Harmonics Analysis and Mitigation Using Passive Filters

By:

Rooh Ul Amin Shaikh 11EL01

Abdul Basit Lashari 11EL16

Irfan Ansari 11EL37

Supervised By:

Prof. Dr. ZUBAIR AHMED MEMON

DEPARTMENT OF ELECTRICAL ENGINEERING,

MEHRAN UNIVERSITY OF ENGINEERING & TECHNOLOGY,

JAMSHORO

Submitted in partial fulfillment of the requirement for the degree of

Bachelors of Electrical Engineering

January, 2015

In the name of Almighty Allah,

The most gracious and the most

merciful

CERTIFICATE

This is to certify that the work presented in this thesis titled “Harmonics Analysis

and Mitigation Using Passive Filters” is written by the following students as a

partial fulfillment of the requirements for the degree of Bachelors of Electrical

Engineering under the supervision of the Prof. Dr. Zubair Ahmed Memon

Rooh Ul Amin Shaikh 11EL01

Abdul Basit Lashari 11EL16

Irfan Ansari 11EL37

ACKNOWLEGEMENTS

We are grateful to our thesis mentor, Prof. Dr. Zubair Ahmed Memon for providing

us the opportunity and guidance to complete this work, which is an integral part of the

curriculum of Bachelors of Electrical Engineering at Mehran University of

Engineering & Technology.

i

ABSTRACT

Both electric utilities and end users of electric power are becoming increasingly

concerned about the quality of electric power. It is an umbrella concept for a

multitude of individual types of power system disturbances. One such major concern

is the harmonics which is made the focus of study in this work. When electronic

power converters first became commonplace in the late 1970s, many utility engineers

became quite concerned about the ability of the power system to accommodate the

harmonic distortion. Harmonics problems counter many of the conventional rules of

power system design and operation that consider only the fundamental frequency.

Therefore, the engineer is faced with unfamiliar phenomena that require unfamiliar

tools to analyze and unfamiliar equipment to solve.

This thesis is basically concerned with the Analysis and Mitigation of Harmonics

generated by Power Electronic Converters. The investigation of harmonics has been

carried out using Fast Fourier Transform (FFT) to evaluate the Total Harmonic

Distortion (THD) of the converters with and without filters. And

MATLAB/SIMULINK has been employed for presenting the simulation results

because it is well established and recognized simulation software for the power

system. Next, the designing of Passive Filter is carried out after a literature review and

have been applied to the converters for harmonics mitigation.

In the future, we would proceed to work on Active Filters for Harmonics Mitigation.

