Load Model Impact in Distribution System Reconfiguration Part I: Problem Analysis and Reformulation

Transcription

1 16th NATIONA OWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, oad Model Impact n Dstrbuton System Reconfguraton art I: roblem Analyss and Reformulaton Devender Sngh and Rakesh. K. Msra Abstract-- The present work shows that omsson of load models results n erroneous formulaton of reconfguraton problem. A fundamental analyss establshng the sgnfcant mpact of load model and problem reformulaton ncludng load models have been done n ths part of the two part paper. A crtcal evaluaton of formulaton approaches proposed n the lterature has also been carred out to show the far reachng mpact of ncluson of load models. Index Terms oad management, load modelng, power dstrbuton., NOMENCATURE oltage exponents of real and reactve loads. oltage angle dfference between bus and. Const., Res. Constant and resdental load models. Ind., Com. Industral and commercal load Models. Mx. Mxed load Model. N Number of buses N B Number of lne N, N Number of voltage lmt and lne loadng volatons. 0, 0 Real and reactve load at bus at nomnal voltage., Real and reactve lne flow n lne,, 0(, ) Real and reactve lne flow n lne, at nomnal voltage at bus., Real and reactve power nectons at bus. ntake, ntake Real and reactve power ntake at bus 1., System real and reactve power losses D, D Sum of, for all buses S ntake MA ntake at bus 1. oltage of th node Y G B Elements of the bus admttance matrx correspondng to bus and. Devender Sngh and Rakesh K. Msra are wth Department of Electrcal Engneerng, Insttute of Technology, Banaras Hndu Unversty, aranas, U, Inda (e-mal: dsngh.eee@tbhu.ac.n; rkmshra.eee@tbhu.ac.n). R I. INTRODUCTION ECONFIGURATION of dstrbuton networks has been proposed n the lterature as one of the most nexpensve way of achevng dfferent obectves. There have been dfferent obectves such as system loss reducton, voltage profle mprovement, load balancng, voltage stablty enhancement, relablty mprovement, and reducton n transformer and feeder loadngs. Most of the studes show that n achevng a partcular obectve other benefts also follow. For example, the MW loss reducton also leads to better voltage profle and MAr loss reducton. oad models are well known n stablty studes [1]-[4]. These studes are normally amed towards voltage or frequency dependent representaton of loads especally for dynamc or statc stablty studes of power systems. Exhaustve revew and subsequent recommendatons of load models for power flow has been presented n [] by IEEE Task Force. The effect of load models n plannng studes was demonstrated n optmal capactor placement / swtchng by D.T. Rzy et al. [5] n a dstrbuton system, by Stefan Arnborg et al. [6] n undervoltage load sheddng studes and by D. Sngh et al. [7] n dstrbuted generaton plannng n a dstrbuton system. The authors demonstrated that consstent wth the modelng of feeder load as constant power, t was expected that the swtchng of capactor bank to mprove the power factor would result n decreased real and reactve power nectons at the substaton. Ths decrease n real and reactve power nectons s due to mproved voltage profle. In fact the measured real and reactve power nectons ncrease. In ths case, contrary to the constant power load modelng, a reducton n real and reactve power necton reflectng the reduced lne losses s not observed at the substaton. An assumpton of constant power load modelng leads to general (ms-) understandng of reduced power necton due to reduced losses. Analyss of the expermental results [5] usng voltage senstve load models showed that whle the feeder losses are reduced followng the capactor placement; the attendant mprovement n voltage profle results n an ncrease n loads that exceeds the amount of loss reducton. The other purpose of reconfguraton could be to defer the system upgrade such as deferrng the nvestment on man substaton transformer replacement due to ncrease S ntake of the system or lne upgrades can be deferred by fndng the less Department of Electrcal Engneerng, Unv. College of Engg., Osmana Unversty, Hyderabad, A., INDIA.

