A

SEMINAR REPORT

ON

SHUNT ACTIVE POWER FOR POWER QUALITY

IMPROVEMENT IN DISTRIBUTION SYSTEMS

Submitted in partial fulfillment of the requirements for the degree of

MASTER OF TECHNOLOGY

(Power Systems)

By

P. Jothsna Praveena

(P13PS015)

: Supervisor:

Prof. H.R.Jariwala

DEPARTMENT OF ELECTRICAL ENGINEERING

SARDAR VALLABHBHAI NATIONAL INSTITUTE OF TECHNOLOGY

SURAT – 395007

November – 2014

1

SARDAR VALLABHBHAI NATIONAL INSTITUTE OF

TECHNOLOGY

SURAT-395 007, GUJRAT, INDIA

DEPARTMENT OF ELECTRICAL ENGINEERING

SVNIT

CERTIFICATE

This is to certify that the seminar report entitled “Shunt Active Power Filter for

Power Quality Improvement in Distribution systems ” submitted by P.JothsnaPraveena,

(P13PS015) is a record of bonafide work carried out by him in partial fulfillment of the

requirement for the award of the degree of “MASTER OF TECHNOLOGY IN

ELECTRICAL ENGINEERING (Power Systems)”.

Date: 11/11/2014

Place: SURAT

Prof.H.R.Jariwala( Faculty Supervisor )

Prof.H.R.Jariwala

( PG In-charge )

Dr. (Mrs.) A. Chowdhury

( Head of Department )

1.2ACKNOWLEDGMENT

I would like to express my heartfelt gratitude to my Seminar guide Prof. H.R.Jariwala, who

provided me valuable suggestions, and support in execution of seminar.

I am also thankful to Dr. Ananditha Chowdhury, Head of the Department of ElectricalEngineering for her support and direction.

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I am thankful to The Department of Electrical Egg, for giving me the opportunity to

execute this Seminar, which is an integral part of the curriculum in M. Tech program at the

Saradar Vallabhbhai National Institute Of Technology Surat.

I would also like to take this opportunity to express heartfelt gratitude for

Prof.H.R.Jariwala, my P.G. In charge, Electrical Engineering Department, for giving

permission to utilize lab resources of Power Systems lab.

I will also like to take this opportunity to thank all the staff members of Electrical

department, friends and parents for their support and blessings.

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2.2ABSTRACT

The most common problem in the supply network is current harmonics caused by non-linear

loads. Active Power Filters (APFs) is widely used solutions to eliminate the power line

harmonic generated by non-linear loads. Many APF configurations are suggested in literature

for mitigating supply current harmonics produced by non-linear loads. Popularly used APF

configuration for mitigating supply current harmonics is Shunt Active Power Filter. The

instantaneous reactive power theory has been the most used in non-linear load compensation.

In this report, APF control circuit have been studied. The control strategy is p-q original

theory. The formation of calculating compensation current has been studied. Next, the

behaviour of an Active Power Filter with that control algorithm has been studied.

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CONTENTS

ACKNOWLEDGMENT …………………………………………………………………………… 5

ABSTRACT……………………………………………………………………………………… 5

LIST OF FIGURES.............................................................................................................................. 5

LIST OFTABLES ........................................................................................................................... 5

Chapter 1 Introduction ...........................................................................................................1

1.1 Introduction...................................................................................................................2

1.2 Outlines of report..........................................................................................................3

Chapter 2 Review of Filtering Techniques............................................................................4

2.1 Passive Filters...............................................................................................................4

2.2 Active Filters................................................................................................................4

2.2.1 Series Active Power Filter ……………………………………………………………....5

2.2.2 Shunt Active Power Filter ……………………………………………………………...6

2.2.3 Hybrid Active Power Filter …………………………………………………………....7

2.2.4 Series-Shunt Active Power Filter(UPQC) ……………………......................................8 2.3 Principle of operation of Shunt Active Power Filter …………………………………………9Chapter 3 Simulation study of p-q theory based Shunt APF ……………………………………12 3.1 p-q theory ………………………………………………………………………………….13 3.2 Basic formulations ………………………………………………………………………...13 3.3 Reference current calculation ……………………………………………………………....15 3.4 Simulation study ……………………………………………………………………………17Chapter 4 Conclusion and Suggested Future Work ………………………………………………22 4.1 Conclusion ………………………………………………………………………………...22

