thesis-harmonics in buildings

MSc

ELECTRICAL POWER SYSTEMS

Dissertation

Department of Electronic & Electrical Engineering

UNIVERSITY OF BATH

DEPARTMENT OF ELECTRONIC & ELECTRICAL ENGINEERING

MSC IN ELECTRICAL POWER SYSTEMS BY DISTANCE LEARNING

DISSERTATION

STUDY OF HARMONICS IN BUILDINGS

This dissertation is submitted in accordance with the requirements of the degree of Master of Science of the University of Bath

JYOTHIMON ABRAHAM

Supervisor : Dr. Francis Robinson

September 2013

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i

Abstract

Building electrical installation uses traditional engineering methodologies and well proven

technologies to minimize safety risks and to maximize comfort of persons who are residing in

buildings. In recent years, electronic equipments like Variable Frequency Drives for motors,

UPS for Emergency type loads, other loads like SMPS based equipments, Lighting Dimmers

occupy most part of building loads. This trend necessitates for building electrical engineers to

understand problems associated with electronic equipment to ensure quality of power supply .

Harmonics are predominant power quality problem in Power Electronic loads. This study

focuses on analyzing harmonics in building loads and means to reduce the harmonics as per

widely accepted Industry standard of IEEE519.

Because of complex nature of interaction of harmonics in power system, traditional method of

manual calculation may not be practical and modeling software is required to model the system

in hand. In this study, a typical commercial bank of G+26 floors building in middle-east is

modeled in the software and results are compared with IEEE519 standard. Passive filters are

generally used to mitigate harmonics due to its low cost compared with active filters. So passive

filters are used in this study to comply with IEEE standards.

Mathematical basis of Harmonic analysis helps in deriving critical understanding of the subject

of Harmonics & related optimization of harmonic mitigation equipments. Hence a typical power

flow algorithm is constructed and implemented in General Algebraic Modeling Software

(GAMS) for a simpler two bus system. Also a compensation strategy has been devised for the

same system.

ii

Table of Contents

Abstract................................................................................................................. i

Table of Contents................................................................................................. ii

Acknowledgements.............................................................................................. V

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

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

1.2 Objectives of Dissertation............................................................................... 2

1.3 Outline of Dissertation................................................................... 2

Chapter 2 – Harmonic Phenomenon and It’s mitigation 4

2.1 Introduction............................................................................................... 5

2.2 Classification of Electrical Loads......................................................... 5

2.3 Time Domain and Frequency Domain............................................................ 6

2.4 Fourier Series Analysis........................................................... 7

2.5 Harmonic Effects on Power System........................................................... 7

2.6 Harmonic Cancellation........................................................... 8

2.7 Harmonic Distortion Indices…........................................................ 9

2.8 Displacement Power Factor…....................................................... 9

2.9 Stiff Systems and Soft Systems…....................................................... 10

2.10 IEEE Standard 519…....................................................... 11

2.11 Parallel Resonance........................................................... 12

2.12 Series Resonance........................................................... 13

2.13 Harmonic Mitigation Measures........................................................... 14

2.14 Types of Filters........................................................... 15

2.15 Filter Design & IEEE 1531........................................................... 18

iii

2.16 Conclusion 21

Chapter 3 – Building Power Systems & Electronic Loads 22

3.1 Introduction............................................................................................... 23

3.2 Classification of Electronic Loads in Buildings ............................................ 23

3.3 Variable Frequency Drives(VFD)........................................................... 24

3.4 Uninterruptable Power Supplies(UPS)........................................................... 27

3.5 Office Equipment Electronic Loads........................................................... 29

3.6 Lighting Dimmer Loads........................................................... 31

3.7 Conclusion........................................................... 33

Chapter 4 – Mathematical Modeling of Harmonics 34

4.1 Introduction............................................................................................... 35

4.2 Aims of Harmonic Modeling........................................................... 35

4.3 Budeanu’s Distortion Power Concept:......................................................... 35

4.4 Fryze’s Current Source Concept ........................................................... 37

4.5 IEEE Std 1459-2010 Method........................................................... 39

4.6 Power Factor Compensation Method................................................................. 40

4.7 Harmonic Power Flow Methodology….............................................................. 40

4.8 Harmonic Power Flow Simulation without Compensator Branch........................... 40

4.9 Harmonic Power Flow Simulation with Compensator Branch…………………

4.10 Conclusion...........................................................

46

50

Chapter 5 – Computer Simulation of a Commercial Bank Building 51

5.1 Introduction............................................................................................... 52

5.2 Description of the Case Study......................................................... 52

5.3 Load Profile Analysis........................................................... 52

5.4. Short Circuit Ratio Calculation 54

5.5. Simulation of System............................ 54

5.5.1 Transformer-1 Simulation (without & with Filter)............................... 54

5.5.2 Transformer-2 Simulation (without & with Filter)................................ 58

5.5.3 Transformer-3 Simulation (without &with Filter)............................... 62

5.5.4 Transformer-4 Simulation (without &with Filter)............................... 66

iv

5.6 Conclusion………………………………………………………………….. 70

Chapter 6 – Conclusions and Further Work 71

6.1 Final Discussion.............................................................................................. 72

6.2 Further Work ................................................................................................ 72

References 74

v

Acknowledgements

First of all, I would like to thank gracious God, for he has regarded the lowly state of his servant

and made this Dissertation a fruitful journey.

I would like to thank my Supervisor, Dr. Francis Robinson for his support and supervision. I

would like to thank him especially for his notes and lectures on Power Electronics during the last

residential, which helped me to understand the subject of harmonics better and to gain precious

insights.

I would like to thank my classmates at bath, especially Bennet Mathews for his support.

My hearty thanks to my parents and parents-in-law for their unconditional love.

Finally, I wish to thank my beloved wife, Sharmini Enoch for her patience and perseverance that

she has shown especially at troubled times. I am also grateful to our darling daughter, Joanne

Abraham and dearest son, Jason Abraham for they have filled the joy in my heart.

1

Chapter-1

Introduction

2

1. 1 Introduction

Widespread use of power electronic equipments causes harmonic distortion in building power

systems. Harmonics cause the loss of efficiency and also malfunctioning of devices. For example

it is estimated that 1% harmonic current distortion causes 2% increase in losses (half copper &

half transformer) [22]. Also utility has to suffer voltage distortion due to harmonics. Hence

various standards has been in force to mitigate harmonics in the system. This dissertation aims to

identify ways and means to tackle harmonic problem from a building electrical engineer’s

perspective.

1.2 Objectives of Dissertation

Objectives of the dissertation are divided into following parts:

1) To have an understanding of relevant methodologies to analyze harmonics in power system.

2) To design compensator for mitigation of harmonics.

3) To develop a perspective on various components used in power electronic equipment in

buildings which are major source of harmonics.

4) To derive critical understanding of mathematical modeling behind the functioning of software

used for harmonics.

1.3 Outline of Dissertation

Following the introductory chapter, the remainder of the chapters are laid out in the

chronological order that best suits the work carried out.

Chapter 2 examines harmonic phenomenon and its mitigation .Also introduces to terminologies,

standards and techniques to deal with it.

Chapter 3 deals with modern trends in power electronic loads encountered in building power

systems. Single most important buzz word is PWM (Pulse Width Modulation) which makes

waveforms look like almost sine waves. But in markets, where cost rules the days, everyday

electrical engineer has to compromise for high THD equipments and then do a system study to

keep voltage distortion to less than 5% at utility bus.

Chapter 4 presents mathematical methods underlying software analysis which is the soul of the

subject. The long searched journey of engineering community to develop a power system model

for the jumbled waveforms called harmonics and its compensation methods are investigated.

3

Harmonic power flow model for a simple power system has been developed using GAMS

software(demo version).

Chapter 5 performs the harmonic power flow analysis and its mitigation with passive filters

using Cyme PSAF(demo version) software. Many approximations like combining of several

small loads into aggregate loads has been used for keeping the model simple and yet converging

to real analysis of the system at hand.

Finally Chapter 6, concludes the dissertation, summarizing the work as a whole and giving

recommendation for further work.

4

Chapter-2

Harmonic Phenomena and Mitigation

5

2.1 Introduction

In this chapter, relevant terminologies and concepts related to harmonic phenomenon and its

mitigation are discussed in detail.

2.2 Classification of Electrical Loads:

Electrical loads can be classified into Linear and Nonlinear Electrical loads.

A linear load is one, which draws a purely sinusoidal current, when connected to a sinusoidal

voltage source, i.e., resistor, capacitor and inductors. They all have linear V-I characteristics that

results in sinusoidal current wave forms. In olden days, in building power system all the

electrical equipments connected were linear loads. Examples are transformers, electric motors

and resistive heaters.

A non linear load is one, which draws a non sinusoidal current when connected to a sinusoidal

voltage source, i.e., diode bridge, thyristor bridge etc. They all have nonlinear V-I characteristics,

that results in non sinusoidal current wave form or distorted wave form. As many power

electronic devices and loads coming into building power system in modern days, now a majority

of building loads are non linear loads.

Fig 2.1: V-I Characteristic Graph of Electronic Ballast of Fluorescent Lamp

(Source: [13])

6

2.3 Time Domain and Frequency Domain:

Time domain graphs and analysis tells us how current/voltage (amplitude, in generic terms)

changes over time.

Frequency domain graphs and analysis tells us how current/voltage changes over frequencies. In

many applications, frequency domain analysis is required.

In time domain, waveforms are jumbled over for a complex frequency waveform while in

frequency domain we can separate them into distinct frequencies, i.e., harmonic order. Fourier

transform helps in converting a time domain signal to frequency domain. Power system software

has built in functions to convert time domain to frequency domain based on Fourier transform.

Fig 2.2: Time Domain Graph (Source: [14])

Fig 2.3: Frequency Domain Graph (Source: [14])

7

2.4 Fourier Series Analysis:

Jean Baptiste Joseph Fourier while trying to solve famous “Heat Equations” come across the

“Fourier Series” [1] [2]. He stated that any periodic functions or periodic signals are constituted

by simple oscillating functions, namely sines and cosines, i.e.;

�� = �� + �� + ��

��

Or �� = �� + �� + �� + �� 2�� + �� + + �� 3�� + �� +…

Where �� = �. � ��

�� = �� !�� "# ℎ�%� � �

� = �!��& �%�'!��(

�� = )ℎ�� &�

Here ‘n’ is a multiple that represent order of frequency. Oscillating wave, that is of fundamental

frequency (f) can be separated from higher order frequency (nf) and these higher order

oscillating waves are called Harmonics.

