psh 1 harmonics

POWER SYSTEM

HARMONICS

Prof.Dr. Aydoğan ÖZDEMİR

İstanbul Technical University

Faculty of Electrial-Electronics Engineering

Department of Electrical Engineering

[email protected]ü.edu.tr

REFERENCES

1. Power System Harmonics: fundamentals, analysis, and filter design , George

J.Wakileh, Springer Verlag Press, 2001

2. Power Quality in Electrical Machines and Power Systems, Ewald

F.Fuchs,Mohommad A.S.Masoum, Elsevier Academic Press, 2008

3. Power systems harmonics : computer modelling and analysis, Enrique Acha,

Wiley, c2001.

4. Power Quality in Electrical Systems, Alexander Kusko, Marc T.Thompson,

McGraw Hill P.C., 2007

5.Power quality, C. Sankaran, CRC Press, c2002

6.Harmonics and Power Systems, Francisco C. De La Rosa, CRC Press, 2006

7.Electrical Power Systems Quality, Roger C.Dugan, Mark F. McGranagham,

Surya Santoso, H.Bayne Beaty, McGraw Hill P.C., 2002

REFERENCES-Cont.

8. Power System Analysis: Short Circuit, Load Flow and Harmonics, J.C.Das,

2002

9. Handbook of Power Quality, Edited by Angelo Baggini, John Willey, 2008.

10. Power System Harmonics, J.Arrilaga, D.A.Bradley, P.S.Jodger, John Willey

and Sons, 1985.

11. Power System Harmonic Analysis, Jos Arrillaga, Bruce C Smith, 2000

2012-2013 Fall Term Grading Policy:

Homeworks : 30%

Term Project : 30%

Final : 40%

POWER SYSTEM HARMONICS - OUTLINE

OUTLINE

1. POWER QUALITY AND HARMONICS

1.1. Introduction

1.2. Power Quality Problems

1.3. Fundamentals of Harmonics

2. HARMONIC ANALYSIS

2.1 Basic Concepts

2.2 Fourier Series and Fourier Coefficients

2.3 Finite Interval Functions

2.4 Complex Form of Fourier Series

2.5 The Fourier Transform

2.6 Discrete Fourier Transform (DFT) Fast Fourier Transform (FFT)

2.7 Fast Fourier Transform (FFT)

2.8 Window functions


3. FUNDAMENTALS OF HARMONICS

3.1 Phase Sequence Characteristics of Harmonics in Power Systems

3.2 Measurements of Harmonic Distortion

3.3 Active and Reactive Power

3.4 Current and Voltage Crest Factors

3.5 Telephone Interference and the IT Product

3.6 Power in Passive Elements

3.7 Calculation of Distortion

3.8 Resonance

3.8.1 Series Resonance

3.8.2 Parallel Resonance

3.9 Capacitor Banks and Power Factor Improvement

3.10 Bus Voltage Rise and the Resonance


4. HARMONICS IN POWER SYSTEMS

4.1 Sources of Harmonics

4.2 Transformers, rotating machines, arc furnaces, fluorescant lamps

4.3 Static VAR Compensators

4.4 Cycloconvertors

4.5 Single Phase Controlled Rectifiers

4.6 Three Phase Power Convertors

5. EFFECTS OF HARMONIC DISTORTION ON

POWER SYSTEMS

5.1. Thermal Losses

5.2 Harmonic Effects on Power System Equipment

5.3 Capacitor Banks

5.4 Transformers and Rotating Machines

5.5 Protection, Communication and Electronic Equipment


6. MITIGATION OF POWER SYSTEM HARMONICS

6.1 Passive Harmonic Filters

6.2 Power Convertors

6.3 Transformers and Rotating Machines

6.4 Capacitor Banks

6.5 Harmonic Filter Design

6.6 Active Filters

8. MODELING OF POWER SYSTEM

COMPONENTS FOR HARMONIC ANALYSIS

9. POWER SYSTEM HARMONIC STUDIES

7. STANDARDS FOR THE LIMITATION AND

CONTROL OF POWER SYSTEM HARMONICS

I. POWER QUALITY AND HARMONICS


1.1. Introduction

Electrical energy is the most convenient form of energy from the point

of generation, transformation, transmission, consumption, control and

environmental aspects.