5

4.2 Suggested Future Work ………………………………………………………………….22

LIST OF FIGURES

Figure 2.1 Series active power filter……………………………………………………………….6Figure 2.2 Shunt active power filter……………………………………………………………….6Figure 2.3 Hybrid power filter topologies…………………………………………………………7-8Figure 2.4 Series-Shunt active power filter………………………………………………………..8Figure 2.5 Basic principle of Shunt active power filter……………………………………………9Figure 2.6 Shunt active power filter VSI-PWM configuration……………………………………10Figure 2.7 Power exchanges in Shunt active power filter system…………………………………10Figure 3.1 Three phase four wire source with non-linear load and Shunt active power filter…….12Figure 3.2 Control strategy for shunt compensation based on p-q theory…………………………16Figure 3.3 System without Shunt Active Power Filter…………………………………………….17Figure 3.4 source current without Shunt Active Power Filter……………………………………..18

Figure 3.5 FFT Analysis of source current without Shunt Active Power Filter

…………………..18

Figure 3.6 System with Shunt Active Power Filter…………………………………………………19Figure 3.7 Compensating currents to be produced by SAPF………………………………………19Figure 3.8 Compensating currents produced by SAPF…………………………………………….20Figure 3.9 source current with Shunt Active Power Filter…………………………………………20

Figure 3.10 FFT Analysis of source current with Shunt Active Power Filter

……………………..21

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LIST OF TABLESTable 3.1 Common system parameters…………………………………………………………...13Table 3.2 performance of SAPF using p-q theory………………………………………………...21

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3.2Chapter 1

IntroductionThe subject of power quality has been given increased attention over the past decade. Broadly

defined, power quality refers to the degree to which voltage and current in a system represent

sinusoidal waveforms. Increasing in harmonics and demand of reactive power has become a

serious concern for electrical engineers following the wide use of electronic appliances. In

this chapter, some basics of power quality problems include harmonics, its effects and

sources are elaborated.

4.2 IntroductionThe quality of electrical power in commercial and industrial installation is undeniably

decreasing. With the increasing use of solid-state circuit equipment, harmonic distortion in

supply systems becomes more frequent and severe due to non-linear characteristics of such

circuits. Well known non-linear devices include converters, inverters, electronic-ballast,

variable frequency drives, lifts and computer equipment. These voltage or current distortions

may cause unsafe and unreliable electrical power supplies, malfunction of equipment,

overheating of conductors and can reduce the efficiency, and life of most connected loads.

Therefore, harmonic distortion is an undesirable effect for electrical systems. “Clean ” power

refers to voltage and current waveforms that represent pure sine waves and are free of any

distortion. “Dirty” power refers to voltage and current waveforms that are distorted and do

not represent pure sine waves. Alternating current power supply has always suffered from the

effects of harmonics. In an electrical power system, there are various kinds of power quality

problems/disturbances like voltage sag, voltage swell, under voltage, over voltage, transient,

harmonics, voltage unbalance etc. Since the rapid development of semiconductor industry,

power electronics devices have gained popularity in our daily used electrical house-hold

appliances. Although these power electronic devices have benefited the electrical and

electronics industry, these devices are also the main source of power harmonics in the power

system. These power harmonics are called electrical pollution which will degrade the quality

of the power supply. As a result, filtering process for these harmonics is needed in order to

improve the quality of the power supply [1]. There are many solutions available to improve

the power quality like passive filtering and active filtering devices.

Harmonic is defined as “a sinusoidal component of a periodic wave or quantity having

frequency that is an integral multiple of the fundamental frequency”. Circulation of these

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harmonic currents creates losses in and determines overheating and overrating of the power

system. Furthermore, harmonic currents cause harmonic voltage distortion, undesirable for all

other equipment connected to the power system, such as capacitors, ac machines, control and

protection equipment, measuring instruments and electronic power converters. For the

metering and comparison of harmonic contents of waveforms, a parameter is defined as a

total harmonic distortion (THD). THD is defined for both current and voltage as follows:

For voltage: ------------ (1.1)

For current: ------------- (1.2)

There are many non-linear loads drawing non-sinusoidal currents from electrical power

systems. These non-sinusoidal currents pass through different impedances in the power

systems and produce voltage harmonics. These voltage harmonics propagate in power

systems and affect all of the power system components.

