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ORIGINAL PAPERJ. A. Ghijselen W. A. Ryckaert J. A. MelkebeekInfluence of electric power distribution systemdesign on harmonic propagationReceived: 5 June 2003/ Accepted: 11 September 2003/Published online: 14 November 2003? Springer-Verlag 2003Abstract The impact of the design parameters of electricpower distribution systems on the propagation of har-monic distortion is investigated. This conceptual study isbased on simulations on a generalized distribution sys-tem model, and leads to an increased insight in themechanisms of the generation and propagation of volt-age distortion. Moreover, analytical expressions arepresented that predict the impact of changing designparameters on voltage distortion.Keywords Distribution systems Voltage distortion Harmonics Power quality Power system impedance1 IntroductionBecause of the increasing penetration of non-linear loadsin electric power distribution systems, utilities andequipment manufacturers are increasingly concernedwith harmonic pollution of the voltage waveform.Voltage distortion is known to exhibit many adverseeffects 1, and especially in areas where the electricitytrade is being liberalized, it is feared that voltage dis-tortion will increase in the near future 2. In many partsof the world, the actual voltage distortion levels aremaintained within planning levels by imposing appro-priate emission limits to the harmonic line currents ofequipment 3.To determine appropriate equipment emission limits,both measurement campaigns 4 and simulations 5, 6are required to study the harmonic propagation in anactual network. At first sight, it seems easier and cheaperto conduct simulations instead of measurements. How-ever, the parameters and design strategies may be verydifferent from one network to another 7, making alarge number of simulations necessary. Moreover, manyparameters are unknown and are therefore estimated oreven neglected, rendering results that may differ largelyfrom measured data 8. Finally, as harmonic propaga-tion studies are mostly limited to rather specific cases(e.g., 5), fundamental insight in the mechanisms ofharmonic propagation and the influence of the distri-bution system design is not obtained.In this paper, the impact of different distributionsystem design parameters on harmonic propagation isinvestigated. The study is based on the analysis of ageneralized distribution feeder model of which theparameters are varied. Some preliminary and qualitativeresults, based on simulations of a specific case study, arereported in 9. In the present paper, however, a morefundamental approach is adopted. Analytical expres-sionsandquantitativeresultsarepresentedthatapproximately predict the impact of changing designparameters on the distortion levels. The validity of theanalytical predictions is confirmed by simulations. Sub-sequently, the analysis is extended to include the effectsof shunt capacitance, which are strongly related withpower system resonances.2 Basic power system setup2.1 Network topologyIn order to investigate the influence of different distri-bution system parameters on harmonic propagation, asimplified model of a typical medium voltage (MV)distribution system is adopted (Fig. 1). The high-to-medium voltage (HV/MV) transformer, which is feedingthe point of common coupling (PCC), is represented byits short-circuit impedance Zm. Several parallel andidentical radial feeders, having five nodes each, connectto the loads. The conductor segments interconnectingJ. A. Ghijselen (&) W. A. Ryckaert J. A. MelkebeekFaculty of Engineering,Electrical Energy Laboratory (EELAB),Ghent University, Sint-Pietersnieuwstraat 41,9000 Gent, BelgiumE-mail: jozef.ghijselenugent.beTel.: +32-9-2643442Fax: +32-9-2643582Electrical Engineering (2004) 86: 181190DOI 10.1007/s00202-003-0201-7the feeder nodes are represented by their series imped-ances Zs,k.The MV/LV transformers may be located betweenthe MV bus and the feeders (Zl, Fig. 1a) or between thefeeder nodes and the loads (Zc, Fig. 1b). The formerpractice calls for extended low voltage (LV) feeders,which is the practice in large parts of Europe. The latterpractice calls for extended MV feeders, which is thepractice in many North American regions.The loads connected to the nodes are modeled asideal current sources; this