SMART VAR Generator to Manage Grid Voltage

SMART VAR Generator to Manage Grid Voltage
SMART VAR Generator to Manage Grid Voltage
Stability issue of Low Frequency Switching
Photovoltaic Inverters.
Kurukulasuriya Sam Prasanna Perera
[740113-P318]
Kachchakaduge Sumith Ruwan Dharmasiri [701109-P357]
Master of Science Thesis
KTH School of Industrial Engineering and Management
Energy Technology EGI-2015-090MSC EKV1116
Division of Energy
SE-100 44 STOCKHOLM
Master of Science Thesis
EGI-2015-090MSC EKV1116
Title : SMART VAR Generator to Manage Grid
Voltage Stability issue of Low Frequency
Switching Photovoltaic Inverters
Kurukulasuriya Sam Prasanna Perera
740113-P318
Kachchakaduge Sumith Ruwan Dharmasiri
701109-P357
Approved
Examiner
Supervisor
03/11/2015
Prof. Anders Malmquist
Dr. K. A. C. Udayakumara
Commissioner
Contact person
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Abstract
The global energy mix is undergoing a massive change as the world makes an effort
to reduce its dependence on the limited and pollution–causing fossil fuels. Solar power,
clean and abundant, is a central metaphor in this transition, but seamlessly integrating
renewable energy into the public distribution grid has its own set of challenges.
Traditionally, large scale (MW range) centralized power generating units have been
built with long distance extremely high voltage transmission lines with distributed
supply network to generate and distribute electricity. Now, the small scale distributed
power generators are being connected, whiz through to the low voltage distribution
network and because of the power feeding duration is depends on the availability of
the solar irradiation, controllability, regulation, grid requirements; grid voltage stability
is becoming a challenge. The smart grid technology and operation has been taking
over the conventional grid gradually to meet the new challenges.
The solar micro inverters have gained greater visibility during the past several years
as a convenient and promising renewable energy converter for usability .They carry
several advantages compare to conventional string type centrally coupled inverters.
They are able to mitigate the entire system performances deficiencies due to shading
effects with the sun movement. As a result, solar harvesting bandwidth has
comparatively extended.
The PV micro inverter technologies have been continuously improving for higher
performances, life expectancy and to meet the required grid regulations. However, only
few of the PV micro inverter developers successfully demonstrate with patents, for their
technology differentiation, the DC to AC fly back conversion technology, usage of
electrolytic capacitors to thin film capacitors for high life expectancy and safe low
voltage operation, level of switching frequency , VSI ( voltage sources inverter), and
CSI (current source inverters ) are summaries of these inventions.
These inventions eventually discussed about the inverter performance in terms of
efficiency of energy conversion, thermal limitations, safety of operating low voltage,
harmonic content, component selection and usage, circuit topology and cost
performances. Each key differentiator has been accomplished with an expense of
another. Therefore each technology has its own strengths and limitations. During the
literature review, it was revealed that the low frequency switching inverters have
limitations to generate reactive power to maintain the voltage stability in the grid.
Reactive power plays a vital role in grid voltage stability. Reactive power supply has to
match the demand in real time basis and also transmit based on where the reactive
power generated and consumed in the network. Many research works has proved that
reactive power generation locations must balance and coordinated throughout the
electricity grid, high voltage, medium and low voltages (< 1000V) levels for the optimum
and efficient network operation with greater voltage stability.
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Higher level of solar penetration has identified as a potential cause of low voltage grid
instability due to lack of reactive power feeding and keep on increasing the voltage
higher than grid at point of common connection [PCC] to inject the current to the grid.
Studies and experience in voltage stability has resulted in, introducing many new grid
regulations to manage the grid voltage stability throughout the world.
VDE-AR-N-4105-2011 is a German grid regulation standard specifically focused on the
low voltage grid connected power generators. This regulation is clearly has addressed
the requirements of reactive power requirements in terms of power factor management
and demands to maintain the PV inverter voltage less than 3% at the PCC, when
connecting any type of distributed power generators to the low voltage network.
Objectives of the thesis work
•
Investigate the low voltage PV Inverter Technologies: capabilities and limitations.
•
Investigate low frequency switching [LFS] inverters connected to the low voltage
distribution network- voltage stability and reactive power requirements for the
connection to and parallel operation.
•
Conceptualize; develop the theory and functionality of the SMART VAR Generator
for LFS Inverter in order to comply with low voltage grid regulation - VDE-AR-N4105-2011.
•
Identify, design and test the key components of the SMART VAR Generator
Inverters with low frequency switching have its own limitations to control the power
factor and meeting the power factor requirements of the new regulations discussed in
the standard VDE-AR-N-4105-2011. However this technology has proven to be high
efficiency, low voltage operation and longer life of operation. In order to support the
reactive power requirement and meeting the regulation, there should be a smart var
generator couple together with series of inverters at the low voltage distribution
network.
Power factor management is based on the electricity demand and utility companies
are managing the supply and demand of electricity. Therefore, there is a constant
interaction between utility operator and the VAR generator. Further VAR generator
must response quickly (ideally real time basis) to the network voltage variation and
inverter power generation based on solar irradiance and temperature.
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Acknowledgement
We would like to thank Mr. Viraj Andrabadu, who exposed us to grid connected low
voltage generator regulations and correlated issues related to micro inverters. He is
very knowledgeable on the micro inverter testing and related regulations. We were
fortunate to associate him to understand the renewable energy industry regulations
and global trends.
We also would like to thank Mr. Paul Garrity and Mr. Aaron Jungreis for helping us to
understand the electronic controlling, microprocessor programming, electronic
components and their limitations.
Most importantly, we would like to thank Dr. Udayakumar and Prof. Anders Malmquist
for guiding us to concrete the topic and our objectives.
We would like to give a special thanks to Dr Udayakumar for asking right questions, so
that it opened our thinking process. He listened to our presentations carefully,
challenged and questioned the points. He encouraged us to be thorough the subject
and clear on our points. It helped us considerably to review the literature thoroughly
and also talk to the industry to develop a practical solution.
Mr. Ruchira Abeyweera did a fantastic work by scheduling and arranging presentation
meetings in timely manner. He followed up and coordinates us to make sure everything
is on time. He is dedicated and focus, great coordinator. Thank you
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1 Table of Contents
Abstract ...................................................................................................................... 3
1
Introduction ........................................................................................................ 12
2
Methodology....................................................................................................... 13
3
Back Ground ...................................................................................................... 14
3.1
Higher PV energy penetration as an alternative to fossil fuel energy .......... 14
3.2
Kyoto Protocol makes a difference .............................................................. 15
3.3
Centralized power generation vs distributed generation. ............................. 18
3.4
Photovoltaic systems and Inverters ............................................................. 20
3.4.1
Solar cells ............................................................................................. 20
3.4.2
String Inverters ...................................................................................... 23
3.4.3
Micro Inverter compared with string inverters. ...................................... 25
3.5
3.5.1
US regulation connection ...................................................................... 28
3.5.2
US National Electric Cord (NEC) .......................................................... 29
3.5.3
Inverter Testing as of UL1741 2005 ...................................................... 30
3.5.4
Utility voltage and frequency test .......................................................... 30
3.5.5
Utility Interconnection testing as of UL1741 and IEEE1547 .................. 31
3.5.6
Australia regulation ............................................................................... 31
3.5.7
US distributed related standard scope. ................................................. 32
3.6
4
Inverter Regulation and Testing................................................................... 28
Regulation Change ...................................................................................... 32
Power System Stability ...................................................................................... 33
4.1
Power System Stability Introduction ............................................................ 33
4.1.1
Rotor Angle Stability.............................................................................. 35
4.1.2
Frequency Stability................................................................................ 35
4.1.3
Voltage Stability .................................................................................... 35
4.2
Modeling of Power Systems ........................................................................ 36
4.2.1
System Topology Representation ......................................................... 37
4.2.2
Determination of Critical Bus or Busses ................................................ 37
4.2.3
Static Analysis – Power system stability ............................................... 38
4.2.4
Active Power vs Voltage OR P-V curves............................................... 38
4.2.5
Reactive Power and voltage stability .................................................... 39
4.2.6
Reactive Power vs Voltage OR V-Q curves .......................................... 40
4.3
Grid Connected PV Powered Generator Systems ....................................... 41
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5
6
7
4.3.1
Reactive and Active power vs Bus voltage ........................................... 42
4.3.2
PSS®E Simulation software .................................................................. 42
4.3.3
Definitions ............................................................................................. 43
4.3.4
Bus voltage vs Active Power generation / simulation using PSSE ........ 44
4.3.5
Bus voltage vs Reactive Power generation / simulation using PSSE .... 46
Solution approaches for VAR controls ............................................................... 47
5.1
Solution approaches for static Var controls ................................................. 47
5.2
Power One: VSI approach .......................................................................... 48
5.3
Apparent power: impedance matching approach ........................................ 49
Dynamic, smart Var generator Approach ........................................................... 49
6.1
Basic Theory................................................................................................ 49
6.2
Inductor theory............................................................................................. 55
6.2.1
Soft Magnetic materials......................................................................... 56
6.2.2
UI Core inductor .................................................................................... 56
6.2.3
Toroidal core Inductor ........................................................................... 60
6.2.4
C-Core inductor ..................................................................................... 66
6.3
Capacitor ..................................................................................................... 66
6.4
Conceptual Var box design.......................................................................... 67
6.4.1
Major Parts of the VAR box design approach ....................................... 68
6.4.2
Operation Algorithm, ............................................................................. 72
Analysis and Conclusion .................................................................................... 75
7.1
Meeting the PF resolution ............................................................................ 75
7.2
Unit efficiency .............................................................................................. 76
8
Conclusion ......................................................................................................... 77
9
References ......................................................................................................... 79
10 Appendix A : Inductor Calculation ...................................................................... 82
10.1
UI Core : Design Output .......................................................................... 82
10.2
Toroidal Core 50mH Inductor Calculation ................................................ 84
10.3
Toroidal Core 100mH Inductor Calculation .............................................. 85
10.4
Toroidal Core 150mH Inductor Calculation .............................................. 86
10.5
Toroidal Core 200mH Inductor Calculation .............................................. 87
11 Appendix B: Smart Var generation operation algorithm ..................................... 88
11.1
Algorithm Calculation Approach ............................................................... 88
11.2
Algorithm .................................................................................................. 89
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Figures
Figure 3-1: Energy sources and total consumption 1973 and 2010. ......................... 15
Figure 3-2: Country comparison of PV peak power. ................................................. 17
Figure 3-3: Total world energy consumption ............................................................. 18
Figure 3-4: Solar panel diagram: no copy rights. ...................................................... 20
Figure 3-5: current- Voltage curves depending on the ambient temperature ........... 21
Figure 3-6: Typical I-V characteristic of a solar cell in steady-state operation .......... 21
Figure 3-7: Equivalent circuit of solar cell with active load ........................................ 22
Figure 3-8: Basic configuration of string inverter ...................................................... 23
Figure 3-9: Micro Inverter circuit ............................................................................... 25
Figure 3-10: Inverter interconnection and testing ..................................................... 29
Figure 3-11: Power factor range ............................................................................... 33
Figure 4-1: Classification of power system stability. ................................................. 34
Figure 4-2: Single-Line diagram of radial distribution system ................................... 37
Figure 4-3: Active power and bus voltage ................................................................. 39
Figure 4-4: Reactive power required and bus voltage V-Q curve for dynamic and static
stability...................................................................................................................... 41
Figure 4-5: Lower voltage grid simulation models .................................................... 44
Figure 5-1: Current Source Inverter Models ............................................................. 48
Figure 6-1: Flux pattern inside the core and outside the core ................................... 58
Figure 6-2: Inductor schematic diagram ................................................................... 61
Figure 6-3: Major parts of a VAR box – schematic ................................................... 68
Figure 6-4: circuit diagram VAR generator . ............................................................. 69
Figure 6-5: STPM01 Micro controller ........................................................................ 71
Graphs
Graph 6-1: Inductance and current and flux densities .............................................. 58
Graph 6-2: UI inductor testing for 50Hz .................................................................... 60
Graph 6-3 : Toroidal inductor .................................................................................... 65
Picture
Picture 3-1: commercial string inverter 250kW: (270cm X 275cm X 150cm) (H XL X
W), 1800kg. .............................................................................................................. 24
Picture 3-2: commercial string inverter 100kW: (200cm X 130cm X 80cm) (H XL X W),
850kgs. ..................................................................................................................... 24
Picture 3-3: Residential string inverter
2 kW: (47cm X24cm X 9cm) (H XL X W),
5kgs. ......................................................................................................................... 24
Picture 3-4: PV module connections ........................................................................ 24
Picture 3-5: Micro Inverter ........................................................................................ 27
Picture 3-6: PV module parallel connections ............................................................ 27
Picture 6-1: UI inductor construction ......................................................................... 59
Picture 6-2: UI inductor construction ......................................................................... 59
Picture 6-3: Toroidal inductor construction. .............................................................. 61
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Picture 6-4: Toroidal inductor Testing ....................................................................... 64
Picture 6-5: C core .................................................................................................... 66
Picture 6-6: capacitors .............................................................................................. 67
Picture 6-7: Micro controller ...................................................................................... 72
Tables
Table 3-1 : PV country base consumption figures. ................................................... 16
Table 3-2 : UL 1741 2005, page 129 ........................................................................ 30
Table 4-1: Bus Voltage Vs Active power ................................................................... 45
Table 4-2 : Bus voltage vs. Reactive Power. ............................................................ 46
Table 6-1: Case 1, Vgrid max and Power Factor:0.95 condition. .............................. 53
Table 6-2: Case 2, Vgrid max and Power Factor :0.99 condition. ............................. 54
Table 6-3 : Type of inductor core materials .............................................................. 56
Table 6-4: UI Inductor test data for 50Hz. ................................................................. 60
Table 6-5 : main parameters of the four inductors .................................................... 62
Table 6-6 : Toroidal inductor test data. ..................................................................... 64
Nomenclature.
PV
: photovoltaic
LFS
: Low frequency Switching
AC
: Alternating current
DC
: Direct current
MPPT
: Maximum power point tracking.
PLL
: phase lock loop.
EU
: European Union
PWM
: pulse width modulation
IGBT
: Insulated Gate Bipolar Transistor.
MOSFET
: Metal Oxide Semiconductor Field Effect Transistor
SCR
: Silicon Controlled Rectifire
NEC
: National Electric code
EMC
: Electromagnetic Compatibility
EPS
: Electrical Power System.
IEEE
: Institute of Electrical and Electronics Engineers.
PVPS
: Photovoltaic Power Systems.
IEA
: International Energy Agency.
DR
: Distributed Resources.
PCC
: Point of Common Coupling
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LTC
: Load tap Changer.
VAR
: Volt-Ampere Reactive
MPP
: Moly-perm alloy Powder Cores.
FACTS
: Flexible AC Transmission Systems.
VSI
: Voltage Sources Inverter
CSI
: Current Source Inverter.
PVPS
: Photovoltaic Power systems
TSO
: Transmission system operators
PF
: Power Factor
Parameters and Variables.
I sys_max_Vmax
: Current delivered by the micro inverter system at maximum
grid voltage
I sys_max_Vmin
: Current delivered by the micro inverter system at minimum
grid voltage
I grid_ V max
: Total current to the grid at maximum grid voltage with
power factor correction
I grid_ V min
: Total current to the grid at minimum grid voltage with power
factor correction
I z_Vmax
: Current through the inductor or capacitor at maximum grid
and inverter voltage
I z_Vmin
: Current through the inductor or capacitor at minimum grid
and inverter voltage
LV max
: Inductance
at maximum voltage
LV min
: Inductance
at minimum voltage
Cvmax
: Capacitance at maximum voltage
Cvmin
: Capacitance at minimum voltage
Ps (W)
: Maximum inverter Power capacity
Ist (A)
: Instantaneous solar inverter current
Vst (V)
: Instantaneous solar inverter voltage
Pst
: Instantaneous Inverter Power

