2602 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 4,...

2602 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 4, OCTOBER 2005

Analyzing Systems With Distributed HarmonicSources Including the Attenuation

and Diversity EffectsEmad Ezzat Ahmed, Wilsun Xu, Fellow, IEEE, and Guibin Zhang

Abstract—This paper investigates the inclusion of attenuationand diversity effects in harmonic distortion assessment for systemswith distributed harmonic sources. The concept of device char-acteristic curves is introduced to represent the effects. An itera-tive method is proposed to include the effects in system wide har-monic assessment. The method is illustrated using a system withdistributed personal computer loads. Test results have confirmedthe effectiveness of the proposed method.

Index Terms—Distributed harmonic loads, harmonic analysis,harmonic attenuation and diversity effects, harmonic sources.

I. INTRODUCTION

ANOTICEABLE trend in power systems nowadays isthe emergence of distributed harmonic-producing loads.

These loads typically have comparable sizes and are distributedall over an electric network. Traditional harmonic assessmenttechniques have difficulties in determining the collective dis-tortion effects of these sources. There is a need to developnew techniques to assess harmonic distortions for systems withdistributed harmonic sources.

The difficulties are due to two factors. One is that the supplyvoltage distortions will change the harmonic generation be-havior of the distributed harmonic-producing loads. Both theamplitude and phase angle of the harmonic current injected bya load will vary with the degree of supply voltage distortion.The former effect is called attenuation while the latter effect iscalled diversity [1]. Both effects tend to reduce the harmoniccurrents produced by the loads, resulting in reduced harmonicdistortion levels in the system. The second factor is the randomvariations of the loads. It is necessary to determine the proba-bilistic harmonic distortion levels in such cases.

The objective of this paper is to introduce a method that cantake into account the first factor in (deterministic) harmonicassessment. A typical case that can be analyzed by the proposedmethod is the commercial electric systems. Such systems havemany distributed harmonic-producing office electronics. The

Manuscript received May 11, 2004; revised December 31, 2004. This workwas supported by the Alberta Energy Research Institute (AERI). Paper no.TPWRD-00221-2004.

E. E. Ahmed is with the Department of Electrical Engineering, Cairo Univer-sity-Fayoum Campus, Fayoum, Egypt (e-mail: [email protected]).

W. Xu is with the Department of Electrical and Computer Engineering,University of Alberta, Edmonton, AB T6G 2V4, Canada (e-mail: [email protected]).

G. Zhang with the University of Alberta, Edmonton, AB T6G 2V4, Canada(e-mail: [email protected]).

Digital Object Identifier 10.1109/TPWRD.2005.855441

Fig. 1. Main setup of the conducted experiments for the PC load harmonicmeasurements.

Fig. 2. Investigating the effect of supply impedance variation.

main focus of this paper is a single-phase harmonic source usesa capacitor-filtered diode bridge rectifier circuit. Traditionalharmonic assessment methods ignore the attenuation and diver-sity effects [2]. They can result in significant overestimation ofthe harmonic distortion levels when applied to such systems.

The concept of diversity and attenuation effects was intro-duced in [1]. The attenuation factor “ ” of the resultant

th harmonic current with the operation of “ ” PCs sharing acommon supply impedance is defined as follows:

(1)

where is the th harmonic current when PC’s are in op-eration and is the th harmonic current when 1 PC is inoperation. The diversity factor “ ” is defined as follows:

(2)

where is the th harmonic current injected by the th load.The impact of the attenuation and diversity effects on the har-

monic-generation characteristics of a PC-type load was investi-gated in [3]. It revealed that a reduction of 30% of harmonic cur-rent injection is possible due to these effects. However, no work

0885-8977/$20.00 © 2005 IEEE

AHMED et al.: ANALYZING SYSTEMS WITH DISTRIBUTED HARMONIC SOURCES 2603

Fig. 3. PC current THD as a function of the supply voltage THD or CF (due to supply impedance variation).