approximation is allowed asfor moderate voltage distortion levels (total harmonicdistortion (THD)45?, the harmonic impedance forharmonics h3 is approximately inductive and equal to:Zm;l;ch ? jh Zm;l;c?sinhZm;l;c1Consequently, the harmonic transformer impedancedepends on both the magnitude and phase angle of thefundamental transformer impedance. For instance, itfollows from (1) that the small HV/MV and MV/LVtransformers exhibit an harmonic impedance that is 1.39and 3.48 times smaller, respectively, than the harmonicimpedance of the large HV/MV transformer.2.3 Conductor parametersBecause of the considerable length of the conductors inmany distribution systems, voltage drop is generallymore important than power loss. The maximal allowablemagnitude |Zs| of the (fundamental) conductor imped-ance is determined to limit the (fundamental) voltagedrop DV=|VFl|)|VF5| to 0.12 pu along the feeder, whilethe voltage at the beginning of the feeder equals|VFl|=1.06 pu. The total feeder load is supposed toequal 1 pu at a power factor of cos/=0.8, and is equallydivided among the nodes. These values are typical fordistribution system operation.The conductor type (overhead or cable) of all con-ductor segments is considered equal, but the conductorsection may be tapered. For simplicity, the impedance ofthe feeder segments is supposed to increase linearlytowards the end of the feeder. Mtdenotes the taperingfactor determining the impedance of the last feedersegment:Zs;4 MtZs;12A non-tapered line is obtained for Mt=1. The fol-lowing maximal conductor impedance values are thenfound and serve in the following sections to obtain dif-ferent feeder arrangements with equal (fundamental)voltage drops DV:Zs jZsjejhZs 0:04815 pu55?regular overhead line; no taperingZs jZsjejhZs 0:06089pu80?widely spaced overhead line; no taperingZs jZsjejhZs 0:04626 pu30?cable; no taperingZs;1 jZs;1jejhZs;1 0:02898 pu55?regular overhead line; Mt 3Fig. 1 Basic MV distribution system model: a MV/LV transformerlocated at the beginning of the feeder, b MV/LV transformerslocated in the feeder nodes182Zs;1 jZs;1jejhZs;1 0:02070 pu55?regular overhead line; Mt 5Zs jZsjejhZs 0:09300 pu55?regular overhead line;no tapering; expected load power factor cos/ 1The pu values are referred to the rating of a singlefeeder. As with the transformer impedance, the con-ductor impedance is considered to be resistive-inductive.Because hZs30?, the harmonic impedance of the con-ductors is approximately inductive:Zsh ? jh ZsjjsinhZs3Consequently, when the regular overhead line isreplaced by the cable or the widely spaced overhead line,the magnitude of the harmonic impedance (3) decreaseswith a factor 1.71 or increases with a factor 1.52,respectively. When expected power factor of the feederload is increased from 0.8 to 1, the harmonic impedanceof the regular overhead line increases by Modeling peak rectifier loadsIn this paper, peak rectifiers are supposed to be the mostcommon non-linear load. Because of the limited numberof nodes in a single feeder, a large number of loads isaggregated in every single node. A realistic load currentspectrum should therefore include the effects of attenu-ation and diversity 11. A typical current spectrumcomplying with these requirements is listed in Table 112.It should be remembered that the numerical results ofvoltage distortion calculations depend on the actual loadcurrent spectrum. Some examples, illustrating in moredetail the specific influence of the zero-sequence (h=3, 9,15, .) and higher-order (h 17) harmonic load cur-rents, are given in 9.3 Influence of neutral conductor practiceWhen the load current contains a zero-sequence com-ponent (e.g., caused by load unbalance or triplen har-monics), the impact of the neutral conductor practice onthe voltage distortion throughout the distribution sys-tem becomes important. Both the arrangements of thefeeder conductor and transformers influence the neutralconductor practice.3.1 Feeder conductor arrangementIn this paper, two typical feeder conductor arrangementsare studied. For a symmetrical three-phase, four-wirearrangement with equal conductor sections, the imped-ance for zero-sequence currents equals four times theimpedance for the positive- and negative-sequencecomponents.Insuchsystems,triplenharmonics(behaving as zero-sequence currents in balanced sys-tems) may