INVESTIGATIONS ON SHUNT ACTIVE POWER FILTER FOR POWER QUALITY IMPROVEMENT

INVESTIGATIONS ON SHUNT ACTIVE POWER FILTER FOR POWER QUALITY IMPROVEMENT
INVESTIGATIONS ON SHUNT ACTIVE POWER
FILTER FOR POWER QUALITY IMPROVEMENT
A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE
REQUIREMENTS FOR THE DEGREE OF
Master of Technology
In
Power Control and Drives
By
D. Pradeep kumar
Department of Electrical Engineering
National Institute of Technology
Rourkela
2007
INVESTIGATIONS ON SHUNT ACTIVE POWER
FILTER FOR POWER QUALITY IMPROVEMENT
A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE
REQUIREMENTS FOR THE DEGREE OF
Master of Technology
In
Power Control and Drives
By
D.Pradeep Kumar
Under the Guidance of
Prof. P.C. Panda
Department of Electrical Engineering
National Institute of Technology
Rourkela
2007
National Institute of Technology
Rourkela
CERTIFICATE
This is to certify that the thesis entitled, “Investigations On Shunt Active Power Filter For
Power Quality Improvement” submitted by Sri D. Pradeep Kumar in partial fulfillment of
the requirements for the award of MASTER of Technology Degree in Electrical
Engineering with specialization in “Power Control and Drives” at the National Institute of
Technology, Rourkela (Deemed University) is an authentic work carried out by him/her
under my/our supervision and guidance.
To the best of my knowledge, the matter embodied in the thesis has not been submitted to any
other University/ Institute for the award of any degree or diploma.
Date:
Prof. P.C.Panda
Deptt.of Electrical Engg.
National Institute of Technology
Rourkela - 769008
Dedicated To My Mother
ACKNOWLEDGEMENT
I would like to articulate my profound gratitude and indebtedness to my thesis guide
Prof. P.C. Panda who has always been a constant motivation and guiding factor throughout
the thesis time in and out as well. It has been a great pleasure for me to get an opportunity to
work under him and complete the project successfully.
I wish to extend my sincere thanks to Prof. P. K. Nanda, Head of our Department,
for approving our project work with great interest.
I would also like to mention Mr.Jaganmohan Rao, fellow Student, for his cooperation
and constantly rendered assistance.
I feel a deep sense of gratitude for my father Sri.D.Rajireddy and mother Smt.
Nirmala who formed a part of my vision and taught me the good things that really matter in
life. I would like to thank my brother and other family members for their support.
An undertaking of this nature could never have been attempted with our reference to
and inspiration from the works of others whose details are mentioned in references section. I
acknowledge my indebtedness to all of them. Last but not the least, my sincere thanks to all
of my friends who have patiently extended all sorts of help for accomplishing this
undertaking.
CONTENTS
Abstract
iii
List of Figures
iv
List of Tables
vi
1.
Introduction
1
1.1
Background
2
1.1.1 Power quality
2
1.1.2 Solutions to power quality problems
4
1.1.3 Power filter topologies
4
1.1.4 Voltage source converters
6
1.1.5 Control strategies
8
1.2
Objective
10
1.3
Thesis Outline
10
Shunt Active Power Filter
12
2.1
Basic compensation principle
14
2.2
Estimation reference source current
15
2.2
Role of DC side capacitor
15
2.3
Selection of Lc and Vdc,ref
16
2.4
Design of DC side capacitor (Cdc)
18
2.
3.
4.
5.
PI Control Scheme
19
3.1
Dc voltage control loop
20
3.2
Transfer function of PWM converter
20
3.3
Selection of PI controller parameters
21
Fuzzy Control Scheme
23
4.1
Basic fuzzy algorithm
24
4.2
Design of control rules
27
Modeling of the System
30
5.1
Modeling of Nonlinear Load
30
5.2
Modeling of PWM Converter
30
5.3
Estimation of Peak Supply Current
31
5.4
Estimation of Instantaneous Reference Supply Currents
32
i
5.5
32
Hysteresis Current Controller
6.
Simulation Results
33
7.
Conclusion and Scope for the Future Work
44
References
45
Appendix A
ii
ABSTRACT
Most of the pollution issues created in power systems are due to the non-linear characteristics
and fast switching of power electronic equipment. Power quality issues are becoming stronger
because sensitive equipment will be more sensitive for market competition reasons, equipment
will continue polluting the system more and more due to cost increase caused by the built-in
compensation and sometimes for the lack of enforced regulations. Efficiency and cost are
considered today almost at the same level. Active power filters have been developed over the
years to solve these problems to improve power quality. Among which shunt active power filter
is used to eliminate and load current harmonics and reactive power compensation.
In this work both PI controller based and fuzzy logic controlled, three-phase shunt
active power filter to compensate harmonics and reactive power by nonlinear load to improve
power quality is implemented for three-phase three wire systems. The advantage of fuzzy control
is that it is based on linguistic description and does not require a mathematical model of the
system. The compensation process is based on sensing line currents only, an approach different
from conventional methods, which require sensing of harmonics or reactive power components
of the load.
A MATLAB program has been developed to simulate the system operation. Various
simulation results are presented under steady state conditions and performance of fuzzy and PI
controllers is compared. Simulation results obtained shows that the performance of fuzzy
controller is found to be better than PI controller. PWM pattern generation is based on carrier
less hysteresis based current control to obtain the switching signals to the voltage sourced PWM
converter.
iii
LIST OF FIGURES
Title
Page No
Figure.1.1
Voltage source converter topology for active filters.
6
Figure.1.2
The PWM carrier Technique (triangular carrier).
7
Figure.1.3.
Current waveforms obtained using different modulation
8
techniques for an active power filter:
(a) PS method, (b) HB method, (c) TC method.
Figure.2.1
.Shunt active power filter topology.
12
Figure.2.2
Filter current IF generated to compensate load-current harmonics.
12
Figure.2.3
Shunt active power filter Basic compensation principle.
13
Figure.2.4
Shunt active power filter-Shapes of load, source and desired
13
filter current wave forms.
Figure.2.5
Active power filter and its phasor diagram.
17
Figure.3.1
Schematic diagram of shunt active filter.
19
Figure.3.2
APF Control scheme with PI controller.
19
Figure.3.3
Block diagram of voltage control loop.
20
Figure.4.1
Schematic diagram of closed loop fuzzy logic controlled
23
shunt active power filter.
Figure.4.2
Fuzzy Control scheme.
24
Figure.4.3
Internal structure of fuzzy logic controller.
24
Figure.4.4
Different types of membership functions.
25
Figure.4.5
Normalized triangular functions used in fuzzification.
27
(a)Membership functions for e and ce
(b)Membership function for δImax
Figure.4.6
Time step response of a stable closed loop system.
28
Figure.4.7
Phase plane trajectory of step response.
28
Figure.6.1
Source voltage.
33
Figure.6.2
Source current when the compensator is not connected.
34
Figure.6.3
Source current PI controller.
34
Figure.6.4
Compensating current of PI controller.
34
iv
Figure.6.5
DC Capacitor voltage during switch-on response with PI controller.
35
Figure.6.6
Source current fuzzy controller.
35
Figure.6.7
Compensating current of fuzzy controller.
35
Figure.6.8
DC Capacitor voltage during switch-on response with fuzzy controller.
35
Figure.6.9
Source voltage.
36
Figure 6.10
Load current.
36
Figure.6.11
Compensating current of PI controller.
37
Figure.6.12
Compensating current of fuzzy controller.
37
Figure.6.13
Source current PI controller.
37
Figure.6.14
Source current fuzzy controller.
38
Figure.6.15
DC side Capacitor voltage with PI controller.
38
Figure.6.16
DC side Capacitor voltage with fuzzy controller.
38
Figure.6.17
Voltage and current in phase with PI controller after compensation.
39
Figure.6.18
Voltage and current in phase with fuzzy controller after compensation.
39
Figure.6.19
Source voltage.
40
Figure 6.20
Load current.
40
Figure.6.21
Compensating current of PI controller.
41
Figure.6.22
Compensating current of fuzzy controller.
41
Figure.6.23
Source current PI controller.
41
Figure.6.24
Source current fuzzy controller.
42
Figure.6.25
DC side Capacitor voltage with PI controller.
42
Figure.6.26
DC side Capacitor voltage with fuzzy controller.
42
Figure.6.27
Voltage and current in phase with PI controller after compensation.
43
Figure.6.28
Voltage and current in phase with fuzzy controller after compensation.
43
v
LIST OF TABLES
List of Tables
Page No
Table 5.1.
Control rule table
29
Table 6.1.
System parameters used for simulation
33
Table 6.2.
