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Electric Power Systems Research 76 (2006) 200208

A new method for measurement of harmonic groups in power systemsusing wavelet analysis in the IEC standard framework

Julio Barros , Ramon I. Diego

Department of Electronics and Computers, University of Cantabria, Santander, Spain

Received 23 December 2004; received in revised form 20 April 2005; accepted 12 June 2005

Available online 2 September 2005

Abstract

The paper presents a new method based on the wavelet-packet transform for the analysis of harmonic groups in power systems, compatible

with the standards of the International Electrotechnical Commission. The paper studies the performance of the new method in the analysis

of harmonic groups and the spectral leakage associated with the presence of interharmonic components, synchronized and non-synchronized

with the fundamental component, and also due to the loss of synchronization between the sampling window width and the fundamental

frequency. Finally, the results obtained in the application of this method to different test waveforms are compared with the results obtained

using the IEC method.

2005 Elsevier B.V. All rights reserved.

Keywords: Harmonic distortion; Power quality; Wavelets

1. Introduction

Since the beginning of the distribution of electricity, the

harmonic distortion has been one of the most widely studied

disturbances in voltage and current waveforms. The study of

the effect of the harmonic distortion has lead to the develop-

ment of standards to limit its magnitude in order to prevent

damage on equipment and on the power system itself. The

interest both, in the development of measurement methods

and in the study of the levels of harmonic distortion in dis-

tribution networks, has prompted interest in other aspects of

power quality to arrive at the present situation. IEEE stan-

dard 519-1992 [1] and IEC standard 61000-4-7 [2] are the

main international standards for measurement and analysis ofharmonics in power systems. In these standards the Fourier

analysis is proposed as the signal-processing tool to obtain

the harmonic components in voltage and current waveforms.

At present, two main factors affect the harmonic distortion

in power supply systems: first, the growing use of non-linear

loads that are increasing the level of harmonic distortion up

Corresponding author.

E-mail address: [email protected] (J. Barros).

to near to the limits defined in the standards, and second, the

increasing use of non-synchronously pulsating loads with thefundamental power system frequency produce interharmonic

components that are covering the spectra with new frequency

components. These new frequency components are not accu-

rately computed using the current processing methods.

To take into account the changing situation, the IEC has

defined a new method for harmonic and interharmonic anal-

ysis in the second edition of standard IEC 61000-4-7. The

main contribution of this standard is the definition of the

harmonic and interharmonic groups and sub-groups where

different frequency components are computed as single mag-

nitudes in order to have a more accurate representation than

the oneutilizedup to now using singleharmonic components.The standard proposes the use of the Fourier analysis as the

processing tool for the reference instrument for harmonic and

interharmonic analysis, but the standard itself states that the

use of the Fourier analysis does not preclude the application

of other analysis principles.

Other processing tools have been proposed in the litera-

ture for the analysis of harmonics. Kalman filters can be used

for measurement and tracking of power system harmonics

[3,4]. The correct application of this method requires

0378-7796/$ see front matter 2005 Elsevier B.V. All rights reserved.

doi:10.1016/j.epsr.2005.06.004


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202 J. Barros, R.I. Diego / Electric Power Systems Research 76 (2006) 200208

Fig. 2. Wavelet-packet decomposition tree and grouping of output bands

compatible with the harmonic groups defined by the IEC.

to 3.2 kHz, one additional level must be added to the wavelet

decomposition tree ofFig. 2 and double the number of har-

monic groups (up to 30th order) that could be computed in

the input signal.Theuse of theWPT methodproposedin this paper directly

computes all the frequency components included into uni-

form frequencybandsthat correspond to the harmonic groups

of the signal as defined by the IEC. Using the WPT method

the single line harmonic components of the signal cannot be

obtained.

4. Measurement of harmonics and spectral leakage

In order to evaluate the performance of the method pro-

posed in the measurement of harmonics, Table 1 shows the

rms value of each of the grouped output frequency bands of

Fig. 2 when a 1 p.u. single tone at fundamental frequency

and at odd harmonic frequencies from 3rd to 15th orderare introduced as the input signal. The rms value of each

grouped output frequency band (coefficients d1(n) to d15(n))

is obtained using the square root of the mean square of the

coefficientsof thetwo sub-bandsincludedin each band, using

the method proposed in [5].

