A New Approach of Harmonic Load Flow for Radial Distribution Networks

Transcription

1 A New Approac of Harmonc Load Flow for Radal Dstrbuton Networks Pawan San M.Tec. student Nkl Gupta Member, EEE Anl Swarnkar Member, EEE Department of Electrcal Engneerng Malavya Natonal nsttute of Tecnology, Japur, Rajastan, nda K. R. Naz Senor Member, EEE Abstract Ts paper presents a novel volt-ampere balance equaton for non-lnear load caracterstc. Te applcaton of ts balance equaton converts non-lnear load nto equvalent constant power armonc source. Te couplng between te proposed volt-ampere balance equaton wt Newton- Rapsonbased power flow equatons enables to separate calculatons for every armonc order. Ts wll greatly reduce te complexty level and computaton burdenattrbuted wt armonc power flow. Te proposed volt-ampere balance equaton combnes wt Newton-Rapsonbased algortm and tested on dstorted EEE 33-bus radal dstrbuton system. Te obtaned results are compared wt exstng metod avalable n lterature, and are found promsng. Keywords-armonc load flow; non-lnear load; dstrbuton systems. NTRODUCTON N te last few decades, armonc load flow analyss as become an mportant tool of power system analyss and desgn [, ]. Nonlnear loads are contnuouslyncreasng.harmoncs ave become an mportant power qualty problem because of te ncreased dstorton levels n te power system as a result of an ncreasngnumber of armonc producng loads [3, 4]. Te man effects of armoncs n power systems are eatng, overloadng, agng of equpment, ncreased losses and system unbalancng. Harmoncs may lead to malfunctonng of power system components and electronc devces. Relays and measurement equpment may functon erroneously under non-snusodal voltage and currents. Harmonc analyss s ten appled to te study of resonant condtons n network, armonc flter desgns and also to nvestgate oter effects of armoncs on te power system,.e., notcng and rngng, neutral currents, saturaton of transformers, and overloadng of system components. dentfcaton and measurement of armonc producng load as become an mportant ssue n electrc power systems snce ncreased use of power electronc devces and equpment senstve to armoncs as ncreased te number of adverse armonc related events. Many metods ave been proposed to solve te armonc polluton produced by nonlnear loads. Te commonly used armonc analyss metods can be dvded nto two categores. Te frst category s based on te transent-state analyss tecnques, suc as te tme doman analyss and Wavelet analyss, etc. [7] [9]. Te second category s te steady-state analyss [0] []. Frequency scan s te most commonly used non-teratve metod n many commercal software packages. n ts metod, a armonc current source of specfed magntude s njected nto a lnear network to determne te voltage dstorton level.one of te lmtatons of ts metod s tat n te presence of multple armonc sources, a fundamental frequency load flow s requred to determne te magntudes and pase angles of te njected currents accurately. Anoter drawback of frequency scan s ts relance on typcal armonc spectra to represent nonlnear devces. Ts results n naccurate results under condtons of voltage-dependency, unbalanced operaton, and te generaton of non-caracterstc armoncs. Te steady-state algortms are developed based on load-flow programs and employed frequency-based component models. Te steady state-based algortms are more effcent tan te transent state-based algortms. Steady state-based algortms are better coce for large-scale power system analyss due to te computatonal economy. Te conventonal armonc analyss metods used te Newton-Rapson power flow metod, te admttance matrx, or te mpedance matrx to obtan armonc penetraton n dstrbuton systems [3]-[5]. Tese metods aceve separaton of te nonlnear elements from te lnear part of te network and obtan soluton teratvely usng te Newton-Rapson load flow.references [6, 7] present a revew of te modelng and analyss of armonc propagaton n electrc power