situations however, because of the large voltage drop across it. A solution can be
to use a variable inductance. This subsection investigates the usefulness of such a device
and presents a possible implementation.
4.3.1 Variable inductance value
A typical example of a network in which a variable inductance can be useful is shown in
Fig. 4.8. The loads and DG units are aggregated and connected to the end of the line.
Branch A has both a load and a DG connected whereas branch B only has a load. Due to
the DG the voltage in branch A can become too high in cases of high generation and
low load. The tap-changer at the distribution transformer can decrease the voltage at the
substation, but this can result in a too low voltage at the end of feeder B. A variable
inductance, in combination with reactive power control by the DG unit, can avoid
violation of the voltage limits [Ton 05].
Lv
Transmission
Grid
Za
DG
HV/MW
load a
Zb
load b
Fig. 4.8. Model of network with variable inductance, DG unit and loads
The inductance value that is needed to obtain a certain voltage change depends on
the line impedance, the load and the active and reactive power supplied or consumed by
the DG unit converter. The voltage drop across the inductance depends on the active
and reactive power of DG unit and load. The active power supplied by the DG unit will
result in a voltage increase, whereas the reactive power that is consumed results in a
voltage drop. The voltage drop that can be achieved as a function of the value of the
variable inductance is shown in Fig. 4.9. A variable inductance of 10mH equals ~3 p.u..
The curves are shown for 4 values of the difference between the reactive power of the
DG unit and the load. The results of Fig. 4.9a have been obtained for Pdg – Pl = 0.025
p.u. and the results of Fig. 4.9b for Pdg – Pl = 0.05 p.u..
56
50
dg
40
Voltage change [%]
Voltage change [%]
40
50
Q − Q = 0.025
dg
l
Q − Q = 0.05
dg
l
Q − Q = 0.075
dg
l
Q − Q = 0.1
l
30
20
10
0
0
Q − Q = 0.025
dg
l
Q − Q = 0.05
dg
l
Q − Q = 0.075
dg
l
Q − Q = 0.1
dg
l
30
20
10
2
4
6
Variable Inductance [mH]
8
10
0
0
2
4
6
Variable Inductance [mH]
8
10
(a)
(b)
Fig. 4.9. Voltage drop that can be achieved with reactive power as a function of a variable inductance for
different values of the reactive power; (a) Pdg – Pl = 0.025 p.u.; (b) Pdg – Pl = 0.05 p.u.
The voltage change that is achieved increases with increasing inductance. Above a
certain inductance it decreases again however. At that point the voltage change due to
the active power starts dominating the voltage change due to the reactive power. This
implies that there is a maximum in the voltage change that can be achieved with a
variable inductance. For a larger value of Pdg – Pl the maximum is reached at a lower
inductance and a lower voltage change. The figure shows further that with a small
inductance already a high voltage change can be achieved. It is assumed that the DG
unit has the capability to consume enough reactive power. In reality measures like
overrating or generation curtailment might be necessary to achieve the required amount
of reactive power.
4.3.2 Implementation
A device with a variable inductance can be implemented in different ways. In this
section an implementation is used that is similar to the thyristor controlled reactor
circuit [Boh 89] and the advanced series compensation concept proposed by [Par 97]. The
device will be called a ‘Variable Inductor’ (‘VI’). It consists of an inductor in parallel
with two anti-parallel thyristors, as shown in Fig. 4.10a. The current through and the
voltage across the inductor are shown in Fig. 4.10b. The thyristors are fired with phase
shift α, with respect to the zero crossing of the current. When thyristor ‘T1’ is fired
(with angle α) the current through the inductance remains constant. The turn-on of ‘T1’
shunts Lv, effectively removing it from the circuit. This condition lasts until the thyristor
current becomes zero. Then ‘T1’ turns off and the current through Lv starts decreasing.
The process is repeated in the negative half cycle using ‘T2’. By changing the firing
angle of the thyristors the time can be determined that the inductor will be inserted
during each period. This results in an average (equivalent) inductance. Snubber
4. Voltage control contribution of DG units
57
components are necessary to avoid over-voltages by switching transients. During
normal operation the device can be by-passed.
Voltage
Current
T2
T1
α
Lv
0.12
0.125
0.13
time [s]
0.135
0.14
(a)
(b)
Fig. 4.10. Variable Inductor: (a) circuit; (b), thyristor voltage and current for 45 degrees firing angle
Introducing the VI in the line will increase the voltage control capabilities of the DG
unit converter. Fig. 4.11a shows the voltage at the DG unit terminal of Fig. 4.8, for a
sequence of conditions. At t = 0.4 s reactive power control is applied (without VI). This
has a limited effect because of the small network inductance. When the VI is inserted (t
= 0.7 s), a significant reduction in voltage can be obtained. In both last cases the DG
unit is absorbing maximum reactive power (Idg,max = 165 A). The inductance Lv has a
value of 20 mH (~6 p.u.), Za = 4.5 p.u. with an X/R ratio of 1/3, and the load consumes
no power. The voltage across and the current through the VI are shown in Fig. 4.11b.
The figure shows the period in which the VI is turned on. The firing angle is ~45° (this
means an effective inductance of 10 mH). Oscillations occur in the voltage across the
VI. This is caused by resonance between the VI and the cable capacitance. It results in a
THD of about 4%.
2
12
0.2
Voltage
Current
No control
11.5
1
0.1
0
0
Q
dg
+L
v
11
10.5
10
0.2
−1
0.4
0.6
time [s]
0.8
1
−2
0.68
Current [kA]
dg
Voltage [kV]
Voltage [kV]
Only Q
−0.1
0.7
0.72
0.74
time [s]
0.76
−0.2
0.78
(a)
(b)
Fig. 4.11. Effect of Variable Inductor (VI): (a) voltage at the DG unit terminal; (b) voltage over and current
through VI; (0 - 0.4 s: no control and no VI; 0.4 - 0.7 s: control only with DG unit, without VI; 0.7 - 1 s:
control with both VI and DG unit
58
4.4 Maximum DG penetration
4.4.1 Introduction
This section will determine how many DG units can be connected to a network when
the voltage change caused by the DG units should stay below a certain limit. The DG
units are assumed to absorb as much reactive power as possible to limit the voltage
increase they cause. The strategies and devices proposed in the previous sections are
used to achieve a further increase in maximum allowable DG unit penetration. The
maximum penetration level will be determined in three steps:
• Firstly the penetration level is determined when the DG units use the maximum
possible reactive power to compensate the voltage change they cause.
• Secondly it is investigated how (much) the penetration level can be increased by
using overrating and generation curtailment.
• The third step investigates how the VI can be used to achieve a further increase in
the penetration level.
In section 4.5 the results of this section are applied to two practical cases.
4.4.2 DG only
Violation of the voltage limit is most likely to occur in high-generation situations. In
that case the DG unit operates at, or close to, its nominal power and the reactive power
capability is limited. The active power that is supplied to the grid will result in an
increase of Vdg due to the voltage drop across the line impedance. As Pdg is independent
of Vdg this results in a decrease of the active current (Pdg=VdgIdgcosϕ) and thus in an
increase of the reactive power margin. In this way the converter can undo a part of the
voltage increase caused by its active power. First only the margin obtained in this way
will be used and the maximum penetration level for this case will be determined. The
voltage change caused by the DG unit active and reactive power can be calculated from:
V dg = V s + Z sc
S *dg
V *dg
(4.9)
The maximum amount of installed DG unit power (Pdg,nom) that is possible for a
particular limit can be calculated by solving (4.7) – (4.9) iteratively. The maximum
allowable installed DG unit power is shown in Fig. 4.12 as a function of the maximum
voltage change, and for different X/R ratios. The results are obtained for a DG unit that
absorbs the maximum available reactive power.
The X/R ratio of the network strongly influences the maximum installed DG unit
power. Fig. 4.12 shows that for an X/R ratio of 3 the voltage change becomes never
4. Voltage control contribution of DG units
59
larger than ~1.5%. This implies that in this network a large amount of DG can be
installed. Also for lower X/R ratios the maximum penetration level can be increased, by
absorbing reactive power. According to (4.6) the DG unit power without compensation
is 0.04 p.u. for a 4% voltage change. For example in a network with X/R = 1 the
maximum installed DG unit power can be ~ 0.09 p.u. when a 4% voltage change is
allowed and the maximum amount of reactive power is absorbed.
Maximum installed DG unit power [pu]
0.25
X/R= 3
X/R= 1
X / R = 1/3
0.2
0.15
0.1
0.05
0
0
2
4
ΔVdg [%]
6
8
10
Fig. 4.12. Maximum allowable installed DG unit power (per unit of short-circuit power) as a function of
maximum allowable voltage change for different X/R ratios (Vdg=1)
4.4.3 Overrating and curtailment
It has been shown in the previous section that the voltage control capability of a DG
unit can be improved by converter overrating and generation curtailment. Fig. 4.13
shows for three different values of the allowed voltage change the maximum installed
DG as a function of the converter overrating. The curves are shown for X/R = 1 (Fig.
4.13a) and for X/R = 1/3 (Fig. 4.13b). (For X/R = 3 no curves are shown as for this X/R
ratio the voltage change is low already, as can be seen from Fig. 4.12.)
0.04
0.02
ΔV < 1%
dg
ΔVdg < 2%
ΔV < 3%
Increase in maximum DG power [pu]
Increase in maximum DG power [pu]
0.05
dg
0.03
0.02
0.01
0
0
2
4
6
Overrating [%]
8
10
0.015
ΔV < 1%
dg
ΔV < 2%
dg
ΔV < 3%
dg
0.01
0.005
0
0
10
20
Overrating [%]
30
40
(a)
(b)
Fig. 4.13. Increase in maximum allowable installed DG unit power (per unit of short-circuit power) as a
function of converter overrating; (a) X/R = 1; (b) X/R = 1/3; (Vdg = 1 p.u.)
60
The results are obtained by solving (4.7) – (4.9) for an increasing overrating of the
converter. Comparing the results shows that overrating is much more effective for the
higher X/R ratio. For X/R = 1/3 the effect is rather limited.
The increase in installed power that can be achieved with generation curtailment is
shown in Fig. 4.14a and b for an X/R ratio of 1 and 1/3 respectively. Comparing the
graphs with Fig. 4.13 shows that, especially for lower X/R ratios, curtailment is more
effective than converter overrating. Due to the high resistance the reduction in active
power is very effective.
0.04
0.05
ΔV < 1%
dg
ΔV < 2%
dg
ΔV < 3%
Increase in maximum DG power [pu]
Increase in maximum DG power [pu]
0.05
dg
0.03
0.02
0.01
0
0
2
4
6
8
Active power curtailment [%]
10
0.04
ΔV < 1%
dg
ΔVdg < 2%
ΔVdg < 3%
0.03
0.02
0.01
0
0
10
20
30
Active power curtailment [%]
40
(a)
(b)
Fig. 4.14. Increase in maximum allowable installed DG unit power (per unit of short-circuit power) as a
function of active power curtailment; (a) X/R = 1; (b) X/R = 1/3; (Vdg = 1 p.u.)
The values that are obtained from the curves of Fig. 4.13 and Fig. 4.14 can be added to
the values obtained from Fig. 4.12. This gives the allowable penetration level when for
example a combination of reactive compensation and generation curtailment is applied.
4.4.4 Variable Inductance
This section investigates how a VI can increase the maximum DG unit penetration. The
increase in DG penetration that can be achieved is shown in Fig. 4.15, as a function of
the inductance value. The curves are shown for three different voltage changes and for
X/R = 1 (Fig. 4.15a) and X/R = 1/3 (Fig. 4.15b). The results are obtained for a case
without load. The VI increases the network inductance. When the DG unit absorbs too
much reactive power voltage instability will occur. This implies that the range in which
the VI works correctly is limited.
The VI shows to be more effective in the network with the highest X/R ratio. In both
cases a significant increase in allowable penetration level can be achieved however. An
inductance of 0.5 p.u., for example, results already in an increase of 0.03 p.u. and 0.01
p.u. respectively.
4. Voltage control contribution of DG units
0.025
0.03
ΔVdg < 1%
ΔVdg < 2%
ΔVdg < 3%
Increase in maximum DG power [pu]
Increase in maximum DG power [pu]
0.03
61
0.02
0.015
0.01
0.005
0
0
0.2
0.4
0.6
0.8
Variable Inductance [pu]
0.025
ΔVdg < 1%
ΔVdg < 2%
ΔV < 3%
dg
0.02
0.015
0.01
0.005
0
0
1
0.5
1
1.5
Variable Inductance [pu]
2
(a)
(b)
Fig. 4.15. Increase in maximum allowable installed DG unit power (per unit of short-circuit power) as a
function of variable inductance; (a) X/R = 1; (b) X/R = 1/3; (Sl = 0, Vdg = 1 p.u.)
4.4.5. Discussion
The results in this section show that the maximum allowable DG unit power becomes
significantly higher when the DG units absorb reactive power to compensate a part of
the voltage change they cause. The allowable penetration level can be increased further
by overrating, generation curtailment and the application of a variable inductance.
The results are obtained under the assumption that Vdg = 10 kV. When it is higher
also Qdg,max will be higher. Therefore the voltage change caused by the DG unit can be
kept smaller. Fig. 4.16 shows how the results of Fig. 4.12 change for increasing Vdg. For
the lowest X/R ratio (Fig. 4.16a) the influence is rather limited, but for X/R=1 (Fig.
4.16b) the maximum allowable power increases significantly.
0.2
0.05
0.04
Vs = 10kV
V = 10.2kV
s
V = 10.4kV
s
V = 10.6kV
s
Maximum installed DG unit power [pu]
Maximum installed DG unit power [pu]
0.06
0.03
0.02
0.01
0
0
1
2
ΔV
dg
3
[%]
4
5
0.15
Vs = 10kV
V = 10.2kV
s
Vs = 10.4kV
Vs = 10.6kV
0.1
0.05
0
0
1
2
ΔV
dg
3
4
5
[%]
(a)
(b)
Fig. 4.16. Maximum allowable installed DG unit power (per unit of short-circuit power) as a function of
maximum allowable voltage change for different values of Vdg; (a) X/R = 1/3; (b) X/R = 1;
A higher Vdg will also affect converter overrating and active power curtailment. Fig.
4.17a shows, for different values of Vdg, the increase in power that can be achieved by
62
converter overrating. Fig. 4.17b shows the same for active power curtailment. Both
graphs show that a higher Vdg has a considerable influence on the active power that can
be installed. For voltages above the nominal grid voltage, a higher penetration level of
DG can thus be allowed.
0.03
0.05
Vdg = 10kV
Vdg = 10.2kV
V = 10.4kV
dg
V = 10.6kV
Increase in maximum DG power [pu]
Increase in maximum DG power [pu]
0.04
dg
0.02
0.01
0
0
2
4
6
Overrating [%]
8
10
0.04
V = 10kV
dg
V = 10.2kV
dg
V = 10.4kV
dg
Vdg = 10.6kV
0.03
0.02
0.01
0
0
2
4
6
8
Active power curtailment [%]
10
(a)
(b)
Fig. 4.17. Increase in maximum allowable installed DG unit power (per unit of short-circuit power) as a
function of converter overrating (a) and active power curtailment (b) for different values of Vdg; X/R = 1;
In this chapter it was assumed that, besides the limitations imposed by the maximum
converter current, there are no limitations on the reactive power supplied by the DG
units. In reality there might be other limitations, such as for example the maximum
current that is allowed in the network, or the minimum power factor that is allowed by
grid operators. Other issues that have not been considered, but that can be important are
the influence on the losses in the network and the optimal location of the DG units.
4.5 Cases
Several voltage control techniques are considered in this chapter. The analyses can be
used to determine the voltage change that is be caused by DG units and to determine
maximum allowable penetration levels. This will be demonstrated with two cases.
4.5.1 Case 1
The influence of a 1.5 MW wind turbine connected to node 3 of the rural network
described in appendix A.2 is considered. Currently three constant speed wind turbines
are connected with a total rated power of about 1.5 MW. The network has a rather low
short-circuit power and the wind turbines cause large voltage fluctuations. This can be
seen from Fig. 4.18, which shows for a period of one week the power supplied by the
4. Voltage control contribution of DG units
63
turbine and the voltage at its terminals. (The active power was measured for each wind
turbine separately. The power shown in the figure is the total active power for the three
turbines.) For the analysis the wind turbines are replaced by a single variable speed
wind turbine with a synchronous generator and a PEC, with a rated power of 1.5 MW.
2
1.1
1.08
Voltage [pu]
Power [MW]
1.5
1
1.06
1.04
0.5
1.02
0
0
1
2
3
4
Day
5
6
7
0
1
2
3
4
5
6
7
Day
(a)
(b)
Fig. 4.18. Wind turbine output power (a) and voltage and wind turbine terminals (b)
The effect of the wind turbine on the voltage is determined in a number of steps:
1.
The voltage change due to the introduction of one or more DG units can be
determined approximately by (4.6). The short-circuit power at the node to which
the wind turbine is connected is 21 MVA, with an X/R ratio of 0.35. According to
(4.6) the maximum rated power of the DG unit is 0.6 MW when the maximum
allowable voltage change is 3%. The wind turbine has a rated power of 1.5 MW,
implying a maximum voltage change of ~ 7%. This is in compliance with Fig. 4.18.
2. The change in voltage caused by the wind turbine is thus too large. In the previous
paragraphs several solutions are proposed to overcome this problem. Their
usefulness will be considered.
a. The wind turbine has a PEC and thus it can absorb reactive power. When a
maximum voltage change of 3% is allowed, the maximum installed DG unit
power will be 0.7 MW, as can be determined from Fig. 4.12. This is only
slightly higher than in a case without voltage control. This is, of course, due to
the low X/R ratio of the network.
b. Overrating of the converter will increase its voltage control capability and
therefore the maximum amount of power that can be installed. Fig. 4.13b
shows that a 40% overrating of the converter results in a 0.4 MW increase in
power that can be installed. The total installed power is then 1.1 MW, which is
still too low.
64
c.
Another solution is generation curtailment. Fig. 4.14b shows that 30%
curtailment results in 0.8 MW increase in active power that can be installed.
Adding this to the 0.7 MW for a case without control, the total installed DG
power is 1.5 MW.
d. The third option that has been discussed is the usage of a variable inductance.
Fig. 4.15 shows that the maximum variable inductance value is about 1.2 p.u..
The increase in installed power that can be obtained with this inductance is 0.5
p.u., which is too low.
3. Generation curtailment shows to be the only option that makes it possible to install
the 1.5 MW wind turbine without violating the 3% voltage change limit. The
highest 30% of the wind turbine power has to be curtailed. For a 1.5 MW wind
turbine the maximal power that may be supplied is thus 1.05 MW. This means a
significant reduction in the total energy that is produced. Fig. 4.18a shows the
power output for one week. The total energy produced in this week is ~1100 MWh.
When the power is limited to 1.05 MW the energy production is ~940 MWh, a
reduction of ~15%.
4.5.2 Case 2
In the second case the maximum rated DG unit power that can be connected to node 4
of the Testnet will be determined. (Details of the network are given in appendix A.1.)
This is done in a number of steps:
1. The short-circuit power at node 4 is 50 MVA, with an X/R ratio of 0.75. According
to (4.6) the rated power of the DG should not be higher than 1.5 MW (for a voltage
change of 3%).
2. To increase the maximum allowable DG unit penetration level the DG unit can
absorb reactive power, possibly in combination with one of the proposed
techniques. The following options to reach a penetration level of 5 MW are
compared:
a. By absorbing maximum reactive power an installed power of 0.05 p.u. is
allowable for a 3% voltage change, as can be seen from Fig. 4.12. This implies
a maximum DG unit power of 2.5 MW.
b. Fig. 4.13a shows that a 10% overrating of the converter results in an additional
increase in power of about 0.05 p.u.. The total power that can be installed in
that case is thus about 5MW.
c. Fig. 4.14a shows that for example 8% curtailment results in a 2.5 MW increase
in installed power, resulting in a total power of 5 MW.
d. To increase the allowable penetration level to 5 MW by using a VI is not
possible without causing voltage instability, as can be seen from Fig. 4.15a.
4. Voltage control contribution of DG units
3.
65
A comparison can be made between the different solutions. The best solution can
be defined in different ways. For example the highest annual energy yield or the
lowest kWh-price.
a. When the highest annual energy yield has to be obtained, overrating of the
converter or the use of a VI will be the best solution, as generation curtailment
will reduce the annual energy yield.
b. Another possibility is to determine for which option the lowest price per kWh
is obtained. For this case the DG units are assumed to be two wind turbines of
2.5 MW each. The cumulative wind power distribution function of one turbine
is shown in Fig. 4.19. It shows how large the chance is that the active power of
the wind turbine is below the value shown on the horizontal axis. In point 2.c it
was concluded that an 8% curtailment was enough to allow the installation of 5
MW. For one wind turbine this implies a maximum power of 2.3 MW. The
chance that the output power is below 2.3 MW is about 0.9, as can be obtained
from Fig. 4.19. Curtailment implies thus that in 10% of the time 0.2 MW less is
produced. This implies an annual energy loss of 175 MWh. When the price per
kWh is known, the annual loss in revenues can be calculated. This can be
compared with the investment costs of overrating or a VI to determine the most
cost effective solution.
Fig. 4.19. Cumulative wind turbine output power distribution
4.5.3 Discussion and conclusion
From the two cases a number of conclusions can be drawn. They show in the first place
that the allowable penetration level increases when the DG unit is able to absorb
reactive power. The increase is higher for a higher X/R ratio. (15% increase in case 1,
with an X/R ratio of 0.35 and a 40% increase in example 2, with an X/R ratio of 0.75.)
The effect of overrating is limited in networks with a low X/R ratio. Case 1 showed
that a 40% overrating results in an increase in installed power of no more than 55%. In
networks with a higher X/R ratio overrating will become more effective. Case 2 showed
66
that 10% overrating was enough to double the amount of DG power that can be
installed.
Both examples show that generation curtailment is a good option. In the second
case, for example, a curtailment of 8% was enough to allow an increase in rated power
of 100%. In the first case a higher curtailment was required, about 30%; leading to a
decrease in annual energy yield of only 15%
The VI will increase the total grid inductance. When the total inductance is high and
the amount of reactive power that is consumed is large, voltage stability problems can
occur. This stability problem poses a limit on the use of the VI.
4.6 Summary and conclusion
In this chapter the voltage control contribution of DG unit converters is investigated.
Reactive compensation showed to be of limited effect because of the low inductance in
DNs. Converter overrating and generation curtailment have been proposed as solutions
to partially overcome these limitations. Section 4.3 proposed to use a variable
inductance. An implementation with two anti-parallel thyristors was proposed for the
variable inductance. It should be realised that this device will have a significant
influence on the short-circuit power and the power quality of the DN.
Section 4.4 presented an approach to determine the maximum allowable DG
penetration level, with respect to the voltage change that is caused by the DG units. The
increase in voltage they cause, offers the possibility to increase the reactive power
consumption to limit the voltage increase. Using this reactive power significantly
increases the maximum allowable penetration level. Especially in networks with a high
X/R ratio a significantly higher penetration level of DG can be allowed. For networks
with a low X/R ratio generation curtailment and the use of a VI offer good possibilities
to increase the DG unit penetration level, although its effect is limited: for too high
values voltage instability occurs. The effect of overrating is limited in a network with a
low X/R ratio.
Finally in section 4.5 the maximum DG penetration levels in some typical networks
were determined. They showed that reactive power control by the DG unit increased the
allowable DG power with 15 – 40% already, depending on the X/R ratio. A 10%
overrating can increase the allowable penetration level by 50% in networks with an X/R
ratio of ~1. 8% curtailment was in this network enough to achieve a 100% increase in
allowable penetration level.
Chapter 5
Ride-through and grid support during
faults
5.1 Introduction
Short-circuits regularly occur in power systems. They can be caused by lightning
strikes, degradation of isolation material, and so on. They lead to the flow of large shortcircuit currents. Protection systems protect the network by isolating the faulted area
from the main grid. The removal of generators and loads from the main grid may result
in power imbalance and frequency deviations, as will be discussed in chapter 6. The
short-circuit currents that flow in the grid and the switching events that are taken by the
protection system also result in voltage dips. The interaction between DG units and the
grid during voltage dips is investigated in this chapter.
Most DG units will intentionally disconnect from the grid during a dip. There are
several reasons for this disconnection. The first is that up to now most standards for DG
require disconnection in case of a fault (for example IEEE-Std. 1547-2003), because
DG units can disturb the protection schemes of the network. Another reason is that the
power electronic converters (PECs) that connect the DG units to the grid may be
sensitive to over-currents and over-voltages. The easiest way to avoid detrimental
effects is to disconnect the DG unit. In networks with a large DG penetration level the
disconnection will cause serious problems. Disconnection of all DG units may result in
a large power generation deficit and in stability problems [Slo 02]. In addition they can
not support the grid voltage and frequency during and immediately after the grid failure.
The goal of this chapter is to investigate how PEC-based DG units can support the grid
(voltage) during faults and how damage to the DG unit can be avoided.
Section 5.2 analyses the response of DG units to voltage dips. In section 5.3 it is
investigated how the disturbance of the classical grid protection by DG units can be
minimised. Section 5.4 will investigate how DG units can support the grid voltage
during dips and will determine how large this contribution is. During a fault the power
that the DG unit can deliver to the grid is often limited because of the reduced grid
68
voltage. Section 5.5 discusses the consequences for the DG units and describes
protection techniques that can be applied to avoid malfunctioning of the DG unit. A
special case, when it comes to short-circuits and protection, is a wind turbine with a
doubly-fed induction generator. It is analysed separately in section 5.6.
5.2 Fault response of DG units
During a fault a voltage dip is experienced by DG units connected to the grid. Their
response depends on the type of DG unit, especially whether it is connected to the grid
with a machine or a PEC. The response of an electrical machine is completely different
from that of a converter. This paragraph compares their responses. The network shown
in Fig. 5.1a is used to compare the voltage dip response of PECs and synchronous
machines (SMs). It contains a DG unit and a load. The rated power of the DG unit is
~5% of the short-circuit power of the grid.
In the first case the DG unit is the SM shown in Fig. 5.1b. The stator current and
voltage during the dip are shown in Fig. 5.2a and c. The response of the SM is
determined by the fundamental electro-mechanical laws and physical construction of the
machine, and by its excitation control. The initial short-circuit current reaches a high
value, but decays after some time. The peak current mainly depends on the sub-transient
reactance of the generator which is inherent to its physical construction and on the
excitation of the machien. The machines are developed to be able to withstand these
currents and dynamic forces for a certain time. Therefore no special protection is
required for the SM.
HV Grid
DG
Load
Sub-station
(a)
DG
DG
Prime
Source
SM
Prime
Source
Control
(b)
(c)
Fig. 5.1. Network with DG unit and fault: (a) network; (b) DG unit with synchronous machine; (c) DG unit
with power electronic converter
5. Ride-through and grid support during faults
69
5
1
Current [pu]
Current [pu]
0.5
0
0
−0.5
−1
−5
0.2
0.3
0.4
0.5
time [s]
0.6
0.7
0.2
0.8
0.3
0.4
1
0.5
0.5
0
−0.5
0.7
0.8
0.6
0.7
0.8
0
−0.5
−1
0.2
0.6
(b)
1
Voltage [pu]
Voltage [pu]
(a)
0.5
time [s]
−1
0.3
0.4
0.5
time [s]
0.6
0.7
0.8
0.2
0.3
0.4
0.5
time [s]
(c)
(d)
Fig. 5.2. Response to voltage dip: (a) synchronous machine current; (b) converter output current; (c)
synchronous machine stator voltage; (d) converter output voltage;
In the second case the DG unit is the PEC shown in Fig. 5.1c. Fig. 5.2b and d show
the output current and the terminal voltage. In contrast to the SM, the current is not
determined by the converter construction but by its control. During normal operation
PECs have a low-impedance output. This implies that when they are not controlled, they
will supply a large current when the voltage drops. The current control of the converter
limits the current however, to avoid breakdown of the semiconductor devices which are
sensitive to high currents. When the controllers are fast enough the current can be
limited as shown in Fig. 5.2b. Breakdown of the semiconductor switches is thus avoided
and the converter can stay connected during the dip. When the current control loop is
not fast enough there will be a short peak in the converter current.
