Aggregate Harmonic Load Model

8/10/2019 Aggregate Harmonic Load Model

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324 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 22, NO. 1, JANUARY 2007

Fig. 1. Aggregate harmonic load model.

current spectrum. Net harmonic current produced by aggregateharmonic loads (AHL) is usually signi cantly smaller than thealgebraic sum of the harmonic currents produced by the indi-vidual nonlinear/harmonic load, mainly due to phase cancella-tion [5], [6] .

The harmonic current spectra of aggregateharmonic loads areprimarily in uenced by their harmonic load composition andtypes which, in general, varies according to the class of cus-tomers. Forexample, electronic home appliances, such as televi-

sion sets, video players, and uorescent lamps form the majorityof nonlinear loads of residential consumers, whereas uorescentlamps and computers are typical nonlinear loads of commercialconsumers. As a result, the composite harmonic current spec-trum of a residential AHL is likely to be different from that of the commercial AHL.

of the aggregate load (i.e, at the PCC) is in-uenced by both the participation (fraction) of linear loads intothe total demand of the aggregate load as well as composite har-monic current spectra of the AHL. Field measurements have in-dicated that at the PCC of low-voltage buses typically donot exceed 20% in comparison to of an individual non-

linear load, which ranges between 20% 120%. In this case, asigni cant reduction in at the PCC can be attributed tothe large fraction of linear loads in the power demand of aggre-gate load and harmonic current cancellation due to phase-anglediversity.

Another characteristic of harmonic currents produced by ag-gregate harmonic loads is that they are random with a changingaverage over time. The randomness of harmonic currents pro-duced is due to a variety of factors, such as the random varia-tion of nonlinear load composition based on consumer needs,random operating condition (phase-angle control) of individualnonlinear loads, changes in system parameters, etc. At the sametime, the average level of harmonic current distortions at thePCC changes with the total power demand of the aggregate loadas illustrated in Figs. 2 and 3.

Fig. 2. Fundamental current and third harmonic current variation over time of a residential aggregate load.

Fig. 3. Timechart of the measured fundamental current and harmonic currentdistortions of a hotel load.

III. A GGREGATE HARMONIC LOAD MODELING

In the current injection model, aggregate harmonic loads arerepresented by a single harmonic current source in parallel withthe resistive, inductive, and capacitive element [1]. The singleharmonic current source represents the net harmonic currentspectrum of the AHL connected to the respective bus whereasresistive and inductive elements represent linear loads, and thecapacitive element typically refers to power factor correction ca-pacitors. Establishing net harmonic current spectrum of AHL ishighly complex and, therefore, the estimation technique usingdiversity and the attenuation factor is proposed in [5] and [6] .

To develop an adequate AHL model, a probabilistic approachis taken as harmonic currents produced at the PCC are randomand time variant due to continual changes in system and loadparameters, and power demand [2] , [11].

A. Representation of Harmonic Loads

An AHL isusually made upof a large numberand a varietyof harmonic loads. Hence, it is not practical and ef cient to repre-sent each and every harmonic load individually with a harmoniccurrent source. However, the harmonic loads can be generallyclassi ed based on their characteristic harmonic currents andits level. In this paper, it is proposed that harmonic loadsfound in a particular class of AHL be grouped into four com-posite types based on their characteristic harmonic currents and


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AU AND MILANOVIC : DEVELOPMENT OF STOCHASTIC AGGREGATE HARMONIC LOAD MODEL 325

TABLE IDESCRIPTION OF COMPOSITE HARMONIC LOADS

(i.e, low, medium, or high). Table I gives a descriptionof the proposed composite harmonic loads.

B. Harmonic Load Composition

Harmonic load composition is a crucial parameter in aggre-gate harmonic load modeling as it is changing over time andhas a signi cant in uence on the harmonic current spectrum and

of aggregate harmonic load. In a broad sense, harmonicloads compositions are related to load types based on customeractivities and energy usage pattern. For example, during the dayperiod (9.00 17.00 h) of an of ce complex load, its harmonicload composition is most likely made up of 30 40% type 1 har-monic loads(magnetic ballast uorescent lamp, etc.), 50% 60%of type 2 harmonic loads (computers, electronic devices, etc.)and 10 15% of type 4 harmonic loads (three-phase converters).On the other hand, during the night period (17.00 24.00 h) of a residential load, its harmonic load composition is likely madeup of 30% 40% of type 1 harmonic loads (magnetic ballast u-orescent lamp, etc.), and 60% 70% of type 2 harmonic loads(computers, electronic home appliances, television, electronicballast uorescent lamps, etc.).