ii

CONTENTS

CHAPTER 01

INTRODUCTION

1.1 ELECTRIC POWER QUALITY 01

1.2 SOURCES OF ELECTRIC POWER QUALITY DETERIORATION IN

A POWER SYSTEM 02

1.3 NEED FOR ASSESSMENT OF ELECTRIC POWER QUALITY 02

1.4 CLASSIFICATION OF POWER SYSTEM DISTURBANCES 03

1.5 WHY ARE WE CONCERNED ABOUT POWER QUALITY? 06

CHAPTER 02

FUNDAMENTALS OF HARMONICS

2.1 INTRODUCTION 07

2.2 TYPES OF HARMONICS 08

2.2.1 Odd harmonics 08

2.2.2 Even harmonics 08

2.2.3 Inter harmonics 08

2.2.4 Sub harmonics 08

2.3 NON-SINUSOIDAL WAVEFORM 09

2.3.1 Average value 09

2.3.2 RMS value 09

2.3.3 Form factor 09

2.3.4 Harmonic power 09

2.3.5 Total active power 10

2.4 SOURCES OF HARMONICS 10

2.4.1 Magnetization nonlinearities of transformer 10

2.4.2 Rotating machines 11

iii

2.4.3 Arcing devices 12

2.4.4 Power supplies with semiconductor devices 12

2.4.5 Inverter Fed A.C drives 12

2.4.6 Thyristor controlled reactors 12

2.4.7 Phase controllers & AC regulators 12

2.5 EFFECTS OF HARMONICS 12

2.5.1 Resonance and effect on capacitor banks 13

2.5.2 Poor damping 13

2.5.3 Effects of harmonics on rotating machines 13

2.5.4 Effects on transformer 13

2.5.5 Effects on transmission lines 13

2.5.6 Harmonic interference with power system protection 14

2.5.7 Effects of harmonics on consumer equipment 14

2.6 HARMONIC INDICES 14

2.6.1 Total harmonic distortion 15

2.6.2 Total demand distortion 15

2.7 PRINCIPLES FOR HARMONICS CONTROL 16

2.8 WHERE TO CONTROL HARMONICS 16

2.8.1 on utility distribution Feeders 17

2.8.2 In End-User Facilities 17

2.9 USEFUL TOOLS FOR HARMONICS ASSESMENT 18

CHAPTER 03

HARMONIC FILTERS

3.1 INTRODUCTION 19

3.2 PASSIVE FILTERS 19

3.2.1 Passive shunt filters 20

iv

3.2.2 Passive series filter 22

3.3 ACTIVE FILTERS 22

3.4 HYBRID FILTERS 23

3.5 DESIGN STEPS OF SERIES TUNED FILTERS 23

3.6 DESIGN STEPS OF 2ND ORDER HIGH PASS FILTER 24

3.7 QUALITY FACTOR, BANDWIDTH AND SELECTIVITY 25

CHAPTER 04

STANDARD LIMITS OF HARMONIC DISTORTION

4.1 INTRODUCTION 27

4.2 VOLTAGE HARMONIC DISTORTION LIMITS 27

4.3 CURRENT HARMONICS DISTORTION LIMITS 28

CHAPTER 05

MATLAB SIMULATION & RESULTS

5.1 POWER CONVERTERS HARMONIC BEHAVIOUR 30

5.2 HARMONIC ANALYSIS OF THREE PHASE 12 PULSE AC-DC

CONVERTERS 31

5.3 HARMONIC ANALYSIS OF THREE PHASE INVERTER 36

CHAPTER 06

CONCLUSIONS

REFERENCES

v

LIST OF FIGURES

Figure 1.1 Harmonics of laptop 04

Figure 1.2 Utility Capacitor Switching Transient 04

Figure 1.3 Voltage Sag 04

Figure 1.4 Voltage Swell 05

Figure 1.5 Flicker 05

Figure 2.1 Harmonic representation 07

Figure 2.2 Harmonic currents flow in a radial system 17

Figure 3.1 Passive shunt filters 20

Figure 3.2 Impedance vs Frequency curve of series tuned filter 21

Figure 3.3 Impedance vs Frequency curve of damped filter 21

Figure 3.4 Passive series filter 22

Figure 3.5 Quality factor effect on resonance curve 25

Figure 3.6 Quality factor effect on selectivity 26

Figure 5.1 Displacement of harmonics as a function of firing angle 30

Figure 5.2 FFT analysis of three phase inverter 31

Figure 5.3 Three phase 12 pulse AC-DC converter model 32

Figure 5.4 Source voltage without filters 32

Figure 5.5 Source current without filters 33

Figure 5.6 FFT analysis of distorted source voltage 33

Figure 5.7 FFT analysis of distorted source current 33

Figure 5.8 Impedance vs Frequency response of designed filter 34

Figure 5.9 Source voltage after filtration 35

vi

Figure 5.10 Source current after filtration 35

Figure 5.11 FFT analysis of filtered source voltage 35

Figure 5.12 FFT analysis of filtered source voltage 36

Figure 5.13 Inverter circuit with MOSFETs 36

Figure 5.14 Three phase inverter model schematic 37

Figure 5.15 AC side voltage and FFT analysis without filters 37

Figure 5.16 AC side current and FFT analysis without filters 38

Figure 5.17 Three phase inverter model schematic with filter 38

Figure 5.18 AC voltage with filtration 39

Figure 5.19 FFT window of AC voltage with filtration 39

Figure 5.20 AC current with filtration 40

Figure 5.21 FFT window of AC current with filtration 40

vii

ABBREVATIONS

EPQ Electric Power Quality

THD Total Harmonic Distortion

TDD Total Demand Distortion

FFT Fast Fourier Transform

RMS Root Mean Square

APFs Active Power Filters

PPFs Passive Power Filters

viii

TABLES

Table 4.1- ANSI/IEEE 519 voltage distortion limits

Table 4.2-IEC 61000-2-2 voltage harmonic distortion limits in public

low-voltage network

Table 4.3- IEC 61000-2-4 voltage harmonic distortion limits in industrial

plants

Table 4.4-IEC 61000-22-4 class 3

Table 4.5-IEC 61000-3-2 maximum permissible harmonic currents for

class D equipment

Table 4.6- IEEE 519 current distortion limits.

Table5.1- Circuit parameters of 12 pulse AC-DC converter

Table 5.2-Designed Series tuned filter specifications

Table 5.3- Circuit parameters of three phase inverter

Table5.4-Designed Passive series filter specifications

1

CHAPTER # 1

INTRODUCTION

1.1 ELECTRIC POWER QUALITY

“Electric Power Quality (EPQ) is a term that refers to maintaining the near sinusoidal

waveform of power distribution bus voltages and currents at rated magnitude and

frequency”

Thus Electric Power Quality is often used to express voltage quality, current quality,

reliability of service, quality of power supply, etc.

Power Quality is ultimately a consumer driven issue defined as:

“Any power problem manifested in voltage, current or frequency deviation that results

in failure or mal-operation of consumers equipment”.

In the study of (EPQ), different branches are being formed which deals with different

issues related to electric power quality .These branches are divided into following

stages.

1. Fundamental concepts

2. Sources

3. Effects

4. Modeling and Analysis

5. Instrumentation

6. Solutions

(i) Fundamental concepts

The ‘fundamental concept’ of EPQ identifies the parameters and their degree of

variation with respect to their rated magnitude which are the base reason for

degradation of quality of electric power.

(ii) Sources

Sources are the regions or locations or events which causes the unwanted variation of

those parameters. It’s really a big challenge to the power engineers to find out the

exact sources of power quality related disturbance in the ever increasing complex

network.

2

(iii) Effects

Effects of poor quality of power are the effects faced by the system and consumer

equipment after the occurrence of different disturbances.

(iv) Modeling and Analysis

In modeling and analysis, attempts are taken to configure the disturbance, its

occurrence, sources and effect; mainly based on the mathematical background.

(v) Instrumentation

For monitoring of EPQ, constant measurement and ‘instrumentation’ of the electric

parameters are necessary.

(vi) Solutions

Complete solution, i.e. delivery of pure power to the consumer side is practically

impossible. Our target is to minimize the probability of occurrence of disturbances

and to reduce the effects of EPQ problems.

1.2 SOURCES FOR ELECTRIC POWER QUALITY DETERIORATION IN A

POWER SYSTEM

The sources of poor power quality can be categorized in two groups:

(i) Actual loads, Equipment and Components.

(ii) Subsystems of transmission and distribution systems.

Poor quality is normally caused by power line disturbances such as impulses, notches,

voltage sag and swell, voltage and current unbalances, momentary interruption and

harmonic distortions. The major contributors to poor power quality are harmonics and

reactive power. Solid state control of ac power using high speed switches are the main

source of harmonics whereas different non-linear loads contribute to excessive drawl

of reactive power from supply.

It leads to catastrophic consequences such as long production downtimes, mal-

function of devices and shortened equipment life.

1.3 NEED FOR ASSESSMENT OF ELECTRIC POWER QUALITY

It is common experience that electric power of poor quality has detrimental effects on

health of different equipment and systems. Moreover, power system stability,

continuity and reliability fall with the degradation of quality of electric power.

3

To avoid such effects, it is important to continuously assess the quality of power

supplied to a consumer.

1.4 CLASSIFICATION OF POWER SYSTEM DISTURBANCES

Power quality problems occur due to various types of electrical disturbances. Most of

the EPQ disturbances depend on amplitude or frequency or on both frequency and

amplitude. Based on the duration of existence of EPQ disturbances, events can

divided into short, medium or long type. These disturbances are mainly classified as:

(i) Interruption/under voltage/over voltage

During power interruption, voltage level of a particular bus goes down to zero. The

interruption may occur for short or medium or long period. Under voltage and over

voltage are fall and rise of voltage levels of a particular bus with respect to standard

bus voltage. Such disturbances increase the amount of reactive power drawn or

deliver by a system, insulation problems and voltage stability.

(ii) Voltage/Current unbalance

Voltage and current unbalance may occur due to the unbalance in drop in the

generating system or transmission system and unbalanced loading. During unbalance,

negative sequence components appear. It hampers system performance and voltage

stability.

(iii) Harmonics

Harmonics are sinusoidal voltages or currents having frequencies that are integer

multiples of the frequency at which the supply system is designed to operate (termed

the fundamental frequency; usually 50 or 60 Hz). Periodically distorted waveforms

can be decomposed into a sum of the fundamental frequency and the harmonics.