As can be seen from the results reported in Table 1,

the spectral leakage is higher in the output sub-bands at

the center of the decomposition tree, coefficients d7(n) and

d9(n), respectively. To accurately characterize the frequency

response of the filter bank selected and to compare the perfor-

mance of the method proposed with the IEC method, a single

tone of 1 p.u. in a range from 1 to 800 Hz, in steps of 1 Hz,

has been introduced as the input signal in Fig. 2 and has beenused to compute the harmonic groups from 1st to 15th order

using the IEC method. Fig. 3a and b shows, respectively, the

results obtained using both methods.

As can be seen in Fig. 3a, the frequency response of each

sub-band is different and depends on the type of decomposi-

tion tree and the type and the sequence of filters (LP or HP)

through which the input signal goes. On the other hand, the

frequency response of each harmonic group is the same using

the IEC method, therefore, it is necessary to compare the fre-

quency characteristics of each group separately to assess the

performance of both methods. As an example, Fig. 4 repre-

sents the frequency response of thefirst order harmonic groupusing both methods.

Whenthetoneisintherangefrom25to75Hzthatisinside

the first order harmonic group, the results obtained using the

IEC method have no error when the tone is synchronous with

the window width used that is when the frequency of the tone

is a multiple of 5 Hz. Otherwise, the error in the estimation

Table 1

rms values of the output bands of the wavelet decomposition tree when a 1 p.u. single tone at odd harmonic frequencies is used as the input signal

50 Hz 150 Hz 250 Hz 350 Hz 450 Hz 550 Hz 650 Hz 750 Hz

d1(n): 2575 Hz 0.9916 0.0541 0.0277 0.0176 0.0117 0.0076 0.0043 0.0014

d2(n): 75125 Hz 0.0579 0.0843 0.0300 0.0179 0.0117 0.0075 0.0042 0.0014d3(n): 125175 Hz 0.0205 0.9876 0.0792 0.0207 0.0130 0.0082 0.0046 0.0015

d4(n): 175225 Hz 0.0098 0.0703 0.0806 0.0258 0.0146 0.0088 0.0048 0.0015

d5(n): 225275 Hz 0.0080 0.0881 0.9880 0.0393 0.0189 0.0117 0.0060 0.0019

d6(n): 275325 Hz 0.0047 0.0181 0.0814 0.0935 0.0304 0.0122 0.0063 0.0020

d7(n): 325375 Hz 0.0025 0.0090 0.0263 0.9318 0.3253 0.0074 0.0040 0.0013

d8(n): 375425 Hz 0.0029 0.0099 0.0225 0.0895 0.0896 0.0225 0.0099 0.0029

d9(n): 425475 Hz 0.0031 0.1050 0.0237 0.3315 0.9346 0.0360 0.0136 0.0039

d10(n): 475525 Hz 0.0022 0.0070 0.0147 0.0234 0.0854 0.0858 0.0184 0.0048

d11(n): 525575 Hz 0.0017 0.0054 0.0103 0.0178 0.0369 0.9861 0.0833 0.0071

d12(n): 575625 Hz 0.0017 0.0053 0.0096 0.0159 0.0283 0.0948 0.0782 0.1060

d13(n): 625675 Hz 0.0015 0.0046 0.0082 0.0131 0.0209 0.0825 0.9875 0.0217

d14(n): 675725 Hz 0.0013 0.0041 0.0072 0.0113 0.0174 0.0293 0.0831 0.0505

d15(n): 725775 Hz 0.0014 0.0043 0.0077 0.0118 0.0177 0.0279 0.0536 0.9915


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J. Barros, R.I. Diego / Electric Power Systems Research 76 (2 006) 2002 08 203

Fig. 3. Frequency characteristics: (a) WPT method and (b) IEC method.

Fig. 4. Frequency response of the first order harmonic group using the IEC

method and the WPT method.

of the harmonic group is higher using the IEC method than

the one obtained using the WPT method. If the frequency

of the tone is outside the frequency range of the first order

harmonic group, the spectral leakage is null using the IEC

method, when the tone is again synchronous with the window

width, but the error is higher than the one obtained using the

WPT algorithm when the frequency tone is desynchronizedwith the window width.