From power system point of view, utility and customers use many nonlinear loads/sources and

these constitute distortion of voltage and current wave forms, i.e., as seen from Fourier series

above, they introduce harmonics into the electrical system. These harmonics practically do not

contribute to any usable power.

2.5 Harmonic Effects on Power System:

Not only harmonics do not contribute to useful power, but they cause distortion in voltage and

current waveform as evident from voltage and current waveforms. These distortions manifests

into following bad effects which is proven by equations and experimentation;

(i)Harmonic Distortion reduces Power Factor: we can prove that power factor is reduced due to

harmonic distortion by a factor called distortion factor.

(ii)Each characteristic harmonics flows in a particular direction.

8

Based on above facts we can analyze following problems caused by harmonics;

1. Voltage Notching in power electronic equipments

2. Erratic electronic equipment operation

4. Overheating of equipments

5. Vibrations of motors

6. Audible noise creation in transformer and rotating machines

7. Nuisance operation of circuit breaker

8. Malfunctioning of Voltage regulator

9. Malfunctioning of Generator regulator

10. Malfunctioning of Timing clock in micro processor based devices

11. Electrical Fires

2.6 Harmonic Cancellation:

It is found that harmonic distortion at individual load bus not wholly transmitted to higher buses.

But due to a combination of factors, net distortion produced by large number of distributed loads

at higher bus is significantly less than sum of individual load distortion by a factor called

“Distortion factor”. A precise formula for this factor is not possible, but varies highly on load

statistics. Various factors affecting this are outlined below.

• If single phase loads and three phase loads are connected at same voltage level, it is

found that combined harmonic distortion at bus is reduced.

• Due to phase angle diversity of different types of loads at same bus level also leads to

significant reduction in harmonics. In this case distortion factor can be as less as 0.5.For

same type of loads connected at same bus also ,cancellation occurs due to change of

various parameters between loads like impedance magnitude, x/r ratio, DC link capacitor

at loads. In this case mainly higher order harmonics are affected.

9

• In delta-star transformers 30o phase shift occurs. Result is that positive sequence

harmonics are shifted by +30o and negative sequence harmonics are shifted by -30o and

triplen harmonics are impededed by delta winding. These phase shifts cause their mutual

cancellation.

A strategic understanding at design stage on the cancellation factors helps in allocating loads at

various buses to minimize harmonic distortion to optimum at main bus.

2.7 Harmonic Distortion Indices:

IEEE 519 adopts two parameters, whose influence on power equations was proved by Alexander

Immanuel, to measure harmonic distortion.IEC 61000-2-2 also agrees with this definition [2]

[27]. First one is THDv (Total Voltage Harmonic Distortion) and second one is THDi (Total

Current Harmonic Distortion).

Voltage distortion index is defined as

THDv = .∑ 012345620� x 100% (1)

Similarly current distortion index is

THDi = .∑ 812345628� x 100% (2)

Higher harmonic order is restricted to 50 by this definition as can be seen from equations.

2.8 Displacement Power Factor

If V(t) and I(t) are periodic current wave forms, this may be expressed in Fourier series as [27];

V�t� = V� + ∑ VnCos�nwt − Ψn�∞1�� (3)

I�t� = I� + ∑ InCos�nwt − θn�∞1�� (4)

So average power PCDEFCGE = H V�t�I� I�t�dt (5)

= V�I� + ∑ 0181�∞1�� Cos�Ψn − θn�

10

(To evaluate the above integral, multiplying out infinite series we get integrals of cross product

terms are zero. Only contribution of integral comes from product of voltage and current

harmonics of same frequency).

If supply voltage contains no DC component and harmonics,

PCDEFCGE = 0K 8K � Cos�Ψ� − θ�� (6)

Now RMS value of periodic wave form for voltage is =.��I� H V��t�dtI

�

=.V�� + ∑ 0L2�∞1�� (7)

Similarly RMS value of current =.I�� + ∑ 8L2�∞1�� (8)

Definition of power factor is M0NMOPN QRSNO

�OTU 0RVIMPN��OTU WXOONYI�

=� ZK√2 �W\]�ΨK^θK�

.842_ ∑ ZL22∞L6K (10)

� ZK√2 �.842_ ∑ ZL22∞L6K

is called as Distortion Factor and Cos�Ψ� − θ�� is called as Displacement Power

factor.But THD is given by THDi = .∑ 812345628� .So Distortion factor =

�`�_�abc�2

So by measurement, when truly sinusoidal P1=V1I1(COS(Ψ1-θ1) ). But when load current is non

sinusoidal, we have to multiply by a factor called distortion factor. So original power factor is

called displacement power factor and when we multiply it with distortion factor, we get True

power factor.

2.9 Stiff Systems and Soft Systems:

A stiff load in mechanical context means a system which does not undergo any type of

interaction or deformation when we apply forces to load.

11

In Electrical context, it means stiff system is the one that is stable or it can absorb distortions

when subjected to disturbances. Magical ratio, Isc/IL which is called as short circuit ratio helps in

defining this.

Higher the value of Isc compared to IL value, lower will be the impedance, hence only lower

voltage drop at Thevinin’s impedance of system. This causes lower voltage distortion, so system

can safely absorb more harmonic current distortion. Converse is the case when Isc/IL is less.

IEEE Std.519 table 10.3 is developed based on this concept.

2.10 IEEE Standard 519:

The “Characteristic Short Circuit Ratio (Isc/Il)” determines stiffness of system. Widely accepted

harmonic standard IEEE519 uses this ratio to specify THD indices [23]. As shown in Table 1

from IEEE519, as the stiffness of system increases, it is capable of absorbing more harmonic

current. For building power systems we normally encounter soft systems whose value of

Isc/Il<20. So the total acceptable current (demand) distortion allowed stands around 5% from

table. This is defined at point of common coupling (PCC), i.e., where utility is connected to

building system.

Table 2.1: Current Distortion Limits for General Distribution Systems

(120V through 69000 V) [Source: 23]

12

Similarly IEEE519 defines voltage distortion also in Table 2.Since building power systems deal

with 11KV/415V in a typical Middle East context, acceptable value of Total Voltage Distortion

shall be less than 5%.

Table 2.2: Voltage Distortion Limits (Source : 23)

2.11 Parallel Resonance:

At parallel resonance, XL=XC at a specific frequency called resonance frequency (fp). So the

branch currents, IL and IC are equal in magnitude. Since they are 1800 out of phase with each

other, they cause the circuit to look like high impedance.

XL=XC =>2*(pi)*f*L = 1/(2*(pi)*f*C) => fp = 1/(2*(pi)*SQRT(L*C)) (11)

From fig.;

Zp = XC(XL+R)/ XC+(XL+R) ~ XL2/R ~ XC

2/R (12)

But Quality Factor (Q) is defined as Q= XL/R= XC/R & R<< XL

QXL=Q XC (13)

So the Voltage (Vp) can be defined as product of impedance (Zp) and main current (Ih),

Vp = (QXL) Ih (14)

13

Above equation shows that during parallel resonance, a small harmonic current can cause a large

“voltage drop, since it creates an open circuit condition of high impedance. This phenomenon is

called voltage magnification.

Similarly Iresonance = Vp/ XC =(QXCIh)/ XC = QIh. So current in the capacitor bank is also

magnified Q times. This phenomenon is called current magnification.

Fig 2.4: Parallel Resonance Condition (Source: [12])

In power system of buildings, this condition is created when source transformer comes in parallel

with shunt capacitor bank and harmonic injecting load comes as shown in the Fig 2.4. This

condition causes capacitor failure, fuse blowing and transformer overheat.

2.12 Series Resonance:

Fig 2.5: Series Resonance Circuitry (Source: [2])

14

At series resonant frequency, voltage across Capacitor and Inductor are equal in magnitude.

Since these voltages are 1800 out of phase with each other, they cancel out causing zero voltage

across the combination. This looks like a short during series resonance.

Ih = Vh/(XL+XC+R) & XL= -XC (15)

= Vh/R(Harmonic current flows freely in circuit only limited by

damping resistance).

So voltage across capacitor bank is given by,

Vc =( Vh/R) XC =(XC/R) Vh (16)

So voltage at power factor capacitor is magnified and is highly distorted.

2.13 Harmonic Mitigation Measures

Various measures that can be taken for reducing the effects of harmonics are given below;

1. Neutral Conductor Sizing:

As discussed earlier, harmonic currents behave like sequence currents. Triplen harmonics behave

like zero sequence currents. Hence they are flowing in neutral. Also they themselves are additive

on neutral. So the usual practice is to provide higher conductor size for neutral to accommodate

this additional current.

2. Line Reactors:

Main problem with power electronic converters is that they make the sinusoidal current wave

form discontinuous and adding line reactors at appropriate places makes line current continuous

and so harmonic distortion is reduced. Since de = 2�fg��h for reactors, it offers high impedance

to flow of higher order harmonics and so voltage distortion is reduced.

3. Capacitor based Filters:

Filters acts as sink to higher order harmonics and thus eliminates them. Main element of filter is

capacitor which provide all the harmonic current needed by the nonlinear element and so

harmonics are not flowing back to the source. Main problem is that nonlinear loads freely absorb

15

all the harmonic energy needed by it as per load conditions from filter and this may overload the

capacitor. So an inductor is added to limit the current intake as per V=Liji". In general we can say

capacitor reduces voltage distortion and inductor reduces current distortion. A resistor is also

added to the filter which acts as a damping resistor which helps in reducing value of harmonic

resonance to acceptable limits.

4. Multi pulse techniques:

It can be shown that characteristic harmonics generated by VFD equipment is reduced if the

pulse number of their converter can be increased. Simplest of three phase converter configuration

is 6-pulse.We can increase 6-pulse converters to 12- pulse by connecting two six pulse bridges in

parallel and is phase shifted to each other by 300.Limiting factor for using higher order pulse

configuration is its economic cost. In 18-pulse configurations all lower order harmonics are

eliminated. But because of rising cost of using higher order harmonics, 12-pulse is normally the

best compromise.