Harmonic distortion originates due to the nonlinear characteristics of devices and

loads on the power system. Harmonics are classified as integer harmonics, sub

harmonics and inter harmonics. Integer harmonics have frequencies which are integer

multiple of fundamental frequency, sub harmonics have frequencies which are smaller

than fundamental frequency and inter harmonics have frequencies which are greater

than fundamental frequencies. Sometimes harmonics are classified as time harmonics

and spatial (space) harmonics. Monitoring of harmonics with respect to fundamental

is important consideration in power system application.

4

Figure 1.1

(iv) Transients

Transients which are the sudden rise of signal may generate in the system itself or

may come from the other system. Transients are classified into two categories: dc

transient and ac transient. The figure 1.2 shows utility capacitor-switching transient.

Figure 1.2

(v) Voltage Sag

It is a short duration disturbance. During voltage sag, RMS voltage falls to a very low

level for short period of time. It is actually a reduction in RMS voltage over a range of

0.1–0.9 pu for a duration greater than 10 ms but less than 1 s

Figure 1.3

5

(vi) Voltage Swell

It is a short duration disturbance. During voltage sag, RMS voltage increases to a very

high level for short period of time. It is an increase in RMS voltage over a range of

1.1–1.8 pu for a duration greater than 10 ms but less than 1 s.

Figure 1.4

(vii) Flicker

It is undesired variation of system frequency. The voltage variations resulting from

flicker are often within the normal service voltage range, but the changes are

sufficiently rapid to be irritating to certain end users. Flicker can be separated into two

types: cyclic and noncyclic. Cyclic flicker is a result of periodic voltage fluctuations

on the system, while Non-cyclic is a result of occasional voltage fluctuations.

The usual method for expressing flicker is similar to that of percent voltage

modulation. It is usually expressed as a percent of the total change in voltage with

respect to the average voltage ( V/V) over a certain period of time. The figure 1.5-

shows a typical flicker waveform.

Figure 1.5

6

(viii) Ringing waves

Oscillatory disturbance of decaying magnitude for short period of time is known as

ringing wave. It may be called a special type transient.

(ix) Outage

It is special type of interruption where power cut has occurred for not more than 60 s.

1.5 WHY ARE WE CONCERNED ABOUT POWER QUALITY?

The ultimate reason that we are interested in power quality is economic value. There

are economic impacts on utilities, their customers, and suppliers of load equipment.

The quality of power can have a direct economic impact on many industrial

consumers. There is big money associated with these disturbances. It is not

uncommon for a single, commonplace, momentary utility breaker operation to result

in a $10,000 loss to an average-sized industrial concern by shutting down a

production line that requires 4 hours to restart. In the semiconductor manufacturing

industry, the economic impacts associated with equipment sensitivity to momentary

voltage sags resulted in the development of a whole new standard for equipment ride-

through.

The electric utility is concerned about power quality issues as well. Meeting customer

expectations and maintaining customer confidence are strong motivators. The loss of

a disgruntled customer to a competing power supplier can have a very significant

impact financially on a utility.

7

Chapter # 2

FUNDAMENTALS OF HARMONICS

2.1 INTRODUCTION

A pure poly-phase system is expected to have pure sinusoidal alternating current and

voltage waveforms of single frequency. But, the real situation deviates from this

purity. Real voltage and current waveforms are distorted. Normally they are called

non sinusoidal waveforms. Non sinusoidal waveform is formed with the combination

of many sine waves of different frequencies. Thus actual power system signals have

fundamental component as well as harmonic components.

Harmonic distortion is caused by nonlinear devices in the power system. A nonlinear

device is one in which the current is not proportional to the applied voltage. When a

waveform is identical from one cycle to the next, it can be represented as a sum of

pure sine waves in which the frequency of each sinusoid is an integer multiple of the

fundamental frequency of the distorted wave. This multiple is called a harmonic of the

fundamental, hence the name of this subject matter. The sum of sinusoids is referred

to as a Fourier series, named after the great mathematician who discovered the

concept.

Harmonic component of current of order n can be represented as

in = In sin 2πnft (2.1)

Where In is the amplitude of harmonic component of order n.

Figure 2.1

8

Figure 2.1 illustrates that any periodic, distorted waveform can be expressed as sum

of sinusoids.

2.2 TYPES OF HARMONICS

Integer harmonics are divided into two categories: odd harmonics and even

harmonics. Other than integer harmonics there are sub and inter harmonics where n is

fractional.

2.2.1 Odd Harmonics: Integer harmonics having frequencies which are odd integer

multiple of fundamental frequency are known as odd harmonics. Odd harmonics may

be expressed as

in = In sin 2πnft (2.2)

Where, n = 3, 5, 7, . . . etc. and In is the amplitude of harmonic component of order n.

2.2.2 Even Harmonics: Integer harmonics having frequencies which are even integer

multiple of fundamental frequency are knows as even harmonics. Even harmonics

may be expressed as

in = In sin 2πnft (2.3)

Where, n = 2, 4, 6, . . . etc. and In is the amplitude of harmonic component of order n.

2.2.3 Inter Harmonics: Often in non-sinusoidal waveform there are harmonics

having frequencies which are greater than fundamental but not integer multiple of

fundamental frequency. These are known as inter-harmonics. Mathematically,

in = In sin 2πnft (2.4)

Where, n > 1 but not integer; e.g.: 1.2, 1.5, 2.7 . . . etc

2.2.4 Sub Harmonics: Often in non-sinusoidal waveform there are harmonics having

frequencies which are smaller than fundamental frequency. These are known as sub-

harmonics. Mathematically,

in = In sin 2πnft (2.5)

Where, n < 1; e.g.: 0.2, 0.5, 0.7 . . . etc

9

2.3 NON-SINUSOIDAL WAVEFORM

Non-sinusoidal wave is constituted by the combination of odd-even harmonic

components as well as fundamental component. Thus, mathematically, it can be

expressed as:

i=∑ ∑ (2.6)

A non-sinusoidal wave may be expressed in terms of harmonics as

i=∑ ∑ =

= I1 sin 2πft + I2 sin 4πft + I3 sin 6πnft + I4 sin 8πnft + I5 sin 10πnft+· · · ·

= I1 sin 2πf1ft + I2 sin 2πf2t + I3 sin 2πf3t + I4 sin 2πf4t + I5 sin 2πf5t . . . . (2.7)

2.3.1 Average Value

Harmonic components having phase angle (αn) can be expressed as:

in = In sin (2πfnt − αn) (2.8)

Average value is given by:

inav = (

) (

) (2.9)

2.3.2 RMS Value

RMS value of the non-sinusoidal current wave is given by:

iRMS = √ = √∑

(2.10)

2.3.3 Form Factor

Form factor is the ratio of RMS value to average value. In case of non-sinusoidal

wave it is given by:

Form Factor =

(2.11)

2.3.4 Harmonic Power

The current and voltage are respectively given as:

i = ∑ (2.12)

10

v = ∑ (2.13)

Power contributed by harmonic components of voltage and current waveforms can

be expressed as:

Average power of harmonics of order n, Pn

= ∫

= in RMS vn RMS cos (2.14)

Where = = phase difference between harmonic component of voltage

and current waveforms of order n.