Fig. 4. PC current harmonics as functions of supply voltage THD or CF (due to supply impedance variation).

has been published on including the effects for system wide har-monic assessment. Time-domain simulation that models all har-monic-producing loads in detail could be one method to solvethe problem. But such a method is not practical when there aremany distributed harmonic sources. In view of this situation,we propose a harmonic domain iterative method to address theneed. Single-phase systems with distributed computer loads areused as an example to illustrate the method.

II. CHARACTERIZING THE ATTENUATION

AND DIVERSITY EFFECTS

As the proposed method deals with the attenuation and diver-sity effects, the first step is to establish a method to characterizethe effects. For this purpose, extensive laboratory experimentswere conducted to quantify the impact of supply voltage distor-tion on the harmonic currents generated by the switched mode

power supplies. The power supply is commonly used in of-fice appliances and consists of a capacitor-filtered diode bridgerectifier.

No relationship could be extracted between the input har-monic currents and the parameters of the capacitor-filtered recti-fier circuit. Therefore, it is not easy to predict the current wave-form from circuit parameters [4]. Rather, the distortion of theterminal voltage waveform in this research work is adopted topredict the magnitude and the phase angle of the input harmoniccurrents to reflect the impact of the supply impedance or othersystem connected harmonic sources.

Two types of experiments were conducted. The first experi-ment is to change the supply impedance so a different level ofharmonic distortion is created at the terminal of a test PC re-specting a switched mode power supply. The second experimentis to change the number of other harmonic sources in the system,creating different amount of background voltage distortions.


Fig. 5. PC harmonic current phase angles as functions of the supply voltage THD or CF (due to supply impedance variation).

The measurements are conducted using a Data AcquisitionNicolet Transient Recorder BE256-LE. This instrument haseight channels for simultaneous recording with an adjustablesampling rate. The voltage and current waveforms are mea-sured using voltage and current probes. The waveform datacan be acquired by connecting the recorder to a laptop viaIEEE-488 interface unit. The recorder has special softwarecalled “TEAM256” (Transient Evaluation and Analysis Man-ager) which is installed on the laptop to control the recordingprocess. The main set up of the conducted experiments and theinstruments used in the measurements are shown in Fig. 1.

Adjustable speed drive loads, the most common three-phaseharmonic sources, use the same circuit topology used in the PCpower supply, but this load is out of the scope of this paper.Different harmonic source types can be considered by other re-searchers and following the way presented in this paper is anoption while finding a new way is encouraged to further explorethe inclusion of harmonics attenuation and diversity in harmonicanalysis for additional load types.

A. Supply Impedance Variation

The circuit configuration for the first experiment is shown inFig. 2 where the PC load is supplied through variable impedancecomponents and . The supply impedance is changed in 10steps for a given ratio, and in each step the feeding voltage“ ” and the supply current “ ” are measured with a samplingrate of 7.5 kHz. This process is repeated for different ratiosof supply impedance with magnitudes causing a voltage drop upto 3.15%.

Fig. 3 shows the variation of the supply current total harmonicdistortion (THD) with the feeding voltage THD or crest factor

Fig. 6. Investigating the effect of background voltage distortion.

(CF) indices. The results show that there is a consistent nega-tive or positive slope relationship between the between the PCcurrent THD and supply voltage THD or CF.

Fig. 4 depicts the variation of the individual harmonic cur-rent magnitudes in percent of the fundamental component andFig. 5 presents the variation of the phase angles of the harmoniccurrents.

The figures confirm that the harmonic current spectrum can nolonger be assumed as constant. The supply voltage distortion cansignificantly change the harmonic current output of the load. Themagnitude of each harmonic current is almost linearly related tothe THD or CF of the supply voltage. The variation of the indi-vidual harmonic current phase angles, though scattered slightly,has a specific trend. The phase angles become more delayed withthe increase in voltage THD and the decrease in voltage CF.