2.14 Types of Filters:

Filters are commonly used harmonic mitigation equipment in building power system due to its

performance and compactness. Filters can be classified into mainly passive and active types.

Types of passive filters are;

a) Series Passive Filter

b) Shunt Passive Filter

a) Series Passive Filter: Series passive filter is connected in series to the line equipment. It

eliminates only the harmonics to which it is tuned. Major disadvantage is that since it is in series,

Filter has to be rated to carry the rated load current.

16

Fig 2.6: Series Passive Filter [Source: 15]

b) Shunt Passive Filter: Shunt passive filter is connected in parallel to the bus to where

harmonics has to be eliminated. Mainly there are two types are available:

(1)Single tuned shunt filter

(2)High pass shunt filter

Fig 2.7: Single tuned shunt filter [Source: 16]

17

Fig 2.8: High Pass Shunt Filter (Source: [5])

Single tuned filters can eliminate a specific frequency to which it tuned while high pass filter

provides filtering to a corner frequency to which it is tuned and also to frequencies above this

corner frequency. Sharpness of filtering is reduced in high pass filter and so usual practice is to

use single tuned filters for lower order harmonics and high pass filter to higher order harmonics,

whose magnitudes are very less compared to fundamental frequency.

Fig 2.9: Active Filter (Source: [11])

18

DSP chips based shunt active filters can dynamically check the compensation required online

and can mitigate harmonics as per load conditions. This is done by injecting a current equal in

magnitude but opposite in phase to the harmonic current to be eliminated. Main limiting factor

for it not becoming popular as that of passive filters is that its associated high cost.

Active filters consists of mainly following components;

(1) Controller: It monitors the line current and line voltage at nonlinear load and then generates

the reference current that enable inverter to generate compensating current.

(2) Interface Reactor: It is the coupling point between non sinusoidal output of inverter and

sinusoidal voltage supply. It allows dc capacitor to be charged more than the line to line voltage

so as to maintain the inverter voltage (Vinv) as required.

(3) Voltage Source Inverter: Inverter uses capacitor as the input supply and by PWM method

(Refer Chapter 3 for detailed explanation on PWM Technique) generates high frequency signals

.Power flow mechanism reveals its action in filtering harmonics which is described below:

In active filter mechanism, we can see that IQ + IR = I0, i.e., source voltage (Vs) only delivers

active current, IR and inverter supplies reactive part of the current, IQ.Vs is leading IQ by 900

since it is the reactive current. To happen this, voltage across Lf (Vlf) must be in phase with Vs.

Also, Vinv = Vlf + Vs ,ie, what voltage source inverter required to produce the voltage which is

the scalar sum of Vlf and Vs.

Now take the case of Vinv required to for compensating 3rd harmonic at nonlinear load. Here Vs

has no component since it is producing only fundamental current.

So Vinv = Vlf = 2*(pi)*(3f)* Lf*I3

2.15 Filter Design & IEEE 1531

IEEE std1531 [24] specifies following four essential steps in filter design;

Step 1 � Determine harmonic filter bank KVAR size.

Step 2 � Select initial harmonic filter tuning.

19

Step 3 � Optimize the harmonic filter configuration to meet the harmonic guidelines.

Step 4 � Determine the component ratings.

A brief methodology as applicable to my case study on the commercial bank building is given

below:

(1) Determine harmonic filter bank KVAR size:

In a building power system, at each Point of Common Coupling (PCC) a capacitor bank is added

to improve power factor to 0.95 as per utility regulations. For all types of filters, capacitors are

essential components to reduce voltage distortion. When we design filters, we first calculate

value of capacitor bank KVAR required to improve power factor and then same value of

capacitance is added to filter element. KVAR value is found out by equation;

(2) Select initial harmonic filter tuning:

Harmonic modeling software is used for finding out dominant harmonics at PCC bus. After this,

we add combination of various types of filters tuned to required harmonic value (h) as per

percentage of THDi value to the level that we need to mitigate to. Now we can calculate

elements of filter using following general equations;

dkllkm"jnk � opqq,stsuvwxyzz (17)

d{ � | }2}2~K��yzzy��y

(18)

de � ��#2 (19)

� = de � (20)

Explanation: IEEE1531 recommends to tune the filter from approximately 3% to 15% below the

desired frequency. So it helps in sufficient filtering, along with giving sufficient allowance for

detuning of the filter.

20

(3) Optimize the harmonic filter configuration to meet the harmonic guidelines:

We can now add the filters to the given system to model in the software and see that harmonic

levels are sufficiently reduced to meet the IEEE519 standards and do the optimization of filters.

(4) Determine the component ratings:

(a) Voltage Rating:

�� = ∑ g�ℎ�∞#�� dm�ℎ� (21)

It can be split into fundamental and harmonic components;

�� = �{ �1� + �{ �ℎ� (22)

Where

�{ �1� = gl �1�d{ (23)

Where gl �1� = �s��^�q

�{�ℎ� = ∑ �z�#��#� (24)

(b) Determination of MVAR rating of filter:

��"ki = �√� ��y��2�� (25)

We can see that this value is greater than original rating of capacitor bank (at Step 1).

(c) Nominal Current Rating:

g��"ki = ��y�√� ��y� (26)

(d) Checking of the Dielectric Heating of Capacitor acceptable:

Dielectric heating can be evaluated using following inequality constraint:

�∑ ��ℎ�# g�ℎ�� ≥ |1.35��"ki| (27)

21

If this inequality is satisfied, proposed filter design is satisfactory.

2.16 Conclusion:

Harmonics are very complex phenomenon and quantification of harmonic distortion is

not an easy task. However many international standards have been developed to give

necessary guidelines for mitigation of harmonics.

22

Chapter 3

Building Power Systems & Electronic

Loads

23

3.1 Introduction

In this chapter, the classifications of the main electronic loads are made and also discussed

internal mechanisms of devices that contribute to harmonic content. Also, the modern trends in

these devices are investigated for harmonic mitigation to comply with IEC product standards.

Harmonic spectra which are used for case study is presented as well.

3.2 Classification of Electronic Loads in Buildings

For modeling building power system, we need to classify the building non linear loads based on

their harmonic spectrum. It will simplify the modeling efforts to arrive at valid conclusion since

we are dealing with numerous equipments. Main categories of building electronic loads are:

1. Variable Frequency Drives- In building, it is common to use VFD drives for almost every

motors due to reasons of energy efficiency. VFDs emit considerable harmonics.

2. UPS, Servers –For a data center application like Bank, not only critical loads but also some

essential loads coming under UPS category. However highly reliable switching mechanisms like

IGBT are used here.

3. Computers, Printers, Fax machine-These office equipments draws nonlinear current not in

significant amounts but they also adds to some amount of harmonic distortion. When thousands

of such equipments are coming into the system, it is a cause of concern and to be modeled in the

modeling software.

4. Lighting electronic ballasts-Magnetic ballasts used for lights are replaced nowadays with

electronic ballast for energy efficiency and also for dimming the lights for creating a pleasant

environment.

We will now analyze inside components of electronic loads and how these components are

responsible for harmonic distortion so that we can derive the harmonic spectrum of various

equipments.

24

3.3 Variable Frequency Drives (VFD):

Motors used in buildings have variable load requirement .At low loads, if motor runs at rated

voltage and rated speed, it is causing waste of energy. So VFDs are used, which as shown in

block diagram below has a Converter part which converts supply A.C voltage to D.C voltage, a

D.C bus(L,C elements) which stores energy and an inverter which supplies variable speed A.C

voltage to motor.

Fig 3.1 VFD Internal Details (Source: [9])

From Equations n=120f/p and V/f = k1Ø = k2T (n-desired speed of motor, V-Supply voltage, f-

supply frequency, Ø –flux level, T-desired torque, k1 &, k2 are constants) we can deduce the

following:

1. Change of speed need proportional change in frequency.

2. If frequency is changed, it affects flux, so a constant torque cannot be maintained and so to

maintain a constant torque, voltage also has to be changed proportionately. From motor load

characteristic curve, we can know how much torque is required to drive the motor at a particular

load. We will maintain this torque but at reduced speeds for low loads by increasing voltage

proportionately. Also increase in flux causes more magnetizing current and hence more iron

losses, so flux has to be kept within limits.

25

Also for starting, it has been found from current-speed curves that, if we start motor at or below

2Hz, starting current will be only 1.5 times motor rated current. If we start at 50Hz, it takes 6

times the full load current. So VFDs change the frequency to 2Hz at starting without decrease in

starting torque required, i.e., it increases voltage correspondingly.

We can see how VFD achieves variable voltage and variable frequency. There are two methods:

(1) Pulse amplitude modulation

(2) Pulse width modulation.

In Pulse amplitude modulation, to keep V/f ratio constant, magnitude of D.C bus voltage is

changed by rectifier bridge for a change in voltage and for frequency control switching of

thyristors is changed in inverter bridge. But it has many disadvantages. So widely used method

is Pulse width modulation (PWM) especially Sinusoidal pulse width modulation

(SPWM),which will be examined in detail;

Here a pulse train is generated as gating signal to inverter thyristor bridge by following method:

A comparator generates gating signals to the thyristor bridge as shown in Fig 3.2 by comparing

sinusoidal wave which is called as a reference wave (with frequency fr) and a triangular wave

(with frequency fc) which is called as a carrier wave based on desired inverter switching

frequency.

Fig 3.2 PWM Comparator Circuitry

26

Fig 3.3 PWM Wave Form Triangle Intersection Principle (Source: [9])

If we analyze the waveforms in Fig 3.3, we can understand that at intersections of Vr (Reference

voltage) and Vc (carrier voltage), pulses are generated.VAN is the output when reference

waveform is greater than triangle wave form (for positive legs of thyristor bridge conduction).

VBN is the output when reference waveform, which is shifted 180°, is greater than triangle wave

form. So VAB can be defined as VAN- VBN.