: Power increment factor
V grid (V)
: Gird voltage
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Fgrid (Hz)
: Grid frequency
PF
: Power Factor
PF Lag
: Utility required lagging Power factor
PF Lead
: Utility required Leading Power factor
PF’ lag
: Calculated lagging Power Factor
PF’ lead
: Calculated Leading Power Factor
lag
: Lagging utility required phase angle
lead
: Leading utility required phase angle
’lag
: Lagging Calculated Phase angle
’lead
: Leading Calculated Phase angle
RDP
: Reactive Power Difference
RTRP
: Required Total Reactive Power
CIRP
: Calculated Inductive Reactive Power
CCRP
: Calculated Capacitive Reactive Power
I
: Diode current
Is
: Reverse bias saturation current
K
: Boltzmann constant
Q
: Charge
Im
: Optimum point current
Vm
: Optimum point voltage
Voc
: Open circuit voltage
Isc
: Short circuit current
L
: Inductance in Henry (H)
μ0
:P=4
r
: Relative permeability of the core material
N
: Number of turns
A
: Area of cross-section of the coil in square meters (m2)
L
: Length of coil in meters (m)
× 10−7 H/m
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1 Introduction
The global energy mix is undergoing a massive change, as the world makes an effort
to reduce its dependence on limited and pollution–causing fossil fuels. The renewable
energy sources, clean and abundant, is a central metaphor in this transition, but
seamlessly integrating renewable energy into the public distribution grid has its own
set of challenges. Power feeding time and amount can vary depending on the
availability of the renewable energy sources. The small scale power generator
controllability, regulation and grid stability in the low voltage grid is becoming a
challenge.
The consumer type photovoltaic [PV] systems are contributing significantly to generate
and feed electricity into the grid. They are scattered, decentralized and grid tied to low
voltage network close to the consumer. Hence the transmission lines are barely loaded
by those PV systems. High penetration of PV systems together with other renewable
energy sources to the low voltage distribution network causes instability in the grid due
to many reasons. Many countries, specially, USA, and some EU countries are studying
the grid decentralization and possible consequences. In order to prevent grid instability
due to high penetration of renewable energy sources, the new German directive,
“connecting small generation plants to medium or low voltage power grid” has been
released in 2011. The aim of this directive is to maintain the safety and reliability of
the network operation with an increasing trend of decentralizing electricity generation
plants.
The PV systems are connected to the electric grid by an inverter interface that converts
direct current [DC] voltage to alternative current [AC] voltage and also it has to match
the grid voltage and frequency. There are different scales of inverters for different
power levels available in two different topologies, i.e. string inverters and micro
inverters. The string inverters are traditional transformer or switch mode power supply
based grid tie units. They are larger units that connects many solar panels together.
The micro-inverters are small grid-tie inverters in the range of 150-300W that convert
the DC output of one or few PV panel to AC. Unlike string inverters, micro inverters
offer greater design flexibility, enhanced safety due to the absence of high DC voltage
and increased energy harness due to the single panel maximum power point tracking
[MPPT] process. At the moment micro Inverters are taking over the PV market due to
many advantages, however certain micro Inverter topologies are unable to provide the
required reactive power demand to the grid to maintain its stability.
Reactive power is primarily required to maintain the voltage of the electric power
system within the defined limits. Inadequate reactive power supply may cause voltage
to drop or increase at different points of the system and eventually collapse the grid
stability.
Voltage collapse typically occurs in power systems which are heavily stressed. It may
or may not be initiated by a disruption, but is usually characterized by shortage of fast
responding reactive reserves. The voltage collapse often involves specific areas of the
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power system, although the entire system may also be involved. Many system
variables may participate in this phenomenon.
In the new German regulation, VDE-AR-N-4105 2011, this issue has been addressed
by defining the inverter power factor requirements to fulfill the demands of static
reactive power controls. The PV generating devices has to provide reactive power in
every operating point between any power factor [PF] 0.95 under excited to 0.95
overexcited.
In order to meet the reactive power requirements, an external reactive power generator
needs to be connected together with an array of micro inverters. There are many
parameters involves in the decision of amount of reactive power required or the
operating power factor in a given moment, at a connection point. In general, it will be
decided by the inverter output power and utility company reactive power reserve
management guidelines. The PV power output is a function of time of the day, whether,
level of irradiance and therefore the power output of the inverter keeps on changing
throughout the day. Reactive power demand is a function of the nature of loads and
grid characteristics. Therefore, operation and control of a VAR generator in the vicinity
of distributed power generator [DPG] in the low voltage grid is a more complex and
challenging than traditional VAR control.
With the introduction of the new regulations in 2011, the grid compatibility of the some
of the existing PV micro inverter architectures has been put to question by the reactive
power requirements of the new regulations. One of the objectives of this thesis work
is to study the global smart grid regulations in order to compare and discuss the new
challenges impose by the regulations on the growth of the PV power generation
systems connected to the low voltage power distribution system.
The other objective of the thesis work, is to conceptualize a smart VAR generator for
grid tied micro inverters to comply with grid regulations. More specifically, to develop
the conceptual design of a smart VAR generator need to have enough capacity and
controllability to support series of micro inverters that deliver up to 12 kW of power to
the grid.
2 Methodology
In order to meet the first objective, information was gathered from the smart grid
regulations, VDE, IEEE, NEC, UL are some of the strong matured regulation
references. The regulations are developed based on the studies and reviews done by
the experts on the grid system safety and stability and also it brings a common focus
and standardization to the system. The regulations are subject to continual
improvements in line with technology developments. They also create opportunities
for technology developments. Therefore regulations and understanding the
approaches are highly resourceful for this thesis.
Globally, there are many companies build PV cells and also inverters. Some of the
approaches are technologically matured and some are just starting to fulfill the
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technological gaps. There are wide varieties of solar inverter technological approaches
to fulfill the grid requirements. Also there are wide varieties of PV cell technologies to
capture the solar energy. The white papers publish by many different manufacturers to
describe their technological approach differentiation, provided an in-depth knowledge
of available PV inverter technologies.
In next chapters, the main advantageous of micro inverter technology and low voltage
grid connection requirement are discussed in detailed. There are only few companies
that manufacture micro inverters in the world. This is fairly new technology compare
to string large scale inverters. There are recent technological break though in this
industry. We have consulted the industry experts on low frequency switching, high
reliable, micro inverters to learn the inverter operation and grid regulation fulfillments.
This study also involves grid reactive power management and voltage stability. Many
studies had been done in this area on the conventional centralized power generation
system. There are few studies that have been done with smart grid reactive power
management and voltage stability. This is a strong part of the literature review in this
thesis.
The conceptual design of the smart VAR generator will involve the overall system
architecture design, mathematical calculation of optimal inductors, capacitors,
switching algorithm, micro process program and critical component design.
Most of the passive components’ (such as inductors and capacitors), manufactures
have introduced their own design software to help use their raw materials. However
these design programs are not straight forward to find an optimum solution. Therefore,
studying these component and design was a major area of this study to find the right
selection of component for the smart VAR generator.
The electrical engineering principles and mathematical modeling was used to design
the smart VAR controller.
3 Back Ground
3.1 Higher PV energy penetration as an alternative to
fossil fuel energy
Together with social developments, association of social comfort equipment is rapidly
increasing. In parallel, energy consumption also is increasing. The energy consumption
is a measure of social development and also a country development. From year 1973
to year 2010, global energy consumption has doubled (IEA, 2012). Traditionally all the
energy was generated with fossil fuel at the expense of environmental impacts such
as pollution of water and air, destruction of forests and top soils, and climate change.
Figure 3-1 show percentage of use of energy sources in 1973 and 2010 respectively.
According to the figures, oil based energy generation in 1973 is 46.1% out of total 6115
Mtoe. In 2010 oil based energy generation is 33.2% of 12267Mtoe. Even though the
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percentage of oil based energy consumption is less in 2010, amount in Mote is 44%
higher in 2010 compared to 1973 and therefore the corresponding carbon emission.
Mtoe = Mega ton of oil equivalent
1toe = 11.63 Mega Watt hours
There is no indication of PV based energy supply to the public consumption in the
figure 3-1 below. The solar energy technology was started to commercialize in year
2000, however the contribution was not enough even in year 2010, but it is included in
the category specify as “other”. The 0.9% of other sources include solar, geothermal
and wind.
Figure 3-1: Energy sources and total consumption 1973 and 2010.
Source: www.iea.org 2012 report.
3.2 Kyoto Protocol makes a difference
The Kyoto protocol was signed in 1997 in Kyoto and affected from 2005 onwards, 190
member countries got together and agreed to reduce greenhouse gas emission. The
developed countries have to reduce their greenhouse gas emissions by 5.2% from their
1990 level by the target period of 2008-2012. In the European Union, commitment is
to an overall reduction of 8%. In order to help to reach this target, the EU has also
agreed to a target to increase its proportion of renewable energy from 6% to 12% by
2010. The goal is to reduce the green house emission by 40 % compare to 1990 level
by 2020. The developing countries should reduce their greenhouse gas emissions by
15 to 30%, as compared to the projected growth of their emissions by 2020 (Kyoto
Protocol, UNFCCC, and retrieved 9 December 2011)
These directions forced the public to develop alternative energy systems to support the
escalating energy demands and also reduce the greenhouse gas emission. For the
past 5 years, solar and wind energy direct conversion showed a rapid growth.
Germany’s solar energy direct conversion is over 8% of the total. Further table (3-1)
shows the direction of global renewable energy development in 2010 and 2011.
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In fact, there are many developing countries currently depend on the fossil fuels. This
is a good opportunity to work on the PV based energy generation together with the
direction and opportunities provided by the Kyoto protocol. One of the biggest
advantages of the PV energy is that the grid connection is in the low voltage network.
They do not load the transmission lines and therefore avoid the higher upgrading cost
to meet the growth of energy demand.
PV Peak Power Capacity (MW)
Country
Germany
Italy
Japan
United States
Spain
China
France
Belgium
Czech Republic
Australia
United Kingdom
South Korea
Greece
Canada
Slovakia
India
Switzerland
Israel
Ukraine
Austria
Portugal
Bulgaria
Netherlands
Taiwan
Slovenia
South Africa
Total 2010
Total 2011
17,320
3,502
3,617
2,519
3,892
893
1,025
803
1,953
504
72
662
206
200
145
189
111
66
3
103
131
18
97
32
36
40
24,875
12,764
4,914
4,383
4,214
3,093
2,831
2,018
1,960
1,298
1,014
754
631
563
488
461
216
196
190
176
144
133
118
102
90
41
Table 3-1 : PV country base consumption figures.
Source: Global Market Outlook for Photovoltaics, retrieved 6 December 2012
At present, Europe is taking the PV energy generating leadership. The Peak energy
demand occurs during the day time for the most developed industrialized countries. PV
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energy is ideal to meet the peak energy demand. Fig 3-2 shows the use of PV energy
to meet the peak demand in different countries.
By 2013, installed PV systems may produce 110 billion kWh. This represent around
0.5% of the electricity demand of the world. In Europe, PV contribute around 2.5 % of
the total electricity demand. [IEA, A snap short of global PV 1992-2012]
Germany is the country uses most PV energy during peak demand. They have most
experience on the PV energy during peak hours, variation, voltage regulation issues
and reactive power demands.
Figure 3-2: Country comparison of PV peak power.
Source: IEA, A snap short of global PV 1992-2012.
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Figure 3-3: Total world energy consumption
Source: Renewables 2012 Global Status Report.
The development of renewable energy sources makes a paradigm shift of the
conventional centralized energy generation systems. PV systems are vary from small
scale 200 W to 500 kW, however, their capacities are still smaller compare to the
tradition large fossil fuel power plants. PV systems are connected to low voltage grid
close to the consumer and skip long distance transmission.
3.3 Centralized
generation.
power
generation
vs
distributed
Over 90 % of the global power generation systems are centralized. “There is however
no consensus in the literature on the upper limit to be set”, to call a generation unit a
centralized system however, “this limit can range from 1 MW to over 100MW”
[Ackermann et al., 2001]. Long distance transmission lines deliver the power with
extremely high voltage (220kV-110kV) to the required distribution hubs and connected
to the distribution lines after step down the voltage to the distribution level.
There are several strong reasons behind the centralized electricity generation.
1. Economies of Scale: Overall plant capacity, size of the generation plan, size of
turbines, construction scale; decide the economies of scale which eventually
reach the lower cost for 1 unit of electric generation.
2. High efficiency: Overall system level optimization reaches higher system
efficiency than looking certain component efficiency.
3. Electricity transmission: Transmission techniques were developed. High voltage
transmission keeps the losses lower and carries the energy long distances.
4. Reliability: few large scale system interconnections bring focus maintenance
and simplify the system control and monitoring capabilities.
-18-
The main drawback of the centralized electricity generation is the transmission and
distribution costs and losses. Transmission carries around 30 % of the delivered
electricity cost.
Other major drawback for developing countries is higher capital investment cost for
rural electrification. In Sri Lanka, most of the electricity generation takes place in the
central part of the country and transmit to the rest of the country.
In the renewable energy context, most of the power generating systems are small scale
and output voltage is low (less than 1000V) considerations. “As per Pepermans et al.
(2005), the definition varies significantly in terms of characteristics of the generators.
Dondi et al. (2002) define distributed generation as a generator with small capacity
close to its load that is not part of a centralized generation system. Chambers (2001)
puts a limitation on the maximum capacity of distributed generation (30 kW)”. These
power systems need to be connected to the low voltage distribution system.
“For the purposes of this Distributed Generation (DG) Review, DG is defined to be any
generation which is connected directly into the distribution network”(Ofgem, 2007
May).
Presently, the distribution net works are not purposely developed to connect the
distributed generation (DG). Some of the challenges are,

Managing the distributed generators (DG) in the low voltage network.

VAR, voltage, Power factor control.

Grid, voltage, system stability.