B. Variation of Background Voltage Distortion

The set up for this experiment is shown in Fig. 6. Sevencomputer and monitor loads were connected in sequence to the


Fig. 7. Variation of PC current THD with voltage THD or CF due to background voltage distortion variation.

Fig. 8. Variation of PC individual harmonic current magnitudes with voltage THD or CF due to background voltage distortion variation.

common point of the test PC to create different backgroundvoltage distortions. The feeding voltage and supply current ofthe test PC were measured. The first measurement point is takenwhen none of the external loads is connected so that we got a totalof eight measurement points for the same supply impedance.The measurement was repeated for different ratios.

Fig. 7 shows the variation of the PC current THD with thefeeding voltage indices THD or CF. There is also a good correla-tionbetweenthePCcurrentTHDandeithervoltage indices.Fig.8depicts the variation of the harmonic current magnitudes whileFig. 9 illustrates the variation of the current phase angles. Bothfigures show similar trends to those observed in the impedancevariation case. Note that there is a plateau in the curves. This iscaused by the connection of computer monitors. The monitorloads have different harmonic current characteristics from the PCloads. The monitors are connected just to provide wider range ofvoltage distortion. The figures show that the voltage distortioncan uniquely characterize the harmonic currents except in therange where the monitors are connected. Therefore, with only PCloads, i.e., with distributed harmonic sources of comparable sizes

and same circuit topology dominating the system, the harmoniccurrents can be identified by the voltage distortion.

C. Characterizing the Attenuation and Diversity Effects

Figs. 10 and 11 compare the harmonic current magnitudesand phase angles obtained under both test conditions. An im-portant conclusion is that the harmonic magnitude results arecomparable. As for the harmonic phase angles, even they arescattered, they show a specific trend and averaging the two ef-fects is acceptable to consider the interaction with the supplyvoltage distortion which is overlooked by the traditional har-monic analysis methods. It will be shown later that the slightspread of the phase angles will not result in a pronounced ef-fect on the results. Therefore, it can be inferred that the causeof voltage distortion has no significant effect on the harmoniccurrent generated by the loads. The diversity and attenuation ef-fect can be represented approximately using either the supplyvoltage THD or CF as the sole independent variable.

The main concern of this paper is a single-phase harmonicsource employs a capacitor-filtered diode bridge rectifier cir-


Fig. 9. Variation of PC individual harmonic current phase angles with voltage THD or CF due to background voltage distortion variation.

cuit as the most common single-phase harmonic source usedin residential and commercial systems. However, in order toconfirm the drawn conclusions for other harmonic sources usethe same circuit topology, the same procedure was followedusing simulation studies for adjustable speed drive load (ASD).Fig. 12 depicts the obtained results for the fifth harmonic cur-rent. It can be asserted that the harmonics generated from thiscircuit topology for either single-phase or three-phase harmonicsources can be reasonably characterized by the distortion of thesupply voltage. This adds a significant feature that can be uti-lized in harmonic analysis to include the harmonics attenuationand diversity which are commonly ignored by traditional har-monic analysis methods.

From the aforementioned, we propose to model the diversityand attenuation effects using the following functions:

(3)

(4)

where (VTHD) denotes the magnitude of the th harmoniccurrent as a function of the supply voltage THD. (VTHD)denotes the phase angle of the th harmonic current as a functionof the supply voltage THD. The above functions are determinedusing curve fitting techniques. Sample results are as follows:

(5)

(6)

Similar functions can also be determined with the voltage CFas the variable.

In summary, it is shown that attenuation and diversity effectsof a harmonic-producing load can be characterized using theharmonic currents versus voltage THD or voltage CF curves.Some of the significant implications of these curves are asfollows.

• It is interesting to note that when the resultsof (5) and (6) are the harmonic current spectrum of theload used for traditional harmonic power flow calculations[5]. Since the traditional methods can only use one pointon the curves, it is clear that they are unable to include thediversity and attenuation effects.

