Harmonics created by nonlinear loads such as arc furnaces, cycloconverters and motor drives destroys the power quality in the system. They not only affect the working of adjacent loads but also shorten the life of power equipment by creating excessive losses. ‘Shunt Active Power Filter’ is a modern addition to family of compensating devices. It has superior qualities over its contemporaries namely SVCs and STATCOMs. It not only mitigates harmonics within the allowable limits defined by IEEE Std 519-1992, but also compensates unbalancing and reactive power in the system. Consequently, only active power is supplied by the source thus power factor approaches unity. A fully functional Simulink model of Shunt Active Power Filter has been designed based on ‘Instantaneous Power Theory’ or ‘p-q Theory’. The results of simulation comply with all the features described by the theory, justifying employment of SAPF in the industry.

1. DESIGN AND SIMULATION OF THREE
PHASE SHUNT ACTIVE POWER FILTER
USING THE p-q THEORY
BE (EE) PROJECT REPORT
Prepared By:
Muhammad Jawwad Iqbal
Muhammad Waleed Khan
Muhammad Danish Shaikh
Hafiz Muhammad Furqan
Farhan Rajput
EE-09-129
EE-09-094
EE-09-101
EE-09-122
EE-09-074
Project Advisor:
Muhammad Ali Baig
Dr. Abdul Qadir
(Internal Advisor)
(External Advisor)
N.E.D. University of Engineering & Technology,
Karachi-75270

2. i
ABSTRACT
Harmonics created by nonlinear loads such as arc furnaces, cycloconverters and
motor drives destroys the power quality in the system. They not only affect the
working of adjacent loads but also shorten the life of power equipment by creating
excessive losses. ‘Shunt Active Power Filter’ is a modern addition to family of
compensating devices. It has superior qualities over its contemporaries namely
SVCs and STATCOMs. It not only mitigates harmonics within the allowable limits
defined by IEEE Std 519-1992, but also compensates unbalancing and reactive
power in the system. Consequently, only active power is supplied by the source
thus power factor approaches unity. A fully functional Simulink model of Shunt
Active Power Filter has been designed based on ‘Instantaneous Power Theory’ or
‘p-q Theory’. The results of simulation comply with all the features described by
the theory, justifying employment of SAPF in the industry.

3. ii
ACKNOWLEDGEMENTS
We thank Almighty Allah who gave us the opportunity to complete this project and
to explore more knowledge in power systems. We learned so many new things and
concepts due to its research based nature.
Secondly, we are deeply indebted to our beloved parents for their unconditional
support and prayers throughout our lives.
And then, we offer our profound gratitude to our Internal Advisor Mr. Mirza
Muhammad Ali Baig for being calm and supportive through the whole course of
project, and for tolerating us. We are also magnanimous to our External Advisor
Dr. Abdul Qadir for his vision and guidance. Also we are grateful to our FYP
committee members namely, Sir Umer Sajid and Sir Muhammad Omar.
Lastly, we want to thank Miss Samiya Zafar for listening to our ideas and for her
altruistic suggestions. And Sir Fezan Rafique, for appreciating our project and hard
work.

4. CONTENTS
___________________________________
PREFACE
v
1. INTRODUCTION
1.1 Introduction
1.2 Types of Load
1.2.1 Linear Load
1.2.2 Non-Linear Load
1.3 Power Quality
1.4 Harmonic Injection Limit
1.5 Problems caused by Harmonics
1.5.1 Effect on Power System itself
1.5.2 Effect on Consumer itself
1.5.3 Effect on Communication System
1.5.4 Effect on Revenue Billing
1
1
2
2
2
3
3
4
4
4
4
5
2. BACKGROUND
2.1 Harmonic Mitigation Techniques
2.2 Passive Harmonic Filters
2.2.1 Promising features of Passive Harmonic Filters
2.2.2 Non-Promising features of Passive Harmonic Filters
2.3 Active Harmonic Filters (AHF)
2.3.1 Operation of AHF
2.3.2 Advantages of AHF
6
6
6
7
8
8
8
9
3. THE INSTANTANEOUS POWER THEORY
3.1 Historical Background of Power Theory
3.2 Basis of the p-q Theory
3.3 Background of p-q Theory
3.4 The Clarke Transformation
3.5 The p-q Theory
3.6 Use of p-q Theory in Shunt Active Filters
3.7 Symmetrical Components
10
10
10
11
11
13
15
16
4. SHUNT ACTIVE POWER FILTER
4.1 Shunt Active Filters
4.2 General description of Shunt Active Filters
4.3 The Active Filter Controller
18
18
18
19

5. 4.4 Optimal Power Flow
4.5 Three Phase Three Wire Shunt Active Filter
4.6 The Simulink Model
4.6.1 3-Phase Source
4.6.2 Line Impedance (Zt)
4.6.3 V-I Measurement
4.6.4 Circuit Breaker
4.6.5 POWERGUI
4.6.6 Non-Linear Load
4.7 SHUNT APF
4.7.1 PQ and I-Compensation calculation
4.7.1.1 Clarke V
4.7.1.2 Clarke I
4.7.1.3 PQ Calculation
4.7.1.4 Low Pass Filter
4.7.1.5 Alpha-Beta Current
4.7.1.6 Compensation Currents
4.7.2 Hysteresis Controller
4.7.3 Universal Bridge
4.7.4 Capacitor
4.7.5 PI Controller
4.7.6 Coupling Inductor
20
20
22
22
22
22
23
23
23
24
24
24
25
25
25
26
26
26
26
26
26
26
5. SIMULATION RESULTS
5.1 Case I: Compensation of Non-Linear Load
5.2 Case II: Compensation of Non-Linear plus Unbalance Resistive Load
5.3 Case III: Compensation of Unbalance Resistive Load
5.4 Case IV: Compensation of Unbalance Inductive Load
5.5 Case V: Compensation of Unique Unbalance Resistive Load
5.6 Conclusion
27
29
30
32
33
34
A. SYMMETRICAL COMPONENTS
A.1 Simulink Model Of Sequence Power
35
36
B. HYSTERESIS CONTROLLER
B.1 Simulink Model Example
B.2 Hysteresis Band in Digital Hysteresis Current Controller
39
40
41
BIBLIOGRAPHY

