IEEE-Digital Measurement of Voltage Flicker

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IEEE Transactions on Power Delivery, Vol. 6, No. 4, October 1991 1593

DIGITAL MEASUREMENT OF VOLTAGE FLICKERKrishnaswamy Srinivasan, Senior Member IEEEIRE Q-Hydro Quebec, 1800Montee SteJ ulie, Varennes, QuBbec, J 3X 1S1, Canada.

ABSTRACTQuality of power is of prime concern to power companies. Thispaper deals with cyclic variations in the envelope of voltage

waveforms. The Europeanpower utilities have done a substantialwork already in its characterization, based on he effects on visualperception. They have also established a norm for the calculationof an instantaneous flicker level, a short-term severity coefficient,and a long-term severity coefficient. The measurement techniques,that they propose, are basically designed for analoginstrumentation. It can be readily seen that digitalimplementations of the analog design are neither cost effective noroptimal in performance. This paper proposes a method for directcalculation of flicker level from digital measurements of voltagewaveforms. Results based on simulated data indicate that theproposed approach yields sufficiently accurate results for 1024pointFFTwith 480Hz. sampling using a 12 bit A/D.Thus a valueof instantaneous flicker level canbe obtained every 2.13 seconds.Ke y Words: Flicker, Power, Voltage,Pruned,Fourier transform.In t roduct ion

The electric power utilities are now in a maturity stage, with theeconomic operation and the quality of power receiving the primeconsideration[l]. One of the degradations in quality is the slowand repetitive (1 Hz. to 30 Hz.) variation of the rms voltage. Thisis referred to as flicker[2,3]. Even when the variation is within therecommended limits, its cyclical nature may lead to problems.Flicker afects the starting torque, slip, starting current,temperature rise and overload capacity of motors and generators.Flicker reduces the life of electronic. incandescent, fluorescent andCRT devices. Electronic controllers are likely to misbehaveduring voltage variations. Flicker influences visual perception oflight.

High power loads, with sudden changes in load demand are oneof the chief sources of flicker. Some such loads are reciprocatingpumps, c o m ~ e s s o r s . utomatic spot-welders, arc welders, elevatormotors and other types of variable loads. Their propagationcharacteristics are similar to the voltage sags and swells. Flickerhas usually been quanwied on the basis of human visualirritation[4]. Efforts have been ma& by many organizations toobtain a weighting function, which is the combined effect of threefactors:

(a)@)(c) typeof voltage fluctuation.human eye's response to lightcharacteristics of the luminescent device

91 WM 087-7 PWRDby the IEEE Transmission and Distribution Committeeof the IEEE Power Engineering Society for presentationat the I E E E / P E S 1991 Winter Meeting, New York, NewYork, February 3, 1991. Manuscript submittedFebruary 13, 1990; made available for printingNovember 30, 1990.

A paper recommended and approved

One such weighting curve (figure 2) has been standardized bythe Union Tntemationale dklectrothermie[6](m). onventionalflicker-meters[5] apply the frequency weighting curve as a Fiter onthe rms voltage signal. The signal resulting after squaring andsmoothingis referred to as the instantaneous flicker level.

A Short-term flicker severity coefficient FST, has also beenproposed by UIk, ased on the fact that a higher level of flickercan be tolerated for a shorter period of time and vice versa. Thiscoefficient is obtained from the distribution function of theinstantaneous flicker level (IFL) over typically ten minuteintervals. The formula proposed (1) is the square root of theweighted sum of five values of instantaneous flicker on thedistribution function curve.FST = 4 ( 0 . 03 1 4 F 0 . 1 + 0 . 0 5 2 5 F 1 . 0

+ 0.0657 F 3 . 0 + 0 . 2 8 F1o + 0 . 0 8 F50) (1)whereFo 1Fl .F3FloF,,

=IFL.that is exceeded during0.1%of the time=IFL. hat is exceeded during 1O% of the time=IFL, hat is exceeded during3.0%of the time=IFL. that is exceeded during 10%of the time=IFL, that is exceeded during 50% of the time