2.3.5 Total Active Power

Total active power is contributed by fundamental as well as harmonic components of

voltage and current waveform. Thus total power is written as:

p = ∑ = ∑

= i1 rmsv1 rms cos ϕ1 + i2 rmsv2 rms cos ϕ2 + i3 rmsv3 rms cos ϕ3 (2.15)

2.4 SOURCES OF HARMONICS

The main sources of harmonics in electric power systems can be categorized as:

a) Magnetization nonlinearities of transformer

b) Rotating machines

c) Arcing devices

d) Semi-conductor based power supply

e) Inverter fed A.C drives

f) Thyristor controlled reactors

g) Phase controllers

h) A.C regulators

2.4.1Magnetization nonlinearities of transformer

Transformers magnetic material characteristic is non-linear. This non linearity is the

main reason for harmonics during excitation. Sources of harmonics in transformer

may be classified into four categories as follows:

11

a .Normal Excitation: Normal excitation current of a transformer is non-sinusoidal.

The distortion is mainly caused by zero sequence triplen harmonics and particularly

the third present in the excitation current.

b .Symmetrical Over Excitation: When transformers are subjected to a rise in voltage,

the cores face a considerable rise in magnetic flux density, which often causes

considerable saturation. This saturation with symmetrical magnetizing current

generates all the odd harmonics.

c .Inrush Current Harmonics: A switched-off transformer with residual flux in the

core is re-energized, the flux density rises to peak levels of twice the maximum flux

density or more, thus producing high-ampere turns causing magnetizing currents to

reach up to 5-10 per unit of the rated value, typically known as inrush current. This

causes generation of enormous second order harmonic component in the transformer

current

d .D.C Magnetization: Under magnetic unbalance, the core contains an average value

of flux (φdc), which is equivalent to a direct component of excitation current of the

transformer which contains both odd and even harmonic components.

2.4.2 Rotating machines

Rotating machines also contribute in generation of harmonics, this maybe further

classified as:

a) Magnetic Nonlinearities of the core material causes harmonic generation

b) Non-uniform flux distribution in the air gap leads to harmonic production

c) Slots and Teeth presence changes the reluctance of magnetic flux and this

variation results in harmonics

d) Rotor Saliency also brings the variation of reluctance in the magnetic path and

reactance in electric path which contribute to harmonics generation

e) Crawling is a common problem faced by induction motors. During this fault, odd

harmonics like 5th and 7th orders appear.

f) Cogging, a problem when motor fails to start produces harmonics different from

those in the normal condition

g) Some other causes are Rotor misalignment, Mass unbalance, Fractal error and

Unsymmetrical faults.

12

2.4.3 Arcing devices

Electric Arc Furnace, Discharge type lighting, Arc welders have highly non-linear

voltage vs current characteristics. Therefore, arc ignition is equivalent to a short-

circuit with a decrease in voltage. Hence they are a major source of power system

harmonics.

2.4.4 Power supplies with semiconductor devices

Harmonics generated by such supplies include integer, inter and sub harmonics whose

magnitudes and frequencies depend upon the type of semiconductor devices used,

operating point, nature of load variation, etc.

2.4.5 Inverter Fed A.C drives

The use of switching devices like GTO, IGBT, etc. along with PWM technique has

become popular in AC Drives applications which are sources of integer as well as

fractional harmonics.

2.4.6 Thyristor controlled reactors

Different types of thyristor controlled reactors used in power system like series

controller, shunt controller, static VAR compensator (SVC), fixed capacitor thyristor

controlled reactor (FCTCR), thyristor switched capacitor thyristor controlled reactor

(TSCTCR) are sources of harmonics in power system.

2.4.7 Phase controllers & AC regulators

Phase Controller for the supply of balanced electric power and AC voltage regulators

when applied both online and offline for voltage regulation will result in harmonic

generation.

2.5 EFFECTS OF HARMONICS

Harmonics are not desirable in most applications and operations of electrical power

system; therefore it has wide adverse effects on the system. The effects of harmonics

may be classified as:

13

2.5.1 Resonance and effect on capacitor banks:

Resonance occurs when the frequency at which the capacitive and inductive reactance

of the circuit impedance are equal. At the resonant frequency, a parallel resonance has

high impedance and series resonance low impedance. Harmonic resonances create

problems in operation of power factor correction capacitors. Capacitors used for

power factor correction cause system resonances due to harmonic frequencies. This

results in excessive high current, which can produce damage to the capacitors. Change

of harmonic contents sometimes increases reactive power over permissible

manufacturer tolerances.

2.5.2 Poor damping:

In the presence of harmonics, undesirable variation of the degree of damping changes

the operating performance of different measuring and controlling instruments.

2.5.3 Effects of harmonics on rotating machines:

Harmonic voltages and currents increase losses in the stator windings, rotor circuit,

and stator and rotor lamination; resulting in overheating and efficiency reduction.

Harmonic currents present in the stator of an AC machine produce induction motoring

action (i.e. positive harmonic slips Sn), which gives rise to shaft torques in the same

direction as the harmonic field velocities in such a way that all positive sequence

harmonics will develop shaft torques aiding shaft rotation whereas negative sequence

harmonics will have the opposite effect, thus affecting the speed/torque characteristic

considerably.

2.5.4 Effects on transformer:

Harmonic Voltage increases the core losses in laminations and stresses the insulation,

while harmonic current increase copper losses. They also cause increase in core

vibrations.

2.5.5 Effects on transmission lines:

Harmonics tend to increase Skin and Proximity Effects since both are frequency

dependent. Harmonic currents reduce the power transmitting capacity by increasing

copper losses and also produce harmonic voltage drops across various circuit

impedances. As a result, a weak system of large impedance has low fault level and

14

greater voltage disturbances where as a stiff system of low impedance has high fault

level and lower voltage disturbance. Harmonic voltages reduce dielectric strength of

cables by causing an increase in dielectric losses.