In this example the converter current is limited to its nominal value. Other control
strategies are possible however. In principle converter designers can implement a
number of different control schemes in the same converter. In the installation phase and
during operation the grid operators can choose the appropriate control.
70
5.3 Disturbance of protection during faults
5.3.1 Introduction
In distribution networks (DNs) protection schemes are applied to minimise the
detrimental effect of faults in the DN. The connection of DG units will influence the
operation of the protective devices. This has been discussed extensively in literature
[Dug 02], [Kau 04], [Mäk 04], [Kum 05]. Most publications consider machine-based DG units
and generally it is concluded that the DG units can prevent the proper operation of the
feeder protection [McD 03], [Kum 04], [Ver 04]. This is not necessarily true however.
Especially PEC-based DG units can limit their current during a fault and minimise he
influence of the DG unit on the network protection.
This section will discuss shortly how the DG units can be controlled to minimise the
influence on the protection. The most important problems mentioned in literature are
[Kau 04], [Jer 04]:
1. Blinding of protection
2. False tripping (unnecessary disconnection of a healthy feeder)
3. Failure of reclosing
4. Islanding
The issue requires more research however, before general conclusions can be drawn.
5.3.2 Blinding of protection
DG units can prevent the proper operation of feeder protection [Dug 02], [Kau 04], [Mäk 04].
This happens when the fault current measured by the protective device decreases due to
the short-circuit current supplied by the DG unit, as illustrated by Fig. 5.3a and b. In a
situation without DG all fault current is flowing through the protective device at the
beginning of the feeder (Fig. 5.3a). In a case with DG, the DG unit also supplies a part
of the short-circuit current, resulting in a lower current through the protective device
(Fig. 5.3b). The current can drop below the breaking current and as a result the breaker
will not disconnect the feeder and the fault current continues to flow. This can cause
damage to grid components.
An example will be given for the chance on blinding in a realistic case. When,
without DG unit, a fault occurs at node 3 of the Testnet (see appendix A.1) a 3.5 kA
current flows through the protective device. When a 5 MW DG unit is connected to
node 2, this current reduces to 3.2 kA, in the case that the DG unit current is limited to
its nominal value. This example shows that the reduction in current through the
protective device is limited. In normal operation the nominal current through the
protective device is only ~120 A. Discrimination between a normal situation and a fault
will not be difficult.
5. Ride-through and grid support during faults
Icb = If
71
If
HV Grid
Icb < If
If
HV Grid
Protective
device
Z
Z
Protective
device
DG
Sub-station
Sub-station
(a)
(b)
Fig. 5.3. Blinding of protection due to fault downstream of DG: (a) fault current If completely observed by
protective device; (b) protective device is blinded because DG delivers a large part of fault current If
5.3.3 False tripping
It is concluded in a number of publications that DG units can cause false tripping and
unnecessary disconnection of a healthy feeder [Kau 04], [Mäk 04]. This is explained with
reference to Fig. 5.4, where a fault occurs in feeder 2. The DG unit connected to feeder
1 feeds this fault through the substation bus. The current of the DG unit can be large
enough to trip protective device 1 in feeder 1, before protective device 2 is tripped. This
type of malfunctioning can be avoided when a converter based DG unit is used
however. Depending on the settings of the two protective devices the DG unit can limit
its current during the fault to avoid tripping.
HV Grid
1
Protective
device
Z
DG
2
Sub-station
Z
Fig. 5.4. False tripping of protective device 1 due to fault in another feeder
Again an example will be given. The fault is assumed to occur at node 3 (feeder B)
of the Testnet, while a 5 MW DG unit is connected to feeder A. The fault current
through the protective device of feeder B is 3.5 kA and through that of feeder A it is
~300 A, when the DG unit current is limited to its nominal value. The chance on false
tripping is thus small.
5.3.4 Failure of auto-reclosing
Auto-reclosing is a fault clearing technique that is normally applied in networks with
overhead lines. Most line faults are due to arcs caused by lightning over-voltages and
they are self-clearing when the line is disconnected. When a fault is detected the circuit
breaker is opened, which interrupts the current that is fed into the short-circuit and
72
therefore the arc will disappear. After a short period (~0.3s) the breaker is closed again
automatically.
Many papers mention that DG units can prevent the successful operation of autoreclosers [Dug 02], [Kau 04], [Mäk 04], [Kum 04]. When a DG unit is connected to the feeder,
it can continue to supply current to the fault and as a result the arc may not disappear.
To avoid problems PEC-based DG units can reduce their output current to almost zero
during the period that the recloser is open. This increases the chance that an arc is
cleared, as the DG unit feds almost no current into it.
5.3.5 Islanding
The fourth issue is islanding [Ye 04], [Kat 05], [Peç 05]. It occurs when a DG unit continues
to energise a section of the utility system that has been separated from the main utility
system. Islanding can pose a serious safety threat for maintenance personnel, if they
expect a system to be de-energised. The islanded network will probably not comply
with power quality and protection requirements. Therefore most grid operators do not
permit islanded operation.
The big issue for DG units is to detect when the network becomes islanded. The
detection method should be reliable. On one hand it has to be sure that the DG unit will
disconnect in case of an island, while on the other hand unnecessary tripping should be
avoided. A whole range of islanding detection techniques has been developed [Jer 04],
[Ye 04], [Yin 04]. With these techniques unnoticed islanding can be avoided in most cases.
5.4 Grid support during dips
5.4.1 Introduction
So far faults have been investigated which occur close to the DG unit, i.e. in the same
DN. They mostly result in a large short-circuit current. When the fault occurs further
away (outside the DN), the DN protection will not react and disturbance of protection
will not occur.
Faults further away result in a voltage dip. They are experienced as a reduction in
rms voltage at the terminals of DG units and loads. The dip can be problematic for the
loads connected to the network. Several types of loads, such as adjustable-speed drives,
process-control equipment, and computers are very sensitive to voltage dips. Some of
them disconnect when the rms voltage drops below 90% for longer than one or two
cycles [Bol 00]. Also most DG units disconnect in case of a fault. This is mainly because
of the current grid codes, as was explained already in the introduction of this chapter.
When DG units stay connected to the grid however, they can supply active and reactive
5. Ride-through and grid support during faults
73
power during the dip. In this way they can limit the depth of the voltage dip and thus
reduce the chance that loads are disconnected.
On some places it is required already for larger DG units that they have ride-trough
capability (stay connected) and support the grid voltage during dips. Fig. 5.5 shows an
example (from E.On Netz, a grid operator in Northern Germany [E.On 03]). This
requirement is for wind farms directly connected to the transmission grid. For voltages
above the curve (in duration and voltage level), the turbine should stay connected. For
voltages in the gray area, the turbine should supply reactive power.
This section will investigate how DG units can support the grid during voltage dips
and how large their contribution can be. As a first step the effectiveness of reactive
power is investigated. In most cases this is limited. Therefore techniques will be
proposed to improve the voltage control capabilities, such as overloading of the
converter and the use of a variable inductance.
Fig. 5.5. E.On Netz requirements for wind park behaviour during faults ([E.On 03])
5.4.2 Voltage control with (re-)active power
In chapter 4 it has been concluded that voltage control with reactive power is mostly
limited because of the low inductance in the grid and the limited current rating of the
PECs. An additional problem in case of voltage dips is that due to the low voltage, the
power that can be supplied to the grid without exceeding the rated converter current is
lower than at nominal voltage. An important difference with chapter 4 is, however, that
most voltage dips have a limited duration (generally < 1 s) and short-term overloading
of the converter might be possible. For most converters in the MW-range a 100%
overloading for a short time (~ 1s) could be acceptable (or the converter can be
designed for it). This subsection will investigate how much DG units can increase the
grid voltage in case of a dip. The basic theory on voltage control that is presented in
chapter 4 is used to derive the results in this section. All results are in per unit with the
74
short-circuit power Ssc = 100 MW and the supply voltage Vs = 10 kV as the base values.
The rated power of the DG unit is 0.1 p.u .in all cases.
Fig. 5.6a shows the voltage change that can be achieved with reactive power, as a
function of the overloading of the converter. Curves are shown for three different X/R
ratios. The active current of the converter is kept constant. (This means that the active
power is directly proportional to the voltage.) Fig. 5.6b shows for three different X/R
ratios how the results depend on the rated power of a 100% overrated DG unit. The
figures show that a considerable overrating and installed power are required to obtain a
significant voltage increase in voltage.
0.25
0.2
0.2
0.15
Voltage change [pu]
Voltage change [pu]
X/R= 3
X/R= 1
X / R = 1/3
0.1
0.05
0
0
X/R= 3
X/R= 1
X / R = 1/3
0.15
0.1
0.05
20
40
60
Overloading [%]
80
100
0
0
0.05
0.1
Sdg,nom [pu]
0.15
0.2
(a)
(b)
Fig. 5.6. Voltage increase that can be achieved during voltage dip by supplying reactive power; (a) as a
function of converter overloading (Sdg,nom / Ssc= 0.1); (b) as a function of rated DG unit power (overrating of
100%)
In networks with a low X/R ratio it might be better to increase the active power to
increase the voltage. The DG unit should be able to supply this power (fast enough).
This will not always be possible. DG units with rotating parts can use their kinetic
energy, such as will be proposed in chapter 6 for frequency control support. Fig. 5.7
shows the voltage change that be achieved by controlling active power. The reactive
power is zero. Fig. 5.7a shows the voltage change that can be achieved by overloading
the converter. Fig. 5.7b shows, for an overrating of 100%, how the voltage change that
can be achieved depends on the rated power of the DG unit.
Comparing the figures shows that in case of a low X/R ratio active power is slightly
more effective than reactive power. For the other two cases reactive power is more
effective. This is partly due to the fact that for a given active power and current, the
amount of reactive power that can be achieved by overloading the converter is higher
than the active power. In general the increase in voltage that can be achieved is limited
however.
5. Ride-through and grid support during faults
75
0.2
0.1
Voltage change [pu]
Voltage change [pu]
0.08
X/R= 3
X/R= 1
X / R = 1/3
X/R= 3
X/R= 1
X / R = 1/3
0.06
0.04
0.15
0.1
0.05
0.02
0
0
20
40
60
Overloading [%]
80
0
100
0
0.05
0.1
S
dg,nom
0.15
0.2
[pu]
(a)
(b)
Fig. 5.7. Voltage change that can be achieved during voltage dip by supplying active power; (a) as a function
of converter overloading (Sdg,nom / Ssc= 0.1, Qdg = 0); (b) as a function of rated DG unit power (overrating of
100%, Qdg = 0)
5.4.3 Variable inductance
The variable inductance proposed in chapter 4 can be very useful to compensate voltage
dips, as it can increase the inductance between the fault and the DG unit. Fig. 5.8a
shows the voltage change that can be achieved as a function of the inductance, for
different values of the reactive power that is supplied by the DG unit. The maximum
value of the variable inductance (20 mH) is ~6 p.u..
0.2
0.5
0.15
dg
[pu]
0.3
I
/I
= 1.25
dg,max dg,nom
I
/I
= 1.5
dg,max dg,nom
I
/I
= 1.75
dg,max dg,nom
Idg,max / Idg,nom = 2
0.1
Q
Voltage change [pu]
0.4
Q = 0.025
dg
Qdg = 0.05
Q = 0.075
dg
Qdg = 0.1
0.2
0.05
0.1
0
0
5
10
15
Variable Inductance [mH]
20
0
0
0.2
0.4
0.6
Vdg [pu]
0.8
1
(a)
(b)
Fig. 5.8. Voltage change that can be achieved with variable inductance; (a) Voltage change as function of
variable inductance and reactive power (Sdg,nom / Ssc= 0.1); (b) reactive power that is available as function of
voltage and overloading (Sdg,nom / Ssc= 0.1)
The reactive power that can be supplied by the DG unit will depend on the grid
voltage, the active power that is supplied by the converter and the maximum converter
current, as has been defined in (4.7). Fig. 5.8b shows how much reactive power Qdg can
be supplied as a function of the grid voltage, for different values of the converter
76
overloading and a constant active current. Comparing the graphs of Fig. 5.8 to those of
Fig. 5.6 and Fig. 5.7 shows that when a variable inductance is used, a much larger
voltage change can be achieved.
5.4.4 Example
The results in this section showed that the voltage increase that can be achieved by the
DG units is limited. Generally the DG units will not be capable to compensate a dip
completely. A certain reduction of the dip depth (for example a 10 or 20% higher
voltage) might be possible however. This subsection will give an example too show that
such a small reduction can be very useful already.
The circles in Fig. 5.9 show the voltage dips that in a certain period have been
measured at a 150 kV / 10 kV substation in the Netherlands. The solid line is a part of
the so-called ITI-curve, which is defined by the American Information Technology
Industry Council. When the voltage is above the line (in voltage level and duration),
computer and telecommunication appliances should stay connected to the grid. In this
case 40% of the dips are above the line. When a DG unit is connected that can achieve a
10% voltage increase, the ITI-curve can be lowered with 10% (the DG unit will increase
the voltage during the dips by 10%). This is shown by the dashed line in Fig. 5.9. In this
case the appliances should stay connected for 65% of all dips. When a DG unit is
connected that can achieve a 20% voltage increase even 85% of all dips is above the
line. This means that less appliances will disconnect.
1
0.6
V
dip
[pu]
0.8
0.4
0.2
0 −2
10
−1
10
Dip duration [s]
0
10
Fig. 5.9. Measured voltage dips and ITI voltage tolerance curves
The dips are assumed to be measured at the substation of the Testnet and the DG
unit is assumed to be connected to node 3 of this network. From the figures presented in
the previous subsections it can be seen how the DG unit can achieve a 10 or 20%
increase in voltage. Fig. 5.6a for example shows that in case of compensation with
reactive power an overrating of ~100% is needed (for Sdg,nom / Ssc= 0.1). When a variable
5. Ride-through and grid support during faults
77
inductor is used, a lower overrating is required. From Fig. 5.8, in combination with Fig.
5.6, it can be concluded that with a 25% overrating and a variable inductance of ~8 mH,
a 20% increase in voltage can be achieved (5% due to the grid impedance and 15% due
to the variable inductance).
5.5 DG unit ride-through during voltage dips
5.5.1 Introduction
The previous paragraph investigated how DG units can support the grid voltage during
dips. A prerequisite for grid support is that the DG units ride through the dip (stay
connected). In paragraph 6.2 the response of PECs to voltage dips was investigated.
When the current controllers of the converter are fast enough fault ride-through is no
problem. Only the response of a converter has been investigated however, and not the
response of the whole DG unit. This is done in this section.
A voltage dip manifests itself as a decrease in voltage amplitude at the converter
terminal. To keep the power supplied to the grid constant, the current should increase. It
will be limited by the current controller however, to avoid overloading of the converter.
This will thus limit the power that the DG unit can supply to the grid during a dip. For
some DG unit types the power limitation can be a problem. This section will present
protection measures and control strategies that can be used to avoid problems. Three
types of DG unit will be considered: wind turbines with a full-size converter, micro
turbines and fuel cells. One specific DG unit, a wind turbine with a doubly-fed
induction generator, will be discussed in section 6.6.
5.5.2 Variable speed wind turbine with full-size converter
Fault ride-through of variable speed wind turbines with a full-size converter has not
gained much attention till now. In [Sac 02] a thorough investigation of the operation and
control of the converter is given, but it does not investigate the impact on the wind
turbine itself. The same holds for [Mul 05b] which presents a non-linear dc-link controller
that enables fault ride-through. The issue is discussed in more papers, but all focus on
the converter control and do not investigate how the wind turbine operation is affected.
Control principle - First the basic principles of a control strategy to enable fault ridethrough are described. Variable speed wind turbines with a full-size converter generally
use (permanent magnet) synchronous generators. The generator is connected to the grid
by a back-to-back converter. A dc-link separates the two converters and therefore they
can be controlled independently. During normal operation the generator-side converter
78
controls the rotational speed of the wind turbine to capture as much power as possible
from the wind. A power setpoint Pref is generated based on the measured wind speed.
The power from the rectifier is fed to the dc-link. The grid-side converter supplies the
dc-link power to the grid. The generator-side converter determines the overall power of
the system and the inverter has to supply this power to the grid. Fig. 5.10a shows the
control structure.
A fault in the network will result in a drop of the rms value of the voltage at the
converter terminals and, due to the current limitation, in a reduction of the power that
the inverter can supply to the grid. As a result the dc-link voltage will increase, as long
as the power from the turbine is not decreased. To avoid a too high dc-link voltage, the
grid-side converter should become the master, and determines the overall power. Its
reference power is determined by the maximum power that can be supplied to the grid.
The rectifier limits its power to avoid a too high dc-link voltage. This control structure
is shown in Fig. 5.10b. As the power that the rectifier supplies to the dc-link will
reduce, the speed of the generator will increase. Decreasing the mechanical power input
by pitching the blades might be necessary to avoid overspeeding of the turbine. Pitching
is a rather slow process however and thus the rotational speed will thus continue to
increase for some time.
Generator
PM
Back-to-back converter
Rectifier Cdc
Pref,rect
Control
Inverter
Pref,inv
Control
Generator
PM
Back-to-back converter
Rectifier
Pref,rect
Control
Cdc Inverter
Pref,inv
Control
(a)
(b)
Fig. 5.10. Control of permanent magnet synchronous machine; (a) normal situation; (b) current limitation
during voltage dip
Implementation - The control principles described above can be implemented in
different ways. An important issue is to decide when the operation of the two converters
has to be changed. One possibility is to monitor the grid voltage. When it drops below a
predefined threshold, the control of the converters is changed: the rectifier starts
controlling the dc-link while the inverter determines the maximum power that is
supplied to the grid. Another possibility is to use the dc-link voltage as an indicator.
When the currents in the grid converter are limited, it will not be able to supply all dclink power to the grid during a dip, resulting in an increase in dc-link voltage. When the
voltage exceeds a predefined level the rectifier has to reduce its power and can start
controlling the dc-link voltage.
5. Ride-through and grid support during faults
79
Analysis - The amount of energy stored in the dc-link is small. This requires fast
control, as the voltage of the dc-link will change very fast when there is a mismatch
between rectifier and inverter power. The dc-link voltage is given by
C dc vdc
dvdc
= Prect − Pinv
dt
(5.1)
with Prect and Pinv the rectifier power supplied to the dc-link and the inverter power
absorbed from the dc-link respectively. When a voltage dip occurs, Pinv will decrease, as
the inverter current will be limited by the current controller. How far the voltage dc-link
voltage increases depends on how fast Prect is decreased. When the converter operates at
nominal power, the per unit drop in power can be assumed to be equal to the per unit
drop in voltage. Defining Δvdc,max as the maximum change in dc-link voltage that is
allowed, the response time in which the rectifier power Prect should be reduced is:
Δt rt =
C dc v dc Δv dc ,max
rdip Pnom
(5.2)
with rdip the dip ratio (rdip = 1 - Vg/Vg,nom) and Δtrt the delay caused by the complete ridethrough control. The minimum value of Cdc is a function of the rated power of the
converter Pnom, the switching frequency fs, and the maximum allowable voltage ripple
due to the switching Δvdc,r. It can be approximated by:
C dc,min =
Pnom
2 f s Δv dc,r v dc
(5.3)
By combining the two equations the maximum allowable delay can be determined:
Δt rt ,max =
Δvdc ,max
2 f s rdip Δvdc,r
(5.4)
Under some assumptions an approximate value for Δtrt,max can be obtained. Assuming
Δvdc,max to be 4 times larger than Δvdc,r, and for rdip= 1, Δtrt,max should be smaller than 2
switching periods. As the switching frequency of MW-class converters is not very high
(a few kHz at maximum) this maximum delay should be realisable.
The ride-through control will result in an increase of rotational speed, as the
electrical torque will decrease, because of the reduction in electrical power. How far the
rotational speed will increase depends on the inertia of the turbine and the pitch speed.
The relation between power, inertia and rotational speed ωwt, is given by:
Jω wt
dω wt
= Pa − Pe
dt
(5.5)
80
with Pa and Pe the aerodynamic and electrical power respectively. Combining this
equation with that for the inertia constant H, given in (5.2), and assuming ΔPa = 0 and
the nominal active power of the turbine equal to the nominal apparent power, gives
1 dω wt rdip ΔPa (θ )
=
−
ω wt dt
2 H 2 HS nom
(5.6)
where ΔPa is the reduction in aerodynamic power due to the pitching of the blades, θ the
pitch angle, and Snom the nominal power of the wind turbine. The inertia constant of
wind turbines is in the range 2 – 5 [Knu 05]. This implies that in case of a 85% dip, and
assuming ΔPa to be zero, the change in rotational speed is between 9% and 21% per
second. The pitch speed of wind turbines is normally less than 5° per second, but can
increase to 10° during emergencies [Knu 05]. The reduction in power that is achieved for
a certain pitch angle differs per turbine, but can rise to a 50% reduction for a 10° pitch
angle. The increase in speed for the 85% dip mentioned before becomes than 4% to 9%
for a one second dip.
Case study - A case study is done to demonstrate the proposed solution. The wind
turbine is connected to node 4 of the Testnet (see appendix A.1). Data of a 1.5 MW
direct-drive wind turbine with a permanent magnet generator is used to model the
turbine. A description of the wind turbine model can be found in appendix C and [Pie 04].
The dc-link voltage of the converter is continuously measured. When it becomes larger
than 1.05 p.u., the rectifier limits its power and starts controlling the dc-link voltage,
while the inverter determines the maximum power flow to the grid. The controller used
by the inverter is similar to the dc-link voltage controller used by the inverter during
normal operation. It is described in appendix B. When the rotational speed of the wind
turbines exceeds 1 p.u. the pitch angle is reduced to avoid overspeeding of the turbine.
The wind turbine operates at almost nominal power. A 50% - 0.5 s voltage dip is
applied to the voltage source of the Thévenin equivalent of the grid. This results in a
voltage dip at the wind turbine terminals, as shown in Fig. 5.11a. To avoid overloading
of the converter, the converter currents are limited, as shown in Fig. 5.11b. As a result
the power that the converter supplies to the grid decreases (Fig. 5.11c), resulting in an
increase in the dc-link voltage (Fig. 5.11d). The grid converter now controls the power
(with its setpoint determined by the maximum current), while the generator converter
controls the dc-link voltage. It reduces the stator power to avoid a too high dc-link
voltage. The controller causes some oscillations before a constant value is reached, as
can be seen from the dc-link voltage (Fig. 5.11d) and stator power (Fig. 5.11e). The
reduction in stator power results in an increase in rotational speed (Fig. 5.11f). The
increase in speed is very small, due to the large inertia and the short dip duration.
5. Ride-through and grid support during faults
81
Increasing the pitch angle to avoid overspeeding is not necessary. When the dip ends the
generator converter becomes again the master and normal operation is resumed.
1.5
1.1
Converter current [pu]
Converter voltage [pu]
1.05
1
0.5
1
0.95
0.9
0.85
0
0
0.5
1
1.5
time [s]
2
2.5
0.8
0
3
0.5
1
(a)
1.5
time [s]
2
2.5
3
2
2.5
3
2
2.5
3
(b)
1.5
dc−link voltage [pu]
Converter power [pu]
1.15
1
0.5
1.1
1.05
1
0.95
0
0
0.5
1
1.5
time [s]
2
2.5
0.9
0
3
0.5
1
(c)
(d)
1.1
Rotational speed [pu]
Stator power [pu]
1.5
1
0.5
0
0
1.5
time [s]
0.5
1
1.5
time [s]
2
2.5
3
1.05
1
0.95
0.9
0
0.5
1
1.5
time [s]
(e)
(f)
Fig. 5.11. Response of wind turbine with permanent magnet generator to 50% - 0.5 s voltage dip at t = 1 s: (a)
grid voltage; (b) grid converter current; (c) grid converter power; (d) dc-link voltage; (e) stator power; (f)
rotational speed of turbine
5.5.3 Micro turbine and fuel cell
The electrical part of a micro turbine is similar to that of the variable speed wind turbine
described in the previous subsection: a (permanent magnet) synchronous generator and
82
a back-to-back converter. Fault ride-through can therefore be achieved in the same way.
There are some differences however. The first is that the switching frequency of a micro
turbine converter can be higher as the rated power of micro turbines is normally much
smaller than that of wind turbines. This can imply a smaller response time Δtrt as can be
seen from (5.4). The second difference is that the gas turbines that are used in the micro
turbine generally are fast controllable. This implies that no large increase in rotational
speed will occur.
A fuel cell system is different from wind turbines and micro turbines. As a fuel cell
is a dc-source it does not need a rectifier. Instead of that the system has mostly a dc-dc
converter that connects the fuel cell to the dc-link. The main problem during a voltage
dip is the same however. Due to the current limitation the inverter will supply less
power to the grid, and the dc-link voltage will increase. The dc-dc converter can limit
the current from the fuel cell to avoid a too high dc-link voltage. At the same time the
fuel flow to the fuel cell has to be reduced.
5.6 Doubly-Fed Induction Generator
5.6.1 Introduction
The previous paragraph analysed the fault ride-through capability of DG units that are
connected to the grid with a converter. This section will investigate the behaviour of a
wind turbine with a doubly-fed induction generator (DFIG). Most modern variable
speed wind turbines are based on this type of generator. Instead of a converter between
the stator and the grid, it has a converter between the rotor windings and the grid, as
shown in Fig. 2.5b. This has a major impact on the operation during grid faults. The
voltage drop at the terminals will result in large, oscillatory currents in the stator
windings of the DFIG. Because of the magnetic coupling between stator and rotor these
currents will also flow in the rotor circuit and through the PEC. The high currents can
cause thermal breakdown of the converter.
A possible solution to avoid destruction of the converter is to short-circuit the rotor
windings of the generator with so-called crowbars during a fault, and disconnect the
converter. Resuming normal operation without transients when the fault is cleared is not
properly feasible however. First the converter has to be re-synchronised with the grid
and the rotor. Most turbines using doubly-fed induction generators therefore are
automatically disconnected from the grid nowadays, when a fault occurs [Slo 03a].
Worldwide there is an ambition to install more wind power. The interaction with the
grid becomes increasingly important then [Slo 02]. It is worldwide recognized that to
enable large-scale application of wind energy without compromising system stability,
5. Ride-through and grid support during faults
83
the turbines should stay connected to the grid in case of a failure. They should – similar
to conventional power plants – supply active and reactive power for frequency and
voltage support immediately after the fault has been cleared, which is normally within a
fraction of a second. For wind turbines connected to higher voltage levels most grid
operators require fault ride-through capability already. An example of such a
requirement was shown in Fig. 5.5.
A number of papers have been published that discuss the protection of DFIGs during
grid disturbances. Some papers assume operation of a crowbar followed by
disconnection of the wind turbine [Per 04]. Other papers propose the use of a crowbar
and disabling of the converter, but without disconnecting the wind turbine from the grid
[Sun 04b]. The generator operates then as an induction machine with a high rotor
resistance. The transition back to normal operation will take time in this case and grid
support during the fault is not possible. Other papers assume overrating of the converter
[Pet 04], [Ana 05], to cope with the transient currents and voltages.
Some papers propose fault ride-through by using a kind of an ‘active crowbar’. With
this protection the generator can stay connected to the grid and it is not necessary to
disconnect the converter. The most extensive and detailed publication on this type of
protection is [Mor 05]. With the control proposed in this paper it is possible to keep the
wind turbine connected to the network and to resume normal operation immediately
after clearance of the fault. When the dip lasts longer than a few hundred milliseconds,
the wind turbine can even support the grid during the dip. Most other papers give little
or no information on the way in which the protection and the control is implemented
[Hud 03], [Nii 04], [Dit 05], [Nii 05]. They also give only limited information on the behaviour
of the rotor voltage and current during disturbances [Eka 03], [Dit 05], while these signals
are very important. Rotor currents or voltages that are too high might destruct the
converter in the rotor circuit.
This section proposes a method that makes it possible for wind turbines using
DFIGs to stay connected to the grid during grid faults and support the grid. First the
response of a DFIG to a voltage dip will be analysed. Then the protection technique is
described. The section ends with a case study that shows the operation of the protection.