The dependence of modern life upon the continuous supply of

electrical energy makes system reliability and power quality issues of

upmost importance in electric power system area.

It can either be generated from fossil and nuclear sources as well as

from renewable sources as hydraulic, wind, solar, biogas etc.

Its voltage level is increased at generation point for the sake of less

losses, transmitted either as AC or DC, voltage level is decreased and

distributed to the load centers.


Power system comprises generators, transformers, transmission and

distribution lines and the loads. It can be represented by R, L, C

networks.

Power Quality is generally used to express the quality of the voltage.

This quality signifies the deviation of the voltage magnitude and

frequency from the rated values and the deviation of the waveform

from a pure sinusoid.

That is, variation of the voltage magnitude, outages, impulses, flicker,

inclusion of DC component, variation of the frequency, unbalances in

3-phase systems can be defined as power quality problems.

Power quality can be defined at an arbitrary point of the system.

However, it is more important at the consumption side.

Power quality problems are created by auxiliary sources, (lightning),

non-linear circuit components (saturated transformer) or non-linear

loads (Rectifier).


1.2. Power Quality Problems Power quality problems encompasses a wide range of different phenomena.

General steps that are often followed in power quality problems is as follows.

Identify PQ Problem Disturbance, Unbalance,

Distortion, Voltage Fluctuation/Flicker

Problem

Characaterization Measurements/Data collection

Causes, Characteristics, Equipment Impacts

Identify Range of

Solutions Transmission, Distribution, End user,

Equipment/design

EvaluateSolutions

Optimum Solution

Modeling/Analaysis Procedures

Evaluate Economics of Possible Solutions


1.2 Power Quality Problems – Cont.

Power quality problems

Disturbances,

Unbalances

Distortions

Voltage Fluctuations and Flicker


1.2.1 Disturbances

A disturbance is a temporary deviation from a steady-state waveform caused by

the faults of brief duration or by sudden changes in power systems.

Voltage Dips (Voltage Sags) : A voltage dip is a sudden reduction (between

10% and 90%) of the voltage lasting for 0.5 cycle to several seconds. Dips with

durations of less than a half cycle are regarded as transients. Switching

operations and the flow of heavy currents (energization of large loads which

require high starting currents) are the basic sources of voltage dips. Their effects

are: extinction of discharge lamps, incorrect operation of control devices, speed

variation of motors, tripping of contactors, communication failure in line

commutated inverters.

Td > 0.5 T


Brief Interruptions (brief outages):

A brief interruption can be considered as a voltage dip with 100% magnitude

lasting at least one period. Blown fuses and breaker tripping are the basic

sources of brief outages.


Brief Voltage Increases (swells):

They are brief increases in r.m.s. Voltages. Non-symmetric short circuits and load rejections are the basic sources of voltage swells. They can upset electric controls and motor drives, they can cause extra stresses upon sensitive computer components and shorten their lives.


Transients:

Voltage disturbances shorter than sags and swells are called as transients.

Switching transients resulting from switching operations in the network.

Impulse transients are the results of atmospheric phenomena and their duration

is less than switching transients.

1

Switching transient

impulse transient


Voltage Notches

They are periodic transients occurring as a result of the phase to phase short

circuits caused by the commutation process in AC-DC converters. They may

upset electronic equipments and damage inductive components. Voltage notches

can also be classified as voltage distortions.


Frequency Changes

Temporary frequency increases and decreases are generally caused by switching

operations if the regulators are not good enough to hold the frequency.