Production cost and economies of scale.
“The Government’s Energy Review Report of July 2006 highlighted the challenges we
face in addressing climate change and ensuring security of energy supplies. A key part
of responding to this challenge is to investigate to what extent DG could complement,
or in the longer term potentially offer an alternative to, a centralized system”( Ofgem,
2007 May).
Based on the studies, centralized power generation is considerably cheaper at the
expense of carbon emission which needs to be quantified to add to the cost for a fair
cost assessment.
“Due to alternative energy, energy independence, Kyoto protocol, greenhouse gas
emission” (Perpermans et al., 2005), pressure is being built up for the electricity market
liberalization.
Distributed generators are smaller in size, fast turnaround time, rapid market approach,
geographically and operationally flexible. Therefore loading the distribution network
with renewable energy sources is rapidly increasing.
PV system is one of the rapidly increasing renewable energy sources to the distribution
network.
-19-
Now the regulations are developing to make sure the distribution net work is safe and
healthy to connect the distributed generators. This study connected with voltage
stability and power factory control.
3.4 Photovoltaic systems and Inverters
There are two major parts in the solar power generation system the solar cell and the
inverter. Solar cell is the reservoir and it harvests the solar energy whereas the inverter
convert the DC voltage generated from the solar cell to the AC voltage that can be
couple to the grid.
3.4.1 Solar cells
The solar panels shown in figure (3-4) exposed to solar irradiation and convert the
energy into electricity. Solar cell is a p-n junction. When the photons strike the surface
of the solar cell, it allow the electrons to release. If there is a conductor between “n”
junction and “p” junction, a current can be experienced. It creates a direct current.
Most of the energy that reach a cell in the form of sun light is lost before it can be
converted into electricity. Maximum sunlight to electricity conversion efficiency for solar
cell is range up to 30%. However typical efficiencies are 10-20%. Major reasons for
lowering the efficiency are, reflection from the cell surface, light that are not energetic
enough to separate electrons from their atomic bonds, material defects, resistance to
current flow and shading effect,
Figure 3-4: Solar panel diagram: no copy rights.
Source: http://etap.com/renewable-energy/photovoltaic-101.htm
Solar cell efficiency also depend on the material, mainly thin film or crystalline and the
operating temperature.
-20-
In order to run the solar system in the optimum efficiency, it is important to track the
maximum power point (MPP) shown in figure (3-5) and (3-6). The MPP point is
changing depend on the irradiance and temperature conditions at a given time.
Presently, technology is available to track the MPP and switch the inverters for
optimum energy harvesting.
Figure 3-5: current- Voltage curves depending on the ambient temperature
Source:http://solarprofessional.com/articles/products-equipment/inverters/how-inverters-work/page/0/1
Optimum point
Vm , I m
Figure 3-6: Typical I-V characteristic of a solar cell in steady-state operation
The following schematic digram (3-7) represent the function of solar p-n junction.
Current that flow through the solar cell can be mathematically represent as follows.
-21-
RL
Iph
I
Is (𝑒 𝑞𝑉/𝑘𝑇 − 1)
V
L
Figure 3-7: Equivalent circuit of solar cell with active load
Diode equation (eqn-3-1)
I = Is * { 𝐸𝑥𝑝 (𝑞𝑉/𝑘𝑇 ) − 1} – Iph…………..(3-1)
Where I: Diode current
Is : Reverse bias saturation current
K : Boltzmann constant
q : charge
I m : optimum point current
Vm : optimum point voltage
Voc : open circuit voltage
Isc : short circuit current
𝑘𝑇
Optimum voltage:
Vm = Voc -
Optimum current:
Im = - Iph ( 1-
Power is given by; Pm
𝑞
ln [1 +
𝑞 𝑉𝑜𝑐
𝑘𝑇
𝑞𝑉𝑜𝑐
𝑘𝑇
] ……………..(3-2)
) ……………………... (3-3)
= Vm x I m ………………………………(3-4)
-22-
3.4.2 String Inverters
String inverters are transformer base or transformer less large scale solar inverters.
Power conversion capacity vary from 1.0 kW to 100 kW range. The major functions of
the inverter are:
•
Inversion: This is the switching method used to convert DC to AC.
•
Maximum power point tracking (MPPT): This a technique uses to find where I_V
curve maximize for maximum power output
•
Grid disconnection: As per UL1741, IEEE1547 the grid should trip off the system
when the voltage or frequency changes above or below the system defined
acceptable levels. Further, in case of islanding, “grid disconnect should operate
and trip off the inverter from the mains. Islanding means there is no power
delivering into the grid in any direction.
Figure 3-8: Basic configuration of string inverter
Source:http://solarprofessional.com/articles/products-equipment/inverters/how-inverters-work.
Figure 3-8 shows the basic configuration of a string inverter. Towards the solar cell
and basic energy storage side, high frequency PWM switching takes place. At that
point, current can be shifted to get a required level of phase shift with voltage.
All inverters today use some combination of power semiconductors, IGBTs, MOSFETs
or both. They do the DC to AC conversion. Other major components are the
capacitors, inductors, transformers. Operating frequency can be 50/60Hz or higher.
Transformers are used to adjust the output voltage to the required level. Transformer
also provides the galvanic isolation between the DC, solar cell side and the AC output
side. The 50/60Hz transfomer based inveters typically used H bridge topololgy for the
DC to AC conversion. Switching the H bridge based on pulse width modulation
techniques, sinusoidal wave can be generated. Transfomer is used to step down the
-23-
voltage. Inductors are used to smooth the wave forms . These string inveters can off
set the voltage and current to generate the required-var . String Inveters are capable
of feedding or consume reactive power inline with utility demand without any external
devices.
String inverters are in large scale and there are series of solar cells connected to string
inverters. Refer picture (3-1, 3-2, and 3-3) below
Picture (3-1)
picture (3-2)
picture (3-3)
Picture 3-1: commercial string inverter 250kW: (270cm X 275cm X 150cm) (H XL X W), 1800kg.
Picture 3-2: commercial string inverter 100kW: (200cm X 130cm X 80cm) (H XL X W), 850kgs.
Picture 3-3: Residential string inverter
2 kW: (47cm X24cm X 9cm) (H XL X W), 5kgs.
Power conversion capacity Watt per kg will go up considerably when the inverter
capacity goes down. Transformer less inverters show that they can convent higher
watt level per unit weight.
Picture 3-4: PV module connections
Source: “Enphase Microinverter M190″, Enphase Energy. www.enphase.com.
-24-
3.4.3 Micro Inverter compared with string inverters.
Micro Inverters are also grid tied inverters. However they are considerably smaller in
size. Internal switching and inversion takes place with high frequencies. Micro inverter
power conversion capacity is 200~300 W. These inverters are now directly attached
to the solar cell. Further micro inverters operate at lower voltages. In this thesis, we
mainly consider micro inverters. Commercial micro inverter 200W: (19cm X 12cm X
5cm) (H XL X W), 1.3kgs.
3.4.3.1
Two stage topology for solar micro inverter
Figure 3-9: Micro Inverter circuit
Software used to generate above diagram: www.powersimtech.com. Free demo
version.
Micro inverter circuit is shown in figure (3-9). PV input is DC and it is stored in the input
capacitor for smooth power intake. This is a two stage PWM conversion with a step
up fly-back transformer. Sine modulated PWM operation of the fly back MOSFET
transfers the packets of energy to the inverter intermediate capacitor. The fly-back
transformer also provides galvanic isolation from the DC side to the main electric grid.
PWM in the stage one is high frequency switching and stage two is low frequency
switching. There are several advantages on low frequency switching at the output.
Mode 1
Stored energy in the input capacitor push to the fly-back transformer primary when the
fly-back MOSFET turn on. Transformer secondary diodes are reversed bias for the
voltage applied across at this time and therefore diodes are in the blocking mode. The
transformer primary act as an inductor, stored the electromagnetic energy. Primary
current of the transformer rises linearly. Current is supplied by the input capacitor. This
capacitor is feeding by the PV cells.
-25-
PWM feeding to input MOSFET generate modulated sine primary current and voltage
across the transformer primary. Otherwise the transformer is not able transfer the
energy and voltage conversion.
The MOSFET switching in this stage is high frequency.
Mode 2.
When the fly-back MOSFET turns off, the voltage applied across the primary winding
is become reversed. Therefore secondary winding voltage become 180deg phase shift
and forward biases the output diodes.
At this time stored electromagnetic energy in the fly-back transformer primary step up
and transferred to the secondary winding side. It charges the intermediate capacitors
in the secondary side of the fly-back transformer and store energy.
Inductor in between the diodes and intermediate capacitor support smoothing the
waveforms and filter harmonics.
The snubber circuitry diodes, capacitors, active clamp circuitry MOSFET are used to
clamp the fly-back primary MOSFET voltages to a safe value.
Voltage applied across the drain to source will be a summation of input voltage, clamp
voltage across and leakage spikes voltage due to transformer leakage inductance.
Next step is to connect the intermediate capacitor across the main grid voltage. The
main grid voltage is operate in 50 or 60 Hz low frequencies. Therefore SiliconControlled Rectifier (SCR) full-bridge is used to convert the intermediate capacitor
stored voltage/ current to a sinusoidal output. The switching frequency must be same
as the line frequency. The output of the inverter is synchronized with the grid by digital
PLL (phase lock loop).
The MPPT controls the magnitude of the output current. The shape of the output
current is controlled by the current controlled loop.
The output common mode chokes filter the common mode harmonics.
3.4.3.2
Advantages of micro inverters over the string inverters
There are significant advantages of micro inverters over the conventional string
inverters and therefore becoming very popular among commercial range PV
application
Following are the main advantages of micro inverters over the string inverters
-26-
1. Moving from centralized inverters to distributed inverters optimizes the energy
harvest
2. Incorporated converters into the solar panel reduce the operation cost
3. Improves the system reliability from 5-20 years by reducing the converter
temperature and removing fans
4. Improve efficiency and reduce heat dissipation by replacing the hard switching
techniques with soft switching
5. Standardized designs
6. Eliminate electrolytic capacitors reduce high failure rates
Following picture (3-5) shows a micro inverter available in the market. It’s liquid proof
and robust design allows it to assemble close to the PV cells. The lightweight aluminum
molded body and fins help to keep weight low and dissipate more heat to keep the
internal electronics cool.
Picture 3-5: Micro Inverter
The picture (3-6) shows an array of micro inverters. Any number of micro inverters can
be connected in parallel to harvest more solar energy. Most economical range is from
few hundreds of watts to 12-15kW.
Picture 3-6: PV module parallel connections
Source: “Enphase Microinverter M190″, Enphase Energy. www.enphase.com.
-27-
3.4.3.3
Active power generation by the Inverter
The Inverter output current is based on solar irradiance. In basic, high performing,
economically inverter technologies show that it operates with unity power factor.
Reactive power generation is possible by shifting the current adjusting the switching
frequency and sequence.
However, micro inverters with low frequency switching have difficulties to generate
reactive power economically. Other major issue is the higher losses in the inverter that
generates heat inside the unit and that causes failure due to exceeding thermal limit.
3.5 Inverter Regulation and Testing
Regulations contribute to maintain the system health and safety. Many countries use
the fundamentals and develop their own regulations to suit for their own network.
Some countries adopt regulations already developed by other similar countries after
reviewing and adjusting to suit their own network. In fact, Sri Lanka adopts many
standards developed by other countries or organizations. Some of them are British
standards or IEEE standards. When it comes to PV inverter grid connection, following
standards are some of the matured standards.
•
•
•
•
•
•
•
•
US : UL 1741 standard for static inverters , converts , and controllers for use in
independent power systems
US: IEEE1547 IEEE 929-299 recommended practice for utility interface for
photovoltaic systems: approved in January 2000 now replaced with IEEE 1547
covering all distributed generators.
US; NEC article 690
UK : G83
Germany : VDE 0126-1-1
Canada : CSA 107.1
Spain : Royal Decree RD 1663 and recent RD 661
IEC 61727 and IEC 62116
3.5.1 US regulation connection
UL1741 standard was first release in May 1999, which covers the inverters, converters
and controllers for use in isolated power systems. It was written to match the
requirements of IEEE 929-2000 and IEEE1547.
UL1741 2001 version was
incorporated the testing requirements of the IEEE929 and IEEE1547 with frequency
range, voltage limits, power quality and non-islanding inverter testing. However, in
UL1741 (2005 version), voltage limits, frequency range, anti-islanding was deleted
effective from the 2007. These requirements are part of IEEE1547. The main goal of
the UL1741 standard is to ensure the safety of the inverter. Therefore the UL1741
standard tests and evaluation methodologies are meant for product safety. The
-28-
interaction between the PV inverter and grid is regulated in the IEEE1547. Utility
voltage, frequency, Power factor, Power quality and Islanding are major areas
discussed within the scope of grid and PV inverter interaction. IEEE 929-2000
represents an excellent basic coverage on PV inverter interconnection issues.
IEEE1547
UL 1741
Interconnection system
requirements





Voltage Regulation
Grounding
Disconnecting
Monitoring
Islanding
IEEE1547-1
Interconnection system
testing









Output voltage
Frequency
Synchronization
EMI
Surge withstand
DC injection
Harmonics
Islanding
Reconnection
Interconnection
Equipment




Construction
Protection against risks
of injury to persons
Rating, Marking
Specific DR tests for
various technologies
Figure 3-10: Inverter interconnection and testing
3.5.2 US National Electric Cord (NEC)
Article 690 of NEC addresses safety standard for the PV system installations. There
are more articles related to the same subject.
•
•
•
•
•
•
•
Article 110
Article 230
Article 240
Article 250
Article 300
Article 685
Article 705
: Requirements for electrical installations
: Disconnect means
: Over current protection
: Grounding
: Wiring methods
: Integrated electrical system
: Interconnected Electrical Power distribution system
NEC requires approvals or listing for components and electrical hardware. NEC is not
providing those approvals. There are third parties recognized for approval bodies.
Some of the top of the line laboratories are given below.