5.6.2 Fault response and protection of doubly-fed induction generator
This subsection will analyse the response of a DFIG to a dip in the voltage at its
terminals. Appendix D gives a mathematical analysis and explanation of the fault
response of an induction machine. The analysis and explanation of the voltage dip
behaviour of the DFIG will be given with reference to this appendix. The response of a
DFIG is to a large extent the same as that of an induction machine. The differences will
be high-lighted in this and the following subsection.
84
The stator voltage equation of the induction machine is given in (D.1). In a
stationary reference frame it is expressed as:
v s = Rs i s +
dψ s
dt
(5.7)
In normal operation the space-vectors rotate at a synchronous speed with respect to the
reference frame. Ignoring the stator resistance, the derivative of the stator flux is
directly proportional to the grid voltage. When the voltage drops to zero (in case of a
fault at the generator terminals) the stator flux space-vector will stop rotating. This will
produce a dc-component in the stator flux. The dc-component in the rotor flux of the
machine is fixed to the rotor and will continue rotating, adding an alternating
component to the dc-component of the stator flux. The maximum value that the currents
reach depends mainly on the dip depth and the stator and rotor leakage inductance. How
fast the dc-component will decay is mainly determined by the transient time constants
of the stator and rotor, given by (D.14) and (D.15).
The voltage dip will cause large (oscillating) currents in the rotor circuit of the DFIG
to which the PEC is connected. A high rotor voltage will be needed to control the rotor
current. When this required voltage exceeds the maximum voltage of the converter, it is
not possible any longer to control the current as desired. This implies that a voltage dip
can cause high induced voltages or currents in the rotor circuit that can destroy the PEC.
In order to avoid breakdown of the converter switches there should be a by-pass for
the rotor currents in case of a voltage dip. This can be achieved by connecting a set of
resistors to the rotor winding via bi-directional thyristors, as shown in Fig. 5.12. When
the rotor currents become too high the thyristors are fired and the high currents do not
flow through the converter but into the by-pass resistors. Meanwhile it is not necessary
to disconnect the converter from the rotor or the grid. Because generator and converter
stay connected, the synchronism of operation remains established during the fault.
When the fault in the grid is cleared, or the dc offset in voltage and current has
decayed far enough, the resistors can be disconnected by inhibiting the gating signals of
the thyristors and the generator can resume normal operation. A control strategy has
been developed that takes care of the transition back to normal operation. Without
special control action large transients would occur. During the period that the resistors
are connected to the rotor circuit the controller signal should be limited in a small band
around the values they had at the moment that the fault occurred. The controllers will
try to control the currents, the power, the rotational speed and so on to the reference
values. This is not possible however as long as the by-pass resistors are connected to the
rotor circuit. When the signals are not limited large overshoot in the signals will occur.
5. Ride-through and grid support during faults
85
Generator
gear
box
Grid
ASM
Converter
Thyristors
Control
Control
By-pass
resistors
Fig. 5.12. DFIG by-pass resistors in the rotor circuit
5.6.3 Short-circuit current and by-pass resistor value
This subsection will derive an (approximate) equation for the stator and rotor currents of
the DFIG during a fault. The fault current supplied to the grid is important to know for
grid operators. When the value is known it is also possible to determine a good value for
the by-pass resistors. To derive an (approximate) equation for the short-circuit current
supplied by the DFIG the equations derived for the induction machine will be used (see
appendix D). Two important assumptions that are made during the analysis of the
induction machine are not valid for a DFIG. The first is that when the by-pass resistors
are connected to the rotor in case of a fault, the resistance no longer can be neglected.
The second is that the slip of a DFIG is not always close to zero, as is the case for an
induction machine. The consequences of these differences for the short-circuit
behaviour of the DFIG will be described in this section. A worst-case analysis will be
done, which assumes that a short-circuit occurs at the stator of the machine and that the
turbine operates at full power.
The maximum stator current of an induction machine in case of a short-circuit at the
stator terminals is given by (D.25):
is ,max
T
⎡ T
− '⎤
2Vs ⎢ − 2Ts'
2Tr ⎥
e
=
+ (1 − σ )e
⎥
X s' ⎢
⎣
⎦
(5.8)
with Xs’ the transient stator reactance, σ the leakage factor, T the period of the grid
frequency, and Ts’ and Tr’ the transient time constants of the stator and rotor
respectively. All parameters are defined in appendix D. The equation was obtained in
two steps. First the term outside the rectangular brackets was determined. It represents
the initial value of the current prior to the fault. In the next step the two terms inside the
86
brackets were determined. They represent the damping of the dc-components in the
stator and rotor flux respectively.
The initial value of the current is determined under the assumption that the stator
and rotor resistance can be neglected. When the by-pass resistors are connected in cause
of a fault this assumption is no longer valid. This implies that (D.16) becomes:
V s e jω s t
jX s + Rbp
I s e jω s t =
(5.9)
and that the transient time constant of the rotor becomes:
Tr' =
L'r
'
Rr' + Rbp
(5.10)
'
the resistance of the by-pass resistors, reduced on the stator side.
with Rbp
The two exponential functions inside the brackets in (5.8) are based on the
assumption that the rotor and stator flux are 180° out of phase after half a period,
implying that the current reaches its maximum value at at t = T/2. This assumption is
approximately valid for an induction machine where the slip is small and where the
stator and rotor flux are approximately in phase with each other, at the moment that the
fault occurs. A doubly-fed induction generator can operate at a much larger slip
however. This implies that at the moment of the fault the two flux vectors are not in
phase with each other. When the DFIG is in over-synchronous mode the rotor flux will
lead the stator flux and it will take less than half a period before the two fluxes are 180°
out of phase (which gives the maximum current, see appendix D). When the DFIG is in
under-synchronous mode, the opposite holds and it will take more than half a period.
When the voltage at the stator terminals drops to zero, the stator and rotor flux
vector stop rotating, as explained in appendix D. In reality they will rotate slowly,
depending on the stator and rotor resistance. The larger the resistance the faster they
rotate. For an induction machine this rotation can be neglected because of the small
resistance. For a DFIG with by-pass resistors the rotation is no longer negligible. This is
another reason why it can take less than half a period before the first peak in the current
is reached.
Taking into account these differences between an induction machine and a doublyfed induction generator, (5.8) becomes:
i s ,max =
2Vs
2
'
X s' + Rbp
2
Δt
⎡ − Δt'
− ⎤
⎢e Ts + (1 − σ )e Tr' ⎥
⎢
⎥
⎣
⎦
(5.11)
5. Ride-through and grid support during faults
87
where Δt gives the time after which the current reaches its first peak. It is dependent on
the slip of the machine and the value of the by-pass resistors. For small by-pass resistor
'
values, ( Rbp
≤ X s' ), this equation showed to give a good approximation of the
maximum current. For large resistance values it gives a too low value.
A larger by-pass resistance will result in a smaller Tr’. At the same moment Δt
decreases. As a result the term inside the brackets in (5.11) stays approximately
constant. As a rough approximation the maximum stator current is then given as:
i s ,max ≈
2.4Vs
2
'
X s' + Rbp
2
(5.12)
The last part of this subsection describes how a good value for the by-pass resistance
can be determined. On one hand the resistance should be high, to limit the short-circuit
current. On the other hand it should be low to avoid a too high voltage in the rotor
circuit. A too high voltage can result in breakdown of the isolation material of the rotor
and the converter. It is further possible that when the voltage becomes higher than the
dc-link voltage, large currents will flow through the anti-parallel diodes of the
converter, charging the dc-link to an unacceptable high voltage. The thermal time
constant of the rotor will be high enough to handle the short-circuit currents for a short
period and the by-pass resistors should be designed for it.
An approximation of the maximum stator current is given by (5.12). As all
parameters are transferred to the stator side, the maximum rotor current (reduced on the
stator side) will have approximately the same value. The voltage across the by-pass
resistors, and thus across the rotor and converter is:
' '
2Vr ≈ Rbp
ir ,max
(5.13)
Combining this with (5.12) the maximum value of the by-pass resistors can be
determined:
'
Rbp
<
2Vr ,max X s'
5.8Vs2 − 2Vr2,max
(5.14)
with Vr,max the maximum allowable rotor voltage. Note that it only is an approximation,
as it is based on a number of assumptions and approximations.
The minimum value is determined by the maximum current that is allowed in the
rotor circuit of the induction generator or by the maximum value of stator short-circuit
current that is allowed.
88
5.6.4 Simulation results
In order to show the effectiveness of the protection scheme, some simulation results will
be presented. A model has been used in which the DFIG is connected to node 4 of the
Testnet. Data of a 2.75 MW wind turbine with doubly-fed induction generator has been
used for the simulations. The wind turbine model and the parameters are given in
appendix B. The by-pass thyristors are activated when the rotor current exceeds 1.1 p.u.
All values are referred to the stator with the nominal generator power and voltage as the
base values. The maximum allowable rotor voltage is 0.35 p.u. The transient stator
inductance is 0.2 p.u. The maximum value of the by-pass resistors is obtained from
(5.14) as 0.06 p.u. A value of 0.05 p.u. is used.
In the first place the behaviour of the DFIG during a voltage dip of 85% (15%
remaining voltage) and 200 ms is simulated. The stator voltage and current are shown in
Fig. 5.13a and b and the rotor voltage and current are shown in Fig. 5.13c and d,
respectively. A large peak in the stator and rotor current can be noted. The rotor current
is not flowing through the converter however, but in the by-pass resistors. The power
that is consumed by the resistors is shown in Fig. 5.13e. The rotor voltage oscillates to
~0.3 p.u. This is slightly below the maximum rotor voltage of 0.35 p.u. Due to the drop
in stator power, the wind turbine will accelerate. Because of the large inertia of the wind
turbine rotor the increase in rotational speed is limited however, as can be seen from
Fig. 5.13f. When the dip lasts longer eventually the pitch controller can be used to
reduce the aerodynamic power and to limit the increase in rotational speed.
After ~50 ms the by-pass resistors are disconnected and the DFIG can resume
normal operation (at a lower voltage). The clearance of the voltage dip results again in
high oscillating currents and the by-pass resistors will be turned on again to protect the
converter. After the current has decayed far enough the resistors are disconnected again
and the turbine can resume normal operation.
By appropriate control the wind turbine can supply reactive power during the dip, as
is demanded by some grid connection requirements for wind turbines (see Fig. 5.5).
When the by-pass resistors are de-activated the turbine can resume normal operation
and supply reactive power. This will be shown in an example. The same network and
wind turbine as in the previous example are used. Now a 50% - 1 s dip is applied. The
stator voltage is shown in Fig. 5.14a and the active and reactive power supplied by the
DFIG are shown in Fig. 5.14b and c respectively. It can be seen that ~0.25 p.u. reactive
power is supplied, while the generator is still supplying ~0.5 p.u. active power. When
more reactive power has to be supplied, the active power should be reduced, or a higher
current should be allowed. Fig. 5.14d shows the rotor current. During the dip it is 1 p.u.
The rotor voltage is shown in Fig. 5.14e and the rotational speed is shown in Fig. 5.14f.
5. Ride-through and grid support during faults
89
Large reactive power peaks can be noted at the occurrence and clearance of the fault.
They are cause by the (de-)magnetizing of the machine. The large amount of reactive
power that is absorbed immediately after fault clearance may cause voltage stability
problems and in a further study it should be investigated how it can be limited.
1.5
4
Stator Current [pu]
Stator Voltage [pu]
3.5
1
0.5
3
2.5
2
1.5
1
0.5
0
0.3
0.4
0.5
0.6
time [s]
0.7
0
0.3
0.8
0.4
0.5
(a)
0.6
time [s]
0.7
0.8
0.7
0.8
0.7
0.8
(b)
0.5
4
3.5
0.4
Rotor Current [pu]
Rotor Voltage [pu]
3
0.3
0.2
2.5
2
1.5
1
0.1
0.5
0
0.3
0.4
0.5
0.6
time [s]
0.7
0
0.3
0.8
0.4
0.5
(c)
0.6
time [s]
(d)
Rotational speed [pu]
By−pass Power [pu]
1.5
1
0.5
0
0.3
0.4
0.5
0.6
time [s]
0.7
0.8
1.15
1.1
1.05
0.3
0.4
0.5
0.6
time [s]
(e)
(f)
Fig. 5.13. Voltage dip of 85%, 0.2 s applied to DFIG with protection: (a) stator voltage; (b) stator current; (c)
rotor voltage; (d) rotor current; (e) power consumed in by-pass resistors; (f) rotational speed of generator
90
1.5
2.5
Active Power [pu]
Stator Voltage [pu]
2
1
0.5
1.5
1
0.5
0
0
0.5
1
time [s]
1.5
0
0
2
0.5
(a)
1
time [s]
1.5
2
1.5
2
1.5
2
(b)
2.5
1.5
1
Rotor Current [pu]
Reactive Power [pu]
2
0.5
0
−0.5
−1
1.5
1
0.5
−1.5
−2
0
0.5
1
time [s]
1.5
0
0
2
0.5
(c)
1
time [s]
(d)
0.25
Rotational speed [pu]
Rotor Voltage [pu]
0.2
0.15
0.1
1.15
1.1
0.05
0
0
0.5
1
time [s]
1.5
2
1.05
0
0.5
1
time [s]
(e)
(f)
Fig. 5.14. Voltage dip of 50%, 1 s applied to DFIG with protection: (a) stator voltage; (b) DFIG active power;
(c) DFIG reactive power; (d) rotor current; (e) rotor voltage; (f) rotational speed
5.7 Conclusion
Most distribution network operators require the disconnection of DG units when faults
occur in the network. One reason for this requirement is that they fear that DG units
disturb the classical protection schemes that are applied. It has been shown in this
5. Ride-through and grid support during faults
91
chapter that disturbance of protection not necessarily occurs when power electronic
interfaced DG units are controlled properly.
When DG units stay connected during faults, they can support the grid during a
voltage dip. For some larger DG units directly connected to the transmission network
this is often required already [E.On 03]. Voltage dips occur for a short period only.
Overloading of a converter will mostly be possible for this short period. In combination
with a variable inductance a significant reduction in dip depth can be achieved. It should
be noted however, that in some cases the variable inductance can reduce the shortcircuit current that flows in the network, causing blinding of protection. Before
implementation of a variable inductance this issue should be considered.
In the last two sections of this chapter it has been shown that there are generally no
problems to keep DG units connected to the grid during voltage dips. In case of a wind
turbine with a doubly-fed induction generator some special measures have to be taken.
The key of the technique is to provide a by-pass for the high currents in the rotor circuit
with a set of resistors, without disconnecting the converter from the rotor or the grid.
The wind turbine can resume normal operation when the voltage and current oscillations
have decayed enough (generally within a few hundred milliseconds). In this way the
turbine can supply reactive power to the grid during a voltage dip.
The short-circuits and the proposed protection techniques can result in large torque
fluctuations in the gearbox of variable speed wind turbines. This important issue falls
outside the scope of this thesis, but requires further attention.
92
Chapter 6
Frequency-control contribution of DG
units
6.1 Introduction
In electrical power systems there must always be an equilibrium between the power that
is generated and the power that is consumed, as there is hardly energy storage. An
imbalance manifests itself by changes in the frequency, which arise from a change in
kinetic energy of the rotating masses. For satisfactory operation of electrical power
systems the frequency should remain as constant as possible. There are continuously
small variations in the power balance due to variations in generation and load. Due to
the large inertia of the synchronous generators in the grid, the frequency fluctuations are
small. Larger variations are mostly due to disturbances such as short-circuits, which can
result in opening of circuit breakers and loss of generation or load. Frequency changes
are observed by all power stations and they respond by changing the power of their
prime mover.
At this moment DG units do not contribute to frequency control and most DG units
do not have inertia. An increasing penetration level of DG can therefore result in larger
frequency deviations. This issue did not receive much attention so far. Some
publications mention that most DG units are connected to the grid by power electronic
converters (PECs), which have no inertia [Kna 04], [Rez 05]. Some other papers
determined the inertia contribution of wind turbines [Eka 04], [Lal 04], [Lal 05], [Mul 05a].
The goal of this chapter is to investigate how and to what extent (combinations of
different) DG units can contribute to frequency control. The chapter begins with a
review of the response of a conventional power system to load imbalances and
frequency deviations and then continues with a description of the conventional
frequency control. Section 6.3 briefly describes the effect that different types of DG unit
have on frequency control. In section 6.4 a method is derived to determine upper and
lower boundaries for the penetration level of different types of DG unit. When DG units
have to contribute to frequency control, they should be able to increase their output
power. For generators based on renewable energy sources this is generally not possible,
94
as they operate at the maximum available power. Section 6.5 investigates if and how
(fast) DG units can increase their output power. The proposed solutions are
demonstrated with a case study simulation in section 6.6.
6.2 Classical power-frequency control
6.2.1 Introduction
The response of the power system and the synchronous generators to a change in power
balance, together with the resulting frequency deviations can be divided into three
phases.
In the first phase, when controllers have not yet been activated, the rotor of the
synchronous generators releases or absorbs kinetic energy; as a result, the frequency
changes. The response is mainly determined by the equation-of-movement of the system
and is called inertial response here, as the inertia dampens the frequency deviations.
When the frequency deviation exceeds a certain limit, controllers are activated to
change the power input to the prime movers. This is the second phase, the primary
frequency control.
After restoration of the power balance there is still a steady-state frequency
deviation. In the third phase, secondary frequency control, the frequency is brought
back to its nominal value.
6.2.2 Inertial response
The power generated in a power system preferably matches the load power at all times.
Initially, in order to avoid excessive control action, there is no control response to small
imbalances. Therefore imbalance between generation and load will result in a change in
frequency. The initial rate of change is determined by the system dynamics [Sac 03]:
⎛1
⎞
d ⎜ Jω e2 ⎟
(6.1)
2
⎝
⎠ =P −P
g
l
dt
with Pg being the power that is generated, Pl the power that is demanded by the loads, J
the total inertia of the system and ωe the grid frequency. The left-hand side of (6.1) is
the derivative of the kinetic energy stored in the rotational mass of the generator. As a
measure for this kinetic energy, in relation to the power rating, the so-called inertia
constant H is often used, which is defined as:
H=
Jω e2
2S
(6.2)
6. Frequency-control contribution of DG units
95
with S being the nominal apparent power of the system. The inertia constant has the
dimension time and gives an indication of the time that the system can provide nominal
power by using only the energy stored in its rotating masses. Typical inertia constants
for the generators of large power plants fall in the range of 2 – 9 s, depending on both
the type of power plant in which they are used and their nominal rotational speed [Gra
94]. A minimal value of H is necessary to avoid too large fluctuations in frequency.
6.2.3 Primary control
An imbalance between generated and consumed power will result in a change in the
frequency. When this frequency deviation becomes too large, controllers are activated.
These controllers adapt the amount of prime power in order to restore the power
balance. Actually they control the speed of the turbine. The primary-control
contribution of the generators is based on their so-called droop constant, which gives
the additional power that is be supplied as a function of the frequency deviation:
ΔPG = − K pfc Δf
(6.3)
The percentage of change in power as a function of the percentage of change in
frequency for a generator, or a whole network, is often given by the so-called droop:
− Δf / f nom
D pfc =
⋅ 100%
(6.4)
ΔPG / PG ,nom
with fnom the nominal frequency, ΔPG the change in the output power of the generator
and PG,nom the nominal power of the generator. From this equation the droop constant
Kpfc can be defined as:
100 ⋅ PG ,nom
K pfc =
(6.5)
D pfc ⋅ f nom
Fig. 6.1 shows an example of a droop characteristic.
PG
PG,nom
ΔPG
1/Dpf
Δf
fnom
f
Fig. 6.1. Droop characteristic: Input power from prime mover, PG, as a function of frequency
Two important parameters are the primary control reserve and the deployment time
of the generator. The primary control reserve is, for a certain operational point, the
maximum additional power that can be supplied by the generator. It is the difference
96
between the rated power and the power that is supplied at a given moment. The
deployment time is the time that it takes to increase or decrease the output power to the
new value. The values for different generators should be in the same range to minimise
dynamic interaction [UCT 04]. A typical frequency response, such as might occur when a
large generator is disconnected or when a large load is connected to the grid, is shown
in Fig. 6.2.
f
fdyn,max
Δf
t
Fig. 6.2. Typical frequency response in a network in which a large generator is disconnected or a large load is
connected
The maximum dynamic frequency deviation fdyn,max mainly depends on [UCT 04]:
• the amplitude and development over time of the power disturbance affecting the
balance between power output and consumption;
• the kinetic energy of the rotating machines in the system;
• the number of generators subject to primary control, the primary control reserve
and its distribution between these generators;
• the dynamic characteristics of the machines (including controllers);
• the dynamic characteristics and particularly the self-regulating effect of loads.
The quasi-steady-state frequency deviation Δf depends on the amplitude of the
disturbance and the network power frequency characteristic, which is mainly influenced
by [UCT 04]:
• the droop of all generators with primary control in a system;
• the sensitivity of consumption to variations in system frequency.
6.2.4 Secondary control
After the primary control has re-established the frequency, it will generally be different
from the reference value. The goal of the secondary control is to bring the frequency
back to the reference value (normally 50 Hz). This is done by increasing or decreasing
the droop characteristic as shown in Fig. 6.3. As a result of the imbalance the frequency
decreases from point 1 to point 2 on the curve and the output power increases
correspondingly. In point 2 the system is stable again, but at another frequency. By
increasing the entire droop characteristic the frequency can be brought back to its
6. Frequency-control contribution of DG units
97
nominal value, as is shown by the movement from point 2 to point 3. Secondary
frequency control is not considered further.
PG
3
PG,nom
ΔPG 2
1
Δf
fnom
f
Fig. 6.3. Droop characteristic
6.3 Effect of DG units on frequency response
The response to frequency fluctuations of most DG units is fundamentally different
from that of conventional generators. There are two main reasons for this difference. In
the first place most types of DG unit have a PEC and therefore do not have an inherent
inertial response. Secondly several types of DG unit are driven by an uncontrollable
source and therefore they can only partly participate in primary frequency control (they
can not increase but only decrease their power on demand).
Considering inertial response and primary frequency control separately, several
groups of DG units can be distinguished. With respect to inertial response the ability to
increase the power fast is the most important. In response to a decreasing frequency
there are DG units that:
I. can increase their output power inherently by releasing kinetic energy (e.g.
constant speed wind turbines).
II. can increase their output power fast (e.g. micro turbines and variable speed wind
turbines (by using their kinetic energy)).
III. can increase their output power slowly (e.g. fuel cells) or not (e.g. solar cells).
With respect to primary frequency control there are DG units that:
IV. are driven by a controllable power source (e.g. fuel cells and micro turbines).
V. are driven by an uncontrollable power source (e.g. solar cells and wind turbines).
In reality the distinction between the different groups will not be as strict as presented
here. Often the changes are gradual. Photovoltaic systems for example often have a
small amount of energy stored in their dc-link capacitor, which they can use to increase
their output power for a short period. There are also DG units that belong in different
groups, such as a micro turbine, which has a rotating machine (group II) and is driven
by a controllable source (group IV).
98
DG units of group I have an inherent inertial response. The extent of their
contribution to the inertia constant depends on the type and size of the machine. The
DG units of group II have no inherent inertial response, but they have kinetic energy in
their rotating mass, which they can use to increase their output power quickly. By
implementing an additional control loop, it is possible to make this ‘hidden inertia’
available to the grid, as will be explained later. No contribution to inertial response is
possible with the DG units in group III unless they are driven by controllable sources
whose power can be changed rapidly.
Participation in primary frequency control is possible for the DG units in group IV
as long as they have a primary control reserve margin (i.e., when they are not working
at full power yet). At first sight DG units of group V are not able to participate in
primary frequency control as they cannot control their prime energy source; however, it
will be shown later that in some cases some of them can have a small contribution.
The introduction of DG units results in a mix of different generator types (conventional
and DG). The response of this mix to load changes is different from the conventional
system. For example, it can be expected that the primary control reserve of the system
will decrease, resulting in larger frequency deviations during disturbances. The
reduction of the inertia will result in larger and faster frequency fluctuations.
In this chapter a method to analyse the influence of DG units on the inertial response
and the primary frequency control of the grid is developed. This method can also be
used to synthesise a group with different combinations of DG units such that the
mentioned control still works.
The method to determine and synthesise the response on system level is based on a
summation of the individual responses. At system level the inertial response to a change
in load change is determined primarily by the total (emulated) inertia of the system
including DG units. The primary frequency control response to a load change is at
system level primarily determined by the total primary control reserve that is available
from both the conventional generators and the DG units.
In order to be able to determine the above-mentioned responses it is necessary to
know for each type of DG unit:
• the behaviour that is inherent to its physical (construction) properties.
• its ability to increase its stationary power and the associated dynamics.
• the size of its (emulated) inertia.
Some DG units that do not have inertia or whose inertia is decoupled from the grid can
be given an artificial inertia. Within certain limits this inertia can be chosen freely. The
inertia obtained in this way is called ‘emulated inertia’.
6. Frequency-control contribution of DG units
99
A description of the DG units and their responses is given in section 6.5. First
section 6.4 describes a method to obtain a good mix of types of DG unit.
6.4 Method
In this section a method will be developed that can be used to analyse if and to what
extent the inertial response and primary frequency control still work properly, with an
increasing percentage of DG in the grid. Besides that a method will be developed that
can be used to synthesise a group with different combinations of DG units (eventually
with additional control) such that the mentioned control still works.
6.4.1 Primary control
The power Pi, that is generated by a certain generator i is written as the product of its
nominal power Pnom,i and its thus defined utilisation factor ki:
Pi = k i Pnom,i
(6.6)
For stable operation of power systems there should always be a balance between the
power that is generated and the power that is supplied, thus
N
M
i =1
i =1
∑ k i Pnom,i =∑ Pload ,i
(6.7)
with Pload,i the power consumed by load i.
In order to be able to contribute to primary frequency control DG units should have
an utilisation margin Δki in which the utilisation factor can be increased in case of
disturbances. The power margin ΔkiPnom,i can be considered as an equivalent of the
primary control reserve of conventional power plants. It is different for different types
of DG unit. For photovoltaic systems operating at their maximum power point for
example, Δki is zero. For DG units which can control their prime energy source, such as
for example fuel cells, it is 1-ki.
The total available power margin should at least be equal to the maximal change in
power due to a disturbance, Pdist,max, that can be expected
N
∑ Δki Pnom,i ≥ Pdist ,max
(6.8)
i =1
The maximum change in power that can occur is mostly the sudden disconnection of the
largest generator (or interconnection) in a network, or the connection of the largest load.
For instance in a grid with a large percentage of renewable generators it might be
100
impossible to fulfil the requirement of (6.8). Other DG units, such a for example micro
turbines, might bridge the gap however.
The equations are used to determine how the actual power in a network can be
spread over DG units and conventional power plants, such that the maintained primary
control reserve (power margin) is large enough to re-establish the power balance after
the largest possible disturbance. Some examples for networks with fuel cells (or more
general: DG units of group IV) and wind turbines (or more general: DG units of group
V) will be given.
In the first example requirements are given for the minimal required fuel cell
utilization margin Δkfc. The utilization margin of the conventional generator is set to 0.1
and the utilization margin of the wind turbine to zero. The maximum disturbance that
can occur is a 10% increase in load power. The result is shown in Fig. 6.4a. For a given
load power it is analysed how the generation can be spread over fuel cells (Pfc), wind
turbines (Pwt) and conventional generators (Pc). For each combination of Pfc, Pwt, and Pc
it is calculated what should be the minimal value of Δkfc, such that the system is able to
re-establish the power balance after the maximum disturbance. The regions in the figure
correspond to the minimal required fuel cell utilization margins that are needed to be
able to re-establish the power balance. For example for all combinations in the dark
gray area the fuel cell utilization margin should be between 0.1 and 0.2. Each point in
the triangle represents a certain combination of percentages of the three types. The
combination always adds up to 100%. The more close a point is to a certain corner of
the triangle, the higher the fraction of the respective generator type is. On the ribs one of
the fractions is zero.