System parameters used in simulink
40
vi
INTRODUCTION
Background
Objective
Thesis Outline
INTRODUCTION
Early equipment was designed to withstand disturbances such as lightning, short
circuits, and sudden overloads without extra expenditure. Current power electronics (PE)
prices would be much higher if the equipment was designed with the same robustness.
Pollution has been introduced into power systems by nonlinear loads such as transformers
and saturated coils; however, perturbation rate has never reached the present levels. Due to its
nonlinear characteristics and fast switching, PE create most of the pollution issues. Most of
the pollution issues are created due to the nonlinear characteristics and fast switching of PE.
Approximately 10% to 20% of today’s energy is processed by PE; the percentage is estimated
to reach 50% to 60% by the year 2010, due mainly to the fast growth of PE capability. A race
is currently taking place between increasing PE pollution and sensitivity, on the one hand,
and the new PE-based corrective devices, which have the ability to attenuate the issues
created by PE, on the other hand.
Increase in such non-linearity causes different undesirable features like low system
efficiency and poor power factor. It also causes disturbance to other consumers and
interference in nearby communication networks. The effect of such non-linearity may
become sizeable over the next few years. Hence it is very important to overcome these
undesirable features.
Classically, shunt passive filters, consist of tuned LC filters and/or high passive filters
are used to suppress the harmonics and power capacitors are employed to improve the power
factor. But they have the limitations of fixed compensation, large size and can also exile
resonance conditions.
Active power filters are now seen as a viable alternative over the classical passive
filters, to compensate harmonics and reactive power requirement of the non-linear loads. The
objective of the active filtering is to solve these problems by combining with a much-reduced
rating of the necessary passive components.
Various topologies of active power filters have been developed so far [1-12]. The
shunt active power filter based on current controlled voltage source type PWM converter has
been proved to be effective even when the load is highly non-linear [1,4,11]. Most of the
active filters developed are based on sensing harmonics [7,10,11] and reactive volt-ampere
requirements of the non-linear load [1,3,12,17] and require complex control. A new scheme
has been proposed in [10], in which the required compensating current is determined by
sensing load current which is further modified by sensing line currents only [8,13]. An
instantaneous reactive volt-ampere compensator and harmonic suppressor system is proposed
1
[13] without the use of voltage sensors but require complex hardware for current reference
generator.
However, the conventional PI controller was used for the generation of a reference
current template. The PI controller requires precise linear mathematical models, which are
difficult to obtain and fails to perform satisfactorily under parameter variations, nonlinearity,
load disturbance, etc.
Recently, fuzzy logic controllers (FLCs) have generated a good deal of interest in
certain applications [18,19,21]. The advantages or FLCs over conventional controllers are
that they do not need an accurate mathematical model, they can work with imprecise inputs,
can handle lion-linearity, and they are more robust than conventional nonlinear controllers.
In this work both PI and fuzzy logic controlled shunt active power filter for the
harmonics and reactive power compensation of a nonlinear load are implemented. The
control scheme is based on sensing line currents only; an approach different from convention
ones, which arc based on sensing harmonics and reactive volt-ampere requirements of the
nonlinear load. The three-phase currents/voltages are detected using only two current/voltage
sensors. The DC capacitor voltage is regulated to estimate the reference current template. The
role of the DC capacitor is described to estimate the reference current. A design criterion is
described for the selection of power circuit components. Both the control schemed are
compared and performance of both the controllers is investigated. A detailed simulation
program of the schemes is developed to predict the performance for different conditions and
simulink models also has been developed for the same for different parameters and operating
conditions.
1.1.
BACKGROUND
1.1.1. Power quality
The PQ issue is defined as “any occurrence manifested in voltage, current, or frequency
deviations that results in damage, upset, failure, or misoperation of end-use equipment.”
Almost all PQ issues are closely related with PE in almost every aspect of commercial,
domestic, and industrial application. Equipment using power electronic devise are residential
appliances like TVs, PCs etc. business and office equipment like copiers, printers etc.
industrial equipment like programmable logic controllers (PLCs), adjustable speed drives
(ASDs), rectifiers, inverters, CNC tools and so on. The Power Quality (PQ) problem can be
detected from one of the following several symptoms depending on the type of issue
involved.
2
•
Lamp flicker
•
Frequent blackouts
•
Sensitive-equipment frequent dropouts
•
Voltage to ground in unexpected
•
Locations
•
Communications interference
•
Overheated elements and equipment.
PE are the most important cause of harmonics, interharmonics, notches, and neutral
currents. Harmonics are produced by rectifiers, ASDs, soft starters, electronic ballast for
discharge lamps, switched-mode power supplies, and HVAC using ASDs. Equipment
affected by harmonics includes transformers, motors, cables, interrupters, and capacitors
(resonance). Notches are produced mainly by converters, and they principally affect the
electronic control devices. Neutral currents are produced by equipment using switched-mode
power supplies, such as PCs, printers, photocopiers, and any triplets generator. Neutral
currents seriously affect the neutral conductor temperature and transformer capability.
Interharmonics are produced by static frequency converters, cyclo-converters, induction
motors & arcing devices.
Equipment presents different levels of sensitivity to PQ issues, depending on the type
of both the equipment and the disturbance. Furthermore, the effect on the PQ of electric
power systems, due to the presence of PE, depends on the type of PE utilized. The maximum
acceptable values of harmonic contamination are specified in IEEE standard in terms of total
harmonic distortion.
Power electronics are alive and well in useful applications to overcome distribution
system problems. Power electronics has three faces in power distribution: one that introduces
valuable industrial and domestic equipment; a second one that creates problems; and, finally,
a third one that helps to solve those problems. On one hand, power electronics and
microelectronics have become two technologies that have considerably improved the quality
of modern life, allowing the introduction of sophisticated energy-efficient controllable
equipment to industry and home. On another hand, those same sensitive technologies are
conflicting with each other and increasingly challenging the maintenance of quality of service
in electric energy delivery, while at the same time costing billions of dollars in lost customer
productivity.
3
1.1.2. Solutions to power quality problems
There are two approaches to the mitigation of power quality problems. The first
approach is called load conditioning, which ensures that the equipment is made less sensitive
to power disturbances, allowing the operation even under significant voltage distortion. The
other solution is to install line-conditioning systems that suppress or counteract the power
system disturbances. Passive filters have been most commonly used to limit the flow of
harmonic currents in distribution systems. They are usually custom designed for the
application. However, their performance is limited to a few harmonics, and they can
introduce resonance in the power system. Among the different new technical options
available to improve power quality, active power filters have proved to be an important and
flexible alternative to compensate for current and voltage disturbances in power distribution
systems. The idea of active filters is relatively old, but their practical development was made
possible with the new improvements in power electronics and microcomputer control
strategies as well as with cost reduction in electronic components. Active power filters are
becoming a viable alternative to passive filters and are gaining market share speedily as their
cost becomes competitive with the passive variety. Through power electronics, the active
filter introduces current or voltage components, which cancel the harmonic components of
the nonlinear loads or supply lines, respectively. Different active power filters topologies
have been introduced and many of them are already available in the market.
1.1.3. Power filter topologies
Depending on the particular application or electrical problem to be solved, active
power filters can be implemented as shunt type, series type, or a combination of shunt and
series active filters (shunt-series type). These filters can also be combined with passive filters
to create hybrid power filters.
The shunt-connected active power filter, with a self-controlled dc bus, has a topology
similar to that of a static compensator (STATCOM) used for reactive power compensation in
power transmission systems. Shunt active power filters compensate load current harmonics
by injecting equal-but opposite harmonic compensating current. In this case the shunt active
power filter operates as a current source injecting the harmonic components generated by the
load but phase-shifted by 180°.
Series active power filters were introduced by the end of the 1980s and operate
mainly as a voltage regulator and as a harmonic isolator between the nonlinear load and the
utility system. The series-connected filter protects the consumer from an inadequate supply-
4
voltage quality. This type of approach is especially recommended for compensation of
voltage unbalances and voltage sags from the ac supply and for low-power applications and
represents an economically attractive alternative to UPS, since no energy storage (battery) is
necessary and the overall rating of the components is smaller. The series active filter injects a
voltage component in series with the supply voltage and therefore can be regarded as a
controlled voltage source, compensating voltage sags and swells on the load side. In many
cases, series active filters work as hybrid topologies with passive LC filters. If passive LC
filters are connected in parallel to the load, the series active power filter operates as a
harmonic isolator, forcing the load current harmonics to circulate mainly through the passive
filter rather than the power distribution system. The main advantage of this scheme is that the
rated power of the series active filter is a small fraction of the load kVA rating, typically 5%.
However, the apparent power rating of the series active power filter may increase in case of
voltage compensation.