Underwriters Laboratory ( UL) : www.ul.com
ETL Seiko : www.etlsemko.com
Canadian standard Association ( CSA ):www.csa.com
FM Global : www.fmglobal.com
-29-
3.5.3 Inverter Testing as of UL1741 2005
UL standard for safety for inverters, converters, controllers and interconnection system
equipment for use with distributed energy resources. This standard covers the safety
and risk of the operation to operator and property as well as the utility requirements.
Power Quality Test
•
•
•
•
•
•
Harmonics
Power factor
Voltage flicker
Transient voltage limits
DC current injection test
EMC
Safety tests
•
•
•
Testing to electrical safety standard
Anti-islanding test
Under/over voltage and frequency test
3.5.4 Utility voltage and frequency test
Above test is conducted with a simulated utility source. The inverter should feed the
power within the defined voltage range and frequency. In case the voltage of the utility
goes beyond the set limits of voltage and frequency, the PV inverter must be able to
cease exporting the power within the defined time scale.
Table 3-2 : UL 1741 2005, page 129
-30-
3.5.5 Utility Interconnection testing as of UL1741 and IEEE1547
One of the main objectives of this work is to focus on the voltage stability of the grid.
Voltage stability is directly connected with the reactive power.
Voltage regulation describes the PV inverter to maintain the voltage within the
acceptable limits. There are applications in which the area power system operator may
request that the PV inverter supply or absorb the reactive power.
Feeder reactors are set to regulate the voltage between the regulator and the load and
maintain constant voltage downstream from the regulator. However, PV inverter that
couples closer to the regulator may cause the voltage regulator to lower the voltage
unless the inverter feed the sufficient reactive power to the system. In this scenario,
location of the regulator or alternative regulator or location of PV inverter coupling need
to rearrange to maintain the voltage regulation in the EPS.
The PV inverters are set to operate in the range of 88% - 110% of the nominal voltage.
If the voltage at nodes of the EPS due to the drop becomes less than the set low
voltage limits, the inverter may trip and cause the voltage drop further. To avoid that
there must be a mechanism to feed leading reactive power to the EPS. On the other
hand, if the voltages at nodes of EPS becomes greater than upper limit, it also causes
tripping the PV inverter. To avoid that there must be a mechanism to absorb reactive
power from EPS.
IEEE 1547, does not specifically asked the PV inverter to equip with power factor
correction. However it identifies the voltage variation issue and VAR compensation to
regulate the voltage.
3.5.6 Australia regulation
Australia energy regulation has identified the general requirements such as voltage
flickering, voltage regulation, harmonic content, frequency regulation, DC injection etc.
However they have not clearly defined the common coupling point voltage regulation
and injecting or consuming reactive power to or from the low voltage (LV) grid. This
direction is mainly based on the grid experience, available technology and policy.
“Currently, small grid connected inverters are required to inject energy to the grid at
power factor close to unity. This does allow the inverter to do any local compensation
for poor power factor which is a functionality that will probably be offered in the future.
The draft standard does however allow for this functionality to be negotiated with the
local electricity utility” (E.D. Sponner).
Australia regulation allow the inverters to operate in the power factor range 0.8 leading
to 0.95 lagging. The grid system average power factory is generally lagging. Therefore,
-31-
they allow higher leading power factory to compensate the higher grid system reactive
power.
They consider 30 kW as smaller power generators. The above limits are applicable for
output power range from 100% down to 20 %. They do not consider any power factor
control requirement below 20 %.
3.5.7 US distributed related standard scope.
In the USA, the electric grid and interconnected distributed resources (This can be any
electricity generating sources, such as solar, wind, are discussed under one umbrella.
Main focuses are safety of the people and property, grid reliability / performances, cost
consideration and farness.
IEEE 1547 is a generalized regulation of all the DR
system. North American approach to bulk system standard tends to be technology
neutral. However technologies, operating and power generating characteristics may
different from one power sources to other source. European standards are more
technology focus and written to address the focus issues when interconnecting to the
grid. USA also identified that and several efforts are underway to address the PV
inverters voltage, frequency tolerances, reactive power capability, and voltage and
Frequency control.
3.6 Regulation Change
European (Germany, Spain, France, and Italy) standard makers are already set up
technology base DR system standards.
-
VDE-AR-N-4105 - 2011-08
Germany, Spain
extend and stringent the regulations to include all the power
generation systems above 4.6 kVA should comply with system voltage stability. This
is considered at the time of applying for the connection. The network connection of the
power generation system based on procedure covers series of requirements and the
network operator determines the suitable network connection point that ensure the safe
network operation.
German regulation has tight the rapid voltage change in the low voltage distribution to
less that 3%. Voltage changes at the point of common coupling (PCC) attribute to the
simulation connection and disconnection of power generation units do not allow to
inadmissible network reactions if the maximum voltage change does not exceed a
value of 3% at the PCC.
As per the VDE standard E DIN V VDE 0124-100, Power generation systems shall
allow for operation under normal operating condition with voltage tolerance band of +/10% and in their permissible operating points starting with active power output of more
than 20% of the rated active power within following power factors.
-32-
a) Power generation system with the capacity less than or equal to 3.68 kVA,
the generation system can be operated within cos = 0.95 under-excited to
cos = 0.95 over excited. There is no requirement to follow any low voltage
network utility company/ operator, (for example in Sri Lanka it could be Lanka
Electric Company, or Ceylon Electricity Board), characteristic curves.
b) Power generation system with the capacity greater than or equal 3.68 kVA
and less than 13.8 kVA , In this case the operating characteristic curve will be
provided by the low voltage network utility company or the operator within cos
= 0.95 under-excited to cos = 0.95 over excited . See the figure ( 3-11)
c) Power generation system with the capacity greater than or equal 13.8 kVA,
In this case the operating characteristic curve will be provided by the utility
company or the operator within cos = 0.95 under-excited to cos = 0.95 over
excited . See the figure (3-11 )
Note: 3.68 kVA and 13.8 kVA values are taken based on the German standard
mentioned above. The standard bodies concluded the above numbers are based on
their local network grid and maintain the grid stability. These numbers can be changed
from country to country. However the calculation model can be used to other countries
to localized and suit to their operation.
Figure 3-11: Power factor range
Source: VDE standard E DIN V VDE 0124-100
4 Power System Stability
4.1 Power System Stability Introduction
Power systems are constantly exposed to various different disturbances, such as loss
of loads and generators, short circuits and failures in system components. Therefore
the stability of the system is an important aspect of the power system design and
operation. Power system stability is becoming an increasingly important topic with the
introduction of distributed grid tied renewable energy based generation units. The main
-33-
reasons are, firstly conventional system stability mechanisms designed for centralized
generating system are not fully capable of handling the distributed generation units and
secondly most of the renewable energy driven generators are intermittence in nature
e.g. PV power generators.
Power system stability is defined as “the ability of an electric power
system, for a given initial operating condition, to regain a state of operating equilibrium
after being subjected to a physical disturbance, with most system variables bounded
so that practically the entire system remains intact” [IEEE/CIGRE Joint Task Force on
Stability Terms and Definitions, 2004]
Power system stability can be classified in to three different areas,
• Rotor angle stability
• Frequency stability
• Voltage stability
Following figure (4-1) shows the different types of stability categories and time frame
of interest for modeling and analysis.
Figure 4-1: Classification of power system stability.
Source: IEEE/CIGRE Joint Task Force on Stability Terms and Definitions, 2004
When an electric grid or part of the grid is subjected to a physical disturbance, one or
more than one type of instabilities can be present. The above classification helps in
instability analysis by underlining the causes and symptoms. Rotor angle stability and
frequency stability will be discussed only in brief in this report because the main aim of
the project work is to study and find solutions for voltage instability, more specifically,
caused by shortage of reactive power by the grid tied photo-voltaic distributed power
generators (PV DPG). But we should not forget that instabilities are correlated such a
way that one type of unresolved instability can cause other types of instability.
-34-
4.1.1 Rotor Angle Stability
The system considered to be in rotor angle stability when all generators are
synchronized each other i.e. rotor angle instability occurs when there is a loss of
synchronism at one or more synchronous generators in a particular power system.
Unresolved rotor angle instability can lead to voltage instability. Rotor angle instability
is categorized as short term phenomena and the typical time frame of interest is 3-20
seconds. [P. Kundur, 1994] and [IEEE/CIGRE Joint Task Force on Stability Terms and
Definitions, 2004].
4.1.2 Frequency Stability
The system is considered frequency stable when the total generation output matches
system load plus loss demand. Frequency instability may occur due to splitting of a
larger interconnected system into islands or as a result of a significant loss of load or
generation within a given island. The frequency instability may be a short term
phenomena occur within fraction of a second or long term that long last for few minutes
based on what cause the frequency instability. [IEEE/CIGRE Joint Task Force on
Stability Terms and Definitions 2004]
4.1.3 Voltage Stability
Voltage instability, the main focus of this report, is refers to the “ability of a power
system to maintain steady voltages at all buses in the system after being subjected to
a disturbance from a given initial operating condition” [IEEE/CIGRE Joint Task Force
on Stability Terms and Definitions 2004].
The consequences of the voltage instability can be tripping the elements in a power
system by their protective controllers, or change or loss of load, leading to cascading
outages. [T. Van Cutsem and C. Vournas, 1998]
Usually the main driver of the voltage instability is the loads trying to restore after a
disturbance that increase the stress on the system by increase in reactive power
consumption. The major factor contributing to the voltage instability is the voltage
change (Drop for most of the inductive network and increase if the network
characteristics are capacitive) occurs due to active and reactive power flow through
the network. [IEEE/CIGRE Joint Task Force on Stability Terms and Definitions, 2004].
While the most common cause of voltage instability is related to loads, with the
increase of grid tied, low and medium voltage, distributed power generation units such
as Photovoltaic systems, combined heat and power systems and small scale wind
turbines can also cause voltage instability in areas where generation capacity of those
units are significant portion of the total generation. Because energy supply of sun, wind
and heat is unpredictable and intermittence in nature, supply to the power system can
change or loose rapidly, leading quick changes in voltage of some of the voltage bus,
especially the ones located far end of the grid. [VDE-AR-N 4105, 2011]
In some of the literature, voltage stability has been subdivided in to two categories,
namely,
-35-
4.1.3.1
Large disturbance – voltage stability
System faults, loss of large generation (MW range) or circuit contingencies are
classified as large voltage disturbances. The voltage stability study after a large
disturbance requires the analysis of the nonlinear response of the system over a long
period of time enough to capture the operation and interaction of the power system
elements. Normally the time frame of interest is from few seconds to few minutes.
4.1.3.2
Small disturbances – Voltage stability
Small change in the system such as incremental change or loss of load or generation
are classified as small disturbances. The small disturbance study is carried out to see
how the system will respond to a small disturbance at any given instant of time. The
useful system equations are linearized to help analyses the dynamic system response.
It is very important to make right assumptions and use those linearized equations under
right conditions. If small disturbance study requires to account for nonlinear scenarios
such as transformer tap changing and time delays appropriate nonlinear equations
should be used.
For the ease of voltage stability studies, response of the system to disturbances are
further sub categorize in to two, short term and long term. For the short term voltage
stability, called also as dynamic analysis, the dynamics of the fast acting system
elements such as loads and dynamic compensators are considered. The analysis
require voltage dependent load models and system differential equations. The long
term voltage stability, called also as static analysis, the method used in this report to
determine the static voltage changes, involves slower acting machines and linearized
system equations. In many cases static analysis is use to estimate the stability margins.
[IEEE/CIGRE Joint Task Force on Stability Terms and Definitions, 2004], [VDE-AR-N
4105, 2011]
In next chapters the small disturbance long term stability analysis or static analysis will
use to explain why DPG units require to deliver real time varying reactive power to
maintain static voltage stability.
4.2 Modeling of Power Systems
Power systems can be modeled and represented in mathematical form to help
analyzing the characteristics of the entire power system or part of it. There are two
method of modeling the power systems, i.e. load model representation and system
topology representation. Load model representation can be sub categorized in to two
different models namely, static load model representation and dynamic load model
representation. In static load model, the load can be represented as a function of the
bus voltage and frequency and can be used to study the short to long term voltage
stability of a post-disturbed system. Dynamic load models are used to determine short
-36-
term and transient voltage stability and involve critical load and other power system
element functions.
System topology representation helps identify the location and interaction of various
system elements such as generation, load, transformer tap changers and other system
components. [Kundur, P, 1994] [C. W. Taylor, 1993].
4.2.1 System Topology Representation
It is very important to define the region of interest for the voltage stability studies since
power system generally are very complicated and contain transmission and distribution
lines, transformers, thousands of buses, and other system components. Power system
and elements that are not influenced by the disturbance can be excluded from the area
of study because there is no impact upon the voltage stability of the area under study.
Following figure 4-2 shows a system topology representation of low and medium
voltage single-line radial distribution system.
Figure 4-2: Single-Line diagram of radial distribution system
Grid or the Voltage bus Uo, represents the universal bus where both reactive and active
power flow in and out without any limitation. It is also assumed that the voltage Uo is
maintained at a constant voltage level by the upstream voltage regulators or
transformer tap changers. U1 and U2 are distribution transformer input and output
buses and rated power of the transformer is P TX and QTX. U1, PL and QL represent the
load bus voltage and power and P1 or 2, Q1 or 2 represent the power flow through the
lines.
4.2.2 Determination of Critical Bus or Busses
Next important step of the voltage stability study is to determine the critical bus or a set
of critical busses. These busses can then be analyzed for different types and levels of
disturbances as they will drive the voltage instability and collapse.
In a radial distribution system, critical or weak bus is generally the one located
electrically and physically furthest away from the generator. But in a radial system
where many distributed generator units are connected, finding the weakest bus or a
-37-
set of weak busses is not as easy as conventional radial distribution system. Industry
experience has proved that the weakest bus or set of busses are generally located in
locations with highest reactive power deficiencies occur or the one having lowest
reactive power margin. [WECC Guide: Planning Standards I.D, 2006]
4.2.3 Static Analysis – Power system stability
There are two methods of analyzing power system stability i.e. static and dynamic
analysis. Out of those two methods, static analysis is mainly used to study voltage
stability of a power system. In static analysis, also called load-flow or steady-state
analysis, all the possible stable operating points of a system under study is determined
by using the power flow equations, assuming that the frequency in the “area of study”
is constant. A common way of developing the stable points is to develop relationships
between transmitted power (P), receiving end voltage (V), and reactive power injection
(Q), also called P-V and V-Q curves.
4.2.4 Active Power vs Voltage OR P-V curves
The P-V graphs are developed for a bus of interest, using simulation techniques by
varying the power in small increments in and out of the bus. In typical voltage stability
study only the load is taken in to account, but to study the voltage of a bus, having a
distributed generation unit connected to it, generator and/or load has to be considered.
A series of curves can be produced, each one as shown in Figure 4-3, with each curve
depicting one or more disturbances.
Each equilibrium point on the curve represents a steady-state operating condition i.e.
stable operating point for over ½ hour. This means that the power generation and load
are balanced and all the voltage regulating devices are set and operating in a stable
point system meets its reliability limits. Beyond the operating limit, further increase in
power may result in a violation of one or more of the reliability criteria. The operating
limit is the maximum power that a system can generate and deliver to its loads and still
can return to steady-state reliability limits after a disturbance.
Typical Power versus Voltage curves
-38-
Figure 4-3: Active power and bus voltage
4.2.5 Reactive Power and voltage stability
Reactive power is defined with alternating current (AC) in an electrical system. When
the voltage and current are in phase, it transfers only active power. In case of the
phase shift between the voltage and current, it produces both active and reactive
power.
4.2.5.1
Analogy to understand the reactive and active Power
When an object is thrown from point A to B, very close to ground level, it cannot be
thrown straight reference to the ground. It should be thrown in a parabolic path. There
are two forces act on the object – one perpendicular to the ground and one parallel to
the ground. The force that parallel to the ground move the object from point A to B i.e.
does the work. However, without vertical force [to overcome gravity], it is not possible
for horizontal component to move the object from point A to B and does the work. The
vertical component is the reactive power which is necessary to push the active Power.
Amount of reactive power required for voltage stability of the power system is depend
on the amount of active power on demand and reactive power loses (stored in various
reactive components in the system) at any given time. Active power demand changes
in real time based on the consumption and therefore, reactive power injected into the
system and location has to be adjusted in real time. It is more convenient to express
the amount of reactive power required as a ratio between reactive power and apparent
power. Cosine of the ratio between reactive and apparent power is called the power
factor and therefore the power factor is widely used to define reactive power demand
and minimum limits e.g. Power factor > 0.95. The voltage at each node or bus can be
controlled by injecting the right amount of reactive power to the node or visa-versa.
-39-
Unlike active power, reactive power cannot be transmitted or distributed efficiently in
long distances. The reason is that the reactive impedances of high voltage lines are
very high compared to real impedance e.g. reactive impedance of 345kV line is ten
times of the real impedance, therefore reactive power flows encounter heavy power
losses. In order to minimize losses, reactive power consumption and generation has
to be close to each other. The voltage regulation is a localized event that controlled by
transmission system operators (TSOs), using generators and few number of reactive
power compensators. However, TSOs cannot control tens of thousands of distributed
generation (DG) units connected to the grid, therefore, it is important that DG
participate in real time reactive power control of the power system. Due to that reason,
a new set of regulations focusing on DG, has been introduced in many countries
around the world. [Omid Alizadeh Mousavi and Rachid Cherkaoui, 2011]
The reactive power compensators are two fold, static and dynamic. The dynamic
reactive power compensators should react with in a cycle after a disturbance, but static
are acting much slower, takes a long time to obtain a feasible operating point. Many of
the voltage collapse and blackout incidents around the world, are caused by the
improper reactive power control or reactive power deficits.
4.2.6 Reactive Power vs Voltage OR V-Q curves
Power system designers use V-Q curves to determine how much reactive power
required to maintain the voltage stability of any power system. They use the load model
representation and system topology representation to demonstrate the power system.
Then by creating deliberate set of disturbances, the bus voltage and reactive power
required to bring the bus to a stable equilibrium point is determine using power system
simulation software. The graphs that are created by changing the reactive power
injected and bus voltage called V-Q curves. Each point in the curve gives equilibrium
point of operation. [Omid Alizadeh Mousavi and Rachid Cherkaoui, 2011]
Following V-Q graph shows static and dynamic reactive power requirement of a power
system. Minimum reactive power required is the difference between the reactive power
required or generated after the system reach a new stable point of operation and the
post-disturbance reactive power consumption. Total reactive power required is sum of
dynamic and static reactive power required to maintain the system stability after a worst
case disturbance. In case of low voltage grid tied DGs, only the static reactive power
will be considered. The reason is that the dynamic reactive power resources normally
should be responded to a disturbance very fast and only synchronous generators and
condensers fulfill the requirements of dynamic Var.
-40-
Figure 4-4: Reactive power required and bus voltage V-Q curve for dynamic and static stability
[Source WECC Guide: Planning Standards I.D, 2006]
After a disturbance, first dynamic reactive power resources responds and bring the
system to an intermediate stable point and then slow responding static reactors take
charge and bring the system to a long term stable equilibrium point.
4.3 Grid Connected PV Powered Generator Systems
This section discuss about the impacts on the power system stability by the low voltage
grid connected DGs. In some of the countries, such as Germany and Italy, low and
medium voltage grid connected PV DGs represent a significant part of its total
generation capacity. In some of the days in summer, PV generation can go as high as
40-50% of the total generation in some areas. With the higher number of DGs
connected to the grid at the same time producing varying amount of power, it is very
difficult for TSOs to control the active and reactive power input and flow in the system,
therefore DGs can adversely affect the voltage stability of the system. In the recent
past, tight regulations has been introduced on the voltage regulation of low and medium
grid tied DGs. One of the main requirements of the new standards is, similar to
generators connected to the higher voltage levels, power generation systems
supplying low and medium voltage levels should also contribute to the voltage stability
by generating reactive power and closely controlling active power input to the system.
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As an example, German regulation for stable operation of the system on low and
medium grid tied DGs, VDE-AR-N 4105:2011-08 requires that the voltage change
caused by the DGs at the common connection point in a low or medium voltage
network shall not be more than 3% as compared with the voltage without the DGs.
Common connection point is where the DGs are connected to the grid.
i.e At any bus in the power system; Delta U < 3%
as per the new regulation DGs cannot increase the active power input to the system
suddenly, It has to be done step by step confirming that after each step of active power
increase, voltage and frequency of the bus is stable.
4.3.1 Reactive and Active power vs Bus voltage
The impacts of reactive power and active power generation on voltage of the low and
medium distribution system has been evaluated by using the Siemens PSSE power
system simulation software. Figure (4-5) shows the single line diagram of the radial
distribution grid model and the scenario used for the evaluation. The model used for
the simulation is similar to the representative low voltage radial grid model given in the
standard “VDE-AR-N 4105:2011-08”. Primary side of the distribution transformer, 11kV
has been considered as the universal bus and therefore all the parameters such as
voltage, power factor remain constant on the universal bus. Power can flow in and out
through the universal bus without any limitation. Capacity of the distribution
transformer is 400kVA. Two DGs, 35kW and 10kW at unity power factor are already
connected to the low voltage grid. The main objective of the simulation study is to
analyze how a third DG unit having maximum active power generation capacity of
25kW and variable power factor, 1 to 0.9 and 1 to -0.9, affect the bus voltages and
angles in the low voltage grid. The inductive PF, also called lagging PF because current
waveform is lagging the voltage and mathematically represent by a positive number
from 1 to 0 and the capacitive PF similarly called leading PF because current waveform
leading the voltage and mathematically represent by a negative number from 0 to 1.
e.g. -0.9 or -0.95.
4.3.2 PSS®E Simulation software
PSS®E university edition was used to simulate power flows under different condition
of the new DG and calculate bus voltages and angles. Student version is capable of
doing the same amount of processing as commercially licensed software. PSSE
software developed by Siemens power technologies help students with the
fundamentals needed to analyze power systems. The PSS®E University edition
includes the following components.
[Source – Siemens power technologies international, University, PSS E, 09.2013,
Siemens AG and Siemens Industry, Inc.]
The single line radial grid and other power system elements such as transformers, DGs
and voltage buses has to be defined first. All interconnection lines should have the
correct real and reactive impedance values. It is also important to define the universal
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bus or also called swinging bus (Grid bus) as only a part of the power system is used
for the simulation.
4.3.3 Definitions
4.3.3.1
Universal bus OR swinging bus (Grid)
Swinging bus is considered as the bus with a constant voltage and also both active
and reactive power can freely flow in and out of the bus. The assumption is that the
upstream controllers and regulators are capable of maintaining the conditions of the
bus independent of the disturbances at the downstream of the bus. However, in order
to be within the limits of upstream regulators and controllers, downstream system
should also meet certain requirements like reactive power input and delta voltage
limits. The voltages of the remaining buses are stated with reference to the universal
bus, i.e. per unit (PU) voltage of the universal bus is equal to 1.
4.3.3.2
Distribution transformer
Rated power and real and reactive impedance values should be defined. Primary side
of the transformer and universal bus are considered to be at the same conditions.
4.3.3.3
Distributed generators – DGs
There are two distributed generators are already connected to bus # 3 (TRA SEC) and
# 4 (PV DG1) 35kW and 10kW respectively. A third DG having 25kW capacity and
variable power factor 0.9 or -0.9 is connected to the bus # 5 (PV DG NEW)
4.3.3.4
Interconnection
NAYY-J 4 x 95, 200m long underground cable is used to interconnect bus # 3 and # 4.
Overhead line Al70 is used to connect the bus #4 and #5.
The Figure (4-5) shows system topology of the part of the low voltage grid. “Grid”
represents the swinging bus (universal bus) where the voltage is maintained at a
constant value. A new PV powered DG is connected to the far most bus (# 5) from the
Grid or universal bus (#1).
-43-
Figure 4-5: Lower voltage grid simulation models
Following are the ratings of the components
Short Circuit level of the upstream grid = 100 MVA
Distribution Transformer rating 400 kVA, Uk = 4%, Pcu = 4600 W
Underground Cable =200 m, R = 0.32 ohm/km, X = 0.082 ohm/km
Overhead line = 300 m, R = 0.436 ohm/km, X = 0.309 ohm/km
GRID – universal bus 11kV – Voltage reference, PU = 1
DG1 = 35kW, PF =1, DG2 = 10kW, PF =1, DG3 25kW, PF= 0.9 ~ 1 OR 1 ~ -0.9
4.3.4 Bus voltage vs Active Power generation / simulation using
PSSE
In the first simulation, the power factor of the third DG3 was set to 1 (unity power factor).
voltage of each bus #1 to #5 in the radial grid has been calculated for different power
input levels starting from 0kW to 25kW in steps of 5kW using the PSSE simulation. Bus
voltages are expressed in PU with reference to the voltage (11kV) of the Grid or
universal bus. Following graph shows the variation of the voltage against the active
power generation. Red horizontal line represent the maximum voltage change
acceptable according to VDE-AR-N 4105:2011-08. Each line represent the PU voltage
of each bus in the grid.
-44-
Table 4-1: Bus Voltage Vs Active power
As per the above graph, if the power factor of the third DG3 is fixed at 1 (unity power
factor) and when the active power input to the grid through Bus #5, generated by the
DG3 is between 20kW - 25kW then the voltage of the far most bus, i.e. bus #5, “PV
DG NEW” exceed the 3% static voltage limit.
It can also observed that the voltage of the bus # 5 changes much more compared to
other buses. In a normal day, power generated by PV DG can change in a wide range
depending on the availability of solar energy and other environmental changes like
shading or sudden clouding. Therefore active power feeding to the bus #5 can change
suddenly. We can conclude that, if the DG3 is allowed to function at unity power factor,
it will cause higher voltage fluctuations and cause voltage instability in the area and
also affect the upstream stability.
Another important point we should observe is that the voltage on all the buses vary
depending on the active power input. Therefore the counter action (as we know
reactive power) to keep the voltage within limits has to be delivered on real time. The
reactive power, inductive or capacitive required by the bus to control the voltage is
proportional to the active power it produce and need to deliver quickly with in few
seconds to avoid voltage fluctuations.
-45-
4.3.5 Bus voltage vs Reactive Power generation / simulation using
PSSE
Second simulation demonstrate how the bus voltage varies when the leading or lagging
reactive power is injected to the bus together with the active power. Active power input
to the far most bus #5 or “PV DG NEW” was maintain at 25kW. In earlier simulation it
was shown that 25kW of active power cannot be delivered at unity power factory to
bus # 5 without hindering the voltage stability. Five different scenarios has been
created to study the voltage variation.
1. 25kW active power input at unity power factor - reference case.
2. 25kW active power input at 0.9 leading power factor or consume reactive power
3. 25kW active power input at 0.95 leading power factor or consume reactive
power
4. 25kW active power input at 0.9 lagging power factor or reactive power
generating
5. 25kW active power input at 0.9 lagging power factor or reactive power
generating
Following graph shows the simulation results of the simulation. Similar to previous
simulation Grid or the universal bus is maintained at constant voltage of 11kV or PU=1.
The voltage values given below are PU quantities with reference to universal bus
voltage.
Table 4-2 : Bus voltage vs. Reactive Power.
-46-
AS per the graph, reactive power injection to the bus # 5, “PV DG NEW” or operating
the DG at lagging power factor can bring the system back to stability. It is important to
observe that leading power factor or reactive power consumption by the DG further
deteriorate the voltage stability, i.e. operating at leading power factor will be more
unstable. Voltage on the bus #5 drops to PU 1.029 and 1.026 when the DG is running
at 0.95 and 0.9 power factor respectively from 1.034 at unity power factor.
In case of our simulation model, static voltage difference at the far most bus, bus # 5
drops with the increase of the reactive power input. Similar voltage stability studies has
shown that even though most of the parts in the power system require inductive or
lagging power factor in some areas or instant of time, power system needs DG to run
at leading power factor or consume reactive energy means of capacitive loads. [VDEAR-N 4105:2011-08]
It is clear from the simulation that adding more and more DG units running at unity
power factor cause voltage fluctuations and thereby voltage instability. Further, amount
of reactive power required to stabilized the bus voltage depends on the active power
generate by DGs and direction of power flow through the grid. Due to the heavy losses
incurred while delivering reactive power from one area of the power system to another
area, reactive power required to regulate bus voltage has to be generated close to
where it is required. The voltage changes caused by sudden changes in active power
can get aggravated by the respond of certain type of loads and will lead to fluctuations,
i.e. voltage sensitive loads. Therefore voltage changes need to be fixed quickly to avoid
cascading effects and voltage collapse.
The solution is a static reactive power (Var) generator that can monitor the active power
input and nature of the power system (whether it needs leading or lagging PF, provided
by TSO on real time or as fixed curves) and deliver the required amount and type of
reactive power on right time.
5 Solution approaches for VAR controls
5.1 Solution approaches for static Var controls
Petro solar current sources approach
“Nasser Kutkut” and “Petra Solar” publishes an article and discussed a solution to
generate reactive power from the micro inverter. The logic is to have two current
sources, one with zero phase shift and other with 90 o phase shift. This is shown in
figure (5.1).
I1 is the current from the solar cell and I2 is generated from the inverter with a phase
shift of 90o based on the demand of reactive power. This result has been achieved by
integrating four quadrant inverter. Reactive Power is generated based on the demand.
-47-
.
Figure 5-1: Current Source Inverter Models
This method cannot be used together with the low frequency switching (LFS) solar
micro inverters with high reliability i.e. 20 years warranty. Generating a internal current
source at with 90 deg phase angle shift significantly reduces the efficiency of LFS
inverter and reduce the reliability of the inverter.
5.2 Power One: VSI approach
There are two types of inverter topologies. They are voltage sources inverter (VSI)
and current sources inverters (CSI). An ideal voltage source has zero internal
resistance so that changes in load resistance will not change the voltage supplied. An
ideal current source has infinite internal resistance so that changes in load resistance
will not change the current supplied.
A battery bank is a good example for the voltage sources and similarly solar cell can
be considered as voltage source.
Current source inverters require relatively large inductors to smooth the rate of change
of current. Inductor stores energy and release with a variation of current. Therefore
CSI topology is inefficient and, have higher harmonics. Whereas, voltage sources
inverters do not use any inductor. VSI topology use capacitors to support current
spikes. VSI is recommendable for high efficiency high performance applications.
There are companies which came up with new generation micro inverter topologies
that inject or absorb reactive power to the grid or from the grid.
Power-One, Inc. a leading provider of renewable energy and energy-efficient power
conversion and power management solutions presented a new voltage source inverter
concept with extended grid services in 2012.
But new topology cannot use together with LFS type micro inverters.
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5.3 Apparent power: impedance matching approach
Apparent Power Company has published a paper in February 2011 and discussed a
patented technology called “dynamic Impedance matching”.
PV inverters are usually designed to correct the power factor at their output so that CSI
deliver only active power to the grid. With voltage sources inverter (VSI), the output
voltage of the VSI is always slightly higher than grid voltage; otherwise current would
not flow into the grid. The topology does not make it easy to control the current or the
power factor.
The situation is different with current sources inverter (CSI). Their goal is to produce
current but maintain the voltage equal to the grid voltage. CSI construction allow full
control over the power factor because of the full control over the current. Current phase
angle can be adjusted with respect to the grid voltage and change the power factor.
Existing solutions cannot meet VDE AR-N-4105 – 2011-08 regulation
Literature resources showed that many companies have identified the requirement of
reactive power and running the inverter in lead of lag mode. However, none of the
solutions adequately demonstrate a system that follows the German new regulation
VDE-AR-N-4105 - 2011-08
6 Dynamic, smart Var generator Approach
6.1 Basic Theory.
For the design process, it has been decided to focus on 6.0 kW integrated micro
inverters. However, the design approach can be used for different power ratings. The
two critical components of the Var generator is the reactor (inductor) and capacitor.
Our approach is to find a modular approach to make the design flexible and
economical. We also did a market research on the availability and technologies of
capacitors and inductors. We found standard series of capacitors. However inductor
availability is not straight forward. The main reason is that the inductor are design for
application specification requirement considering many parameters. For this particular
application, inductor requires, specific inductance values, operate in 50/60Hz, need
high efficiency with minimum no load losses, lighter in weight, smaller in size, also need
multiple taps for different inductor values. Inductor is a key components and this
particular project, we spend considerable time and effort to study, design, develop and
manufacture a required inductor.
-49-
The studies has indicated that most of the time, utility companies are requesting the
lagging or leading power factor characteristic curves. Since the delivering power, grid
voltage, frequency and power factor are variables, delivering or consuming reactive
power changes. Therefore the inductors and capacitors should be flexible enough to
support the reactive power in order have get the power factor difference less than or
equal to 0.01 for every 20% of the inverter delivering power. Therefore, it requires a
series of capacities and inductors to achieve the required higher resolution. However
practical point of view, capacitors are available in multiple steps and they are in
compact sizes. Inductors are bulky and not flexible in size or achieving required values
as capacitors. Therefore in our solution we choose limited number of inductors values
while capacitors are used for correction when necessary.
Calculation given below, shows how to find an inductance range and capacitor range.
Single phase series of micro inverter power delivery capability = 6.0kW
Series of micro inverter power: P system_max = 6.0kW
The minimum power that the inverter can run without power factor adjustment:
P system_ min = 3.68kW
Grid frequency: f grid = 50 Hz
Power factor which utility company request 0-0.95 lead or lag: pf correction = 0.95
Minimum grid voltage: V grid_min = 230V X 0.9 = 207V
Maximum grid voltage: V grid_max = 230 X 1.1 = 253V