TimeFig 1. A typical voltage flicker

Frequency in Hz. 0Fig 2. Weighting curve proposed by UIk

0885-8977/91$01.ooO 991 IEEE


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1594A long term flicker severity coefficient for Characterizing theflicker level over periods of days or weeks, recommended by U8

is given in (2)FLT = average F S ~ 3 ver seve ral interval. ( 2 )This papex deals with the instantaneous flicker level andproposes a direct method for obtaining it from digitalmeasurements of voltage. Results based on simulated data are

included.Digital representation of a modulated voltage

The power frequency voltage, modulated by several frequenciesfrom 0.5 Hz to 25Hz.. an be represented by a discrete time seriesby sampling the analog voltage. The frequencies of interest in thevoltage signal will be between 35 Hz. nd 85 Hz. (for a 60Hz.power system). There will be no loss of informationas long as thesampling frequency is more than twice the maximum frequency ofinterest, namely 170 Hz. n order to avoid aliasing errors, theanalog signal should be filtered before sampling, to eliminatefrequencies higher thanhalf the sampling frequency. The equation(3) represents a digitized sinusoidal power signal whose waveformis modulated by several low frequencies (figure 1).vi = A [l + X g, con((2x/N) ki + cpk)]mk=l

* C OS ( (2x/N) ri + cpr) (3)represents a multiplication operationi

viQ0AN numberofdatapointsfs sampling frequencyfs/N frequency resolutionr f f l fundamental power frequencyk fs/N k-th modulation frequency'pkcxkwk

uniformly spaced instants of time (0.1.2.....N-1)voltage at the i-th instant of timeinitial phase of fundamental power frequencyamplitude of fundamental power frequency

initial phase of k-th modulation frequencyamplitude of k-th modulation frequencyweighting factor for k-th modulation frequency

Analog Measurement of IFLThe following steps summarize he analog implementation[6] fthe instantaneous flicker level IF^) calculation.(a) A demodulation is performed by squaring the voltage signal.The squaring of each term on the right hand side of (3) and usingthe equality cos28 =(l+cos28)/2 equation (4) is obtained.

mk= lv = A2[l + X g, cos((2ff/N) i + cpk)I2*cos2((2n/N) ri + cp,)

mk= 1= A2[1+ Z 2q co s (2x/N) i + cpk) + o (a') 3

[l+coa (2n/N) ri+2cpr)]/2 (4)Since the modulation factors a are generally very smallcompared to 1O, their squares are neglected.(b) The signal is normalized by dividing by its average value,namely 0.5*A2.The products of sine terms of frequencies

2*r*i*fs/N nd koi-ffl lead to frequencies of (2.r.i +k + f a and

(2-rei - k=i).fa. These frequencies as well as the 2 ~ i - f J Nfrequency term is lumped into a term xli, which includes allfrequencies higher than m*f.JN. The resulting signal xi is givenby (5 )

mk=lxi= 1+ X 2g,cos( (2i)ki +%) + x i (5)

(c) A weighting filter which has a frequency response equal toWk for a frequency of k*(ffl) is applied to the above signal. Itshould be noted that Wk is zero for frequencies greater thanm*(f,/N) as well as for zero fnequency. The resulting signal yi isgiven by (6).

The U6 has proposed a four pole analog filter F(s), whichapproximatestheirweighting curve.F ( s ) = ( 7 )k y 6 (1 + s / y )

k =1.74802 9 =2~2 .21979X =2-~4.05981 y =2.~1.2253501 =2 ~ ~ 9 .1 5 4 9 4 04 =20~21.9

(S2+ 2 X E + Of) 1 + S / % ) (1+ S/04)

(d) As a final step, the resulting signal is squared and averagedover short periods of time during which the flicker is assumedconstant, to obtain instantaneous flicker level IFL. Squar in5eright hand side of (6). using the fact that the average of cos 8 is0.5, the relation (8) is obtained.

Digital Implementatio nof the Analog Weighting FilterThe reference [6] reports a digital implementationof the analogtechnique. The major problem is in the digital implementation ofthe weighting filter. The following alternatives are available.(a) The filter transfer function (7) is represented by a set ofintegral equations relating the input to the output. It is thenimplementedusing digital integrations (figure 3).

out n

Fig. 3. Implementation of the analog filter.