The effects of harmonics in power systems and electrical loads are described below.

1. Overheating of transformer and motor

2. Disturbance to electric and electronic devices

3. Failure of capacitor banks due to dielectric breakdown or reactive power overload

4. Extra neutral current

5. Improper working of metering devices

6. De-rating of distribution equipment

7. Resonance problem

8. Mal-operation of circuit breaker

9. Lower power factor

10.Nuisance for sensitive loads

11. Interference with ripple control and power line carrier systems, causing misoperation

of systems.

The compensation for harmonic and reactive currents becomes increasingly important both

for utilities and industries to feed their sensitive equipment with quality power; thereby

avoiding malfunction and loss of revenue. Active power filters (APFs), also called active

power line conditioners or active power quality conditioners, have been known as the best

tool for harmonic mitigation as well as reactive power compensation, load balancing, voltage

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regulation and voltage flicker compensation.APF’s are basically categorised into two types,

namely, single phase, three phase configurations to meet the requirements of the non-linear

loads in the distribution systems. Many configurations, such as the series active filter [2],

shunt active filter [2][3], and combination of shunt and series filter [3] has been developed.

Control strategy plays a vital role in the overall performance of the power conditioner. Rapid

detection of disturbance signal with high accuracy, fast processing of the reference signal and

high dynamic response of the controller are the prime requirements for desired

compensation. This control is realized using discrete analog and digital devices or advanced

programmable devices. The control action is initiated through the detection of essential

voltage or current signals using PTs, CTs, Hall-effect sensors to gather system information.

Typical voltage signals are ac terminal voltage, dc bus voltage of APF, and voltage across

series elements. The current signals to be sensed are load currents, supply currents,

compensating currents and dc link current of APF. Based on these measured signals,

compensating commands in terms of current or voltage levels are derived in time-domain or

frequency-domain. Finally appropriate gating signals for the solid-state devices of the APF

are generated using sinusoidal PWM, hysteresis band current control. Generation of

appropriate switching pattern or gating signal with reference to command compensating

signal determines the control strategy of the APF’s. since derivation of reference signal from

measured distorted signals plays major role.

5.2 Outlines of reportThe outlines of the report are as below:

Chapter 1 deals with an introduction about harmonics, harmonic sources and effects of

harmonics and proposed different harmonics mitigation methods by researchers.

Chapter 2 deals with brief idea about different filtering techniques. It also includes principle

of operation shunt active power filter.

Chapter 3 deals with simulation of shunt active power filter based on pq theory with

balanced supply and non-linear load. It also includes conclusion.

References

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Chapter 2

Review of Filtering Techniques

In this chapter power quality problem and various harmonic mitigation techniques are

discussed. 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 condition is to install line-conditioning systems that suppress or counteract the power

system disturbances. Among the different new technical options available to improve power

quality, active power filters (line conditioning) have proved to be an important and flexible

alternative to compensate for current and voltage disturbances in power distribution systems.

The various harmonic mitigation techniques are explained below:

2.1 Passive Filters

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 power

system. They consist of capacitors, inductors and damping resistors. Passive filters have some

advantages such as simplicity, reliability, efficiency and low cost. However, passive filters

have many disadvantages, such as

1. Resonance problem

2. Large size

3. Fixed compensation characteristic

4. Possible overload

5. Poor dynamic behaviour

These drawbacks are overcome with the use of active power filters. Nowadays, active filters

are used to cancel harmonics generated by non-linear load. Tuned filters are used with active

filters to cancel specific frequencies and decrease the power rating of the active filters.