Current delivered by the micro inverter system at maximum grid voltage :
I sys_max_Vmax

Current delivered by the micro inverter system at minimum grid voltage:
I sys_max_Vmin.

Total current to the grid at maximum grid voltage with power factor correction:
I grid_ V max.
Total current to the grid at minimum grid voltage with power factor correction:
I grid_ V min.
Current through the inductor or capacitor at maximum grid and inverter voltage:
I z_Vmax
Current through the inductor or capacitor at minimum grid and inverter voltage
I z_Vmin
Inductance at maximum voltage : L V max
Inductance at minimum voltage : L V min
Capacitance at maximum voltage : Cvmax






-50-

Capacitance at minimum voltage : Cvmin
P system_ max
I sys_max_Vmax =
equation……………………….…… …… ((6.1)
V grid _max
6000
I sys_max_Vmax =
253
= 23.71 A
P system_ max
I sys_max_Vmin =
equation…………………………..….……(6.2)
V grid _min
6000
I sys_max_Vmin =
207
= 28.98 A
I sys_ max _𝑉 𝑚𝑖𝑛
I grid_ V min
=
I grid_ V min
=
28.98
I grid_ V max
=
23.71
equation………………………………… .(6.3)
pf correction
0.95
0.95
= 30.50A
= 24.96A
Current though the impedance
I z_Vmax = √I
grid _𝑉𝑚𝑎𝑥 2 – 𝐼 𝑠𝑦𝑠_ max _𝑉 max 2
I z_Vmax = √30.5^ 2 –
I z_Vmin = √I
28.98^2
= 9.50 A
grid _𝑉𝑚𝑖𝑛 2 – 𝐼 𝑠𝑦𝑠_ max _𝑉 min 2
Inductance at V max and V min
L V max =
L V min =
Vgrid_max
Iz
Vmax
x 2X  x f grid
Vgrid_min
Iz
Vmin
x 2X  x f grid
= 103.37mH
=
equation…..…………(6.4)
69.1mH
Capacitance calculation
Iz_Vmax
CV min = V grid_ max x 2 x  x f grid = 98.12 F
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= 7.80 A
Iz_Vmin
CV max = V grid_ min x 2 x  x f grid = 146.57 F
Minimum Capacitor size
P min _correction = P system _ max x 20%
I Z min_ step =
P min correction X √0.962 − 0.952
V grid _ max
Iz
0.66A
step
Vmin
C min _step = V grid_ max
= 8.25 F
x 2 x  x f grid
Scenario Calculation using a spread sheet.
Below effort is to find out the required inductor range using above formulas for power
factor 0.99 to 0.95. Based on above formulas, a micro-soft excel based spread sheet
was developed to identify inductance and capacitance in various voltages and Power
Factor conditions. Case 1, is to calculate the inductance at Power Factor 0.95 within
the +/- 10 % ( 207-253V )voltage variation and case 2 is to calculate the inductance at
Power Factor 0.99 within the voltage range +/-10% .
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Case 1: V grid min and Power Factor:0.95
Spread Sheet for Inductance and capacitance
calculation
Frequency
50
Power factor
0.95
System Power
6000
V nominal
230
Vmax_grid
253
V min grid
207
I sys max
23.72
I sys min
28.99
I grid vmin
30.51
I grid max
24.96
Iz max
7.79
Iz min
9.53
Hz
PF
W
V
V
V
A
A
A
A
A
A
Lmax
Lmin
103.37
69.20
mH
mH
C max
C min
98.12
146.57
F
F
P min correction
0.66
A
C min_step
C selector value
Caps required
8.25
6.00
24.405
F
F
Table 6-1: Case 1, Vgrid max and Power Factor:0.95 condition.
-53-
Case 2: V grid max and Power Factor: 0.99.
Spread Sheet for Inductance and capacitance
calculation
Frequency
50 Hz
Power factor
0.99 PF
System Power
6000 W
V nominal
230 V
Vmax_grid
253 V
V min grid
207 V
I sys max
23.72 A
I sys min
28.99 A
I grid vmin
29.28 A
I grid max
23.95 A
Iz max
3.38 A
Iz min
4.13 A
Lmax
Lmin
238.43 mH
159.61 mH
C max
C min
42.54 F
63.54 F
P min correction
0.66 A
C min_step
C selector value
Caps required
8.25 F
6.00 F
24.405
Table 6-2: Case 2, Vgrid max and Power Factor : 0.99 condition.
Table 6-1 and 6-2 calculation showed, that the inductance requirement is in the range
of 69.20mH to 238.43mH. Maximum capacitance is 146.57μF. Minimum Capacitance
for PF 0.01 resolution is 8.25μF.
Based on the component research, capacitor values are more flexible than the
inductors. Further, the capacitors are cheaper than the inductors. Therefore it has
been decided to use a single inductor with few taps and serious of capacitors.
Based on our evaluation, we decided to use 24 parallel connected capacitors with the
each capacitance of 6μF are used. We will get the capacitance range 6μF to 144 μF.
We can step up the capacitance in the range of 6 μF. This is sufficient to maintain the
power factor resolution within 0.01.
-54-
The value of inductor is 200mH with the taps on 50mH, 100mH, 150mH and 200mH.
When the inductance requirement reaches 238.43mH, system will switch to 200mH.
Then the current through the inductor will go up around 19% and increase the
reactive power, which will be compensated through capacitance. Therefore 50200mH rang is good enough.
6.2 Inductor theory
Required inductance is in the range of 69.20 mH to 238.43 mH. Inductor core sizes
are fixed due to its construction difficulties. In the event of power factor lagging
requirement, it has been decided to use low inductance to increase the current. Once
the low inductance is switched on, the power factor lag more than what it requires.
That will be corrected with capacitors. However in order to minimize number of
capacitors for the correction, It was decided to use 4 taps in the inductor. This also
helps to minimize the copper and core losses and improve the efficiency.
Therefore it has been decided to use 50mH as a minimum inductance and 200mH as
the maximum inductance with taps on every 50mH. Maximum and minimum current
through the inductor are 9.53A and 3.38A respectively. Following are the currents
through the inductor at each tap.
50mH :
100mH :
150mH :
200mH :
9.53A
5.89A
4.13A
3.38A
At the design stage, above current values will be considered for the copper size
selection.
An Inductance (L) is formed when variable current is flowing through in coil and it
creates a magnetic field. Inductance is a measure of the amount of the electro motive
force (EMF) generated per unit change of current.
L=μ0μrN2A/l






equation………..(6.5)
L - inductance in Henries (H)
μ0 - permeability of free space = 4 × 10−7 H/m
r - relative permeability of the core material
N - number of turns
A - area of cross-section of the coil in square meters (m2)
l - length of coil in meters (m)
Inductors can be design with many different core materials and core shapes.
 EI core inductor
-55-