2 16th NATIONA OWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, overloaded confguraton. Smlarly the reducton n ntake may be desred f ntake s also the part of the tarff structure. Theoretcally, confguratons can sgnfcantly depend on voltage-dependent load models. If load models are not ncorporated n the studes then the so obtaned optmum soluton may gve a msleadng pcture of hgher effcency of the system whch may lead to fnancal losses. Therefore, t s necessary to ncorporate load models to plan the benefts sutably. It s shown that the common understandng of reduced losses leadng to mproved voltage profle and ncreased system effcency does not hold n general. The formulaton of reconfguraton problem and correspondng soluton methodologes need to be renvestgated n the lght of sgnfcant mpact of load models. As far as the present lterature on reconfguraton s concerned, load models have attracted less nterest of researchers. Therefore, t s desrable to make a survey of lterature to fathom out the extent and scope of effects of fndngs of the present work on the exstng soluton methodologes. II. ITERATURE SUREY In ths part, a lterature revew s presented to establsh and demonstrate the mpact of load models on the purposes and methods employed n reconfguraton studes reported so far. A sgnfcant lterature has emerged mostly n last two decades on the varous aspects of reconfguraton studes n dstrbuton systems. For the purpose of survey, the research papers can be dvded nto two broad categores. The frst category s the purpose for whch the reconfguraton s employed. The second category gves the methods, concepts and the heurstcs employed for achevng the approprate confguraton. A. urpose A representatve collecton of papers ndcatng the purposes of reconfguraton s arranged n Table I. The remarks column n table gves some specfc detals or comments hghlghtng devaton for a partcular reference from the group. On the bass of lterature survey summarzed n Table I, followng observaton are made. Real ower oss ) mnmzaton s one of the maor crtera for whch the reconfguraton was prmarly proposed. The loss s understood to be the mportant component whch can reduce the power ntake of a dstrbuton system. Also, the reducton n losses not only reduces the ntake but also mproves voltage profle and reduces ntake. A smlar approach could be to mnmze reactve power loss ( ) and reduce the over all ntake. The mnmzaton of not only leads to voltage stablty enhancement but also mproves voltage profle and reducton n. In most of the earler lterature voltage constrants were taken care of as loss reducton would defntely lead to mproved voltage profle. The capactor placement n plannng stages and capactor control n operatonal stages could be strategcally approached by combnng t wth a reconfguraton problem. The obectve of voltage profle mprovement could also be translated as a power qualty (voltage sag) enhancement problem TABE I ITERATURE SUREY OF UROSES OF RECONFIGURATION urpose References Remarks oss Mnmzaton [8] [9] [10] [10]loss allocaton n deregulated envronment oltage stablty Enhancement [11] oss Reducton and capactor [1] [13] placement / control Fnancal loss Mnmzaton [14] [14]fnancal loss due to voltage sags durng faults. oltage profle mprovement [15] Servce Restoraton [16][17] Feeder oad Balancng [18][19] [19]unbalanced systems [0] oadablty Maxmzaton [1] Mult-obectve [] Relablty maxmzaton [3] [4] rotectve devce coordnaton [5] [6] to reduce the fnancal losses ncurred due to senstve loads leadng to process nterrupton durng system faults. The basc purpose of provdng the te swtches was load restoraton n dstrbuton system. As the numbers of teswtches ncrease n dstrbuton system the best swtchng optons for load restoraton, become computatonally complex. Reconfguraton studes may also be ncorporated n the plannng studes to maxmze the relablty of the systems n terms of amount of load restored or to maxmze the relablty of load served at certan bus or set of buses. As the confguraton of the system changes, the flows may change consderably n terms of magntude and drecton. Thus, the protectve devces are to be coordnated and set accordng to new flow pattern. The mult-obectve crtera of power loss mnmzaton have also been consdered. However, as reported n most of the references mnmzaton of losses also leads to betterment of other mportant system performance characterstcs such as; voltage profle mprovement, reducton n reactve power ntake, and mprovement n load balancng. It may be worth notcng that except ssues lke relablty and protectve devce co-ordnatons, n general all of the optmzaton obectves would be sgnfcantly affected by ncluson of load models. B. Methods, Concepts and Heurstcs Table II presents a summary of the methods, concepts and the heurstcs employed for achevng the approprate confguraton for any partcular purpose. On the bass of lterature survey summarzed n Table II followng observaton are made. The heurstc technques are most popular n reconfguraton studes especally for mnmum loss confguraton as an obectve. Bascally, the heurstc technques are varatons of a method called Branch-Exchange Method (BEM). In BEM, a te-swtch s frst closed thereby Department of Electrcal Engneerng, Unv. College of Engg., Osmana Unversty, Hyderabad, A., INDIA.