With reference to Fig. 1 , coef cients representthe fraction (participation) of the respective compositeharmonicloads (type 1, type 2, etc.) into the total demand of AHL. The netharmonic current spectrum of the AHL is the vectorsum of the harmonic current spectrum generated by individual

composite harmonic loads connected to the PCC, whichcan be expressed as follows:

(1)

which can be written in compact phasor form as follows:

(2)

where and are the magnitudeand phase angle corresponding to the th harmonic current

distortion, respectively produced by the AHL,is the weighted coef cient representing the

fraction of the respective composite harmonic loads (type1, type 2, etc.) into the total demand of AHL, and

are the magnitude and phase angle corresponding to theth harmonic current distortion, respectively, of the th type

composite harmonic loads.

IV. A GGREGATE LOAD MODEL AT PCC

At the PCC, in particular, those with small aggregate loads,harmonic and linear loads are fed through the same cable.Hence, it is not possible to separately measure harmoniccurrent distortions produced by AHL (see Fig. 1 ).Therefore, from a practical point of view, an expression forharmonic current distortions at the PCC (which is inclusive of current drawn by all linear loads) needs to be formulated asshown in (3) .

A. Participation of Harmonic Loads

The harmonic current distortion at the PCC is therefore de-pendent on the power participation (fraction) of harmonic loadsinto the total demand of aggregate load (see Fig. 1 ). From (2),the harmonic current spectrum at PCC can then be expressed asfollows:

(3)

where and are the magni-tude and phase angle, respectively, corresponding to the th har-monic current distortion at PCC, is the frac-tion of harmonic loads participating into the total demand of theaggregate load.

B. Stochastic Model

Field measurements indicate that harmonic current distor-tions at the PCC vary randomly with a trend component closelycorrelating with the power demand of the aggregate load.The random variation is primarily due to the combined effectof continuous changes in operating conditions (for example,ASD which produced different harmonic current distortionsdepending on its load conditions), and/or usage pattern of linearand nonlinear loads (switching on and off based on needs).At the same time, there is a need to account for uncertainties inharmonic current distortions of the respective composite har-monic loads due to various factors. For example, the harmoniccurrent spectrum of composite harmonic loads is expectedto deviate from sample measured results within a range dueto the different types/manufacturers of electronic equipments(personal computers, printers, photocopy machines, television,etc.) (see Table IV ).

Hence, random variables are used to represent aggregate har-monic load parameters ( , , , ) associated with theproduction of harmonic current distortions at the PCC. Equation(3) is therefore modi ed and written in its normalized form asfollows to represent random characteristics of harmonic current


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TABLE IIMEAN AND STANDARD DEVIATION OF AHL P ARAMETERS ESTABLISHED BASED ON FIELD MEASUREMENT RESULTS

Fig. 4. Fifth harmonic current distortion at the PCC of shopping complex loadbased on a one-week period.

distortions at the PCC:

(4)

where denotes random variables cor-responding to the probability density function (PDF) thatdescribes harmonic current spectrum at the PCC,denotes random variables that correspond to the PDF thatdescribes a fraction of the AHL participating into the totaldemand of the aggregate load, denotes random variablescorresponding to the PDF that describes a weighted coef cientrepresenting the fraction of the respective composite harmonicloads (type 1, type 2, etc.) into the total demand of AHL,and denote random variables corresponding to the PDFthat describes the magnitude and phase, respectively, of the thharmonic current distortion of the th-type composite harmonicloads.

C. Time-Variant Harmonic Current Spectrum

As mentioned previously, harmonic currents at the PCC varyrandomly with a trend component closely associated with the

power demand of the aggregate load. Since overall power de-mand of most aggregate loads varies with time, harmonic cur-rent distortion at the PCC is therefore time variant. For example,it can be seen in Fig. 4 that the 5th and 7th harmonic currentdistortions closely correlate with the fundamental current (i.e,power demand) of the hotel load, where higher overall harmoniccurrent distortions corresponds to a period of high demand inthis case.

Hence, to account for the time-variant characteristic of har-monic current distortions at the PCC, periods of high- and low-power demand are de ned for each category of aggregate loads,and random variables representing AHL parameters ( , ,

, ) are characterized based on respective periods. For ex-ample, in the case of the hotel load shown in Fig. 4, its low de-mand period is de ned as being between 0.00 10.00 h and ahigh demand period between 10.00 24.00 h. Periods of low andhigh demand of the hotel, residential, bank, hospital, shoppingcomplex, and printing factory loads and their correspondingAHL parameters de ned by mean and standard deviation

are shown in Table II .