The series-shunt active filter is a combination of the series active filter and the shunt
active filter. The shunt active filter is located at the load side and can be used to compensate
for the load harmonics. On the other hand, the series portion is at the source side and can act
as a harmonic blocking filter. This topology has been called the Unified Power Quality
conditioner. The series portion compensates for supply voltage harmonics and voltage
unbalances, acts as a harmonic blocking filter, and damps power system oscillations. The
shunt portion compensates load current harmonics, reactive power, and load current
unbalances. In addition, it regulates the dc link capacitor voltage. The power supplied or
absorbed by the shunt portion is the power required by the series compensator and the power
required to cover losses.
Hybrid power filters are a combination of active and passive filters. With this
topology the passive filters have dynamic low impedance for current harmonics at the load
side, increasing their bandwidth operation and improving their performance. This behavior is
reached with only a small power rating PWM inverter, which acts as an active filter in series
with the passive filter.
Multilevel inverters are being investigated and recently used for active filter
topologies. Three-level inverters are becoming very popular today for most inverter
applications, such as machine drives and power factor compensators. The advantage of
multilevel converters is that they can reduce the harmonic content generated by the active
filter because they can produce more levels of voltage than conventional converters (more
than two levels). This feature helps to reduce the harmonics generated by the filter itself.
5
Another advantage is that they can reduce the voltage or current ratings of the
semiconductors and the switching frequency requirements. The more levels the multilevel
inverter has, the better the quality of voltage generated because more steps of voltage can be
created.
1.1.4. Voltage source converters
Most of the active power filter topologies use voltage source converters, which have a
voltage source at the dc bus, usually a capacitor, as an energy storage device. This topology,
shown in Figure 1.1, converts a dc voltage into an ac voltage by appropriately gating the
power semiconductor switches. Although a single pulse for each half cycle can be applied to
synthesize an ac voltage, for most applications requiring dynamic performance, pulse width
modulation (PWM) is the most commonly used today. PWM techniques applied to a voltage
source inverter consist of chopping the dc bus voltage to produce an ac voltage of an arbitrary
waveform. There are a large number of PWM techniques available to synthesize sinusoidal
patterns or any arbitrary pattern. With PWM techniques, the ac output of the filter can be
controlled as a current or voltage source device.
Figure 1.1.Voltage source converter topology for active filters.
Figure 1.2 shows the way PWM works by means of one of the simplest and most common
techniques: the triangular carrier technique. It forces the output voltage va over a switching
cycle, defined by the carrier period of Vcar, to be equal to the average amplitude of the
modulating wave Va ref. The resulting voltages for a sinusoidal modulation wave contain a
6
sinusoidal fundamental component Va(1) and harmonics of unwanted components. These
unwanted components can be minimized using a frequency carrier as high as possible, but
this depends on the maximum switching frequency of the semiconductors (IGBTs, GTOs, or
IGCTs).
Figure.1.2. The PWM carrier Technique (triangular carrier).
The modulation strategy shown in Figure 1.3 uses a triangular carrier, which is one of
many strategies applied today to control power inverters. Depending on the application
(machine drives, PWM rectifiers, or active power filters), some modulation strategies are
more suitable than others. The modulation techniques not only allow controlling the inverters
as voltage sources but also as current sources. Figure 1.3 shows the compensating current
generated for a shunt active power filter using three different modulation techniques for
current-source inverters. These three techniques are periodical sampling (PS), hysteresis band
(HB), and triangular carrier (TC). The PS method switches the power transistors of the active
filter during the transitions of a square wave clock of fixed frequency: the sampling
frequency. The HB method switches the transistors when the error exceeds a fixed
magnitude: the hysteresis band. The TC method compares the output current error with a
fixed amplitude and fixed triangular wave: the triangular carrier. Figure 1.3 shows that the
HB method is the best for this particular waveform and application because it follows more
7
accurately the current reference of the filter. When sinusoidal waves are required, the TC
method has been demonstrated to be better.
Figure.1.3. Current waveforms obtained using different modulation techniques for an active
power filter: (a) PS method, (b) HB method, (c) TC method.
Voltage source converters are preferred over current source converter because it is
higher in efficiency and lower initial cost than the current source converters [3, 4, 9]. They
can be readily expanded in parallel to increase their combined rating and their switching rate
can be increased if they are carefully controlled so that their individual switching times do
not coincide. Therefore, higher-order harmonics can be eliminated by using converters
without increasing individual converter switching rates.
1.1.5. Control strategies
Most of the active filters developed are based on sensing harmonics [7,10,11] and
reactive volt-ampere requirements of the non-linear load. [4,12,17] and require complex
control. In some active filters, both phase voltages and load currents are transformed into the
α-β orthogonal quantities, from which the instantaneous real and reactive power. The
compensating currents are calculated from load currents and instantaneous powers. The
harmonic components of power are calculated using high pass filters in the calculation
circuit. The control circuit of the dc capacitor voltage regulates the average value of the
voltage to the reference value [4]. Reactive power compensation is achieved without sensing
and computing the reactive current component of the load, thus simplifying the control
circuit. Current control is achieved with constant switching frequency producing a better
switching pattern. An active filter based on the instantaneous active and reactive current
component in which current harmonics of positive and negative sequence including the
fundamental current of negative sequence can be compensated. The system therefore acts as a
8
harmonic and unbalanced current compensator. A comparison between the instantaneous
active and reactive current component - method and the instantaneous active and reactive
power method is realized [17].
A new scheme has been proposed in [10], in which the required compensating current
is generated using simple synthetic sinusoid generation technique by sensing the load current.
This scheme is further modified by sensing line currents only [8,13]. An instantaneous
reactive volt-ampere compensator and harmonic suppressor system is proposed [13] without
the use of voltage sensors but require complex hardware for current reference generator. The
generated reference current is not a pure sine wave but stepped sine wave. Also, without the
use of voltage sensors, the scheme generates balanced sine wave reference currents but do not
compensate reactive power completely (if source voltage is unbalanced/distorted) due to
waveform difference between voltage and current [14]).
Control scheme based on sensing line currents is described in [2]. The 3-phase
currents/voltages are detected using only two current/voltage sensors compared to three used
in [8,16]. DC capacitor voltage is regulated to estimate the reference current template.
Selection of dc capacitor value has been described in [4,7,13].
Conventional solutions for controller requirements were based on classical control
theory or modern control theory. Widely used classical control theory based design of PID
family controllers requires precise linear mathematical models. The PID family of controllers
failed to perform satisfactorily under parameter variation, non linearity, load disturbance,
etc.[18]
During the past several years, fuzzy control has emerged as one of the most active and
fruitful areas for research in the applications of fuzzy set theory, especially in the realm of
industrial processes, which do not lend themselves to control by conventional methods
because of a lack of quantitative data regarding the input-output relations. Fuzzy control is
based on fuzzy logic-a logical system that is much closer in spirit to human thinking and
natural language than traditional logical systems. The fuzzy logic controller (FLC) based on
fuzzy logic provides a means of converting a linguistic control strategy based on expert
knowledge into an automatic control strategy[19,21]. Recently, fuzzy logic controllers
(FLC’s) have generated a good deal of interest in certain applications. The advantages of
FLC’s over the conventional controllers are:
1. It does not need accurate mathematical model;
2. It can work with imprecise inputs;
3. It can handle nonlinearity, and
9
4. It is more robust than conventional nonlinear controllers.
1.2. OBJECTIVE
In modern electrical distribution systems there has been a sudden increase of single
phase and three-phase non-linear loads. These non-linear loads employ solid state power
conversion and draw non-sinusoidal currents from AC mains and cause harmonics and
reactive power burden, and excessive neutral currents that result in pollution of power
systems. They also result in lower efficiency and interference to nearby communication
networks and other equipments. Active power filters have been developed to overcome these
problems. Shunt active filters based on current controlled PWM converters are seen as viable
solution. The techniques that are used to generate desired compensating current are based on
instantaneous extraction of compensating commands from the distorted currents or voltage
signals in time domain. Time domain compensation has fast response, easy implementation
and less computation burden compared to frequency domain.
In this work both PI and fuzzy logic controlled shunt active power filter for the
harmonics and reactive power compensation of a nonlinear load are implemented. Both
controllers performance under certain conditions and different system parameters is studied.
The advantages of fuzzy controllers over conventional controllers like PI controllers are that
they do not need accurate mathematical model, they can work with imprecise inputs, can
handle non-linearity, load disturbances etc.
1.3. THESIS OUTLINE
The body of this thesis consists of the following seven chapters including first chapter:
•
In Chapter 2, a description of the structure of the shunt active power filter, the basic
compensation principle, how reference source current is estimated and role of DC side
capacitor is given.
•
Chapter 3 gives the PI control scheme of shunt active power filter in which DC
voltage control loop design n how to select PI controller parameters is presented.