systems, along wt practcal consderatons and sample case studes. n [6],te teoretcal aspects of armoncs modelng and smulaton are focused. Concepts and caracterstcs of power system armoncs, modelng of armonc sources and network components, and tecnques for network-wde armonc analyss are dscussed. n [7], te revew on te nature and modelng of armonc sources n electrcal power systems and te analyss of armoncs propagaton s presented. n ts paper, a new volt-ampere balance equaton s developed for non-lnear load caracterstc. n ts proposed formulaton te non-lnear load s converted nto constant power armonc source. Te proposed volt-ampere balance equaton combnes wt Newton-Rapson power flow algortm for armonc load low analyss and tested on dstorted EEE 33-bus radal dstrbuton system.ts s based on te balance of actve power and reactve volt-amperes, rrespectve of fundamental or armonc frequency. Te actve and reactve power balance s forced to zero by te bus voltage teratons. Te system soluton, wt lnear and nonlnear loads under balanced non-snusodal tree-pase condtons, s aceved by forcng total (fundamental and armonc)

2 msmatc actve and reactve powers to zero usng te Newton-Rapson metod.. PROBLEM DESCRPTON A. Objectves Te purpose of armonc analyss s to ascertan te dstrbuton of armonc voltages and armonc dstorton ndces n a power system. To fnd out voltage THD levels ( THD )n radal dstrbuton system. To fnd out total real power losses n te system wt te presence of armoncs. Consder a system wt n+ buses, bus s a slack bus, buses troug m are conventonal load buses, and buses m to n ave non-lnear loads. t s assumed tat te actve power and te reactve volt ampere balance are known at eac bus and tat te nonlnearty s known. Te power balance equatons are constructed so tat te actve power P and te reactve power Q at all non-slack buses are zero for all armoncs. Te form of P and Q as a functon of bus voltage and pase angle s te same as n conventonal load flow, except tat admttance matrx Y bus s modfed for armoncs. ΔM = J ΔU () wereδm s msmatc actve and reactve volt-amperes, ΔU s voltage correcton andjs Jacoban matrxfor te armonc power flow analyss, te power flow equatons are defned accordng to Xa et al.[0, ]. B. Constrants Bus oltage Lmts:Te bus voltage magntudes are to be kept wtn acceptable operatng lmts trougout te optmzaton process mn max () were mn and max lower and upper bound of bus voltage lmts; s te root mean square (rms) value of tetbus voltage and defned by max ( ) =, 3,,n (3) 0 weren s te number of buses, s te armonc order, 0 and max represents fundamental andgest armonc order of nterest, respectvely. Te rms value of te nt bus voltage nvolves only te fundamental component, te frst term of (3), wen armoncs are not of nterest. Total Harmonc Dstorton Lmts: Te total armonc dstorton at eac bus s to be kept less orequal to te maxmum allowable armonc dstorton level as sown. THD (%) THD max (4) werethd max stemaxmum allowable armonc dstorton level at eac bus. C. General Harmonc ndces Te general armonc ndces may be defned as THD sumof squaresof ampltudes of all armoncs squaresof ampltudes of max H ; 00% fundametal component (5) max THD 00% (6) were H s equvalent totalzed armonc component of te voltage, sarmonc component of voltage of te order.. MATHEMATCAL MODELLNG Before startng wt te development of te matematcal framework, te man assumptons to be consdered are as follows. Tree-pase balanced system s consdered. Skn effect s neglected n te system. n dstrbuton systems, te pase sft between te system bus voltage angles s very small. ) Power system component modellng a) Lne parameter s modelng at armonc frequences: At armonc frequences, accurate models for dstrbuton lnes and sunt capactors are avalable. However, armonc modelng of te power system supplyng te dstrbuton feeder, substaton transformer, lnear and nonlnear loads are not well establsed. f skn and proxmty effects are gnored, a feeder segment and sunt