Toroidal core inductor
C – Core inductor.
6.2.1 Soft Magnetic materials
As the inductor is a critical component of the project, efforts were made to identify the
proper soft magnetic materials for the inductor core. Iron Powder cores and Ferrite
cores are used mainly in the high frequency applications. The ferrite cores are smaller
in size and overall energy handling capacity is relatively low. Silicon steel and
amorphous materials can handle relatively higher energy. Those materials can be
used for applications that require higher inductance at higher currents. Further those
materials are suitable for low frequencies. 3% silicon steel is capable of handling 50/60
Hz up to 400Hz. Amorphous alloy materials can be used for somewhat higher
frequencies since the material thickness is low. Some of the soft magnetic material
that can be used for the core are given below
Steel
Silicon steel 3%
Nickel steel
Silicon steel 6 %
Oxides
Powder
Amorphous alloys
Ferrites of various
mixers to achieve
different permeability
levels
MPP core
Cobalt base amorphous
Sandust core
Iron base amorphous
High flux core
Nickel base amorphous
Iron powder cores
Nano-crystalline alloys
Various material
mixers to achieve
different permeability
levels
Table 6-3 : Type of inductor core materials
Sources:
-
www.micrometals.com
www.mag-inc.com/products/powder-cores/mpp-cores
www.metglas.com
6.2.2 UI Core inductor
UI inductors are constructed in a tradition method with winding is wound in a bobbin
and insert it to core limb. There are two windings in the UI inductors. They can be
connected in series or parallel to increase or decrease inductance. The size of the
inductor is determined by energy (E) = (1/2) L I 2 and Inductance (L) = 0 N2 A / l
-56-
UI inductors has better thermal dissipation characteristic since the part of the core is
outside the winding and also the mounting mechanism allow the heat conduction to the
mounting chassis.
Design calculation Refer Appendix A.
6.2.2.1
Inductor design using UI inductor design software
Parameters of the inductor has been calculated using the Inductor calculation software.
http://www.rale.ch/
RALE Transformer Design Software 10mVA to 10MVA and Inductor Design Software.
6.2.2.2
Design Inputs
Inductance and current rating
50mH :
100mH :
150mH :
200mH :
9.53A
5.89A
4.13A
3.38A
Number of Air Gaps 2: It is preferable to have 85%-90% of the inductance in the air
gap to maintain a linear inductance. Since the inductor can be connected to low line (10% of the rated voltage) and high line (+10% of the rated voltage) during its normal
operation, high line voltage can draw a current 10% higher than the rated current. If
the inductance drops below a certain limit then, current increases pushing the inductor
further in to saturation and lowering the inductance.
Core size: Selection of the core size involves with lot of calculations. Since the core
size also link with inductance and heat losses calculation involves statistical methods.
Equations are complex and interrelated. Therefore to do an optimized design it is far
better to use a design software tool. There are many different design software tools
developed by various core material manufactures such as Hitachi, Magnetics and
individuals or companies. The present work used Rale design software to calculate the
inductor.
Temperature rise: Total losses of the core govern the temperature rise and therefore
the insulation class. Class B insulation has been selected to optimize the design while
keeping the costs at lower side.
-57-
6.2.2.3
Inductance, current and Flux densities
There is a limitation for the amount of flux that can be handled by any core. The flux is
propertinal to the current. Therefore “flux vs current” and “Indutance vs current” are
vital relationships of any inductor. In order to avoid collapse of the indutance and to
maintain constant inductance through out current range it is important to analyse the
relationship between “flux” and “indutance vs current. For slicon steel It is required to
maintain inductance at 1.55-1.6T range to avaoid saturation.
Graph 6-1: Inductance and current and flux densities
6.2.2.4
Flux pattern inside the core and outside the core
Following two graphs shows the flux pattern inside and outside the core.
Figure 6-1: Flux pattern inside the core and outside the core
-58-
6.2.2.5
Inductor construction
Picture (6-1) and picture (6-2) shows the constructed UI inductor for the 6 kW. It also
describes the mounting and wiring configuration. The UI inductors can be mounted
horizontal as shown in the picture or vertically up right. The horizontal mounting is ideal
for VAR box designs because the height of the complete enclosure can be reduced.
Picture 6-1: UI inductor construction
Picture 6-2: UI inductor construction
6.2.2.6
UI Inductor testing
In order to test the inductance and saturation point, we apply voltage across the
inductor winding starting from 16V through a variac and measure the current through
the leads. Then increase the voltage step by step and measure the current. Applied
voltage is sinusoidal and frequency is 50Hz. At some point, we see inductance started
decreasing where we reach the saturation point.
-59-
The Following graph shows the UI inductor test data. The variation in the inductance
over the range of operating current is 5% and in acceptable level. The inductance
variation can be further reduced i.e. 3% but design simulations suggested that the cost
increases quite dramatically with the lower inductance variation. The most optimum
and economical design of the VAR box can be achieved by 5% inductance variation.
SA488 4.38A I L-I Diagram(T=φ1.25mm*820TS Parallel NO bobbin)
GAP=3.5mm
0.25
Curretn(A)
16.0
Voltage(V)
203.8
Inductance(mH)
0.75
1.00
1.25
1.50
1.75
2.00
2.25
2.50
2.75
3.00
3.25
3.59
3.75
4.00
4.38
4.50
48.2
64.6
80.7
97.1 113.3 129.8 145.9 163.1 181.1 199.1 216.7 237.9 247.2 261.8 274.2 287.5
204.7 205.7 205.6 206.2 206.2 206.7 206.5 207.8 209.7 211.4 212.3 211.0 209.9 208.4 199.4 203.5
Table 6-4: UI Inductor test data for 50Hz.
Current Vs Voltage and Inductance
350
Voltage (V ), Inducatnce (mH)
300
250
200
Voltage(V)
150
Indutance (mH )
100
50
0
0
1
2
3
4
5
Current (A)
Graph 6-2: UI inductor testing for 50Hz
UI inductor design was wound as per the design and inductor started saturating when
the current reach 3.25A. This is marginally sufficient and we decided to use it as it is.
All design review and test outcome is as per the design, refer appendix A, 10.1
6.2.3 Toroidal core Inductor
Toroidal inductors are manufactured by a copper wire wound around circular core
materials. There are different types of core materials that are commonly used. Grain
oriented silicon steel (3% silicon), iron powder core, ferrite core etc. Silicon steel
comes in bigger reels. Those materials have to be slit to the required size of the core
height. Then using a bobbin, core outer diameter and inner diameter is formed. Core
is built with one or many air gap to avoid core saturation. Silicon steel is good for
-60-
frequency 50/60 Hz and up to 400 Hz, whereas ferrite and powder cores are good at
higher frequencies, they can be used over 1 MHz range.
Picture 6-3: Toroidal inductor construction.
Toroidal inductor turns are wound over 360 deg around the core. Magnetic flux in a
high permeability toroid is almost entirely confined to the core. Therefore the leakage
inductance is very minimal and also shows high quality factor.
6.2.3.1
Toroidal Core Inductor Design
This project is focused on the 50Hz frequency operation. The goal of the design was
to keep the core and winding losses as low as possible. Further the total harmonic
distortion should be lower than 2 %. Other aspects of the design is to have dimension
of as compact as possible with light weight. Economical manufacturing , design for
manufacturability, raw material availability, lead time of manufacturing, life expectancy
are some of the other considerations. We have decided to design with traditional EI
approach and toroidal approach, two widely used core construction methods.
We used basic inductor design formulas to calculate the Inductor core and number of
turns. Used the Excel supported formulas and calculations for the iterations. Later on
the formulas can be programmed with an advanced programming language for
advanced design usability.
200mH, 3.38A
N4
150mH, 4.13A
N3
100mH, 5.89A
N2
50mH, 9.53A
N1
Figure 6-2: Inductor schematic diagram
Refer Appendix-A 10.2 for detailed calculation.
-61-
6.2.3.2
Design summary
Following table gives the main parameters of the four inductors
Inductance Number W
Winding (mH)
of Turns turn
N1
50
245 245
N2
100
346 101
N3
150
424
78
N4
200
490
66
Diameter
of
copper
wire x
number
of
copper
wires
1.2mmx2
1.2mmx1
1.2mmx1
1.2mmx1
Resistance
of
winding
Cu loss St
Total
Cu
m
(W)
loss(W) loss(W) wt(kg)
454
41.84
3.99
45.83
1.2
828.8
28.75
3.99
32.74
0.25
1117.98
18.59
3.99
22.58
0.2
1362
15.56
3.99
19.55
0.17
Table 6-5 : main parameters of the four inductors
Optimizing the inductor design is very important to reduce the losses. Iron loss and
copper loss are the main areas to focus on to reduce the inductor losses. The above
design is made to marginally pass the saturation point with 4 air gaps to reduce the
gap losses. Core OD and ID is optimized for high copper fill factor considering the
manufacturability. It minimizes the steel amount that reduces the weight and core
losses. Copper sizes are selected based on the current. Steel weight is 5.3 kg and cu
weight is 1.82kg.
6.2.3.3
Toroidal Design Manufacturing
Inductor Manufacturing Instructions

Schematic diagram
200mH, 3.38A
N4: 66 turns 1.2mm
copper
150mH, 4.13A
100mH, 5.89A
N3: 78 turns
copper
1.2mm
N2: 101 turns
1.2mm
50mH, 9.53A
N1: 245 turns 2* 1.2mm
-62-

Core size and core material
Core: Outer diameter =
Inner diameter =
Height
=
135mm
60mm
60mm
Grain oriented silicon steel, M5 or higher. Steel thickness 0.27mm
Core preparation process prior cutting

Air Gap cutting.
Gap size:
1mm x 4 gaps.
Standard air gap cutting process
Air gaps must be cut in slow process to make the cut surface smooth.
Cores must be robustly bonded to avoid vibration, gap length change and mechanical
noise during the operation.

Core insulation
Polyester insulation takes should be used with two layers 50 % over lap.

Core winding.
1.1 mm diameter copper wire will be would with 528 turns. Then wind two
insulation layers with Polyester film with 50 % over lap.
Wind the second winding layer 1.1 mm with 528 turns

Leads wire connection
Stranded lead wire with size 18 AWG, wire style 1015 connected to each
winding start and end. Wire length 350mm

Final insulation
Two layers of polyester insulation will be wound with 50 % over lap