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1595(b) A bi-linear transformation, namely replacing s by

(2/r) 1-z-1) / (1+ ~- 1) ill lead to an imprecise filter, because thefrequency characteristic s not piecewise constant-(c) A finite impulse response filter was designed by windowmethod. A FIR filter (figure 4.) of at least 200-th order wasnecessary to represent the desired frequency response adequately.O.OGr .................................................................................................,II

Sampling Instants.Fig 4. Impulse response of FIR filter.It can be readily seen that digital implementation of the analogapproaches are neither cost efficient nor optimal in performance.

Instantaneous Flicker Level (IFL)From equation (8), it follows that the instantaneous flicker levelIFL, defined by VI& can be obtained from the digitalrepresentation (3) of an amplitude modulated power frequencysignal by the relation (9).m

IFL = ,E, 2 4In t h i s paper we propose a method for the direct digitalcalculation of the a k s from sampled values of the voltage signal,followed by an IFL computation using the weighted summation

(9).

Digital Measurement of IFLIn this paper, we propose a direct method for digital computationof instantaneous flicker level. The method employs the following

StepS.(a) The voltage signal is sampled and converted to digital form

by an analog to digital converter. The frequency of samplingshould match the anti-aliasing fiiter characteristics. At a samplingrate of fs, N datapoints will be acquired in N/fs seconds.The equation (3) can be rewritten as (10). using a change ofsummation variable k.

vi= A [ C O ~(2x/N) r i + 9,)mXk = l+ %cos ( (2x/N) k i + 'pk) *COS ( (2x/N) ri + cpr]

r+m

k=r-mkvi = (A/2) [ c cos (21t/N)ki + q k ) 3 (10)where& = 2 &-k=&+k=ak %+k =4.+'%

(b) The block of N real data points is Fourier transformed toobtain its representation in the frequency domain. Each point willrepresent a frequency resolution of fs/N. The highest frequencyrepresented will be fsn. The DFT of the time function vi givesfrequency function Vk

Since4=2,

(c) The instantaneous flicker level is computed by the summation(9)with the weight factors wkIt is not necessary to obtain all the N E complex values of theFourier transform Vk The IFL computation requires only thosefrequencies, that influence the amplitude ak of modulationfrequencies. N m a l FFT routines compute the complex vkvalues for k =0 to (N-l)n . However since ak for k=1 to m only,are required, one needs to compute the Fourier transform v k for k=r-m to r only. A technique called Fl T pruning [7] can increase

the efficiency of FFT by eliminating the butterflies which affectvalues outside the range of interest.

FFT PruningThe pruning technique[7] is used for eliminating thecomputations, which involve just zeros. The reference [7]

illustrates its use for zero filled time sequences with decimation infrequency FlT. It can also be used with decimation in time FlT fonly a part of the frequency spectrumis required. Let 2M=N bethe total number of complex data points in the time domain. I t canbe shown that, with radix-2 FlT, there are M stages, eachrequiring N/2 butterflies. A butterfly[lO] is a one complexmultiplication and two addition operation illustrated by figure 5.The multiplication factor is called the twiddle factor. Thus the totalnumber of radix-2 butterflies will be M*2M-1. Let 2L =R be thenumber of frequency points required. The pruning technique[7]amounts to the elimination of the butterflies that do not affect thefinal results and hence not required. Thus the number ofbutterflies r uired at each stage will not be (N/2), but rather varyand then will remain the same for the remaining ( L l ) stages. Thetotal number of butterflies (figure 5. ) is given byfrom 2L, 2L+"i L+2 etc. until it reaches (NE) n (M-L-1) stages

No of bflies =2L [1+ 2 +22 +23+...2M-L-1]+(L-1)*2'-1=(L+1) 2M -1- 2L

YxxI::Fig. 5. Butterfly with Twiddle factor b


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1596The following table lists the number of butterflies for different MandL. The last row indicates the number without pruning.

M 10 11 122M 1024 2048 40963520 7104 142728064 162568 256 4352 8960 18176!g I 3968

M 2M 5120 11264 24576The pruning technique can be applied with the split radix[8]algorithms also.