•
Chapter 4 deals with the fuzzy logic, fuzzy login controllers and implementation of
fuzzy control scheme for shunt active power filter. In this chapter basic fuzzy
algorithm and design of control rules is also described.
•
The entire active filter system is composed mainly of a three-phase source, a nonlinear load, a voltage source PWM converter, and a PI or fuzzy controller. All these
components modeling is described separately in chapter 5.
10
•
In chapter 6, simulation results are put and discussed in detail. Both PI and fuzzy
controller performances are compared under certain conditions.
•
The conclusions of the thesis and recommendations for future work are summarized
in Chapter 7.
11
SHUNT ACTIVE POWER FILTER
Basic compensation principle
Estimation of reference current
Role of DC side capacitor
Selection of Lc and Vdc,ref
Design of DC side capacitor (Cdc)
SHUNT ACTIVE POWER FILTER
The shunt-connected active power filter, with a self-controlled dc bus, has a topology
similar to that of a static compensator (STATCOM) used for reactive power compensation in
power transmission systems. Shunt active power filters compensate load current harmonics
by injecting equal-but opposite harmonic compensating current. In this case the shunt active
power filter operates as a current source injecting the harmonic components generated by the
load but phase-shifted by 180°.
Figure.2.1.Shunt active power filter topology.
Figure.2.2. Filter current IF generated to compensate load-current harmonics.
12
Figure 2.1 shows the connection of a shunt active power filter and Figure 2.2shows how the
active filter works to compensate the load harmonic currents.
2.1. BASIC COMPENSATION PRINCIPLE
Figure 2.3. shows the basic compensation principle of a shunt active power filter. It is
controlled to draw / supply a compensating current ic from / to the utility, so that it cancels
current harmonics on the AC side, and makes the source current in phase with the source
voltage. Figure.2.4. shows the different waveforms. Curve A is the load current waveform
and curve B is the desired mains current. Curve C shows the compensating current injected
by the active filter containing all the harmonics, to make mains current sinusoidal.
Figure.2.3.Shunt active power filter Basic compensation principle.
Figure.2.4.Shunt active power filter-Shapes of load, source and desired filter current wave
forms.
13
2.2. ESTIMATION OF REFERENCE SOURCE CURRENT
From Figure.2.1.1, the instantaneous currents can be written as
i s (t ) = i l (t ) − i c (t )
(2.2.1)
Source voltage is given by
v s ( t ) = v m sin ω t
(2.2.2)
If a non-linear load is applied, then the load current will have a fundamental component and
harmonic components which can be represented as
i L (t ) = ∑ ∞n =1 I n sin( nωt + φ n )
= I 1 sin( nωt + φ1 ) + ∑ n = 2 sin( nωt + φ n )
∞
(2.2.3)
The instantaneous load power can be given as
PL (t ) = vs (t ) * il (t )
∞
2
= Vm I1 sin ωt * cosφ1 + vm I1 sinωt * cosωt *sinφ1 +Vm sinωt * ∑ I n sin(nωt + φn )
(2.2.4)
= Pf (t) + Pr (t) + Ph (t)
(2.2.5)
n=2
From (2.2.4), the real (fundamental) power drawn by the load is
Pf (t ) = Vm I 1 sin 2 ωt * cos φ1 = v s (t ) * is (t )
(2.2.6)
From (2.2.6), the source current supplied by the source, after compensation is
i s (t ) = Pf (t ) / v s (t ) = I 1 cos φ1 sin ωt = I m sin ωt
Where Ism=I1cosΦ1.
There are also some switching losses in the PWM converter, and hence the utility
must supply a small overhead for the capacitor leakage and converter switching losses in
addition to the real power of the load. The total peak current supplied by the source is
therefore
Isp = Ism+ Isl
(2.2.7)
If the active filter provides the total reactive and harmonic power, then is(t) will be in
phase with the utility voltage and purely sinusoidal. At this time, the active filter must
provide the following compensation current:
ic (t ) = iL (t ) − is (t )
(2.2.8)
14
Hence, for accurate and instantaneous compensation of reactive and harmonic power it is
necessary to estimate, i.e. the fundamental component of the load current as the reference
current.
2.2. ESTIMATION OF REFERENCE SOURCE CURRENT
The peak value of the reference current Isp can be estimated by controlling the DC
side capacitor voltage. Ideal compensation requires the mains current to be sinusoidal and in
phase with the source voltage, irrespective of the load current nature. The desired source
currents, after compensation, can be given as
i sa
*
= I
sp
sin ω t
i sb = I sp sin(ωt − 120 0 )
*
i sc = I sp sin(ωt + 120 0 )
*
Where Isp (=I1cosΦ1+Isl)
the amplitude of the desired source current, while the phase
angle can be obtained from the source voltages. Hence, the waveform and phases of the
source currents are known, and only the magnitudes of the source currents need to be
determined. This peak value of the reference current has been estimated by regulating the DC
side capacitor voltage of the PWM converter. This capacitor voltage is compared with a
reference value and the error is processed in a fuzzy controller. The output of the fuzzy
controller has been considered as the amplitude of the desired source current, and the
reference currents are estimated by multiplying this peak value with unit sine vectors in phase
with the source voltages[6].
2.3. ROLE OF DC SIDE CAPACITOR
The DC side capacitor serves two main purposes: (i) it maintains a DC voltage with
small ripple in steady state, and (ii) serves as an energy storage element to supply real power
difference between load and source during the transient period. In the steady state, the real
power supplied by the source should be equal to the real power demand of the load plus a
small power to compensate the losses in the active filter. Thus, the DC capacitor voltage can
be maintained at a reference value.
However, when the load condition changes the real power balance between the mains
and the load will be disturbed. This real power difference is to be compensated by the DC
capacitor. This changes the DC capacitor voltage away from the reference voltage. In order to
15
keep satisfactory operation or the active filter, the peak value of the reference current must be
adjusted to proportionally change the real power drawn from the source. This real power
charged/discharged by the capacitor compensates the real power consumed by the load. If the
DC capacitor voltage is recovered and attains the reference voltage, the real power supplied
by the source is supposed to be equal to that consumed by the load again.
Thus, in this fashion the peak value or the reference source current can be obtained by
regulating the average voltage of the DC capacitor. A smaller DC capacitor voltage than the
reference voltage means that the real power supplied by the source is not enough to supply
the load demand. Therefore, the source current (i.e. the real power drawn from the source)
needs to be increased, while a larger DC capacitor voltage than the reference voltage tries to
decrease the reference source current. This change in capacitor voltage has been verified from
the simulation results.
The real/reactive power injection may result in the ripple voltage of the DC capacitor.
A low pass filter is generally used to filter these ripples, which introduce a finite delay. To
avoid the use of this low pass filter the capacitor voltage is sampled at the zero crossing of the
source voltage. A continuously changing reference current makes the compensation noninstantaneous during transient. Hence, this voltage is sampled at the zero crossing of one of
the phase voltage, which makes the compensation instantaneous. Sampling only twice in
cycle as compared to six times in a cycle leads to a slightly higher DC capacitor voltage
rise/dip during transients, but settling time is less.
The design of the power circuit includes three main parameters:
•
Selection of filter inductor, Lc.
•
Selection of DC side capacitor, Cdc.
•
Selection of reference value of DC side capacitor voltage, Vdc,ref.
2.4. SELECTION OF Lc AND Vdc,ref
The design of these components is based on the following assumptions:
1. The AC source voltage is sinusoidal.
2. To design of Lc, the AC side line current distortion is assumed to be 5%.
3. Fixed capability of reactive power compensation of the active filter.
4. The PWM converter is assumed to operate in the linear modulation mode (i.e.
0≤ma≤1).
16
As per the compensation principle, the active filter adjusts the current ic1 to
compensate the reactive power of the load [2]. If the active filter compensates all the
fundamental reactive power of the load, is1 will be in phase and ic1 should be orthogonal to
Vs, as shown in Fig.2.5. (the 1 stands here for the fundamental component).
Is1
I1
Vs
Vc1
Ic1
jωLcI1
Figure.2.5. Active power filter and its phasor diagram
The three-phase reactive power delivered from the active filter can be calculated from a
vector diagram
Qc1 = 3Vs I c1 = 3VsVc1 / ωLc (1 − (Vs / Vc1 ))
(2.4.1)
i.e. the active filter can compensate the reactive power from the utility only when Vc1 > Vs.
If the PWM converter is assumed to operate in the linear modulation mode (i.e. 0≤ma≤1), the
amplitude modulation factor ma is
m
a
= v m /( V
dc
/ 2)
Where vm=√2 Vc, and hence Vdc = 2√2 Vc1 for ma=1.