6. v
PREFACE
___________________________________
The concept of harmonic compensation is the underlying idea of our project. The compensation
is not done by signal comparison, as it is done in active filtering, but on the basis of ‘power
selection’ in harmonic components and unbalanced component of fundamental current
component. The inspiration behind this idea comes from our curiosity of power properties under
semiconductor load (nonlinear load). We went through H. Akagi’s book “Instantaneous Power
Theory and Applications to Power Conditioning”. It helped us understanding ‘the p-q Theory’
proposed by H. Akagi et al, originally in 1982. Proponent of p-q’s rival theory; Lesczek S.
Czarnecki pointed out many limitations and flaws in the theory, and put forward his own
‘Current Physical Component Theory’. Czarnecki made a comprehensive discourse on ‘Voltages
and Currents in Non Sinusooidal Conditions’, his research publication, by comparing power
definitions of various power theories.
This report is divided into five chapters. In chapter 1, we have discussed basic power definitions
and idea of harmonics in power systems. Chapter 2 discusses the aged solutions of harmonic
problem; ‘Passive Harmonic Filters’ are discussed in detail. Chapter 3 puts forward H. Akagi and
A. Nabae’s “Instantaneous Power Theory”, and tries to explain its various power terms. Chapter
4 is titled as per our project name, ‘Shunt Active Power Filter’, describes working algorithm
based on the p-q Theory, and our Simulink model, its building blocks and specifications in detail.
Chapter 5 is dedicated to simulation results, five cases of nonlinear and unbalanced load were
considered to demonstrate the feats of Active Power Filters. Appendices on Symmetrical
Components and Hysteresis Controller are also attached to assist the reader.
Finally, we want to acknowledge that we are immensely grateful to above mentioned scholars
and our teachers, without whom it would not be possible.
JAWAD, WALEED, DANISH,
FURQAN AND FARHAN

7. 1
Chapter 1
INTRODUCTION
___________________________________
1.1 INTRODUCTION
Electric power is the rate of electrical energy flow at any point. In other words it can also be
defined as the product of the instantaneous voltage and current. If i(t) and v(t) represent the
instantaneous sinusoidal current and voltage respectively then the instantaneous power P(t) can
be given as;
( )
( )
( )
)
(
( ) ( )
(
)
( )
( )
( )
( )
)
)
(
)
)
(
)
(
)
)
(
(
(
(
)
(
)
(
If we consider θv as reference i.e. θv = 0o and θi = ø then the above equation will become:
( )
(
( )
( )
)
(
)
( )
Where pact(t) is the real or active power absorbed by the electrical components and preactive(t) is
the power oscillating in the power system due to the charging components like inductance and
capacitance. This reactive power is in the form of increasing current which causes higher line
losses, voltage drops, etc.

8. 2
Figure 1.1 - Conventional concept of active and reactive power
But according to modern definitions pact(t) is not the total useful power and preactive(t) is also
cause by power electronic components or non-linear loads (Further discussion of 3-phase power
and various terms involved in it are explained in Chapter No. 3). Moreover, non-linear loads like
switching circuits, speed control circuits, welding plants, thermal loads, variable frequency
drives; motor controls, power invertors, cyclo convertors, high frequency induction furnaces, etc
tends to produce harmonics distortion in power lines. These high frequency harmonic
components cause greater magnetization and heating losses in the cores of electrical machines
and transmission lines.
The effects of harmonic distortion are hard to measure but the end results are easy to understand,
higher operating costs and lower reliability.
1.2 TYPES OF LOAD
Loads can be characterized into many types according to their nature, function etc. The type of
load we are interested in are
1. Linear load
2. Non-linear load
1.2.1 LINEAR LOAD
Electrical loads whose current wave has a linear relation with the voltage wave are termed as
linear loads. These loads do not cause any harmonic in the electrical system .
1.2.2 NON-LINEAR LOAD
The nonlinear loads are referred to as the loads that distort the current waveform shape due to
the switching action and the current and voltage waveforms are not identical in shape, e.g.
fluorescent lamp, PC and TV etc.Figure 1.2 shows how harmonics injected by non -linear
loads distort the current waveform.

9. 3
Figure 1.2 – Distortion in current waveforms due to harmonics
1.3 POWER QUALITY
Power quality is an issue of great concern for electrical power industry (utility and consumer
both) as the power quality determines the fitness of electrical power to consumer devices and the
efficiency of consumer devices. There are many ways in which electric power can be of poor
quality. The presence of harmonic content in AC power is an important factor that describes
quality of electrical power. Power quality may be defined as;
“The deviation of voltage from the ideal, continuous single-frequency sine wave with a rated
constant frequency and amplitude. Also current deviation from the ideal, single-frequency sine
wave with a constant frequency and amplitude that is in phase with the supply voltage.”
1.4 HARMONIC INJECTION LIMIT
The increasing use of power electronic devices has result in greater control over electric power
and larger production but power systems are often subjected to harmonic distortion due to
increasing applications of these nonlinear loads. Non-linear loads inject harmonics into the
power system which travel through the system and create problems even for those consumers
who do not actually use non-linear loads, by making the supplied voltage non-linear at PCC
(Point of Common Coupling).
Therefore, there is a limit for every individual customer for harmonic injection depending upon
full load current and short-circuit capacity. Table 10.3 of IEEE Std. 519 prescribes limits for
TDD (Total Demand Distortion) for individual customers.

10. 4
Table 10.3: Current Distortion Limits for General Distribution System (120V through 69,000V)
Maximum Harmonic Current Distortion in Percentage of IL
Individual Harmonic Order (Odd harmonics)
ISC/IL
h<11
11 ≤ h <17 17≤ h <23
23≤ h <35
35< h
TDD
<20*
4.0
2.0
1.5
0.6
0.3
5.0
20<50
7.0
3.5
2.5
1.0
0.5
8.0
50<100
10.0
4.5
4.0
1.5
0.7
12.0
100<1000
12.0
5.5
5.0
2.0
1.0
15.0
>1000
15.0
7.0
6.0
2.5
1.4
20.1
Even harmonics are limited to 25% of the odd harmonic limits above
Current distortions are result in a DC offset (e.g. half wave converters) are not allowed
*
All power generation equipments are limited to these values of current distortion regardless of
actual ISC/IL
Where,
ISC = maximum short circuit current at PCC
IL = maximum Demand load current (fundamental frequency component) at PCC
Table 1.1 – Harmonic Limits
1.5 PROBLEMS CAUSED BY HARMONICS
Following are the problems that are caused by the presence of harmonics in power system.
1.5.1 EFFECT ON POWER SYSTEM ITSELF
The major effect of power system harmonics is to increase the current in the system. This is
particularly the case for the third harmonic, which causes a sharp increase in the zero
sequence current, and therefore increases the current in the neutral conductor.
1.5.2 EFFECT ON CONSUMER ITSELF
Non-linear loads also causes harmonics/distortions in utility supplied voltages due to which
even the linear loads draw non -linear current. Harmonics can also cause thyristor firing errors
in converter. The performance of consumer equipment, such as motor drives and computer
power supplies, can be adversely affected by harmonics.
1.5.3 EFFECT ON COMMUNICATION SYSTEM
Harmonic currents flowing on the utility distribution system or within an end -user facility
can create interference in communication circuits sharing a common path. Voltages included
in parallel conductors by the common harmonic currents often fall within the bandwidth of
neutral voice communications. Harmonic currents on the power system are coupled into
communication system by either induction or direct conduction.

11. 5
1.5.4 EFFECT OF REVENUE BILLING
Electrical utility companies usually measure energy consumption in two quantities energy
consumed and the maximum power used for given period. Both energy and demand are
measured using the so-called watt -hour and demand meters.
Harmonic currents from non -linear loads can impact the accuracy of watt-hour and demand
meter adversely. Traditional watt -hour meters are based on the induction motor principle.
Conventional magnetic disk watt -hour meters tend to have a negative error at harmonic
frequencies. That is, they register low for power at harmonic frequencies if they are properly
calibrated for fundamental frequency. This error increases with increasing frequency.