The results obtained from the comparison of the other har-

monic groups are similar, except in the case of the harmonic

groups at the center of the decomposition tree, where the per-

formance of the wavelet method is worse than that obtained

using the IEC method. The use of filters with better roll-off

characteristics or the use of scaling factors to compensate

the distortion introduced by the filter bank could improve the

performance of the WPT method proposed [810].

The spectral leakage can also be produced when there

is an error in synchronizing the fundamental power system

frequency and the time window used in the measurement sys-

tem. According to IEC 61000-4-7, the maximum permissibledesynchronization error for a harmonic measurement instru-

ment is 0.03% and this requirement should be fulfilled for

measurement within a range of at least 5% of the nomi-

nal system frequency. The loss of synchronisation should be

indicated by the instrument and the data so acquired should

be flagged.

In order to specify the performance of the WPT method

proposed in the case of failure of synchronization, as is

required in standard 61000-4-7, Fig. 5 represents the error in

percentage, in the determination of the magnitude of the fun-

damental component and harmonics of third and fifth order,

when the IEC and the WPT methods are applied to a 1 p.u.single tone in a range form 49.5 to 50.5 Hz (5% of the

nominal system frequency and the frequency range variation

accepted in the European standards). As can be seen from

the results reported in Fig. 5, the spectral leakage produced

Fig. 5. Error in themagnitude of fundamental,thirdand fifth order harmonic

groups in the case of synchronization error using the IEC method and the

WPT method.


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using the IEC method is a function of the magnitude of the

synchronization error and of the harmonic order, whereas the

error in the determination of the magnitude of the fundamen-

taland harmonic components of third andfifth order using the

WPT method is in all cases 0%, showing that this method is

insensitive to the fluctuations of the power system frequency

in the range studied.

5. Comparative study of the WPT and the IEC

methods

In this section a comparative study of the performance of

the two methods, the WPT method and the IEC method, is

done using different test waveforms. Firstly, the two methods

are compared using stationary signals with different har-

monic components and secondly, the comparative study is

done using non-stationary signals and interharmonic com-

ponents synchronized and non-synchronized with the funda-

mental component.

5.1. Comparative study using stationary signals

In order to do this study, we haveused the daily mean mag-

nitude of the harmonic distortion measured in our low voltage

distribution system as the test signal, which is represented in

Table 2 under column input signal.

Table 2 reports the results obtained using this signal as the

input signal in both, the WPT method and the IEC method.

The spectral leakage caused by the filtering characteristics

of the WPT gives very large errors, while the IEC method

gives the exact values. After different simulations we haveverified that the spectral leakage produced using the WPT

method is mainly due to the fundamental component. The

spectral leakage produced by the rest of the harmonic com-

ponents in the neighboring harmonic groups is very small

due to their small magnitude. To compensate the effect of the

fundamental component in the spectral leakage we propose

the following two-stage process: a first stage where the fun-

damental component is estimated and a second stage where

the fundamental component is filtered out in the input sig-

nal and the WPT method is applied to the resultant signal to

compute the rest of the harmonic components. The resultsobtained using this two-stage process are reported in Table 2,

under column filtering + WPT. As can be seen in Table 2,

the errors in the estimation of the harmonic groups from 2nd

to 15th order are very small and they are within the accepted

range for a harmonics measurement instrument.

5.2. Comparative study using fluctuating harmonics and

interharmonic components

In this section a comparative study of the performance

of the two methods is done using different test waveforms

proposed in standard IEC 61000-4-7. The precision in the

determination of the magnitude of the harmonic componentsusing both methods is compared with the total rms value of

each test waveform calculated over 10 cycles of the funda-

mental frequency.

The following case studies are considered: Examples 1

and 2 study the case of fluctuating harmonics. In Example 1,

a large harmonic current fluctuation is considered, whereas

Example2 considersthe case of a harmonic current controlled

by the zero-crossing multicycle method. Examples 35 study

two possible interharmonic producing conditions in a power

system: the case of a communication signal connected to the

power system with a frequency non-integer multiple of the

fundamental frequency not-coexisting and coexisting withdifferent harmonic components (Examples 3 and 4) and the

case of a voltage harmonic with a sinusoidal voltage modula-

tion, as produced by an electronic motor drive with a varying

torque (Example 5).