2.5.6 Harmonic interference with power system protection:

Harmonics degrade the operating characteristics of protective relays. Some digital

relays and algorithms operate on sample data and zero crossing moment. Harmonic

distortion creates error on such operation. Harmonics make higher di/dt at zero

crossings and the current sensing ability of the thermal magnetic breakers and change

trip point due to extra heating in the solenoid. Current harmonic distortion affects the

interruption capability of circuit breakers and fuses.

2.5.7 Effects of harmonics on consumer equipment:

IEEE Task Force on the Effects of Harmonics on Equipment has made a wide study

on this matter. The result can be summarized as follows:

a) Television Receivers: Harmonics changes in TV picture size and brightness. Inter-

harmonics change amplitude modulation of the fundamental frequency. For

example, even a 0.5% inter harmonic level can produce periodic enlargement and

reduction of the image of the cathode ray tube.

b) Fluorescent and mercury arc lighting: Capacitors used in such lighting

applications together with the inductance of the ballast and circuit produce a

resonant frequency. It results in excessive heating and failure in operation.

Audible noise is produced due to harmonic voltage distortion.

c) Computers: Harmonics create problems in monitor and CPU operation. Harmonic

rate (geometric) measured in vacuum must be less than −3% (Honeywell, DEC) or

5% (IBM). CDC specifies that the ratio of peak to effective value of the supply

voltage must equal to 1.41±0.1.

2.6 HARMONIC INDICES

The two most commonly used indices for measuring the harmonic content of a

waveform are the Total Harmonic Distortion (THD) and the Total Demand Distortion.

15

2.6.1 Total harmonic distortion

The THD is a measure of the effective value of the harmonic components of a

distorted waveform. That is, it is the potential heating value of the harmonics relative

to the fundamental. This index can be calculated for either voltage or current:

THD=√∑ ⁄ (2.16)

Where Mh is the RMS value of harmonic component h of the quantity M.

The RMS value of a distorted waveform is the square root of the sum of the squares

as shown in Equations (2.16) and (2.17). The THD is related to the rms value of the

waveform as follows:

RMS=√∑ = M1√ (2.17)

The THD is a very useful quantity for many applications, but its limitations must be

realized. It can provide a good idea of how much extra heat will be realized when a

distorted voltage is applied across a resistive load. Likewise, it can give an indication

of the additional losses caused by the current flowing through a conductor. However,

it is not a good indicator of the voltage stress within a capacitor because that is related

to the peak value of the voltage waveform, not its heating value. The THD index is

most often used to describe voltage harmonic distortion.

Harmonic voltages are almost always referenced to the fundamental value of the

waveform at the time of the sample. Because fundamental voltage varies by only a

few percent, the voltage THD is nearly always a meaningful number.

2.6.2 Total demand distortion

Current distortion levels can be characterized by a THD value but this can often be

misleading. A small current may have a high THD but not be a significant threat to

the system.

For example, many adjustable-speed drives will exhibit high THD values for the input

current when they are operating at very light loads. This is not necessarily a

16

significant concern because the magnitude of harmonic current is low, even though its

relative current distortion is high.

Some analysts have attempted to avoid this difficulty by referring THD to the

fundamental of the peak demand load current rather than the fundamental of the

present sample. This is called total demand distortion and serves as the basis for the

guidelines in IEEE Standard 519-1992, Recommended Practices and Requirements

for Harmonic Control in Electrical Power Systems. It is defined as follows:

TDD=

√∑

(2.18)

IL is the peak, or maximum, demand load current at the fundamental frequency

component measured at the point of common coupling (PCC).

2.7 PRINCIPLES FOR HARMONICS CONTROL

Harmonic distortion is present to some degree on all power systems. Fundamentally,

one needs to control harmonics only when they become a problem. There are three

common causes of harmonic problems:

1. The source of harmonic currents is too great.

2. The path in which the currents flow is too long (electrically), resulting in either

high voltage distortion or telephone interference.

3. The response of the system magnifies one or more harmonics to a greater degree

than can be tolerated.

When a problem occurs, the basic options for controlling harmonics are:

1. Reduce the harmonic currents produced by the load.

2. Add filters to siphon the harmonic currents off the system, block the currents from

entering the system, or supply the harmonic currents locally.

3. Modify the frequency response of the system by filters, inductors, or capacitors.

2.8 WHERE TO CONTROL HARMONICS?

The strategies for mitigating harmonic distortion problems differ somewhat by

location. The following techniques are ways for controlling harmonic distortion on

both the utility distribution feeder and end user power system.

17

2.8.1 On Utility Distribution Feeders

Harmonic problems on distribution feeders often exist only at light load. The voltage

rises, causing the distribution transformers to produce more harmonic currents and

there is less load to damp out resonance. Switching the capacitors off at this time

frequently solves the problem.

Should harmonic currents from widely dispersed sources require filtering on

distribution feeders, the general idea is to distribute a few filters toward the ends of

the feeder. Figure 2.2 shows one example of a filter installed on an overhead

distribution feeder. This shortens the average path for the harmonic currents, reducing

the opportunity for telephone interference and reducing the harmonic voltage drop in

the lines. The filters appear as nearly a short circuit to at least one harmonic

component. This keeps the voltage distortion on the feeder to a minimum.

Figure 2.2

2.8.2 In End-User Facilities

When harmonic problems arise in an end-user facility, the first step is to determine if

the main cause is resonance with power factor capacitors in the facility. If this is the

case, a simple solution would be to use a different capacitor size. Installation of filters

on end-user low-voltage systems is generally more practical and economical than on

18

utility distribution systems. The criteria for filter installation are more easily met, and

filtering equipment is more readily available on the market.

2.9 USEFUL TOOLS FOR HARMONICS ASSESSMENT

The basis of all harmonic assessment still depends on the measurement of amplitude

and phase angle of the harmonics components. Different mathematical tools have

come out for this purpose. Some of them are capable of measuring both integer and

non-integer order of harmonics. Some of them are capable of measuring only integer

type of harmonics. Also, in many cases, signals could not be captured in continuous

form.To overcome these limitations modified mathematical tools have been

developed to handle discrete signals. Mathematical tools for harmonics analysis may

be in time domain, or frequency domain or both time-frequency domains.

One of old techniques used in analysis of non-sinusoidal signals is Fourier transform.

Fourier analysis has been used for power quality assessment for a long period.