12. 6
Chapter 2
BACKGROUND
__________________________________
2.1 HARMONIC MITIGATION TECHNIQUES
The growing concern of good power quality and awareness with the harms to power system due
to harmonics along with the penalties imposed by utility companies and the standards to the limit
of THD made by IEEE and other organizations are the driving factors for invention and adoption
of various methods, devices and equipment for harmonic mitigation. These equipment include:
1.
2.
3.
4.
5.
Line reactors
Isolation transformers
K-Factor transformers
Phase shifting transformer
Harmonic filters
The most effective and useful of the list are current harmonic filters. There are two types of
harmonic filters: 1) passive harmonic filter and 2) active harmonic filters.
2.2 PASSIVE HARMONIC FILTERS
Conventional solutions to the harmonic distortion problems have existed for a long time. The
passive filtering is the simplest conventional solution to mitigate the harmonic distortion. A
passive harmonic filter is built using an array of capacitors, inductors and/or resistors. They
restrict the harmonic currents to flow into power system and divert them by providing a low
resistance path. They remove distortion due to harmonic currents and hence remove distortions
in voltages caused by non-linear voltage drop across the line impedance. They are connected as
shunt branch or parallel with load. Passive filters are designed to be capacitive at fundamental
frequency in order to correct displacement power factor and provide reactive Volt-Amperes.
Passive filters provide a low impedance path compared to the system impedance and hence the
harmonic current flows proportional to the impedance of parallel paths, therefore, performance
of passive harmonic filter largely depends upon the system impedance and its topologies and this
factor is not accurately known and is subjected to changes very frequently. Usually a separate
tuned harmonic filter is required to mitigate a single harmonic.

13. 7
Single-Tuned
High-Pass
Double-Tuned
C-Type
Figure 2.1 – Typical Passive Harmonic Filters
Single tuned, double tuned, high pass and c-type are four types of passive harmonic filter but
most common of them is single tuned filters. Tuned filter is the most common type of passive
filters. It is a series combination of inductor and capacitor which resonates at tuning frequency,
therefore, its impedance is very low for tuned harmonic. Because of low impedance at tuned
frequency the filter now becomes the source of harmonic current rather than the utility. Another
popular type of passive filter is the high-pass filter (HPF). A HPF will allow a large percentage
of all harmonics above its corner frequency to pass through.
The following figure shows impedance vs. frequency curve of a tuned passive harmonic filter.
The response is highly capacitive (with high impedance) at fundamental frequency, therefore
provides reactive power at fundamental frequency as well. At tuned frequency the response is
resistive while above tuned frequency response is inductive.
Capacitive
Response
Inductive
Response
Figure 2.2 – Frequency vs. Impedance curve of Single Tuned Filter
2.2.1 PROMISING FEATURES OF PASSIVE HARMONIC FILTERS
Passive filters are the most common and economical solution to current harmonic distortion
problems because of their simple design and low initial cost. The most promising features of
passive harmonic filters are:
1. They are simple to design
2. Low initial cost (compared to Active Harmonic Filter)

14. 8
3. Shunt passive filters have extra advantage of providing reactive power. Hence they
correct distortion power factor and displacement power factor as well.
4. Brings down the THD in line current to the allowable limits.
2.2.2 NON-PROMISING FEATURE OF PASSIVE HARMONIC FILTERS
Some non-trivial issues with passive current harmonic filters are:
1. Filtering characteristics depend upon the source impedance (i.e. impedance of system and
its topology) which may not be well defined or may be subjected to variations.
2. Resonance problem may occur with loads and network
3. Usually a series of passive harmonic filters are required to compensate various
harmonics
4. Works good when power factor is not very low and the magnitude of specified harmonic
remains constant
5. The response is not dynamic i.e. if the requirement of certain harmonic increases or with
the change of load or if certain other harmonics are required the filters have to be
redesigned
6. Doesn’t solve the problem of load unbalancing or neutral shifting
2.3 ACTIVE HARMONIC FILTER (AHF)
Static response of passive harmonic filter and other problems have led to a power electronic
solution of harmonic distortion i.e. Active Harmonic Filters (AHF); a modern solution to old
harmonic current problems. Nowadays, passive filters are used to cancel the switching frequency
of active filters and high frequencies. Tuned filters are used besides the active filters to cancel
specific frequencies and decrease the power of active filters. Active filters have been designed,
improved, and commercialized in the past three decades. They are applicable to compensate
current-based distortions such as current harmonics, reactive power, and neutral current. They
are also used for voltage-based distortions such as voltage harmonics, voltage flickers, voltage
sags and swells, and voltage imbalances and load unbalancing and neutral shifting. Moreover,
unlike passive filters, they do not cause harmful resonances with the power distribution systems.
Consequently, the AHFs performances are independent of the power distribution system
properties.
2.3.1 OPERATION OF AHF
The main aim of the APF is to compensate for the harmonics and reactive power dynamically.
The APF overcomes the drawbacks of passive filters by using the switching mode power
converter to perform the harmonic current elimination. AHF continuously monitors the load
current, filter out the harmonic content and generates compensation current signals using any of
the algorithms like P-Q Theory, dq transform, sliding mode control, unity power factor method,
algorithm based on DSP, etc. compensation current signals are fed to hysteresis controller or
PWM converter as reference signals to generate gating signals for fast switching IGBT inverter.
The inverter generates harmonic currents required by the load through charging and discharging
of capacitor. These currents are injected into the system near the load through an interfacing

15. 9
inductor or a coupling transformer. The performance of AHF is independent of system
impedance as it compares the injected currents with reference signals and tries to minimize the
error.
There are three topologies of AHF: i) Series AHF, ii) Shunt AHF and iii) Hybrid AHF. We have
selected Shunt AHF for this project which is ideal for current harmonic compensation. A
generalize block diagram of SAHF is given below;
Figure 2.3 – Generalized Block Diagram of Active Filter
2.3.2 ADVANTAGES OF ACTIVE HARMONIC FILTER
1.
2.
3.
4.
5.
6.
Widely compensated harmonic spectrum
Only one filter needed to eliminate all the unwanted harmonics
Improved stability of the power system due to the lack of parallel resonance
Its performance is dynamic and take into account the changes in load
It may also be programmed to eliminate specific number of harmonics
They may also be programmed to eliminate harmonics with or without compensation of
reactive power