P
fc
0.1 < Δkfc < 0.2
0.2 < Δkfc < 0.3
0.3 < Δkfc < 0.4
Pfc
Pc
P
wt
0 < Δkc < 0.1
0.1 < Δk < 0.2
c
0.2 < Δkc < 0.3
Pc
Pwt
(a)
(b)
Fig. 6.4. Minimal required utilisation margins for different distributions of the power over fuel cells, wind
turbines and conventional generators; (a) required fuel cell margin, Δkc = 0.1, Δkwt = 0; (b) required
conventional generator margin, Δkfc = 0.2, Δkwt = 0
6. Frequency-control contribution of DG units
101
The same type of diagram is repeated in Fig. 6.4b for a constant value of Δkfc (0.2)
and requirements for Δkc (0.1, 0.2 0.3). Both pictures show that, as expected, the amount
of allowable wind power is limited. For increasing utilisation margins, the allowable
wind power is also increasing.
The relations in Fig. 6.4a and b are given for conventional generators, fuel cells and
wind turbines. They are not limited to those three types however. The fuel cells can be
replaced by other DG unit types that have a controllable source, such as for example
micro turbines and the wind turbines by other DG units that have a non-controllable
source, such as for example solar cells.So far a relation has been laid down between the
actual powers of the three generator types. It is also possible to derive requirements for
the minimal installed capacity of a certain type of generator. In the next example a
relation is obtained for the minimal required installed capacity of fuel cells as a function
of the installed capacity of wind turbines. As wind turbines can not contribute to
primary frequency control, it is required in this example that fuel cell power has to be
installed to provide the primary frequency control contribution of the wind turbines. It is
required that the per unit contribution to primary frequency control of wind turbines and
fuel cells together is equal to the per unit contribution of the conventional generators.
(For example: in a network with 40% DG and 60% conventional, 40% of the additional
power that is needed for primary frequency control comes from the DG units and 60%
from the conventional generators.)
Fig. 6.5 shows the minimal percentage of installed capacity of fuel cell power that is
required as a function of the percentage of actual wind power (both as a percentage of
the total installed capacity), for a disturbance that causes a drop in power of 10% of the
total installed capacity. The requirements are given for four different values of the
minimal utilisation margins which the fuel cells maintain as primary control reserve.
45
40
35
fc
P [%]
30
Δk = 0.25
fc
Δkfc = 0.50
Δkfc = 0.75
Δk = 1.00
fc
25
20
15
10
5
0
0
20
40
60
P
wt
80
100
[%]
Fig. 6.5. Minimal installed fuel cell capacity (percentage of total generated power) as a function of actual
wind power (percentage of total generated power)
102
In the Netherlands a target of 6 GW of installed wind power has been set. This 6
GW will be about 25% of the total installed capacity. From Fig. 6.5 the minimal
required installed fuel cell capacity for 25% wind power can be obtained as 16.7%,
6.3%, 3.8%, and 2.8% for Δkfc is 0.25, 0.5, 0.75, and 1 respectively. When the 6 GW is
generated in a low-load situation, it might be much more than 25% of the total power
that is generated at that moment. Correspondingly the installed capacity or the
maintained utilisation margin of the fuel cells needs to be higher. A possible solution
can be to increase the utilisation margin of the fuel cells when the percentage of wind
increases.
A similar strategy can be followed to take the changes in wind power as a function
of wind speed into account. It is possible to increase the utilisation margin of the fuel
cells as a function of the wind speed, as is shown in Fig. 6.6, for three different values
of the installed capacity of fuel cells. It is assumed that there is 6 GW of installed wind
power.
0.5
Pfc,nom = 1 GW
P
= 2 GW
fc,nom
P
= 3 GW
fc,nom
Δkfc
0.4
0.3
0.2
0.1
0
0
5
10
15
Wind speed [m/s]
20
25
Fig. 6.6. Minimal required fuel cell utilisation margin (primary control reserve) as a function of wind speed
for three different values of installed fuel cell power and for 6 GW wind energy
So far it has only been investigated if the primary control reserve is large enough.
Another important issue is the implementation of control loops on the DG units. An
example of such an implementation, on a fuel cell system, is shown in Fig. 6.7.
Valve
Gas
Reformer
H2
Fuel
Cell
Pdroop
KFC
Pset
Converter
Δf
fgrid
fref
Droop controller
Fig. 6.7. Fuel cell system with droop controller for primary frequency control
6. Frequency-control contribution of DG units
103
The contribution of conventional generators to primary frequency control is
determined by their droop constant, as defined in (6.5). The same type of droop control
can be implemented on DG unit i:
ΔPDG ,i = − K DG ,i Δf
(6.9)
It will now be analysed how the value of KDG,i for each DG unit can be determined. First
the total DG power is defined as:
PDG ,tot = ∑i PDG ,i
(6.10)
and the total power of all DG units that can support primary frequency control as:
PDGpfc,tot = ∑ j PDGpfc, j
(6.11)
In the conventional grid most generators have the same droop. It implies that each of the
generators supply the same amount of additional power (as a percentage of the nominal
power), when the frequency changes. As has been discussed, not all DG units can
contribute to primary frequency control. A good assumption can be however, that all
DG units together should be considered as one ‘virtual’ power plant. This ‘virtual’
power plant can be obliged to have the same droop as the conventional generators. The
droop is then:
− Δf / f n
⋅100%
D pf =
(6.12)
ΔPG / PDG ,tot
The value of the droop constant KDG,i for a DG unit i that can contribute to primary
frequency control can then be defined as:
PDG ,i
100 ⋅ PDG ,tot
K DG ,i =
⋅
(6.13)
D pfc ⋅ f n PDGpfc ,tot
6.4.2 Inertial response
In the conventional power system the inertial response is by definition the behaviour of
the grid without control, i.e. it is behaviour that inherently follows from the structure of
generators (and motors) that are directly coupled to the grid. This behaviour will be
referred to as ‘inherent behaviour’. The dynamics of the grid after a disturbance are
given by:
d ⎛1
2⎞
⎜ Jω g ⎟ = Pdist
dt ⎝ 2
⎠
(6.14)
with ωg the grid frequency and Pdist the change in power due to a disturbance. The
relation between the kinetic energy stored in the rotating mass of a generator and its
rated power is given by the inertia constant H [s]. It is normally defined for a single
generator, but can also be defined for a total grid:
104
⎛1
⎞
∑i ⎜⎝ 2 J i ω g2 ⎟⎠
H tot =
∑i Pnom,i
(6.15)
The term above the line gives the energy stored in rotating masses which are directly
coupled to the grid. With an increasing penetration of DG it is to be expected that the
inertia J will decrease, implying that the dωg/dt after disturbances will increase. Several
types of DG units have some form of energy storage. This stored energy can be used to
emulate inertia. The inertia constant becomes then:
⎛1
⎞
∑ j ⎜⎝ 2 J j ω g2 ⎟⎠ + ∑k E DG,stored ,k
H tot =
∑i Pnom,i
(6.16)
with EDG,stored,k the stored energy of DG unit k that does not contribute to the inertia by
itself, but that can be used to emulate inertia.
The value of Htot of a grid will determine the initial rate of change of the frequency
after a disturbance in the power balance. The equations derived in this section are first
used to determine how large the inertia constant of a grid with DG units is (or can be).
Afterwards they are used to determine which combinations of DG units and
conventional generators are needed to obtain a certain minimal value for Htot. The value
of Htot depends on:
• types of DG
• installed capacity of each type
• utilisation margin of each type
• the value of emulated inertia of each type
First two examples are given which show the influence of DG units on the inertia
constant of the grid. As a first example Fig. 6.8a shows the inertia constant Htot of a
network for an increasing DG penetration and for three different mixes of DG types. It
is assumed that the DG units replace conventional power plants, thereby reducing the
conventional inertia. The inertia constant drops significantly in case that the DG units
only consist of fuel cells (or more general: DG units of group III). When also wind
turbines are used instead of fuel cells Htot drops less because wind turbines can emulate
inertia [Mor 06]. Fig. 6.8 applies to the case where the inertia constant H of the
conventional generators and the wind turbines is 5s for both. This clarifies that Htot does
not change when only wind turbines are introduced (dotted line). The rate of change of
frequency after a disturbance is determined by the inertia constant of the grid. In the
second example it is shown how DG units with emulated inertia can change this rate by
emulating extra inertia. Fig. 6.8b shows the rate of change of frequency in a grid as a
function of the emulated inertia of the wind turbines. The emulated inertia on the
6. Frequency-control contribution of DG units
105
horizontal axis is divided by the average inertia of the conventional generators, Jconv.
The figure shows that an increase of inertia-less DG will result in a smaller inertia
constant and thus a larger initial rate of change of frequency after the occurrence of a
disturbance.
6
1
5.5
0.9
DG
5
dt/dt [Hz/s]
[s]
tot
H
4
3.5
2.5
0.7
0.6
0.5
PDG = Pfc
P = 0.5P + 0.5P
DG
fc
wt
P =P
DG
2
0
tot
0.8
4.5
3
P /P =0
DG
tot
P / P = 0.25
DG
tot
P / P = 0.50
0.1
0.4
wt
0.2
0.3
PDG / Ptot
0.4
0.5
0.3
0
0.5
J
DG
1
/J
1.5
2
conv
(a)
(b)
Fig. 6.8. Relation between DG unit power, inertia (constant) and rate of change of frequency; (a) inertia
constant of total grid as a function of percentage DG, for different combinations of DG unit types; (b) Rate of
change of frequency as a function of emulated inertia Jemu, for different DG unit percentages
It is reasonable to assume that there is a lower limit for the inertia constant of the whole
grid, as it determines the initial rate of change of frequency after a disturbance:
H tot ≥ H min
(6.17)
with Hmin for example the average inertia constant of a grid with only conventional
generators. Combining this equation with (6.16) gives a lower limit to the minimal
amount of energy that should be available for emulating inertia.
An example of possible requirements for a network with conventional generators,
fuel cells and wind turbines is given in Fig. 6.9. In this example the conventional
generators have an inertia constant of 5 s and the wind turbines have an emulated inertia
that corresponds to an inertia constant of 4 s.
Fig. 6.10 shows a DG unit with an additional control loop that emulates inertia. The
controller will supply or absorb power according to
dω g
(6.18)
Pine = J emuω g
dt
with Jemu the emulated inertia. Its value can be chosen freely to some extent, although it
is limited by several parameters, such as the rated power of the generator, the time that
the power has to be supplied (E=P⋅t) and the speed with which the power has to be
increased (dP/dt).
106
P
H > 2s
H > 3s
H > 4s
fc
P
c
Pwt
Fig. 6.9. Inertia constant for different combinations of DG unit types (Hc=5s, Hfc=0s, Hwt=4s)
Normally the speed of the rotating DG unit is controlled. In case of for example
micro turbines mostly a constant power is supplied. Renewable generators such as wind
turbines have a maximum power point tracking control. In both cases additional power
can be subtracted from the kinetic energy of the rotating mass to emulate inertia.
Conventional generators always run at the same speed. Their inertia constant H is
independent from the power they supply. This is not the case for most DG units, where
the kinetic energy is stored in equipment that rotates at variable speed. Therefore their
inertia constant depends on their operating point. In case of a variable speed wind
turbine for example, H depends on the actual wind speed. This is discussed in section
6.5.
DG
Grid
Control
Pref
Pine
Jemu
d/dt
ω
Inertia emulation
Fig. 6.10. DG unit with control loop that emulates inertia
The last part of this subsection analyses how the value of the emulated inertia Jemu of
each DG unit can be determined. First the total kinetic energy stored in all DG units
together is defined as:
E DG , stored ,tot = ∑k E DG , stored , k
(6.19)
6. Frequency-control contribution of DG units
107
and the relation between the emulated inertia Jemu and the kinetic energy of DG unit k
as:
1
J emu , k ω g2
(6.20)
2
It is assumed that the inertia of each DG unit should be proportional to the amount of
kinetic energy stored in that DG unit. The equation for the average inertia constant of
the total grid, Htot, is given in (6.16). It can be rewritten as:
E DG , stored ,k =
1 2
ωg
2
⎛1
⎞
∑k J emu,k = H tot ⋅ ∑i Pnom,i − ∑ j ⎜⎝ 2 J j ω g2 ⎟⎠
(6.21)
Combining (6.19)-(6.21) the value of the emulated inertia for DG unit k is:
J emu , k =
2 ⋅ H tot ⋅
∑i Pnom,i − ∑ j (J j ω g2 )
ω g2
⋅
E DG , stored ,k
E DG , stored ,tot
(6.22)
6.4.3 Mix Requirements (or: ‘Equivalent power plants’)
The 2 previous subsections investigated how DG units can contribute to inertial
response and primary frequency control. In this subsection this distinction is left behind
and it is investigated how a mix of different DG unit types can contribute to frequency
control. Requirements for the ratios between the different types will be derived.
In a conventional grid there is a strict distinction between inertial response and
primary frequency control. Inertial response is the behaviour that inherently follows
from the structure of directly coupled machinery to the grid. It only depends on the
dynamic characteristics of the grid and not on the controllers. During primary frequency
control the response depends on the control that is implemented. With emulated inertia
and DG unit contribution the distinction becomes less clear: Control is implemented to
emulate inertia. Inertial response is therefore no longer only inherent behaviour, as it
was in the conventional grid. Further, the emulated inertia has not necessarily to be
obtained from kinetic energy. If the driving source of the DG unit can increase its
energy production fast enough, also this energy can be used to emulate inertia.
It is therefore good to abandon the strict distinction between inertial response and
primary frequency control. There is actually only one important point when it comes to
frequency control: whether there is enough reserve power available to maintain the
power balance. In the conventional grid inertia is only necessary because the
mechanical power of the large conventional generators can not be changed fast enough.
Therefore the kinetic energy is used to instantaneously restore the power balance. The
main goal is to maintain the power balance. In the conventional grid this is done by first
using kinetic energy (which is fast) and then using mechanical power (which is slower).
108
Fuel cell
Load
Power
Power
For DG units a distinction will be made between those that can change their output
power fast and those that have a slower response and between DG units that have a
controllable power source and DG units that have a non-controllable power source, as
discussed in section 5.3. Fuel cells, for example, can change their output power. The
speed with which this can be done is limited however (as long as no hydrogen storage is
used). Variable speed wind turbine, on the contrary, can increase their output power
very fast by tapping their kinetic energy. They can supply power during the period that
the fuel cell power is increasing. In this way fuel cells and wind turbines can be
complementary to each other. The wind turbines use kinetic energy however. After their
contribution, their output power is reduced in order to let the wind turbine speed up to
its original value. This means that the other generators in the grid have to compensate
for this drop in power. An example of a possible combination of responses is shown in
Fig. 6.11.
Conventional generator
time
Power
Power
time
Wind turbine
time
time
Fig. 6.11. Increase in power; load power (upper left); conventional generator power (lower left); fuel cell
power (upper right); wind turbine power (lower left)
During the analyses the DG units are considered as a group: an ‘equivalent power
plant’. The droop of the equivalent power plant is chosen equal to that of the
conventional generators. The change of DG power after a change in power due to a
disturbance, Pdist, should be:
ΔPDG = PL ⋅ Pdist
(6.23)
with PL the penetration level of DG units, which is defined as:
PDG ,nom
PL =
PDG ,nom + Pconv,nom
(6.24)
with PDG,nom the sum of the nominal powers of all DG units and Pconv,nom the sum of the
nominal powers of all conventional generators. Three different DG unit types are
considered: fuel cell, micro turbine, and wind turbine. They represent the most
important types and it is assumed that other types are comparable to one of these three.
They also represent most of the groups that have been defined in section 6.3.
6. Frequency-control contribution of DG units
109
Variable speed wind turbines are driven by an uncontrollable power source (group
V). They cannot contribute to primary frequency control. The fuel cells and micro
turbines have to provide the steady-state contribution for all DG units together.
Therefore their utilisation margin has to be large enough:
Δk fc Pfc , nom + Δk mt Pmt , nom ≥ PL ⋅ Pdist , max
(6.25)
where Δkfc and Δkmt give the utilisation margin of the fuel cell and the micro turbine
respectively. (Actually this is the same as their primary control reserve.)
The power balance has to be restored immediately. Some DG units that can provide
a steady-state contribution are not fast enough to restore the balance immediately. This
has to be done by the fast DG units and the DG units that have kinetic energy available.
The maximum power that has to be supplied in this phase is therefore equal to the
maximum change in power due to a disturbance. Fuel cells can not contribute to inertial
response, as they can change the power of their source only slowly. Therefore during
this phase:
Δk mt Pmt ,nom + Δk wt Pwt ≥ PL ⋅ Pdist ,max
(6.26)
The relations of (6.25) and (6.26) can be represented graphically. An example is given
in Fig. 6.12. It is assumed that the utilisation margins of the three types of DG unit are
the same. For three different values of the utilisation margin the allowed value of fuel
cell, micro turbine and wind turbine power are shown in the figure.
Pfc
Δk = 0.1
Δk = 0.2
Δk = 0.3
Pmt
Pwt
Fig. 6.12. Allowable range of fuel cell, micro turbine and wind turbine power for different utilisation margins
and PL = 0.5
The requirements are for a case that the maximum drop in load is 10%. The figure
shows that micro turbines are always able to control the frequency correctly. When
wind turbines or fuel cells form 100% of all DG correct control is not possible. They
should always be used in combination with each other or in combination with micro
110
turbines. The figure shows further that larger percentages of fuel cells and wind turbines
are possible, when the utilisation margin increases.
6.5 DG unit contribution to inertia and primary frequency control
In order to be able to analyse the ability of DG units to contribute to inertial response
and primary frequency control some basic properties and capabilities of the DG units
have to be known. Especially important are the ability to increase the stationary power
and the dynamics associated with it and the size of the (emulated) inertia. This section
describes the characteristics of three different DG unit types:
• Wind turbine
• Micro turbine
• Fuel cell
Solar cells will not be considered as they have no possibility at all to increase their
output power. Other types of DG unit will not be considered as they have no PEC or
because they are used on a very limited scale only.
First the most important characteristics of the DG units are discussed. At the end of
this section the possibilities of the different DG units are summarised in a number of
tables.
6.5.1 Wind turbines
The first type of DG unit that is considered is a variable speed wind turbine. The power
supplied by the turbine depends on the wind, which is not controllable. Therefore wind
turbines can not participate in primary frequency control. The large blades of the turbine
give this type of DG unit a significant inertia. For variable speed turbines this inertia is
decoupled from the grid by a PEC to enable variable speed operation. It is possible to
give the wind turbines an emulated inertia however.
Variable speed wind turbines have a speed controller, which has the task to keep the
optimal tip speed ratio λ over different wind speeds, by adapting the steady state
generator speed to its reference value. This reference value is normally obtained from a
predefined power-speed curve as shown in Fig. 2.6. For low wind speeds the generator
speed is kept at a fixed low speed and for wind speeds above the rated value the
rotor/generator speed is limited by progressively pitching the blades in order to limit the
aerodynamic power. The reference torque is obtained from the predefined static P-ω
characteristic. The error between the actual and the reference torque is sent to a PI
controller, which gives a setpoint for the current controller of the turbine. In another
loop the pitch angle of the turbine is controlled.
6. Frequency-control contribution of DG units
111
Kinetic energy - Wind turbines can use their kinetic energy to provide inertial response.
The energy stored in the rotating mass of their blades is given by:
1
E = Jω m2
(6.27)
2
with J the inertia and ωm the rotational speed of the turbine. In electrical power
engineering often the so-called inertia constant H is used:
Jω m2
(6.28)
2S
with S the nominal apparent power of the generator. The inertia constant has the
dimension time and gives an indication of the time that the generator can provide
nominal power by only using the energy stored in its rotating mass. Typical values for
wind turbines are about 2 – 6 s [Knu 05], which is in the same range as the values for
conventional generators (2 – 9 s). This implies that introduction of wind turbines in the
grid does not necessarily reduce the kinetic energy that is available.
The kinetic energy stored in the rotating mass of a wind turbine depends on the
rotational speed of the blades (and thus on the wind speed). The operational output
power of the wind turbine is proportional to the cube of the wind speed:
H =
3
Pwt ~ v wind
(6.29)
Variable speed wind turbines operate at a constant tip speed ratio λ. This implies that
the rotational speed of the turbine is proportional to the wind speed and thus the
rotational speed of the wind turbine is proportional to the cube root of the power:
ω wt ~ 3 Pwt
(6.30)
The rotational speed of the wind turbine varies between ωwt,min and ωwt,nom. The power at
these two points is defined as Pvar,min and Pvar,max respectively. When the power increases
further the speed is kept constant. The approximate relation between power and
rotational speed is then:
ωwt = 3
Pwt
Pvar,max
ωwt , nom
ωwt = ωwt , nom
(Pvar,min < Pwt < Pvar,max )
(Pvar,max < Pwt )
(6.31)
Combining (6.28) and (6.31) gives the approximated inertia constant of the turbine:
2
Jωwt
, nom ⎛
⎜ Pwt
H=
2 Pnom ⎜⎝ Pvar,max
H=
2
Jωwt
, nom
2 Pnom
⎞
⎟
⎟
⎠
23
(Pvar,min < Pwt < Pvar,max )
(Pvar,max < Pwt )
(6.32)
112
Primary control reserve - Variable speed wind turbines are controlled in a way that they
always capture as much power as possible from the wind, as long as the rated wind
speed is not reached. For wind speeds higher than nominal, the pitch controller of the
variable speed wind turbine is used to limit the power that is captured by the turbine, to
avoid overloading of the mechanical and electrical subsystems.
At first sight wind turbines do not have a primary control reserve and therefore they
are not able to contribute to primary frequency control. A possibility to give wind
turbines a primary control reserve is to let them operate at a working point below the
optimal point. This influences their annual power production however. Another method
can be applied when the wind speed is above its nominal value. The power output is
then limited by the pitch controller. By decreasing the pitch angle more power can be
supplied. This results in overloading of the turbine. When this occurs accidentally this
will give no problems. This type of control only works for high wind speeds. The two
possibilities are further not considered in this thesis.
6.5.2 Micro turbines
Micro turbines can essentially be considered as small versions of conventional gasfuelled generators. The important differences however are that they run at much higher
speeds and are connected to the grid with a PEC. Similar to conventional plants, micro
turbines have inertia. It is decoupled from the grid however, and an additional control
loop should be implemented to make the inertia available to the grid. As long as the
micro turbine is not running at full power, it can participate in primary frequency
control.
The response of a micro turbine to a change in torque setpoint is mainly determined
by the gas turbine, which, as a simple approximation, can be modelled as a first order
transfer function:
k gt
G gt (s ) =
(6.33)
τ gt s + 1
The values for the time constant τgt that are found in literature vary from tens of
milliseconds to tens of seconds.
Kinetic energy - In a situation in which power is needed for a short time, or when it is
needed fast, it is possible to use the kinetic energy stored in the rotating mass of the
turbine and generator. How much kinetic energy is available can easily be calculated
from (6.27) and the corresponding inertia constant from (6.28).
Primary control reserve - As long as the micro turbine is not running at full power it
can participate in primary frequency control. How much the output power can be
6. Frequency-control contribution of DG units
113
increased depends on the utilisation margin Δkmt of the micro turbine. The maximum
possible increase in power ΔPmt, at a certain moment, can therefore be defined as:
ΔPmt = Δk mt Pmt ,nom
(6.34)
with Pmt,nom the nominal power of the micro turbine.
The speed with which the output power can be increased depends on some typical
time constants of the gas turbine. The rate of power increase dPmt/dt is:
dPmt Pmt ,nom
=
(6.35)
dt
τ mt
with τmt the time constant of the micro turbine, which is a combination of the delays
associated with the different processes and flows in the gas turbine. The expression
should be used with care; it gives only an approximation.
6.5.3 Fuel cell
Fuel cells are electrochemical devices. Systems for stationary power applications
generally consist of three main parts; a reformer which converts the fuel to hydrogen,
the fuel cell itself, where the electrochemical processes take place and the power is
generated and the power conditioner, which enables grid connection.
Kinetic energy - The electrical response time of fuel cells is generally fast. It is mainly
associated with the speed at which the chemical reaction is capable of restoring the
charge that has been drained by the load. Most fuel cells have a reformer however,
which produces the hydrogen that is necessary for the electrochemical processes. The
processes in the reformer are rather slow, because of the time that is needed to change
the chemical reaction parameters after a change in the flow of reactants. This limits the
rate with which fuel cells can change their output power. Only when there is some form
of hydrogen storage, the fuel cell can increase its power quickly.
Primary control reserve - The capability of fuel cells to contribute to frequency control
depends on how much and how fast the output power can be increased. The maximum
possible increase in power at a certain moment depends on the primary control reserve,
Δkfc, of the fuel cell at that moment. The maximum possible increase in power ΔPfc, at a
certain moment, can therefore easily be defined as:
ΔPfc = Δk fc Pfc , nom
(6.36)
with Pfc,nom the nominal power.
The rate with which the output power can be increased depends on some typical
time constants of the fuel cell and the reformer. The rate of power increase dPfc/dt is:
114
dPfc
dt
=
Pfc ,nom
(6.37)
τ fc
with τfc the time constant of the fuel cell, which is a combination of the delays in the
reformer and the fuel cell itself. Note that this equation only gives an approximation.
Most fuel cells have a large time constant and thus the rate with which the fuel cell can
increase its power is limited, also limiting the fuel cell contribution to frequency
control.
6.5.4. Summary: Primary control reserve, deployment time and inertia
Three different DG units are described in this paragraph, with specific emphasis on their
ability to increase their output power on command. This subsection summarises the
capabilities of the three units: first their primary control reserve (power margin) is
given, then is it summarised how fast they can change their output power, and finally it
is investigated how much kinetic energy is available from rotating DG units.
Primary control reserve - The primary control reserve of a micro turbine and a fuel cell,
which depends on the operation point and the nominal power of the DG units are given
in table 6.1. Wind turbines do not have a primary control reserve as they are not able to
increase the mechanical (wind) power.
Table 6.1: Primary control reserve of DG units
Wind turbine
Micro turbine
Fuel cell
0
ΔPmt = Δk mt Pmt ,nom
ΔPfc = Δk fc Pfc , nom
Rate of change of power – An important issue is the speed with which the power can be
changed. The previous sections showed that the speed of change depends on typical
time constants of the micro turbine and fuel cell. Some values that were found in
literature are given in table 6.2 and 6.3. Both the ramp up and ramp down time are given
(if available). There are significant different in the rate of change of power that can be
achieved. It is unclear what causes these differences.
Table 6.2: Ramp up and ramp down speed of micro turbine output power
Prated [kW]
dP/dt up (p.u./sec)
dP/dt down (p.u./sec)
Source
30
75
100
100
0.012
0.011
0.020
2.0
0.015
0.015
[Yin 01]
[Yin 01]
[Per 05]
[Nik 05]
6. Frequency-control contribution of DG units
115
Table 6.3: Ramp up and ramp down speed of fuel cell output power
Prated [kW]
dP/dt up (p.u./sec)
dP/dt down (p.u./sec)
Source
5
100
0.04
0.01
0.09
[El-S 04]
[Zhu 02]
Inertia - Wind turbines do not have a control reserve as they can not increase their
mechanical power. Micro turbines have a limited speed with which they can increase
their power. Both have kinetic energy available however, which can be used to supply
power for a short time. This can be done very fast. The rate of change is only limited by
the speed of the controllers. The kinetic energy for several wind turbines and micro
turbines that have been found in literature are given in the table below.
Table 6.4: Kinetic energy and inertia constant of wind turbines
Prated [MW]
E [MJ]
H [s]
Source
1.5
2.0
3.7
7
6
18.7
4.7
3
5.1
[Mil 03]
[Per 04]
[Mil 03]
Table 6.5: Kinetic energy and inertia constant of micro turbines
Prated [MW]
E [MJ]
H [s]
Source
20
250
450
0.2
2.1
1.8
10
8.2
3.91)
[Jar 02]
[Zhu 02]
[Can 01]
1)
It is not clear from the description in the paper whether this is only for the generator, or for the combination
of generator and turbine
6.6 Case study
A case study has been done to show the ability of DG units to contribute to frequency
control. First the simulation setup will be described. Next the results of the case study
are presented.
6.6.1 Simulation setup
The case studies are performed on a model of a small network that consists of a
synchronous generator, fuel cells, wind turbines, and loads. A model of the network is
shown in Fig. 6.13. Load 3 is connected to the network to disturb the power balance.
Fig. 6.14 shows a schematic block diagram of the simulation setup.