So the number of pulses per half cycle depends on carrier frequency (fr),which can be as

high as 5khz.Also pulse width varies as per amplitude of sine wave. Ratio( Vr/ Vc) is called

Modulation Index (m).By controlling m, we can control amplitude of output voltage. Maximum

value of m is 1 occurs when Vr = Vc. As the inverter output is very close to sine wave,

harmonics are minimum possible in the above configuration.

In our case study, VFDs are used for controlling various equipments like Chillers ,which consists

of major portion of the load (375kw for each chiller) and other part is for less load equipments

like Extract fans, Lifts etc categorized under MCC (motor control center). Increase of cost is a

27

major factor in obtaining less THD equipments. So a compromise between quality and cost is

considered for selecting Chiller and MCC’s of THDs mentioned in the Table 3.1.

Table 3.1 Harmonic Spectra of VFD Based Equipments

CHILLER--

>12.5%

Harmonic

Order 3 5 7 9 11 13 15 17 19

% Harmonic 0 9.3 4.9 0 5.2 4 0 1.4 1.2

MCC-->7.5%

Harmonic

Order 3 5 7 9 11 13 15 17 19

% Harmonic 0 5.6 2.9 0 3.1 2.4 0 0.9 0.7

3.4 UPS:

A block diagram of On-line UPS is shown in fig 3.4. In simplest terms, AC supply is converted

into DC which is stored in batteries through a battery charger. As needed by load, DC is inverted

back to AC and fed to load. A DSP processor stores necessary algorithm to command PWM

processing [10].

Fig 3.4 UPS Internal Block Diagram

In UPS, inverter also does the power conditioning function as well. It means inverter

supplies/consumes reactive power required to keep power factor close to unity and also to

28

control the output voltage, means inverter does power conditioning function also. This effect is

created by series inductor (jwL) which is connected in series with supply voltage (Vs)source

which then comes parallel with inverter voltage source. Vi (inverter voltage) is determined by

PWM modulation index, m and battery voltage. Inverter supplies reactive power (Vi>Vs) for

under voltage and consumes reactive power (Vi<Vs) for overvoltage situations so that voltage is

regulated within limits. Shift angle (δ) is determined by real power demanded by load as per

equation P=ViVsSin(δ)/jwL

IEC 61000-3-2 pressurizes manufacturers to reduce input harmonic currents ,so computer

related equipment manufacturers redesigned their SMPS (switch mode power supply units)

which is the integral part of computer related equipment to get at 100% load, the input current is

virtually harmonic free and power factor close to unity. These loads when work at less than

100% load lead to leading power factor scenarios. So to accommodate these leading power factor

scenarios, UPS manufacturers has redesigned inverter and filter compartments of ups to provide

a symmetrical ups capability circle diagram (ie,0.7 pf leading and 0.7 pf lagging ) as shown in

Fig 3.5.

Fig 3.5 Modern UPS Capability Diagram (Source : [17])

29

Aim of manufacturers to reduce THD to 3% to 5% and comply with standard. In our case study

scenario of 5% THD is considered and its Harmonic current spectra is given in Table 3.2

Table 3.2 Harmonic Spectra of UPS

UPS-->5%

Harmonic

Order 3 5 7 9 11 13 15 17 19

% Harmonic 0 4.4 1.7 0 1.3 0.8 0 0.6 0.6

3.5 Office Equipment Electronic Loads

Fig 3.6 Full Wave Bridge Rectifier of SMPS (Source: [18])

All electronic office equipments SMPS (Switched Mode Power Supply) as an essential

component for their operation. Main part of SMPS is a full wave bridge rectifier as shown in Fig

3.6.Capacitors which is seen in figure is used for maintaining voltage near to peak value. These

capacitors do not contribute to improvement of power factor due to action of bridge rectifier. So

power factor to remain on low, i.e., 0.7. But IEC 61000-3-2 (<16A, Class D) imposes stricter

limit on harmonics for manufacturers of these equipments. So an additional circuitry as shown in

Fig 3.7 is used for improving power factor and hence the harmonics is called as Continuous

Mode Boost Converter.

30

Fig 3.7 SMPS with PFC Circuitry (Source: [18])

As in Fig 3.7, Q1 is a MOSFET type switch, which is switched on and off continuously so that

inductor (L1) stores energy while MOSFET is on and while MOSFET is off, energy is released

so that we get a sine wave output. To make a perfect sine wave (so that voltage follows current in

a similar way), MOSFET gate signal is controlled by a PWM(Pulse Width Modulated) controller

whose mechanism can be understand from Fig 3.8.

Fig 3.8 PWM Waveform Processing (Source : [19])

To comply with IEC 61000-3-2, manufacturers are forced to reduce the harmonic THD to low

values and here an average case of THD of 2.5% is considered. Detailed Harmonic current

spectrum is given in Table 3.3.

31

Table 3.3 Harmonic Spectra of SMPS Based Equipments

COMPUTERS--

>2.5%

Harmonic

Order 3 5 7 9 11 13 15 17 19

% Harmonic 2.1 0.6 0.5 0.2 0.5 0.7 0 0.4 0.4

3.6 Lighting Dimmer Loads:

Fig 3.9 Dimmer Drive Block Diagram (Source :[20])

A block diagram of Dimmer controlled LED(light emitting diode) lighting is shown in the fig

3.9. As can be seen in the figure, a DIAC-TRIAC combination is used in the first stage to phase

cut the wave as to the desired dimming voltage. RC phase shift is used to delay triggering the

gate to cathode voltage which is fed via diac to triac gating.

This output is fed to a current driver which gives constant current to LED. Control of this

current is achieved by two ways mentioned below;

(a) Analogue Control

In analogue control, it directly controls the driver current. If for e.g., for full illumination, driver

current required is 350ma, then it is reduced to 175ma for half illumination. But colour

temperature also get changed as the driver current is reduced so causes degradation of output. So

the better strategy is another method called PWM control.

(b) PWM Control

In PWM Control, amplitude of pulses is not changed, but the width of the pulses are changed. It

means depending on capacity of human eye to integrate the average amount of light in pulses

32

hence reduce the apparent brightness. For example, for 25% of illumination, LEDs are driven

with on time of pulses equal to 25% and off time of pulses equal to 75%, i.e., LEDs do not see a

constant current, but a continuous stream of current pulses.

Harmonics are considerably reduced in PWM kind of dimming which also helps

manufactures in complying with IEC 61000-3-2 standard (<16A) of Class C equipment (since

P<25W) for recommended limits of voltage distortion of 3% to 5%.

Fig 3.10 Illustration of PWM Process in LED Drivers (Source :[20])

Considering in our case study, majority of the Dimmer loads do not follow latest PWM

technology, harmonic THD considered is high, i.e., around 7.5% and detailed Harmonic current

spectrum is given in table,

Table 3.4 Harmonic Spectra of Dimmer Drives

DIMMER--

>7.5%

Harmonic

Order 3 5 7 9 11 13 15 17 19

% Harmonic 5.6 3.4 2.6 0.8 1.7 1.3 0 0.9 0.6

33

3.7 Conclusion

Our analysis reveals that PWM in combination with high speed switching devices can eliminate

harmonics almost completely. But to restrict escalating rising cost, a cost-benefit analysis has to

be made and choose the devices with lower harmonic spectrum as practical as possible.

34

5 Chapter 4

Mathematical Modeling of

Harmonics

35

4.1 Introduction

In this chapter, mathematical aspects behind complex harmonic modeling are detailed. History of

development of harmonic power theories are mentioned. A sample HPF modeling is done using

GAMS software.

4.2 Aims of Harmonic Modeling

The major aims of harmonic modeling are the following:

1. To measure the Voltage, Watt and Current of load components including harmonic

components.

2. To find out ways to improve power factor of system.

3. To filter out undesired harmonics using various types of filters.

We can start our analysis by seeing how harmonic current is generated. When a sinusoidal

supply is given to non sinusoidal components like VFDs (i.e., nonlinear load), current gets

distorted. This distorted current causes a non sinusoidal voltage drop across Source. Thus we

infer that this is caused by a non sinusoidal voltage felt by the nonlinear load or nonlinear load is

a source of nonlinear voltage. For the simple circuit, non sinusoidal voltage follows same

harmonic spectrum as that of harmonic orders that of current.

Now the question is how we can model the complex interaction of harmonic sources and

non harmonic sources together in the system. In recent years, a well developed view on this

aspect is developed. We will analyze some of the milestones in following sections.

4.3 Budeanu’s Distortion Power Concept:

In 1927, Professor Budeanu in his book titled, “Reactive and Fictive Powers”, has come up very

first with a mathematical expression for harmonic power. He stated that apparent power consists

of three terms:

1. Active power due to fundamentals and harmonics is:

P = ∑ V�I�Cosθ�1�� (28)

2. Reactive power due to fundamentals and harmonics is:

36

Q� = ∑ V�I�Sinθ�1�� (29)

3. The reactive power interactions cause distortions in the wave form, which generated a

new type of power called “distortion power”. He developed an expression for distortion

power which is as follows:

�� = f�+ Q�� + �� (30)

� = .�� − f�− Q�� (31)

Fig 4.1 Budeanu’s Power Triangle (Source: [27])

As shown from fig 4.1, P, Qb, D are mutually orthogonal.

Disadvantages of Budeanu’s method are mentioned below:

1. Linear method of adding reactances to get total Qb led to cancellation, for e.g.,- a series

branch of equal Inductance and capacitance are connected and linear addition of these

two (QL-QC) leads to Qb value to zero. But if we think of physical phenomenon, energy is

flowing backward and forward from inductor and capacitor, i.e., oscillating not zero.

2. Even though proved based on well known mathematical formulation called Lagrange’s

identity, physical meaning of Distortion power, ’D’ is obscure and hence compensating

for this power is impossible.