cause considerable voltage distortion 13.When the three-phase conductors are split into threesingle-phase, two-wire, conductor sets, a three-phase, six-wire arrangement is formed, for which the zero-sequenceimpedance of the conductors equals the positive-andnegative-sequence impedances. Therefore, zero-sequencecurrents cause considerably less voltage distortion thanin a three-phase, four-wire arrangement.To assess the influence of the conductor arrangement,the total harmonic voltage drop DVhof a single con-ductor segment is defined as the RMS value of theharmonic voltage drop:DVhffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiX1h2Zshjj2Ihjj2s4with I(h) denoting the harmonic current componentsflowing in the conductor. If balanced loads are assumed,the reduction of the total harmonic voltage drop DVhwhen changing a four-wire for a six-wire arrangementdepends on the importance of the triplen harmoniccomponents of the load current spectrum and can beapproximated using (4) and (3):DVh;4wDVh;6w?ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPh63=h1h2Ihjj2 k2sPh3=h1h2Ihjj2Ph1h2Ihjj2vuuuut5where ksdenotes the ratio of the zero-sequence topositive-sequence impedances of the conductors in thefour-wire arrangement. For the load current spectrum ofTable 1 and ks=4 (symmetrical four-wire arrangement),the reduction factor (5) equals 2.62. In practice, theneutral conductor section is often chosen smaller thanthe phase conductor sections, causing ks4 and henceresulting in an even greater reduction factor.In the same manner, the reduction factor of the totalharmonic voltage drop of a conductor segment can beTable 1 Line current spectrum of the applied non-linear loadh|I(h)/I(1)|11.00030.82050.53470.31690.166110.082130.015150.010170.0060190.0050210.0030230.0010250.0010270,h25183approximated when the zero-sequence current compo-nents are eliminated before entering the feeder conduc-tors(e.g.,bymeansofanintermediateMV/LVtransformer connected in DY):DVh;neutralDVh;no neutral?ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPh63=h1h2Ihjj2 k2sPh3=h1h2Ihjj2Ph63=h1h2Ihjj2vuuuuut6For the line current spectrum of Table 1, the reduc-tion factor (6) equals 1.28 for ks=1 (six-wire arrange-ment) and becomes 3.36 for ks=4 (symmetrical four-wirearrangement). In practice, the removal of the zero-sequence currents from six-wire arrangements is notpractical and is therefore never encountered; the associ-ated reduction factor is therefore of purely academicvalue.3.2 Transformer arrangementsThe neutral conductor may be interrupted by the MV/LV transformer, e.g., by connecting it in DY arrange-ment, thereby reducing the harmonic voltage drop of theHV/MV transformer located upstream (in the PCC).Using (1), and assuming balanced loads, the reductionfactor of the voltage distortion in the PCC can be cal-culated:THDVPCCneutralTHDVPCCno neutral?ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPh63=h1h2Ihjj2 k2mPh3=h1h2Ihjj2Ph63=h1h2Ihjj2vuuuuut7where kmdenotes the ratio of the zero-sequence to thepositive-sequence impedances of the HV/MV trans-former. For the load current spectrum of Table 1 andkm=1, the reduction of the voltage distortion in thePCC equals 1.28.4 Basic factors governing power system harmonicpropagationTo assess the influence of the power system parameterspresented in the previous sections, simulations have beenperformed on the network of Fig. 1. In this section, theimpedance of the MV/LV transformers is neglected (i.e.,|Zc|=|Zl|=0). Non-zero MV/LV transformer imped-ances will be assumed in Sect. 5, where a case study ispresented. In this section, also the effects of shuntcapacitance are neglected; for moderate feeder conduc-tor lengths (up to several kilometers for cable conduc-tors, and up to a few tens of kilometers for overheadconductors) the shunt capacitance becomes importantfor higher harmonics only, for which the injected currentis usually small. The effects of capacitance are discussedin Sect. 6.The total (fundamental) load of a single feeder equals1 pu at cos/=1, and is balanced and equally dividedamong the feeder nodes. The voltage in the first feedernode (closest to the PCC) is controlled to |VFl|=1.06 pufor all simulations. The source voltage from the HV busis considered to be purely sinusoidal. The total amountof distorting loads (with a line current spectrum