2.2 Active Filters

Active power filter has been proposed since 1970’s. The advantage of the active filtering

process over the passive one caused much research to be performed on active power filters

for power conditioning and their practical applications. 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,

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voltage sags and voltage swells and voltage imbalances. Active power filter consists of an

inverter with switching control circuit. The inverter of active power filter will generate the

desired the desired compensating harmonics based on the switching gates provided by the

controller. The active power filter injects an equal but opposite distortion harmonics back into

the power line and cancel with the original distorted harmonics on the line. Active filters are

categorised into two main groups: single-phase and three-phase. Three-phase active filters

may be with or without neutral connection. Single-phase active filters are used to compensate

power quality problems caused by single phase loads such as DC power supplies. Three-

phase active filters are used for high-power non-linear load such as adjustable speed drives

and AC/DC converters. An active filter can utilize current source inverters (CSIs) or voltage

source inverters (VSIs). CSI-based active filters employ an inductor as the energy storage

device. VSI-based active filters use capacitor as energy storage device [5][6]. Many

configurations such as series, shunt, hybrid (a combination of shunt and series active filters),

and unified power quality conditioner (UPQC), which is a combination of series and shunt

active filters, have been introduced.

2.3 Series Active Power Filter

The series connected active filter protects the consumer from an inadequate supply-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 element

(battery) is necessary and the overall rating of the components is smaller [2]. 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. Figure 2.1 shows the connection of a series active power filter, the series filter is used to

compensate the voltage harmonics on the load side. Series filters can also be useful for

fundamental voltage disturbances. The compensating voltage, of the series active filter is

added into the phase of supply voltage to cancel harmonic voltage in each phase. Thus,

supply becomes sinusoidal and free from voltage harmonics.

Figure 2.1 Series active power filter

2.4 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

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transmission systems [2][3]. 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. Figure 2.2 shows the connection of a shunt active power

filter, the compensating current is exactly equal and opposite to the load harmonic

components, thus supply current is becoming sinusoidal.

Figure 2.2 Shunt Active Power Filter

2.5 Hybrid Active Power Filter

Hybrid Active Power Filters are a combination of active and passive filters. There is series

hybrid active power filter, which is combination of series active power filter and shunt

passive filters, and shunt hybrid power filter, which is combination of shunt active power

filter and shunt passive filters. There are numerous topologies of hybrid active power filter;

two among them are shown in Figure 2.3. Figure 2.3(a) shows the series hybrid active power

filter and Figure 2.3(b) shows shunt hybrid active power filter. In hybrid active power filter, it

allows the passive filters to have dynamic low impedance for current harmonics at load side,

increasing their bandwidth operation and improving their performance. This behaviour is

reached with only a small power rating PWM inverter, which acts as an series active filter

with the shunt passive filter. The passive filter is used to remove higher order harmonics, so

that active power filter has to remove the lower order harmonics.

Figure 2.3 (a) Series hybrid active filter

Figure 2.3 (b) Shunt hybrid active power filter

2.2.4 Series-Shunt Active Power Filter (UPQC)As the name suggests, the series-shunt active filter is a combination of the series active filterand the shunt active filter. An interesting combination topology is shown in Figure 2.4. Theshunt active filter is located at load side and can be used to compensate for load currentharmonics. On the other hand, the series portion is at the source side and can act as aharmonic blocking filter. This topology has been called the Unified Power QualityConditioner. The series portion compensates for supply voltage harmonics and voltageunbalances, act as a harmonic blocking filter, and damps power system oscillations. Theshunt portion compensates load current harmonics, reactive power, and load currentunbalances. In addition, it regulates the dc link capacitor voltage. The power supplied or

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absorbed by the shunt portion is the power required by the series compensator and the powerrequired to cover losses [8].

Figure 2.4 Series-Shunt active power filter (UPQC)

2.3 Principle of operation of Shunt Active Power FilterThe basic principle of shunt active power filter is explained using Figure 2.5. The harmonic

current compensation by the active power filter is controlled in a closed loop manner. The

active power filter will draw and inject the compensating current, to the line, based on the

changes of the load in the power supply system. The supply line current, is described by the

following equation,

-------- (2.1)

Figure 2.6(a) shows a typical VSI-PWM shunt active power filter, which is mostly used for

the harmonic current compensation [10].