37

4.4 Fryze’s Current Source Concept:

Fryze in 1932 tried another approach based on harmonic current source. He proposed following

circuit model:

Fig 4.2 Fryze’s Current Source Model (Source :[27])

As shown in fig 4.1, he divided circuit into two parallel branches, one consisting of active

current branch and other consisting of reactive current branch. He defined active branch

conductance (Gc) to the ratio of active currents to respective voltages:

�{ = j�KnK = j�}

n} … … = �2 = ��

� (32)

Similarly reactive current branch is defined as �� = j¡�"�n�"� and is represented as current source

of what is termed as ‘watt less current’, ib. This is the first time harmonic source is represented as

a current source which became a standard in later years. ia & ib are orthogonal and so can be

represented as:

� = �� + ¢� (33)

So we can write apparent power, S as:

�� = f� + �£� (34)

Where, S=VI, P=VIa & QF = VIb

38

Disadvantages of Fryze’s method are that quantity P & QF do not correspond to actual real and

reactive powers and hence does not enable to design a compensator for compensating this.

Because of this difficulty, Mr.Czarmecki (1984) modified Fryze’s current component equation to

include harmonic and non harmonic reactive components separately. His circuit model is

depicted in following Fig 4.3.

Fig 4.3 Czarmecki’s Harmonic Model (Source: [27])

He postulated that

� = �� + ¤� + �� (35)

Each term of this expression can be explained as follows:

1) ia � active component just like Fryze’s ,i.e., � = �{¥ where �{ = f ¥� ¦

�ℎ�%� f = ��¥��

2) ir � reactive current due to reactive elements ir = `∑ §�� ¥��

3) is � is the extra distortion component just like Budeanu predicted, but more fits to the

reality, i.e., is = `∑�� − �m��¥��

So power equation can be modified to:

39

�� = f� + �¤� + � � (36)

Where Ds = Uis ; Q = Uir

4.5 IEEE Std 1459-2010 Method

This method also known as Emanuel’s method as this method is proposed by Emanuel(1995)

[27] [25].He considered the Fourier series assumption that voltage source and current source can

be split into harmonic components as follows;

�� = �� + �#� & g� = g�� + g#� (37)

where

� #� = �#�#¨�

g #� = g#�#¨�

Now we can find out apparent power, S using usual formulae as follows:

S� = V�I� = �V�� + V�� I�� + I��

S� = �V�I�� + �V�I�� + �V�I�� + �V�I��

S� = S�� + D8� + D0� + S©�

Fundamental Apparent Power, S� = V�I� = `P�� + Q�� & S© = `P©� + Q©�

Non Fundamental Apparent Power, SY = `�D8� + D0� + S©� �

Where D8 is called as Current Distortion Power, DD is called as Voltage Distortion Power, S© is

called as Harmonic Apparent Power.

Since Total Harmonic Distortions, THD8 = 8ª8K & THDD = 0ª

0K , we can prove following

relationships;

D8 = S� �THD«�; D0 = S� �THD« �;�b = �� ¬��¬�j�

40

4.6 Power Factor Compensation Method

By definition Power Factor, PF = QU = QK_Qª

.UK2_U2̄

Hence we are able to arrive value of compensating power, Qc required as a result of above

methods and running a Harmonic Power Flow (HPF).So from this we may assume that a single

capacitor in parallel would be fully compensated for harmonics. But this idea suffers a drawback

because of possibility of multiple resonance points. So we are using tuned L-C branches so that

tuning is more accurate and at same time THD values are reduced.

4.7 Harmonic Power Flow Methodology

D. Xia & G.T Heydt on their classic paper [28] [29], formulated harmonic power flow for the

first time. Main idea behind it is formation of complete set of equations to describe complete

fundamental and harmonic power flow mechanisms of the system. First set of equations consists

of, as in conventional power flow, formation of fundamental power flow equations ,i.e., for n-bus

power system 2(n-1) equations are required. Second set of equations comes from Kirchoff’s

Current Law (KCL) applied to buses to solve for ‘q’ harmonic frequencies of interest,i.e.,2(n)(q)

equations. Third set of equations consists of again applying KCL but for this time running only

for harmonic producing buses ,say, ’m’ numbers and for fundamental current flow,i.e.,2m

equations. So total number of equations to solve are 2(n-1)+2(n)(q)+2m equations.

For example ,for the system shown in fig 4.4,n=3,q=1 & m=1(since only 5th harmonic source at

bus-2 is considered).so 2(n-1)+2(n)(q)+2m = 2(3-1)+2(3)(1)+2(1) =12 equations for solving

variables V��, δ��

, δ��, V��

, V��±�, δ��±�

, V��±�, δ��±�

, V��±�, δ��±�

We will now demonstrate HPF [5] [8] [21] first without compensator branch for fig 4.4 and

calculate harmonic distortion. Then we will add compensator as in Fig 4.4 and re-simulate

system for complete harmonic mitigation.

4.8 Harmonic Power Flow Simulation without Compensator Branch

Consider a simple 3-bus system as shown in Fig 4.4, whose input parameters are given below:

(all units are standard SI units and in Per Unit-PU)

41

Fig 4.4 3-Bus System for Formulation of HPF

Voltage at slack bus(1) = |V1|< Θ1 =1<0

Voltage at Bus(2) = |V2|< Θ2

Voltage at Bus(3) = |V3|< Θ3

Bus1 Shunt Impedance, z1 1 = j6 =>Shunt Admittance, y11= - j0.16

Bus1-Bus2 Line Impedance,z1 2 = j0.25 => Line Admittance,y12 = - j4

Bus2-Bus3 Line Impedance,z23 = j0.25 => Line Admittance,y11 = - j4

Total Power delivered by Non Linear Load at Bus2, Pd2 + j Qd2 = 0.6 + j 0.4

Let’s assume Nonlinear Device current at Bus-2 is given by following two equations (V-I

relationship)=>

Real Part,GF,��±� = 0.3´V��µ�Cos´3δ��µ + 0.3´V��±�µ�Cos´3δ��±�µ =K1

Imaginary Part,G«,��±� = 0.3´V��µ�Sin´3δ��µ + 0.3´V��±�µ�Sin´3δ��±�µ=K2

42

Fundamental Line Admittance Matrix (without Compensator Branch,Bus-3,ie,without applying Filter)

From KCL, considering ‘I’ sign convention arbitrarily positive and entering towards Bus;

I1 = V1 y11 + (V1-V2) y12

I2 = (V2-V1)y12

¶I�I�· = ¸y�� + y�� −y��−y�� y�� º ¶V�V�·

= ¶−j4.16 +j4+j4 −j4· ¶V�V�·

So Y-Matrix is ¶Y�� Y��Y�� Y��· = ¶−j4.16 +j4+j4 −j4·

Fundamental Power Flow Equations (without Compensator Branch,Bus-3,ie,without applying

Filter)

P« = �V«��G«« + ∑ |Y«1V«V1|Y1��1¨« Cos (Θ«1 + δ1 − δ«)

Q« = −�V«��B«« − |Y«1V«V1|Y1��1¨«

Sin(Θ«1 + δ1 − δ«) P� = 0 + |Y��V�V�|Cos(Θ�� − δ�) = 4V� Sin(δ�)

Q� = − �V��B��^|Y��V�V�|Sin(Θ�� − δ�) = +4V�� − 4V�Cos(δ�)

For conservation of Power;

P� − �PG� − PÁ� � = 0 => 4V� Sin(δ�) + 0.6 = 0

Q� − �QG� − QÁ� � = 0 => +4V�� − 4V�Cos(δ�) + 0.4 = 0

Harmonic Current Flow Equations (without Compensator Branch,Bus-3,ie,without applying

Filter)

So Y-Matrix for 5th Harmonic is ÂY��(±) Y��(±)Y��(±) Y��(±)Ã = ¶−j0.832 +j0.8+j0.8 −j0.8·

5th Harmonic Current at Bus-2, IF,�(±) + GF,�(±) = ∑ Y�,Å(±)VÆ(±)Cos´Θ�,Æ(±) + δÆ(±)µ + GF,�(±) �Æ�� (real part)

= Y21(5)V1(5)Cos ´Θ21(5) + δ1(5)µ + Y22(5)V2(5)Cos ´Θ22(5) + δ2(5)µ + Gr,2(5)

= 0.8V1(5)Cos ´90 + δ1(5)µ + 0.8V2(5)Cos ´−90 + δ2(5)µ + Gr,2(5)

43

= −0.8V�(±)Sin´δ�(±)µ + 0.8V�(±)Sin´δ�(±)µ + GF,�(±) = 0

5th Harmonic Current at Bus-2 I«,�(±) + G«,�(±) = ∑ Y�,Å(±)VÆ(±)Sin´Θ�,Æ(±) + δÆ(±)µ + G«,�(±) �Æ�� (imaginary)

= 0.8V1(5)Sin ´90 + δ1(5)µ + 0.8V2(5)Sin ´−90 + δ2(5)µ + Gi,2(5)

= 0.8V�(±)Cos´δ�(±)µ − 0.8V�(±)Cos´δ�(±)µ + G«,�(±) = 0

Fundamental Current at Bus-2 IF,�(�) + GF,�(�) = ∑ Y�,Å(�)VÆ(�)Cos´Θ�,Æ(�) + δÆ(�)µ + GF,�(�) �Æ�� (real)

= Y21(1)V1(1)Cos ´Θ21(1) + δ1(1)µ + Y22(1)V2(1)Cos ´Θ22(1) + δ2(1)µ + Gr,2(1)

= 4V1(1)Cos ´90 + δ1(1)µ + 4V2(1)Cos ´−90 + δ2(1)µ + Gr,2(1)

= −4V�(�)Sin´δ�(�)µ + 4V�(�)Sin´δ�(�)µ + GF,�(�) = 0

Fundamental Current at Bus-2 I«,�(�) + G«,�(�) = ∑ Y�,Å(�)VÆ(�)Sin´Θ�,Æ(�) + δÆ(�)µ + G«,�(�) �Æ�� (imaginary)

= 4V1(1)Sin ´90 + δ1(1)µ + 4V2(1)Sin ´−90 + δ2(1)µ + Gi,2(1)

= 4V�(�)Cos´δ�(�)µ + 4V�(�)Cos´δ�(�)µ + G«,�(�) = 0

5th Harmonic Current at Bus-1 IF,�(±) = ∑ Y�,Å(±)VÆ(±)Cos´Θ�,Æ(±) + δÆ(±)µ �Æ�� (real)