capactor may be represented by te followng admttances at te t armonc frequency [8, 9]:, ( R, jx Y (7), were R, and X, represent te resstance and reactance of te lne segment between busses and +. b) Sunt capactor modelng at armonc frequences: n a armonc-rc envronment, sunt capactors are mportant elements to be modeled for armonc studes as tey may amplfy armonc dstorton levels []. Tus, modelng of suc components s very mportant. Generally, sunt capactors are specfed by ter kar ratngs and nomnal voltages. Sngle-pase sunt capactors are represented by sngle-pase sunt capactances, wle tree-pase capactors are descrbed by tree-pase sunt capactances [8, 9].Sunt capactor banks are represented as sunt connected elements Y capactor, Ycapactor, (8) werey capactor s te admttance of sunt capactor C at bus. ) Lnear load modelng at armonc frequences: )

3 Lnear loads are bascally tose loads tat can be descrbed as passve loads n terms of armoncs. n ts proposed formulaton te generalzed model of lnear load, composed of a resstance n parallel wt an nductance, s consdered. Te load admttance of te t bus s expressed by P jq Y ; Y f Y, (9) Y ; Y f Y, (0) R jx were te voltage s determned from te fundamental load flow. Ts expresson depends on te fundamental voltages only because of te ypoteses of no armonc voltage nfluence on power consumpton and non-lnear load beavor [0]. Lnear passve loads tat do not produce armoncs ave a sgnfcant effect on system frequency response prmarly near resonant frequences. Wt respect to lnear loads, t s suggested [, 8] to use a generalzed model wc s composed of a resstance n parallel wt an nductance selected to account for te respectve actve and reactve powers at fundamental a sunt capactor and feeder segment may be represented by te followng admttances at te t armonc frequency [3]: jq P Y for, =, 3,, m () werep s real power of load (kw), Q s reactve power of load (kar), s fundamental t bus voltage (p.u.) and Y s sunt admttance at ttearmonc order. Te equatons (9) () depend on te fundamental voltages only because of te ypoteses of no armonc voltage nfluence on power consumpton andnon-lnear load beavor [0]. 3) Non-lnear load modelng at armonc frequences: Te type of nonlnear load s assumed to be of tree pase, sx-pulse converter. Nonlnear loads nject armoncs nto dstrbuton systems, and are commonly modeled as armonc current sources. n ts formulaton non-lnear load s modeled as constant current source. f te Fourer analyss s made on te output wave of ts converter, t would contan all te odd armonc current expect trplets []-[4]. Terefore, te followng observatons can be made (a) Te absence of trple armoncs.(b) Te presence of armoncs of orders 6k ± for nteger values of k.(c) Tose armoncs of orders 6k + are of postve sequenceand tose armoncs of orders 6k are of negatve sequence. (d) Te r.m.s. magntude of te tarmonc s fund ; kq () were s te armonc order, q s te pulse number of te crcut (6 n case of 6-pulse converter), k s an nteger (,,3,, etc.), s te ampltude of te armonc currents of order and fund s te ampltude of te rms value of te fundamental current. 4) Lne Power Losses At te t armonc frequency, lne power loss n te lne secton between busses and + s expressed below: P R ( ) ( ) ( ) Y ( ) loss (, ),,, (3) Te total power loss, ncludng losses at armonc frequences, for an n bus system s H n P loss P loss ( ) (, ) (4) werep loss s total real power losses, s tarmonc order bus voltage, R, + s resstance between brances and + and Y sunt admttance at tarmonc order[8, 9].. PROPOSED HARMONC LOAD FLOW METHOD Conventonally, fundamental frequency load flow soluton wc gves te base operaton pont for system tat s fundamental bus voltages and ten fundamental powers for non-lnear loads and fundamental bus voltages are used to obtan te network power flow. Te current drawn by te nonlnear loads can be evaluated as a functon, wc depends on te fundamental bus voltage and te non-lnear load parameters. Unlke