Figure 2.5 Basic principle of shunt active power filter

Figure 2.6(a) Shunt active power filter VSI-PWM configuration

The load current contains its fundamental plus harmonic components. The compensator

(APF) supplies equal and opposite harmonic current components to the load current,

therefore they cancel each other, and source has to be supply only fundamental component of

the load current. Thus the source current is shaped to be sinusoidal.

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The basic idea of power exchange between source and load with shunt APF is shown in

Figure 2.6

Figure 2.6(b) Power exchanges in shunt active power filter

The instantaneous non-linear load current can be represented by,

------------ (2.2)

The instantaneous load power can be given as:

where, is the peak value of the fundamental load current, is the peak value of the harmonic

load current, and are the phase angle of the fundamental and harmonic component of the

load currents, respectively. In equation (2.3) the instantaneous power of non-linear load is

divided into three terms. The first term is the instantaneous load fundamental power. The

second term is is the instantaneous load fundamental reactive power and third term is the

instantaneous load harmonic power. Shunt APF is designed to be connected in parallel with

the load, to detect its harmonic and reactive current and to inject into the system a

compensating current, identical with the load harmonic and reactive current [4]. Therefore,

instantaneous source current having only fundamental component which is in phase with the

source voltage .

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Chapter 3

3.1 Simulation study of p-q theory based Shunt APF

In this chapter simulation study of shunt APF based on p-q control strategy. The simulation

has been performed and analyzed for balanced sinusoidal supply voltage to balanced non-

linear load.

For evaluating performance of shunt APF, using p-q control strategy the simulation study is

performed in MATLAB software. Figure 3.1 shows shunt active power filter connected to a

three phase four wire source that supplies a non-linear load. The control strategy generates

the reference current (a,b,c) is also shown in Fig. 3.1.

Supply voltage values are considered as;

Figure 3.1 Three-phase four-wire source with nonlinear load and Shunt Active Power

Filter

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Table 3.1 shows the system values with which the simulation work is done

Sr.No Quantity Value

1 Source impedance Rs=0.1ohm , Ls=0.5e-8

2 DC capacitor 2000uF

3 EMI Filter Lf=2mH

4 DC Link Voltage 900V

5 Load Three phase rectifier, R=10Ohm

3.2 p-q theory

The instantaneous reactive power theory (p-q theory) proposed by H.Akagi, Y.Kanazawa and

A.Nabae “Instantaneous reactive power compensators comprising of switching devices

without energy storage components” in 1984 [4]. The ‘p-q’ ththeory is based on the α-β-0

stationary reference frame. This theory is suitable only for three-phase system and its

operation takes place under the assumption that three-phase system is balanced with voltage

waveforms are purely sinusoidal. If this technique is applied to unbalanced or non-sinusoidal,

the resulting performance is proven to be poor.

3.3 Basic Formulation

The p-q theory uses the αβ0 transformation known as the Clarke transformation. The 3-phase

voltages or currents are transformed from a-b-c reference frame to αβ0 stationary reference

frames. The Clarke transformation for the voltage variables and its inverse are given by:

-------------- (3.1)

------------- (3.2)

Similarly the transformation can also be applied for the current variables as:

------------- (3.3)

-------------- (3.4)

One advantage of applying the αβ0 transformation is to separate zero-sequence components

from the a-b-c phase components. The α and β axis make no contribution to zero sequence

components.

In the new co-ordinates system, three power terms are expressed: zero-sequence

instantaneous real power, instantaneous real power , and instantaneous imaginary power

vector , i.e.,

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---------------- (3.5)

The norm of vector defines the instantaneous reactive power as follows:

------------- (3.6)

Equations in (3.5) define the three power variables , and . They may be expressed in the

matrix form as follows:

------------- (3.7)

3.4 Reference current calculation

From Eq. (3.5) instantaneous real power can be written as sum of mean value of

instantaneous real power () and alternating value of instantaneous real power (),

instantaneous imaginary power can be written as sum of mean value of instantaneous

imaginary power () and alternating value of instantaneous imaginary power (), zero sequence

instantaneous real power can be written as sum of mean value of zero sequence instantaneous

real power () and alternating value of zero sequence instantaneous real power ().