16. 10
Chapter 3
THE INSTANTANEOUS
POWER THEORY
___________________________________
3.1 HISTORICAL BACKGROUND OF POWER THEORY
As to our best knowledge, the term power theory has occurred in literature for the first time in
Fryze’s paper in 1931. It is now used as a classifier of various power concepts developed by
scientists who studied power properties of electrical circuits. In such a meaning it is used in
phrases such as, Budeanu’s power theory, Fryze’s power theory, Shepherd and Zakikhani’s
(S&Z) power theory, Kusters and Moore’s (K&M) power theory, Depenbrock’s power theory
also known as FDB method, Nabae and Akagi’s Instantaneous Reactive Power Theory,
Czarnecki’s CPC power theory, Tenti and Tedeschi (T&T) conservative power theory and so on.
When a phrase like Budeanu’s power theory is used, we can have an idea, of what the phrase
refers to, and can find its details in literature. Used in such a way, the term theory can be
regarded as a system of terms defined in this theory, relations between these terms, and their
interpretations. The term power theory is also used sometimes in a different meaning, namely, as
a kind of a database of what is known on power properties of electrical circuits, thus as a
collection of true statements on power related phenomena, and mathematical expressions related
to these proper, ties and interpretations. Individual statements belong to this database, meaning,
to power theory, as long as it is not proven that these statements do not hold truth. Regarded as
such a database, the power theory is not a system of terms and relationships between them, i.e., it
is not a theory in the previous meaning. At the same time, however, anyone who reveals even a
single, but a new power related property, contributes to the development of the power theory
regarded as a database.
3.2 BASIS OF THE p-q THEORY
The p-q Theory is primarily based on a set of instantaneous calculation of powers time domain.
Voltage and current are sampled instantaneously which means there is no restriction on the shape
of their waveforms, and it can be applied to three phase with or without a neutral wire. It is based
in time domain rather than frequency domain. Thus, it is valid in the steady state and also in the
transient state. This shows the theory is very flexible and efficient in designing controllers for
active filters and power conditioners based on power electronics devices.

17. 11
Traditionally a three-phase system is considered as superposition of three single-phase circuits.
The p-q Theory first transforms and map linearly the voltages and currents from the abc
coordinates to αβ0 axes, and then defines instantaneous powers in these coordinates. Hence, this
theory always considers the three-phase system as single unit, not a superposition or sum of three
single-phase circuits.
3.3 BACKGROUND OF THE p-q THEORY
Originally the p-q Theory was born in Japan and its first version was published in the Japanese in
July 1982, in a regional conference and then in IEE Japan. After sometime, it was republished in
1983 in an international conference, and, in the year of 1984 finally it was published in IEEE
Transactions, and came into eyes of international audience. The development of the original p-q
theory was primariy base on the works and visions of previous power electronics specialists.
Many were working in the domain of compensation of nonactive power generated by non linear
loads. In the 1960’s scientists started to doubt the power definitions of Constantin Budeanu, that
its fails to define electrical power in presence of non linear elements. And in the beginning of
1970’s some papers were published which can be considered as a underlying idea of nonactive
power compensation. Many authors said, like “ compensation of distortive power is unknown to
date”, distortive was defined by Budeanu in 1927 . They also presented that “a nonlinear resistor
behaves like a reactive-power generator while having no energy-storing elements,” and showed
the very first practical and complete way to true-power-factor correction. Fukao et al said, “by
connecting a reactive-power source in parallel with the load and by controlling it in such a way
as to supply reactive power to the load, the power network will only supply active power.
Therefore, an ideal power transmission would be possible.”
Gyugyi and Pelly in proposed the point that nonactive power can be compensated by a naturallycommutated cyclo-converter without any use of energy storage elements or conventional
methods of reactive power compensation. presence of nonactive power without any energy
storage elements was also a subjective and highly debated topic. All of the points presented
before were only the ideas of different scholars, and no tangible proof were given. In 1976,
Harashima et al used perhaps for the first time, the term “instantaneous reactive power”, but only
for single phase context. After sometime, Gyugyi and Strycula used the term “active ac power
filters”. And In 1981, Takahashi et al, put forward what can be said as basis of the p-q Theory.
The equations they gave are in fact considered a subset of the p-q Theory. But yet no physical
meaning of the terms introduced in their publications, was given. The p-q Theory will be
discussed in detail in the coming topics.
The p-q Theory uses the Clarke transformation, also known as the
transformation, which
consists of a real matrix that linearly maps three phase voltages and currents into the
frame,
which is a stationary reference frame.
3.4 THE CLARKES TRANSFORMATION
The
transformation or the Clarke transformation maps the three-phase instantaneous
voltages in the abc phases, va, vb, and vc, into the instantaneous voltages on the αβ0-axes vα, vβ,

18. 12
and v0. The Clarke Transformation and its inverse transformation of three-phase generic voltages
are given by,
(3.1)
and
(3.2)
One advantage of applying the αβ0 transformation is to separate zero-sequence components from
the abc-phase components. The α and β axes contains only positive and negative sequence
components. Since there is no neutral in a three- phase, three-wire system and therefore on zero
sequence currents, so i0 can be eliminated from the above equations, thus resulting in matrix
simplification. If the three-phase voltages are exactly balanced in a four wire system, so no zerosequence voltage is present, therefore v0 can be eliminated. However, when zero-sequence
voltage and current components are present, the complete transformation should be considered.
If v0 is eliminated from the transformation matrices, the Clarke transformation and inverse
Clarke transformation becomes,
(3.3)

19. 13
And inverse Clarke transformation,
(3.4)
Similarly, we can transform line currents using above matrices. The matrices in (3.3) and (3.4) is
nothing but an axes-transformation from abc coordinates to αβ0 frame, as illustrated Fig. 3-1.
αβ0 frame is a stationary frame, it should not be confused with the dq0-tranformation or rotation
phase vectors on phasor domain. Note that these all value are instantaneous value of real life
sample taken from line voltage and load current. The a, b and c axes are spatially shifted by 120o
from each other, while the and axis are 90 degrees apart fom each other, and the axis is
parallel to the a axis. This graphical representation explains the above mentioned points,
Figure 3-1 - Graphical representations. (a) The abc to αβ0 transformation (Clarke transformation).
(b) Inverse αβ0 to abc transformation (inverse Clarke transformation).
3.5 THE p-q THEORY
The p-q Theory is defined in three-phase three wire systems or three phase four wire systems
with a neutral conductor. Three instantaneous powers are defined namely,- the instantaneous

20. 14
zero-sequence power p0, the instantaneous real power p, and the instantaneous imaginary power
q, are defined from the instantaneous phase voltages and line currents on the αβ0 axes as,
(3.5)
If there are no zero-sequence current components in three-phase, three-wire systems, that is, i0 =
0. In this case, only the instantaneous powers defined on the axes exist, because the product v0 i0
is always zero. Similarly, if ther is no zero-sequence voltage components in three phase four wire
systems, that is v0 = 0.Hence, in three-phase, three-wire systems, the instantaneous real power p
represents the total energy flow per unit time in terms of components. The power components p
and q are related to the same α-β voltages and currents, and can be written together:
(3.6)
Both of these powers have constant values and a superposition of oscillating components.
Therefore, it is interesting to separate p and q into two parts:
(3.7)
Similarly, if we have three phase four wire system zero sequence power can be expresses as the
sum of an average and oscillating components.
(3.8)
These quantities are illustrated in the following figure for an electrical system represented in a-bc coordinates and have the following physical meaning:
Figure 3.2 - Physical meaning of the various terms defined in the α-β-0 reference frame.

