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Aggregate Harmonic Load Model

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IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 22, NO. 1, JANUARY 2007 323
Development of Stochastic Aggregate HarmonicLoad Model Based on Field Measurements
Mau Teng Au
, Member, IEEE
, and Jovica V. Milanovic´
, Senior Member, IEEE
Abstract—
The stochastic simulation approach in analyzingharmonic propagation in the distribution network requires anadequate stochastic/probabilistic aggregate harmonic load model.The interaction of individual linear and harmonic loads that formaggregate load characteristic harmonic current spectra is usuallyvery complex and, therefore, it is difﬁcult to establish a modelbased on theoretical analysis. This paper presents a methodologyin developing a stochastic/probabilistic aggregate harmonic loadmodel based on ﬁeld measurements. The model is a current injec-tion model characterized by means and variances associated withnet harmonic current spectra produced by aggregate harmonicloads, and a range ofaggregate harmonicload powerparticipation(fraction) into total demand, suitable for application in stochasticharmonic propagation studies in distribution networks.
Index Terms—
Aggregate harmonic load model, distribution net-work, harmonic ﬁeld measurements, harmonic load composition,stochastic.
I. I
NTRODUCTION
P
RESENT DAY electrical loads in all sectors of electricityconsumers (industrial, commercial, and residential) aretypically a mix of linear and nonlinear/power-electronic loads.With the rapid advancement of power-electronic technologyand higher energy efﬁciency achieved from power-electronicdriven loads, the use of power-electronic loads is expected toincrease. Examples of linear loads are incandescent lamps,motors, heaters, conventional ovens, and air conditioning,whereas nonlinear/power-electronic loads include ﬂuorescentlamps, adjustable-speed drives, converters, computers, andother electronic home appliances, such as television sets,video players, etc. While nonlinear/power-electronic loads aresources of harmonics, linear loads act as damping elements toharmonic propagation and affect the resonance frequency of the distribution system [1].At the utility medium and low-voltage bus, loads are repre-sented by the aggregate effect of individual loads. For harmonicpropagation studies based on the current injection method, it is
Manuscript received April 4, 2005; revised January 6, 2006. This work wassupported in part by the Malaysian Utility Company and in part by the TenagaNasional Bhd. Paper no. TPWRD-00192–2005.M. T. Au is with the Electrical and Electronic Engineering Department, Uni-versiti Tenaga Nasional, Kajang 43009, Malaysia (e-mail: mtau@uniten.edu.my).J. V. Milanovic´ is with the School of Electrical Engineering and Elec-tronics, University of Manchester, Manchester M60 1QD, U.K. (e-mail:milanovic@manchester.ac.uk).Color versions of Figs. 2–8, 11, and 12 are available online at http://ieeex-plore.org.Digital Object Identiﬁer 10.1109/TPWRD.2006.881455
generally required that the aggregate harmonic load be repre-sented by a harmonic current source in parallel with some linearcomponents such as resistance, inductance, and capacitance.Published papers on harmonic current measurements taken atutility substations [2]–[4] indicated the random nature of har-moniccurrentsproducedbyaggregateharmonicloads,thusjus-tifying a probabilistic model. Most of the aggregate harmonicloadmodelspresentedinliteraturearelimitedtospeciﬁcgroupsof nonlinear loads or formulated based on extensive harmonicmeasurements. For example, [5] and [6] reported the predic-
tion of net harmonic currents produced by a large number of single-phase power-electronic loads using attenuation and di-versityfactors.Theprobabilisticmodelingofharmoniccurrentsproduced by speciﬁc types of nonlinear loads, such as the elec-tricvehiclebatterychargersandpowerconverterswerereportedin [7] and [8]. A simpliﬁed process using semiempirical expres-
sions to forecast levels of harmonic current produced by homo-geneous nonlinear loads having uniform or normal distributionwas illustrated in [9]. In [10], a stochastic load model based
on comprehensive harmonic measurements was presented andused to perform harmonic simulation using the Monte Carlo ap-proach. In general, there is a lack of an adequate stochastic/ probabilisticaggregateharmonicloadmodelclassiﬁedbasedoncustomers activities suitable for harmonic propagation studiesin the distribution network, particularly at the medium-voltagelevel.This paper presents a generic approach in developing a sto-chastic/probabilistic aggregate harmonic load model based onharmonic ﬁeld measurements. Stochastic/probabilistic modelsof aggregate harmonic loads were established and classiﬁed ac-cording to consumers’ sectors/activities (i.e, commercial, res-idential, and industrial). The application of the model is pri-marily in stochastic harmonic propagation studies in medium-voltage distribution networks. The stochastic model describedin this paper can be used to establish the aggregate harmonicload model at any bus in any distribution network for whichsome measurement results or the information about load typeand composition are available.II. G