• The curves are of general application values. Theyrepresent the input-output or terminal characteristics ofa harmonic-producing load. The complexity involvedin modeling the internal working of the load and theassociated impact on the diversity/attenuation effects isthus eliminated. Similar curves can be determined fordifferent types of loads to form the associated harmoniccurrent source model for the loads.

• The curves or current source models are represented usingeither voltage THD or CF as independent variables. It ispossible that other indices could also be used. As will beshown later, the THD is a much better index than CF formodeling the diversity and attenuation effects.

III. AN ITERATIVE METHOD FOR HARMONIC ASSESSMENT

The next problem to be solved is how to include the diversityand attenuation curves for system wide harmonic assessment.For this purpose, we propose an iterative frequency domain


Fig. 10. Variation of PC harmonic current magnitudes due to the change of supply impedance or background voltage distortion.

Fig. 11. Variation of PC harmonic current phase angles due to the change of supply impedance or background distortion.

harmonic analysis method. The basic idea of the proposedmethod is to revise the current spectrum of the harmonicsources according to the device characteristic curves in aniterative process.

The proposed method starts with the traditional harmonicanalysis method. The method produces results on the harmonicvoltage distortions at various buses of the system, without takinginto account the diversity and attenuation effects. With the cal-


Fig. 12. Variation of ASD fifth harmonic current magnitude and phase angle with voltage THD due to the change of supply impedance or background voltagedistortion.

culated voltage THD results, the harmonic current injected bythe harmonic source at bus is adjusted, with the help of thedevice characteristics developed earlier, as follows:

(7)

(8)

Note that the above two equations are somewhat similar to thoseused in traditional harmonic analysis, which are shown below[5]

(9)

(10)

The difference is that the magnitude and phase angle of theupdated harmonic current are no longer scaled and shifted ac-cording to a simple linear relationship. The scaling of magnitudeand shifting of phase angle are now determined from two non-linear equations that are the functions of bus voltage THD. Thisadjustment has therefore considered the attenuation and diver-sity effects. The adjusted harmonic currents are then re-injectedinto the system to get the new and improved system harmonicvoltages using the nodal voltage equations.

The above process will yield a new set of bus voltage THDresults. In turn, a new set of adjusted harmonic currents is ob-tained according to (7) and (8). This iterative process can berepeated until a convergence of the voltage THDs at all buses isreached. A graphical illustration of the iterative process is shownin Fig. 13.

As discussed earlier, either THD or CF can be used to charac-terize the attenuation and diversity effects of a device. There is aneed to determine which index is more suitable for the proposediterative method. This subject is investigated by analyzing theinteraction between the device curve and the system character-istic curve. Fig. 14 shows both the system characteristic curvesand the device curve together for a simple system of Fig. 15. Inthis case, the supply system impedance is varied so that a familyof system curves is obtained.

In Fig. 14, the characteristic curves are represented using ei-ther voltage THD or CF index. It can be seen that there is usu-ally no intersection between the system and load characteristiccurves when the CF index is used. As a result, one can concludethat a device characteristic curve that is based on the CF index

Fig. 13. Iterative process for harmonic distortion assessment.

Fig. 14. System voltage CF and THD response to the PC current distortion.

is not suitable for the proposed iterative method. On the otherhand, the voltage THD-based characteristic curves usually haveintersection points. This implies that the voltage THD index is


Fig. 15. Investigation of system voltage response to the PC current distortion.

suitable for characterizing the attenuation and diversity effects.Based on the results, the voltage THD index is adopted for theproposed iterative method.

The reason that the CF index is not suitable for characterizingthe diversity and attenuation effects has been investigated. TheCF index represents the sharpness of a waveform peak. Fig. 16shows that when more distorted load current is injected to thesystem, the voltage waveform actually becomes sharper insteadof flatter as commonly believed. This response implies a posi-tive slope for system characteristic curve. The increased sharp-ness of the waveform is due to the voltage drop on the inductivecomponent of the system impedance.