21. 15
̅ = mean value of the instantaneous zero-sequence power in αβ0 frame corresponds to the
energy per time unit which is transferred from the power supply to the load through the zerosequence components of voltage and current.
̃O = oscillating value of the instantaneous zero-sequence power in αβ0 frame it means the
energy per time unit that is exchanged between the power supply and the load through the zerosequence components. The zero-sequence power only exists in three-phase systems with neutral
wire. Furthermore, the systems must have unbalanced voltages and currents and/or 3rd
harmonics in both voltage and current of at least one phase.
̅ = mean value of the instantaneous real power in αβ0 frame corresponds to the energy per time
unit which is transferred from the power supply to the load, through the a-b-c coordinates, in a
balanced way (it is the desired power component).
̃ = oscillating value of the instantaneous real power in αβ0 frame It is the energy per time
unit that is exchanged between the power supply and the load, through the a-b-c coordinates.
̅ = instantaneous imaginary power in αβ0 frame corresponds to the power that is exchanged
between the phases of the load. This component does not imply any transference or exchange of
energy between the power supply and the load, but is responsible for the existence of undesirable
currents, which circulate between the system phases. In the case of a balanced sinusoidal voltage
supply and a balanced load, with or without harmonics, its value is equal to the conventional
reactive power.
̃ = oscillating value of the instantaneous imaginary power in αβ0 frame.
3.6 USE OF THE p-q THEORY IN SHUNT ACTIVE FILTER
The original concept of active filtering was introduced by Strycula and Gyugyi in 1976. Now a
shunt active filter can be implemented practically, and many shunt active filters are working all
over the world. Their controllers determine in real time the compensating current reference, and
source a power converter to synthesize the compensating current reference with high fidelity.
Figure 3.3 illustrates the basic idea behind the shunt current compensation. It shows a source
supplying power to a nonlinear load that is being compensated by a shunt active filter. Shunt
active filter is in actual is a shunt compensator. We assumed that the shunt active filter behaves
as a three phase controlled current source that can generate harmonics in phase opposition
depending upon current references i*ca, i*cb, and i*cc.

22. 16
Figure 3.3 - Basic principle of shunt current compensation.
The calculated real power p of the load can be separated into its average (p) and oscillating (~p)
parts. Likewise, the load imaginary power q can be separated into its average (q) and oscillating
(~q) parts. Then, undesired portions of the real and imaginary powers of the load that should be
compensated are selected.
The reason for incorporating a minus sign in the compensating powers is to emphasize that the
compensator must inject harmonics in perfect phase opposition. Remember that convention of
current direction is selected so in figure 3.3, that source current is the sum of load current and
filter current. Inverse Clarke transformation from αβ0 to abc-coordinates is applied then to
calculate the compensating current references i*ca, i*cb, and i*cc, instantaneously.
Ideally compensating current can be calculated by subtracting line current from a pure sine wave
of the same peak value as the fundamental component of current drawn by non linear load.
3.7 SYMMETRICAL COMPONENTS
Symmetrical components are useful tool in power system analysis. They are discussed in detail
in Appendix A. The following conclusions can be written from the equations for the real and
imaginary powers of the symmetrical components:
1. The positive and negative sequence components in voltages and currents may contribute to the
average real and imaginary powers.
2. The instantaneous active and nonactive powers consists of an oscillating components due to
the vector product of the positive sequence voltage and the negative sequence current, and the

23. 17
negative sequence voltage and the positive sequence current. Therefore circuits without any
harmonic generating load can have oscillating active or nonactive power.
In Appendix A, we have analyzed the instantaneous real and imaginary powers of the sequence
components of symmetrical components.

24. 18
Chapter 4
SHUNT ACTIVE POWER
FILTER
_______________________________________
4.1 SHUNT ACTIVE FILTERS
An idea on shunt active power filter was provided by gyugyi and strycula in 1976. Shunt active
filter is being widely used commercially. The main advantage of using shunt active filter is
finding of compensating current reference and then forcing a power converter to take
synthesizing action accordingly. So we can also conclude that this method is also adaptive. In
other words shunt active filter can efficiently and continuously compensate for harmonics in a
selected non-linear load.
4.2 GENERAL DESCRIPTION OF SHUNT ACTIVE FILTERS
Shunt active filters is comprises consist of two main blocks:
1. The PWM converter (power processing)
2. The active filter controller (signal processing)
Figure 4.1 – Basic configuration of shunt active filter
The PWM converter comprises of a 3 arm bridge inverter and a PWM controller that generates
the gating signals for the bridge inverter. The active filter controller is responsible for calculating

25. 19
the compensatory reference currents which the bridge inverter tries to accurately track and inject
into the system at PCC. The generalized diagram of shunt active filter is shown in figure 4.1
4.3 THE ACTIVE FILTER CONTROLLER
The block diagram of active filter controller based on the pq-Theory is shown in figure
Figure 4.2 – Control block for constant instantaneous power control strategy
Clarke transformation matrix transforms source voltage and load current from abc-coordinates to
αβ-axes. Through these voltage and current, real and imaginary powers are calculated
(instantaneous). According to the power requirements, compensatory current is calculated. And
after calculating, these currents are inversely transformed back to abc-coordinates.

26. 20
4.4 OPTIMAL POWER FLOW
For fulfilling optimal power flow condition, constant instantaneous power control strategy is
used. In this method, only active average real power from the load is used and remaining power
i.e. from harmonics is exchanged with shunt active filter
Figure 4.3 – Optimal power flow provided by shunt current compensation
The PWM converter takes synthesizing action on compensating current. The filter control block
has the job perform signal analysis in real time to calculate the instantaneous compensatory
reference current signals. The figure 4.3 shows the most common topology of an active filter for
harmonic compensation (maximum compensation) of a specific non linear load. It consists of a
voltage source inverter with a PWM current control, here hysteresis current control, and an
active filter controller that performs an instantaneously working control-algorithm. The shunt
active filter controller works in a closed-loop manner, continuously acquiring the samples of the
load current and calculating the instantaneous values of the compensating current reference i*c
for the PWM converter. In an ideal case, the PWM converter may be considered as a linear
power amplifier, where the compensating current ic tracks correctly its reference.
4.5 THREE PHASE THREE WIRE SHUNT ACTIVE FILTER
A distinguishing feature of three phase three wire system is that it does not have a common or
neutral wire, and so there is no zero sequence current components. Therefore there is no need to
calculate zero sequence power is for three phase three wire system. The figure 4.4 depicts the
most significant part of a three phase three wire shunt active power filter for harmonic current
compensation. The control block that calculates the instantaneous power takes phase-voltages of
point of common coupling (PCC) as the inputs and the line currents of the nonlinear load that
should be compensated. This means that the shunt active filter has a selective compensation
characteristic. In other words we can set it to compensate a particular non-linear load even if
there are other non-linear loads connected to PCC.