ts, te proposed metod formulates a new equaton by wc te power consumed by non-lnear load for every armonc order can be drectly calculated as dscussed below. Te complex power flow at te t node s * S P jq Z (5) were Z s mpedance tat means Z s functon of frequency. So Z can be wrtten as: Z f ( Z, ) (6) We can also wrte te above equaton (5) and (6) as below: fund jq Z Z (7) P By equaton () and (7) P jq Z (8) Te above equaton can also be wrtten n te followng form: P jq Z (9) * P jq (0) were P and Q are respectve real and reactve power of non-lnear load, s fundamental t bus voltage, Z s mpedance at tarmonc order, s voltage at tarmonc order and current at tarmonc order. Terefore, usng equaton (0), te real and reactve power of te armonc generatng source can be obtaned to get te correspondng armonc bus voltages, branc currents. n te proposed formulaton, te non-lnear load s modeled as constant power armonc source. System components are accurately modeled by above equaton and te non-lnear load n dstrbuton system s modeled accordng to proposed 3

4 oltage n p.u. oltage THD n % metodology and te Newton-Rapson metod can be employed for armonc load low analyss. Te flowcart of te proposed armonc load flow s sown n Fg.. Start nput system parameters; defne locaton of lnear and nonlnear load armonc) msmatc actve and reactve powers zero usng te Newton-Rapson metod.. SMULATON RESULTS Te proposed algortm s tested on dstorted EEE 33-bus radal dstrbuton system. Te substaton lne voltage s.66 k. Te non-lnear loads are assumed to be connected at bus 6 and 7 and te dstrbuton generators are connected to bus 7, 4 and 5.Te lne and load data of te system s taken from []. Te smulaton s performed on te ntal radal confguraton wt open lnes 33, 34, 35, 36 and 37. Fundamental Power flow Subroutne Set ntal counter for armonc order 8 % oltage THD 6 Modellng of Lnear and non-lnear load Modellng of Lne parameters 4 Obtan te modfed bus admttance matrx [Y () ] Harmonc Power flow (HPF) Subroutne Preserve t order armonc voltage Bus Locaton = + No s = max? Fgure. oltage THD of te dstorted EEE 33-bus system wt multple nonlnear loads and DG s usng proposed metod Yes Obtan voltage THD and losses bus RDS voltage profle oltage profle before Harmonc consderaton oltage profle after Harmonc consderaton.0 End.0 Fgure.Flowcart for armonc load flow algortm 0.99 Te proposedvolt-ampere balance equaton for non-lnear load s coupled wt te conventonal Newton-Rapson metod based algortm for armonc load low analyss. Ts s based on te balance of actve power and reactve volt amperes, weter at fundamental frequency or at armoncs. Te actve and reactve power balance s forced to zero by te bus voltage teratons. Te system soluton (wt lnear and nonlnear loads under balanced nonsnusodal tree-pase condtons) s aceved by forcng total (fundamental and Bus Locaton Fgure 3. oltage profle comparson of EEE 33-bus system before and after armonc consderaton 4

5 Te results of te proposed armonc load flow metod are sown n Fg. and 3. Fg. sows bus voltage THD levels at buses and t can be observed tat te maxmum voltage THD s found as 7.9 % at bus 4 usng te proposed metod. Fg. 3 sows te comparson of bus voltage profles wtout and wt te presence of non-lnear loadsusng te proposed metod. t can be observed from te fgure tat te maxmum rms voltage dstorton also occurs at bus 4. Te results obtaned usng te proposed metod s compared wt te metod of [] n Table. t can be depcted from te table tat te maxmum voltage THD usng [] s 7.4%, tat s ger tan usng te proposed armonc flow. Moreover, mnmum voltage, maxmum voltage, power loss as obtaned usng te proposed metod are found to be better tan tat obtaned usng te metod of []. Ts sows te superorty of te newly proposed armonc flowalgortm. TABLE. COMPARSON RESULTS OF THE PROPOSED METHOD WTH [] Results Metod [] Proposed metod Max oltage THD (%) max (p.u.) mn(p.u.) P loss(kw) CONCLUTON Ts paper presents a new armonc flow metod wc can