Pruned FFT or f l icker com putationThe general pruning technique described above is for obtaining arange of frequencies at the lower end of the frequency spectrum.However, since uk for k = 1 to m is required, one needs tocompute the Fourier transform Vk for k =r-m to r. The Fouriertransforms from k =0 to r-m-1 and from k =r+l to N/2 are notrequired. A customized pruning technique is proposed for flickerevaluation.Let the voltage be sampled at 8 times per cycle (480 Hz.). Let

the N (N/2=2M) samples obtained over a period of N/480 seconds,be used to compute the instantaneous flicker level. Normal FFTtechnique, with N real data will compute the spectrum for 0 to 240Hz as N/2 complex points. A signal with a power frequency of 60Hz., mplitude modulated at 30Hz.,esults in the frequencies 60 +30 and 60 30 Hz. Since amplitude modulations from 0 to 30 Hz.is of interest, we require the spectrumbetween 30 and 60 Hz. (oralternatively between 60 and 90Hz.) nly. This corresponds to thepoints from N/16 to N/8.The figure 6 illustrates the last four stages of the pruned FFTalgorithm. The required points in the spectrum are obtained asfollows.(a) The N point time sequence of real values are re-arranged in abit reversed order, as a fist step for decimation in time FFT(b) The real sequence of N data points is split into 8 sets of N/8

points each. Any decimation in time FFT (radix-2, split radix,radix4 etc.) will transform the eight real time sequences of N/8points each to eight complex sequences of N/16 points each. Thesplit radix algorithm for real data by recombination [9] is one ofthe most efficient techniques.(c) The next stage (M-3)operates on 7N/16 complex points andyields N/4 complex points as illustrated in figure 6. The requiredtwiddle factors for the butterfly computations (figure 5 ) are givenbelow.

algorithm.

b(N/8) =a0 b(3N/8) =a0b(N/8+1) =a 4 b(3N/8+1) =a4b(3N/16-1) =a"- b(7N/16-1) =aNwb(N/4) =a0 b(7N/16) =a0b(N/4+1) =a 4 b(7N/16+1) =a4b(5N/16-1) =a Nwwhere a =e - *m

, -Unpruned U-3 th M-2 th M-1 thFFT Stag. Stage Stage 2" =N/ZFig. 6. PrunedFFT algorithm

(d) The succeeding stage(M-2)perates on N/4 complex pointsand yields N/8 complex points. The required twiddle factors forthe butterfly computations are given below.b(3N/16) =aND b(7N/16) =aNDb(3N/16+1) =aND+2 b(7N/16+1) =aNfi+2b(N/4-lj =aNl-2 wb - 1 ) =aNM-2(e) The final stage (M-1) operates on N/8 complex points andyields the required N/16 complex points. The required twiddle

factors for the butterfly computations are given below.b(5N/16) =aNfl6b(5N/16+1) =aNfl61b(3N/8-1) =aNB-1

Results with Simu lated DataThe FFT based approach for the computation of the IFL wastested with simulated data. The sampling frequency was constantat 480Hz.A 12 bit (1 1 bit with sign) analog to digital conversionwas used. The signals were not allowed to exceed 75% of the fullscale value. The number of points used for computation were 256,512, 1024. 2048. 4096 points, which correspond to 0.533, 1.07,

2.13, 4.27 and 8.53 sec. respectively. The modulation amplitudegiven by UIk to produce unit level of flicker at each frequency wasapplied. and the flicker level was computed. The figures 7,8, 9, 10and 11. show the deviations from th e desired I n , value of one.

ConclusionsDigital implementation of the analog design for flickermeasurement is inefficient as regards to computation, and lacks theflexibility offered by direct digital implementation.The direct digital implementation proposed in ths paper, uses afast Fourier transformation as the first step in the computation. Apruned FFT, ustomized for the flicker level computation is alsoproposed.

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The design of an analog or digital weighting filter is notrequired. The weights are applied directly on he amplitude of therespective frequency components. Hence, different weightingcurves can be used with utmost flexibility. Also, the errorsassociated with squaring demodulation are avoided. In addition,valuable information about individual flicker frequencies arereadily available.