------------ (3.8)

For harmonic elimination from nonlinear load, total , the oscillating term of p and q have to

be removed. So the powers to be compensated chosen as:

, , ------------ (3.9)

For reactive power compensation, total , total q have to be removed. So the powers to be

compensated chosen as:

, , ------------- (3.10)

For harmonic elimination and reactive power compensation from nonlinear load, total , the

oscillating term of p and q have to be removed. So the powers to be compensated chosen as:

, , -------------(3.11)

The compensating powers, and can be extracted from , , . The compensating current

corresponding to unwanted component of active power can be expressed as

------------ (3.12)

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Figure 3.2 Control strategy for shunt current compensation based on p-q

theory

Figure 3.2 shows the control strategy for shunt compensation based on p-q theory. The three

phase load voltages and currents are sensed and converted into α-β-0 component. These α-β-0

voltage and current components are used to calculate instantaneous power. This calculated

instantaneous power having constant part and oscillating part, then selection of power should

be done to compensate the unwanted current generated by non-linear load. From these power,

compensation currents in α-β-0 stationary frame is calculated; it is then converted into a-b-c

frame by using inverse Clarke transformation, which is applied at point of common coupling

to mitigate load current harmonics generated by non-linear loads.

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3.5 Simulation study:

The control strategy derived from p-q theory is compared by simulation results. The

simulation result of this control strategy is tested under balanced supply voltage condition

fed to balanced non-linear load.

Simulation Results:

Results of system without Shunt Active Power Filter

Figure 3.3 System without Shunt Active Power Filter

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Figure 3.4 source current without Shunt Active Power Filter

0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1

- 5 0

0

5 0

S e l e c t e d s i g n a l : 5 0 c y c l e s . F F T w i n d o w ( i n r e d ) : 5 0 c y c l e s

T i m e ( s )

0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 00

5

1 0

1 5

2 0

F r e q u e n c y ( H z )

F u n d a m e n t a l ( 5 0 H z ) = 5 9 , T H D = 2 8 . 0 1 %

Mag

(%

of

Fun

dam

enta

l)

Figure 3.5 FFT Analysis of source current without Shunt Active Power Filter

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Results of system with Shunt Active Power Filter

Figure 3.6 System with Shunt Active Power Filter

Figure 3.7 compensating currents to be produced by SAPF

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Figure 3.8 compensating currents produced by SAPF

Figure 3.9 Source current with Shunt Active Power Filter

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Figure 3.10 FFT Analysis of source current with SAPF

Table 3.2 Performance of SAPF using p-q theorySr.No system %THD1 Without SAPF 28.012 With SAPF 2.53

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Chapter 4Conclusion and Suggestions for Future Work4.1 ConclusionThe increased use of power electronic equipments in the power system has a profound impact

on the power quality. In this study the supply current harmonic mitigation is done by p-q

control strategy.

It is observed from simulation that the proposed control strategy eliminates harmonics

without adding any delay when the supply voltage is sinusoidal and balanced. The proposed

system gives best results when the supply voltage is balanced and sinusoidal.

4.2 Suggestions for Future WorkAs the proposed method gives best results only with balanced and sinusoidal supply voltage

there should be modification p-q theory. So the other modified theories are modified p-q

theory, d-q theory and p-q-r theory. With these theories we can also get better results even

under unbalanced and non-sinusoidal condition.

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REFERENCES[1] Robert D Henderson, Patrick J. Rose “Harmonics: The effect on power quality andtransformer” IEEE Trans. Industry Applications, vol.30, n0.3, (1994):pp.528-532.[2] W.M.Grady, M.J. Samotyj, A.H.Noyola, “Survey of Active Power Line ConditioningMethodologies,” in IEEE Trans. on Power Delivery, vol.5, no.3,pp.1536-1542, July 1990.[3] H.Akagi, “New Trends in Active Filters for Power Conditioning,” in IEEE Trans .onIndustry Applications, vol.32, no.6, pp.1312-1322, Nov./Dec.1996.[4] H.Akagi, Y. Kanazawa and A. Nabae, “Instantaneous reactive power compensatorscomprising of switching devices without energy storage components” IEEETrans.Ind.Appl.Vol.20.no.3,pp.625-630,May/June 1984.

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