V. H ISTOGRAM SAMPLES OF HARMONIC CURRENTDISTORTIONS FROM FIELD MEASUREMENTS

Statistical plots of harmonic current distortions at the PCC

based on eld measurements over a one-week period indicatethat statistical distribution of harmonic current distortions at thePCC of most load types are complex and cannot be expressedin terms of common PDF, such as the normal distribution. Thisis primarily due to very distinct variations in power demand atdifferent periods of the day, which are indicated by the pres-ence of two peaks in histogram plots (see Fig. 4). To simplifythe statistical analysis, harmonic current distortions are dividedinto subtime intervals corresponding to high and low demandperiods of the aggregate loads. As can be observed from Fig. 5 ,statistical distribution of the fth harmonic current distortion of the shopping complex load corresponding to a period of highpower demand (11.00 23.00 h) is approximately a normal dis-tribution. However, for certain types of loads, such as the hotelload, where high- and low-power demand of the aggregate load


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Fig. 5. Fifth harmonic current distortion at the PCC of the shopping complexload based on a subtime interval between 11.00 23.00 h.

Fig. 6. Third harmonic current distortion at the PCC of the hotel load based ona one-week period.

is not so distinct, it is observed that its harmonic current distor-tion at the PCC over a one-week period remains normally dis-tributed as can be seen in Fig. 6 . Hence, in general, the modeling

of harmonic current distortions at the PCC is divided into twotime periods corresponding to high- and low-power demand of the aggregate load.

VI. E STABLISHING AHL P ARAMETERS BASED ON HARMONICFIELD MEASUREMENT RESULTS

In modeling the stochastic nature of the harmonic currentspectrum at the PCC based on (4), its statistical distribution canbe determined given the AHL parameters PDF and their respec-tive characteristic parameters (i.e, mean and standard deviationin the case of normal distribution). However, in most cases, theAHL parameters are not available.

In this paper, the AHL parameters are established based oneld measurement results of harmonic current spectra at the

Fig. 7. Comparative CDF of the modeled and measured results of low-voltageresidential loads. (a) Third harmonic current distortion. (b) Fifth harmonic cur-rent distortion.

PCC of the respective load types. PDF characteristicparameters (e.g, mean and standard deviation in the case of normal distribution, maximum, and minimum in the case of uni-form distribution) assumed to represent the respective AHL pa-rameters in (4) are varied experimentally (numeroustrials) until an approximate solution is found, where the cumu-lative distribution curve/function (CDF) of the two most domi-nating harmonic currents distortions derived based on the model[i.e, (4) ] and harmonic eld measurements are in good agree-ment (see Fig. 7 and Fig. 8 ). In this investigation, parameters

and are assumed to be normally distributed with meanand standard deviation as unknowns to be solved, whereasand are uniformly distributed with a range of values given inTable IV . (Note: The ranges in Table IV are derived from mea-surements of individual harmonic loads.)

Based on the CDF curve tting technique described before,the mean and standard deviation of AHL parameters andfor the respective load types and corresponding time periodsare established and shown in Table II . Ideally, numerical values


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Fig. 8. ComparativeCDF of modeled and measured results of medium-voltageshopping complex loads. (a) Fifth harmonic current distortion. (b) Seventh har-monic current distortion.

shown in Table II should be veri ed with loads information ob-tained from utility/customer load data base. However, such in-formation is generally lacking and, therefore, it is assumed that

the numerical values are within an acceptable range based ontypical aggregate loads. (Note: It should be mentioned that anideally coef cient should be established based on the exactknowledge of nonlinear load composition. The approach takenhere relies on local harmonic measurements in the absence of this knowledge, which is generally the case in real life, and as-suming that the harmonic contribution from the rest of the distri-bution system compared to the contribution from local nonlinearloads is small, which again is generally the case.)

Corresponding phase angles of the harmonic currents distor-tions are also available from the model. However, due to thelimitation of the recording instrument which does not generatemeasured phase-angle values of harmonic currents distortions,phase-angle variations over a speci c period based on the modelcould not be validated.

Fig. 9. Stochastic current injection model of an AHL

A. Case of PCC at Low-Voltage Bus

Typically, dominant characteristic harmonic currents at a low-

voltage bus are the 3rd and 5th. Hence, in order to establish nu-merical values (mean and standard deviation) of AHL parame-ters and based o n eld measurement results, a CDF curvetting is based on the 3rd and 5th harmonic current distortions.The results are shown in Fig. 7 .

B. Case of PCC at Medium-Voltage Bus

At the medium-voltage bus, triplen harmonic currents are notpresent due to delta winding of distribution transformers. Hence,the CDF plot of the two most dominant harmonic currents atmedium-voltage buses (i.e, 5th and 7th) are used to establishthe mean and standard deviation of and . The results are

shown in Fig. 8 .