27. 21
The filter control consists of following control block:
1. Instantaneous powers calculation
2. Powers-compensation select
3. dc-voltage regulation
4. Determine reference current
The Instantaneous powers calculation block calculate the instantaneous power of the non linear
load. According to p-q Theory, only the active and reactive power exist, because there is no
neutral, zero-sequence power is not present. The Powers-compensation select block determine
the working output of the shunt active filter. In other words, it selects the parts of the active (real)
and reactive (imaginary) power of the non linear load, that should be compensated by the filter.
Moreover, the dc-voltage regulation block determines the extra amount of power ploss, that
causes an additional flow of energy to (from) the dc link to keep its voltage fixed around
reference voltage Vref. This active power ploss is summed up to the compensating active power
pc, and together with the compensating reactive power qc, are passed to the calculation of
reference current block. It determine the instantaneous compensatory current reference from the
udesired powers. The power injector of the shunt active filter consists of a three-phase voltage
source inverter made up of IGBT or power MOSFETs and anti parallel diodes. The PWM
current controller force the inverter to simulate a controlled current source. In order to avoid high
inductive kick, the coupling of a inverter to the system must be made through a coupling
inductor, commonly known as a commutation inductor or a series coupling inductor. The leakage
inductive reactance of a coupling transformer can also serve this purpose, that is to limit di/dt, so
the coupling inductor can be eliminated ftom the power circuit. Figure also shows a small RC
pssive filter, it filters the higher order harmonics generated due to the switching of power
converter.
Figure 4.4 – Three-phase, three-wire shunt active filter

28. 22
4.6 SIMULINK MODEL DESCRIPTION
Figure 4.5 shows the complete system design of Shunt Active Power Filter in a three-phase
three-wire system. Harmonic contents in Line and load currents, voltage at PCC and unbalancing
in load is observed in presence and in absence of SAPF.
4.6.1 3-PHASE SOURCE
3-Phase Source block of SimPower System is used as 3Ф Voltage source with following ratings:
 Phase-to-phase rms voltage (V)
400V
 Frequency (Hz)
50Hz
 Internal connection
Yg
 Source resistance (Ohms)
0.001
 Source inductance
1e-8
4.6.2 LINE IMPEDANCE (Zt)
Line impedance (Zt) is a three phase RLC branch used to represent line impedance having
following parameters.
 Resistance R (Ohms)
0.01
 Inductance L (H)
1e-6
4.6.3 V-I MEASUREMENT
Three phase VI Measurement block is used to measure line to ground voltages and line currents.

29. 23
Figure 4.5 - Complete System
4.6.4 CIRCUIT BREAKER
A three phase Circuit Breaker is connected in series with line and SAPF. Breaker timing is
defined such that it connects SAPF with system after some time simulation has started in order to
have a better look at line current harmonics and the effect of SAPF.
4.6.5 POWERGUI
This block is needed to run any SimPower System model. It provides option for configuration of
simulation and analysis of system.
4.6.6 NON-LINEAR LOAD
The non-linear load has two components connected in parallel as highlighted in figure 4.6. One
is three phase rectifier and the other is an unbalance resistive load. The two loads are switched on
one after another to have a better look at compensation of harmonics and balancing of system
with SAPF.
Figure 4.6 –Non-linear and unbalance resistive load

30. 24
4.7 SHUNT APF
The design and simulation of Shunt APF, shown in figure 4.7, is the main objective of our
project. We shall look under mask of this object to find components and blocks integrated to
design SAPF.
Figure 4.7 - Shunt APF
4.7.1 PQ & I-COMPENSATION CALCULATION
This is the heart of APF. PQ Theory algorithm for calculation of active and reactive power and
compensation currents (currents that are to be injected in order to compensate harmonic
distortion) is implemented in this block. Embedded MATLAB Function block is used to
implement all the mathematical operations involved in the algorithm. Figure 4.8 shows all the
blocks required for calculation of compensation currents.
4.7.1.1 CLARKE V
This block takes phase voltages Va, Vb and Vc as input and transforms them to Vα and Vβ using
Clarke transformation through the following functions:
function [x,y] = VCT(u,v,w)
x = sqrt(2/3)*(u-(0.5*v)-(0.5*w));
y = sqrt(2)*(0+(0.5*v)-(0.5*w));

31. 25
Figure 4.8-I-compensation calculation
4.7.1.2 CLARKE I
This block takes line currents Ia, Ib and Ic as input and transforms them to Iα and Iβ using Clarke
transformation through the following functions:
function [x,y] = ICT(u,v,w)
x = sqrt(2/3)*(u-(0.5*v)-(0.5*w));
y = sqrt(2)*(0+(0.5*v)-(0.5*w));
4.7.1.3 PQ CALCULATION
This block calculates active and reactive powers of three phase system using Vα, Vβ and Iα, Iβ.
The functions used in this block are:
function [P,Q] = PQ(x1,x2,y1,y2)
P = (x1*y1)+(x2*y2);
Q = (x2*y1)-(x1*y2);
4.7.1.4 LOW PASS FILTER
Analog Filter Design block is used to implement 5th order Butterworth Low pass filter with cut
of frequency of 2*pi*50 rad/sec. this is used to filter out the component of active power
transferred only due to the fundamental current component.

32. 26
4.7.1.5 ALPHA BETA CURRENT
Now oscillating component of active power, reactive power, Vα and Vβ are used to find
harmonic currents in alpha-beta co-ordinates.
function [Ic1,Ic2] = ICOM(Posc,q,V1,V2)
Ic1 = (-1/(V1^2 + V2^2))*((Posc*V1)+(q*V2));
Ic2 = (-1/(V1^2 + V2^2))*((Posc*V2)-(q*V1));
4.7.1.6 COMPENSATION CURRENTS
Compensation currents in terms of abc phases are calculated by taking inverse Clarke transform
of alpha-beta compensation currents.
function [ICa,ICb,ICc] = Ical(Ic1,Ic2)
ICa = sqrt(2/3)*(Ic1);
ICb = sqrt(2/3)*((-0.5*Ic1)+((sqrt(3)/2)*Ic2));
ICc = sqrt(2/3)*((-0.5*Ic1)-((sqrt(3)/2)*Ic2));
4.7.2 HYSTERESIS CONTROLLER
Hysteresis Current Controller is one of the technique available for the generation of PWM
signals that controls the gates of inverter’s transistors. A detailed description is given in
Appendix B.
4.7.3 UNIVERSAL BRIDGE
Gating signals generated by hysteresis current controller are fed to Universal Bridge three-arm
IGBT fast switching inverter. The inverter generates exactly the required harmonic currents.
4.7.4 CAPACITORS
Capacitors are discharged through the inverter to generate compensation currents. These
capacitors then become the source of harmonics rather than the main source.
4.7.5 PI CONTROLLER
PI controller is used to remove steady sate error. Here we want it to maintain Vdc by comparing it
with a constant value of Vref. If Vdc is lesser than Vref then it would create a positive ploss signal
and if Vdc is greater than Vref it would create negative ploss signal.
4.7.6 COUPLING INDUCTOR
An inductor is used to couple power inverter with point of common coupling (PCC). Its job is to
limit L.di/dt effects. Leakage inductance of a coupling transformer can also be used.