116
Synchronous
Generator
Cable
Wind Turbine
Fuel cell
Load 1
Load 2
Load 3
Fig. 6.13. Case study network
Busbar
Valve
Steam
Shaft
HST(s)
PSM
Generator
Δy
Governor
(Fig. 6.15)
Paero
ωm
ωm,ref
Generator
+
Converter
Wind
Turbine
Tref
WT
Control
f-control
(Fig. 6.16)
Reformer
Fuel cell
+
Converter
Valve
Gas
Pset
Pdroop
f-control
(Fig. 6.7)
Δf
PWT
Δf
System
+
Loads
fmeas
fref
PFC
fmeas
fref
Fig. 6.14. Block diagram of simulation setup
Conventional power plant - The conventional power plant is modelled as a synchronous
machine driven by a steam turbine. The synchronous machine is modelled as a three
winding representation in dq coordinates. The model can be found in [Pie 04]. Damper
windings are not taken into account. For the voltage regulator and exciter a so-called
type 1 model from [And 77] is used. Primary frequency control is performed by the speed
governor shown in Fig. 6.15, which increases or decreases the steam flow to the turbine,
depending on the frequency error (ωm- ωref). It has a small dead-zone around the
nominal frequency.
6. Frequency-control contribution of DG units
117
Valve
Shaft
Steam
Turbine
Δy
1
s
K
To generator
ωm
ωref
Δωm
Speed ref.
R
Governor
Fig. 6.15. Governor
The reheat steam turbine is modelled as a second order transfer function [Kun 94]:
1 + sFHP TRH
H ST (s ) =
(6.38)
(1 + sTCH )(1 + sTRH )
with TCH the time constant of main inlet volumes and steam chest, TRH the time constant
of the reheater, and FHP the fraction of total turbine power generated by the highpressure section. The parameters are obtained from [Kun 94].
Fuel cell – The model of the 100 kW solid-oxide fuel cell (SOFC) that is used is
described in appendix C. The fuel cell is connected to the grid with a three-phase
voltage source converter. When the fuel cell contributes to primary frequency control,
the response of the fuel cell system is mainly determined by the reformer, which can be
modelled as a first order transfer function [Zhu 02]:
H R (s ) =
1
1 + sT R
(6.39)
with TR the time constant of the reformer (5 s). A control loop with a certain droop has
been implemented on the system, in order to let it contribute to primary frequency
control. The system was already shown in Fig. 6.7.
Wind turbine – The model of the 2.75 MW variable speed wind turbine with doubly-fed
induction generator that is used is described in appendix C. Normally the controllers of
variable speed wind turbines try to keep the turbine at its optimal speed in order to
produce maximum power. The controller gives a torque setpoint that is based on
measured speed and power, see Fig. 6.16. An additional controller is implemented that
can adapt the torque setpoint to extract power from the rotating mass of the generator, to
support primary frequency control. During this support the main dynamics of the
turbine are given by the following torque-equation:
dω wt
J
= Ta (v w , θ , λ ) − Te
(6.40)
dt
118
with J the inertia and ωwt the rotational speed of the wind turbine, and Ta the
aerodynamic torque which depends on the wind speed vw, the pitch angle θ, and the tip
speed ratio λ.
The controller response is chosen in such a way that it complements the power
supplied by the fuel cell, such that the sum of their powers is constant. The power
increases first to KWT⋅Δf and decreases then with the time constant τfc, which is the time
constant with which the fuel cell output power increases.
Speed control
ωm,meas
Pref
P
ωm
fgrid
fref
Tω,ref
Tref
Generator
+
Converter
Frequency control support
Δf
1
KWT(1- τ s )
fc
Tf,ref
Fig. 6.16. Wind turbine controller; upper branch: maximum power control, lower branch: frequency control
support
6.6.2 Parameters
The most important parameters used in the case study are given in table 6.6. Other
parameters can be found in the appendices. The total power of the network is small.
This is done to be able to see a significant contribution of the DG units, without the
necessity to model and simulate a large network. The percentage of wind power in this
case study is about 25%. From Fig. 6.5 it can be obtained that the minimal required
amount of installed fuel cell capacity should be about 6.5%. The 10% used in this case
study should therefore be enough.
The fuel cells and wind turbines are considered together as one equivalent generator.
It is required in the case study that the conventional generator and the equivalent
generator have the same droop. This strategy is well-known, as it is normally also
followed in networks with only conventional generators. It implies that each of the
generators supplies the same amount of additional power (as a percentage of their
nominal power), when the frequency changes. A droop of 3% has been chosen. The
smaller the droop is, the smaller the frequency deviation will be. A droop that is too
small can cause instability however.
The value of the droop of the fuel cell has to be much larger than 3% however, as it
also has to supply the primary frequency control support of the wind turbines. The
droop of the fuel cell is thus given by:
6. Frequency-control contribution of DG units
DFC =
119
Pfc ,nom
Pfc ,nom + Pwt ,nom
⋅ Dsyst
(6.41)
with Dsyst the droop of the system (3%). Correspondingly the droop of the wind turbine
is given by:
Pwt ,nom
DWT =
⋅ Dsyst
(6.42)
Pwt ,nom + Pwt ,nom
With (6.5) the droop constants KFC and KWT can be derived from the droops DFC and
DWT. With these equations the values for K that are given in table 6.6 can be calculated.
Note that the droop constant of the synchronous machine is given by R, which changes
the power setpoint as a function of ω instead of f.
Table 6.6: Parameters for case study
Parameter
Value
Unit
Parameter
Value
Unit
Pconv
Pwt,nom
Pfc,nom
90
27.5
10
MW
MW
MW
K
R
FHP
1⋅1012
1⋅107
0.3
W/rad⋅s-1
W/rad⋅s-1
Pload1
10
MW
TCH
0.3
Pload2
90
MW
TRH
7.0
s
s
Pload3
kfc
kconv
10
0.5
0.8
MW
-
KFC
KWT
2.5⋅107
2.5⋅107
15
kw
0.95
-
τfc
W/Hz
W/Hz
s
6.6.3 Case study: Frequency control with fuel cells and wind turbines
The case study investigates how fuel cells and wind turbines can work together to
contribute to primary frequency control. The fuel cell has a reformer that produces
hydrogen from natural gas. The reformer slows down the speed with which the fuel cell
power can increase. The wind turbines are used to compensate the slow response of the
fuel cells. A load of 10% is suddenly connected to the grid at t = 5 s. The load power
change is shown in Fig. 6.17a. The frequency response of the network is shown Fig.
6.17b. As a result of the drop in frequency the synchronous generator, the fuel cells, and
the wind turbines will increase their output power. Fig. 6.17c shows the power of the
synchronous machine. The power of wind turbines and fuel cells together is shown Fig.
6.17d. The output power of the fuel cell and the wind turbine is shown in Fig. 6.17e and
Fig. 6.17f respectively.
The power of the fuel cell increases rather slow. The ‘gap’ is bridged by the wind
turbine power however. The speed with which the wind turbine power decreases is
120
equal to the speed with which the fuel cell power increases. As a result, the combined
power stays constant, as can be seen from Fig. 6.17d. The output power of the wind
turbine drops below its original value after finishing its frequency control support. This
is shown in Fig. 6.17f. The controller determines how large the drop is. The smaller the
drop is, the longer the period will be that the power is below its normal value. This drop
is compensated by the fuel cell. The deployment time of the wind turbine (the speed
with which it increases the power) has been chosen approximately equal to that of the
synchronous machine. This gives a better sharing of the power between the
conventional generator and the wind turbine.
Oscillations can be seen in the wind turbine power at t = 5 s. They are due to the fact
that the sudden connection of the load causes a small voltage dip. Although DFIGs are
sensitive to voltage dips it can cope with this small dip.
36
120
115
Power [MW]
Power [MW]
34
110
105
100
32
30
95
90
0
10
20
30
time [s]
40
50
28
0
60
10
20
50.1
10
50
8
49.9
49.8
49.7
0
30
time [s]
40
50
60
40
50
60
40
50
60
(d)
Power [MW]
Frequency [Hz]
(a)
6
4
10
20
30
time [s]
40
50
2
0
60
10
20
(b)
30
time [s]
(e)
82
30
80
Power [MW]
Power [MW]
28
78
76
74
26
24
72
70
0
10
20
30
time [s]
40
50
60
22
0
10
20
30
time [s]
(c)
(f)
Fig. 6.17. Response of frequency and power to 10% load disturbance at t = 5 s: (a) load power; (b) grid
frequency; (c) synchronous machine power; (d) combined power of fuel cell and wind turbine; (e) fuel cell
power; (f) wind turbine power
6.6.4 Discussion
The case study shows that in principle it is possible to let a combination of DG units
contribute to primary frequency control. In the case study only a small network is used.
6. Frequency-control contribution of DG units
121
Some important differences with implementation in a large network are discussed.
In the case studies a percentage of 25% wind power and a load change of 10% have
been considered. In a large interconnected system these values will generally be much
smaller. Due to the larger inertia in the interconnected power systems the rate of change
of frequency will be smaller, which implies that the additional power has to be released
slower. Therefore the frequency control will be easier than in small networks. In small
(island) networks even more extreme cases might be expected however, especially in
low-load situations and high wind speeds. It is possible that a large percentage of the
power is generated by wind turbines. At some moment the proposed control no longer
works.
Another important issue is the speed with which fuel cells with a reformer can
increase their output power. The increase shown in Fig. 6.17 is based on the reformer
transfer function that is given in [El-S 04], which is relatively fast. Not all fuel cell system
will be able to show this response. With a slower response, the time during which the
wind turbines have to supply additional power will also increase. Above a certain fuel
cell time constant this will no longer be possible due to the limited amount of kinetic
energy that is available.
The primary frequency control re-establishes the power balance at a frequency
below 50 Hz, as can be seen from Fig. 6.17b. Secondary frequency control is necessary
to bring the frequency back to 50 Hz.
6.7 Summary and conclusion
This chapter investigated which contribution DG units can provide to frequency control.
A number of categories are defined for DG units, with respect to their ability to
contribute to inertial response and primary frequency control. The contribution will
depend on the type of DG unit. It was concluded that with a good mix of different DG
unit types, they can participate in frequency control. The inertial response is provided
by DG units that have kinetic energy available, such as wind turbines and micro
turbines. The primary frequency control is performed by the DG units that are driven by
a controllable power source, such as fuel cells and micro turbines. Requirements are
derived for which combination of DG units this is possible.
In the Netherlands a target of 6 GW of installed wind power has been set. An
example showed that for fuel cells operating at a power margin of 0.5, 1.6 GW of fuel
cell power is needed to provide the primary frequency control support for these wind
turbines. In case of a margin of 0.75 less than 1 GW is needed.
122
A case study has been performed on a network with wind turbines and fuel cells.
The wind turbines made up 21% of the total installed power and the fuel cells 8%. The
simulation results show that with this mix of DG units frequency control can be
supported.
Chapter 7
Implementation of grid support control
7.1 Introduction
In the preceding chapters a number of control strategies were developed to let the DG
units support the grid. It was analysed how large the contribution of the DG units could
be and the control strategies were demonstrated with case study simulations. All control
strategies were developed independently from each other. This chapter will analyse how
the different strategies can cooperate and can be implemented in the control circuit of a
DG unit. In this way a smart DG unit is obtained that supports the grid in different
situations.
An important issue is the question how the DG unit ‘knows’ at what moment which
control strategy has to be performed. Preferably this should be done autonomously.
Another issue is how the control should react when different disturbances, for example a
voltage dip and a frequency deviation, occur at the same time. So far no attention was
paid to the question whether the different control strategies can be performed at the
same moment.
The goal of this chapter is to investigate how the different control strategies can be
implemented. A decision tree will be constructed on the basis of which the different
actions can be performed. In the second part of this chapter a number of case study
simulations will be done to demonstrate the implementation.
7.2 Controller implementation
This section investigates how the different control strategies derived in chapter 5 and 6
can be implemented. The DG unit should have one overall controller that can handle the
different events and can decide which control strategy should be activated. The decision
should be made autonomously, based on measured (local) grid parameters and DG unit
124
parameters. The overall controller output commands are the reference signals for the
conventional control (for example current control) of the DG unit and its converter, as is
shown by the block diagram in Fig. 7.1.
The only grid quantity that the grid support control measures is the grid voltage.
From this measurement the amplitude and frequency of the voltage are derived. Based
on the frequency it can decide when the frequency control should be activated. A drop
in amplitude will indicate a voltage dip.
DG Unit
Grid
Control
Control
Grid support control
Fig. 7.1. Block diagram of DG unit and converter with overall controller
The grid support controller bases its operation on the state diagram shown in Fig.
7.2. In normal operation the amplitude and frequency of the grid voltage are
continuously measured. Further the dc-link voltage of the DG unit is measured. Based
on these parameters the decisions are made. The grey circles in Fig. 7.2 represent the
(control) states in which the DG unit is operating. The arrows give the conditions for
which the system changes from state. Although it is not shown in the figure, there is a
hysteresis band around each of the conditions, to avoid oscillations around the
condition.
Five different states have been identified:
• Normal operation. None of the grid support strategies is needed in this state.
• Fault ride-through. This state is entered when the controller measures a drop in the
amplitude of the grid voltage. Because of the current limitation of the converter the
power transferred to the grid is limited. The fault ride-through control proposed in
section 5.5 and 5.6 is activated then.
• Grid protection control. This control is necessary for DG units in DNs to avoid
disturbance of the over-current protection of the feeders, as described in section 5.3.
Depending on the type of protection that is applied and on its settings the DG units
can limit their current to the rated current, or to lower values. It is entered when a
drop in voltage amplitude is measured.
7. Implementation of grid support control
•
•
125
Fault ride-through & grid protection control. They will often be needed at the same
moment, as they can both be necessary during a voltage dip.
Frequency control. In this state the DG unit will support the frequency control. It is
entered when a change in frequency is measured.
Vdc<Vdc,th
AND fmin<f<fmax
AND Vdg>Vdg,th
Vdc>Vdc,th
Vdc<Vdc,th
Fault ridethrough
Vdg<Vdg,th
Normal
operation
Vdc>Vdc,th
Fault
ride-through
& grid
protection
control
Vdg>Vdg,th
Grid
protection
control
Vdg>Vdg,th
f>fmin
AND
f<fmax
Vdg>Vdg,th
Vdg<Vdg,th
Vdg<Vdg,th
f<fmin
OR
f>fmax
Vdc>Vdc,th
Vdc>Vdc,th
Vdg<Vdg,th
Frequency
control
f<fmin
OR
f>fmax
Vdc>Vdc,th
Fault
ride-through
& grid
protection
control
Vdc>Vdc,th
Fig. 7.2. State diagram for overall controller of DG unit (Grey circles represent states and arrows conditions
for which is switched between states)
The transition between the different states is based on 3 different conditions:
• Vdc>Vdc,th. During a voltage dip, the power of the DG unit that can be transferred to
the grid can be limited. This results in an increase in dc-link voltage and the fault
ride-through control should be activated. A wind turbine with doubly-fed induction
generator uses the rotor current to detect when the fault ride-through control should
be activated.
• Vdg<Vdg,th. The grid voltage is continuously measured to detect when a voltage dip
occurs. The dip can be caused by a short-circuit and the grid protection control
should be activated to avoid possible distortion of the DN protection.
• f<fmin or f>fmax. When the grid frequency comes outside a pre-defined band the
frequency control will be activated.
There is a hierarchy in the order in which the states are entered. The fault ride-through
control and grid protection control have a higher priority than the frequency control.
126
Therefore, when the DG unit is in its frequency control state it will immediately go to
the fault ride-through or grid protection control mode when the dc-link voltage or grid
voltage exceeds the appropriate limits. This is done to protect the converter.
7.3 Case study
This section presents two case studies that show the performance of the controller
implementation described in the previous section.
7.3.1 Setup
The network shown in Fig. 7.3 is used for the case study. It consists of two 10 kV
networks that are connected by a 150 kV transmission line. The first part consists of
five small synchronous generators, which represent conventional power plants, and two
large loads. The second part consists of a 10 kV DN with fuel cells, micro turbines,
wind turbines with a doubly-fed induction generator, and loads. The wind turbines are
directly connected to the DN, while the fuel cells are connected to a cable. The loads are
connected to the substation by a cable. The micro turbines are connected to the same
cable as the loads. At locations 1 and 2 faults are applied.
2
10kV/150kV
WT
Load 1
Load 2
150kV/10kV
FC
1
Synchronous
Generators
MT
Load 3
Fig. 7.3. Simulation setup showing two distribution networks connected by a 150kV transmission line; faults
are applied at location 1 and 2
7. Implementation of grid support control
127
7.3.2 Models
The five synchronous generators are modelled according to the description in section
6.6. For the fuel cells, wind turbines, and micro turbines one model is used for each.
The output current is multiplied by the appropriate constant to obtain the required total
power. A description of the converter and generator models can be found in appendix B
and C, respectively. The frequency control implementation of the synchronous
generators, fuel cells, and wind turbines is given in section 6.6.
The micro turbine setup is shown in Fig. 7.4. The frequency control is performed in
the same way as for the fuel cell. When the frequency change exceeds a limit value the
output power is increased according to a droop line.
The wind turbine is protected with the fault ride-through control described in section
5.6. The protection of the fuel cell and micro turbine is similar to that of the wind
turbine with permanent magnet generator described in section 5.5.
The models of the transformers and cables that are used can be found in [Pie 04]. All
generators, converters and grid components are modelled in the dq-reference frame
described in appendix E.
Valve
Gas
PM
Generator
Gas
Turbine
Pdroop
KMT
Pset
Converter
Δf
fgrid
fref
Droop controller
Fig. 7.4. Micro turbine setup with frequency controller
7.3.3 Parameters
The most important parameters used in the case studies are given in table 7.1. Other
parameters can be found in table 6.6 and the appendices A, B and C. The total power of
the network is small. This is done to be able to see a significant contribution of the DG
units, without the necessity to model and simulate a large network. The percentage of
DG power is 10%. The droop constants for the DG units are obtained in the same way
as in section 6.6. Again a system droop of 3% is chosen. As the DG units now form
only 10% of the total power instead of 25% as in section 6.6, also the droop constants
are 2.5 times lower than in chapter 6.
128
Table 7.1: Parameters for case study
Parameter
Value
Unit
Parameter
Value
Unit
Pconv
5 × 50
MW
kmt
0.6
Pfc,nom
5.0
MW
kwt
1.0
Pmt,nom
4.8
MW
τfc
15
s
Pwt,nom
Pload1
Pload2
Pload3
kconv
kfc
16.5
185
11.5
5.5
0.7
0.6
MW
MW
MW
MW
-
K
R
KFC
KMT
KWT
1⋅1012
1⋅107
1.1⋅107
1.1⋅107
1.2⋅107
W/rad⋅s-1
W/rad⋅s-1
W/Hz
W/Hz
W/Hz
7.3.4 Results case 1
Two events occur during the simulation. The first is that at t = 5 s a short-circuit occurs
at the end of the distribution feeder with the micro turbines and the load (location 1).
The fault is assumed to clear automatically after 0.2 s. The second event occurs at t = 15
s, when one of the five synchronous generators is suddenly disconnected (location 2),
resulting in a loss of generation of ~20%.
Fig. 7.5a and b show the grid frequency and the voltage at the micro turbine
terminals during the two events. The short-circuit results in a small decrease in
frequency, whereas the loss of the synchronous generators results in a much larger
frequency drop. Due to the short-circuit the voltage at the micro turbine terminals drops
almost to zero, as can be seen in Fig. 7.5b. The loss of the synchronous generator does
not affect the voltage.
1.5
50.1
Voltage [pu]
Frequency [Hz]
50
49.9
49.8
1
0.5
49.7
49.6
0
20
40
time [s]
60
80
0
0
20
40
time [s]
60
80
(a)
(b)
Fig. 7.5. Response to different faults: (a) grid frequency; (b) voltage at micro turbine terminals; (short-circuit
in distribution network at t = 5 s; disconnection of a large synchronous generator at t = 15 s)
7. Implementation of grid support control
129
1.1
7
1
6
0.9
5
Current [kA]
Current [pu]
The micro turbine detects the short-circuit as a voltage dip at its terminals. Because
of the reduced voltage the output power of the converter will be limited. This results in
an increase in dc-link voltage and the converter controller goes to its ‘fault ride-through
& grid protection control’ state. The ‘grid protection control’ operates the micro turbine
at its nominal current during the fault, as there is no chance that the DG unit will
prevent the proper operation of the DN protection. Fig. 7.6a shows that the micro
turbine current is indeed 1 p.u.. The current through the circuit breaker is shown in Fig.
7.6b. There is almost no difference between the current with micro turbine (solid line)
and without micro turbine (dashed line).
Due to the current limitation the dc-link current increases, as shown in Fig. 7.7a. The
protection technique described in section 6.5 is applied to limit the dc-link voltage. As
the protection limits the power of the micro turbine, it will speed up. Because of the
short duration of the voltage dip and the high inertia constant of the micro turbine the
speed increase is limited, as can be seen in Fig. 7.7b.
0.8
0.7
4
3
0.6
2
0.5
1
0.4
4
4.5
5
time [s]
5.5
0
4
6
4.5
5
time [s]
5.5
6
(a)
(b)
Fig. 7.6. Response to short-circuit at t = 5 s: (a) output current of micro turbine; (b) current through circuitbreaker
1.15
1.02
Rotational speed [pu]
Voltage [pu]
1.1
1.05
1
1.01
1.00
0.95
0.9
4
4.5
5
time [s]
5.5
6
0.99
4
4.5
5
time [s]
5.5
6
(a)
(b)
Fig. 7.7. Response of micro turbine to short-circuit at t = 5 s: (a) dc-link voltage of micro turbine converter;
(b) rotational speed of micro turbine (b)
130
The second event occurs at t = 15 s when one of the five synchronous generators is
disconnected. The loss of ~20% of the total generation, results in a significant frequency
drop, as shown in Fig. 7.5a. The frequency drop is detected by the DG units, which go
to their frequency control state. The output power of the fuel cell, the micro turbine, and
the wind turbine are shown in Fig. 7.8a, b, and c respectively. The fuel cell power
increases slowly, because of the reformer. It is compensated by the wind turbine, which
uses its kinetic energy. The power of all DG units together is shown in Fig. 7.8d. The
figure shows that also after the occurrence of the short-circuit at t = 5 s the frequency
control is activated, because of the frequency drop caused by the short-circuit. The
frequency deviation, and therefore the contribution of the DG units, is limited. The
synchronous machines bring the frequency back to 50 Hz after the disturbance. This
takes about 5 s. After t = 15 s a much larger increase in power can be noted.
The results show that the DG units with grid support control can handle different
events. They ride through a voltage dip and limit their current to avoid disturbance of
protection (micro turbine), followed by a contribution to frequency control.
6
5
4
4
Power [MW]
Power [MW]
5
3
3
2
2
1
1
0
0
20
40
time [s]
60
0
0
80
20
(a)
40
time [s]
60
80
(b)
20
26
25
18
Power [MW]
Power [MW]
24
16
14
23
22
21
20
12
19
10
0
20
40
time [s]
60
80
18
0
20
40
time [s]
60
80
(c)
(d)
Fig. 7.8. Response of DG unit output power to different faults: (a) fuel cell; (b) micro turbine; (c) wind
turbine; (d) sum of all DG units (short-circuit in distribution network at t = 5 s; disconnection of a large
synchronous generator at t = 15 s)
7. Implementation of grid support control
131
7.3.5 Results case 2
In the second case the order of the two events is reversed. First, at t = 5 s the
synchronous generator is disconnected, resulting in a change in frequency, and one
second later a short-circuit occurs. The goal of this case is to show that the grid support
control goes from its frequency control state to its fault ride-through state. Fig. 7.9a
shows the output power of the micro turbine. After the synchronous machine is
disconnected at t = 5 s, the power starts increasing. At t = 6 s a short-circuit occurs and
the micro turbine power is reduced, due to the current limitation in the converter
control. An increase in dc-link voltage is the result, as shown in Fig. 7.9b. It is properly
limited by the fault ride-through control however.
5
1.15
4
1.1
Voltage [pu]
Power [MW]
6
3
1.05
2
1
1
0.95
0
5
5.5
6
time [s]
6.5
7
0.9
5
5.5
6
time [s]
6.5
7
(a)
(b)
Fig. 7.9. Response to different faults: (a) micro turbine output power; (b) micro turbine dc-link voltage;
(disconnection of synchronous generator at t = 5 s followed by short-circuit at t = 6 s)
7.4 Discussion and conclusion
This chapter investigated whether the different grid support control strategies derived in
the previous chapters can be combined in one DG unit. An overall grid support
controller has been proposed and a state diagram is derived that can be used to achieve
the appropriate control in each situation. This control works almost autonomously. Only
the grid voltage at the DG unit terminal needs to be measured.
The grid support controller can be implemented relatively easy. It requires in most
cases only adaptation of the control software, and in some cases it can require some
additional measurement equipment. This implies that the proposed control can be
implemented at low cost.
This chapter focused mainly on the fault ride-through and the frequency control
support of DG units. Active damping and voltage control have not been considered in
132
this chapter but can easily be added to the overall grid support controller. They might
require overrating of the converter however, implying some additional investment costs.
Besides these investments related to the overrating of the converter, the main
obstacles for implementation of the grid support control are international standards and
grid-connection requirements of system operators which in most cases do not allow grid
support by the DG units.
Chapter 8
Conclusions and recommendations
8.1 Conclusions
The objective of this thesis is to investigate if and how the power electronic converters
(PECs) of DG units can be used to solve some of the problems caused by the
introduction of DG. It has been shown that the DG units are able to solve a number of
problems or at least mitigate them:
• By implementing an active damping control loop on PECs they can contribute to
the damping of harmonics and resonances in the network.
• By controlling their (re-)active power, possibly in combination with overrating of
the converter, curtailment of the active power and the use of a variable inductance
the DG units can compensate a part of the voltage change they cause. In this way
they can increase the maximum allowable DG penetration.
• DG units can ride through grid faults, and minimise the chance on causing
malfunctioning of the network protection. They can thus support the grid (voltage)
during the fault.
• Although most DG unit types are not able to contribute to frequency control on
their own, a combination of different DG unit types can contribute to the
conventional frequency control.
In this way a multi-functional DG unit is obtained that can autonomously support the
grid in several ways. The general conclusion will be split up in more specific
conclusions for each of the issues that were considered.
The first two chapters provided an introduction to the thesis. Chapter 2 explained the
basic principles of PECs. It concluded that for frequencies far enough below the
bandwidth of the current controller a voltage source converter (VSC), which is the type
of converter that is used by most DG units, can be considered as a controlled current
source. It was further shown that the behaviour of another type of converter, a current
134
source converter (CSC), generally is the same as a VSC, as long as the voltage control
of the CSC is fast enough. The results of this thesis, which are obtained for a VSC, can
therefore also be applied to a CSC.
Detailed simulation of power electronic converters, taking into account the
switching of all individual semiconductors, is a time-consuming process. Therefore in
this thesis reduced models have been used for simulation of the converters, except in
section 3.3.3. Chapter 2 concluded, with reference to appendix F, that for frequency
below half the switching frequency reduced models of the converters can be used.
Damping of harmonics – Introduction of DG results in an increase of the capacitance in
the grid. Due to this increase there is a risk on harmonics and resonances, as the
capacitance forms resonance circuits with the grid inductance. To avoid resonances and
a high level of harmonic distortion, there should be enough damping in the grid. In
passive grids the damping is obtained from the resistance of the loads and lines. Chapter
3 investigated the influence of DG unit converters on the damping of the harmonics and
resonances. It concluded that the contribution is limited. Some types of converter even
reduce the damping. They have a current reference waveform that is a copy of the grid
voltage. This gives these converters a negative incremental impedance, and thus a
negative damping.
Chapter 3 showed that it is possible to implement an additional control loop on the
DG unit converter which gives the output impedance of the converter a resistive
behaviour for a large frequency range. In this way the damping in the network can be
increased and thus harmonics and resonances can be mitigated. Due to the active
damping controller the voltage and current of the converter will increase. This limits the
maximum damping contribution of the converter. Harmonics at the resonance frequency
of the grid can be compensated easily. A 90% reduction requires only a ~10% increase
in current and voltage (for a converter with a rated power of 1% of the short-circuit
power of the grid). Harmonics at three times the resonance frequency require a ~80%
increase in current and a ~180 increase in voltage however, to obtain a reduction of
90%. This implies that harmonics at the resonance frequency, which cause the largest
problems, can be most easily damped.