= Y12(5)V2(5)Cos ´90 + δ2(5)µ + Y11(5)V1(5)Cos ´−90 + δ1(5)µ

= −0.8V2(5)Sin ´δ2(5)µ + 0.832V1(5)Sin ´δ1(5)µ=0

5th Harmonic Current at Bus-1 I«,�(±) = ∑ Y�,Å(±)VÆ(±)Sin´Θ�,Æ(±) + δÆ(±)µ �Æ�� (imaginary)

= Y12(5)V2(5)Sin ´90 + δ2(5)µ + Y11(5)V1(5)Sin ´−90 + δ1(5)µ

= 0.8V2(5)Cos ´δ2(5)µ − 0.832V1(5)Cos ´δ1(5)µ = 0

Modified Power Flow Equations to include harmonic components(without Compensator

Branch,Bus-3,ie,without applying Filter)

P�(±) = I�(±)V�(±)Cos(δ�(±) − γ�(±))

44

= .K�� + K�� V�(±)Cos(δ�(±) − Atan |K2K1�)

F�,F(±) = Y��(±)V�(±)V�(±)Cos(Θ��(±) − δ�(±))

= 0.8V�(±)V�(±)Cos(90 − δ�(±))

= 0.8V�(±)V�(±)Sin(δ�(±))

Q�(±) = I�(±)V�(±)Sin(δ�(±) − γ�(±))

= .K�� + K�� V�(±)Sin(δ�(±) − Atan |K2K1�)

F�,«(±) = −(V�(±))�B��(±) − Y��(±)V�(±)V�(±)Sin(Θ��(±) − δ�(±))

= 0.8(V�(±))� − 0.8 V�(±)V�(±)Sin(90 − δ�(±))

= 0.8(V�(±))� − 0.8 V�(±)V�(±)Cos(δ�(±))


P�(�) + P�(±) + F�,F(�) + F�,F(±) = 0

Q�(�) + Q�(±) + F�,«(�) + F�,«(±) = 0

GAMS CODE for full system(without Compensator Branch,Bus-3,ie,without applying Filter)

VARIABLES X1,X2,X3,X4,X5,X6,Z,K1,K2;

EQUATIONS EQ1,EQ2,EQ3,EQ4,EQ5,EQ6,EQ7,EQ8,EQ9,EQ10,OBJ;

EQ1..4*X2*SIN(X1)+0.6+SQRT(SQR(K1)+SQR(K2))*COS(X5-ARCTAN(K2/K1))*X6+0.8*X6*X4*SIN(X5)=E=0;

EQ2..4*X2*X2-4*X2*COS(X1)+0.4+SQRT(SQR(K1)+SQR(K2))*SIN(X5-ARCTAN(K2/K1))*X6+0.8*X6*X6-

0.8*X6*X4*COS(X5)=E=0;

EQ3..-0.8*X4*SIN(X3)+0.8*X6*SIN(X5)+SQRT(SQR(K1)+SQR(K2))*COS(X5-ARCTAN(K2/K1))=E=0;

EQ4..0.8*X4*COS(X3)-0.8*(X6)*COS(X5)+SQRT(SQR(K1)+SQR(K2))*SIN(X5-ARCTAN(K2/K1))=E=0;

EQ5..-0.8*X6*SIN(X5)+0.832*X4*SIN(X3)=E=0;

EQ6..0.8*X6*COS(X5)-0.832*X4*COS(X3)=E=0;

EQ7.. -K1+0.3*X2*X2*X2*COS(3*X1)+0.3*SQR(X6)*COS(3*X5)=E=0;

EQ8.. -K2+0.3*X2*X2*X2*SIN(3*X1)+0.3*SQR(X6)*SIN(3*X5)=E=0;

EQ9..4*X2*SIN(X1)+(0.6*COS(X1-33.66)/(X2*COS(33.66)))=E=0;

EQ10..4-4*X2*COS(X1)+(0.6*SIN(X1-26.56)/(X2*COS(33.66)))=E=0;

45

X1.l=0;X2.l=0.9;X3.l=0.1;X4.lo=0.001;X5.l=0.1;X6.l=0.01;K2.L=.01;K1.Lo=.02;

OBJ..Z=E=0;

MODEL LPKKT1 /OBJ,EQ1,EQ2,EQ3,EQ4,EQ5,EQ6,EQ7,EQ8,EQ9,EQ10/;

SOLVE LPKKT1 USING dnlp minimizing Z;

GAMS OUTPUT for full system(without Compensator Branch,Bus-3,ie,without applying

Filter)

LOWER LEVEL UPPER MARGINAL

---- VAR X1 -INF -0.180 +INF .

---- VAR X2 -INF 0.868 +INF .

---- VAR X3 -INF -19.398 +INF .

---- VAR X4 0.001 0.140 +INF .

---- VAR X5 -INF -0.549 +INF .

---- VAR X6 -INF 0.146 +INF .

---- VAR Z -INF . +INF .

---- VAR K1 0.020 0.168 +INF .

---- VAR K2 -INF -0.107 +INF .

Distortion Calculation for full system(without Compensator Branch,Bus-3,ie,without applying

Filter)

Fundamental line current,I��(�) = (V�(�) − V�(�))y��(�) =(0.868<10.32 – 1<0)*4<90 = 0.84<-43.48

Harmonic line current, I��(±) = (V�(±) − V�(±))y��(±) = (0.1468<31.47 -0.140<-1111.98)*0.8<-90 = 0.15<-85

Current Distortion,THD8 = I12(5)I12(1) ∗ 100 = 0.15*100/0.84 = 17.85%

(From Budeanu’s method) Apparent Power,S = VI = .(V�(�))� + (V�(±))� ∗ .(I��(�))� + (I��(±))� =`(0.868)� + (0.146)� ∗ `(0.84)� + (0.15)� = 0.73

Active Fundamental Power, P2(1) = 0.6 Active Harmonic Power, P�(±) = V�(±)I�(±)Cos´Θ�(±)µ = 0.146 ∗ 0.15 ∗ Cos(−53.43) = .013

Total Active Power ,P= P�(�) + P�(±) = 0.613

46

Reactive Fundamental Power, Q2(1) = 0.4 Reactive Harmonic Power, Q�(±) = V�(±)I�(±)Sin´Θ�(±)µ = 0.146 ∗ 0.15 ∗ Sin(−53.43) = −.0175

Total Reactive Power ,Q= Q�(�) + Q�(±) = 0.3825

So Distortion Power, D = `S� − (P� + Q�) = `0.73� − (0.613� + 0.3825�) = 0.207

4.9 Harmonic Power Flow Simulation with Compensator Branch

Fundamental Line Admittance Matrix (with Compensator Branch,Bus-3,ie,with applying Filter)

Y Matrix is =ÏY�� Y�� Y��Y�� Y��Y�� Y�� Y��Y��Ð = Ï−j4.16 j4 0j4 −j80 j4 j4−j4Ð

Fundamental Power Flow Equations (with Compensator Branch,Bus-3,ie,with applying Filter)

P« = �V«��G«« + ∑ |Y«1V«V1|Y1��1¨« Cos (Θ«1 + δ1 − δ«)

Q« = −�V«��B«« − |Y«1V«V1|Y1��1¨«

Sin(Θ«1 + δ1 − δ«) P� = 0 + |Y��V�V�|Cos(Θ�� − δ�) + |Y��V�V�|Cos(Θ�� + δ� − δ�) & P� − �PG� − PÁ� � = 0

From above two equations=> 4V�Sin(δ�) − 4V�V� Sin(δ� − δ�) + 0.6 = 0

P� = 0 + |Y��V�V�|Cos(90 + δ� − δ�) & P� − �PG� − PÁ� � = 0

From above two equations=> 4V�V� Sin(δ� − δ�) = 0

Q� = − �V��B��^|Y��V�V�|Sin(Θ�� − δ�) − |Y��V�V�|Sin(Θ�� + δ� − δ�) & Q� − �QG� − QÁ� � = 0

From above two equations=>+8V�� − 4V�Cos(δ�) + 4V�V�Cos(δ� − δ�) + 0.4 = 0

Harmonic Current Flow Equations (with Compensator Branch,Bus-3,ie,with applying Filter)

So Y-Matrix for 5th Harmonic is ÑY��(±) Y��(±) Y��(±)Y��(±) Y��(±)Y��(±) Y��(±) Y��(±)Y��(±)Ò = Ï−j0.832 j0.8 0j0.8 −j1.60 j0.8 j0.8−j0.8Ð

47

5th Harmonic Current at Bus-2 IF,�(±) + GF,�(±) = ∑ Y�,Å(±)VÆ(±)Cos´Θ�,Æ(±) + δÆ(±)µ + GF,�(±) �Æ�� (real)

= Y21(5)V1(5)Cos ´Θ21(5) + δ1(5)µ + Y22(5)V2(5)Cos ´Θ22(5) + δ2(5)µ + Y23(5)V3(5)Cos ´Θ23(5) + δ3(5)µ + Gr,2(5) = −0.8V�(±)Sin´δ�(±)µ + 1.6V�(±)Sin´δ�(±)µ − 0.8V�(±)Sin´δ�(±)µ + GF,�(±) = 0

5th Harmonic Current at Bus-2 I«,�(±) + G«,�(±) = ∑ Y�,Å(±)VÆ(±)Sin´Θ�,Æ(±) + δÆ(±)µ + G«,�(±) �Æ�� (imaginary)

= 0.8V�(±)Cos´δ�(±)µ − 1.6V�(±)Cos´δ�(±)µ + 0.8V�(±)Cos´δ�(±)µ + G«,�(±) = 0

Fundamental Current at Bus-2 IF,�(�) + GF,�(�) = ∑ Y�,Å(�)VÆ(�)Cos´Θ�,Æ(�) + δÆ(�)µ + GF,�(�) �Æ�� (real)

= Y21(1)V1(1)Cos ´Θ21(1) + δ1(1)µ + Y22(1)V2(1)Cos ´Θ22(1) + δ2(1)µ + Y23(1)V3(1)Cos ´Θ23(1) + δ3(1)µ + Gr,2(1)

= −4V�(�)Sin´δ�(�)µ + 8V�(�)Sin´δ�(�)µ − 4V�(�)Sin´δ�(�)µ + GF,�(�) = 0 Fundamental Current at Bus-2 I«,�(�) + G«,�(�) = ∑ Y�,Å(�)VÆ(�)Sin´Θ�,Æ(�) + δÆ(�)µ + G«,�(�) �Æ�� (imaginary)

