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Abstract—With the increase in sensitive modern electrical

equipment, harmonics as a disturbance in power systems have

become increasingly problematic. Harmonics, defined as the

undesirable frequency components that are integer multiples of a

fundamental in the supplied voltage, rise from proliferation of

non-linear circuit elements such as computers, variable

frequency drives, and rectifiers. In power systems, harmonics

destabilize the supplied voltages and increase the power

consumption of the loads, both of which are detrimental to power

quality. This paper aims to explore the common sources of

harmonics, the impacts of harmonics to loads, and the possible

mitigation measures to improve power quality.

Index Terms—Non-linear Circuits, Power Quality, Power

Systems, Power System Harmonics, Power Transmission

I. INTRODUCTION

any power quality problems such as equipment

overheating, microprocessor malfunctioning, and

variable speed drive misfiring are caused by harmonic effects.

Harmonic distortions not only affect power quality in today’s

sensitive electromagnetic environment, but also increase

unnecessary power losses. The remaining part of this paper

will explain what harmonics are, what power quality is, the

effect of harmonics on power quality, and several ways to

eliminate harmonics.

II. HARMONICS

A. Definition

AC voltage, like any time domain signal, can be represented

mathematically by a summation of different frequency

components using the Fourier Transform [1]. In North

America, voltage supplied to loads is ideally consisted only of

a 60 Hz component; the very same frequency it is generated at

the source. Since neither the generation nor the consumption

of power is perfectly sinusoidal; voltage in power systems is

prone to distortions known as harmonics. As noise

superimposed on a fundamental component, harmonics add

many smaller, but faster waveforms at integer multiples of the

fundamental frequency as the following:

This paper is submitted on April 1, 2015.

All authors are full-time students of the University of British Columbia,

2329 West Mall, BC Canada V6T 1Z4. (e-mail: zhi.qu@alumni.ubc.ca)

where

f(t) is the time domain function

n is the harmonic number (integer)

An is the amplitude of the nth harmonic component

T is the length of one cycle in seconds

Figure A shows the time-domain waveform of a pure 60 Hz

voltage with an amplitude of 120V rms and a harmonic at 300

Hz (fifth harmonic) with one-fifth of the amplitude. If both

signals were to exist in the same power system

simultaneously; superposition of the two would result in

Figure B. Although the resultant of the two is still periodic, it

is no longer purely sinusoidal with 60Hz.

B. Sources of Harmonics

Harmonics in power systems are mainly caused by non-

Harmonics and Power Quality

Zhi Qu, Ty Li, Vincent Chen, Rebecca Dong, Chengcheng Zhu

EECE 392 Students, University of British Columbia

M

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linear loads [1]. Although all electrical equipment posses some

kind of nonlinearity, most of their effects can be safely

neglected. However, the same cannot be said with loads like

transistors, MOSFETs, and transformers. Unlike linear loads,

which draw currents either in or out of phase with the supplied

voltage, non-linear loads draw currents in abrupt pulses [2].

For example, currents in modern digital circuit elements like

DC/DC choppers are in square waves, which contain odd

multiples of the fundamental frequency like the following

figure:

In other words, voltage drops in linear devices are merely

scaled version of the supplied voltage, whereas non-linear

devices draw currents in a non-sinusoidal fashion that is

neither in phase nor at the same frequency as the source. Some

examples of devices that cause harmonics include:

1) Variable speed drives(VFDs)

2) Computers

3) PWM drivers

4) Switch mode power supplies

5) DC/DC choppers

III. POWER QUALITY

A. Definition

Power quality can be viewed as a compatibility factor

between the power grid and the end users. The higher quality

means the system is more compatible, in other words the

failure rate of the system is lower. Voltage frequency/phase

synchronization is crucial to optimize the performance of an

electrical system, in other words the power quality.[3]

Common parameters used to measure power quality includes

the continuity of power, harmonic distortion level, and power

factor.