1.2.2 Unbalances

An unbalance is a situation in which either the voltages of a three phase system

are not equal in magnitude or the phase differences between them are not 120

degrees or both. The degree of unbalance is usually defined by the proportion

of negative or zero sequence component to the positive-sequence component.

They are caused by unbalanced loadings and single phase loads. It may also be

the result of blown fuses in one phase of a three-phase capacitor banks.


1.2.3 Distortion (Harmonics)

Waveform distortion is defined as a steady-state deviation from an ideal sine

wave of power frequency. It is an indication of harmonics, which are

sinusoidal signals having frequencies that are integer multiples of the

fundamental frequency at which the system is designed to operate.

)5(*5.0)3(*7.0)()( wtCoswtCoswtCostx

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

0 0.005 0.01 0.015 0.02 0.025

Cos (wt)

0.7*Cos (3wt)

0.5*Cos(5wt)

x(t)


The frequencies those are not the integer multiples of the fundamental

frequency are termed interharmonics.

Both the harmonic and the interharmonic distortion are generally caused by the

equipment having non-linear voltage-current characteristics.

Noise, defined as unwanted electrical signals with broadband spectral content

lower than 200 kHz is also another kind of distortions. They are generally

generated by PE devices, control circuits, arcing equipment etc.

The main effects of harmonics are :

- Additional thermal losses in capacitors, transformers and rotating machines

- Insulation stress because of increased voltage,

- Additional losses

- Telephone interference

- Maloperation of control devices, mains signaling systems and protective

relays.


Main solutions to keep the harmonic distortion within the recommended levels

are:

- The use of high pulse rectification

- Passive filter

- Active filters and conditioners

The harmonic sources can be grouped into three main categories with respect to

their origin, size and predictivibility

- Small and predictable : Single phase converter fed power supplies, gas

discharge lamps.

- Large and random : Arc furnaces

- Large and predictable : Large power converters.


1.2.4 Voltage Fluctuation and Flicker

Voltage fluctuation is defined repetitive (systematic) variations of the voltage

envelope or random variations in the magnitude of the supply voltage. The

magnitudes of these variations do not usually exceed 10% of the nominal

supply voltage. However, small magnitude changes occurring at particular

frequencies can give rise to an effect called lamp flicker. Actually, voltage

fluctuation is an electromagnetic phenomenon while flicker is an undesirable

result of the voltage fluctuation in some loads.

The defining characteristics of voltage fluctuations are:

The amplitude of voltage change (difference of maximum and minimum rms

or peak voltage value occurring during the disturbance);

The number of voltage changes over a specified unit of time; and

The consequential effects (such as flicker) of voltage changes associated with

the disturbances.


Voltage fluctuations can be classified into three-broad categories:

Step voltage changes, regular and irregular in time. Fluctuations produced by

welding machines, rolling mills and mine winders are of this type.

Cyclic or random voltage changes produced by corresponding variations in

the load impedance. (Arc furnace load)

Flicker is the impression of fluctuating luminance or color occurring when the

frequency of the variation of the light stimulus lies between a few hertz and the

fusion frequency of images. Flicker varies person to person and depends on

many factors. Flicker is essentially a measure of how annoying the fluctuation

in luminance is to the human eye.


Step voltage changes

Cyclic or random voltage variations

factor modulation :m

frequency modulation :

frequencyangular lfundamenta :

)(*)(*1)(

m

o

om

w

w

twCostwCosmVtv


In an ideal power system, electrical energy is supplied at a single and constant

frequency and at specified voltage levels of constant magnitude. The problem

of voltage and frequency deviations and the means of keeping them under

control are the concerns of conventional power system analysis.

The problem of waveform distortion is the problem of this course. Waveform

distortion is an indication of existence of harmonic frequency frequencies.

Actually, it is not a new phenomenon. Harmonics have existed in power

systems for many years. The recent growing concern on the subject is because

of :

increasing numbers and power ratings of highly non-linear power electronic

devices seeking higher system reliability and effectiveness,

increased use of capacitor banks to improve power factors.