It permits mapping of signals from time domain to frequency domain by

decomposing the signals into several frequency components. The transform method

suffers from limitation to handle discrete or discontinuous, multi-valued and

undefined signals which are often faced by electrical applications. In this thesis, we

have employed Fast Fourier Transform (FFT) built-in tool available in MATLAB

which can be directly applicable or after some alteration on captured discrete signals.

19

Chapter # 3

HARMONIC FILTERS

3.1 INTRODUCTION

Any combination of passive (R, L, C) and/or active (transistors, op-amps) elements

designed to select or reject a band of frequencies is called a filter. Filters are used to

filter out any unwanted frequencies due to nonlinear characteristics of some electronic

devices or signals picked up by the surrounding medium.

Filters are one of those corrective (remedial) solutions aimed at overcoming harmonic

problems and to keep them within safe limits. They provide a low impedance path or

‘trap’ to a harmonic to which a filter is tuned, hence are called tuned (resonant)

circuits. The process of tuning aims at setting the circuit to fr (resonant frequency)

where the response is or at maximum. The circuit is then said to be in state of

resonance.

There are three types of filters.

1. Passive filters

2. Active filters

3. Hybrid filters

We will be dealing with only Passive Filters as these are the main concern of this

thesis work. A short description about active and hybrid filters is also provided in

what follows:

3.2 PASSIVE FILTERS

Passive filters are basically topologies or arrangements of R, L and C elements

connected in different combinations to gain desired suppression of harmonics. They

are employed either to shunt the harmonic currents off the line or to block their flow

between parts of the system by tuning the elements to create a resonance at a selected

frequency. The also provide the reactive power compensation to the system and hence

improve the power quality. However, they have the disadvantage of potentially

interacting adversely with the power system and the performance of passive filter

depends mainly on the system source impedance. On the other hand they can be used

20

for elimination of a particular harmonic frequency, so number of passive filters

increase with increase in number of harmonics on the system. They can be classified

into:

1. Passive shunt filter

2. Passive series filter

Passive shunt filters are the main focus of study in this thesis and are discussed here in

detail while a little thought is presented on series filters.

3.2.1 Passive Shunt Filters

They are classified as shown in the figure 3.1 below:

Figure 3.1

Single Tuned Filter:

The most common type of passive filter is the single-tuned “notch” filter. This is the

most economical type and is frequently sufficient for the application. The notch filter

is series-tuned to present low impedance to a particular harmonic current and is

connected in shunt with the power system. Thus, harmonic currents are diverted from

their normal flow path on the line through the filter Notch filters can provide power

factor correction in addition to harmonic suppression. In fact, power factor correction

capacitors may be used to make single-tuned filters. They are tuned at low harmonic

frequencies. At the tuned harmonic, capacitor and reactor have equal reactance and

the filter has purely resistive impedance. A general schematic diagram of series tuned

filter is shown in the figure 3.1.

The impedance vs frequency curve of this filter is shown in Figure 3.2.

21

Figure 3.2

Double Band Pass Filters:

A double Band Pass Filter is a series combination of a main capacitor, a main reactor

and a tuning device which consists of a tuning capacitor and a tuning reactor

connected in parallel. The impedance of such a filter is low at two tuned frequencies.

Damped Filters:

They can be 1st, 2

nd, or 3

rd order type. The most commonly used is the 2

nd order. A 2

nd

order damped filter consists of a capacitor in series with a parallel combination of a

reactor and a resistor. It provides low impedance for a moderately wide range of

frequencies. When used to eliminate high order harmonics ( 17th

and above), a

damped filter is referred to as High Pass Filter, providing a low impedance for high

frequencies but stopping low ones.

Damped filters are usually tuned to hn<hr, that is 10.7, 16.5 and so on. The

Impedance Vs Frequency curve of Second-Order High Pass Filter is shown in figure

3.3

Figure 3.3

22

3.2.2 Passive Series Filter

Unlike a notch filter which is connected in shunt with the power system, a series

passive filter is connected in series with the load. The inductance and capacitance are

connected in parallel and are tuned to provide high impedance at a selected harmonic

frequency. The high impedance then blocks the flow of harmonic currents at the tuned

frequency only. At fundamental frequency, the filter would be designed to yield low

impedance, thereby allowing the fundamental current to flow with only minor

additional impedance and losses. Figure 3.4 shows a typical series filter arrangement.

Series filters are used to block a single harmonic current (such as the third harmonic)

and are especially useful in a single-phase circuit where it is not possible to take

advantage of zero-sequence characteristics. The use of the series filters is limited in

blocking multiple harmonic currents. Each harmonic current requires a series filter

tuned to that harmonic. This arrangement can create significant losses at the

fundamental frequency.

Figure 3.4

3.3 ACTIVE FILTERS

Active filters are relatively new types of devices for eliminating harmonics. They are

based on sophisticated power electronics and are much more expensive than passive

filters. However, they have the distinct advantage that they do not resonate with the

system. They can work independently of the system impedance characteristics. Thus,

they can be used in very difficult circumstances where passive filters cannot operate

successfully because of parallel resonance problems. They can also address more than

one harmonic at a time and combat other power quality problems such as flicker.

They are particularly useful for large, distorting loads fed from relatively weak points

on the power system

23

3.4 HYBRID FILTERS

Since the APFs (Active Power Filters) topologies are not cost-effective for the

application of high power because of their high rating and very high switching

frequency of PMW (Pulse Width Modulator) converters. Thus LC PPFs (Passive

Power Filters) are used for harmonic filtration of such large nonlinear loads.

However, Passive filters suffer from some shortcomings for example, the performance

of these filters is affected due to the varying impedance of the system and with the

utility system the series and parallel resonances may be created, which cause current

harmonics increase in the supply. Therefore, another solution of harmonic mitigation,

called HAPF (Hybrid Active Power Filter), has been introduced. HAPF provides the

combined advantages of APF and PPF and eliminate their disadvantages. These

topologies are cost effective solutions of the high-power power quality problems with

well filtering performance.

3.5 DESIGN STEPS OF SERIES TUNED FILTERS

In design of the filter, the proper selection of the capacitor size is very essential from

power factor point of view. A series-tuned filters is a capacitor designed to trap a

certain harmonic by adding a reactor such that XL=Xc at the frequency fn.

To design series-tuned following step are followed:

Determine the capacitor size Qc in MVAR, say the reactive power requirement of

the source.

The capacitor reactance is

(3.1)

Capacitance for filters is calculated by

(3.2)

Where n=number of filters to be designed

The resonance condition will occur when capacitive reactance is equal to

inductive reactance as:

XL=XC (3.3)

24

To trap the harmonics of order h, the reactance should be of size

(3.4)

The resistance of filter depends on the quality factor (Q) by which sharpness of

the tuning is measured.