Mounting:
Center potted 20mm below top with through hole 6.5mm provide with rubber
pad 2mm
6.2.3.4
Toroidal Inductor testing
Toroidal inductors has more linear inductance over it full operating current range
compared to UI inductors but cost wise more expensive than the UI construction. The
following picture shows the testing of the toroidal inductor sample and table and graph
shows the inductance vs current relationship.
-63-
Picture 6-4: Toroidal inductor Testing
Current(A) Voltage(V) Inductance(mH )
0.25
16.90
215.29
0.75
51.00
216.56
1.00
68.30
217.52
1.25
85.50
217.83
1.50
103.30
219.32
1.75
121.80
221.66
2.00
141.10
224.68
2.25
162.30
229.72
2.50
185.90
236.82
2.75
206.50
239.14
3.00
227.50
241.51
3.25
247.30
242.33
3.59
275.30
244.22
3.75
288.60
245.10
4.00
309.00
246.02
4.25
333.00
249.53
4.38
341.30
248.16
4.50
351.60
248.83
5.00
394.60
251.34
Table 6-6 : Toroidal inductor test data.
-64-
Current Vs Voltage and Inductance
450
Voltage (V ), Inducatnce (mH)
400
350
300
250
Voltage(V)
200
Indutance (mH )
150
100
50
0
0
1
2
3
4
5
6
Current (A)
Graph 6-3 : Toroidal inductor
6.2.3.5
Test Data analysis and conclusion
Based on the above test results, it shows that the inductance is stable between 190V
to 300V and current 0.25A to 4.5A. After 300V, inductor starts saturation. However the
d300V is sufficient and well below the maximum voltage 253V. The Design reached
close but the number of turns adjusted to 528 instead of 490 turns resulted from the
theoretical design. This is due to the air gap variation due to practical consideration.
Now the turns adjusted to
Tap
Inductance
(mH )
Turns
N1
50mH
264
N2
100mH
109
N3
150mH
84
N4
200mH
70
-65-
The toroidal core inductor losses are within the design specification. It is important to
maintain minimum core losses. It is theoretically proven that the C-core can be
optimized with less material content and practically a compact design due to its
optimum magnetic path and construction easiness. Therefore C-core will be a better
approach for future consideration.
6.2.4 C-Core inductor
The C – core is built as per picture 6-5, amorphous material is used in most of the Ccores. Amorphous material has low losses due to thin material. This is a composite
material. Amorphous metal is a unique alloy that exhibits a molecular arrangement
that is random in structure rather than the organized crystalline structure of the silicon
grain oriented steel. Amorphous metal cores are more readily magnetized and
demagnetized when energized with low losses.
Winding the turns in a C-core is considerably simpler than toroidal cores. The turns
wind in bobbin externally and then the wound coil can be inserted to the straight part
of the core. Leakage inductance is comparatively lower than tradition EI cores.
Picture 6-5: C core
6.3 Capacitor
Mainly two types of capacitors are taken into consideration. They are the AC
compatible electrolytic capacitors and the film capacitors. Considering high reliability,
high voltage handling capability and life expectancy, it has been decided to use film
capacitors for this application.
The advantage of the film capacitors are the internal construction that has direct
contact with electrodes. This keeps all current paths to the entire electrode very short
by which reduce the internal ohmic losses and also geometry keep the parasitic
inductance low. They are good for application with high surge currents or high
frequencies.
Polypropylene, Polyethylene Naphthalene, Polyethylene Terephthalate and
Polyethylene sulfide are some of the popular dielectric material used to construct the
film capacitors. These materials has capabilities to withstand very high voltages, and
wide temperature range brings the long life expectancy. The dielectric strength of these
capacitors can reach into the four-digit voltage range.
-66-
The formula for capacitance (C) of a parallel plate capacitor is:
...............................Equation (6.6)
where ε dielectric permittivity; A - electrode surface area; and d - distance between
the electrodes.
Picture 6-6: capacitors
6.4 Conceptual Var box design
On this study, we designed the inductor and built. However we were not able to build
the complete var box due to time constraints. We theoretically model and also study
the components to build the units for the next step.
For this we have chosen 6kW inverter. This is a common residential solar inverter size.
Further, we can modularize this with steps of 6kW.
As per the regulation, inverter power feeding is allowed with a steps of 10%. Required
power factor is defined by the utility company for given power feeding ratings.
Another variation is the main line voltage. The voltage can be changed +/-10 % to the
nominal voltage.
Input variables are the inverter power feeding, defined power factors for each 10%
increments of power and line voltage variations.
Based on these variables, the indictor and the capacitor are switched to meet the given
power factor within the range of +/-0.1.
-67-
Refer Appendix B for detailed calculation and algorithm.
6.4.1 Major Parts of the VAR box design approach
The input information collection accurately and real time response is a major area of
the design. We found an input data collection module that has a capability of accessing
the active power, reactive power, voltage, current and frequency from the main utility
input and solar inverter output.
A Microprocessor is installed with data array tables, assign numbers and provided
instructions to get the correct inductor tap and number of capacitors. The Input
collector protocol monitor the active power, reactive power, voltage, current and
frequency in the utility line and the solar inverter. This information covert to digital using
A/D converter and feed to microprocessor. The Microprocessor is programed to
respond and contain instruction to connect the required inductance and number of
capacitors.
When changing the inductor or capacitor taps, the microprocessor should delay the
connection process till the energy built up in the inductor and capacitor to release via
freewheeling diodes. Otherwise the connections can short circuit and burn the unit.
It also requires the electrical isolation between the microprocessor and the capacitor
/Inductor. Following figure shows the block-schematic diagram of the design.
Mains
Solar
micro
inverter
Input
collection
protocol
Isolation
and
switching
Capacitor
and
Inductor
Micro
processor
Smart VAR Generator
Figure 6-3: Major parts ofVabox
a VAR box – schematic
-68-
6.4.1.1
Inductor and Capacitor
The following circuit diagram shows the power circuit design of the Smart VAR
generator. It consists of inductors, capacitors, solid state relays and other supporting
sub circuits.
Figure 6-4: circuit diagram VAR generator .
Software used to generate above diagram: www.powersimtech.com. Free demo
version.
There are 4 taps in the inductor. The micro processer provides switch on or off signal
to solid state relay to get the correct inductance. There are many reasons to have a
number of taps in the inductor. If there is only one inductance, then it should run always
with a lowest lagging power factor when lagging. The Power factor required and
correction will be taken place by using many capacitor switching. This will increase the
-69-
number of capacitors and also the energy loss in the capacitor.
There are 24
capacitors in the capacitor bank and all of them are connected in parallel with a switch.
Since we have used the same capacitor value to all 24 capacitors. For a given
combination, the delay time can be reduced by switching the remaining capacitors if
the number of capacitor requirement is less than the number of capacitors are on.
Further capacitor switch on can be takes place on a random basis. The film capacitor
are reliable and have low losses. Freewheeling diodes allow fast switch change and
respond to the reactive power requirements.
It can be theoretically proven that the inductor can support that power factory lagging
requirement by itself and capacitors can support the power factor lead requirement by
itself. However from a practical point of view, capacitor size and availability is more
flexible compared to designing an inductor. The inductor required many taps and
switching will be complicated. Therefore, we focus on the inductor design with 4 taps
and all correction through capacitors.
Another factor is that the inductors are heavier in weight and bulky. Also expensive
compared to capacitors.
6.4.1.2
STPM01 micro controller
Depending on the area where the solar inverters are connected to mains, the utility
company decides the power injecting PF. Therefore the required PF is given for a
feeding power and it changes. The inverter power feed in to grid also an input for the
calculation. The system main voltage changes +/-10%, reactive power requirement is
also vary with input voltage. Therefore system main voltage is an input.
During our component study, we found the IC, STPM01 is suitable and can support to
acquire main line voltage and power feed by the inverter.
The IC STPM01 (Programmable single phase energy meeting IC) was design by
STMicroelectronics. This IC is for effective measurement of active, reactive and
apparent energy in a power line system. It requires a rogowski coil, current transformer
and voltage sensor to access the information for the mains and inverter output.
The analogy to Digital converter (A/D) take the analog measurement and convert to
digital form.
-70-
Figure 6-5: STPM01 Micro controller
6.4.1.3
Micro Controller
Micro controller is the brain of executing the operation algorithm. Information from the
STPM01 and Vlook up tables stored in the micro process are run based on the
calculation program and generate output to switch the capacitors and indictors to meet
the VAr requirement. When the status of the input are changing, the microprocessor
should hold the information till it reaches the next level to change the output. However
output cannot be changed immediately since the energy stored in the capacitor or
inductor need to be dissipated through a freewheeling diode prior to switching the next
group.
Since we have chosen same capacitor value with 24 capacitors, during the lead
running the capacitor may add or deduct reactive power without any delays. When the
unit is running in the lagging mode, inductor cannot be switched to the next tap without
freewheeling the energy stored in the present state.
-71-
Picture 6-7: Micro controller
6.4.2 Operation Algorithm,
Appendix B, discussed the detailed approach of the microprocessor programming
requirement conditions.
For the Thesis analysis process, we developed a micro-soft excel spread sheet to
calculate all the scenarios based on the operation algorithm.
When we are developing the operation algorithm and spread sheet, we use the fact
that the utility companies predefine the power factor requirement for preprogramming
the processors. However, we can easily automate this processes based on direct
communication channel between the smart VAR box and the utility company.
-72-
6.4.2.1
Lag running
We developed a software model to extract the data. The above snap shot is extracted
from the output after running. When the inverter requires a lagging power factory to
maintain, the inductor will be switched depending on the lagging PF and the inductor
is set to over react every time. The excess amount of
reactive power will be
compensated by the capacitors to adjust the required PF within the tolerance of +/-0.1.
In the above operation, the inverter is running 6 kW. Required power factory is 0.96
lagging. Inductor switch to 100mH and it generate 2.04kVar. However the system
-73-
required only 1.68 kVar. Therefore 6F x3 capacitors are switched in and compensate
to correct it.
The above algorithm run for many different values and all are within the required scope.
6.4.2.2
Lead running
When the inverter requires a lead power factory to maintain the inductor will not be
switched. Only capacitors are switched to maintain PF within the tolerance of +/-0.1.
In the above operation, the inverter is running 6 kW. Required power factory is 0.98
lead. It requires 0.6kVar Therefore 6F x7 capacitors switched. The above algorithm
run for many different values of power factors within the defined scope and all are
within the required scope.
-74-
7 Analysis and Conclusion
7.1 Meeting the PF resolution
Results obtained with the developed algorithm : lead with over voltage
Power (kW)
0.60 1.20 1.80 2.40 3.60
4.20
4.80
5.40
6.00
PF ( Lead )
1
1
1
1
1
0.98
0.97
0.96
0.95
Input voltage 10% above
Power factor correction
nominal voltage (253V )
required only above 3.68kVA
253
253
253
253
Inductance (mH)
0
0
0
0
0
0
0
0
0
Capacitance(F)
0
0
0
0
0 6*7=42 6*10=60 6*13=78 6*16=96
Power factor obtain
0
0
0
0
0
0.98
0.969
0.958
0.949
Power factor difference
0
0
0
0
0
0
0.001
0.002
0.001
Results obtained with the developed algorithm : lead with under voltage
Power (kW)
0.60 1.20 1.80 2.40 3.60
4.20
4.80
5.40
6.00
PF( Lead )
1
1
1
1
1
0.98
0.97
0.96
0.95
Input voltage 10% below
the nominal voltage
Power factor correction
(207V )
required only above 3.68kVA
207
207
207
207
Inductance (mH)
0
0
0
0
0
0
0
0
0
Capacitance (F )
6*10=60 6*14=84 6*19=114 6*23=138
Power factor reach
0.982
0.972
0.96
0.952
Power factor difference
-0.002
-0.002
0
-0.002
Results obtained with the developed algorithm : lag ( “- “use calculation purpose ) with over voltage
Power (kW)
0.60 1.20 1.80 2.40 3.60
4.20
4.80
5.40
6.00
PF(lag)
1
1
1
1
1
-0.98
-0.97
-0.96
-0.95
Input voltage 10% above
Power factor correction
nominal voltage (253V )
required only above 3.68kVA
253
253
253
253
Inductance (mH)
0
0
0
0
0
200
150
100
100
Capacitance (F )
6*2=12 6*2=12 6*2=12
6*1=6
Power factor reach
-0.983
-0.973
-0.959
-0.949
Power factor difference
-0.003
-0.003
-0.001
-0.001
Results obtained with the developed algorithm : lag( “- “use calculation purpose ) with under voltage
Power (kW)
0.60 1.20 1.80 2.40 3.60
4.20
4.80
5.40
6.00
PF(lag )
1
1
1
1
1
-0.98
-0.97
-0.96
-0.95
Input voltage 10% below
nominal voltage (207V )
207 207 207 207 207
207
207
207
207
Inductance (mH)
0
0
0
0
0
150
100
50
50
Capacitance (
6*1=6
6*2=12 6*15=90 6*11=66
Power factor obtained
-0.981
-0.969
-0.961
-0.95
Power factor difference
-0.001
0.001
0.001
0
-75-
Above summary results were obtained using the algorithm developed. The program
runs with extreme over and under voltages. The maximum over voltage is 253V and
maximum under voltage is 207V. The Power factor was randomly selected based on
lead or lag operation between 1 and -/+0.95. Note that +/- or notation is taken to
differentiate the lead /lag identification and programming calculation purpose only. PF
values are assigned by the utility service provider. In the calculation, we assume that
the values are preprogrammed since the values are fixed for a given common point of
coupling. However the program is easily modified to change the values frequently
online.
The power factor values difference is considerably less than 0.01. Capacitor and
inductor values are calculated for higher resolution assuming the future considerations.
7.2 Unit efficiency
Another significant consideration is the use of multiple capacitors with same minimum
capacitance. This will simplify a number of things.





Switching efficiency: switching the inductor and capacitors are complicated due
to stored energy. The MOSFETs are equipped with freewheeling diodes to
dissipate the energy to achieve faster switch. This operation delay the system
PF moving from one state to the other. Since the capacitors are of the same
value, switching from one state to other will be only few capacitors and process
is very short and fast. In this thesis, we have not calculated the time, it takes
from moving on one PF to another. However, in the above lead calculation,
switching from 7 capacitors to 10 capacitors, system will add three more
capacitors. In case the capacitors are switching from 10 to 7, the system will
switch off only three. This is faster.
Operation system efficiency: when there is a need to reduce the number of
capacitors, it will only reduce the difference. Therefore the energy freewheeling
is the difference. Further, it switches the inductance for four stages. It helps to
reduce the resistive losses and also the number capacitors required to correct
the PF.
Manufacturing efficiency: System manufacturing point of view, capacitor bank is
one block with similar physical arrangement. The assembly process is easier
and also easily automated due to the same size. Another advantage is the
modular assembly approach. Further material inspection, bill of material and
testing is simplified due to less components
Cost efficiency: Using a single capacitor block increases the volume of
purchase. So the unit price can be minimized. Spend of assembly, handling,
ordering, communication can be well optimized to reduce the cost.
Maintenance efficiency: Field operation is simplified due to less number of
components. Higher MTBF.
-76-