The filter inductor Lc is also used to filter the ripples of the converter current, and
hence the design of Lc is based on the principle of harmonic current reduction. The ripple
current of the PWM converter can be given in terms of the maximum harmonic voltage,
which occurs at the frequency mfω:
I ch ( mfω ) = Vch ( mfω ) / m f ωLc
(2.4.2)
By solving (2.4.1) and (2.4.2) simultaneously, the value of Lc, and Vc1 (i.e.Vdc) can be
calculated. Vc1, and hence Vdcref, must be set according to the capacity requirement of the
17
system (i.e. Vs≤Vc1≤2Vs). As the switching frequency is not fixed with the hysteresis
controller, a practically feasible value of 10 kHz has been assumed.
2.5. DESIGN OF DC SIDE CAPACITOR (Cdc)
The design of the DC side capacitor is based on the principle of instantaneous power
flow. The selection of Cdc can be governed by reducing the voltage ripple [2]. As per the
specification of the peak to peak voltage ripple (Vdc p-p(max)) and rated filter current (Ic1,rated),
the DC side capacitor Cdc can be found from equation
Cdc = (π * I c1,rated ) /( 3ωVdc , p − p (max) )
18
(2.5)
PI CONTROL SCHEME
Dc voltage control loop
Transfer function of PWM converter
Selection of PI controller parameters
PI CONTROL SCHEME
The complete schematic diagram of the shunt active power filter is shown in figure
3.1. While figure 3.2.gives the control scheme realization. The actual capacitor voltage is
compared with a set reference value.
Figure .3.1. Schematic diagram of shunt active filter.
Figure .3.2. APF Control scheme with PI controller.
19
The error signal is fed to PI controller. The output of PI controller has been
considered as peak value of the reference current. It is further multiplied by the unit sine
vectors (usa, usb, and usc) in phase with the source voltages to obtain the reference currents
(isa*, isb*, and isc*). These reference currents and actual currents are given to a hysteresis
based, carrierless PWM current controller to generate switching signals of the PWM
converter[2]. The difference of reference current template and actual current decides the
operation of switches. To increase current of particular phase, the lower switch of the PWM
converter of that particular phase is switched on, while to decrease the current the upper
switch of the particular phase is switched on. These switching signals after proper isolation
and amplification are given to the switching devices. Due to these switching actions current
flows through the filter inductor Lc, to compensate the harmonic current and reactive power
of the load, so that only active power drawn from the source.
3.1. DC VOLTAGE CONTROL LOOP
The block diagram of the voltage control loop is shown in figure 3.3. Where, Gc is the
gain of the PI controller and Kc is the transfer function of the PWM converter.
Figure.3.3.Block diagram of voltage control loop.
3.2 TRANSFER FUNCTION OF PWM CONVERTER (KC)
The derivation between input (ac link) and output (dc link) quantities of the PWM
converter is obtained by equating average rate of change of energy associated. Equating the
average rate of change of energy quantities of input and output side of the PWM converter
Pcap = Pconv - Pind
(3.2.1)
In order to linearize the power equation a small perturbation ∆Ic is applied in the input filter
current of converter Ic, about a steady state operating point Ico, the average dc link voltge will
also get perturbed by a small amount ∆Vdc, about its steady state operating point Vdco (Vdcref).
20
The transfer function of the PWM converter for a particular operating point can be obtained
from (3.1) as
Kc =
Vdc 3[Vs − Lc I co s − 2 I co Rc ]
=
Ic
CdcVdco s
(3.2.2)
3.3. SELECTION OF PI CONTROLLER PARAMETERS
A proportional-integral-derivative controller (PID controller) is control loop feed back
mechanism used in industrial control systems. In an industrial process a PID controller
attempts to correct the error between a measured process variable and a desired set point by
calculating and then outputting a corrective action that can adjust the process accordingly.
The PID controller calculation (algorithm) involves three separate modes; the Proportional
mode, the Integral mode and Derivative mode. The proportional mode determines the
reaction to the current error, the integral mode determines the reaction based on recent errors
and the derivative mode determines the reaction based on the rate by which the error has been
changing. The weighted sum of the three modes is outputted as a corrective action to a
control element such as a control valve or heating element. By adjusting constants in the PID
controller algorithm the PID can provide individualized control specific to process
requirements including error responsiveness, overshoot of set point and system oscillation.
Some applications may require only using one or two modes to provide the appropriate
system control. A PID controller will be called a PI, PD, P or I controller in the absence of
respective control actions. PI controllers are particularly common, since derivative action is
very sensitive to measurement noise.
Proportional mode responds to a change in the process variable proportional to the
current measured error value. The proportional response can be adjusted by multiplying the
error by a constant Kp, called the proportional gain or proportional sensitivity.
With integral mode, the controller output is proportional to the amount and duration
of the error signal. The integral mode algorithm calculates the accumulated proportional
offset over time that should have been corrected previously (finding the offset's integral).
While this will force the controller to approach the set point quicker than a proportional
controller alone and eliminate steady state error, it also contributes to system instability as the
controller will always be responding to past values. This instability causes the process to
overshoot the set point since the integral value will continue to be added to the output value,
even after the process variable has reached the desired set point.
21
The characteristic equation of the voltage control loop is used to obtain the constants of PI
controller in this case, can be written as [2]:
1 + (K p +
K i 3[V s − L c I co s − 2 I co R c ]
)
=0
s
C dc V dco s
(3.3)
Thus a second order transfer function can be found for the closed loop system. This
characteristic equation is used to found the components of PI controller. The analysis of this
characteristic equation shows that Kp determines the voltage response and Ki defines the
damping factor of the voltage loop. The current controller has been designed on the basis of
5% overshoot, to step the change in the amplitude of current reference.
22
FUZZY CONTROL SCHEME
Basic fuzzy algorithm
Design of control rules
FUZZY CONTROL SCHEME
Fig. 4. (1) shows the block diagram of the implemented fuzzy logic control scheme of a shunt
active power filter. Fig.4. (2) shows the schematic diagram of the control algorithm. In order
to implement the control algorithm of a shunt active power filter in closed loop, thee DC side
capacitor voltage is sensed and then compared with a reference value. The obtained error e
(=Vdc,ref-Vdc,act) and the change of error signal ce(n)=e(n)-e(n-1) at the nth sampling instant as
inputs for the fuzzy processing. The output of the fuzzy controller after a limit is considered
as the amplitude of the reference current Imax takes care of the active power demand of load
and the losses in the system.
Figure.4.1.Schematic diagram of closed loop fuzzy logic controlled shunt active power filter.
The switching signals for the PWM converter are obtained by comparing the actual
source currents (isa, isb, and isc) with the reference current templates (isa*, isb*, and isc*) in the
hysteresis current controller. Switching signals so obtained, after proper amplification and
isolation, are given to switching devices of the PWM converter [6].
23
Figure.4.2.Fuzzy Control scheme
4.1. BASIC FUZZY ALGORITHM
In a fuzzy logic controller, the control action is determined from the evaluation of a
set of simple linguistic rules. The development of the rules requires a thorough understanding
of the process to be controlled, but it does not require a mathematical model of the system.
The internal structure of the fuzzy controller is shown in Fig.4.2.
δImax(n)
e(n)
Defuzzification
Fuzzification
Vdc
Imax=Imax(n-1)+δImax(n)
e(n-1)
Vdcref
Decision Making
Figure 4.3. Internal structure of fuzzy logic controller.
A fuzzy inference system (or fuzzy system) basically consists of a formulation of the
mapping from a given input set to an output set using fuzzy logic. This mapping process
provides the basis from which the inference or conclusion can be made. A fuzzy inference
process consists of the following steps:
•
Step 1:Fuzzification of input variables
24
•
Step 2: Application of fuzzy operator (AND,OR,NOT) in the IF(antecedent) part of
the rule
•
Step 3: Implication from the antecedent to the consequent(THEN part of the rules)
•
Step 4: Aggregation of the consequents across the rules
•
Step 5: Defuzzification
The crisp inputs are converted to linguistic variables in fuzzification based on
membership function (MF). An MF is a curve that defines how the values of a fuzzy variable
in a certain domain are mapped to a membership value µ (or degree of membership) between
0 and 1. A membership function can have different shapes, as shown in figure 4.4. The
simplest and most commonly used MF is the triangular-type, which can be symmetrical or
asymmetrical in shape. A trapezoidal MF has the shape of a truncated triangle. Two MFs are
built on the Gaussian distribution curve: a simple Gaussian curve and a two-sided composite
of two different Gaussian distribution curves. The bell MF with a flat top is somewhat
different from a Gaussian function. Both Gaussian and bell MFs are smooth and non-zero at
all points.
Figure.4.4. Different types of membership functions.
25
The basic properties of Boolean logic are also valid for Fuzzy logic. Once the inputs
have been fuzzified, we know the degree to which each part of the antecedent of a rule has
been satisfied. Based on the rule, OR or AND operation on the fuzzy variables is done.