√

(3.5)

Where Q is the quality factor and for series tuned is 30<Q≤100.

3.6 DESIGN STEPS OF 2ND

ORDER HIGH PASS FILTER

To design 2nd

order high pass filter, following step are followed:

Determine the capacitor size Qc in MVAR, say the reactive power requirement of

the source.

The capacitor reactance is

(3.6)

Capacitance for filters is calculated by

(3.7)

Where n=number of filters to be designed

The resonance condition will occur when capacitive reactance is equal to

inductive reactance as:

XL=XC (3.8)

To trap the harmonics of order h, the reactance should be of size

(3.9)

The resistance of filter depends on the quality factor (Q) by which sharpness of the

tuning is measured.

R = √

* Q (3.10)

Where Q, the quality factor is 0.5 <Q< 5.

25

3.7 QUALITY FACTOR, BANDWIDTH AND SELECTIVITY

The quality factor of a resonant circuit is defined as the ratio of reactive power of

either the inductor or capacitor to the average power of resistor at resonance.

Q

For a Series Resonant Circuit,

Qs=

=

√

(3.11)

Where XL is the inductive reactance, R is the resistance, Qs is the quality factor of

series resonant circuit and is the angular frequency that account for resonance.

Then, fS=

√ is called the resonant frequency of the series resonant circuit.

The quality factor is a measure of the sharpness of the tuning frequency. It is

determined by the resistance value. The effect of Q factor on the response curve is as

shown in the figure 3.5

Figure 3.5

In terms of Qs, if R is large for the same XL, then Qs is less. A small Qs, therefore, is

associated with a resonance curve having a large bandwidth and a small selectivity

while a large Qs indicates otherwise.

The selectivity indicates that one must be selective in choosing the frequency to

ensure that it is in the bandwidth. The smaller the bandwidth, the higher is its

selectivity as shown in the figure 3.6

26

Figure 3.6

The larger value of the quality factor gives the best reduction in harmonic reduction.

However, it is necessary to take care of the harmonic frequencies because these

harmonic current frequencies will also follow the least impedance path. These

currents cause the increased power loss. Therefore it is necessary to perform the

computer based harmonic simulation for analyzing the performance of the filters.

The Bandwidth is related o the Quality Factor as:

BW=

or (3.12)

BW= f2-f1 =

(3.13)

Where f1 and f2 are the cutoff frequencies or half power frequencies which specify the

range of Band Width

27

Chapter # 4

STANDARD LIMITS OF HARMONIC DISTORTION

4.1 INTRODUCTION

The limits of allowable voltage and current harmonics distortion set by IEEE and IEC

have been presented in this chapter which are just based on the personal experiences

and involvement of Power Quality analysts in harmonic analysis research. These

standards provide guidelines for power quality usages and practices.

4.2 VOLTAGE HARMONIC DISTORTION LIMITS

Bus voltage at PCC Individual Vh , % Voltage THD , %

V<69KV 3.0 5.0

69≤V<161KV 1.5 2.5

V≥161KV 1.0 1.5

Table 4.1- ANSI/IEEE 519 voltage distortion limits

Odd harmonics Even harmonics Triplen harmonics

H % Vh H % Vh H % Vh

5 6 2 2 5

7 5 4 1 9 1.5

11 3.5 6 0.5 15 0.3

13 3 8 0.5 15 0.3

177 2 10 0.5 ≥21 0.2

19 1.5 ≥12 0.2

23 1.5

Table 4.2-IEC 61000-2-2 voltage harmonic distortion limits in public low-voltage

network

28

Even harmonics Triplen harmonics

H % vh H % Vh H % Vh

5 6 2 2 3 5

7 5 4 1 9 1.5

11 3.5 6 0.5 15 0.3

13 3 8 0.5 15 0.3

17 2 10 0.5

19 1.5 ≥12 0.2

23 1.5

25 1.5

≥29 x

Table 4.3- IEC 61000-2-4 voltage harmonic distortion limits in industrial plants

Odd harmonics Even harmonics Triplen harmonics

H % , Vh H % , Vh H %, Vh

5 8 2 3 3 6

7 7 4 1.5 9 2.5

11 5 ≥6 1 15 2

13 4.5 21 1.75

17 4 ≥27 1

19 4

23 3.5

Table 4.4-IEC 61000-22-4 class 3

4.2 CURRENT HARMONIC DISTORTION LIMITS

H 3 5 7 9 11 13 15…………39

Max Ih 2.3 1.14 0.77 0.40 0.33 0.21 0.15……….15 ∕ h

Equipment input current ≤ 16 A per phase

Table 4.5-IEC 61000-3-2 maximum permissible harmonic currents for class D

equipment

29

ISC/IL Ih / IL , % ---- general distribution systems (120V-69KV) TDD

h<11 11≤h<17 17≤h<23 23h≤h<35 h≥35

<20 4.0 2.0 1.5 0.6 0.3 5

20-50 7.0 3.5 2.5 1.0 0.5 8

50-

100

10 4.5 4.0 1.5 0.7 12

100-

1000

12 5.5 5.0 2.0 1.0 15

>1000 15 7.0 6.0 2.5 1.4 20

ISC/IL Ih / IL , % ---- general sub transmission systems (69-161KV) TDD

h<11 11≤h<17 17≤h<23 23≤h<35 h≥35

ISC/IL Ih / IL , % ---- general transmission systems (>161KV) TDD

% h<11 11≤h<17 17≤h<23 23≤h<35 h≥35

<50 2.0 1.0 0.75 0.3 0.15 2.5

≥50 3.0 1.5 1.15 0.45 0.22 3.75

Table 4.6- IEEE 519 current distortion limits.

30

Chapter # 5

MATLAB SIMULATION & RESULTS

5.1 POWER CONVERTERS HARMONIC BEHAVIOUR

In almost all electronic equipment, the devices directly connected with the power

network are converters; their characteristics determine the harmonic behavior of the

complete system and the impact on power supply depends on the rectifier topology

and the type of power devices employed.

The characteristic harmonic components of the current pulses supplying converters

have harmonic orders n, such as n = k · p±1, where k = 1, 2, 3, 4… and p is the

number of converter arms (pulse number).

Thyristor rectifiers have the advantage of a relatively simple control system over

uncontrolled rectifiers and can be found in D.C drives or other many applications. The

harmonics generated by a phase-controlled rectifier on the A.C side may be calculated

as for uncontrolled rectifiers, depending on pulse number.