as inTable 1) represents 10% of the total fundamental load,while the remaining (linear) load only draws funda-mental current.In accordance with IEC regulations 14, only the first40 harmonics are considered when calculating THDvalues. By analogy with (4), the total harmonic voltagedrop DVFhof the feeder is defined as:DVFhffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiX40h2VF1h ? VF5hjj2vuut8This measure allows to explain the difference betweenthe voltage distortion in the PCC and at the end of thefeeder. Indeed, except when the neutral conductor isinterrupted, the operating conditions encountered in thispaper allow for the following approximation if DVFhisexpressed in per units:THDV5 ? THDVPCC DVFh9This is confirmed by the simulation results, which aresummarized in Table 2 and are discussed in the follow-ing subsections. Simulation no. 1 is considered to be thebase case, to which the effects of all parameter variationsare compared.4.1 Transformer choiceThe impact of the transformer parameters on voltagedistortion is explained by comparison of simulation nos.13 from Table 2. The results are graphically repre-sented in Fig. 2a. From Sect. 2.2, it follows that forsimulation nos. 2 and 3 the magnitude of the harmonictransformer impedance is 3.48 and 1.39 times smaller,respectively, than the harmonic impedance for simula-tion no. 1 (base case). As expected, this causes thevoltage THD in the PCC to decrease with about thesame factor.At the end of the feeder, the voltage THD is severaltimes greater than in the PCC because of the harmonicvoltage drop of the feeder conductors. This result is inaccordance with recent measurements in the French LVsystem 13. Because the total harmonic voltage drop ofthe feeder conductor DVFhremains constant betweensimulation nos. 1, 2, and 3, the reduction of the voltageTHD at the end of the feeder is rather small and isapproximately equal to the reduction of the voltageTHD in the PCC.184Concluding, the impact of the transformer impedanceon voltage distortion is quite important in the PCC, butless important at the end of the distribution feeder,where the total harmonic voltage drop of the feederconductors becomes dominant. It turns out that thevoltage distortion in the PCC increases when the (fun-damental) transformer impedance increases or becomesmore inductive.4.2 Feeder conductor typeThe impact of the feeder conductor type on voltage dis-tortion is explained by comparing simulation nos. 46from Table 2. The results are graphically represented inFig. 2b. For simulation no. 4, the phase angle of theconductor impedance is decreased from 55? to 30?, ascompared with simulation no. 1. According to Sect. 2.3,this causes the harmonic impedance of the feeder to re-duce with a factor 1.71. As expected, the total harmonicvoltage drop of the feeder DVFhis reduced by about thesame factor as well. In turn, this causes a significantreduction of the voltage THD at the end of the feeder.Similar results are obtained when comparing simulationnos. 1 and 5, where the conductor impedance angle isincreased from 55? to 80? (causing the harmonic imped-ance of the feeder to increase by about 1.52), and forsimulation no. 6, where the expected displacement factoris increased from 0.8 (inductive) to 1.0 (causing the har-monic impedance of the feeder to increase by about 1.93).It is to be noted that the increase of the expected fun-damental displacement factor (simulation nos. 1 and 6)has more impact than the increase of the phase angle ofthe conductor impedance (simulation nos. 1 and 5).Table 2 Voltage THD for different network parametersSim. no.|Zm| (% pu)hZm(deg)|Zs,l| (% pu)hZs;1(deg)MlVoltage THDDVFh(% pu)CommentsVPCC(%)V5(%)110.0804.8155514.1213.319.57Typical HV/MVtransformer impedancebasecase234.010.045454.8154.8155555111.213.0310.6312.349.579.57Low HV/MVtransformer impedanceLow HV/MV transformerimpedance angle45610.010.010.08080804.6266.0899.3003080551114.223.984.1210.2816.9224.436.2713.8819.35Cable feederWidely spaced overhead feederExpected load cosF=17810.010.080802.8982.0705555354.104.0913.2813.269.589.57Moderate tapering factorHigh tapering factor910111210.010.010.010.0808080804.8154.8154.8154.815555555551123.216.1611.007.926.572.819.573.623.62Neutral conductor interruptedin nodesNeutral conductor interruptedin PCC3-ph, 6-w (or 3 1-ph) feeders3-ph, 6-w (or 3 1-ph)feeders, neutral conductorinterrupted in PCCFig. 