The implication step helps to evaluate the consequent part of a rule. There are a
number of implication methods in the literature, out of which Mamdani and TS types are
frequently used. Mamdani, proposed this method which is the most commonly used
implication method. In this, the output is truncated at the value based on degree of
membership to give the fuzzy output. Takagai-Sugeno-Kang method of implication is
different from Mamdani in a way that, the output MFs is only constants or have linear
relations with the inputs.
The result of the implication and aggregation stpes is the fuzzy output which is the
union of all the outputs of individual rules that are validated or “fired”. Conversion of this
fuzzy output to crisp output is defines as defuzzification. There are many methods of
defuzzification out of which Center of Area (COA) and Height method are frequently used.
In the COA method (often called the center of gravity method) of defuzzification, the crisp
output of particular variable Z is taken to be the geometric center of the output fuzzy value
µout(Z) area, where this area is formed by taking the union of all contributions of rules whose
degree of fulfillment is greater than zero. In height method of defuzzification, the COA
method is simplified to consider the height of the each contributing MF at the mid-point of
the base.
Here in this scheme, the error e and change of error ce are used as numerical variables
from the real system. To convert these numerical variables into linguistic variables, the
following seven fuzzy levels or sets are chosen as: NB (negative big), NM (negative
medium), NS (negative small), ZE (zero), PS (positive small), PM (positive medium), and PB
(positive big) [6].
The fuzzy controller is characterized as follows:
•
Seven fuzzy sets for each input and output.
•
Triangular membership functions for simplicity.
•
Fuzzification using continuous universe of discourse.
•
Implication using Mamdani's 'min' operator.
•
Defuzzification using the 'height' method.
Figure. 4.5. shows the normalized triangular membership functions used in fuzzification.
26
µe, µce
NB
NM NS
-1
-0.5
ZE
PS
-0.25
0
0.25
PM
0.5
PB
1
µδImax
NB
NM NS
-1
-0.5
ZE
-0.2
PS
0
0.2
PM
0.5
PB
1
Figure.4.5. Normalized triangular functions used in fuzzification
(a)Membership functions for e and ce
(b)Membership function for δImax
4.2. DESIGN OF CONTROL RULES
The fuzzy control rule design involves defining rules that relate the input variables to
the output model properties. As FLC is independent of the system model, the design is
mainly based on the intuitive feeling for, and experience of, the process. A new methodology
for rule base design based on the general dynamic behavior of the process has been
introduced in [18] which is further modified [14].
The input variables of the FLC are the error e and the change of error ce. The output is the
change of the reference current (δImax). The time step response of a stable closed loop system
27
should have a shape shown in figure 4.6. and figure 4.7. shows the phase plane trajectory of
the step response, which shows the mapping of the error against the change in error.
Figure.4.6. Time step response of a stable closed loop system.
Figure.4.7. Phase plane trajectory of step response.
The system equilibrium point is the origin of the phase plane. The time response has
been divided into four regions A1,A2,A3, and A4 and two sets of points - cross-over (b1, b2)
and peak (c1, c2). The index used for identifying the response area is defined as
A1: if e>0&ce<0, A2: if e<0&ce<0
A3:if e<0&ce>0, A4: if e>0&ce>0
The cross over index:
b1 : e>0 to e<0,ce<0
b2 : e<0 to e>0,ce>0
28
and the peak valley index:
c1: ce=0,e<0, and c2: ce=0,e>0
Based on these four areas, two sets of points and phase plane trajectory of e and ce, the rule
base is framed. The corresponding rule for the region 1 can be formulated as rule R1 and has
the effect of shortening the rise time
R1 : if e is + ve and ce is - ve, then δImax is +ve
Rule 2 for region 2 decreases the overshoot of the system response, which can be written as
R2 : if e is - ve and ce is - ve; then δImax is – ve
Similarly, rules for other regions can be formed. For are determined based on the
theory that in the transient better control performance finer fuzzy partitioned sub- state, large
errors need coarse control, which requires spaces (NB, NM, NS, ZE, PS, PM, PB) are used,
and coarse input/output variables; in the steady state, are summarized in Table 4.2.1. The
elements of this table however, small errors need fine control, which requires fine
input/output variables. Based on this, the elements of the rule table are obtained from an
understanding of the filter behavior and modified by simulation performance.
error(e)
A2
NB
NM NS
ZE
PS
NB
NB
NB
NB
NM NS
NM NB
NB
NB
NM NS
NB
NB
NB
NM NS
ZE
NB
NM NS
PS
NM NS
PM
NS
PB
ZE
NB
c1
Change
in
error(ce)
b1
A1
ZE
ZE
Ps
ZE
PS
PM
ZE
PS
PM
PB
ZE
PS
PM
PB
PB
ZE
PS
PM
PB
PB
PB
PS
PM
PB
PB
PB
PB
A3
Table.4.1.Control rule table
PM PB
a,c2
A4
b2
29
MODELING OF THE SYSTEM
Modeling of nonlinear load
Modeling of PWM converter
Estimation of peak supply current
Estimation of instantaneous reference supply currents
Hysteresis current controller
A program is developed to simulate the fuzzy logic based shunt active power filter in
MATLAB. The complete active power filter system is composed mainly of three-phase
source, a nonlinear load, a voltage source PWM converter, and a fuzzy controller or a PI
controller. All these components are modeled separately, integrated and then solved to
simulate the system.
5.1. MODELING OF NONLINEAR LOAD
A three-phase diode rectifier with input impedance and R-L load is considered as a
nonlinear load. Due to the presence of source inductance, six overlapping and six nonoverlapping conduction intervals occur in a cycle. During a non-overlapping interval only
two devices will conduct while during an overlapping interval three devices of the bridge will
conduct simultaneously. The dynamic equations during non-overlap and overlap intervals are
given in (1) and (2) respectively:
pi d = (V o − ( 2 R s + R L ) i d − 2 v d ) /( 2 L s + L )
(5.1.1)
pi d = (Vo − (1 .5 R s + R L )id − 2 v d ) /(1 .5 Ls + L )
(5.1.2)
Where Rs and Ls are the elements of the source inductance, vd is the voltage drop across each
device, RL and L are the elements of load impedance, id is the load current flowing through
the diode pairs and p is the differential operator d/dt). V0 is the AC side line voltage segment
(vac, vbc, vba, vca, vcb, vab during non-overlap, and vbc+vac/2, vba+vbc/2, vca+vba/2, vcb+vca/2,
vab+vcb/2, vac+vab/2 during overlap intervals) based on diode pair conduction. The phase
currents isa, isb, and isc are obtained by id, considering the respective diode pair conduction.
5.2. MODELING OF PWM CONVERTER
The PWM converter has been modeled as having a three phase AC voltage applied
through a filter impedance (Rc ,Lc) on its input, and DC bus capacitor on its output. The three
phase voltages vfa, vfb, and vfc reflected on the input side can be expressed in terms of the DC
bus capacitor voltage Vdc and switching functions stating the on/off status of the devices of
each leg Sa, Sb, and Sc as
v fa = (Vdc / 3)(2 S a − S b − S c )
v fb = (Vdc / 3)(− S a + 2S b − S c )
v fc = (Vdc / 3)(− S a − S b + 2S c )
30
(5.2.1)
The three phase currents ifa, ifb, and ifc flowing through impedances (Rc, Lc) are obtained by
solving the following differential equations:
p ifa = (1 / Lc )( Rc i fa + (v sa − v fa )
p ifb = (1 / Lc )( Rc i fb + (v sb − v fb )
(5.2.2)
pifc = (1 / Lc )( Rc i fc + (v sc − v fc )
The DC capacitor current can be obtained in terms of phase currents ifa, ifb, and ifc and the
switching status (1 for on and 0 for off) of the devices Sa, Sb and Sc
i dc
= i
fa
S
a
+ i
fb
S
+ i
b
fc
S
(5.2.3)
c
From this, the model equation of the DC side capacitor voltage can be written as
pV
dc
= (1 / C
dc
)( i
fa
S
a
+ i
fb
S
b
+ i
fc
Sc)
(5.2.4)
5.3. ESTIMATION OF PEAK SUPPLY CURRENT
Peak value of the supply current (Imax) is estimated using PI controller and fuzzy
controller over the voltage of the APF dc bus. The DC voltage is sensed at every one sixth
period of AC source frequency. The dc bus voltage (Vdc(n)) is compared with its reference
value (Vdcref). The resulting voltage error Ve(n) at nth sampling instant is expressed as
Ve(n) = Vdcref – Vdc(n)
(5.3.1)
The output of PI controller V0(n) at the nth sampling instant is expressed as:
V0 ( n) = V0 ( n − 1) + K p {Ve ( n) − Ve ( n − 1)} + K iVe ( n)
(5.3.2)
Where Kp and Ki are proportional and integral gain constants of the voltage controller. V0(n1) and Ve(n-1) are the output voltage controller and voltage error at (n-1)th sampling instant.