Results with simulated data indicate that the F IT approach yieldssufficiently accurate results for 1024 point FFT with 480 Hz.sampling using a 12 bit A/D. Thus a value of IFLcan be obtainedevery 2.13 seconds. Under these conditions the deviation is lessthan 2.5% at flicker level of one, for al l frequenciesin the range of0.5 Hz. o 23 Hz.A error of upto 5% is considered acceptable atsuch low levels of flicker. The nominal signal level is set at 75% offull scale. If a 14 bit A/D is used, the nominal signal level can beset at 20% of full scale.

E" (1024 pt) 2.13 sec.-1.1094

................... ................... .................... ..................

3h 0 9 5 .................... 1.................... 4.............................................................94 - I , , , ,E o.900 5 10 15 20 IFrequency in Hz .

The flicker computation can be implemented using software orhardwareDFFT.

-1.109rlW! l . 05;p 1.0032 0.903

0.95

FFT (256 pt ) 0.53 sec

0 5 10 15 20 25Frequency in Hz.Fig. 7htantaneous Flicker level.

Frqwncy in Hz.Fig. 8.Instantaneous Flicker level.

1597

1

Fig. 9.Instantaneous Flicker level.

FFT (2048 pt) 4.27 sec.- .10 j9

Frequency in Hz.Fig. 1O.Instantaneous Flicker level.

FFl (4096 p t) 8.53 sec.- .109rl

.................... . .........

Frequency in Hz.Fig. 11 Instantaneous Flicker level.


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ACKNOWLEDGEMENTSThe author wishes to acknowledge the contribution of Mr.Claude Lafond in producing the simulations.REFERENCES

[ l] F.D. Martzloff and TM. Gruzs, "Power quality site surveys:facts, fiction and fallacies", IEEE transactions on PaverIndustry Applications, Vol24, n0.6, Nov. 1988, pp 1005-1018.[2] Stanley Stokes , Visual perception and tolerance of flicker",Utilities Coordinated Research Inc., Report for committee forproject no. 10,1937.[3] M.K. Walker, "Electric utility flicker limitations", ZEEETram actw ns on Industry Applications, Vol 15, Nov 1979, pp644-655.[4] P.Duveau, "FlickermBtre Num6rique". Revue GtW ra led'e'lectricite'.Tome 80, no. 11. Nov 1971, pp851-853.[5] P.P. Biringer and R.L. Quinn. "Voltage flicker meters - A stateof art review", Canadian Electrical Association ResearchReport, Project no 78-63A.[6] C. Mirra, Chairman, " Flicker measurement and evaluation",union Internationale dhxtrothermie, Groupe de travailPerturbations, Rapport 1986, Tour Atlantique, Ca e x 6,92080Paris-la-Dbfense,

[7] J.D. Markel, "FFT Pruning", IEEE Transacrions on Audio andElectroacoustics, Vol AU-19, no.4, Dec.1971, pp305-311.[8] H.V. Sorenson, "On omputing the split radix FFT". IEEETransactwns on Acoustics, speech and signal processing, VolASSP-34, no.1, February 1986,pp 152-156.[9] H.V. Sorenson et al, "Real valued fast Fourier transformalgorithms", IEEE Transactions on Acoustics, speech andsignalprocessing, Vol ASSP-35, no.6, June 1987, pp 849-863.[l o] A.V. Oppenheim and R.W. Schafer, Digital Signal

Processing, Prentice-Hall, Englewood Cliffs, N.J. 1975.Krishnaswamy Srinivasan (S'67,M'70,SM79) received his B.Sc. (Physics,University of Delhi) in 1962, B.E.(Electrical Engineering, 1.1.S~.Bangalore)in 1965, M.A.Sc (Power Systems) in 1967and Ph.D. (Automatic Control) in 1970from Univerity of Waterloo, Canada. He iswith the Hydro-QuBbec utility's research

t centre (IREQ) since 1972. His currentmterests are in micro-computers, estimation and controlapplications in Power Systems. He is a member of IEEE Powerand Computer Societies and is a registered professional engineer inQUBbeC.

IEEE-Digital Measurement of Voltage Flicker

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