2 Influence of different parameters: a transformer parameters,b feeder conductor parameters, c tapering185The impact on the voltage THD in the PCC is rathersmall. However, it is noticed that the voltage THD in thePCC is slightly reduced, when the conductor impedanceangle is increased. This is caused by phase angle diversitybetween the nodes 11, and becomes more important forincreasing harmonic orders and increasingly inductiveconductors. The stronger the higher harmonics of theload current, the more this effect becomes noticeable; anexample is given in 9.Concluding, the impact of the feeder conductorimpedance on voltage distortion is quite important atthe end of the feeder, but very small in the PCC. Similaras with the transformer impedance, it turns out that theharmonic voltage drop of the feeder increases when the(fundamental)conductorimpedanceincreasesorbecomes more inductive.4.3 Feeder conductor taperingThe impact of feeder conductor tapering on the voltagedistortion is explained by comparing simulation nos. 1,7, and 8 from Table 2. The results are graphically rep-resented in Fig. 2c. For simulation nos. 7 and 8, thetapering factor Mtis increased from 1 to 3 and 5,respectively, as compared with simulation no. 1. Theimpact on the voltage THD in the PCC and at the end ofthe feeder is negligible. This is mainly due to the equalfundamental voltage drop criterion for calculating theconductor segment impedances Zs,k(Sect. 2.3). There-fore, feeder conductor tapering will not be explored anyfurther in this paper.4.4 Neutral conductor practice4.4.1 Four-wire conductor arrangementThe impact of interrupting the neutral conductor onvoltage distortion is explained by comparing simulationnos. 1, 9, and 10 from Table 2. The results are graphi-cally represented in Fig. 3a. In simulation no. 9, theneutral conductor is interrupted between the feeder andload nodes by DY transformers with negligible imped-ance Zc=0. It follows that the expected decrease of thevoltage THD in the PCC by about 1.28 (Sect. 3.2)matches the simulations quite well. Also, the reductionof the harmonic voltage drop of the feeder (about thefactor 3.36 as predicted in Sect. 3.1) causes a consider-able reduction of the voltage THD at the end of thefeeder.The same harmonic voltage reduction in the PCC asabove is found when comparing simulation nos. 1 and 10,where,inthelatter,theneutralconductorisinterruptedinthe PCC by a DY transformer with negligible impedanceZl=0. However, the harmonic voltage drop of the feederconductor is not influenced leading to only a smallreduction of voltage THD at the end of the feeder.4.4.2 Six-wire conductor arrangementIn simulation nos. 11 and 12, a six-wire conductorarrangement is applied instead of the four-wire con-ductor arrangement of simulation no. 1. The results aregraphicallyrepresentedinFig. 3b.Thesimulationresults match well the predicted reduction of the totalharmonic voltage drop of the conductor (with a factor2.62, Sect. 3.1), again causing a considerable reductionof the voltage THD at the end of the feeder.Finally, in simulation no. 12, the neutral conductor isinterrupted in the PCC by a DY transformer with neg-ligible impedance Zl=0. As with the four-wire conduc-tor arrangement, this reduces the voltage THD in thePCC (and equals the value of simulation nos. 9 and 10),but not the harmonic voltage drop of the conductorDVFh(which equals the value of simulation no. 11),yielding only a small reduction of the voltage THD atthe end of the feeder.4.4.3 ConclusionConcluding, the neutral conductor practice has signifi-cant impact on the voltage distortion throughout thedistribution system, because it affects the harmonicFig. 3 Influence of different parameters: a interrupting the neutralconductor, b three-phase, four-wire vs. six-wire or single-phasecircuits, c North American and European design styles186voltage drop caused by the zero-sequence currents.Interrupting the neutral conductor always reduces thevoltage distortion in the PCC, and also the harmonicvoltage drop of the feeder conductors upstream of theinterruption. Also switching between four- and six-wireconductor arrangements reduces the harmonic voltagedrop of the feeder conductors significantly.5 Case study: differences between power system designpractice in Europe and North America5.1 Power system setup and typical parametersIn this section, a comparison is made between the harmonicpropagation properties of the two distribution system structures ofFig. 