Table 2

Magnitude of the 15 harmonic groups obtained using the IEC and the WPT methods for a stationary signal corresponding to daily mean magnitude of the

harmonic distortion measured in our low voltage distribution system

Harmonic group Input signal IEC method WPT method Filtering + WPT

V % V % V % V %

1 230 100 230 100 228.0705 99.1611 0.2900 0.1261

2 0 0 0 0 13.0247 5.6629 0.3392 0.14753 1.15 0.50 1.15 0.50 4.5445 1.9759 1.2955 0.5632

4 0 0 0 0 1.8192 0.7910 0.5116 0.2224

5 6.21 2.70 6.21 2.70 6.2541 2.7192 6.1241 2.6626

6 0 0 0 0 1.3703 0.5958 0.3541 0.1539

7 2.53 1.10 2.53 1.10 2.5929 1.1273 2.5441 1.1061

8 0 0 0 0 0.9832 0.4275 0.3165 0.1376

9 0.69 0.30 0.69 0.30 1.0917 0.4746 0.5084 0.2211

10 0 0 0 0 0.6742 0.2931 0.1759 0.0765

11 0.46 0.20 0.46 0.20 0.7095 0.3085 0.4839 0.2104

12 0 0 0 0 0.5538 0.2408 0.1676 0.0729

13 0 0 0 0 0.4642 0.2018 0.1268 0.0551

14 0 0 0 0 0.4084 0.1776 0.1038 0.0451

15 0 0 0 0 0.4306 0.1872 0.1076 0.0468


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J. Barros, R.I. Diego / Electric Power Systems Research 76 (2 006) 2002 08 205

Fig. 6. Large fifth harmonic current fluctuation.

Fig.7. Spectral components of the waveformofFig. 6 using theIEC method.

Example 1. Fig. 6 shows the case of rms fifth harmonic cur-

rent fluctuating from 3.536 to 0.7071 A and Fig. 7 shows the

corresponding spectrum using the IEC method. The change

in the magnitude of the current occurs after 21.25 periods of

the fifth harmonic. The total rms value of the time function

calculated over a time interval of 0.2 s is 2.367 A. Table 3

Fig.8. Waveformof third harmoniccurrentcontrolled by zero-crossingmul-

ticycle method.

shows the results obtained in the measurement of the 15 har-

monic groups in the current waveform using the IEC and the

WPT methods.

The magnitude in the estimation of the fifth order har-

monic group using the IEC method is 2.34 A, with an error

of 1.14%. On the other hand, the estimation obtained usingthe WPT method is 2.3267 A. In this case, the error is 1.70%,

slightly higher than the error obtained with the IEC method

but in the range acceptable for a measurement instrument.

The spectral leakage in the rest of harmonic groups is similar

using both methods.

Example 2. Fig. 8 shows the typical waveform of a third

harmonic current produced by a microwave appliance. The

average power is controlled by the zero-crossing multicycle

method with, in this case, a repetition rate of 5 Hz and a duty-

cycle of 50%. The total rms current calculated over 0.2 s is

0.707 A. Fig. 9 shows the corresponding spectrum obtained

using the IEC method. The magnitude of harmonic groupsfrom 1st to 15th order calculated using the IEC and the WPT

methods is reported in Table 3.

Using the IEC method the estimation of rms value of the

third harmonic group is 0.6925 A, with an error of 2.05%.

Table 3

rms values of the 15 harmonic groups using the IEC and the WPT methods for the test waveforms of Examples 15

Harmonic group order Example 1 Example 2 Example 3 Example 4 Example 5

WPT IEC WPT IEC WPT IEC WPT IEC WPT IEC

1 0.0763 0.0629 0.0537 0.0531 0.2490 0.2320 1.3902 1.3830 0.2506 0.0388

2 0.0863 0.0753 0.0831 0.0957 0.2562 0.2689 1.8836 1.9051 0.2721 0.04513 0.1806 0.1094 0.6913 0.6925 0.2931 0.3514 14.1416 15.2743 0.7862 0.0616