The proposed active damping controller and the analysis how large its contribution
to damping can be in a practical network are the main contributions of chapter 3.
Voltage control – In the connection requirements of most grid operators there is a
maximum on the allowable voltage change caused by DG units. This limits the
maximum amount of DG that can be connected to a network. The DG unit converters
can control the voltage to (partly) compensate the voltage change they cause. In this
8. Conclusions and recommendations
135
way a higher penetration can be allowed. Chapter 4 investigated how effective the
voltage control of DG unit converters can be. Reactive compensation showed to be of
limited effect because of the low inductance in most distribution networks. Converter
overrating, generation curtailment and the use of a variable inductance were proposed as
solutions to partially overcome these limitations.
An approach has been presented to determine how the maximum allowable DG unit
penetration can be determined, and how it can be increased. Due to the active power
injection, DG units cause an increase in voltage. The voltage increase offers the
possibility to increase the reactive power consumption, which will reduce the voltage
again. Using this reactive power to lower the voltage, increases the maximum allowable
penetration. Especially in networks with a high X/R ratio a significantly higher
penetration of DG can be allowed. An example showed that in a network with an X/R
ratio of 0.75 already a 40% higher penetration level can be allowed. For networks with a
low X/R ratio generation curtailment and the use of a variable inductance offer good
possibilities to increase the DG unit penetration. An example for the rural network
showed that a 30% curtailment results in a doubling of the allowable DG power.
Overrating was not very effective in this case. An example for the Testnet (which has a
two times larger X/R ratio) showed that with an 8% curtailment or a 10% overrating the
allowable amount of DG can be doubled already.
The main contribution of chapter 4 is the approach to determine the maximum
penetration level of DG units that use their reactive power margin to minimise the
voltage change they cause. Another contribution is the proposed variable inductance.
Ride-through and grid support - Most grid operators require the disconnection of DG
units when faults occur in the network. One reason for this requirement is that they fear
that DG units disturb the classical protection schemes that are applied. It was shown in
chapter 5 that power electronic interfaced DG units do not necessarily disturb the
protection schemes, as they do not supply large short-circuit currents.
Disconnection of power electronic interfaced DG is thus not necessary, generally.
The units can then be used to support the grid (voltage) during the fault. The duration of
voltage dips is generally less than 1 s. Overloading of a converter will mostly be
allowable for this short period. A combination of DG units and a variable inductance
showed to be able to limit the detrimental effect of voltage dips.
Wind turbines with a doubly-fed induction generator are rather sensitive to voltage
dips. Some special measures are proposed to protect them. The key of the technique is
to limit the high currents in the rotor circuit with a set of resistors, without
disconnecting the converter from the rotor or the grid. The wind turbine can resume
normal operation when the voltage and current oscillations have decayed enough
136
(generally within a few hundred milliseconds). In this way the turbine stays
synchronised and it can supply reactive power to the grid during a voltage dip.
For the other types of DG units it is not difficult to let them ride through grid faults.
Control strategies have been derived to achieve a correct behaviour.
The main contributions of chapter 5 are the proposed protection techniques for
variable speed wind turbines (especially those with doubly-fed induction generator).
Frequency control - In order to be able to support frequency control, DG units should
have fast controllable power or stored energy and they should be able to increase their
output power on command. A number of categories have been defined for DG units,
with respect to their ability to contribute to inertial response and primary frequency
control. DG units that have kinetic energy available, such as wind turbines and micro
turbines, provide the inertial response. Although most individual DG units do not fulfil
both requirements, chapter 6 concluded that a combination of different DG unit types
can be used to contribute to frequency control. The primary frequency control is
performed by the DG units that are driven by a controllable power source, such as fuel
cells and micro turbines. Requirements have been derived which can be used to
determine the percentage of each of the DG unit types (or groups of types) that is
required to obtain a good overall response.
In the Netherlands a target of 6 GW of installed wind power has been set. An
example showed that for fuel cells operating at a power margin of 0.5, 1.6 GW of fuel
cell power is needed to provide the primary frequency control support for these wind
turbines. In case of a margin of 0.75 less than 1 GW is needed. A case study has been
performed on a network with wind turbines and fuel cells. The wind turbines made up
21% of the total installed power and the fuel cells 8%. The simulation results show that
with this mix of DG units frequency control can be supported.
The main contributions of chapter 6 are the idea to use the kinetic energy stored in
the rotating mass of wind and micro turbines to support frequency control, the proposed
controller implementations, and the structured analysis of the required percentages of
each of the types of DG unit.
Grid support control - Chapter 7 showed that the different grid support control
strategies can be combined in one DG unit. An overall grid support controller has been
proposed and a state diagram is derived that can be used to achieve the appropriate
control in each situation. The control works almost autonomously. Only the grid voltage
at the DG unit terminal needs to be measured. It was shown in two case studies that the
control handles the different events correctly. The control can be implemented at low
cost as it only requires some adaptation of the control software.
8. Conclusions and recommendations
137
The overall grid support controller proposed in chapter 7 forms the main
contribution of this chapter.
8.2 Recommendations
From the results of this thesis a number of recommendations for further research can be
obtained. First three important general recommendations are given:
• One of the limitations for the grid support by the DG unit is the nominal current of
the converter. For most converters it is possible to operate them at a higher current
for a short period. The maximum allowable overloading (in magnitude and time) of
a converter will depend on the specific converter design. An economical trade-off
can be made between the cost of overloading and the economical value of the
additional margin, which for example can be used for voltage control or active
damping.
• The way of operation of the DG unit converters proposed in this thesis sometimes
conflicts with international standards and grid-connection requirements of system
operators. To allow grid support the standards and requirements have to be
changed.
• This thesis focused on the use of DG unit converters for grid support. Also many
loads are connected to the grid with a PEC. Some of the control strategies proposed
in this thesis can also be implemented in load converters.
Some more specific recommendations for each chapter are given below.
Damping of harmonics – In chapter 3 only networks with a single converter have been
considered. In principle the results can be extended to a network with more converters,
by adding up the emulated conductance of each converter. In practice interaction
between the converters can occur however. It has to be investigated whether this causes
problems. Only single-phase systems have been considered. It should be investigated
whether the results can be extended to three-phase systems.
Voltage control – Chapter 4 proposed several methods to increase the voltage control
capability of the converter. A methodology should be developed to determine in each
practical case the most cost-effective solution.
Each DG unit is assumed to compensate only the voltage change that it causes itself.
When a large number of DG units are used, one converter might be able to compensate
a larger voltage change than another converter, for example because it has a larger
138
margin for reactive power. It should be investigated how the contribution to the
compensation could be spread in an optimal way amongst a number of DG units.
Different implementations are possible for the variable inductance. In this thesis a
device with two anti-parallel thyristors was used. These thyristors result in a significant
harmonic distortion. It should be investigated how the variable inductance can be
implemented in another way.
Ride-through and grid support –Chapter 5 stated that in case of power electronic
interfaced DG units disturbance of protection can be avoided in most cases, because the
converters can limit their current during a fault. The issue requires more research
however, to determine in which cases and under which conditions disturbance of
protection can occur.
It has been shown that it is possible to let a wind turbine with a doubly-fed induction
generator ride through a fault. When the dip is cleared the induction generator will
absorb a large amount of reactive power from the grid. It has to be studied how this
affects the stability of the grid and if it is possible to limit the amount of reactive power
that is absorbed.
Frequency control –The simulations in chapter 6 have been done with rather detailed
models. More simple models can be derived however, that correctly represent the
behaviour of the DG units during their contribution to frequency control. With these
simplified models the response of a much larger network with a large number of DG
units can be simulated.
When a large number of DG units are used, a good cooperation between the DG
units might become problematic. This issue requires more attention. A challenging issue
will especially be how the responses of a large number of slow DG unit types (for
example fuel cells) and a large number of fast DG unit types (for example wind
turbines) can be matched such that they exactly compensate each other.
Another important issue is how secondary frequency control can be implemented
when a large number of DG units are connected to the grid.
Grid support control – The case studies in chapter 7 have been done with one fuel cell,
one micro turbine and one wind turbine. When a large number of DG units are
connected to the network, some form of communication might be necessary. This
communication has not to be real-time, but for example setpoints for the frequency
control or the appropriate behaviour to avoid disturbance of protection might depend on
the number and type of DG units that are connected. When there are large changes in
the number of DG units it might be necessary to change the setpoints.
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Appendix A
Network model description
For the case studies that are done in this thesis simplified models of an electricity
network are used. The networks will be described shortly in this appendix.
A.1 Urban network
The Nuon ‘Testnet’ is a 10kV cable distribution network in a residential area in
Lelystad, The Netherlands, and it can be characterised as a strong MV network. It
consists of a MV distribution substation with a number of radial feeders. A simplified
layout of the network is shown in Fig. A.1. Only the feeders that are used in this thesis
are shown.
1
Transmission
Grid
Saturation
coils
CHP
150kV/10kV
Feeder A
2
3
Feeder B
4
Feeder C
Wind
turbine
Fig. A.1. Schematic layout of 10 kV ‘Testnet’ cable network
The 10 kV substation is connected with the 150 kV HV transmission network by a 47
MVA transformer. The feeders are connected to the substation by a series reactor to
limit the short-circuit current. The total load of the Testnet is about 8 MW and 4 MVAr.
146
Three small wind turbines with a total installed capacity of about 1.5 MW are connected
to feeder C. They are modelled as one equivalent turbine. Feeder A has a CHP plant of
about 2.5 MW. The network is rather lightly loaded and can be considered as a ‘strong’
network.
When the network is used, it is modelled as a Thévenin equivalent circuit, with the
impedance given by the short-circuit impedance of the node under consideration. The
parameters of the four nodes that are used are given in table A.1.
Table A.1. Parameters of the Testnet
Node
Ssc [MW]
Xsc/Rsc
1
2
3
4
320
105
60
50
45
1.25
0.75
0.75
A.2 Rural network
The Maarhuizen network is an extensive rural 10 kV cable network in the north of the
Netherlands. It can be characterised as a weak MV network. It is fed from a 110 kV
transmission network by 3 parallel 30 MVA transformers. One feeder is considered in
the studies. Three wind turbines with a total rated power of 1.6 MW are connected to
this network. The feeder has a high impedance. In some cases this results in large
voltage deviations. The layout of the network is shown in Fig. A.2. The short-circuit
impedance at the three nodes that have been used is given in table A.2. When the
network is used, it is modelled as a Thévenin equivalent circuit, with the impedance
given by the short-circuit impedance of the node under consideration.
1
Transmission
Grid
110kV/10kV
2
3
Wind
turbine
Fig. A.2. Layout of a part of the Maarhuizen 10 kV rural cable network
Appendix A. Network model description
147
Table A.2. Parameters of the rural network
Node
Ssc [MW]
Xsc/Rsc
1
2
3
153
103
21
41
2.20
0.35
A.3 Low-voltage network
The low-voltage network in Vroonermeer-Zuid, a suburb of Alkmaar, is a typical 400 V
network with a large fraction of DG (solar cells). The maximum power feedback from
the PV generators in the area is planned to be 36 MW [Ens 04]. The complete network is
still under development and not all PV systems are installed yet. The maximum loading
of the area is around 60 MVA. The individual homes with roof mounted PV arrays are
connected to a number of network sections that are supplied from separate 10 kV/400 V
transformers. The network is of particular interest because severe problems with
harmonic distortion and resonances have been noted in it [Ens 04]. The problems are due
to the low resonance frequencies in the grid, which are due to the high amount of
capacitance. The capacitance is mainly formed by the output capacitance of the power
electronic converters (loads and PV inverters) in the grid.
In this thesis a lumped model of one of the 400 V networks is used. The model is
shown in shown in Fig. A.3. The section has a peak solar generation of 235 kW and an
average load of 26 kW. The grid impedance consists of a resistance Rg and an
inductance Lg which are mainly determined by the transformer and cable impedance.
The capacitance Cl is formed by the parallel connection of the filter capacitance of the
solar inverters and load. The resistance Rl represents the loads in the network. The
parameters are given in table A.3.
Rg
Lg
Vg
Cl
Rl
Fig. A.3. Lumped representation of one 400V feeder of the Low-voltage network
Table A.3 Parameters of the Vroonermeer-Zuid network
Parameter
Value
Unit
Parameter
Value
Unit
Lg
Rg
140
0.1
μH
Ω
Cl
Rl
300
2
μH
Ω
148
Appendix B
Converter model description
This appendix describes the power electronic converter models that have been used.
B.1 Single-phase full-bridge converter
The case studies in chapter 3 are performed with a model of a 5 kW single-phase fullbridge converter switching at 20 kHz. The converter has an LCL-filter, with a resonance
frequency of ~9 kHz. The filter design is based on the procedure described in [Lis 01].
Fig. B.1 shows the complete converter model. The converter has been modelled in the
SimPowerSystems blockset of Matlab. For the full-bridge IGBT-converter the universal
switch block is used. Fig. B.2 shows the structure of the current controller.
Lfc
Lfg
icf
Udc
PWM
vc*
io
vo
Cf
Measurement
Control
iref
Fig. B.1. Model of single-phase converter with LCL filter
kd,f
icf
vo
PLL
vc*
PR
sin
X
2
Iref
io
Fig. B.2. Structure of current controller of single-phase converter with LCL filter
The reference sine wave for the current control is obtained from an internally generated
waveform that is synchronised to the grid voltage with a PLL. This sine wave is
150
multiplied with the rms value of the reference current Iref. The current is controlled with
a PR controller. It uses second-order generalised integrators to achieve zero steady-state
error [Hau 02]. The transfer function of the PR-controller shown in Fig. B.2 is:
K s
G PR (s ) = K p + 2 r 2
(B.1)
s +ω0
The gain of the transfer function becomes infinite at ω0 and thus it can bring the steadystate error at this frequency back to zero. The size of the proportional gain Kp from the
PR controller determines the bandwidth and phase margin of the system, in the same
way as for classical PI-controllers [Lis 06]. In the high-frequency range (above the
bandwidth of the PR-controller) the stability is related to the damping of the LCL-filter.
A feed-forward control loop is used to avoid oscillations in the filter. The parameters
that have been used for the filter and the controller are given in table B.I.
Table B.1 Parameters of single-phase inverter
Parameter
Value
Unit
Parameter
Value
Unit
Pnom
Vnom
fs
Vdc
Cf
5
230
20
600
2
kW
V
kHz
V
μF
Lfc
Lfg
Kp
Kr
kd,f
0.2
0.8
10
10000
10
mH
mH
-
For the comparison in section 3.3.3 the model described above is used. For the other
simulations the PWM-block and the switches are replaced by a controlled voltage
source that is directly controlled by the output of the current controller.
B.2 Three-phase full-bridge converter
The DG units in chapter 4, 5, 6, and 7 are connected to the grid by a three-phase fullbridge IGBT-converter. The converter model is shown in Fig. B.3. The dc-link of the
converter is modelled as a voltage source when the converter is used without DG unit.
The converter uses a first-order filter, with inductance Lf and resistance Rf. The output
current and voltage of the converter are measured and transformed to the dq-reference
frame. The currents are controlled by PI-controllers to get the reference voltage for the
full-bridge. The reference voltages are transformed back to the abc-reference frame. A
triangular-carrier-based PWM circuit converts the reference signals to the on/off signals
for the switches. The structure of the control is shown in Fig. B.4. The reference
currents are obtained from the active and reactive power controllers.
Appendix B. Converter model description
151
Lf
Rf
3-phase
fullbridge
Vdc
6
PWM
Measurement
abc
dq
abc
dq
vdq
*
Control
vdq,meas
abc
dq
idq,meas
Fig. B.3. Model of three-phase full-bridge converter with RL filter
vd,meas
Pref
PI
id,ref
id,meas
Pmeas
iq,meas
Qmeas
Qref
PI
iq,ref
vd*
PI
ωeLf
ωeLf
PI
vq,meas
vq*
Fig. B.4. Scheme of the power and current controller of a three-phase inverter
The remaining part of this section discusses how the controller constants for the current
controller can be obtained. The voltage difference across the filter is:
di
Δvd = R f id + L f ⋅ d + ωe L f iq
dt
(B.2)
diq
Δvq = R f iq + L f ⋅
− ω e L f id
dt
The last terms in the equations cause a cross-coupling of the d- and q-axes. They are
treated as disturbances on the output, as shown in Fig. B.4. The PI controller tracks the
id and iq errors to give Δvd and Δvq respectively. To ensure good tracking of thee
currents, the cross-related flux terms are added to vd and vq to obtain the reference
voltages.
The transfer function of the filter, from voltage to current, is:
1
G (s ) =
(B.3)
Lf s + Rf
Using the Internal Model Control principle [Har 98] to design the controllers yields:
152
K (s ) = K p +
K i α c −1
=
G (s )
s
s
(B.4)
where αc is the bandwidth of the current control loop, Kp is the proportional gain and Ki
is the integral gain of the controller. The gains become [Pet 03]:
K p = α c L f ; Ki = α c R f
(B.5)
Generally some fine-tuning is done to optimise the response.
The converter has an outer control loop that controls the active and reactive power of
the converter. The measured active and reactive power are calculated from:
Pmeas = vd ,meas id ,meas + vq ,meas iq ,meas
(B.6)
Qmeas = vq ,meas id ,meas − vd ,meas iq ,meas
In chapter 5 simulations are presented that are done with a 2 MW converter. The
parameters of this converter are given in table B.2.
Table B.2 Parameters of three-phase inverter
Parameter
Value
Unit
Parameter
Value
Unit
Pnom
Vnom
fs
Vdc
Lf
Rf
2
960
5
1500
0.2
12.5
MW
V
kHz
V
mH
mΩ
Kp,d
Ki,d
Kp,q
Ki,q
Kp,P, Kp,Q
Ki,P, Ki,Q
0.2
12.5
0.1
6.25
0.1
0.001
-
In most cases a ‘reduced model’ of the converter is used, which does not take into
account the modulation and the switching of the IGBTs. Appendix F shows that this
model can be used as long as the frequency of the phenomena that are investigated is
much lower than the switching frequency of the converter. This condition is met in
steady-state situations, but not always during transient phenomena such as short-circuits
and voltage dips. It is shown in [Mor 04] that there are some differences between the
‘full’ and ‘reduced’ model in these situations, but they are limited.
The reduced model is modelled in the dq0-reference frame and simulated in
Simulink. The block diagram of the model is shown in Fig. B.5. The filter block
contains the transfer functions that can be obtained from (B.2). The control block
contains the controller structure shown in Fig. B.4. The reference value for the power,
Pref, is obtained from the DG unit control or from the dc-link control.
Appendix B. Converter model description
153
vdq,grid
idq,grid
filter
vdq
*
Pref
Control
Fig. B.5. Block diagram of three-phase full-bridge converter in dq0-reference frame
B.3 Three-phase back-to-back converter
Introduction - Several types of DG unit use a back-to-back converter, consisting of two
full-bridge IGBT-converters with a dc-link in between. They are modelled according to
the block diagram shown in Fig. B.6. The DG unit and its converter are modelled as one
sub-system. The models are described in appendix C. The 3-phase full bridge converter
model is described in the previous section. It has the task to control the dc-link voltage.
It receives its power setpoint from the dc-link control. The dc-link model is shown in
Fig. B.7. The dc-link control is described in this subsection. The controller design is
based on [Ott 03]. The parameters of the back-to-back converter are given in appendix C,
together with the DG unit parameters.
vgrid
DG unit
+
control
Pdg
dc-link
Pdc,ref
3-phase
full-bridge
converter
igrid
Pconv
Fig. B.6. Block diagram of a model of a DG unit with back-to-back converter in dq0-reference frame
Pdg
1
sCdc
Vdc
dc-link
control
Pdc,ref
Pconv
Fig. B.7. Model of dc-link of back-to-back converter
dc-link control - The dc-link capacitor behaves as an energy storage device. Neglecting
losses, the time derivative of the stored energy equals the difference between the DG
unit power Pdg and the converter power Pconv:
dv 2
1
(B.7)
Cdc dc = Pdg − Pconv
dt
2
This equation is nonlinear with respect to vdc. Therefore a new state-variable is
2
introduced: W = v dc
. Substituting this in (B.7) gives:
154
1 dW
C
= Pdg − Pconv
(B.8)
2 dt
which is linear with respect to W. The physical interpretation of this state-variable
substitution is that the energy is chosen to represent the dc-link characteristics [Ott 03].
The dc-link voltage is assumed to be controlled by the converter. Pconv is written as
vdc⋅idc. The transfer function from idc to W is then:
2
G (s ) = −
(B.9)
sCdc
As this transfer function has a pole in the origin it will be difficult to control it. An inner
feedback loop for active damping is used [Ott 03]:
'
idc = idc
+ GaW
(B.10)
with Ga the active conductance, performing the active damping, and idc’ the reference
current provided by the outer control loop, see Fig. B.8. Substituting (B.10) into (B.8)
gives:
dW
1
'
C dc
= Pdg − vdc idc
− vdc GaW
(B.11)
dt
2
The transfer function from idc’ to W becomes:
2
G ' (s ) = −
(B.12)
sC dc + 2Ga
Using the internal model control principle [Har 98], the following parameters for the PIcontroller can be obtained [Ott 03]:
kp = −
α d Cdc
, ki = −
α d2Cdc
(B.13)
2
When the pole of G’(s) is placed at -αd the following active conductance is obtained:
2
Ga =
α d Cdc
(B.14)
2
The controller is completed by a feed-forward term from Pdg to Pdc,ref’, which improves
the dynamic response of the dc-link controller.
Vdc
iref
u2
PI
2
Vdc,ref
Ga
Pdc,ref
Pdg
Fig. B.8. Model of dc-link control of back-to-back converter
Appendix C
DG unit model description
This appendix describes the DG unit models that are used and gives the used
parameters.
C.1 Fuel cell
In this section the model of the fuel cell system is described. The block diagram of the
model is shown in Fig. C.1. It consists of a reformer, a fuel cell stack, a dc/dc converter,
a dc-link, a three-phase VSC and a controller. The dc/dc converter is modelled with a
fixed transfer ratio between input and output voltage. The dc-link control and the
inverter are described in appendix B. The combined model of the fuel cell, reformer and
its control is shown in Fig. C.2. It is obtained from [Zhu 02].
vgrid
Vdc
Fuel cell stack
+
Reformer
+
Control
Vfc
Ifc
dc-dc
converter
Pdc
dc-link
Pdc,ref
3-phase
full-bridge
converter
igrid
Pconv
Fig. C.1. Fuel cell system block diagram
Reformer - The response of the chemical processes in the reformer is usually slow,
because of the time that is needed to change the chemical reaction parameters after a
change in the flow of reactants. The dynamic response function is modelled as a firstorder transfer function with a time constant Tf.
Fuel cell stack - A model of a SOFC fuel cell is used. The modelling is based on [Kar 03],
[Pad 00] and [Zhu 02]. The overall fuel cell reaction is
156
1
H 2 + O2 → H 2O
(C.1)
2
The stoichiometric ratio of hydrogen to oxygen is 2 to 1. The fuel cell is controlled in
such a way that there is always an oxygen excess, to let hydrogen react with oxygen
more completely. In [Zhu 02] a ratio of 1.145 is proposed.
U max
2K r
Pref
I rfc
1
1 + Te s
Limit
V fcin
q Hin2
I rfc
Kr
2K r
U min
2K r
q Hin2
2K r
U opt
1
1+ Tf s
1
q Hin2
r
qOin2
τ H 2O
1 KH2
1 K H 2O
1 K O2
1+τ H2 s
1 + τ H 2O s
1 + τ O2 s
pH 2
p O2
p H 2O
1/ 2
⎛
RT ⎛⎜ p H 2 pO2 ⎞⎟ ⎞⎟
N 0 ⎜ E0 +
ln
⎜
2 F ⎜ p H 2O ⎟ ⎟
⎝
⎠⎠
⎝
V fc
Fig. C.2. SOFC schematic diagram [Zhu 02]
The anode is assumed to be supplied with H2 only and the cathode with O2 only. The
potential difference between the anode and cathode can be calculated with the Nernst
equation, minus the voltage drop due to ohmic polarisation
⎛
⎛
⎛ RT ⎞ ⎜ p H 2 pO2
⎜
V fc = N 0 ⎜ E0 + ⎜
⎟ ln⎜
⎜
⎝ 2 F ⎠ ⎜ pH 2O
⎝
⎝
⎞⎞
⎟ ⎟ − rI
fc
⎟⎟ ⎟⎟
⎠⎠
(C.2)
where pH 2 , pH 2O , pO2 are the partial pressures of H2, H2O and O2 respectively.
An important parameter for a fuel cell is the fuel utilisation Uf. It is defined as the ratio
between the fuel flow that reacts and the input fuel flow. Typically an 80% – 90%
utilisation is used [Zhu 02]. For a certain input hydrogen flow, the demand current of the
fuel cell can then be restricted in the range
Appendix C. DG unit model description
157
0.8q Hin 2
2K r
≤ I fc ≤
0.9q Hin 2
(C.3)
2K r
The optimal utilisation factor (Uopt) is assumed to be 85% and thus [Kar 03]:
q Hin 2 =
2K r
I fc
0.85
(C.4)
The molar flow of hydrogen that reacts is [Pad 00]:
N 0 I fc
= 2 K r I fc
q Hr 2 =
2F
with Kr [kmol/(s⋅A)] defined for modelling purposes.
(C.5)
Model implementation and parameters - Fig. C.1 and Fig. C.2 show the block diagram
of the complete system and of the dynamic model of the SOFC. Parameters of the 100
kW fuel cell that is used are given in table C.1. Parameters of the converter that is used
are given in table C.2
Table C.1 Fuel cell parameters
Parameter
Value
Prate
Pref
T
F
R
E0
N0
Kr (=N0/4F)
Umax
Umin
Uopt
Unit
100
100
273
96.487⋅103
8314
1.18
384
0.996⋅10-6
0.9
0.8
0.85
kW
kW
K
C/kmol
J/(kmol⋅K)
V
kmol/(s⋅A)
-
Parameter
Value
Unit
-4
KH2
KH2O
KO2
8.43⋅10
2.81⋅10-4
2.52⋅10-3
26.1
78.3
2.91
0.126
0.8
5
1.145
τH2
τH2O
τO2
r
Te
Tf
rH_O
kmol/(s⋅atm)
kmol/(s⋅atm)
kmol/(s⋅atm)
s
s
s
V
s
s
-
Table C.2 Parameters of back-to-back converter of micro turbine
Parameter
Value
Unit
Parameter
Value
Unit
Parameter
Value
Unit
Pnom
Vconv,nom
Vdc
Cdc
100
400
750
1
kW
V
V
mF
Lconv
Rconv
Kp,conv
Ki,conv
0.1
12.5
0.02
4
mH
Kp,dc
Ki,dc
Ga
7.5⋅10-5
7.5⋅10-3
7.5⋅10-5
-
mΩ
-
158
C.2 Micro turbine
This section describes the micro turbine model. The system, shown in Fig. C.3, consists
of a gas turbine, a permanent magnet generator and a back-to-back converter. The
converter was already described in appendix B. The gas turbine and the permanent
magnet generator are described in this section. The parameters of the permanent magnet
generator and the gas turbine are given in table C.3. The parameters of the 300 kW
converter are given in table C.4.
Gas turbine - The gas turbine consists of a compressor, a combustor and a turbine. A
detailed description of the modelling of the individual parts of the system can be found
in [Nik 05]. In the thesis an approximation is used, that models the gas turbine as a first
order transfer function:
1
G gt (s ) =
(C.6)
τ gt s + 1
In literature the values of τgt vary from tens of milliseconds to tens of seconds.