Continuity of service is the most basic parameter of power

quality. Sporadic voltage causes many problems to both the

consumer’s electrical equipment and the power grid. When the

electrical equipment receives power that is on and off

spontaneously, the loss of performance and life of the

equipment is inevitable.

Harmonic distortion level defines the degrees of deviation

between a harmonic wave from a pure sinusoidal wave. It is

dependent on the power source and the non-linear load system

it contains. When this deviation gets noticeably significant, the

compatibility between the power grid and the consumers drops

and ultimately decreases power quality.

Power factor is also extremely important when evaluating

power quality. It measures the effectiveness of how electrical

equipment converts current to useful power output. BC hydro

recommends maintaining system power factor at 90 percent

lagging or better and adds surcharge to consumers who do not

maintain a power factor of 90 percent. [4] In other words,

power factor has to be greater than 90 percent in order to

ensure the power quality.

B. Ways to Improve Power Quality

Power quality determines the compatibility of electric

power to consumer devices. Synchronization of the voltage,

frequency and phase allows electrical systems to function in

their intended manner without significant loss of performance

or life. An effective way to improve power quality is by

modifying the non-linear load such as the adjustable frequency

drive(AFD). Some basic additional add-ons on AFD are listed

as following.

Broadband filters allow a substantial higher percentage

AFD load than other modifications. It increases input

protection, and also optimize system power factor correction.

Despite all the advantages they have, they are considered

fairly costly when compared with other solutions.

Line Reactors, on the other hand, are relatively low cost,

and can achieve moderate reduction in voltage and current

harmonics. They also provide input protection for AFD but are

considerably less optimal when compared with more

expensive solutions like broadband filters.

Series Active Filter is the one and only means to cancel

harmonics from the 2nd to the 51st. It provides VAR currents,

improves system power factor and, most importantly, has no

series connection which means easy installation with no major

system rework.

IV. EFFECT OF HARMONICS ON POWER QUALITY

A. Cause of Harmonics in Power System

When a sinusoidal voltage is applied to linear loads, the

current drawn by the load is proportional to the voltage and

impedance and follows the envelope of the voltage waveform.

Linear loads are loads in which voltage and current follow one

another without any distortion to their sinusoidal behaviour.

Resistive heaters, incandescent lamps, and constant speed

induction and synchronous motors are examples of linear

loads.

On the other hand, most loads are nonlinear, and the

waveforms of their current and voltage are not purely

sinusoidal. Waveforms in non-linear loads are about 60Hz and

contain numerous additional waveforms of other frequencies

superimposed upon it. The multiple frequencies are harmonics

of the fundamental. Examples of nonlinear loads are battery

chargers, electronic ballasts, and variable frequency

drives(VFDs).

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B. Effects of Harmonics on Electrical Equipment

1) Motor

Harmonic current causes audible noise and vibration in a

motor due to the frequency deviation. It also produces

resultant flux between the rotor and the air gap, which causes

cogging or slipping in induction motors [5]. The alternating

magnetic field contributes to iron losses such as eddy current

and hysteresis losses in motor cores. These losses are directly

proportional to frequency which ultimately relates back to the

harmonics. [6] In conclusion, power losses will increase due to

harmonic voltage and currents in numerous ways.

2) Transformer

Transformer have similar reactions to motors under

harmonic effects. The non-sinusoidal excitation voltage

increases current in the magnetic core the same way it does in

a motor [6]. Eddy currents are induced by the leakage

magnetic field and represent a more serious effect of harmonic

loads served by transformers. Eddy current losses increases

with respect to the square of the current and the square of its

frequency. As a result, transformer’s operational temperature

gets significantly affected and the life expectancy gets

reduced. [7]

3) Capacitor Banks

In a power system filled by large voltage and current

harmonics, the rated voltage and reactive power are frequently

exceeded. Capacitor banks act like a sink, attracting harmonic

currents and then become overloaded. [6] The combination of

harmonics and capacitor banks equates to a serious power

quality problem called harmonic resonance. Resonance exists

in series or parallel, one amplifies voltage and the other

amplifies current. In a harmonic rich atmosphere, both types

are present. As a result, life expectancy of the capacitor banks

gets significantly reduced.