For example, for six-pulse rectifiers, the main harmonic components are the fifth and

the seventh. However, in this case, new even and odd harmonics, referred to as non-

characteristic harmonics, of low amplitudes, are produced; on the other hand, the

amplitudes of the characteristic harmonics are modified by several factors including

asymmetry, inaccuracy in thyristor firing times, switching times, imperfect filtering.

A displacement of the harmonics as a function of the thyristor phase angle may also

be observed as shown in the figure 5.1 below:

Figure 5.1

31

Three-phase electronic power converters differ from single-phase converters mainly

because they do not generate third-harmonic currents as shown in the figure 5.2 for a

three phase inverter circuit. This is a great advantage because the third-harmonic

current is the largest component of harmonics. However, they can still be significant

sources of harmonics at their characteristic frequencies.

Figure 5.2

5.2 HARMOINIC ANALYSIS OF THREE PHASE 12 PULSE AC-DC

CONVERTER

In this work, three-phase ac to dc converter has been simulated with and without

passive shunt filters using MATLAB/SIMULINK environment. This system is

analyzed without and with passive filters using Total Harmonic Distortion as an

index.The circuit parameters used in simulation are presented in table below:

Supply Voltage 220 V RMS

Source Inductance 1.06mH

Load (Resistive) 100 ohms

Transformer (three winding) Yg/y/d1, 1200 VA, 220V/100V/100V

Table 5.1

The system considered for harmonic analysis here consists of a three phase converter

consisting of two 6 pulse bridges modeled to work as an uncontrolled rectifier. The

schematic of the system is shown in the figure 5.3.

32

Figure 5.3

The circuit response without filters is demonstrated in what follows. The figure 5.4

and 5.5 shows three phase supply voltage and current respectively. The FFT analysis

windows of VS and Is are given in figure 5.6 and 5.7 which shows the percentage

harmonics in the spectrum before the filters are incorporated. Since the waveforms are

distorted, it implies the presence of harmonics.

Figure 5.4

33

Figure 5.5

Figure 5.6

Figure 5.7

Without passive filters the total harmonic distortion of the current is above the range

specified by the power quality standards. To follow the recommended IEEE 519

power harmonic standards the total harmonic distortion must be less than 5%. This

34

can be obtained by connecting the passive filters to the system. For reducing the THD

below 5% passive filters have been designed. There are three filters used, two of

which are single tuned at 11th

and 13th

harmonic and the other is high pass filter for

high order harmonics. The filters specifications for each type of filter are shown in the

below:

Harmonic Order Capacitance (µF) Inductance(mH) Resistance

11th

165.1 50.71 0.04375

13th

28.5 2.1036 0.21478

Higher order 39.3 1.5535 7.4775

Table 5.2

The Q Factor for the filters is chosen to be 40. The Impedance VS Frequency curve

for the desired response is as shown in the figure 5.8

Figure 5.8

After connecting the filters the three-phase supply currents become near to sinusoidal

and harmonics are decreased below 5%. The simulation results are presented in

Figure 5.9 and 5.10 for the voltage and current on the AC side. The FFT analysis

windows of the source voltage and current are given in figure 5.11 and 5.12

respectively which shows the percentage harmonics in the spectrum with the filters

incorporated.

35

Figure 5.9

Figure 5.10

Figure 5.11

36

Figure 5.12

5.3 HARMONIC ANALYSIS OF THREE PHASE INVERTER

In this analysis, a three phase inverter supplying a three phase resistive load has been

investigated with and without passive series filters and the effects on parameters on

AC side has been analyzed with THD as an index.

The inverter model along with circuit parameters are presented in the table below:

Vdc 678V

Three Phase Load (Resistive) 53kW

Table 5.3

Figure 5.13

37

Figure 5.14

The circuit waveforms without filters for the voltage and current on AC side along

with their FFT analysis are shown respectively in the figures below:

Figure 5.15

38

Figure 5.16

When LC series filter is employed, it is observed that THD becomes less than 5% and

the waveforms become near to sinusoidal. The model is as shown in the figure. Its

waveforms along with FFT analysis are also shown.

Figure 5.17

The values of filter’s inductance and capacitance are :

Capacitance (µF) Inductance (mH)

20 10.33

39

Figure 5.18

Figure 5.19

40

Figure 5.20

Figure 5.21

41

Chapter 5

Conclusions

Thus passive harmonic filters are an effective, easy and economical option to counter

the issue of harmonics arising in small and large scale power systems or networks

involving non-linear loads. However passive filters suffer from the following

shortcomings.

More number of filters is required for mitigating more harmonic orders. This

might increase the initial capital cost.

They are characterized by sharp resonant operating points which might sometimes

cause damage to the apparatus.

Flexibility in control cannot be achieved using passive filters but on the contrary

power systems are dynamic in nature and hence there is a need for flexible and

automated control.

But nevertheless passive filters are always looked upon as a viable choice from

economical point of view. They are also found to be effective when the system is

affected by specific order harmonics to a great extent.

Moreover, while dealing with Fast Fourier Transform, we concluded that:

FFT does not allows analysis of fractional harmonics

FFT leads to incorrect results if signal contains noise or dc component of decaying

magnitude

Active harmonic filters can also be used along with passive filters as hybrid filters to

compensate the shortcomings of passive harmonic filters. They are being developed to

alleviate the disadvantage of conventional passive filters, namely:

The filtering characteristics being dependent on the source impedance

Aggravating the impedance below the lowest tuned harmonic

Being inadequate for filtering non-characteristic harmonics ( different from the

filters tuned frequency), such as those produced by cycloconverters

42

REFERENCES:

I. “Harmonics Mitigation of Industrial Power System Using Passive Filters” by

Zubair Ahmed Memon, Mehran University Research Journal of Engineering &

Technology, Volume 31, No. 2

II. “Design of Three-Phase Hybrid Active Power Filter for Compensating the

Harmonic Currents of Three-Phase System” by Zubair Ahmed Memon, Mehran

University Research Journal of Engineering & Technology, Volume 31, No. 2

III. Electric Power Quality by Surajit Chattopadhyay ,Madhuchhanda Mitra, Samarjit

Sengupta

IV. Bollen, M.H.J.: Understanding Power Quality Problems-Voltage Sags and

Interruptions. IEEE Press, NewYork (2001)

V. Electrical Power Systems Quality, by Roger C. Dugan/ Mark F.

McGranaghan/Surya Santoso, Mcgraw Hill Pulishers.

VI. Power System Harmonics (Filter Designs), George J. Wakileh

VII. Handbook of Power Quality, Angelo Baggini University of Bergamo, Italy