VII. A PPLICATION OF THE AHL M ODEL INHARMONIC SIMULATIONS

The load model at the PCC developed in this paper consistsof a single stochastic harmonic current source that representsnet harmonic current spectra of the aggregate harmonic loads,with R, L, and C components used to represent linear loads (i.e.,induction motors, resistive loads, etc.) as shown in Fig. 9. Typi-cally, the AHL model could be used in two different approachesof harmonic simulations (i.e., commercial harmonic simulation

software such as SUPERHARM [12] ) which gives snapshot re-sults of harmonic voltage distortions, or a Monte Carlo simula-tion method which generates results in probabilistic terms.

For simplicity and illustration purposes, the AHL model isused in SUPERHARM harmonic simulation software to com-pute the 5th harmonic voltage distortion at network buses of a6-bus 11-kV radial distribution feeder as shown in Fig. 10.

In the following case, harmonic current spectra produced bythe AHL corresponding to the respective load types are derivedbased on AHL parameters given in Table II . Results of the 5thharmonic current distortions are shown in Table III .

Load conditions (in kilovolt-ampere/phase) shown in Fig. 10are for the period between 11.00 18.00 h which corresponds tothe period of high load for a shopping complex, hotel, printingfactory and bank, and a period of low load for a residential


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Fig. 10. Six-bus 11-kV radial distribution network.

TABLE IIIPROBABILISTIC HARMONIC CURRENT SPECTRA AT PCC

apartment. Five cases representing critical points of the proba-bility distribution curve of the respective AHL harmonic currentspectra are selected as inputs for harmonic simulation.Case 1) , .Case 2) , .Case 3) ,Case 4) ,Case 5) ,

Results of the fth harmonic voltage distortion at each net-work bus for all ve cases are shown in Fig. 11 . As can be seenin Fig. 11 , the main advantage of the stochastic AHL model inharmonic simulation is that it givesa range of possible harmonicvoltage distortions at each bus instead of a single possible value.In addition, the simulation results are realistic (between 0.5 and0.9%) compared to measured values (see Fig. 12 ) as some of the major phenomena, such as phase-angle diversity, harmonicload compositions in AHL, and power participation of harmonicloads that affect the net harmonic current spectrum of AHL havebeen accounted for in the model equation.

VIII. C ONCLUSION

This paper presented a methodology for the development of a stochastic aggregate harmonic load model based on harmoniceld measurements. The AHL is applicable to loads connectedat the low- and medium-voltage level. The stochastic load modelis realized through a set of probabilistic load parameters that in-uence the production of net harmonic current distortion at the

Fig. 11. Fifth harmonic voltage distortion at network buses based on simula-tion.

Fig. 12. CDF of fth harmonic voltage distortions at four 11-kV sites based oneld measurements.

TABLE IVPROBABILISTIC HARMONIC CURRENT SPECTRA OF

COMPOSITE -TYPE HARMONIC LOADS

PCC. These load parameters are typically available from a cus-tomer load data base and can be obtained at the planning (con-nection of a new supply) or operational stage (facilities manage-ment).

Realistic results regarding harmonic voltage distortionsbasedon the proposed AHL model and using load parameters derivedfrom harmonic eld measurements are obtained.

With more accurate data about load parameters made avail-able, it is envisaged that the proposed AHL model could ndits application in probabilistic-based harmonic simulationsoftware.


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ACKNOWLEDGMENT

The authors would like to thank C. C. Woo and Mr. Megatof TNB Metering Service and Dr. Fadzil of TNB Research fortheir assistance in performing harmonic eld measurements.

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Mau Teng Au (M 04) received the B.S.E.E. degree in electrical engineeringfrom the University of Toledo, Toldeo, OH, in 1986 and the M.Sc. degree inelectrical engineering from Purdue University, West Lafayette, IN, in 1996, andthe Ph.D. degree in electrical engineering from the University of Manchester(formerly UMIST), Manchester, U.K., in 2005.

Currently, he is Principal Lecturer in the Department of Electrical and Elec-

tronic Engineering at the Universiti Tenaga Nasional, Kajang, Malaysia.

Jovica V. Milanovic (M 95SM 98) received the Dipl.Ing. and M.Sc. degreesin electrical engineering from the Universityof Belgrade, Belgrade, Yugoslavia,and the Ph.D. degree from the University of Newcastle, Newcastle, Australia.

Currently he is a Professor of Electrical Power Engineering with the Schoolof Electrical and Electronic Engineering, University of Manchester (formerlyUMIST), Manchester, U.K.

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Aggregate Harmonic Load Model