IV. CASE STUDIES FOR DISTRIBUTED PC LOADS

The proposed iterative method has been verified experimen-tally. Harmonic measurements were conducted on two PC sys-tems shown in Fig. 17. The magnitude of the supply impedance“ ” was increased in steps to vary the system distortion level.The harmonic distortion levels were determined using the tradi-tional and the iterative methods. The results are compared withthe measurements.

A. Measurement and Calculation Results

The supply impedance of PC system 1 is increased in sevensteps with the magnitude of 0.5, 1.25, 1.75, 2.5, 3, 3.75, and 4.25ohm in turn and with a constant X/R ratio of 0.754. The supplyimpedance of PC system 2 is varied in three steps with the samevalues as that in the first three steps for PC system 1. For bothsystems, the voltage at node 2 and the current in branch 1 aremeasured. The convergence criterion of the iterative method isset at 0.05% of the maximum absolute difference of the voltageTHD at all nodes between two successive iterations. Samplemeasurement and calculation results are compared in Figs. 18and 19.

Fig. 18 compares the voltage and current THD results obtainedby the measurements, the proposed iterative method and the tra-ditional method. The results are presented for different studycases in ascending order of the supply impedance magnitude.Fig. 19 compares the individual harmonic magnitudes of supplyvoltage at node 2 and the individual harmonic current magni-tudes of the PC at node 2 for the test system 1. The figure revealsthat the results obtained using the proposed iterative methodare in a good agreement with the measurement results whilethe traditional method leads to considerable overestimation.

Fig. 16. Supply voltage waveform as affected by the load current.

Fig. 17. Single-line diagram of the two PC systems under study.

B. Sensitivity Study

According to Fig. 11, the phase angle has a large variationrange as a function of the voltage THD. So it is difficult to modelthe diversity effect accurately using the function. In this sec-tion, the impact due to the inaccuracy of the function is in-vestigated. In the investigation, the iterative method is appliedto both PC systems without considering the diversity effect. Theresults are seen in Fig. 20 and are compared with those obtainedwith both effects being considered.

It can be seen that there is no noticeable difference betweenthe results for both of the two PC systems. Therefore, one mayconclude that diversity effect is not pronounced and there is noneed to determine the function accurately. This observation


Fig. 18. Comparison of voltage and current THD results.

Fig. 19. Comparison of individual harmonic magnitudes (system 1).

can be explained according to the following analysis. Accordingto (8), the phase angle difference between the th harmonic cur-rent components for two loads connected at buses andis obtained by

(11)

On the other hand, if the traditional method is used where thetwo loads have the same typical harmonic current spectrum, thephase angle difference, using (10), can be obtained by

(12)

Comparing (11) with (12), it can be seen that an externalterm is introduced. If the twobuses have similar voltage distortion level, this term can be verysmall. As a result, the effect of phase angle diversity becomesinsignificant.

C. Convergence Performance of the Proposed Method

Fig. 21 presents the convergence process of the voltage THDat different nodes for the test system 1. The variation of thenumber of iterations required for convergence for different studycases is depicted in Fig. 22. One can see that the number of iter-ations increases with the voltage distortion level and the numberof harmonic sources. It was also found that the convergence isfaster when the diversity effect is ignored. So for systems with a


Fig. 20. Impact of diversity effect on harmonic distortion levels.

Fig. 21. Convergence of the voltage THD for different study cases (system 1).

Fig. 22. Number of iterations required for convergence.


large number of distributed harmonic sources and high voltagedistortion levels, one may need to use some techniques to accel-erate the convergence. As an example, damping factor has beenfound useful to improve the convergence by attenuating the os-cillations in the iterative process.