1, which differ in the placement and arrangement of the MV/LV transformers. The transformers are either placed at the begin-ning of the feeders (which is common to most European distri-bution systems, Fig. 1a), or between the feeder and load nodes(which is common to many North American distribution systems,Fig. 1b).When the MV/LV transformers are located at the beginning ofthe feeders (Zl), their size is usually quite large. In this case, theneutral conductor is interrupted in the MV/LV transformer, whichis common to European practice. When the MV/LV transformersare located between the feeder and load nodes (Zc), their size isusually rather small. In this case, the neutral conductor is notinterrupted in the MV/LV transformer, which is common to NorthAmerican practice.The resulting distribution systems, including the consideredtransformer arrangements, are depicted in Fig. 4. Note that in bothdesign styles under consideration the distribution feeders alwayscontain a neutral conductor. The conductor type may be regularoverhead or cable, while tapering is not considered. The conductorarrangement may be four wire or six wire. The parameters of theconductors and of the transformers are taken from Sects. 2.2 and2.3. The loading of the feeders is the same as in Sect. 4, the resultsare summarized in Table 3.5.2 Propagation of voltage distortionThe simulation results of Table 3 show that the influence of thedifferent parameters is in accordance with the findings of Sect. 4. Inany case, when comparing equal conductor types and arrangements(comparing simulation nos. C1 with C5, C2 with C6, and so on),the resulting voltage THD in the PCC and in the load node at theend of the feeder is always worse for the North American distri-bution style. This is no surprise, as the neutral conductor is inter-rupted in the MV/LV transformers in the European style, contraryto the North American style.However, the North American design style typically results insingle-phase (or six-wire) feeders operated in MV (simulation nos.C2 and C4, Table 3), whereas the European style is mainlyresulting in three-phase (or four-wire) feeders operated in LV(simulation nos. C5 and C7, Table 3) 15. The comparison betweenthe North American and European design styles is graphicallyrepresented in Fig. 3c.Both in Europe and North America, overhead lines are stillwidely present in rural areas. Comparing simulation nos. C2 andC5, it is easily seen that the resulting voltage THD in the PCCwould be larger for the North American distribution style becausethe neutral conductor is not interrupted before reaching the HV/MV transformer. On the other hand, the voltage THD at the end ofthe feeder is quite smaller for the North American style. This ismainly caused by the reduced zero-sequence feeder impedance ofthe associated six-wire arrangement. In practice, this effect will beeven more pronounced than predicted from Table 3 because thesection of the neutral conductor is often chosen smaller than thesection of the phase conductors.In domestic and commercial areas, cable conductors are pre-ferred. The comparison of simulation nos. C4 and C7 shows thesame trend as for overhead lines.Fig. 4 MV distribution system model used for the case study:a large MV/LV transformer located at the beginning of the feeder,b small MV/LV transformers located in the feeder nodesTable 3 Case study - summaryof the simulation results:voltage distortion in the PCCand in the load node at the endof the feederSim. no.MV/LV transformerConductorarrangementVoltage THD (%)VPCCV5C1Small, located in nodesOverhead4-w4.2515.51C2Overhead6-w4.259.84C3Cable4-w4.3512.43C4Cable6-w4.358.778C5Large, located atbeginning of feederOverhead4-w3.2412.90C6Overhead6-w3.248.38C7Cable4-w3.3210.03C8Cable6-w3.327.331876 Influence of shunt capacitanceThe possible presence of shunt capacitance in thefeeders causes resonances. Resonance conditions areintroduced in the power system of Fig. 1 by addingcapacitors to the feeder nodes. The capacitance isrepresented by its total admittance jYC, which isequally divided among the feeder nodes, and repre-sents both conductor capacitance and