Electric Pow uality: A Tutorial lntro

G.T. HEYDT Arizona Sfufe University

Electric power quality is an aspect of power engineering tha t has been with us since the inception of power systems; however, topics in power quality have risen to the forefront since the advent of high power semi- conductor switches and networking of transmission and subtransmission systems. Also, the trends in modern power engineering have been t o extract the most from the existing installed system, and this too has placed stress on issues of sinusoidal waveform fidelity, absence of high and low voltage condi t ions, and other ac waveform distortion.

What exactly is power quality? This is a quest ion with no fully accepted answer, bu t sure ly t h e response involves the waveforms of current and voltage in an ac system, the presence of harmonic signals in bus voltages and load currents, the presence of spikes and momentary low voltages, and other issues of dis- tortion. Perhaps the best definition of power quality is the provision of volt- ages and system design so that the user of electric power can utilize elec- tric energy from the distribution sys- tem successfully, without interference or interruption. A broad definition of power quality borders on system reli- ability, dielectric selection in equip- ment and conductors , long-term outages, voltage unbalance in three- phase systems, power electronics and their interface with the electric power supply, and many other areas. A nar- rower definition focuses on issues of waveform distortion.

One reason for the renewed inter- est in power quality at the distribu- t ion level is tha t t h e e r a of deregulation has brought questions of how electric services might be unbundled and compared from one provider to another. It is possible to

provide additional services to some cus tomers on an opt ional basis , and t o charge for those services. Perhaps several competing distrib- ution companies might base their competition on the level of power quality provided. This is an evolv- ing area. Also, modern power engi- neering is frequently cost-to-benefit ratio driven. Power quality indices often provide ways to measure the level of electrical service and the benefits of upgrading the supply cir- cu i t s . These a reas have brought focus to power quality as evidenced by several new textbooks in t h e area, one magazine, several confer- ences, and a number of programs and departments in electric utility companies’ infrastructures.

Types of Power Quality Problems The main classifications of power quality problems are steady state and transients. Table 1 contains a list of commonly encountered power quali- ty problems.

Harmonics Harmonics are integer multiples of a fundamental frequency of a peri- odic process. If a periodic voltage u(t) of period T is resolved into a Fourier series,

N

v(t) = a, +E ai cos(ici),t + (pi> i =I

individual te rms in t h e sum a r e called harmonics , and a. is a d c term. Sometimes the Fourier series is written as a double-sided sum, and that form is equivalent to the indicat- ed form. Also, there are exponential and rectangular forms of the sum. The fundamental frequency is related to the period T by

2n O - T

ci) --

Some engineers, in analyzing ape-

riodic (nonrepeating) signals have encountered signal components that are not integer multiples of the fun- damental, and these have been called fractional or interharmonics.

The main issues in electric power quality relating to harmonics have been:

Harmonic power flow study. This is a software tool to analyze how harmonics propagate in electric power systems. The method is Newton-Raphson based. Injection current analysis. This is a software technique for the analy- sis of the effects of injecting har- monic signals into power systems. Losses. Losses in magnetic devices (machines, transformers) depend on the harmonics present. The accurate analysis is rather com- plex, and various methods and standards exist for this purpose. Fractional and interharmonics. These signals are not truly har- monics in the Fourier sense, how- ever noninteger multiples of the power frequency d o exist in power systems as a result of asyn- chronous switching, nonlinear effects, and aperiodicity. Probabilistic methods of analysis. Some researchers have proposed to analyze the probability of the occurrence of harmonics. Instrumentation and power. Issues of bandwidth, dynamic range, effects of the interaction of volt- age and current creating power (and react ive power), and t h e standardization of methods have been a point of focus in power quality engineering. A main reason for interest in har-

monics is the presence of nonsinu- soidal voltages and currents in solid s ta te switched circuits. For exam- ple , t h e s ix-pulse th ree -phase Graetz bridge rectifier produces current harmonics on the load side, and these harmonics propagate in the distribution network. A p pulse bridge produces harmonics of the

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Ringing waves (decaying oscillarory)

Three phase JllbalanCe, neuirai currents

Noise

order np 1 where n = O,l,Z, ... in the ideal case. The details of these har- monics depend on the rectifier delay angle, the inductance of the supply circuit , t he d c rectifier load, and other circuit parameters. Other com- mon sources of periodic, nonsinu- soidal signals, and hence harmonics, are adjustable speed drives, invert- ers, and compact fluorescent lamps.