= Y21(1)V1(1)Sin ´Θ21(1) + δ1(1)µ + Y22(1)V2(1)Sin ´Θ22(1) + δ2(1)µ + Y23(1)V3(1)Sin ´Θ23(1) + δ3(1)µ + Gi,2(1)

= 4V�(�)Cos´δ�(�)µ + 8V�(�)Cos´δ�(�)µ + 4V�(�)Cos´δ�(�)µ + G«,�(�) = 0 5th Harmonic Current at Bus-1 IF,�(±) = ∑ Y�,Å(±)VÆ(±)Cos´Θ�,Æ(±) + δÆ(±)µ �Æ�� (real)

= Y12(5)V2(5)Cos ´90 + δ2(5)µ + Y11(5)V1(5)Cos ´−90 + δ1(5)µ

= −0.8V2(5)Sin ´δ2(5)µ + 0.832V1(5)Sin ´δ1(5)µ = 0


= Y12(5)V2(5)Sin ´90 + δ2(5)µ + Y11(5)V1(5)Sin ´−90 + δ1(5)µ

= 0.8V2(5)Cos ´δ2(5)µ − 0.832V1(5)Cos ´δ1(5)µ = 0

5th Harmonic Current at Bus-3 IF,�(±) = ∑ Y�,Å(±)VÆ(±)Cos´Θ�,Æ(±) + δÆ(±)µ �Æ�� (real)

= Y31(5)V1(5)Cos ´Θ31(5) + δ1(5)µ + Y32(5)V2(5)Cos ´Θ32(5) + δ2(5)µ + Y33(5)V3(5)Cos ´Θ33(5) + δ3(5)µ = −0.8V2(5)Sin ´δ2(5)µ + 0.8V3(5)Sin ´δ3(5)µ = 0

48


= 0.8V�(±)Cos´δ�(±)µ − 0.8V�(±)Cos´δ�(±)µ = 0

Modified Power Flow Equations to include harmonic components(with Compensator

Branch,Bus-3,ie,with applying Filter)

P�(±) = I�(±)V�(±)Cos(δ�(±) − γ�(±))

= .K�� + K�� V�(±)Cos(δ�(±) − Atan |K2K1�)

F�,F(±) = Y��(±)V�(±)V�(±)Cos(Θ��(±) − δ�(±))

= 0.8V�(±)V�(±)Cos(90 − δ�(±))

= 0.8V�(±)V�(±)Sin(δ�(±))

Q�(±) = I�(±)V�(±)Sin(δ�(±) − γ�(±))

= .K�� + K�� V�(±)Sin(δ�(±) − Atan |K2K1�)

F�,«(±) = −(V�(±))�B��(±) − Y��(±)V�(±)V�(±)Sin(Θ��(±) − δ�(±))

= 0.8(V�(±))� − 0.8 V�(±)V�(±)Sin(90 − δ�(±))

= 0.8(V�(±))� − 0.8 V�(±)V�(±)Cos(δ�(±))


P�(�) + P�(±) + F�,F(�) + F�,F(±) = 0

Q�(�) + Q�(±) + F�,«(�) + F�,«(±) = 0

GAMS CODE for full system(with Compensator Branch,Bus-3,i.e.,with applying Filter)

VARIABLES X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,K2,K1,Z;

EQUATIONS EQ1,EQ2,EQ3,EQ4,EQ5,EQ6,EQ7,EQ8,EQ9,EQ10,EQ11,EQ12,EQ13,EQ14,OBJ;

EQ1.. 4*X2*Sin(X1)-4*X2*X4*Sin(X3-X1)+SQRT(SQR(K1)+SQR(K2))*COS(X7-ARCTAN(K2/K1))*X8-0.8*X8*X6*SIN(X5-X7)-

0.8*X8*X10*SIN(X9-X7)=e= -0.6;

EQ2.. -(4*X2*X4*SIN(X1-X3))=e= 0;

49

EQ3.. 8*SQR(X2)-4*X2*COS(X1)-4*X2*X4*COS(X3-X1)+SQRT(SQR(K1)+SQR(K2))*SIN(X7-

ARCTAN(K2/K1))*X8+0.8*X8*X6*COS(X5-X7)+0.8*X8*X10*COS(X9-X7)=e= -0.4;

EQ4.. 4*X4*X4-4*X2*X4*COS(X1-X3)=e=0.15;

EQ5..-0.8*X6*SIN(X5)+1.6*X8*SIN(X7)-0.8*X10*SIN(X9)+SQRT(SQR(K1)+SQR(K2))*COS(X7-ARCTAN(K2/K1))=e= 0;

EQ6..0.8*X6*COS(X5)-1.6*X8*COS(X7)+0.8*X10*COS(X9)+SQRT(SQR(K1)+SQR(K2))*SIN(X7-ARCTAN(K2/K1))=e= 0;

EQ7..0.832*X6*SIN(X5)-0.8*X8*SIN(X7)=E=0;

EQ8..-0.832*X6*COS(X5)+0.8*X8*COS(X7)=E=0;

EQ9..-0.8*X8*SIN(X7)+0.8*X10*SIN(X9)=E=0;

EQ10..0.8*X8*COS(X7)-0.8*X10*COS(X9)=E=0;

EQ11..-K1+0.3*X2*X2*X2*COS(3*X1)+0.3*SQR(X8)*COS(3*X7)=E=0;

EQ12.. -K2+0.3*X2*X2*X2*SIN(3*X1)+0.3*SQR(X8)*SIN(3*X7)=E=0;

EQ13..8*X2*SIN(X1)-4*X4*SIN(X3)+(0.6*COS(X1-33.66)/(X2*COS(33.66)))=E=0;

EQ14..4+8*X2*COS(X1)-4*X4*COS(X3)+(0.6*SIN(X1-26.56)/(X2*COS(33.66)))=E=0;

X1.l=0;X2.l=0.9;X3.l=0;X4.l=0.9;X4.up=1.0;X5.l=0;X6.lo=0.0001;X7.l=0;X8.lo=0.0001;X9.l=0;X10.lo=0.0001;K1.L=.2;K2.L=0.001;

OBJ.. Z =E= 0;

MODEL LPKKT /OBJ,EQ1,EQ2,EQ3,EQ4,EQ5,EQ6,EQ7,EQ8,EQ9,EQ10,EQ11,EQ12,EQ13,EQ14/;

SOLVE LPKKT USING dnlp minimizing Z;

GAMS OUTPUT for full system(with Compensator Branch,Bus-3,ie,with applying Filter)

LOWER LEVEL UPPER MARGINAL

---- VAR X1 -INF -0.164 +INF .

---- VAR X2 -INF 0.917 +INF .

---- VAR X3 -INF -0.164 +INF .

---- VAR X4 -INF 0.956 1.000 .

---- VAR X5 -INF -2.064 +INF .

---- VAR X6 1.0000E-4 1.0000E-4 +INF 0.021

---- VAR X7 -INF -2.064 +INF .

---- VAR X8 1.0000E-4 1.0400E-4 +INF .

---- VAR X9 -INF -2.064 +INF .

---- VAR X10 1.0000E-4 1.0400E-4 +INF .

---- VAR K2 -INF -0.109 +INF .

---- VAR K1 -INF 0.204 +INF .

50

---- VAR Z -INF . +INF .

We can see that after applying improvement compensator, Voltage at nonlinear bus significantly

improved due to power factor improvement. During simulation, Capacitor MVAR value

increased gradually and at one point, harmonic voltages are seen diminishing to negligible value

and so distortion to negligible value. Hence compensator improves power factor as well mitigate

harmonics.

4.10 Conclusion

We have seen the historical development of harmonic power flow theory. Simulation done for

sample system with compensator and also without compensator prove that compensator addition

mitigates harmonics.

51

6

7

8

9

10 Chapter 5

Simulation of a Commercial Bank Building

52

5.1 Introduction

In this chapter, we will analyze load profile of a typical high rise bank building of 25 floors and

to be modeled in the harmonic modeling software. Where ever at the point of common coupling

(PCC), harmonic distortion stipulated by IEEE 519 exceeds, we will go for Filter design as per

IEEE 1531.

5.2 Description of the Case Study

Case study for this project consists of a Commercial Bank installation at Middle East. This is a

twenty five floors building (Ground floor + 24 floors). There are four step down transformers

(11KV/415V) each of capacity 1500 KVA feeding directly from utility. All transformers are

located at ground floor transformer room. Bus duct risers are connecting various floor level

panels to ground floor transformers. Chillers which consists of major portion of building, is

located at roof floor. Since this is a bank, to ensure high reliability of supply, essential loads have

a generator backup. Server loads and other critical loads are connected through UPS’s located at

various floors. Some of the lighting is controlled through dimmers partly attributed to green

energy drive and partly due to attracting of customers by creating various light scenes.

5.3 Load Profile Analysis:

Total connected load (TCL) of the building is 5200KW.Detailed break-up of the type of loads

are given in following table:

Table 5.1 Connected Load Schedule

Sl. No. Category KW

1 Chiller 1500

2 MCC 800

3 UPS 630

4 Dimmer 495

5 Computer, Printer, Fax Machine 630

6 Linear Loads 1145

TOTAL 5200

53

It has been found out that 77% Loads are Non Linear Loads and only 23% are Linear Loads. A

detailed pie chart will give a more visual picture of the scenario as in Fig 5.1.

Fig 5.1 Building Load Profile

Fig 5.2 Single Line Diagram of the Building

29%

15%

12%

10%

12%

22%

LOAD PROFILE OF BUILDING

1 Chiller 2 MCC 3 UPS 4 Dimmer 5 Computer 6 Linear

54

There are four transformers as can be seen from SLD(Fig 5.2) feeding from utility. Detailed load

break-up of each transformer are given in simulation section below.

5.4 Short Circuit Ratio Calculation

Transformers used are of rating 1500 KVA with a percentage impedance of 5.75%.Utilty

impedance can be taken as small compared to Transformer Impedance.