1.3 Fundamentals of Harmonics


The deviation from perfect sinusoid is generally expresssed in terms of

harmonic components. The cause of harmonics can simply be stated as the

existence of non-linear components loads).

Linear loads are those in which voltage and current signals follow one another

very closely, such as the voltage drop that develops across a constant resistance,

which varies as a direct function of the current that passes through it.

Resistive linear elements: Incandescent lighting, electric heaters

Inductive linear elements: Induction motors, Current limiting reactors,

Induction generators (wind mills), Damping reactors used to attenuate

harmonics, Tuning reactors in harmonic filters

Capacitive linear elements: Power factor correction capacitor banks, •

Underground cables, Insulated cables,Capacitors used in harmonic filters


Nonlinear loads are the loads in which the current waveform does not resemble the

applied voltage waveform due to a number of reasons. For example, the use of

electronic switches that conduct load current only during a fraction of the power

frequency period. Therefore, we can conceive nonlinear loads as those in which

Ohm’s law cannot describe the relation between V and I.

The most common nonlinear loads in power systems are all types of rectifying

devices like those found in power converters, power sources, uninterruptible power

supply (UPS) units, and arc devices like electric furnaces and fluorescent lamps.

Power electronics: ARC devices

• Power converters Fluorescent lighting

• Variable frequency drives ARC furnaces

• DC motor controllers Welding machines

• Cycloconverters

• Cranes and Elevators

• Steel mills

• Power supplies

• UPS and • Battery chargers

• Inverters


V-I characteristics of a typical nonlinear component and the associated current and

voltages are given in the following figure.

-1

0

1

-1 0 1Angle

An

gle

Current

Voltage

Voltage Waveform

Current Waveform

Load Line


Even some linear loads like power transformers can act as nonlinear components

under saturation conditions. Assume a load supplied through a transformer.

i1 R

v1

Φ, B, H

i2

v2 load


Neglect the fringing fluxes and assume that the input voltage and the current be

pure sinusoids.

terms.harmonic include

willand sinusoids pure benot willdt

(t))(

and)(* (t)ly Consequent

region. saturated at the operateser transformthe

that assuming signal, sinusoidal pure benot will)(

)(H)(

)( with alproportion be will)(

)(I)(

V)(

2

1

1

1

11

111

11

dtv

tBSectionCross

tB

wtCostH

titH

wtCosti

wtCostv


In simple systems, harmonic problems can be analyzed using a spreadsheet.

Harmonic analysis software are further available to analyze large systems.

Those harmonic analysis software performs harmonic load flows. A harmonic

load flow study calculates fundamental and harmonic line currents (line flows)

and bus voltages. The outcomes of individual solutions are later used for the

design of filters.

A harmonic study for an industrial plant will require the following information.

Utility short-circuit capacity and X/R ratio at the concerned bus.

Distribution transformer MVA rating, X/R ratio and percentage impedance.

Voltage and MVAr rating of existing PF correction capacitors.

Measurements of the harmonic source currents.


Having known the above information, harmonic impedance can be computed for

the different components and at the different locations of the system. Bus harmonic

voltages, line harmonic currents and distortion factors can than be calculated. The

resulting quantities can be compared with the limits imposed in the standard.


EXAMPLE

A Diode rectifier drives a quasi-square current of 10 A (peak value) from a

three-phase 11 kV, 50 Hz busbar feeder to a factory. The load is a star-

connected inductive load with RL = 180 Ohm, LL = 0.3 H. A star-connected

capacitance of 1.75 mF is used for power factor correction at the same bus. The

11 kV busbars are fed from an 132 kV/11 kV , 800 kVA transformer having an

equivalent impedance of Zt = 0.01 + j 0.06 pu. The short circuit impedance of

132 kV system is 0.005 + j 0.02 pu.