4) Cables

The flow of current in a cable produces power losses and

current distortion. The effective resistance of the cable is

proportional with frequency due to skin effect. It is important

to make sure a cable is rated for proper current flow because

both fundamental and harmonic current can flow in the

conductor simultaneously. [5]

V. ELIMINATION OF HARMONICS

In three phase systems, while it is impossible to eliminate

harmonics thoroughly due to the large amount of existing non-

linear loads; many steps could be taken to diminish their

effects. There are two main ways of eliminating harmonics,

including the use of phase-shifting transformers and the use of

external compensation circuits. [8] Other methods include

using separated oversized neutral conductors, current limiting

reactors, and special meters. [9]

The most commonly used way of eliminating harmonics is

to use different types of transformers. Delta-wye connected

transformers could reduce harmonics by shifting the phase by

30 degrees, trapping all the triplen harmonics (third, ninth,

fifteenth, etc.) in addition to the naturally eliminated even

harmonics (second, fourth, sixth, etc.).[9] Wye-wye zigzag

connection produces output which is the vector sum of two

phases offset by 120 degrees,[10] thus it could also help to

eliminate the triplen harmonics, plus the 5th and 7th

harmonics.[11] Separated oversized neutral conductors are

commonly used in transmission lines to eliminate the neutral

harmonics. Since the neutral point is not connected in this type

of conductors, there would be no harmonics current generated

on the circuit neutrals. However, this would result in an

increase the copper use by 33% [9], which would significantly

increase the cost and size of the transmission lines. Current

limiting reactors are widely used in motor circuits since they

limit the maximum current flowing in the circuit, which helps

to prevent the circuit from overheating and reduce the

generation of harmonics.

Harmonics could be hardly noticed since standard current

meters are only sensitive to 60 Hz current. To better

investigate in harmonics, special devices are used to sense

current up to the kHz range.[9] Different types of filters are

then made accordingly to eliminate the harmonics with

specific range. Most of the filters being used today are passive

filters, while the use of active filters is becoming more

popular. [8] Specifically, tuned filter, which is achieved by

connecting series RLC circuit, could be used to filter out one

particular harmonic.[8] Damped filter, on the other hand,

filters out a range of harmonics, but has higher loss in the

resistor and reactor.[8] Nonetheless, filters of all types are

expensive and should be avoided if possible.[8]

Indeed, the best way to reduce the influence of harmonics is

to improve the technology used in industrial production. For

instance, multilevel inverters are currently used for high-

power high-voltage applications to reduce the harmonics.[10]

Electronic companies are working together with transmission

companies to seek ways in producing low harmonics

computers, solving the problem from the source.

VI. CONCLUSION

Harmonics have a great impact on power systems and affect

the quality of power delivered to motors, transformers,

capacitor banks, and cables significantly. The effect only

becomes more apparent due to the proliferation of modern

electronic equipment. Commonly used methods of eliminating

harmonics are costly; therefore, better ways to eliminate the

harmonics still need to be developed to maintain the stability

of the entire power system.

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[2] N. Edomah. (2009, June 11). Effects of Voltage Sags, Swell and Other Disturbances on Electrical Equipment and Their Economic

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[6] Yepyep. (August 22, 2011). Effects of Harmonics on Motors and Generators. [Online]. Available:

http://www.powerqualityworld.com/2011/08/effects-harmonics-motors-

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[8] J. Arrillaga, N. R. Watson. (2003). Power System Harmonics. (second edition)

[9] M. Martin. Two Modern Power Quality Issues - Harmonics and

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[10] A.M. Trzynadlowski. (2010). Introduction to Modern Power Electronics.

[11] W.N. Dale. (March 15, 2012). The Effects of Harmonics in Power Systems and Methods to Reduce or Eliminate Them. [Online]. Available: http://www.cvaieee.org/html/past/120315_harmonics.pdf