4 0.2718 0.2357 0.0713 0.0753 0.4477 0.5568 20.9453 20.2313 0.7352 0.1349

5 2.3267 2.3400 0.0731 0.0294 1.4916 1.7360 11.8734 11.7455 10.166 10.264

6 0.2646 0.2353 0.0183 0.0177 9.6415 9.5459 1.2804 0.6654 0.7235 0.1227

7 0.1116 0.1079 0.0090 0.0123 0.4606 0.8376 0.5668 0.4098 0.2386 0.0479

8 0.0803 0.0717 0.0099 0.0094 0.2825 0.4560 0.4960 0.2781 0.2036 0.0302

9 0.0645 0.0555 0.0105 0.0076 0.2977 0.3262 0.4969 0.1987 0.2150 0.0221

10 0.0489 0.0469 0.0071 0.0064 0.4143 0.2614 0.3434 0.1458 0.1338 0.0176

11 0.0397 0.0410 0.0054 0.0056 0.0975 0.2235 0.2619 0.1081 0.0931 0.0148

12 0.0401 0.0368 0.0053 0.0051 0.0876 0.1997 0.2510 0.0796 0.0869 0.0130

13 0.0365 0.0344 0.0046 0.0047 0.0737 0.1844 0.2332 0.0569 0.0749 0.0119

14 0.0352 0.0331 0.0040 0.0044 0.0624 0.1748 0.1997 0.0385 0.0657 0.0111

15 0.0350 0.0320 0.0040 0.0043 0.0637 0.1695 0.2118 0.0239 0.0695 0.0107


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Fig.9. Spectral components of thewaveform ofFig. 8 usingthe IEC method.

The estimation of the rms magnitude of the third harmonicgroup obtained using the WPT method is 0.6913 A. The error

in this case is 2.22% once again slightly higher than that

obtained using the IEC method but in a range acceptable for

a measurement instrument. The spectral leakage in the rest

of harmonic groups is similar using both methods.

Example 3. In this case a communication signal of 9.8 V at

287Hz is considered. Fig. 10 shows the waveform of this sig-

nal and Fig. 11 shows the corresponding spectrum obtained

using the IEC method. Table 3 shows the magnitude of the

harmonic groups obtained using the IEC and the WPT meth-

ods.

The magnitude of the sixth harmonic group using the IEC

method is 9.5459 and 9.6415 V using the WPT method. The

error incurred using the IEC method is 2.59% whereas the

error observed using the WPT method is only 1.61%. The

spectral leakage in the rest of harmonic groups is higher using

the IEC method than the WPT method.

Example 4. Fig. 12 shows the waveform of a communi-

cation signal of an interharmonic of 178 Hz with constant

magnitude of 23 V rms superimposed on a third and fifth

harmonic of 11.5 V each. Fig. 13 shows the corresponding

spectrum obtained using the IEC method and Table 3 shows

Fig. 10. Interharmonic of 9.8V at 287 Hz.

Fig. 11. Spectral components of the waveform of Fig. 10 using the IEC

method.

Fig. 12. Thirdandfifthharmonicwitha interharmonicof 23V rmsat 178Hz.

the magnitude of the harmonic groups obtained using bothmethods.

The magnitude of the fourth order harmonic group is

20.2313 V using the IEC method and 20.9453 V using the

Fig. 13. Spectral components of the waveform of Fig. 12 using the IEC

method.


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[10] V.L. Pham, K.P. Wong, Antidistortion method for wavelet trans-

form filter banks and nonstationay power system waveform harmonic

analysis, in: IEE Proceedings on Generation, Transmission and Dis-

tribution, vol. 148, 2001, pp. 117122.

Julio Barros received the M.Sc. and Ph.D. degrees in Physics in 1978 and

1989, respectively, both from the University of Cantabria, Spain. In 1989,

he joined the Department of Electronics and Computers of the University

of Cantabria, where he is currently an associate professor. His research

areas are real-time computer applications in power systems, harmonics

and power quality.

Ramon I. Diego was born in Santander (Spain) in 1973. He received

the M.Sc. degree in physics in 2000 from the University of Cantabria,

Spain. His main research interests include electromagnetic compatibility

and digital signal processing applied to power quality. He is currently

working on his Ph.D. thesis.

a new method for measurement of harmonic groups in power systems using wavelet analysis in the iec...

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