V. CONCLUSION

An iterative harmonic analysis method has been proposed toassess harmonic distortions for systems with distributed single-phase harmonic sources. It has been focus on harmonic sourcesemploying capacitor-filtered diode bridge rectifier circuit. Themethod can take into account the harmonics attenuation and di-versity effects and has the potential to be investigated for fur-ther harmonic source types. It overcomes the limitations of thetraditional harmonic analysis method and provides more accu-rate results. Main contributions of this paper are summarized asfollows:

• It introduced a general method to characterize the diver-sity and attenuation effects of harmonic-producing loads.The result, device specific harmonic current curves asfunctions of supply voltage THD, is essentially a currentsource model for harmonic sources.

• It proposed an iterative method to include the devicecharacteristics for system wide harmonic analysis. Per-formance of the proposed method has been verified ontwo test systems with good results. The impact of sev-eral factors on the method and its results has also beenanalyzed.

The concepts introduced in this paper are a promising wayto take into account the attenuation and diversity effects. Asshown in the case study results, such effects cannot be ignoredfor system with a large number of harmonic sources. Other-wise, one may overestimate the cost to mitigate the harmonicproblem. As with any new methods, there is a lot of room forimprovement. For example, more sophisticated iterative methodcould be used to improve the convergence speed.

REFERENCES

[1] A. Mansoor, W. M. Grady, A. H. Chowdhury, and M. J. Samotyj, “Aninvestigation of harmonics attenuation and diversity among distributedsingle-phase power electronic loads,” IEEE Trans. Power Del., vol. 10,no. 1, pp. 467–473, Jan. 1995.

[2] Task Force on Harmonics Modeling and Simulation, “Characteristicsand modeling of harmonic sources—Power electronic devices,” IEEETrans. Power Del., vol. 16, no. 4, pp. 791–800, Oct. 2001. IEEE PESHarmonic Working Group.

[3] A. Mansoor, W. M. Grady, P. T. Staats, R. S. Thallam, M. T. Doyle,and M. J. Samotyj, “Predicting the net harmonic currents produced bylarge numbers of distributed single-phase computer loads,” IEEE Trans.Power Del., vol. 10, no. 4, pp. 2001–2006, Oct. 1995.

[4] D.-G. Kim, T. Nakajima, and E. Masada, “Harmonic analysis of a ca-pacitor-filtered rectifier with line impedance,” Electron. and Commun.in Japan, pt. Part 1, vol. 72, no. 4, 1989.

[5] Task Force on Harmonics Modeling and Simulation, “Modeling andsimulation of the propagation of harmonics in electric power networks,part I: Concepts, models, and simulation techniques,” in IEEE Trans.Power Del., S. Ranade, W. Xu, and J. Mahseredjian, Eds., Jan. 1996,vol. 11, pp. 452–465.

Emad Ezzat Ahmed was born in Egypt in 1971. Hereceived the B.Sc. and M.Sc. degrees in electrical en-gineering from the Electrical Power and MachinesDepartment, Cairo University, Cairo, Egypt, in 1993and 1998, respectively, and the Ph.D. degree fromthe University of Alberta, Edmonton, AB, Canada inJune 2003.

He then became an Assistant Professor in theElectrical Engineering Department, Cairo Univer-sity-Fayoum Campus. His research interests includepower quality, harmonic impedance measurement,

harmonic filters, optimization, and distributed generation.

Wilsun Xu (M’90–SM’95–F’05) received the Ph.D. degree from the Universityof British Columbia, Vancouver, BC, Canada, in 1989.

He was with BC Hydro from 1990 to 1996 as an electrical engineer. He ispresently a Professor at the University of Alberta, Edmonton, AB, Canada, andan Adjunct Professor at Shandong University of China. His main research in-terests are harmonics and power quality.

Dr. Xu became an IEEE Fellow for his contributions to the analysis, simula-tion, and measurement of power system harmonics.

Guibin Zhang received the B.Sc. and M.Sc. degrees in electrical engineeringfrom Shandong University, China in 1995 and 1998, respectively, and the Ph.D.degree from Zhejiang University, China, in 2001.

He is currently a Postdoctoral Fellow at the University of Alberta, Edmonton,AB, Canada. His main research interests include power quality, HVDC andFACTS.

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