33. 27
Chapter 5
SIMULATION RESULTS
___________________________________
After having a lot of theoretical background, lets have some simulation results that helps in better
understanding of theory and dynamic and versatile behaviour of Active Power Filter (APF).
Following are the cases differ by nature of load connected across the source. All the simulations
are performed in the SIMULINK environment, a proprietary software from Mathworks Inc. A
detailed description of simulation model was covered in previous chapter.
5.1 CASE I: COMPENSATION OF NON-LINEAR LOAD
Figure 5.1 - Load of case 1 that is to be compensated using APF
Figure 5.1 shows a three phase rectifier with a resistor connected on DC side as a non-linear
load, its powers are shown in Figure 5.2 The source, load and compensation currents are shown
in Figure 5.3, it can be observed from Figure that APF is switched on at 0.02 seconds. After
compensation the source current has become a single frequency pure sinusoid having THD equal
to 0.70% which is within limits as standardized by IEEE in Std. 519.

34. 28
Figure 5.2 - Powers of load shown in Figure 5.1
Figure 5.3 - Currents of the load shown in Figure 5.1

35. 29
5.2 CASE II: COMPENSATION OF NON-LINEAR PLUS UNBALANCE
RESISTIVE LOAD
Figure 5.4 - Load of case 2 that is to be compensated using APF
Figure 5.5 - Powers of load shown in Figure 5.4

36. 30
Figure 5.6 - Currents of the load shown in Figure 5.4
This case is simulated to show the dynamic behaviour of the APF. The APF is switched on at
0.02 seconds with the non-linear load only. The circuit breaker shown in Figure 5.4 is closed at
0.05 seconds and now the load has been changed. And the APF has only taken about 15
milliseconds to respond to the changing behaviour of the load. These switching instants and the
dynamic behaviour of the APF can easily be observed from the Figure 5.6
5.3 CASE III: COMPENSATION OF UNBALANCE RESISTIVE LOAD
Figure 5.7 - Load of case 3 that is to be compensated using APF
This case is simulated to show the capability of APF to make the load balance, that is
compensating negative sequence currents so that the source will provide positive sequence only.

37. 31
Figure 5.8 - Powers of load shown in Figure 5.7
Figure 5.9 - Currents of the load shown in Figure 5.7
One thing that is worth noticing in Figure 5.8 is the presence of q (vai) in case of resistive but
unbalance load. And this is one of the points used by L.S. Czarnecki (author of the CPC Theory)
to criticize the Akagi’s theory.

38. 32
5.4 CASE IV: COMPENSATION OF UNBALANCE INDUCTIVE LOAD
Figure 5.10 - Load of case 4 that is to be compensated using APF
Figure 5.11 - Powers of load shown in Figure 5.10
This is also a very important case, as this case shows the presence of active power, even if the
load is the purely reactive. The oscillations in both the powers is due to the unbalanced load
condition due to which a negative sequence current is also present. On the basis of this and the
previous case following conclusions regarding power due to symmetrical components can be
drawn assuming the source voltages are balanced and having positive phase sequence.
1. The presence of constant instantaneous active power p(W) is due to the positive sequence
current and only in case of purely resistive load but may be unbalance.
2. The presence of constant instantaneous imaginary power q(VAI) is due to the positive
sequence current and only in case of purely inductive/capacitive load but may be
unbalance.
3. The presence of oscillations in both of the instantaneous powers is due to the negative
sequence current whether a load is purely resistive or inductive/capacitive.

39. 33
Figure 5.12 - Currents of the load shown in Figure 5.10
5.5 CASE V: COMPENSATION OF UNIQUE UNBALANCE RESISTIVE
LOAD
Figure 5.13 - Load of case 5 that is to be compensated using APF
This is the unique case, simulated to show that even the load is connected between the single
phase and the ground, but after compensation the balanced three phase current is supplied by the
source i.e. the APF is acting as a resistive load for the remaining two open phases .

40. 34
Figure 5.14 - Powers of load shown in Figure 5.13
Figure 5.15 - Currents of the load shown in Figure 5.13
5.6 CONCLUSION
All the five cases that are discussed, helps in better understanding of power theory presented by
Akagi and his co-workers and some insights which conventional power theory fails to provide in
its phasor domain. Also the five cases shows the dynamic and versatile behavior of APF.

41. 35
Appendix A
SYMMETRICAL
COMPONENTS
___________________________________
Symmetrical components (also known as Fortescue’s components) are basically used for the
analysis of three phase electrical power systems. It’s ubiquitous in power system analysis and an
essential tool in fault analysis. If the phase quantities are expressed in frequency domain and, a
vector can be formed for the three phase quantities or three phase voltages phasors. A vector for
three phase voltages could be written as,
where the subscripts 0, 1, and 2 refer to the zero, positive, and negative sequence components.
The sequence components, only differ by their phase angles, and are symmetrical i.e. all
individual components are equal and are 2/3π radians or 120° apart. Operator α displaces any
phasor by an angle of 120°, if multiplied.
And α3 = 1, so that α−1 = α2.
The zero sequence components always have same phase; denote them as:
And, the positive and the negative phase sequences, respectively written as:

42. 36
Thus,
where
Similarly, we can calculate sequence components by the equation,
A.1 SIMULINK MODEL OF SEQUENCE POWER
Our motive is to calculate Symmetrical components in time domain. We used transport delay
block in SIMULINK library to emulate αphasor vector in time domain. since there are 360
electrical degrees in one cycle of 20m seconds. ifαphasor represents 120 degrees shift in
electrical degrees it corresponds to 6.666m seconds.
Figure A.1 - SIMULINK block of Symmetrical
components

43. 37
Figure A.2 - SIMULINK model of Symmetrical
components in time domain
Figure A.1 shows that sequence currents are fed into PQ measument block because we wish to
calculate power of each sequence and analyse them in the light of Akagi’spqTheory.The
conclusions from pq Theory can be written from the above equations for the real andImaginary
powers of the symmetrical components:
1. Average real power flows in system only due to the product of positive sequence currents and
source voltages.
2.The zero and negative sequence components in currents contribute to the oscillations in real
imaginary powers.
To test above points we coupled our block with APF. In order to have both seqeunces in line
current unbalanced resistive load was connected. APF was set to operate at adelay of 0.06secs,
in order to incorporate before and after compensation affects, in other words negative sequence
currents must be wiped out completely since all imaginary power would be compensated.
Whereas positive sequence current would remain unaltered since they are responsible for active
power transfer to the load.
Fig. A.3, evidently shows that power transfer by positive sequence currents it active, since the
currents are unaltered before and after the APF operation. Hence only positive sequence currents
are coming from the source. Note the transients after 0.06secs are due DC capacitor charging.
Similarly, Fig. A.4 shows that negative sequence currents are completely compensated by APF
and instantaneous powers of negative sequence also eliminated from the system.