Fig. C.3. Micro turbine system block diagram
Permanent magnet generator – Using the generator convention, the stator voltage
equations of a synchronous machine are given by:
dψ ds
vds = − Rs ids − ω sψ qs −
ψ ds = Ls ids + Ψ f
dt
with
(C.7)
dψ qs
ψ qs = Ls iqs
vqs = − Rs iqs + ω sψ ds −
dt
The electrical torque Te of the permanent magnet generator is given by [Sch 01]:
Te = 2 piqsΨ f
(C.8)
with p the number of pole pairs. The stator electrical angular velocity is given by
ω s = pω m , with ωm the mechanical angular velocity [rad/s], which can be obtained
from:
dω m 1
= (Tm − Te )
dt
J
(C.9)
Appendix C. DG unit model description
159
with J the inertia constant of the rotor [kg⋅m2] and Tm the mechanical torque [Nm]. The
generator model is based on these three equations.
Control - In order to apply independent control for the two coordinates the influence of
the q-axis on the d-axis-components and vice versa must be eliminated. This can be
done by decoupling the two components, in the way shown in Fig. C.4. With the
decoupling applied, the linear transfer function of ids to vds is:
ids (s )
1
=
(C.10)
vds (s ) Ls s + Rs
The proportional and integral constants for the PI-controller can be obtained as [Pet 03]:
k p = α c Ls , k i = α c R s
(C.11)
with αc is the bandwidth of the current control loop. The angular velocity ωm can be
controlled by Te which is proportional to iqs. The constants for the speed controller are
[Sch 01]:
kp =
2 p 2ψ f
J
, ki =
2 p 2ψ f Rs
(C.12)
JLs
Table C.3 Micro turbine parameters
Parameter
Value
Unit
τgt
1
300
400
3000
0.0022
kW
V
rad/s
Prate
Vs
ωm
Rs
Parameter
Value
Unit
Parameter
Value
Unit
Ls
40
0.06
0.31
0.3
μH
Vs
kgm2
s
Kp,d
Ki,d
Kp,q
Ki,q
0.145
-
Ψf
J
τgt
2.9⋅10-3
0.145
2.9⋅10-3
Ω
Table C.4 Parameters of back-to-back converter of micro turbine
Parameter
Value
Unit
Parameter
Value
Unit
Parameter
Value
Unit
Pnom
Vconv,nom
300
400
kW
V
Lconv
Rconv
0.1
12.5
mH
mΩ
Kp,dc
Ki,dc
7.5⋅10-4
7.5⋅10-2
-
Vdc
Cdc
750
1
V
mF
Kp,conv
Ki,conv
0.02
4
-
Ga
7.5⋅10-4
-
160
0
*
vds
ids,ref
PI
vds,dec
ids,meas
Ls
Ψf
ωm,meas
iqs,meas
2pΨf
ωm,ref
Ls
vqs,dec
Te,meas
PI
PI
vqs
*
Fig. C.4. Converter + control block diagram
C.3 Wind turbine with doubly-fed induction generator
This section presents the model of the wind turbine with Doubly-Fed Induction
Generator (DFIG) that is used. This type of wind turbine has a converter connected to
the rotor windings instead of the stator windings. A block diagram of the model is
shown in Fig. C.5. This section gives first a short description of the aerodynamical and
mechanical (turbine) model, followed by a description of the electrical generator and its
control. The dc-link model and the model of the full-bridge converter are given in
appendix B. The model of the three-winding transformer can be found in [Pie 04].
vs,dq
is,dq
vwind
Wind
turbine
Pwt
Induction
machine
ωm
vr,dq
Three
winding
trafo
Pconv
ir,dq
Converter P
dg
+
control
dc-link
Pdc,ref
3-phase
full-bridge
converter
igrid
iconv
vconv
Fig. C.5. Block diagram of wind turbine with doubly-fed induction generator
Wind turbine model and control - The description of the turbine model will be brief. A
more detailed description can be found in [Pie 04]. A wind model is used to calculate a
realisation of the stochastically changing wind speed. From this the averaged wind
speed over the turbine rotor is determined to obtain the instantaneous aerodynamic
torque, including the variations caused by the passing of the blades through the
Appendix C. DG unit model description
161
inhomogeneous wind field over the rotor area. The effect of wind speed variations on
the aerodynamic torque is determined by a Cp(λ) curve.
The wind turbine model consists of sub-models for the aerodynamic behaviour of
the rotor, the rotating mechanical system (drive-train), the tower, power limitation by
pitch control and the electrical generator and control. The mechanical model for turbine
rotor, low and high-speed shaft, gearbox and generator rotor is a two-mass spring and
damper model. The tower model consists of a mass-spring-damper model for the
translation of the tower top in two directions: front-aft and sideways.
Since electrical and mechanical dynamics in a wind turbine are of different time
scales (i.e. the electrical dynamics are much faster than the mechanical dynamics), the
whole system can be controlled in a cascade structure. The fast electrical dynamics can
be controlled in an inner loop and a speed controller can be added in a much slower
outer loop. The speed controller of the wind turbine was described in chapter 2 already.
The control of the electrical generator will be described below.
Generator model – The induction generator is represented by a 5th order model in the dq
reference frame. Using the generator convention, the following set of equations results:
dψ ds
vds = − Rs ids − ω sψ qs +
dt
ψ ds = −(Ls + Lms )ids − Midr
dψ qs
vqs = − Rs iqs + ω sψ ds +
ψ
qs = −(Ls + Lms )iqs − Miqr
dt
with
(C.13)
ψ dr = −(Lr + Lmr )idr − Mids
dψ dr
vdr = − Rr idr − ωrψ qr +
dt
ψ qr = −(Lr + Lmr )iqr − Miqs
dψ qr
vqr = − Rr iqr + ωrψ dr +
dt
with M = Lms Lmr the mutual inductance.
The electrical angular velocity of the rotor, ωr, is:
ω r = ω s − pω m
(C.14)
with p the number of pole pairs [-] and ωm the mechanical angular velocity [rad/s]. The
electrical torque of the generator is given by:
Te = p ψ dr iqs − ψ qr ids
(C.15)
(
)
The rotational speed of the generator is given as:
dω m 1
= (Tm − Te )
dt
J
The active and reactive power delivered by the stator are given by:
Ps = vds ids + vqs iqs
(C.16)
(C.17)
162
Qs = vqs ids − vds iqs
(C.18)
The model of the induction generator that has been used is based on (C.13) - (C.18).
Generator control – The structure of the control of the induction generator is shown in
Fig. C.6. Since the stator flux is almost fixed to the stator voltage, it is practically
constant. This implies that the derivative of the stator flux and of the stator magnetizing
current are close to zero, and can be neglected [Pen 96], [Pet 03]. The voltage equations of
the rotor which have previously been given in (C.13) can then be written as:
di
vdr = − Rr idr − Lr dr − ω rψ qr
dt
(C.19)
diqr
+ ω rψ dr
vqr = − Rr iqr − Lr
dt
This equation is comparable to equation (B.2) for the three-phase full-bridge converter
in appendix B.2. The PI-controller parameters for the generator control can be obtained
in the same way as described in appendix B.2.
A synchronously rotating dq reference frame with the direct d-axis oriented along
the stator flux vector position is used to control the generator. Due to the chosen
reference frame, ψqs and vds are zero. Therefore the reactive power and the active power
delivered by the stator can be written as:
⎛ Lm ⎞
⎟⎟iqr
Ps = vqs iqs = vqs ⎜⎜
⎝ Lr + Lm ⎠
Qs = vqs ids = ω s (− (Ls + Lm )ids − Lm idr )ids
(C.20)
(C.21)
As the stator current is equal to the supply current, it can be assumed that it is constant.
The reactive power is then proportional to the direct component of the rotor current idr.
The active power, and thus the speed, can be controlled by iqr.
It is assumed that the current controller is much faster than the speed controller. The
electrical torque is then Te=Te,ref. The reference torque is set to:
Te,ref = Te',ref − Baω m
(C.22)
where Ba is an “active damping torque” [Pet 03]. The transfer function from rotational
speed to electrical torque becomes now:
1
Gs (s ) =
(C.23)
Js + Ba
Using again the IMC method, the following gains of the controller are obtained [Pet 03]:
k ps = α s J , k is = α s Ba
(C.24)
Appendix C. DG unit model description
163
where αs is the desired closed-loop bandwidth of the speed controller. When Ba is
chosen to be Ba=Jαs, changes in the mechanical torque are damped with the same time
constant as the bandwidth of the speed control loop [Pet 03].
v*dr
PI
0
Qmeas
PI
ψqr
idr
ωr
Te
ψdr
iqr
Te,ref
PI
PI
vqr
*
Fig. C.6. Converter + control block diagram
Converter – A DFIG has a back-to-back converter connected between its rotor terminals
and the grid. The generator side converter is used to control the rotor currents of the
machine, according to (B.2) - (B.5) and (C.19), while the grid side converter controls
the DC-link voltage. The converter model is described in appendix B.3.
Parameters – The parameters that have been used for the wind turbine with doubly-fed
induction generator are given in table C.5. The parameters for the converter model are
given in table C.6.
Table C.5 Doubly-fed induction generator machine parameters
Parameter
Value
Unit
Parameter
Value
Unit
Parameter
Value
Unit
Pnom
Vs,nom
Vr,nom
2.75
960
670
1000
3
240
4.55
MW
V
V
rad/s
kgm2
mH
Lmr
Ls
Lr
Rs
Rr
Kp,d
Ki,d
18.2
0.118
0.31
1.2
5.2
0.02
3.2
mH
mH
mH
mΩ
mΩ
-
Kp,q
Ki,q
Kp,s
Ki,s
Kp,Q
Ki,Q
0.2
0.32
25
155
0.00032
0.0032
-
ωm
p
J
Lms
164
Table C.6 Parameters of back-to-back converter of doubly-fed induction generator
Parameter
Value
Unit
Parameter
Value
Unit
Parameter
Value
Unit
Pnom
Vconv,nom
Vdc
Cdc
750
670
1100
1
kW
V
V
mF
Lconv
Rconv
Kp,conv
Ki,conv
0.1
12.5
0.01
0.1
mH
Kp,dc
Ki,dc
Ga
2.5⋅10-4
2.5⋅10-2
2.5⋅10-4
-
mΩ
-
C.4 Wind turbine with synchronous generator and full-size converter
The fourth type of DG unit that is used is a variable speed wind turbine with a
synchronous generator and a full-size converter. The variable speed wind turbine is
equal to that of the model described in section C.3, for a wind turbine with a DFIG. A
permanent magnet generator is used and the generator and converter model are equal to
that of the micro turbine described in section C2. The parameters for the permanent
magnet generator are given in table C.7. The parameters of the 1.5 MW converter are
given in table C.8.
Table C.7 Permanent magnet synchronous machine parameters
Parameter
Prate
Vs
ωm
p
Value
1.5
960
1.7
60
Unit
MW
V
rad/s
-
Parameter
J
Ψf
Ls
Rs
Value
240
9.8
1.3
0.014
Unit
2
kgm
Vs
mH
Ω
Parameter
Value
Unit
Kp,d
Ki,d
Kp,q
Ki,q
6.8⋅10-4
3.4⋅10-3
1.4⋅10-3
2.9⋅10-4
-
Table C.8 Parameters of back-to-back converter of permanent magnet generator
Parameter
Value
Unit
Parameter
Value
Unit
Parameter
Value
Unit
Pnom
Vconv,nom
Vdc
Cdc
1.5
960
1750
3
MW
V
V
mF
Lconv
Rconv
Kp,conv
Ki,conv
0.1
12.5
0.01
0.1
mH
Kp,dc
Ki,dc
2.5⋅10-4
2.5⋅10-2
-
mΩ
-
Appendix D
Short-circuit
machine
response
of
induction
This appendix determines the response of an induction machine to a symmetrical shortcircuit at its stator terminals. Based on this analysis, section 5.6 analyses the response of
a wind turbine with doubly-fed induction generator to a voltage dip. The analysis in this
appendix is based on the analyses in [Kov 59].
For the analysis a space-vector description is used. In a synchronously rotating
reference frame the equations describing an induction machine are [Kov 59]:
dψ s
+ jω s ψ s
dt
(D.1)
dψ r
+ j (ω s − ω r )ψ r
dt
(D.2)
v s = Rs i s +
v r = Rr ir +
ψ s = Ls is + Lm i r
(D.3)
ψ r = Lm is + Lr i r
(D.4)
In these equations all parameters are reduced to the stator side. The equations can also
be written in a fixed reference frame (fixed to the stator of the machine). In that case ωs
is zero. Based on these equations the equivalent circuit of the induction machine shown
in Fig. D.1 can be obtained. It can be used for transient analysis of an induction
machine.
is
vs
Rs
jωsψs
Lsσ
Lrσ
j(ωs-ωr)ψs
Rr
Lm
ir
vr
Fig. D.1. Equivalent circuit of induction machine for transient analysis
Based on (D.3) and (D.4) the currents can be written as a function of the fluxes:
166
1
is =
Ls −
ir = −
Lm
Ls
ψs −
L2m
Lm
Lr
1
Ls −
Lr
1
Lr −
In these equations the term Ls −
ψs +
L2m
Ls
L2m
Lr
ψr
1
L2
Lr − m
Ls
ψr
(D.5)
(D.6)
L2m
is similar to the transient inductance of a
Ls
synchronous machine [Kov 59]. It will be denoted as L's . Knowing that Ls=Lsσ+Lm and
Lr=Lrσ+Lm, the transient stator inductance can be written as:
L's = Lsσ +
Lrσ L m
Lrσ + L m
Similarly the transient rotor inductance can be introduced as:
L L
L'r = Lrσ + sσ m
L sσ + L m
(D.7)
(D.8)
The equations can further be simplified by introducing the stator and rotor coupling
factors:
ks =
Lm
Ls
(D.9)
kr =
Lm
Lr
(D.10)
L2m
Ls L r
(D.11)
And the leakage factor:
σ = 1−
With the inductances and coupling factors the current equations (D.5) and (D.6)
become:
is =
ψs
L's
i r = −k s
− kr
ψs
L'r
ψr
+
L's
ψr
L'r
(D.12)
(D.13)
Appendix D. Short-circuit response of induction machine
167
The equations that have been obtained so far will be used to derive an approximate
equation for the maximum short-circuit current supplied by an induction machine. The
rotational speed of the rotor differs only a few percent from the grid frequency and is
assumed to stay constant during a transient event. This introduces only a limited error
[Kov 59].
The voltage equations of an induction machine are given by (D.1) and (D.2).
Solving these differential equations will give a particular solution, which give the
current in a steady-state situation. The general solution can be obtained by adding the
solution of the homogeneous differential equation to the steady-state currents. The
solution of the homogeneous equation gives the ‘free currents’, which separately satisfy
the homogenous differential equation. The solution of the homogeneous equation can be
obtained by setting the stator and rotor voltage to zero.
During the occurrence of a short-circuit the currents go from the original stationary
state to a new stationary state. The continuity of the transition is assured by the ‘free
currents’. The ‘free currents’ that occur during this compensation process can be
investigated separately from the stationary currents, as if both stator and rotor are shortcircuited [Kov 59]. The ‘free currents’ of an induction machine that rotates approximately
synchronous, are similar to those in a synchronous machine. During the transition from
one stationary state to another the following currents are present in the induction
machine:
1. Stationary currents with frequency fs (stator) and fr=s⋅fs (rotor)
2. Stator dc-current. It can be considered as a space-vector with a fixed position. As
the rotor rotates with ωm=(1-s)ωs (assuming one pole-pair) with respect to this fixed
space-vector, the rotor adds an alternating current with f=(1-s)ωs to this dc-current.
3. Rotor dc-current. This current rotates with the rotor and creates the alternating
current in the stator.
The dc-components are no real dc-currents. In reality the space-vector rotates slowly
and it is damped exponentially. The space-vector rotates faster for a larger stator and
rotor resistance. The time-constant for the damping of the dc-components in stator and
rotor are given by [Kov 59]:
Ts' =
L's
Rs
(D.14)
Tr' =
L'r
Rr
(D.15)
The currents and fluxes in the machine during a short-circuit are determined in two
steps. In the first step the stator and rotor resistance are neglected. The current- and
168
flux-components that are obtained are considered as the start-values. In the next step the
components are multiplied by a damping factor, which is based on the resistance and
leakage inductance of the machine. The results that are obtained in this way have an
error of 10 - 20% [Kov 59].
The short-circuit current of an idle running machine will be determined. Neglecting
the mechanical losses the machine rotates at the synchronous rotational speed ωs. The
stator resistance can be neglected in steady-state. Before the occurrence of the shortcircuit the rotor current is zero: Ir=0. The stator current is:
I s e jω s t =
V s e jω s t V s e j ω s t
=
jX s
jω s Ls
(D.16)
the stator flux is:
V s e jω s t
jω s
(D.17)
Lm Vs e jω st
V e jω s t
= ks s
L s jω s
jω s
(D.18)
Ψs e jω st = I s e jω st Ls =
and the rotor flux is (in a fixed reference frame):
Ψr e jω st = I s e jω st Lm =
At time t = 0 a three-phase short-circuit is assumed to occur at the stator of the machine.
Both the rotor and the stator are short-circuited then. This implies that the flux in both
windings does not change. The stator flux is given by:
ψ s = Ψs ,0 =
2Vs
jω s
(D.19)
The rotor flux has to stay fixed to the rotor winding. As the rotor rotates synchronously
with the angular velocity ωs, also the rotor flux ψr rotates with that angular velocity, as
shown in Fig. D.2. In a fixed reference frame the rotor flux is thus given by:
ψ r = Ψr ,0 = k s
2Vs jω st
e
jω s
(D.20)
At the moment that the short-circuit occurs, the rotor and stator flux ψr and ψs have the
same angle and approximately the same amplitude. The stator flux is fixed to the stator,
but the rotor flux will change with the rotor and after half a period it will be 180° out of
phase and have an opposite direction. The currents in the machine will reach their
maximum value then. They can become very high and are only limited by the leakage
inductances.
Appendix D. Short-circuit response of induction machine
169
ψs=Ψs,0
ψsr
Ψr,0
ωst
vs
Fig. D.2. Induction machine flux vectors during a three-phase short-circuit (with resistance neglected)
The stator short-circuit current can be obtained by substituting (D.19) and (D.20) in
(D.12):
is =
ψs
L's
− kr
ψr
L's
=
ψ s − krψ r
L's
=
2Vs
jω s L's
[1 − k k e ]
r s
jω s t
(D.21)
Writing krks as 1 - σ (see (D.9) - (D.11)) the equation becomes:
is =
2Vs
jω s L's
[1 − (1 − σ )e ]
jω s t
(D.22)
This equation is obtained under the assumption that the stator and rotor resistance can
be neglected, implying that the current is undamped. In reality the current will always
decline.
The first term inside the rectangular brackets of (D.22) represents the dc-component
in the stator current. This current will be damped with the transient time constant Ts' .
The second term represents the ac-component in the stator current, to which a dccomponent in the rotor current belongs. This term will thus be damped with the
transient time constant Tr' . Taking into account these two damping factors, (D.22)
becomes [Kov 59]:
t
⎡ t
− ⎤
2Vs ⎢ − Ts'
jω s t Tr' ⎥
is =
e
− (1 − σ )e e
⎥
jX s' ⎢
⎦
⎣
When the voltage vs has an angle α +
π
2
(D.23)
with respect to stator phase a, at the moment
that the short-circuit occurs, then v s = j 2Vs e jα . The short-circuit current in this phase
is then the projection of the vector is on the a-phase, i.e. its real part:
isa
t
⎡ t
⎤
−
2Vs ⎢ − Ts'
jω s t Tr'
⎥
(
)
(
)
=
−
−
+
e
cos
α
1
σ
e
e
cos
ω
t
α
s
⎥
X s' ⎢
⎣
⎦
The current is shown in Fig. D.3.
(D.24)
170
Although the current-vector does not reach the maximum value exactly at t=T/2, the
current after half a period gives a good approximation of the maximum current [Kov 59].
The maximum current can thus be obtained by substituting t=T/2 in (D.23):
is ,max
T
⎡ T
− ' ⎤
2Vs ⎢ − 2Ts'
2Tr ⎥
=
e
+ (1 − σ )e
⎥
X s' ⎢
⎣
⎦
Fig. D.3. Short-circuit current in one phase of an induction machine
(D.25)
Appendix E
Park transformation
For most simulations in chapter 5, 6 and 7 the Park transformation is used to transform
the models to the dq0 reference frame. As this stationary reference frame is chosen to
rotate with the grid frequency, all voltages and currents in the dq0 reference frame are
constant in steady state situations. Therefore, modelling in the dq0 reference frame is
expected to increase the simulation speed significantly, as a variable step-size
simulation program can apply a large time step during quasi steady-state phenomena.
This is especially useful for the simulations in chapter 6. This appendix describes the
basic properties of the Park transformation and it shows how models in an abc reference
frame can be transformed to the dq0 reference frame.
The Park transformation is instantaneous and can be applied to arbitrary three-phase
time-dependent signals. For θd=ωdt+ϕ, with ωd the angular velocity of the signals that
should be transformed and ϕ the initial angle, the Park transformation is given by:
⎡ xd ⎤
⎡ xa ⎤
⎢ x ⎥ = T (θ ) ⋅ ⎢ x ⎥
dq 0 d
⎢ q⎥
⎢ b⎥
⎢⎣ x0 ⎥⎦
⎢⎣ xc ⎥⎦
[
]
(E.1)
with the Park transformation matrix Tdq0 defined as:
[ Tdq0 (θ d )] =
⎡
⎢ cosθ d
⎢
2⎢
− sin θ d
3⎢
⎢ 1
⎢
⎢⎣
2
2π ⎞ ⎤
2π ⎞
⎛
⎛
cos⎜θ d −
cos⎜θ d +
⎟
⎟⎥
3 ⎠
3 ⎠⎥
⎝
⎝
2π ⎞
2π ⎞⎥
⎛
⎛
− sin ⎜θ d −
⎟ − sin ⎜θ d +
⎟
3
3 ⎠⎥
⎝
⎠
⎝
⎥
1
1
⎥
2
2
⎦⎥
(E.2)
The positive q-axis is defined as leading the positive d-axis by π/2, as shown in Fig. E.1.
Voltages and currents of electrical systems are often given as a set of differential
equations. These differential equations can easily be transformed to the dq0 reference
system. The derivative of a vector in the abc reference system is given by:
172
([
] [ ])
d
[x abc ] = d Tdq 0 (θ d ) −1 ⋅ x dq 0
dt
dt
With the chain-rule for derivatives and knowing that for x=x(t):
d
dx
d
dx
sin x = cos x
and
cos = − sin x
dt
dt
dt
dt
and that ωd=dθd/dt, the following result is obtained:
d
d
Tdq 0 (θ d ) ⋅ [x abc ] =
x dq 0 + ω d ⋅ y ⋅ x dq 0
dt
dt
with y given by:
[
]
[ ]
[ ]
⎡0 − 1 0 ⎤
1 ⎛d
⎞
−1
Tdq 0 (θ d ) ⎟ ⋅ Tdq 0 (θ d ) = ⎢⎢1 0 0⎥⎥
⋅⎜
y=
ω d ⎝ dt
⎠
⎢⎣0 0 0⎥⎦
[
] [
]
(E.3)
(E.4)
(E.5)
(E.6)
It can be seen from (E.6) that differential equations will cause a cross-relation between
the d and the q axis.
b
x
q
xq
d
xc
xb
ωd
xd
a
xa
c
Fig. E.1. Relationship between abc and dq quantities
Some additional properties of the Park transformation can be derived. As the
transformation is orthogonal, it holds that:
[ T (θ )]⋅ [ T (θ ) ] = [ T (θ ) ]⋅ [ T (θ ) ] = [I]
−1
dq 0
d
dq 0
d
T
dq 0
d
dq 0
d
The transformations of (E.2) is unitary. Note that by replacing the factor
(E.7)
2 / 3 by a
factor 2 / 3 the transformation will be amplitude-invariant, implying that the length of
the current and voltage vectors in both abc and dq0 reference frame are the same. This
amplitude-invariant transformation is generally used for modelling of electrical
machines [Paa 00].
The Park transformation does not only transform the fundamental frequency signals.
Also non-fundamental harmonics are correctly transformed as xa, xb and xc are time
Appendix E. Park transformation
173
signals, including all harmonics. In steady state a non-fundamental frequency
component with frequency ωh will appear as a sinusoidal signal with frequency (ωh-ωd)
in the dq0 domain. The highest frequency that can be represented accurately in the dq0
frame depends on the time step that is used.
With (E.7) it can be shown that the Park transformation conserves power:
p(t ) = [v abc ] ⋅ [i abc ]
T
[
] [v ]] ⋅ [ T (θ )] [i ]
= [v ] [ T (θ )] ] ⋅ [ T (θ )] [i ]
= [v ] [ T (θ )]⋅ [ T (θ )] [i ]
= [v ] ⋅ [i ]
= Tdq 0 (θ d )
T
−1
dq 0
dq 0
dq 0
−1
d
dq 0
d
dq 0
(E.8)
−1
T
dq 0
d
−1 T
T
dq 0
−1
dq 0
dq 0
d
dq 0
d
dq 0
T
dq 0
dq 0
The instantaneous active and reactive power can be obtained directly from the voltages
and currents in the dq0 reference system:
p = v d id + v q iq
(E.9)
q = v q id − v d iq
The simulations in chapter 6 and 7 and in section 5.5 and 5.6 are done with models in
the dq0 reference frame. The 0-axis has not been modelled, as only symmetrical
situations are considered. Besides models for the electrical machines and converters also
models for grid components such as cables and transformers have been used. A
description of these models in the dq0 reference frame can be found in [Pie 04].
174
Appendix F
On the use of reduced converter models
For the simulations that have been done in this thesis reduced models of power
electronic converters have been used. This means that no modulation is applied and that
the switches are replaced by controlled voltage sources (one voltage source per phase),
which are directly controlled by the reference waveforms. This appendix will
investigate under which conditions the reduced models can be used. The analyses and
derivations in this appendix are based on [Zio 85], [Moh 95], [Lee 01], [Hol 03].
F.1 Switching functions
The basic principle of a half-bridge converter was described in chapter 2. For
convenience the phase arm shown in Fig. 2.7 is repeated here in Fig. F.1a. The two
switches are controlled by a pulse width modulation circuit, which compares the
reference waveform to a triangular carrier waveform. When the reference waveform is
above the carrier waveform the output is switched to the upper rail, and when it is below
the carrier waveform it is switched to the lower rail. The output voltage van(t) can be
written as:
v an (t ) = SF (t ) ⋅ Vdc
(F.1)
with SF(t) the switching function which can be expressed as [Zio 85]:
∞
SF = ∑ An cos nω 0 t
(F.2)
n =1
An example of a switching function is shown in Fig. F.1b. The switching function is
time-dependent and is a function of the carrier waveform:
x(t ) = ω c t + θ c
(F.3)
and the reference waveform:
y (t ) = ω 0 t + θ 0
(F.4)
176
with ωc and ω0 the angular frequency of the carrier waveform and the reference
waveform respectively and θc and θ0 the angle of the two waveforms respectively.