other capaci-tances(e.g.,powerfactorcorrectioncapacitors).Moreover, the feeder nodes are shunted with equallydivided parasitic resistances, the total admittance ofwhich equals 0.01 pu. The remaining power systemparameters are chosen as in Sect. 4. To assess theimpact of resonance on voltage distortion, a harmonicvoltage amplification factor M is introduced by com-paring the actual voltage distortion (under resonance)tothedistortionpresentifthecapacitancewereremoved:M THDV jYC60THDV jYC010The M values calculated in this section are obtainedusing the load current spectrum of Table 1. The qualityfactor Q of a certain resonance condition is assessed bycalculating (10) using a load current spectrum con-taining only the fundamental and a single harmonic ofthe same harmonic order as the resonance frequency ofthe power system. The simulation results are presentedin Table 4 and are explained in the following subsec-tions. A more detailed analysis, including a moreelaborate discussion on damping effects, is presented in16.6.1 Required capacitance for resonanceThe required total capacitive admittance jYCto obtainresonance at a given harmonic order is of coursefunction of the inductance present in the system. Sim-ulation no. R1 of Table 4 corresponds to the base caseof Sect. 4. In simulation no. R2 (six-wire instead offour-wire feeders), the feeder inductance for zero-sequence currents is reduced by a factor 4, giving riseto a largely increased YCrequirement to obtain reso-nance at the 3rd and 9th harmonics. The same con-clusion is drawn from simulation no. R3 (neutralconductor interrupted at the PCC by a DY trans-former), where the inductance of the HV/MV trans-former is virtually removed for zero-sequence currents.Similar conclusions are drawn for all harmonics insimulation no. R4 (cable feeder), where the feederinductance is significantly reduced as compared to thebase case. It is also noticed that the large zero-sequenceinductance of the base case (simulation no. R1) causesthe required capacitance for 9th harmonic resonance tobe smaller than for 11th harmonic resonance.Table 4 Quality factors and amplification of voltage distortion at different resonant conditionsCase no.h=3h=5h=7h=9h=11CommentsMPCC(QPCC)M5(Q5)MPCC(QPCC)M5(Q5)MPCC(QPCC)M5(Q5)MPCC(QPCC)M5(Q5)MPCC(QPCC)M5(Q5)R1)(4.36)(4.92)6.94(11.50)4.96(11.78)7.38(15.12)4.67(15.62)3.43(9.87)5.23(11.33)4.03(19.89)2.75(20.59)Base case(regular overheadfeeder)Yc=0.389Yc=0.321Yc=0.164Yc=0.045Yc=0.067R23.83(7.09)3.80(7.01)6.75(11.50)6.91(11.78)7.37(15.12)7.60(15.62)5.94(17.90)6.15(18.53)4.09(19.89)4.23(20.59)3-ph, 6-w(or 3 1-ph) feedersYc=0.882Yc=0.321Yc=0.164Yc=0.099Yc=0.067R3)2.94(4.00)8.61(11.50)5.20(11.78)9.41(15.12)5.55(15.62)4.57(10.22)5.06(19.89)(20.59)Neutral conductorinterrupted in PCCYc=0.506Yc=0.321Yc=0.164Yc=0.059Yc=0.067R4)(2.48)(2.66)4.82(8.02)3.54(8.08)5.37(10.81)3.72(10.96)2.55(6.29)3.19(6.96)3.37(15.20)2.76(15.47)Cable feederYc=0.506Yc=0.377Yc=0.194Yc=0.064Yc=0.079R5)(3.75)(4.22)5.43(8.83)4.08(9.05)4.88(9.74)3.21(10.07)1.95(4.69)2.65(5.40)2.22(9.34)1.80(9.67)0.05 pu resistiveshunt admittanceYc=0.389Yc=0.321Yc=0.164Yc=0.045Yc=0.067R6)(3.80)(4.27)4.50(7.14)3.69(7.33)3.70(7.15)2.54(7.41)1.98(4.86)2.75(5.63)1.76(6.04)(6.31)0.01 Fundamental lossfactor of capacitorsYc=0.389Yc=0.321Yc=0.164Yc=0.045Yc=0.0671886.2 Quality factor of resonanceThe quality factor associated with resonance is deter-mined by the amount of damping present in the powersystem. In the power system under study and with theassumed load condition, damping is primarily providedby the series losses of conductor and transformerimpedances. Therefore, the quality factor is increasingwithincreasingharmonicorders16.However,increased parasitic losses in simulation no. R5 (shuntloss, total resistive shunt admittance of 0.05 pu) andsimulation no. R6 (series loss in capacitors, fundamentalloss factor of 0.01) considerably reduce the qualityfactor, especially for higher harmonic orders.6.3 Peak rectifier current spectrumIn practice, the actual load current spectrum containsseveral strong harmonics. Moreover, resonance alsoaffects the power system impedance at other frequenciesaround the resonance frequency. Consequently, theanalytical prediction of the amplification M of voltagedistortion under resonance conditions is not possiblefrom the mere knowledge of the