44. 38
Figure A.3 – Positive sequence powers and currents before and after compensation
Figure A.4 – Negative sequence powers and currents before and after compensation

45. 39
Appendix B
HYSTERESIS
CONTROLLER
__________________________________
Hysteresis current controller is one of the techniques available to control the voltage source
inverter (VSI) through the PWM in a manner that the output current of inverter then tries to
track the reference current fed to the hysteresis current controller which works in a close loop. Its
advantage is that it is very easy to implement while its disadvantage is that its switching
frequency is not constant. A diagrammatic working of hysteresis current controller is shown in
figure B.1
A hysteresis band is defined which sets the upper and lower limits for the output current to
deviate from its reference current signal. The thicker the band the more the deviations hence
more ripples in output current and vice versa.
Figure B.1 - Hysteresis Current Controller
An error signal e(t) which is the difference between the reference current signal i ref(t) and the
actual output current signal iactual(t) of the inverter, is used to generate the gating signals for the
transistors of VSI. Depending on the upper and lower limits of the hysteresis band the range of
error signal can be determined. If e(t) is greater than the maximum value of error emax the
transistors are switched off and if e(t) is less than the minimum value of error emin then the
transistors are switched on. And if the error is within the range i.e. emin < e(t) < emax then the state
of the transistors remain unchanged.
The switching frequency of hysteresis current controller is not constant and depends upon the
following factors:
1. The width of the hysteresis band. Switching frequency is inversely proportional to the
width of the hysteresis band.

46. 40
2. The voltage of the DC side. Switching frequency is directly proportional to the voltage of
the DC side.
B.1 SIMULINK MODEL EXAMPLE
To better understand the working of hysteresis controller, let us simulate a single phase inverter
model in SIMULINK Environment in which gating signals of transistors are controlled through
hysteresis controller. Figure B.2 shows a SIMULINK model in which ‘Relational Operator’ and
‘Logical NOT Operator’ blocks, together acting as a hysteresis controller. The output of
Relational Operator block is directly connected to one diagonal pair of transistors namely IGBT1
and IGBT2, and indirectly through Logical NOT Operator block, connected to another diagonal
pair of transistors namely IGBT3 and IGBT4. Relational Operator compares the reference and
load current values, if reference value is greater than load value than Relational Operator block
gives ‘1’ as output, and ‘0’ if reference value is less than load value.
Figure B.2 - SIMULINK model of single phase inverter
Let us simulate a model for a very short interval of time to see how these two block works
together as hysteresis controller. Refer to figure B.3 which shows a stem plot figure made using
MATLAB’s stem command by importing the SIMULINK data to the workspace. The red
coloured lines are representing the reference current values, the blue coloured lines are
representing the load (tracked) current values and the black coloured filled lines are representing
the decision of Relational Operator block taken by comparing the current values at every Ts
instant.

47. 41
Figure B.3 - Comparison of reference and load current values sampled after every Ts
It can be seen in the figure B.3 that, when the red line (reference value) has higher value than the
blue line (tracked value) the black line (gating signal) is at value equal to ‘1’, that means the
transistor is switched 'ON' and when the opposite is true than the black line (gating signal) is at
value ‘0’, that means the transistor is 'OFF' and this process goes on controlling the gates of the
transistors.
B.2 HYSTERESIS BAND IN DIGITAL HYSTERESIS CURRENT CONTROLLER
When the hysteresis current controller is digitally implemented than the rate at which the
currents are sampled determines the width of the hysteresis band. The higher the sampling rate
the thinner the hysteresis band and vice versa. This thing can easily be understood by simulating
our SIMULINK model with different values of Ts.
Refer to figure B.4 (a) and (b), which shows a comparison of two cases which are simulated by
configuring the powergui block at different Ts values. It can be seen in the figure B.4 (a) and (b)
that, when the Ts value is higher (lower sampling rate) the hysteresis band is thicker. And when
the Ts value is lower (higher sampling rate) the hysteresis band is thinner.

48. 42
(a) Model simulated at Ts = 5e-005 seconds
(b) Model simulated at Ts = 2e-005 seconds
Figure B.4 - Hysteresis Band at different sampling rate
Therefore, one should select a proper value of sampling time or sampling frequency such that the
maximum frequency content present in reference current signal is properly sampled and ripples
in the actual current should be as small as possible. However, higher the sampling rate higher
will be the switching frequency and hence more will be the switching losses .

49. BIBLIOGRAPHY
[1]
M. F. McGranaghan, R. C. Dugan, and H. W. Beaty, Electrical Power Systems Quality.
McGraw-Hill Professional, 2012.
[2]
A. Emadi, A. Nasiri, and S. B. Bekiarov, Uninterruptible power supplies and active
filters. CRC press, 2004.
[3]
G. Sandoval and J. Houdek, “A Review of Harmonic Mitigation Techniques,” Power
Qual. Handbook, Electr. Today, 2005.
[4]
Gregorio Romero Rey and Luisa Martinez Muneta, “Power Quality Harmonics Analysis
and Real Measurement Data,” InTech, 2011.
[5]
H. Akagi, E. H. Watanabe, and M. Aredes, Instantaneous power theory and applications
to power conditioning, vol. 31. Wiley. com, 2007.
[6]
B. Rouge, “Power theories and meta-theory of powers in electrical circuits,” no. 8, pp.
198–201, 2011.
[7]
L. S. Czarnecki and F. Ieee, “Currents ’ Physical Components ( CPC ) In Circuits with
Nonsinusoidal Voltages and Currents Part 1 : Single-Phase Linear Circuits,” vol. 0, no. 2, pp.
1–9.
[8]
L. S. Czarnecki, “Currents ’ Physical Components ( CPC ) In Circuits with
Nonsinusoidal Voltages and Currents Part 2 : Three-Phase Three-Wire Linear Circuits,” pp. 1–
7.
[9]
D. C. Bhonsle and R. B. Kelkar, “Design and simulation of single phase shunt active
power filter using MATLAB,” 2011 Int. Conf. Recent Adv. Electr. Electron. Control Eng., pp.
237–241, Dec. 2011.
[10]
D. Wu, Y. Che, and K. W. E. Cheng, “Design and Performance of a Shunt Active
Power Filter for Three- phase Four-wire System,” pp. 1–4, 2009.
[11]
A. Chaoui, J.-P. Gaubert, F. Krim, and L. Rambault, “On the design of shunt active
filter for improving power quality,” 2008 IEEE Int. Symp. Ind. Electron., pp. 31–37, Jun. 2008.
[12]
L. F. C. Monteiro, J. L. Afonso, J. G. Pinto, E. H. Watanabe, M. Aredes, and H. Akagi,
“COMPENSATION ALGORITHMS BASED ON THE p-q AND CPC THEORIES FOR
SWITCHING COMPENSATORS IN MICRO-GRIDS,” no. October, pp. 32–40, 2009.
[13]
E. Engineering, V. Hills, D. Village, P. Mandal, E. Engineering, V. Hills, D. Village,
and P. Mandal, “Mitigation of Harmonics by Hysteresis Control Technique of VSI Based
Statcom,” vol. 2, no. 1, pp. 146–160, 2013.
[14]
D. Ingram and S. Round, “A fully digital hysteresis current controller for an active
power filter,” Int. J. Electron., 1999.
[15]
Dr. Mohamed Darwish, Trends in Active Power Filters, Brunel University.