Vdc
2
T+
io
a
0
Vdc
Vdc
2
D-
D+
T-
van
n
(a)
(b)
Fig. F.1. Phase-arm of converter
F.2 Fourier analysis theory
From Fourier analysis theory it is known that any time-varying function f(t) can be
expressed as a summation of its harmonic components:
a0 ∞
+ ∑ [a m cos mω t + bm sin mω t ]
2 m=1
f (t ) =
(F.5)
with
am =
bm =
π
1
π
1
π
∫ f (t )cos mω t dω t
m = 0, 1, …, ∞
(F.6)
m = 1, 2, …, ∞
(F.7)
−π
π
∫ f (t )sin mω t dω t
−π
For a function based on two time-varying parameters, (F.5) can be written as [Hol 03]:
f ( x, y ) =
∞
A00 ∞
+ [A0 n cos ny + B0 n sin ny t ] + [Am0 cos mx + Bm0 sin mx ]
2
n =1
m =1
∑
∞
∑
∞
∑ ∑ [Amn cos(mx + ny ) + Bmn sin(mx + ny )]
(F.8)
m =1 n = −∞
(n ≠ 0 )
with
Amn =
1
2π 2
π
π
∫ ∫ f (x, y )cos(mx + ny ) dx dy
−π −π
(F.9)
Appendix F. On the use of reduced converter models
Bmn =
π
1
2π 2
177
π
∫ ∫ f (x, y )sin(mx + ny ) dx dy
(F.10)
−π −π
The two equations can be written in complex form as:
C mn = Amn + jBmn =
1
2π 2
π
π
∫ ∫ f (x, y )e
j (mx + ny )
dx dy
(F.11)
−π −π
F.3 Harmonic spectrum of triangular carrier modulation
In this section the harmonic spectrum of the switching function will be determined. The
modulation circuit uses a triangular carrier waveform, which is compared with a
reference waveform that is defined as:
*
v an
= M cos(ω 0 t + θ 0 )
(F.12)
with M the modulation index (0<M< 1). In [Hol 03] it is shown that for a triangular
carrier waveform the instants that the switching function changes between 0 and 1 can
be expressed as (assuming that θc and θ0 are zero):
π
(1 + M cos ω 0t )
2
when SF changes from 0 to 1 and
x = 2πp −
p = 0, 1, 2, …, ∞
π
(F.13)
(1 + M cos ω 0t )
p = 0, 1, 2, …, ∞
(F.14)
2
when SF changes from 1 to 0. With these equations the harmonic components of the
switching function can be determined. First (F.8) will be written in another form
however. Replacing f(x,y) by SF(x,y), x by ωct+θc and y by ω0t+θ0, (F.8) can be written
as:
A
SF (t ) = 00
dc offset
2
Fundamental
∞
+ [A0 n cos n[ω 0 t + θ 0 ] + B0 n sin n[ω 0 t + θ 0 ]]
component &
n =1
baseband harmonics
(F.15)
∞
+ [Am0 cos m[ω c t + θ c ] + Bm0 sin m[ω c t + θ c ]]
Carrier harmonics
x = 2πp +
∑
∑
m =1
∞
+∑
∞
⎡A
cos(m[ω t + θ ] + n[ω t + θ
])
⎤
∑ ⎢⎣+ mnBmn sin(m[ωc c t + cθ c ] + n[ω0 0t + 0θ 0 ])⎥⎦
m =1 n = −∞
(n ≠ 0 )
Sideband harmonics
178
with m the carrier index variable and n the baseband index variable. This form clearly
shows the different components of the harmonic components of SF(t) as a function of
the carrier and the reference waveform frequency.
With the equations (F.13) and (F.14), (F.11) can be written as:
Amn + jBmn =
π
1
2π 2
∫
π
2
(1+ M cos y )
e j (mx + ny ) dx dy
∫
(F.16)
−π − π (1+ M cos y )
2
This equation can be used to determine expressions for all four terms in (F.15). The dc
offset is given for m=0 and n=0:
A00 + jB00 =
π
π
1
2π 2
2
∫
(1+ M cos y )
∫
dx dy =
−π − π (1+ M cos y )
2
π
1
2π 2
∫ π (1 + M cos y ) dy = 1
(F.17)
−π
The offset in SF(t) is thus ½. The baseband harmonics (m=0, n>0) can be expressed as:
A0 n + jB0 n =
1
2π 2
=
1
2π
π
π
2
∫
(1+ M cos y )
jny
∫ e dx dy =
−π − π (1+ M cos y )
2
π
⎡
∫ ⎢⎣e
jny
+
−π
(
1
2π 2
π
jny
∫ [π (1 + M cos y )e ] dy
−π
(F.18)
)
M j [n+1]y
⎤
e
+ e j [n−1]y ⎥ dy
2
⎦
π
As
∫e
jny
dy = 0 for any nonzero value of n, (F.18) can be reduced to:
−π
A01 + jB01 =
1
2π
π
∫
−π
M
dy = M
2
(F.19)
for n=1. For all other n>1, A0n+jB0n=0 [Hol 03]. This fundamental frequency component
term is equal to the amplitude of the reference waveform defined in (F.12).
The carrier and side-band harmonics are defined as [Hol 03]:
2
π
⎛ π ⎞
J 0 ⎜ m M ⎟ sin m
mπ ⎝ 2 ⎠
2
(F.20)
2Vdc ⎛ π ⎞ ⎛
π⎞
J n ⎜ m M ⎟ sin ⎜ [m + n] ⎟
mπ
2⎠
⎝ 2 ⎠ ⎝
(F.21)
Am0 + jBm0 =
Amn + jBmn =
Appendix F. On the use of reduced converter models
179
F.4 Harmonic voltages in a half-bridge converter
The output voltage van(t) of the half-bridge converter shown in Fig. F.1a can be obtained
by substituting (F.17), (F.19), (F.20), and (F.21) in the equation for the switching
function, (F.15), and substituting the switching function in (F.1):
V
V
v an (t ) = dc + dc M cos(ω 0 t + θ 0 )
2
2
∞
2V
1 ⎛ π ⎞
π
+ dc ∑ J 0 ⎜ m M ⎟ sin m cos(m[ω c t + θ c ])
2
π m=1 m ⎝ 2 ⎠
(F.22)
+
2Vdc
π
∞
∞
1 ⎛ π ⎞ ⎛
π⎞
J n ⎜ m M ⎟ sin ⎜ [m + n] ⎟ × cos(m[ω c t + θ c ] + n[ω 0 t + θ 0 ])
2⎠
⎝ 2 ⎠ ⎝
n = −∞ m
∑ ∑
m =1
(n ≠ 0 )
where J0 and Jn are Bessel functions with argument 0 and n.
The harmonic components of the voltage can be split up in the four groups that have
been defined:
• a dc offset of ½Vdc. This term disappears when the voltage va0 is used instead of van.
Also in full-bridge converters (such as the one used in this thesis) the dc term
disappears).
• a fundamental frequency component that equals the reference waveform defined in
(F.12) times Vdc.
• a group of harmonics with the carrier frequency and multiples of it.
• a group of harmonics defined by the sum and difference between the modulating
carrier waveform harmonics and the reference waveform and its associated
baseband harmonics. They exist as groups around the carrier harmonic frequencies.
F.5 Discussion and conclusion
The fundamental frequency component of the voltage generated by the converter is thus
equal to the reference voltage. The voltage generated by the converter will also contain
higher harmonics, which are centred around the carrier frequency. When the carrier
frequency is much higher than the fundamental frequency (fc >> f0) the harmonics
created by the pulse-width modulation and the switching of the converter will not
interfere with the fundamental frequency behaviour of the converter and other
phenomena with a relatively low frequency. This implies that a reduced model can be
used, as long as the frequency of the phenomena under investigation is sufficiently
lower than the carrier frequency.
180
As the carrier frequency is generally much higher than the fundamental frequency of
the reference waveform, the fundamental frequency can generally easily be separated
from the harmonic frequencies by a low-pass filter. This filter will also limit the
harmonic currents that are injected in the network.
List of symbols
Abbreviations
CSC
DFIG
DG
DN
FC
HV
LV
MT
MV
PEC
SF
VI
VSC
WT
Current source converter
Doubly-fed induction generator
Distributed Generation
Distribution network
Fuel cell
High-voltage
Low-voltage
Micro turbine
Medium-voltage
Power electronic converter
Switching function
Variable inductor
Voltage source converter
Wind turbine
Notation
For the variables in the equations different notations have been used:
x(t)
x(s)
X
X
time-dependent signal
frequency-dependent signal (Laplace domain)
RMS value
Complex value
x
vector
182
Symbols
B
C
D
E
f
F
F
G
G
H
i, I
J
k
k
K
K
K
L
m, M
n, N
p
p
P
PL
q
Q
r
R
R
R
s
S
T
T
T
U
v
v
V
V
X
Z
damping torque [N⋅m]
capacitance [F]
droop [-]
energy [J]
frequency [Hz]
Faraday’s constant [C/mol]
fraction of total turbine power [-]
conductance [S]
transfer function [-]
inertia constant [s]
current [A]
inertia [kg⋅m2]
controller constant [-]
utilisation factor [-]
controller constant [-]
droop constant [W/Hz]
valve molar constant [kmol/(s⋅A)]
inductance [H]
modulation ratio [-]
number [-]
number of pole pairs [-]
partial pressure [N/m2]
active power [W]
penetration level [-]
molar flow [kmol/s]
reactive power [VA]
ratio [-]
resistance [Ω]
governor constant [-]
universal gas constant [J/(mol K)]
Laplace operator [-]
apparent power [VA]
temperature [K]
time constant [s]
torque [N⋅m]
utilisation factor [-]
speed [m/s]
voltage [V]
voltage [V]
volume [m3]
reactance [Ω]
impedance [Ω]
List of symbols
α
ϕ
ω
τ
θ
λ
Ψ
bandwidth [Hz]
angle [rad]
angular velocity [rad/s]
time constant [s]
pitch angle [degrees]
tip speed ratio [-]
flux [Wb]
Subscripts
0
a
a
a
a
c
c
conv
cb
d
dg, DG
dip
dist
dyn
CPL
CPS
dc
df
e
emu
f
f
fc
fc
FC
fg
fl
g
G
gen
gt
h
HP
fundamental
active
amplitude
aerodynamic
phase a
conventional
current control
converter
circuit breaker
d-axis, damping
Distributed Generation
voltage dip
disturbance
dynamic
constant power load
constant power source
dc
damping in filter
electrical
emulated
filter
fundamental
fuel cell
converter side of filter
fuel cell
grid side of filter
fault location
grid
generator
generator
gas turbine
harmonic
high-pressure
183
184
i
ine
inv
l
load
m
max
min
mt, MT
n
nom
o
p
pfc
PR
q
r
r
r
r
R
rect
ref
rt
s
s
syst
sc
th
tot
var
wt, WT
x
input, integral
inertial response
inverter
load
load
mechanical
maximum
minimum
micro turbine
node
nominal
output
proportional
primary frequency control
proportional-resonant
q-axis
real (real-imaginary)
resonant
ripple
resistance
reformer
rectifier
reference
response time
source
switching
system
short-circuit
threshold
total
variable
wind turbine
imaginary
Superscripts
*
’
r
in
out
complex-conjugate
reduced on stator side
resistance
in
out
Dankwoord
Dit proefschrift is het resultaat van vier jaar onderzoek binnen de vakgroep Electrical
Power Processing van de Technische Universiteit Delft. Vele mensen zijn direct of
indirect betrokken geweest bij mijn promotie-onderzoek en de realisatie van dit
proefschrift. Zonder volledig te kunnen zijn wil ik een aantal van hen in het bijzonder
bedanken.
De eerste die ik wil bedanken is mijn toegevoegd promotor ir. S.W.H. de Haan. Als
mijn dagelijks begeleider heeft hij een belangrijke bijdrage geleverd aan de
totstandkoming van dit proefschrift. Hij hield steeds de grote lijnen van het onderzoek
in het oog en heeft een grote bijdrage geleverd aan het steeds weer scherp formuleren
van de vraagstellingen. Ook de leesbaarheid van het proefschrift is er dankzij hem sterk
op vooruitgegaan. Sjoerd, bedankt dat ik met mijn vragen altijd bij je terecht kon.
Als promotor heeft ook prof. dr. J.A. Ferreira een belangrijke bijdrage geleverd aan
de totstandkoming van dit proefschrift. Braham, bedankt voor je frisse blik op het
onderzoek, het waardevolle commentaar dat je gaf tijdens onze voortgangsbesprekingen, en je aandacht voor de praktische relevantie van mijn onderzoek.
Mijn onderzoek maakte deel uit van het IOP-EMVT project “Intelligentie in
Netten”. De samenwerking met de 9 andere promovendi had zeker haar meerwaarde.
Bij deze wil ik, Andrej, Anton, Cai, Frans, George, Jody, Reza, Roald en Sjef dan ook
bedanken voor de plezierige samenwerking. Hetzelfde geldt voor alle begeleiders die bij
het project betrokken waren.
SenterNovem wil ik bedanken voor het mogelijk maken van dit project. De leden
van de IOP-begeleidingscommissie worden bedankt voor het commentaar en de
adviezen tijdens de halfjaarlijkse bijeenkomsten.
Tijdens mijn promotie heb ik veel baat gehad bij het werk dat ik samen met Jan
Pierik van ECN gedaan heb in de Erao-projecten. Jan, bedankt voor de plezierige en
leerzame samenwerking.
186
Gedurende de jaren die ik aan de TU werkte heb ik met veel plezier de kamer gedeeld
met Bart Roodenburg. Bart, bedankt voor alles: de koffie die ’s ochtends klaarstond, de
vele gesprekken over van alles en nog wat, de mogelijkheid om ‘domme vragen’ te
kunnen stellen en je op de praktijk gebaseerde visie op veel van mijn wilde theoretische
plannen.
Zonder ze allemaal bij naam te noemen wil ik ook alle andere collega’s,
medewerkers, promovendi en studenten bij de EPP vakgroep bedanken. Hetzelfde geldt
voor mijn collega’s van de EPS vakgroep. Mijn onderzoek bevond zich op het
grensvlak tussen electriciteitsvoorziening en vermogenselektronica. Vaak kwam ik dan
ook bij hen over de vloer.
During my research I had the opportunity to cooperate with a number of (Ph.D.-)
students. Especially I would like to thank Matteo Tonso, who did a master-project on
the use of a variable inductance for voltage control. Some of his results have been used
in this thesis. Further I would like to thank Jean-Baptiste Defreville, Ivo van Vliet and
Mariel Triggianese. Also the cooperation with them has been very pleasant and helpful.
Mijn huisgenoten hebben jarenlang een ‘burger’ in hun midden geduld. Hoewel onze
ritmes soms wat uit fase liepen heeft dit zelden tot problemen geleidt en heb ik met
plezier op Don Quichotte gewoond. Bedankt voor het samenwonen en jullie
betrokkenheid.
Hoewel misschien wat minder direct bij het onderzoek betrokken, wil ik ook mijn
familie, vrienden en kennissen bedanken voor de belangstelling en interesse die ze de
afgelopen jaren getoond hebben in (de voortgang van) mijn onderzoek. Hoewel ik
misschien niet altijd duidelijk heb kunnen maken wat ik precies deed hebben jullie toch
regelmatig blijk gegeven van jullie betrokkenheid, hartelijk dank daarvoor. In het
bijzonder wil ik Hans Teerds bedanken die de omslag van dit proefschrift ontworpen
heeft. Hans, bedankt.
Mijn leven is in Gods hand. Hij heeft mij de talenten gegeven om dit onderzoek te doen
en Hij heeft mij de afgelopen jaren gezondheid en alles wat ik nodig had gegeven. Hem
komt bovenal de dank voor dit proefschrift toe.
Delft, september 2006
Johan Morren
List of publications
Journal papers
•
•
•
•
•
•
•
•
•
•
Johan Morren, Bart Roodenburg, Sjoerd W.H. de Haan, “Electrochemical reactions and electrode
corrosion in Pulsed Electric Field (PEF) treatment chambers”, Innovative Food Science and Emerging
Technologies, Vol. 4 No. 3, September 2003, pp. 285 – 295.
Johan Morren, Sjoerd W.H. de Haan, “Ridethrough of Wind Turbines with Doubly-Fed Induction
Generator During a Voltage Dip” IEEE Trans. Energy Conversion, Vol. 20, No. 2, pp. 435 – 441, June
2005.
Bart Roodenburg, Johan Morren, H.E. (Iekje) Berg and Sjoerd W.H. de Haan, “Metal release in a
stainless steel Pulsed Electric Field (PEF) system: Part I. Effect of different pulse shapes; theory and
experimental method”, Innovative Food Science and Emerging Technologies, Vol. 6 No. 3, September
2005, pp. 327 – 336.
Bart Roodenburg, Johan Morren, H.E. (Iekje) Berg and Sjoerd W.H. de Haan, “Metal release in a
stainless steel pulsed electric field (PEF) system: Part II. The treatment of orange juice; related to
legislation and treatment chamber lifetime”, Innovative Food Science and Emerging Technologies, Vol.
6 No. 3, September 2005, pp. 337 – 345.
Johan Morren, Jan T. G. Pierik, Sjoerd W. H. de Haan, Jan Bozelie, "Grid interaction of offshore wind
farms. Part 1. Models for dynamic simulation", Wind Energy, Vol. 8, No. 3, pp. 265 – 278, 2005, DOI:
10.1002/we.158
Johan Morren, Jan T. G. Pierik, Sjoerd W. H. de Haan, Jan Bozelie, "Grid interaction of offshore wind
farms. Part 2. Case study simulations", Wind Energy, Vol. 8, No. 3, pp. 279 – 293, 2005, DOI:
10.1002/we.159
Johan Morren, Sjoerd W.H. de Haan, Wil L. Kling, J.A. Ferreira, “Wind Turbines Emulating Inertia and
Supporting Primary Frequency Control”, IEEE Trans. Power Systems, Vol. 21, No. 1, pp. 433 – 434,
February 2006.
Johan Morren, Jan Pierik, Sjoerd W.H. de Haan, “Inertial response of variable speed wind turbines”,
Electric Power Systems Research, Vol. 76, pp. 980 – 987, June 2006.
J. Morren, S.W.H. de Haan, J.A. Ferreira, “Contribution of DG Units to Primary Frequency Control”,
European Transactions on Electric Power, article in press, 2006.
Johan Morren, Sjoerd W.H. de Haan, “Short-Circuit Current of Wind Turbines with Doubly-Fed
Induction Generator”, IEEE Trans. Energy Conversion, accepted for publication, 2006.
Conference papers
•
•
K. Burges, E.J. van Zuylen, J. Morren, “DC Transmission for Offshore Wind Farms: Concepts and
Components”, in Proc. 2nd International Workshop on Transmission Networks for Offshore Wind Farms,
Stockholm, Sweden, 29 – 30 March 2001.
J. Morren, S.W.H. de Haan, J.A. Ferreira, “Design and scaled experiments for high-power DC-DC
conversion for HVDC systems”, in Proc. 32nd IEEE annual Power Electronics Specialists Conference
(PESC), Vol. 3, pp. 791-796, 17 – 21 June 2001.
188
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J. Morren, M. Pavlovsky, S.W.H. de Haan, J.A. Ferreira, “DC-DC conversion for offshore windfarms”,
in Proc. 9th European conference on Power Electronics and applications (EPE), Graz, Austria, 27 – 29
August 2001.
B. Roodenburg, G. de Jong, I.E. Pol, J. Morren, N. Dutreux, P.C. Wouters, R.H.S.H. Beurskens, S.W.H.
de Haan, “Preservation of Liquid Food by Pulsed High-Voltage Arc Discharges”, in Proc. Society For
Applied Microbiology (SFAM) annual meeting, pp. 145-147, Wageningen, The Netherlands, 9 – 11
January 2002.
J. Morren, S.W.H. de Haan, J.A. Ferreira, “High-voltage DC-DC converter for offshore windfarms”, in
Proc. IEEE Young Researchers Symposium in Electrical Power Engineering, Leuven, Belgium, 7 – 8
February 2002.
B. Roodenburg, J. Morren, S.W.H. de Haan, H.A. Prins, Y.L.M. Creyghton, “Modeling a 80 kV Pulse
Source for Pulsed Electric Fields (PEF)”, In Proc. 10th Power Electronics and Motion Control
conference (EPE-PEMC), Cavtat & Dubrovnik, Croatia, 9 – 11 September 2002.
S.W.H. de Haan, B. Roodenburg, J. Morren, H. Prins, “Technology for Preservation of Food with Pulsed
Electric Fields (PEF), in Proc 6th IEEE Africon Conference, Vol. 2, pp. 791-796, 2 – 4 October 2002.
B. Roodenburg, J. Morren, S.W.H. de Haan, P.C. Wouters, G. de Jong, I.E. Pol, Y.L.M. Chreyghton,
“High-Voltage Arc Pulser for Preservation of Liquid Food”, in Proc. European Pulsed Power
Symposium, pp. 26/1 26/6, Saint Louis, France, 22 – 24 October 2002.
J. Morren, S.W.H. de Haan, P. Bauer, J.T.G. Pierik, J. Bozelie, “Comparison of complete and reduced
models of a wind turbine with Doubly-Fed Induction Generator” in Proc. 10th European conference on
Power Electronics and applications (EPE 2003), Toulouse, France, 2 – 4 September 2003.
B. Roodenburg, J. Morren, S.W.H. de Haan, H.E. Berg, “Corrosion Experiments in a Pulsed Electric
Field (PEF) Treatment Chamber with Stainless Steel Electrodes”, in Proc. Workshop on Nonthermal
Food Preservation, Vol. 1, pp. 1 – 4, Wageningen, The Netherlands, 7 – 10 September 2003.
J. Morren, S.W.H. de Haan, J.T.G. Pierik, J. Bozelie, Fast Dynamic Models of Offshore Wind Farms for
Power System Studies”, in Proc. 4th International Workshop on Large-scale Integration of Wind Power
and Transmission Networks for Offshore Wind Farms, Billund, Denmark, 20 – 21 October 2003.
Jan Pierik, Johan Morren, Sjoerd de Haan, Tim van Engelen, Edwin Wiggelinkhuizen, Jan Bozelie,
“Dynamic models of wind farms for grid-integration studies”, in Proc. Nordic Wind Power Conference
2004, Gothenburg, Sweden, 1 – 2 March 2004.
M. Reza, J. Morren, P.H. Schavemaker, J.G. Slootweg, W.L. Kling, L. van der Sluis, “Impacts of
converter connected distributed generation on power system transient stability”, in Proc. 2nd IEEE Young
Researchers Symposium in Electrical Power Engineering, Delft, The Netherlands, 18 – 19 March 2004.
Johan Morren, Sjoerd W.H. de Haan, J.A. Ferreira, “Distributed Generators providing ancillary
services”, Distribution Europe 2004, Amsterdam, The Netherlands, 27-28 April 2004.
Johan Morren, Jan T.G. Pierik, Sjoerd W.H. de Haan, “Fast dynamic modelling of direct-drive wind
turbines”, in Proc PCIM Europe 2004, Nürnberg, Germany 25 – 27 May 2004.
J. Morren, S.W.H. de Haan, J.A. Ferreira, “Model reduction and control of electronic interfaces of
voltage dip proof DG units”, in Proc. 2004 IEEE Power Engineering Society (PES) General Meeting,
Denver, 6- 10 June 2004.
J. Morren, S.W.H. de Haan, J.A. Ferreira, “Distributed Generation Units contributing to voltage control
in distribution networks”, in Proc. 39th International Universities Power Engineering Conference
(UPEC 2004), Bristol, UK, 6- 8 September 2004.
J. Morren, J.T.G. Pierik, S.W.H. de Haan, “Voltage dip ride-through of direct-drive wind turbines”, in
Proc. 39th International Universities Power Engineering Conference (UPEC 2004), Bristol, UK, 6- 8
September 2004.
Johan Morren, Jan. T.G. Pierik, Sjoerd W.H. de Haan, Voltage dip ride-through control of wind turbines
with doubly-fed induction generators, in Proc. IEA Topical Expert Meeting on System Integration of
Wind Turbines (IEA TEM 44), Dublin, Ireland, 7-8 November 2005.
M. Reza, J. Morren, P.H. Schavemaker, W.L. Kling, L. van der Sluis, “Power Electronic Interfaced DG
Units: Impact of Control Strategy on Power System Transient Stability”, in Proc. 3rd IEE Int. Conf. on
Reliability of Transmission and Distribution systems, (RTDN ’05), London, UK, 15-17 February 2005.
G. Papaefthymiou, J. Morren, P.H. Schavemaker, W.L. Kling, L. van der Sluis, “The Role of Power
Electronic Converters in Distributed Power Systems: Stochastic Steady State Analysis”, in Proc. Cigré
Symposium on Power Systems with Dispersed Generation, Athens, Greece, April 13 – 16, 2005.
List of publications
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Henk Polinder, Johan Morren, “Developments in Wind Turbine Generator Systems”, in Proc. 8th Int.
Conf. on Modelling and Simulation of Electric Machines, Converters and Systems (ELECTRIMACS
’05), Hammamet, Tunesia, April 17 – 20, 2005.
Johan Morren, Sjoerd W.H. de Haan, J.A. Ferreira, “Contribution of DG units to voltage control: active
and reactive power limitations”, in Proc. 2005 IEEE St. Petersburg PowerTecch, St. Petersburg, Russia,
27- 30 June 2005.
Johan Morren, Sjoerd W.H. de Haan, J.A. Ferreira, “(De-)Stabilising Effect of Power Electronic
Interfaced DG Units in Distribution Networks”, in Proc. 11th European conference on Power
Electronics and applications (EPE 2005), Dresden, Germany, 11 – 14 September 2005.
Matteo Tonso, Johan Morren, Sjoerd W.H. de Haan, J.A. Ferreira, “Variable Inductor for Voltage
Control in Distribution Networks”, in Proc. 11th European conference on Power Electronics and
applications (EPE 2005), Dresden, Germany, 11 – 14 September 2005.
Johan Morren, Sjoerd W.H. de Haan, J.A. Ferreira, “Contribution of DG Units to Primary Frequency
Control”, in Proc. Int. Conf. on Future Power Systems (FPS 2005), Hoofddorp, The Netherlands, 16 –
18 November 2005.
Jan Pierik, Johan Morren, Tim van Engelen, Sjoerd de Haan, Jan Bozelie, “Development and validation
of wind farm models for power system studies”, in Proc. European Wind Energy Conference &
Exhibition (EWEC 2006), Athens, Greece, 27 February – 2 March, 2006.
Johan Morren, Sjoerd W.H. de Haan, J.A. Ferreira, “Primary Power/Frequency Control with Wind
Turbines and Fuel Cells”, in Proc. 2006 IEEE Power Engineering Society (PES) General Meeting,
Montreal, Canada, 18 – 22 June 2006.
Other publications
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J.T.G. Pierik, J. Morren, E.J. Wiggelinkhuizen, S.W.H. de Haan, T.G van Engelen, J. Bozelie, Electrical
and control aspects of offshore wind turbines II (Erao-2), Vol. 1: Dynamic models of wind farms,
Technical report ECN-C--04-050, ECN, 2004, June 2004.
J.T.G. Pierik, J. Morren, E.J. Wiggelinkhuizen, S.W.H. de Haan, T.G van Engelen, J. Bozelie, Electrical
and control aspects of offshore wind turbines II (Erao-2), Vol. 2: Offshore wind farm case studies,
Technical report ECN-C--04-050, ECN, 2004, June 2004.
190
Curriculum Vitae
Johan Morren was born on 23 October 1976 in Wekerom. From 1989 to 1995 he visited
the athenaeum at the Jacobus Fruytier scholengemeenschap in Apeldoorn. In 1995 he
started his study at the Delft University of Technology, where he received the M.Sc.
degree in Electrical Engineering in 2000. In 2001 he started as a research assistant in the
Electrical Power Processing group of the Delft University of Technology. He worked on
different projects regarding the preservation of food with pulsed electric field (PEF)
treatment and the grid-connection of renewable energy sources. From 2002 to 2006 he
worked, in the same group, on a Ph.D. project on the power electronic aspects of grid
integration of Distributed Generation units. Since 1 October 2006 Johan Morren is with
Essent Netwerk.
Johan Morren
ISBN: 90-811085-1-4
Grid support by power electronic
converters of Distributed Generation units
The introduction of Distributed Generation (DG) causes several problems, which are mainly
related to the differences between DG units and conventional generators. A large part of the
DG units are connected to the grid via power electronic converters. The main task of these
converters is to convert the power that is available from the prime source to the characteristic
voltage and frequency of the grid. The flexibility of the converters offers the possibility to
configure them in such a way that, in addition to their main task, they can support the grid. Four
issues have been considered in this thesis: damping of harmonics, voltage control, the behaviour
of DG units during grid faults, and frequency control. The different control strategies that are
required to achieve the grid support can all be implemented simultaneously in the control of a
DG unit. In this way a multi-functional DG unit is obtained that can autonomously support the
grid in several ways.
Johan Morren
Grid support by power
electronic converters
of Distributed
Generation units
Uitnodiging
Graag wil ik u uitnodigen om
aanwezig te zijn bij de openbare
verdediging van mijn proefschrift
Grid support by power
electronic converters
of Distributed
Generation units
Op D.V. maandag 13 november om
12:30 uur in de Aula van de Technische Universiteit Delft, Mekelweg 5
te Delft.
Voorafgaand geef ik om 12:00 uur
een korte samenvatting van het
onderzoek.
Na afloop van de promotieplechtigheid bent u van harte welkom op de
receptie die op dezelfde locatie zal
plaatsvinden.
Johan Morren
St. Antonielaan 328
6821 GP Arnhem
[email protected]
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