ENERAL
D
ESCRIPTION OF
A
GGREGATE
H
ARMONIC
L
OADS
Typically, a large number of a variety of linear and nonlinearloads connected at the low-/medium-voltage bus of a distribu-tiontransformer,commonlyknownasthepointofcommoncou-pling (PCC), form an aggregate load (see Fig. 1). Linear loadsdo not produce harmonic currents, but are a signiﬁcant compo-nentoftheaggregateloadastheydrawfundamentalcurrentand,therefore, affect the current total harmonic distortionat the PCC. On the other hand, nonlinear/harmonic loads pro-duce harmonic currents according to their individual harmonic
0885-8977/$20.00 © 2006 IEEE
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
ﬁ
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].Theharmoniccurrentspectraofaggregateharmonicloadsareprimarily in
ﬂ
uenced by their harmonic load composition andtypes which, in general, varies according to the class of cus-tomers.Forexample,electronichomeappliances,suchastelevi-sionsets,videoplayers,and
ﬂ
uorescentlampsformthemajorityofnonlinearloadsofresidentialconsumers,whereas
ﬂ
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-
ﬂ
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 atthePCCof low-voltagebusestypicallydonot exceed 20% in comparison to of an individual non-linear load, which ranges between 20%
–
120%. In this case, asigni
ﬁ
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 changeswith the totalpower 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
H
ARMONIC
L
OAD
M
ODELING
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 thecapacitiveelementtypicallyreferstopowerfactorcorrectionca-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
AnAHLisusuallymadeupofalargenumberandavarietyof harmonic loads. Hence, it is not practical and ef
ﬁ
cient to repre-sent each and every harmonic loadindividually with a harmoniccurrent source. However, the harmonic loads can be generallyclassi
ﬁ
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
AU AND MILANOVIC
´
: DEVELOPMENT OF STOCHASTIC AGGREGATE HARMONIC LOAD MODEL 325
TABLE ID
ESCRIPTION OF
C
OMPOSITE
H
ARMONIC
L
OADS
(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 andhasasigni
ﬁ
cantin
ﬂ
uenceontheharmoniccurrentspectrumandof 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
ﬁ
ce complex load, its harmonicload composition is most likely made up of 30
–
40% type 1 har-monicloads(magneticballast
ﬂ
uorescentlamp,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
ﬂ
u-orescent lamp, etc.), and 60%
–
70% of type 2 harmonic loads(computers, electronic home appliances, television, electronicballast
ﬂ
uorescent lamps, etc.).WithreferencetoFig.1,coef
ﬁ
cients representthefraction(participation)oftherespectivecompositeharmonicloads(type1,type2,etc.)intothetotaldemandofAHL.Thenetharmonic current spectrum of the AHL is the vectorsum of the harmonic current spectrum generated by individualcomposite 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 currentdistortion, respectively produced by the AHL,is the weighted coef
ﬁ
cient representing thefraction of the respective composite harmonic loads (type1, type 2, etc.) into the total demand of AHL, andare the magnitude and phase angle corresponding to theth harmonic current distortion, respectively, of the th typecomposite harmonic loads.IV. A
GGREGATE
L
OAD
M
ODEL AT
PCCAt 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-tudeandphaseangle,respectively,correspondingtothe thhar-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 theproductionofharmoniccurrentdistortionsatthePCC.Equation(3) is therefore modi
ﬁ
ed and written in its normalized form asfollows to represent random characteristics of harmonic current
326 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 22, NO. 1, JANUARY 2007
TABLE IIM
EAN AND
S
TANDARD
D
EVIATION OF
AHL P
ARAMETERS
E
STABLISHED
B
ASED ON
F
IELD
M
EASUREMENT
R
ESULTS
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
ﬁ
cientrepresenting the fraction of the respective composite harmonicloads (type1, type2, etc.) into thetotaldemand 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 thepower demand of the aggregate load. Since overall power de-mand of most aggregate loads varies with time, harmonic cur-rentdistortionatthePCCisthereforetimevariant.Forexample,it can be seen in Fig. 4 that the 5th and 7th harmonic currentdistortions closely correlate with the fundamental current (i.e,powerdemand)ofthehotelload,wherehigheroverallharmoniccurrent 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
ﬁ
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
ﬁ
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
ﬁ
ned by mean and standard deviationare shown in Table II.V. H
ISTOGRAM
S
AMPLES OF
H
ARMONIC
C
URRENT
D
ISTORTIONS
F
ROM
F
IELD
M
EASUREMENTS
Statistical plots of harmonic current distortions at the PCCbased on
ﬁ
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
ﬁ
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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