Transients Transients are signals with a finite Ofe, that is, a transient dies to zero in a finite time. Examples of transients a r e impulses caused by lightning s t rokes o r switching. Frequency based analysis has been common since Fourier’s time; however, fre- quency analysis is not ideally suited for transient analysis, because Fourier (frequency) based analysis is based on the sine and cosine functions, which are not transients. This results in a very wide frequency spectrum in the analysis of transients. A solution to the problem is to appeal to the use of transients to analyze transients. As an example, consider the usual Fouri- er transform of a voltage v(Q,

< +-

. . .. . . .

Transient A transient high frequenoy Capaccor swiiching, InrJsli current. (e 9.. -17” harmon%) transformer energi7ation shunt capacitors

Steady Power ireqtiency Three-ph&se systems Unbalanced load. improp- state er ground, unbal-

TransicnV High frequenc es present In many ac systcms Improper ground steady state

__ .- -

a w e d volrage supply .- . -. -. -. . __ .. - __

I V ( 0 ) + - Jv ( t ) e -wt fi --

Notchcs in Steady High frequencies prcscnt sindsoiaal wavc 1 state

The spectrum of ~CO) , the Fourier transform of u(t), shows the frequen-

. .. - .. - . . ... Due to switching of I rdm ive circuits Lasing solid state switches

Adjustable speed drives

cy spectrum (i.e., the component fre- quencies present) in the voltage u(f]. Analysis of a wide bandwidth using Fourier transforms entails consider- able calculation because the analysis must be carried out over a very wide range of frequencies. However, one may use t ransients in t h e defini- t i o n of t h e in t eg ra l t r a n s f o r m ; such is the case in the use of the wavelet transform,

+m

V(a,b) = .f(a)J v(t)w(a,b,t)dt. -c-z

In th i s t ransform, t h e t ran- sient voltage u ( f ) is resolved into its component wavelets denoted w(n,b,f) in t he inte- gral. The terms a and b repre- sent the dilation r time scale factor of t he wavelet, and b represents the shift, or where the wavelet is located in time. The term f(a] is a scale factor. A wavelet is a transient itself as seen in Figure 1. A wavelet is a mathematical funct ion tha t is a transient with spe- cialized oscil latory proper- t ies. The wavelet spectrum

the literature of the area is rich on the selection of the “mother wavelet,” how wavelets are applied, and how they are calculated. This is a new area, and software and valid results have not been commercialized fully.

Power Quality Indices Several indices are in common use f o r t h e quantification of electric power quality. These indices are con- venient for condensing complex time and frequency domain waveform phenomena into a single number. The power acceptability curves have

C 8 L

C b

0 4 -

-1 0 -5 0 5 10

Of is Often more narrow p e ‘-

t r u m g a nd is easier using wavelets. The re a r e many candidate wavelets, and

Figure 1. A Wavelet. The Horizontalscale is time and may be scaled further by a ‘dilation factor’ denoted as ‘a’. The wavelet is centeredatzero here, butmay be shifted by some parameter, b. The vertical scale is the function value ofthe wavelet w (a, b, tj.

a n e f r e q u e

16 IEEE Computer Applications in Power

I CBEMA Power Acceptability Curve

also been used as convenient mea- sures of power. The most common of t h e power quali ty i n d i c e s a r e s h o w n in Table 2 . These indices have the general properties that they

The power acceptability curves are loci of bus voltage deviation ver- sus disturbance time. Figure 2 is a typical power acceptability curve. The interior of the curve represents

IlK Power Acceptability Curve

a region of acceptable power service; that is, disturbances of a particular AlVl and duration time are plotted on the curve, and, if the plotted point falls in the region sufficiently close to