Sketch the diagram of the system and determine the harmonic current and

voltage levels up to 23rd order harmonic.


Equivalent circuit


Base of 800 kVA,

relating the per unit

values to 11 kV

The Base

Impedance 25.1518.0

112

Transformer

Impedance

075.9,5125.1

075.95125.106.001.025.151

TT

TT

XR

jXRjj

System

Impedance

025.3,75625.0

025.375625.002.0005.025.151

SS

SS

XR

jXRjj

Load

Reactance 25.943.0502 jxjX L

Capacitive

Reactance

1819

1075.1502

116

jxxj

XC

C

At 50Hz.

At 50Hz.

At 50Hz.

At 50Hz.


Inspection of the waveform shows that there are no cosine terms, no even

harmonics, and that there is quarter-wave symmetry

6

cos4

sin4

2

6

n

n

IwtnwtdIbn

...

17

17sin

13

13sin

11

11sin

7

7sin

5

5sinsin103.1

wtwtwtwtwtwtIiThe series is:

The value for each harmonic is An

xn

xIn

8.7

2

3

2

104

5th 1.56A ; 7th 1.11A ; 11th 0.709 A ; 13th 0.600A, 17th 0.459 A ; 19th 0.410 A


Equivalent circuit for fundamental frequency

HARMONICS

ZT IS

IC IL

IR

ZS ZL ZC

VB

VS

VA


HARMONICS

AIkVV RB 8.7,351.63/11

AjjZ

VI

AjjZ

VI

C

BC

L

BL

49.31819

3/11000

5.1469.2725.94180

3/11000

AjIIII RCLS 01.1149.35

VjjV

VjZIVV

VjZIVV

HVS

SSAS

TSBA

7.4080.78610)73.40881.6550(*11/132

73.40881.6550*

69.3096490*


Equivalent circuit for each harmonic

Rectifier may be considered as a harmonic generator

HARMONICS


At above figure, the current IR divides into the three parallel arms of the circuit. Given three parallel impedances, Z1, Z2, and Z3, the current I1flowing in Z1 is given by

currenttotalxZZZZZZ

ZZ

213132

32

To calculate the 5th harmonic values, frequency=250Hz, n=5, IR=1.56A.

Impedance of the capacitance arm = -j1819/5 = Z1

Impedance of the load arm = 180 + j5(94.25) = Z2

Impedance of the supply arm = (1.5125+0.75625) + j(5(9.075+3.025) = Z3


Current in the capacitor =

.2.1752735.056.1213132

32 AxZZZZZZ

ZZ o

By like calculation, the load current =

.1.161973.0 AI o

L

And the supply current =

.7.26443.1 AI o

S

HARMONICS


Harmonic phase voltage at the 11kV busbars =

= VB = ICXC/5 = 0.2735 x 363.5 = 99.5V.

Harmonic phase voltage at the 132kV terminals =

= VS = 1.6443[0.756252 + (3.025 * 5)2]1/2 * 132/11 = 298.8V.

HARMONICS


The components for the other harmonics are calculated in a

similar manner. The values, together with those for the

fundamental (50Hz) frequency, are shown below.

HARMONICS

n 1 5 7 11 13 17 19 23

f [Hz] 50 250 350 550 650 850 950 1150

IR [A] 7.80 1.56 1.11 0.71 0.60 0.46 0.41 0.34

IC [A] 3.49 0.27 0.46 1.77 20.50 1.11 0.77 0.50

IL [A] 31.26 0.20 0.17 0.28 2.32 0.07 0.04 0.02

IS [A] 37.16 1.64 1.40 2.20 18.23 0.58 0.32 0.14

VB [kV] 6.498 0.996 0.119 0.293 2.868 0.119 0.0740 0.040

VS-HV [kV] 78.76 0.299 0.356 0.880 8.605 0.356 0.222 0.118

psh 1 harmonics

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