This output V0(n) of the voltage controller is taken as peak value of source current (Imax).
The peak value of the reference current Imax is estimated using fuzzy controller by
controlling the DC side capacitor voltage in closed loop. The output of fuzzy control
algorithm is change in peak current δImax(n). The peak reference current Imax(n), at the nth
sampling instant is determined by adding te previous peak current Imax(n-1) to the calculated
change in reference current:
I max ( n) = I max ( n − 1) + δI max ( n − 1)
(5.3.3)
In classical control theory this is integrating effect, which increases the system type and
improves steady state error.
31
5.4. ESTIMATION OF INSTANATANEOUS REFERENCE SUPPLY
CURRENTS
Harmonic free unity power factor, three-phase supply currents can be estimated using
unit current templates in phase with the supply voltages and their peak values. The unit
current templates are derived as
u sa = v sa / V sm ;
u sb = v sb / V sm ;
(5.4.1)
u sc = v sc / V sm .
The three-phase supply voltages are expressed as
v sa = v sm sin ωt ;
v sb = v sm sin ωt ;
(5.4.2)
v sc = v sm sin ωt .
Where Vsm is the peak value of source voltage and ω is the supply frequency. The
instantaneous reference supply currents are compared as
i sa* = I max u sa
isb* = I maxusb
(5.4.3)
isc* = I maxusc
5.5. HYSTERESIS CURRENT CONTROLLER
The current controller decides the switching patterns of the devices in the APF. The
switching logic is formulated as
if isa < (isa* - hb) upper switch is OFF and lower switch is ON in leg “a” of the APF;
if isa > (isa* - hb) upper switch is ON and lower switch is OFF in leg “a” of the APF.
Similarly, the switches in the legs “b” and “c” are activated. Here, hb is the width of
the hysteresis band around which the reference currents. In this fashion, the supply currents
are regulated within the hysteresis band of their respective reference values.
The performance of active filter is analyzed by solving set of differential equations (5.1.1)(5.4.3), with other expressions by a fourth order Runga kutta method.
32
SIMULATION RESULTS
A program is developed to simulate the both PI controller based and fuzzy logic based
shunt active power filter in MATLAB. The complete active power filter system is composed
mainly of three-phase source, a nonlinear load, a voltage source PWM converter, and a fuzzy
controller or a PI controller. All these components are modeled separately, integrated and
then solved to simulate the system.
Figures 6.1.- 6.8 show the simulations results of the proposed shunt active power filter
controlled by fuzzy logic and a conventional PI controller with MATLAB program. The
parameters selected for simulation studies are given in table 6.1. The three phase source
voltages are assumed to be balanced and sinusoidal. The source voltage waveform of the
reference phase only (phase-a, in this case) is shown in fig.6.1.
A load with highly nonlinear characteristics is considered for the load compensation.
The THD in the load current is 28.05%. The phase-a load current is shown in figure 6.2. The
source current is equal to the load current when the compensator is not connected.
System Parameters
Values
Source voltage(Vs)
100V(peak)
System frequency(f)
50Hz
Source impedance(Rs,Ls)
0.1Ω;0.15mH
Filter impedance(Rc,Lc)
0.4Ω;3.35mH
Load impedance(Rl,Ll)
6.7Ω;20mH
DC link capacitance
2000µF
Reference DClink voltage(Vdcref) 220V
Table6.1.System parameters for simulation study.
100
Vsa(V)
50
0
-50
-100
0
0.02
0.04
0.06
0.08
0.1
0.12
Time(s)
Figure.6.1. Source voltage.
33
0.14
0.16
0.18
0.2
40
Isa(A)
20
0
-20
-40
0
0.02
0.04
0.06
0.08
0.1
0.12
Time(s)
0.14
0.16
0.18
0.2
Figure.6.2. Source current when the compensator is not connected.
The compensator is switched ON at t=0.05s and the integral time square error (ITSE)
performance index is used for optimizing the and coefficients of the PI controller. The
optimum values (Kp and Ki) are found to be 0.2 and 9.32, respectively, which corresponds to
the minimum value of ITSE. The source currents for PI and fuzzy controllers are shown in
Figs.6.3 and 6.6, respectively. Compensating currents of PI and fuzzy controllers are shown
in figures 6.4 and 6.7. The DC side capacitor voltage during switch on response is shown in
figures 6.5. and 6.8 of PI and fuzzy controllers.
40
I s a (A )
20
0
-20
-40
0
0.02
0.04
0.06
0.08
0.1
Times(s)
0.12
0.14
0.16
0.18
0.2
0.1
Times(s)
0.12
0.14
0.16
0.18
0.2
Figure.6.3. Source current PI controller.
20
Ica(A)
10
0
-10
-20
0
0.02
0.04
0.06
0.08
Figure.6.4. Compensating current of PI controller.
34
240
Vdc(V)
220
200
180
160
0
0.02
0.04
0.06
0.08
0.1
0.12
Times(s)
0.14
0.16
0.18
0.2
Figure.6.5.DC Capacitor voltage during switch-on response with PI controller.
Is a(A )
50
0
-50
0
0.02
0.04
0.06
0.08
0.1
Times(s)
0.12
0.14
0.16
0.18
0.2
0.12
0.14
0.16
0.18
0.2
0.14
0.16
0.18
0.2
Figure.6.6.Source current fuzzy controller.
20
ica(A)
10
0
-10
-20
0
0.02
0.04
0.06
0.08
0.1
Time(s)
Figure.6.7. Compensating current of fuzzy controller.
Vdc(V)
250
200
150
0
0.02
0.04
0.06
0.08
0.1
0.12
Times(s)
Figure.6.8. DC Capacitor voltage during switch-on response with Fuzzy controller
35
From the wave forms it is clear that harmonic distortion is reduced after connecting
compensator. Compared to PI controller fuzzy controller fuzzy controller gives better
harmonic compensation.
The system studied has also been modeled using simulink and performance of PI and
Fuzzy controllers is analyzed. The system parameters selected for simulation study are given
in table 6.1 and 6.2. Figures 6.9-6.18 shows the simulation results of the implemented system
with PI controller and fuzzy controllers with simulation parameters mentioned in table 6.1.
The source voltage waveform of the reference phase only (phase-a, in this case) is shown in
fig.6.9. A diode rectifier with R-L load is taken as non-linear load. The THD of the load
current is 27.88%. The optimum values (Kp and Ki) are found to be 0.2 and 9.32 respectively.
Figure.6.9. Source voltage.
Figure.6.10.Load current.
36
Figure.6.11. Compensating current with PI controller.
Figure.6.12. Compensating current with fuzzy controller.
Figure.6.13. Source current with PI controller.
37
Figure.6.14. Source current with fuzzy controller.
Figure.6.15. DC side capacitor voltage with PI controller.
Figure.6.16. DC side capacitor voltage with PI controller.
38
Figure.6.17. Voltage and current in phase with PI controller after compensation.
Figure.6.18. Voltage and current in phase with fuzzy controller after compensation.
From the responses it is depicted that the settling time required by the PI controller is
approximately 8 cycles whereas incase of fuzzy controller is about 6 cycles. The source
current THD is reduced form 27.88% to 2% incase of PI controller and 2.89% incase of fuzzy
controller which is below IEEE standard with both the controllers.
Figures 6.19-6.28 shows the simulation results of the implemented system with PI
controller and fuzzy controllers with simulation parameters mentioned in table 6.2. The
source voltage waveform of the reference phase only (phase-a, in this case) is shown in
fig.6.19. A diode rectifier with R-L load is taken as non-linear load. The THD of the load
current is 28.34%.
39
System parameters
Values
Source voltage(Vs)
325V(peak)
System frequency(f)
50Hz
Source impedance(Rs,Ls)
0.1Ω,0.15mH
Filter impedance(Rc,Lc)
0.4Ω,3.35mH
Load impedance(Rl,Ll)
20Ω,20mH
Reference DClink voltage(Vdcref) 680V
DC link capacitance
2000µF
Table.6.1.System parameters used in simulink.
Figure.6.19. Source voltage.
Figure.6.20.Load current.
40
Figure.6.21. Compensating current with PI controller.
Figure.6.22. Compensating current with Fuzzy controller.
Figure.6.23. Source current with PI controller.
41
Figure.6.24. Source current with PI controller.
Figure.6.25. DC side capacitor voltage with PI controller.
Figure.6.26. DC side capacitor voltage with Fuzzy controller.
42
Figure.6.27. Voltage and current in phase with PI controller after compensation.