W z 5 9 m 3 m z W s 4

i5 5

0 c

0

a

TIME IN SECONDS TIME IN SECONDS

Figure 2. The CBEMA and ITIC power acceptability curves

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t h e Ab k 0 (i .e. , no b u s v o l t a g e d i s tu rbance ) and sufficiently s h o r t dis turbance t ime, the disturbance is assumed to be “ac- c e p t a b 1 e. ” Sever a1 different power ac- ceptability curves have evolved in IEEE, t h e United States military, and in private industry (e.g., the Computer Business Equipment Manufacturers Asso- ciation, CBEMA), but none were truly scientifically gener- ated in the sense that they were cre- ated from the theory of power distur- bances. Instead, the

Figure 3. Power quality instmments: a pictorial

power accept- ability curves were generated by experience gathered by a commit- tee. The questions of the validity of the curves, their use in power distri- bution assessment, and their appro- pr ia teness for different types of loads a r e largely unknown and uncorrelated to actual field evalua- t ions of d i s tu rbances . Also, t h e application of the power acceptabili- ty curves for the three-phase case has not been fully studied. Despite t h e s e sho r t comings , t h e power acceptability curves (especially the

curve promoted by CBEMA) have been widely used for a range of loads. Recently, the CBEMA curve was modi- fied to reflect encouragement of com- puter equipment to accommodate a wider range of supply voltages and the capabilities of modern instrumenta- tion. The CBEMA curve, and its succes- sor t he Information Technology Industry Council (ITIC) curve are shown in Figure 2. The upper locus (labeled overvoltage condition) refers to the upper limit of acceptable bus voltage; above this locus, one has ‘unacceptable power’ due to high volt-

age. The lower locus is labeled under- voltage condition, and this refers to low voltage at the load (i.e., a sag); this locus is the lower limit of acceptable bus voltage. Note that the term accept- able power in this context refers to a qualitative condition of bus voltages in a range that makes the delivered power useable. In this sense the power is acceptable. The upper right and lower right in both the ITIC and CBEMA curves are the unacceptable region. Unfortunately, there is no generic way to define power accept- ability curves that are applicable to all

18 IEEE Computer Applications in Power

load types, and both single and three phase. Nonetheless, the curves are widely used.

Instrumentation and Sensors There a r e many instrumentat ion techniques applied to power quality, as illustrated in Figure 3. The present status of power quality instruments is summarized in Table 3. In this table, the bandwidth, dynamic range, harmonic frequency measurement limits, and typical primary sensors are indicated. Of course, there is a distinct difference between laborato- ry instruments and field, dedicated instruments.

Standards of Electric Power Quality There are many national and interna-

tional s tandards of electric power quality. Two main standards are:

IEEE Standard 1100, “Recommend- ed prac t ice for powering and grounding sensi t ive electronic equipment,” (Emerald book), IEEE Standards, 1992. IEEE Standard 519-1992, “IEEE Rec- ommended Practices and Require- ments f o r Harmonic Control in Electric Power Systems,” IEEE Standards, 1992.

For Further Reading G.T. Heydt, Electric Power Quality, Second edition, Stars in a Circle Publications, Scottsdale, AZ 1995.

W. Shepherd, P. Zand, Energy Flow and Power Factor in Nonsinusoidal Circuits, Cambridge University Press, Cambridge, England, 1985.

J. Arrillaga, D. Bradley, P. Bodger, Power System Harmonics, John Wiley, Chichester, UK, 1985.

A.P.S. Meliopoulos, Power System Grounding and Transients, Marcel Dekker, New York, 1988.

R. Dugan, W. Beatty, M. McCranaghan, Electrical Power Systems Quality, McCraw Hill, New York, 1996.

Biography Gerald Thomas Meydt is the director of the ACEPS Power Quality Center at Ari- zona State University, Tempe, Arizona. He has a BSEE degree from Cooper Union, New York, and MSEE and PhD degrees from Purdue University, West Lafayette, Indiana. He is a registered professional engineer in New Jersey and Indiana, and he is an IEEE Fellow. He may be reached by E-mail, heydtOenuxsa. eas.asu.edu.

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