combne wt te conventonal Newton Rapson load flow metod to obtan network solutons n te presence of armoncs attrbuted due to te presence of non-lnear loads n te dstrbuton systems. Te proposed volt-ampere balance equaton converts non-lnear loads nto constant power armonc source. Te developed volt-ampere balance equaton coupled wt Newton Rapson power flow algortm and tested on dstorted EEE 33-bus radal dstrbuton system. Te results obtaned are found better tan te exstng metod on comparson. Te key feature of te proposed algortm s tat t enables separate calculatons for every armonc order. Te man objectve of ts work s to fnd out armonc r.m.s. voltages and armonc dstorton ndces n power system n te presence of armoncs. Te proposed algortm can also be used to solve reconfguraton, optmal reactve compensaton, fault restoraton, sort-crcut and smlar knd of oter problems of dstrbuton networks n te presence of armoncs. REFERENCES [] J. Arrlaga and N.R. Watson, Power system armoncs, New York: Wley, 985. [] J. C. Das, Power System Analyss Sort-Crcut Load Flow and Harmoncs, Marcel Dekker, nc., 00. [3] EEE standards Board, EEE Recommended Practce for Electrc Power Dstrbuton for ndustral Plants, New York: EEE, 994. [4] EEE Recommended Practces and Requrements for Harmonc Control n Electrc Power Systems, EEE Std , 993. [5] EEE Task Force on Harmonc mpacts, Effects of te armoncs on equpment, EEE Trans. Power Del., vol. 8, no., pp , Apr [6] A. Abou-Gazala, Optmal capactor placement n dstrbuton systems feedng nonlnear loads, n Proc. EEE Bologna Power TecConf., 003, pp [7] S. Herraz, L. Sanz, and J. Clua, Revew of armonc load flow formulatons, EEE Trans. Power Del., vol. 8, no. 3, pp , Jul [8] G. T. Heydt and A. W. Gall, Transent power qualty problem analyzed usng wavelet, EEE Trans. Power Del., vol., no., pp , Apr [9] T. Zeng, E. B. Makram, and A. A. Grgs, Power system transent and armonc studes usng wavelet transform, EEE Trans. Power Del., vol. 4, no. 4, pp , Oct [0] D. Xa and G. T. Heydt, Harmonc power study part Formulaton and soluton, EEE Trans. Power App. Syst., vol. PAS-0, no. 6, pp , Jun. 98. [] D. Xa and G. T. Heydt, Harmonc power study part mplementaton and practcal applcaton, EEE Trans. Power App. Syst., vol. PAS-, no. 6, pp , Jun. 98. [] Y. H. Yan, C. S. Cen, C. S. Moo, and C. T. Hsu, Harmonc analyss for ndustral customers, EEE Trans. nd. Appl. Soc., vol. 30, no., pp , Mar./Apr [3] D. J. Plegg, N. H. Candra and A. E. Emanuel, Predcton of Harmonc oltages n Dstrbuton Systems, EEE Trans. Power App. k3 Syst., ol. PAS-00, No. 3, 98, pp [4] T. Mau and. Mlanovc, Development of Stocastc Aggregate Harmonc Load Model Based on Feld Measurements, EEE Trans Power Del., vol., no., Jan [5] A. Mamoud and D. Sultz, A Metod For Analyzng Harmonc Dstrbuton n A.C. Power Systems, EEE Trans Power Del., vol PAS- 0, no. 6, June. 98 [6] Task Force on Harmoncs Modelng and Smulaton, Modelng and smulaton of te propagaton of armoncs n electrc power network part : Concepts, models and smulaton tecnques, EEE Trans. Power Del., vol., no., pp , Jan [7] Task Force on Harmoncs, Modelng and Smulaton, Modelng and smulaton of te propagaton of armoncs n electrc power network part : Sample systems and examples, EEE Trans Power Del., vol., no., pp , Jan [8] Y. Bagzouz, Effects of nonlnear loads on optmal capactor placement n radal feeders, EEE Trans. Power Del., vol. 8, no. 3, pp. 45 5, Jan. 99. [9] A. Ulnua, M.A.S. Masoum and S. slam Hybrd Genetc-Fuzzy Algortm For olt/ar/total Harmonc Dstorton Control Of Dstrbuton Systems Wt Hg Penetraton Of Non-Lnear Loads, ET Gener. Transm. Dstrb. ol. 5, pp , 0 [0] S. Herraz, L. Sanz, and J. Clua, Revew of Harmonc Load Flow Formulatons, EEE Trans. Power Del., vol. 6, no., pp , July 003. [] T. Seyed Abbas, H. Moammad and K. Al A Novel Metod for Optmal Capactor Placement and Szng n Dstrbuton Systems wt Nonlnear Loads and DG Usng GA, Elsever, Commun Nonlnear Sc Numer Smulat, 85 6, 5 May, 00. 5