Full Load Current of Transformer,IV = �±�� Ó ��√� Ó Ô�± = 2089.2 Amps

Short Circuit Current, IUW = 8×%Ù = ��ÚÛ.�

±.Ü± = 36335 Amps

Short Circuit Ratio, 8ÝÞ 8× = �ß��±

��ÚÛ.� = 17.39 < 20

So as per IEEE 519, Table 10.3 Total Harmonic distortion allowed is 5%.

5.5 Simulation of System

Let us start simulation of system in modeling software-Inputs and outputs are given below

beginning from Transformer-1;

5.5.1 Transformer-1 Simulation (Without & With Filter)

Table 5.2 Transformer-1 Loading Details

Sl.

No

Type of Load KW

rating

KVAR rating KVA rating Power

Factor

1 CHILLER-1 375 282 470 0.80

2 MCC-1 100 61 120 0.85

3 DIMMER-1 220 136 260 0.85

4 COMPUTER LOADS-1 330 255 420 0.79

5 LINEAR LOADS 250 120 280 0.9

6 CAPACITOR BANK - 500 - -

7 TRANSFORMER LOADING AFTER P.F CORRECTION (based on N-R Power Flow)

1275 450 1350 0.94

55

Power factor at Bus feeding has improved from 0.79 to 0.94 after using 500 KVAR capacitor

bank.

Now running Harmonic Power Flow for Transformer-1, we get THD values at Transformer-1

bus-They are THDI = 13.6% &THDV = 5.53%.

Detailed break-up of Resultant harmonic spectrum at Transformer bus is given as below:

Fig 5.3 Harmonic Model at Transformer-1

Table 5.3 Harmonic THD Values for Transformer-1 Before Applying Filter

180Hz 300Hz 420Hz 540Hz 660Hz 780Hz 1020Hz 1140Hz Total

THDI(%) 0 10.15 6.32 0 1.5 0.9 0.24 0.18 13.6

THDV(%) 1.68 4.47 3.57 .07 1.13 0.69 0.19 0.14 5.53

56

Fig 5.4 Transformer-1 harmonics Current versus Frequency

Fig 5.5 Transformer-1 harmonics Voltage versus Frequency

Impedance scan analysis shows Parallel resonance at 420Hz as in fig 5.6 below:

Fig 5.6 Transformer-1 harmonics Impedance versus Frequency

57

Since current and voltage distortions exceeds 5% suggested by IEEE519,we go for filtering

bearing in mind to use minimum amount of filtering to reduce costs;

Fig 5.7 Harmonic Model at Transformer-1 With Filter

Fig 5.8 Transformer-1 harmonics Impedance versus Frequency After Filter

As shown in Fig 5.7, we apply 5th and 7th harmonic filter by dividing filter MVARs in the

approximate ratio of 60:40. As can be seen from Fig 5.7, distortion values reduced to THDI =

1.67% & THDV = 2.22% which is below the acceptable value of 5%. Harmonic resonance also

has come down to acceptable values as shown in Fig 5.8.

58



Sl. No Type of Load KW rating KVAR rating KVA rating Power

Factor

1 CHILLER-2 750 464 880 0.85

2 MCC-2 200 124 240 0.85

3 DIMMER-2 100 62 120 0.85

4 COMPUTER LOADS-2

100 48 110 0.90

5 LINEAR LOADS 150 73 170 0.90

6 CAPACITOR BANK

- 350 - -


1300 510 1410 0.93


bank. When running Harmonic Power Flow for Transformer-2, we get THD values at

Transformer-2 bus-They are THDI = 21.6% &THDV = 8.42%.

Detailed break-up of Resultant harmonic spectrum at Transformer bus is given below:



THDI(%) 0 13.6 17.8 0 0.15 0.4 0.24 0.22 21.6

THDV(%) 0.84 5.25 7.59 0.01 0.02 0.36 0.31 0.32 8.42

59



60


Impedance scan analysis shows Parallel resonance at 420Hz as in diagram below;


61


Fig 5.14 Transformer-2 harmonics Impedance versus Frequency With Filter

As shown in fig 5.13 ,we apply 5th and 7th harmonic filter by dividing filter MVARs in the

approximate ratio of 50:50 .As can be seen from fig 5.13, distortion values reduced to THDI =

4.34% &THDV = 3.10% which is below the acceptable value of 5%. Harmonic resonance also

has come down to acceptable values as shown in fig 5.14.

62

5.5.3 Transformer-3 Simulation (Without & with Filter)


Sl. No Type of Load KW rating KVAR rating KVA rating Power

Factor

1 MCC-3 400 120 420 0.95

2 UPS 630 305 700 0.90

3 DIMMER-3 50 31 60 0.85

4 LINEAR LOADS 220 106 240 0.90

5 CAPACITOR BANK

- 275 - -


1300 380 1360 0.96


bank.

Now running Harmonic Power Flow for Transformer-3,we get THD values at Transformer-2


Detailed break-up of Resultant harmonic spectrum at Transformer bus is given as below:



THDI(%) 0 7.45 3.63 0 0.14 0.17 0.15 0.15 8.80

THDV(%) 0.40 3.27 2.24 0.01 0.01 0.17 0.21 0.23 3.97

63



64



65



As shown in Fig 5.19, we apply 5th harmonic filter by replacing power factor capacitor. As can

be seen from Fig 5.19, distortion values reduced to THDI = 1.89% & THDV = 2% which is below

the acceptable value of 5%. Harmonic resonance also has come down to acceptable values as

shown in Fig 5.20.

66



Sl.

No

Type of Load KW rating KVAR rating KVA rating Power

Factor

1 CHILLER-3 400 232 460 0.86

2 MCC-4 100 61 120 0.85

3 DIMMER-4 125 77 150 0.85

4 COMPUTER LOADS-3

200 97 220 0.90

5 LINEAR LOADS 500 242 560 0.90

6 CAPACITOR BANK

- 300 - -


1325 460 1400 0.95


bank.

Now running Harmonic Power Flow for Transformer-3, we get THD values at Transformer-2


Detailed break-up of Resultant harmonic spectrum at Transformer bus is given below:

67



68





THDI(%) 0 6.60 1.69 0 3.74 1.53 0.29 0.20 8.36

THDV(%) 1.38 3.05 0.82 0.06 2.67 1.27 0.29 0.20 4.07

69


Fig 5.26 Transformer-4 harmonics Impedence versus Frequency After Filter

70

As shown in Fig 5.25, we apply 5th harmonic filter by replacing power factor capacitor. The

distortion values reduced to THDI = 2.35% &THDV = 2.45% which is below the acceptable value

of 5%. Harmonic resonance also has come down to acceptable values as per Fig 5.26.

5.6 Conclusion

Results of simulation show that in building power systems dominant harmonics are 5th and 7th.

So widely used filters are single tuned 5th and 7th order filters. It is found that higher order

harmonics are not very dominant and also they get partially removed by 5th and 7th order filters

and overall results comply with IEEE519.Hence considering cost reduction aspects, high pass

filters for eliminating higher order harmonics not considered.

71

Chapter 6

Conclusions and Further Work

72

6.1 Final Discussion

This dissertation investigated the methods of quantification of harmonics so as to develop

models for harmonic study. Further analysis of these models helped in ways for mitigation of

harmonics like use of passive filters.

Main findings of this dissertation can be summarised as follows;

1. Harmonics can be quantified by two main indices, THDv and THDi . IEEE519 imposes limits

on harmonics based on these parameters.

2. Series resonances and Parallel resonances occurs in circuits and causes voltage and current

amplification, hence damage to equipments. But this can be limited to low values by careful

design of filters and its Q value.

3.Pulse Width Modulation(PWM) based technologies reduces THD (Total Harmonic Distortion)

levels to minimum possible levels but with an increase in cost factor.

4.In Buildings, nonlinear loads occupy significant portion of total loads and involves many

smaller loads. So we have to aggregate the smaller loads in groups in a way to preserve their

phase angle identities. Larger loads can be modelled individually.

5.Active Filters and Passive filters are widely used in the mitigation of harmonics. For buildings,

passive filters are normally used owing to cost factor. Design of passive filters should comply to

IEEE1531.A filter tuned for a particular harmonic can ward off also neighbouring harmonics to

some extent. This property is used for minimization of number of filters.

6.Power flow mechanisms of harmonic loads is a very complex process. Simulation done for an

example 3-bus system reveals this process.

6.2 Further Works

Doing a Harmonic Power Flow simulation , opens up for an inquisitive learner many areas of further

research on compensator design and its optimization.

Lagrange multiplier technique [7][26] of optimization is most widely used since we are dealing with

nonlinear system of equations. Basic idea behind it can be outlined as follows;

73

1. Formation of Objectives : Our aim is negotiating a trade-off between Cost of Filter and

Harmonic Distortion reduction. So our objectives are two folds, first one for minimising

cost of filter(i.e. Minimize Filter Cost Function, say C(U) since cost varies as a function

of filter MVAR value, U).Second one is with introduction of a penalty function, value of

which is small when THD value is away from its limit(as per IEEE519) and larger when

THD value is close to its limit, i.e., Cp(THD).So we get our objective as [26]=>C(U)+

Cp(THD).

2. Formation of Constraints : As we are bounded by power flow mechanisms happening

inside the system, we have two constraints best describes this. one is Harmonic Power

Flow Equations, i.e., F(v,U)=0 and other is THD mechanism (as we know THD is ratio

of Harmonic voltage/current to Fundamental voltage/current) described by THD =g(v).

3. Formation of Lagrange Equations : by combining equations of (1) &(2) steps, and

adding Lagrange multiplier, we get; [26]

L�v, U, THD, λ, µ� = ��¥� + �f�¬�� + λF�v, U� + µ�THD − g�v��

(Note-we have to expand as per system, each term of equation

for eg- λF�v, U� = äλ� λ�å ÂF�v��, U�F�v��, U�Ã)

4. Solution of this will iteratively give the best value of ‘U’ of the filter.

74

References

75

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[3] R.C. Dugan, M.F. Mc Granaghan, S Santoso, H.W Beaty, Electrical Power Systems Quality: Mc Graw Hill,2004

[4] Angelo Baggini, Handbook of Power Quality : John Wiley & Sons Ltd,2008

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thesis-harmonics in buildings

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