quality factor alone.The actual voltage distortion level is therefore obtainedfrom simulations. The results from Table 4 are inaccordance with the conclusions of Sect. 4. Additionalremarkable features are explained below.From Table 4, it follows that the actual voltage dis-tortion amplification factors M tend to decrease withincreasing order of the harmonic resonance, contrary tothe quality factors Q. This results from the rapidlydecreasing amplitude of the line current harmonics ofthe applied non-linear load spectrum. Moreover, theactual amplification factors M are always smaller thanthe corresponding quality factors Q, because the qualityfactor only takes load current components at the reso-nance frequency into account.In the base case (simulation no. R1), it was noticedthat 3rd harmonic resonance is not visible. Indeed, it ismasked out by the closely neighboring 5th harmonicresonance, as is illustrated in Fig.5. The same effect isencountered in simulation nos. R4R6. In simulationnos. R3 and R6, the 11th harmonic resonance is alsomasked out by the 9th harmonic resonance at the end ofthe feeder.Finally, it is no surprise that interrupting the neutralconductor before it reaches the PCC (simulation no. R3)eliminates 3rd and 9th harmonic resonances (caused byzero-sequence currents) in the PCC.7 ConclusionIn this paper, the impact of distribution system param-eters on the propagation of harmonic distortion hasbeen considered. Under the condition that the feederconductor parameters of different designs are chosen toobtain the same fundamental voltage drop of the feederconductors, the following conclusions can be drawnwhen the power system capacitance is negligible: The more inductive the (fundamental) impedance ofthe transformers and the feeder conductors become,the higher is the resulting voltage distortion. At theend of the feeder, the harmonic impedance of thefeeder conductors (and its associated harmonic volt-age drop) becomes dominant. Overhead lines cause greater harmonic voltage dropthan cables, therefore the voltage THD in the loadnodes near the end of the feeders is greater withoverhead lines (and, consequently, also throughoutthe feeders). Feeder conductor tapering has very little influence onthe voltage THD in the PCC and at the end of thefeeder. When zero-sequence currents are present, the appli-cation of six-wire conductor arrangements results inless voltage THD in the load nodes near the end of thefeeder (and, consequently, also throughout the feed-ers) as compared with four-wire conductor arrange-ments. Interruptingtheneutralconductorsignificantlyreduces the harmonic voltage drop of transformersand feeder conductors upstream of the interruptingpoint.Under reasonable assumptions, these effects can beanalytically predicted and match the simulation resultsquite well. The results strongly depend on the harmoniccontent of the load currents. These considerations helpto explain the different harmonic propagation behaviorof different design approaches, as was shown in a casestudy, comparing typical European and North Ameri-can design styles.When the power system capacitance is taken intoaccount, the following conclusions can be drawn:Fig. 5 Voltage distortion in the PCC (THD(VPCC), lower trace)and last node of the feeder (THD(V5), upper trace), case no. R1(base case)189 The required capacitance to obtain resonance at agiven harmonic order increases when cable feeders areapplied instead of overhead feeders. In the case offour-wire feeders, the required capacitance for reso-nance of zero-sequence harmonic currents is muchreduced as compared to six-wire feeders. At low power system loading levels, the quality factorof the resonance tends to increase with increasingharmonic order. However, this effect is noticeablyreduced if parasitic losses are taken into account. The amplification of voltage distortion (as comparedto the situation with negligible power system capaci-tance) is always smaller than the correspondingquality factor. Closely neighboring resonances may cause one ofthem to be masked out by the other when sweepingthe capacitance value. If the neutral conductor is interrupted, the resonanceof zero-sequence current components is not visibleupstream of the interruption.The actual distortion level is not only
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