Figure.6.28. Voltage and current in phase with Fuzzy controller after compensation.
From the responses it is depicted that the settling time required by the PI controller is
approximately 10 cycles whereas incase of fuzzy controller is about 7.5 cycles. The peak
overshoot voltage incase of PI controller is 880Volts (approx) whereas incase of fuzzy
controller is 780volts (approx). The source current THD is reduced form 28.34% to 4.7%
which is below IEEE standard with both the controllers. After compensation both source
voltage and current are in phase with each other means that the harmonics are eliminated and
reactive power is compensated to make power factor close to unity. As the source current is
becoming sinusoidal after compensation power quality is improved.
43
CONCLUSION AND SCOPE FOR THE FUTURE WORK
CONCLUSION
A shunt active power filter has been investigated for power quality improvement.
Various simulations are carried out to analyze the performance of the system. Both PI
controller based and fuzzy logic controller based Shunt active power filter are implemented
for harmonic and reactive power compensation of the non-linear load. A program has been
developed to simulate the fuzzy logic based and PI controller based shunt active power filter
in MATLAB. It is found from simulation results that shunt active power filter improves
power quality of the power system by eliminating harmonics and reactive current of the load
current, which makes the load current sinusoidal and in phase with the source voltage. The
performance of both the controllers has been studied and compared. A model has been
developed in MATLAB SIMULINK and simulated to verify the results. The fuzzy controller
based shunt active power filter has a comparable performance to the PI controller in steady
state except that settling time is very less in case of fuzzy controller. The THD of the source
current is below 5%, the harmonics limit imposed by IEEE standard.
SCOPE FOR THE FUTURE WORK
Experimental investigations can be done on shunt active power filter by developing a
prototype model in the laboratory to verify the simulation results for both PI and fuzzy
controllers.
44
REFERENCES
[1].
W. M. Grady, M. J. Samotyj, and A. H. Noyola, “Survey of active power line
conditioning methodologies,” IEEE Transactions on Power Delivery, vol. 5, no. 3,
Jul. 1990, pp. 1536–1542.
[2].
H. Akagi, Y. Kanazawa, and A. Nabae, “Instantaneous reactive power compensators
comprising switching devices without energy storage components,” IEEE
Transactions on Industry Applications, vol. IA-20, no. 3, May/Jun. 1984, pp. 625–
630.
[3].
S. Jain, P. Agarwal, and H. O. Gupta, “Design simulation and experimental
investigations on a shunt active power filter for harmonics and reactive power
compensation,” Electrical Power Components and Systems, vol. 32, no. 7, Jul. 2003,
pp. 671–692.
[4].
F. Z. Peng, H. Akagi, and A. Nabae, “Study of active power filters using quad series
voltage source PWM converters for harmonic compensation,” IEEE Transactions on
Power Electronics, vol. 5, no. 1, Jan. 1990, pp. 9–15.
[5].
H.Akagi, “Trends in active power line conditioners,” IEEE Transactions on power
Electronics, vol 9, no 3, 1994, pp 263-268.
[6].
S. K. Jain, P. Agrawal, and H. O. Gupta, “Fuzzy logic controlled shunt active power
filter for power quality improvement,” Proceedings of Institute of Electrical
Engineers, Electrical Power Applications, vol. 149, no. 5, 2002.
[7].
L.A.Morgan, J.W.Dixon & R.R.Wallace, “A three phase active power filter operating
with fixed switching frequency for reactive power and current harmonics
compensation,” IEEE Transactions on Industrial Electronics, vol.42, no.4, August
1995, pp 402-408.
[8].
B. Singh, A. Chandra, and K. Al-Haddad, “Computer-aided modeling and simulation
of active power filters,” Electrical Machines and Power Systems, vol. 27, 1999, pp.
1227–1241.
[9].
B. Singh, A. Chandra, and K. Al-Haddad, “A review of active filters for power
quality improvement,” IEEE Transactions on Industrial Electronics, vol.46, no 5, Oct
1999, pp1-12.
[10]. R. M. Duke and S. D. Round, “The steady state performance of a controlled current
active filter,” IEEE Transactions on Power Electronics, vol. 8, Apr. 1993, pp. 140–
146.
45
[11]. J.W.Dixon, J.J.Garcia & L.Morgan, “Control system for three phase active power
filter which simultaneously compensates power factor and unbalanced loads,” IEEE
Transactions on Industrial Electronics, vol.42, no.6, 1995, pp636-641.
[12]. E.H.Watanbe, R.M.Stephan & M.Aredes, “New concepts of instantaneous active and
reactive powers in electrical systems with generic loads,” IEEE Transactions on
Power Delivery, vol.8, no.2, April 1993, pp.697-703.
[13]. K. Chatterjee, B. G. Fernandes, and G. K. Dubey, “An instantaneous reactive voltampere compensator and harmonic suppressor system,” IEEE Transactions on Power
Electronics, vol. 14, no. 2, Mar. 1999, pp. 381–392.
[14]. Shyh-Jier Huang and Jinn-Chang Wu, "A control algorithm for three-phase threewired active power filters under nonideal mains voltages," IEEE Transactions on
Power Electronics, Vol. 14, No. 4, July 1999, pp 753-760.
[15]. D.A.Torey& A.M..Al-Zamel, “A single phase active filter for multiple nonlinear
load,” IEEE Transactions on Power Electronics, vol.10, May 1995, pp.263-272.
[16]. B. Singh, A. Chandra, and K. Al-Haddad, “Performance comparison of two current
control techniques applied to an active filter,” 8th International conference on
Harmonics and Power Qulaity ICHQP, Oct 1998, pp.133-138.
[17]. V.Soares, P.Verdelho & G.D. Marques, “An instantaneous active and reactive current
component method of active filter,” IEEE Transactions on Power Electronics, vol.15,
no.4, July 2000, pp.660-669.
[18]. LEE C.C., “Fuzzy logic in control systems: fuzzy logic controller part I and II,” IEEE
Trans. Syst. Man Cybern, 1990, vol.20, pp.404-435.
[19]. V. S. C. Raviraj and P. C. Sen, “Comparative study of proportional-integral, sliding
mode, and fuzzy logic controllers for power converters,” IEEE Transactions on
Industrial Applications, vol. 33, no. 2, Mar./Apr. 1997, pp. 518–524.
[20]. Mohan, N., Undeland,.T.M, and Robbins,.W.P, “Power electronics :converters,
applications and design,” Singapore,John Wiley and sons, 2003.
[21]. B. K. Bose, “Modern Power Electronics and AC Drives,” Singapore, Pearson
Education,2004.
46
isa
isb
Scope3
ila
Scope
isc
ilb
+
A
+
i
-
ilc
i
-
Scope4
A
Rs1,Ls1
B
i
-
+
+
i
-
+
i
-
+
+
-
+
-
C
i
-
i
-
B
C
T hree-Phase Source
+
Rl,Ll
v
Scope6
+
-
pf
v
Scope1
+
-
i
-
t
Clock
thd
Scope7
Rc1,Lc1
v
signal THD
T otal Harmonic
Distorsion
+
g
vdc
+
A
i
-
Scope2
B
+
C
Vsb
i
-
Cdc
IGBT inverter
+
+
-
v
Vdc
ica
Vsa
icc
Vsc
Vdc
icb
680
Vdcref
Vsa
Continuous
Vsb
Vsc
gatepulse
pow ergui
isa
isb
isc
APF Control Scheme
FIGURE 1. MATLAB SIMULINK MODEL FOR SHUNT ACTIVE POWER FILTER SIMULATION STUDY.
Scope5
2
0.3
Vdcref
kp
1
s
Integrator
butter
-K-
isa*
lIMITER
Scope1
g
Product
boolean
isa
NOT
double
HSC
ki
1
Vdc
isb*
g
3
-K-
Product1
NOT
double
Mux
HSC1
Vsa
4
boolean
isb
-K-
Vsb
boolean
5
1
gatepulse
-K-
isc*
Vsc
g
Product2
isc
HSC2
6
isa
7
isb
8
isc
FIGURE 2. CONTROL SCHEME USING PI CONTROLLER.
NOT
double
2
Vdcref
isa*
Limiter
1
boolean
isa
Fuzzy Logic
Controller
with Ruleviewer
butter
Scope1
g
Product
NOT
double
HSC
Vdc
isb*
g
3
Product1
-K-
NOT
double
Mux
HSC1
Vsa
4
boolean
isb
-K-
Vsb
boolean
5
1
gatepulse
-K-
isc*
g
Vsc
Product2
isc
HSC2
6
isa
7
isb
8
isc
Mux
1
s
Integrator
FIGURE 3.CONTROL SCHEME USING FUZZY CONTROLLER.
NOT
double
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