Life expectancy: Life of the unit will be higher due to less number of switching
since number of capacitors will be always switched on or off to get required base
mode capacitance – no switching.
8 Conclusion
From the year 1973 to year 2008, energy consumption has doubled, from 71117TWh
to 146852TWh, and it will continue to grow since many of the highly populated
countries such as China, India, Middle East and Brazil are still in the developing phase.
As per the Energy outlook 2012, prepared by International Energy Agency, “Global
energy demand increases by over one‐third in the period to 2035”
Fossil fuels remain the principle source of energy worldwide but due to life threatening
environmental issues associated with fossil fuels, renewables started to grow rapidly.
Among many other renewable resources, solar is considered as a highly potential
primary energy source. According to IEA, with effective policies in place, by 2050, PV
could provide more than 11% of global electricity.
As PV matures into a mainstream technology, grid integration and management and
energy storage become key issues. The PV industry, grid operators and utilities will
need to develop new technologies and strategies to integrate large amounts of PV into
flexible, efficient and smart grids.
Since the evolution of PV based electricity generation, overall efficiency of energy
conversion, or amount of active power injected to the grid, is one of the key parameters.
All PV systems was delivering only the active power at unity power factor to the grid
which yields the highest amount of energy and therefore maximizes the return for the
investment. But things started to change when PV based distributed generation units
became a significant component of the conventional centralized power generation
grids.
Sudden voltage sags or total collapse in voltage stability was experienced due to the
deficit of reactive power within the grid sub systems in some parts of the electric grid
in counties such as Germany and Italy where the PV based electricity generation has
a high contribution to the electric power generation. The grid systems become
inefficient because some of the centralized power generation units or Var
compensators have to deliver reactive power to deficit areas. Grid voltage stability
issues initiated new set of grid regulation standards in Germany and Italy and move on
to rest of the world. As per the new regulations, like centralized larger generation units,
distributed generation units including PV based systems have to contribute to static
voltage stability of the grid by generating reactive power. This has been a real threat
to the development of renewable energy as a primary energy source. On one hand
some of the PV systems have been developed as a result of long term research
activities which makes it very difficult to change it without affecting the overall
performance significantly and on the other hand threat to the grid stability by
continuously adding new PV systems that deliver only active power is immense.
The new regulation requires PV power systems to meet certain power factor based on
grid requirements and power it generate and deliver to the grid. Ordinary Var
-77-
generators cannot maintain the power factor within the given tolerance (+/-0.01) by the
grid companies at specific operating condition of the inverter.
Therefore our effort was to develop a low voltage Var compensator to use with micro
solar inverters. We are pleased with the fact that we were able to establish a good
foundation to an Intelligent dynamic Var generator find hear to meet new regulations.
Building a working prototype requires substantial investment on hardware and software
programing and is beyond the scope of this thesis project. But anyone who want to
build the dynamic Var generator, finds here all theoretical models and software flow
charts to carry out the practical work.
We were able to accomplish following in this thesis project
 Explain, why PV based solar power become important primary energy source and
why we think that it will continue to grow.
 Explain, why the traditional centralized power systems need to be changed to
accommodate new distributed renewable energy sources.
 Study of photovoltaic systems and critical components by mainly focusing on micro
inverters
 Examining interconnection and safety regulation and testing and explain, why they
are not adequate to address new grid stability issues.
 Evaluated grid stability and correlation between grid stability and reactive power
using PSSE simulation software
 Study on other methods used to address the reactive power deficit issues in solar
string and micro inverters
 Develop the basic theory and calculation model for Dynamic smart Var generator
based on the German regulation VDE AR-N-4105 – 2011-08
 Identify key components and specification of them
 Design and develop the inductor chokes based on unique topology to optimize the
operation. UI and Toroidal inductors with multiple taps to meet small steps in the
power factor.
 Identify capacitor topology and suitable model numbers
 Identify the micro controller as one of the key components needed to convert the
Var generator in to a smart intelligent Var generator to meet new regulations
 Develop the software algorithms for the micro controller programming
-78-
 Analysis and case study to show that the theory and the model can be successfully
used to build a Smart Var generator
9 References
1. Lehtonen M., Nye S., (2009) “History of electrical network controls and distributed
generation in the UK, and western Denmark “Energy policy.
2. M Brown “Reactive power supplied by PV inverters cost- beneficial analysis.
3. United Nations Framework Convention on Climate Change (UNFCCC) (2011), Kyoto
Protocol, UNFCCC, retrieved 9 December 2011
4. UL1741 2005, standard for inverters, converters, controllers and interconnection
system equipment for use with distributed energy resources.
5. Global Market Outlook for Photovoltaics until 2016, retrieved 6 December 2012
6. C.D Vournas, P.W. Sauer, and M.A. Pai. Relationships between voltage and
angle stability of power systems. International Journal of electrical power and
energy systems 18:493-500, 1996.
7. Chambers, A., (2001). Distributed generation: a nontechnical guide. PennWell,
Tulsa, OK, pp. 283.
8. OFGEM, 2007 May. “Review of Distributed Generation“.
(www.dti.gov.uk/energy/whitepaper)
9. Rawson M., Sugar J., (2007). “Distributed Generation and Cogeneration policy
road map for California “California Energy Commission.
10. Dondi, P., Bayoumi, D., Haederli, C., Julian, D., Suter, M., (2002). “Network
integration of distributed power generation”. Journal of Power Sources 106,
pp.1–9.
11. Ackermann, T., Andersson, G., S.oder, L., (2001). “Distributed generation: a
definition”. Electric Power Systems Research 57, pp. 195–204.
-79-
12. Pepermans, G., Driesen, J., Haeseldonckx, D., Belmans, R., D’ haeseleer, W.,
(2005) “Distributed Generation : definition, benefits and issues” . Energy policy,
13. Strachan N., Farell A., (2006). “ Emission from distributed vs Centralized
generation: the importance of the system performances”
14. WADE., (2006) “ World Survey of Decentralization Energy, 2006 “ World Alliance
for Decentralized Energy.
15. Woodman B., Baker, P., (2008). “Regulation Framework for decentralized energy.
16. H. Patel, V. Agarwal, “ MPPT scheme for a PV –fed single phase single stage grid
connected inverter operating in CCM with only one current sensor”, IEEE
transactions on energy conversion, Vol 24.
17. T. Kerekes, R. Teodorescu, P. Rodriguez, E. Aldabas, “ A new high-efficiency
single phase transformerless PV inveter topology “, IEEE transactions on
Industrial electronics, Vol 58, No1.
18. P. Kundur, J. Paserba, V. Ajjarapu, G. Anderson, A. Bose, C. Canizares, N.
Hatziargyriou, D. Hill, A. Stankovic, C. Taylor, T. V. Custem, V. Vittal, “Definition
and Classification of Power System Stability”, IEEE Transactions on Power
Systems, vol. 19, no. 2, pp. 1387 – 1401, May 2004
19. C. W. Taylor, “Concepts of under voltage load shedding for voltage stability,”
IEEE Transactions on Power Delivery, vol. 7, no. 2, pp. 480– 486, April 1992.
“Load representation for dynamic performance analysis,” IEEE Transactions on
Power Systems, vol. 8, no. 2, May 1993. “Standard load models for power flow
and dynamic performance simulation,” IEEE Transactions on Power Systems, vol.
10, no. 3, August 1995.
20. W. Xu and Y. Mansour, “Voltage stability analysis using generic dynamic load
models,” IEEE Transactions on Power Systems, vol. 9, no. 1, pp. 479 – 486,
February 1994.
21. E.D. Spooner “A new Australian standard for small grid- connected renewable
generation systems connected via inverters”.
22. P. Kundur, Power System Stability and Control. New York: McGraw Hill
Publishing Company, 1994 WECC Guide: Planning Standards I.D Page 5
-80-
23. “ Power electronics converters, Application and Design “ Mohan, Undeland,
Robins (2003)
24. H.Patel and R. G. Hoft, “ Generalized techniques of Harmonic Elimination and
Voltage Control in Thyristor Inverters: Part I, Harmonic Elimination IEEE
Transactions on Industry applications, Vol IA -10, No 5 , September/ October
1974
25. M. Boost and P.D. Ziogas, “ state of the art PWM Techniques: A critical
evaluation IEEE Power electronic specialists conference 1986
-81-
10 Appendix A : Inductor Calculation
10.1
UI Core : Design Output
Following pages from the design program gives the design output data, core size,
copper sizes, number of turns, gap sizes
-82-
-83-
10.2
Toroidal Core 50mH Inductor Calculation
DC-Choke Calculation
Inductance
Cont. DC-current
Cont. AC-current No. 1
Cont. AC-current No. 2
Saturation DC-current
Saturation AC-current
50.00
0
9.6
0
0
0
Tot. saturation current (AC)
0.00
AC-current No. 1 gives U =
150.72
AC-current No. 2 gives U =
Heating Energy
Saturation Energy
Approx. core size, from:
0.00
4608
0
922
Aac
Vac
=
Vac
=
Ws
Ws
VA
0
VA
to:
mH
Adc
Aac
Aac
Adc
Aac
50
100
Hz
kHz
1.23
W/m²
0.00
W/m²
-84-
Core no.
Core OD (mm)
Core ID (mm)
Core H (mm)
No of air gaps
Air gap size
20
135
60
60
4
1.0
Basic air gap const
30
Air gap constant
35
Number of turns
245
Prel. wire diam.
Prel. filling factor
1.53
16%
And Now You Choice
Number of wires
Wire diameter
2
1.20
And Then You Get
Filling factor (%)
Temp rise (°C)
Saturation (Aac)
Saturation (Adc)
Wind. resist. (mOhm)
Copper losses (W)
Iron losses (W)
Copper area (mm²)
Iron area (cm²)
Window area (mm²)
Wire length (m)
20%
69
11.69
16.53
454.03
41.84
3.99
2.26
22.50
2826
59.5
Outer diameter (mm)
Inner diameter (mm)
Height (mm)
Iron weight (kg)
Copper weight (kg)
Total weight (kg)
145
42
77
5.26
1.20
7.11
10.3
Toroidal Core 100mH Inductor Calculation
DC-Choke Calculation
Inductance
Cont. DC-current
Cont. AC-current No. 1
Cont. AC-current No. 2
Saturation DC-current
Saturation AC-current
100.00
0
5.89
0
0
0
Tot. saturation current (AC)
0.00
AC-current No. 1 gives U =
184.95
mH
Adc
Aac
Aac
Adc
Aac
AC-current No. 2 gives U =
0.00
Aac
Vac
=
Vac
=
Heating Energy
3469
Ws
0
Ws
694
VA
0
VA
Saturation Energy
Approx. core size, from:
to:
50
100
Hz
kHz
1.07
W/m²
0.00
W/m²
Core no.
Core OD (mm)
Core ID (mm)
Core H (mm)
No of air gaps
Air gap size
Basic air gap const
30
Air gap constant
35
Number of turns
346
Prel. wire diam.
Prel. filling factor
1.20
14%
And Now You Choice
Number of wires
Wire diameter
1
1.20
And Then You Get
Filling factor (%)
Temp rise (°C)
Saturation (Aac)
Saturation (Adc)
Wind. resist.
(mOhm)
Copper losses (W)
Iron losses (W)
Copper area (mm²)
Iron area (cm²)
Window area (mm²)
Wire length (m)
Outer diameter (mm)
Inner diameter (mm)
Height (mm)
Iron weight (kg)
Copper weight (kg)
Total weight (kg)
-85-
20
135
60
60
4
1.0
14%
74
8.27
11.69
1284.18
44.55
3.01
1.13
22.50
2826
84.2
143
47
73
5.26
0.85
6.73
10.4
Toroidal Core 150mH Inductor Calculation
DC-Choke Calculation
Inductance
Cont. DC-current
Cont. AC-current No. 1
Cont. AC-current No. 2
Saturation DC-current
Saturation AC-current
150.00
0
4.13
0
0
0
mH
Adc
Aac
Aac
Adc
Aac
Tot. saturation current (AC)
0.00
AC-current No. 1 gives U =
194.52
AC-current No. 2 gives U =
Heating Energy
Saturation Energy
0.00
2559
0
Aac
Vac
=
Vac
=
Ws
Ws
512
0
VA
VA
Approx. core size, from:
to:
50
100
Hz
kHz
0.92
W/m²
0.00
W/m²
-86-
Core no.
Core OD (mm)
Core ID (mm)
Core H (mm)
No of air gaps
Air gap size
20
135
60
60
4
1.0
Basic air gap const
30
Air gap constant
35
Number of turns
424
Prel. wire diam.
Prel. filling factor
1.00
12%
And Now You Choice
Number of wires
Wire diameter
1
1.20
And Then You Get
Filling factor (%)
Temp rise (°C)
Saturation (Aac)
Saturation (Adc)
Wind. resist. (mOhm)
Copper losses (W)
Iron losses (W)
Copper area (mm²)
Iron area (cm²)
Window area (mm²)
Wire length (m)
17%
44
6.75
9.54
1572.79
26.83
2.22
1.13
22.50
2826
103.1
Outer diameter (mm)
Inner diameter (mm)
Height (mm)
Iron weight (kg)
Copper weight (kg)
Total weight (kg)
144
44
75
5.26
1.04
6.94
10.5
Toroidal Core 200mH Inductor Calculation
DC-Choke Calculation
Inductance
Cont. DC-current
Cont. AC-current No. 1
Cont. AC-current No. 2
Saturation DC-current
Saturation AC-current
200.00
0
3.38
0
0
0
mH
Adc
Aac
Aac
Adc
Aac
Tot. saturation current (AC)
0.00
AC-current No. 1 gives U =
212.26
AC-current No. 2 gives U =
Heating Energy
Saturation Energy
0.00
2285
0
Aac
Vac
=
Vac
=
Ws
Ws
457
0
VA
VA
Approx. core size, from:
to:
DC 2000 000221/aw
50
100
Hz
kHz
0.87
W/m²
0.00
W/m²
Core no.
Core OD (mm)
Core ID (mm)
Core H (mm)
No of air gaps
Air gap size
20
135
60
60
4
1.0
Basic air gap const
30
Air gap constant
35
Number of turns
490
Prel. wire diam.
Prel. filling factor
0.91
11%
And Now You Choice
Number of wires
Wire diameter
-87-
1
1.20
And Then You Get
Filling factor (%)
Temp rise (°C)
Saturation (Aac)
Saturation (Adc)
Wind. resist. (mOhm)
Copper losses (W)
Iron losses (W)
Copper area (mm²)
Iron area (cm²)
Window area (mm²)
Wire length (m)
20%
34
5.84
8.26
1816.11
20.75
1.98
1.13
22.50
2826
119.0
Outer diameter (mm)
Inner diameter (mm)
Height (mm)
Iron weight (kg)
Copper weight (kg)
Total weight (kg)
145
42
77
5.26
1.20
7.11
11 Appendix B: Smart Var generation operation algorithm
At this level, we will design the concept of the approach, design calculation, critical
component level design and analysis, program/ algorithm and solution analysis.
11.1
Algorithm Calculation Approach
Maximum inverter Power capacity : Ps (W )
Instantaneous solar inverter current : Ist (A)
Instantaneous solar inverter voltage : Vst (V )
Instantaneous Inverter Power = Pst
Inverter Power factor = 1
Inverter Power at the given time : Pst = Vst x Ist
Power equalize to 10% increments of Ps
Power increment factor :  = ( 0.1 to 1 with a increments of 0.1 )
Gird voltage : V grid (Hz )
Note : Grid voltage can change +/- 10% from the nominal
Power factor defined by the utility company
Lagging power factor : (-) sign for lag, value is in the range 1 to 0.95 :( - ) PF
Leading Power factor : value is in the range 1 to 0.95 :(+) PF
Grid frequency : fgrid
PF ; Power Factor.
PF Lag : Utility required lagging Power factor
PF Lead : Utility required Leading Power factor.
PF’ lag : Calculated lagging Power Factor.
PF’ lead : Calculated Leading Power Factor.
lag : lagging utility required phase angle.
lead : Leading utility required phase angle.
’lag : Lagging Calculated Phase angle.
’lead : Leading Calculated Phase angle.
RDP : Reactive Power Difference.
RTRP : Required Total Reactive Power.
CIRP : Calculated Inductive Reactive Power.
CCRP : Calculated Capacitive Reactive Power.
-88-
Look up Table A
Solar Power ( Psr)
PF (-/+)
0.1*Ps
0.2*Ps
0.3*Ps
0.4*Ps
0.5*Ps
0.6*Ps
0.7*Ps
0.8*Ps
0.9*Ps
1.0*Ps
Lead Power factory refers positive (+) for calculation purpose
Lag power factor refers negative ( - ) for calculation purpose.
Phase Angle Lag =  = ACos( -PF) …………….. Eqn
(6.7)
Reactor Power = *Ps * Sin () …………… Eqn (6.8)
Inductance L (mH ) =
𝑉𝑔𝑟𝑖𝑑∗𝑉 𝑔𝑟𝑖𝑑∗1000
𝑅𝑒𝑎𝑐𝑡𝑖𝑣𝑒 𝑃𝑜𝑤𝑒𝑟 ∗𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦∗ 3.14∗2
……… Eqn (6.9)
Based on the inductor design, define a inductance factor to find the inductor tap
connection
Minimum capacitance is calculated. Capacitance factor = minimum capacitance
Phase Angle Lead =  = ACos(PF)
Capacitance C (F ) =
11.2
𝑅𝑒𝑎𝑐𝑡𝑖𝑣𝑒 𝑃𝑜𝑤𝑒𝑟∗1000000
𝑉𝑔𝑟𝑖𝑑∗𝑉𝑔𝑟𝑖𝑑 ∗𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦∗ 3.14∗2
………… Eqn (6.10)
Algorithm
Smart Var generator needs to adjust the amount of reactive power in real time,
depending on the condition (power factor, leading or lagging) of the point it is connected
to the grid and total active power generated by the solar inverter. Response time to the
variations should be less than 10 seconds i.e. it has to re-adjust to the new conditions
within 10 seconds. Following algorithm shows how it can be achieved by using a
programmable micro controller chip. Using the following logic flow charts, software
-89-
codes can be generated to feed into the micro controller. Through the input sensors
smart VAR generator keeps track of the condition of the grid and total active power
generated by the solar inverter. Then it runs the logic to calculate the amount of active
power required by the grid in real time and decide which inductor tap or taps and
number of capacitors need to be switched on.
Symbols used in the flow chart.
Flow chart symbol
Description
Data
Process
Decision
Termination
Summing junction
-90-
Ist (A)
Inverter
calculation
Power
Pst = Ist X Vst
Vst(V )
Ps= Ps X
Pst/Ps),1))
round((
Inverter
capacity
=Ps
Power Factor read from
the look up table based
on the utility company
PF < 1Lag
PF: > 1
PF: < 1
PF: = 1
PF = 1 Active
Reactive power
=0
-91-
Look up table A
Inverter
Power
output
Utility
company
Power
factor
0.1 * Ps
+/-PF1
0.2 * Ps
+/-PF2
0.3 * Ps
+/-PF3
0.4 * Ps
+/-PF4
0.5 * Ps
+/-PF5
0.6 * Ps
+/-PF6
0.7 * Ps
+/-PF7
0.8 * Ps
+/-PF8
0.9 * Ps
+/-PF9
1.0 * Ps
+/-PF
PF > 1Lead
PF >1 Lead
Reactor Power(RP) = *Ps *
Sin ()
V grid
V grid
Capacitance
C
𝑅𝑇𝑅𝑃∗1000000
=
𝑉𝑔𝑟𝑖𝑑∗𝑉𝑔𝑟𝑖𝑑 ∗𝑓𝑔𝑟𝑖𝑑∗ 3.14∗2
(F)
Number of Capacitors (NC) =
𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑎𝑛𝑐𝑒
𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑎𝑛𝑐𝑒 𝑓𝑎𝑐𝑡𝑜𝑟
Activate Capacitors (NC)
8 capacitors or less at a time
CCRP =NC * capacitance factor
*Vgrid*Vgrid* f grid/1000 000
RTRP0.99CCRP<
0
’lead = Asin(CCRP)/Ps)
PF’lead = cos (’lead)
PFlead-PF’lead < +/-0.01
-92-
Power factor < 1 lag
Reactive Power Calculation
Reactor Power (RTRP) = *Ps * Sin
()
fgrid
Inductance : L (mH ) =
𝑉𝑔𝑟𝑖𝑑 ∗ 𝑉 𝑔𝑟𝑖𝑑 ∗ 1000
𝑅𝑇𝑅𝑃 ∗ 𝑓𝑔𝑟𝑖𝑑 ∗ 3.14 ∗ 2
Vgrid
Inductance Tap =
𝐼𝑛𝑑𝑢𝑐𝑛𝑡𝑎𝑐𝑒 (𝐿 )
𝐼𝑛𝑑𝑢𝑐𝑡𝑎𝑛𝑐𝑒 𝑓𝑎𝑐𝑡𝑜𝑟
Inductance
tap
selection
Change Delay
Inductor Reactive Power (CIRP)
=
𝑉𝑔𝑟𝑖𝑑 ∗ 𝑉 𝑔𝑟𝑖𝑑 ∗ 1000
𝐼𝑛𝑑𝑢𝑐𝑡𝑎𝑛𝑐𝑒(𝐿) ∗ 𝐼𝑛𝑑𝑢𝑐𝑡𝑎𝑛𝑐𝑒 𝑓𝑎𝑐𝑡𝑜𝑟 ∗ 𝑓𝑔𝑟𝑖𝑑 ∗ 3.14
No
If
CIRP
>RTRP
Yes
(RPD) = CIRP-RTRP
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Yes
If RPD =0
No
V grid
V grid
RTRP0.99CIRP<0
Capacitance C (F) =
𝑅𝑃𝐷∗1000000
𝑉𝑔𝑟𝑖𝑑∗𝑉𝑔𝑟𝑖𝑑 ∗𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦∗ 3.14∗2
Number of Capacitors (NC)=
𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑎𝑛𝑐𝑒
𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑎𝑛𝑐𝑒 𝑓𝑎𝑐𝑡𝑜𝑟
Activate Capacitors(NC)
max 8 at a time
CCRP =No of capacitors*
capacitance factor *Vgrid
*Vgrid* f grid
RTRPCIRP+CCR
P
’lag = Asin((CIRP)/Ps)
PF’lag = cos (’lag)
PFlag-PFlag’ < +/-0.01
leg’ = Asin((LRP+CRP)/Ps)
PFlag’ = cos (’lag)
PFlag-PF’ lag< +/-0.01
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