3 16th NATIONA OWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, TABE II ITERATURE SUREY OF METHODS, CONCETS AND THE HEURISTICS Soluton Approach References Remarks Heurstc Searches [7] [8] [9] [30] [31] [3] [33] [18] [34][35] [9]all te-branches closed Optmzaton based formulatons Search based Methods Evolutonary [39] programmng Genetc Algorthm [1] [40] [15] [41] [36][37][38] [38]optmal power flow wth contnuous representaton of swtches. [1]runnng tme may be very large Ant colony optmzaton [4] [4]artfcal mmune systems and ACS method Immune algorthms [43] etr nets based methods [44][45][46] [47] [48] [48]used coloured etrnet Artfcal Neural Networks [49] [50] [49]heurstc methods performs better than ANN. Fuzzy ogc methods [10][51] [51] Mult-obectve formulaton; solved usng heurstc rules Knowledge-based expert system [5][53][54][55] [54]expert heurstc rules based on G-nets Smulated annealng [56][57] [13] [58][59] [59]for large practcal systems. formng a sngle loop n a dstrbuton network. The system s made radal by openng any one of the swtched of the loop thus formed. The swtch to be opened can be decded based on crtera such as () mnmum voltage dfference across the lne, () mnmum current through the lne, and () mnmum power flow through the lne. The te-swtched to be closed depend on voltage dfference across the te-lne. However, these methods do not guarantee an optmal loss confguraton and are only applcable when loss mnmzaton s a crteron. An mportant varaton was proposed by S. K. Goswam and S. K. Basu [9] n whch all the te-swtches are closed and the system s made radal by openng those swtches whch have () mnmum current flow through or () mnmum voltage dfference across the lne. In other cases many heurstc technques are appled for loss reducton. These methods do not guarantee optmal soluton but yeld a soluton wth a lower amount of losses. There are several varatons on heurstc technque to make the decsons faster or make t applcable for large dstrbuton systems. The heurstc technques dscussed so far are based on assumpton of constant power load model whch s a serous drawback as the loads are actually voltage dependent. It s shown n the present work that heurstc technques based on constant power load model yeld msleadng confguratons whch may n fact lead to ncrease n ntake at the man substaton. Thus heurstc-based formulatons work well only for the case of loss reducton and cannot be extended to other formulatons such as mnmzaton of ntake, ntake or S ntake. Formulatons based on optmzaton technques are also well documented n the lterature. The nonlnear, dscontnuous and hghly combnatoral problem of reconfguraton can approprately be formulated as a mxednteger non-lnear optmzaton problem where states of the swtches are taken as nteger varables. oss reducton problem has been formulated as a quadratc cost transshpment problem. The voltages, conductor and the substaton lmts are taken as constrants. A specal care has to be taken to nclude the radal constrant. etr Nets (N) s used to model the nference mechansm for dstrbuton system operaton by consderng the utlty restoraton rules. Wth the parallel-lke nference characterstcs, the N approach performs effcently to fnd the proper swtchng operaton to solve the problem of overload and the multple contngences for dstrbuton systems. N s well suted for modelng any dstrbuted system n general. Fuzzy logc based obectve functon are also proposed. The fuzzy logc s normally used to translate the commonly expected benefts nto approprate mult-obectve formulatons. Artfcal Neural Networks (ANN) and unconventonal search methods are also appled and are popular research tools n reconfguraton. The clusterng based tranng methods have been employed for compressng (through generalzaton) excessvely large number of data sets. It can be concluded that normally heurstcs based methods are more suted and ther combnaton wth ANN can be used to some advantage. The unconventonal search methods are also well known n reconfguraton studes. Most of the methods are based on evolutonary approaches to yeld better search structures and capabltes. The methods such as smulated annealng wth dfferent varatons, genetc algorthms wth enhancement n mutaton and other parameters, and ant colony based methods enhanced wth mmune algorthms have been used wth varous obectves functons. When closely and crtcally nvestgated, these methods take a good amount of computaton whch s comparable to exhaustve search. The heurstc approaches are drect result of assumng constant power load model therefore these approaches do not hold n case of practcal load scenaro. The present work shows that ncluson of voltage dependent load models has a maor overhaul effect on heurstc methods and related rule-based Ns and ANN methods whereas n load flow routnes of the search methods ncluson of load models wll be requred. III. ROBEM ANAYSIS AND RE-FORMUATION A. Statc oad Models: The phenomenon of change n the load wth change n voltage s practcally experenced. In an operatng range applances normally consume less power at lower voltages and vce-versa. The values of voltage exponents and n the followng equatons (1) and () bascally model ths behavor of load as a functon of voltage. There are two approaches to model ths load behavor for a partcular system [59]. Department of Electrcal Engneerng, Unv. College of Engg., Osmana Unversty, Hyderabad, A., INDIA.

4 16th NATIONA OWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, () Feld Test based technques: In the feld test-based approach, specfc feeder load models are derved by measurng the response of the system load to staged tests. Also under ths category, models have been derved by measurng the natural varaton of system parameters usng fast data acquston systems. In the component-based approach, load models are obtaned by aggregatng the models of ther ndvdual components. Owng to fast data acquston system [5] avalable now-adays, feld test based technques have become qute popular. In feld test based method, the measured values are ftted to exponental model, 0 ( ) and 0 ( ), of the load to fnd and. () Component based technques: Component based approach can be regarded as a specal case of exponental model (, 0,1, and ), where the load s represented as ZI model (combnaton of constant mpedance, constant current and constant power). The load s expressed as the aggregate of; (a) Impedance type, ; (b) constant current type, ; and (c) Constant power, c type. Therefore the ZI model s expressed as a b c, d e f. In case of exponental load model, t may be noted that n actual studes the goes up to 1.8 whereas the values correspondng to reactve power go up to 6. Therefore, f reactve load s modeled as ZI model, t may not match the measured characterstcs for reactve loads. The sgnfcant characterstc of reactve load s that t vares as a nonlnear functon of voltage characterzed by the hgh value of. Ths s caused by magnetc saturaton n dstrbuton transformers and motors [60]. B. roblem Analyss and Reformulaton: ractcal voltage dependent load models.e. resdental, ndustral, and commercal gven n [] have been adopted for nvestgatons n the present work. The load models can be mathematcally expressed as 0 (1) 0. () In a constant power model, conventonally used n power flow studes, = =0. The values of the real and reactve exponents used n the present work for ndustral, resdental and commercal loads are gven n Table III []. TABE III OAD TYES AND EXONENT AUES oad Type Constant 0 0 Industral Resdental Commercal The power loss n a dstrbuton system s gven by the followng relaton,,, N 0(, ),, r, (3), ) ( (4) 0(, ), ) ( (5) Substtutng (4) and (5) n (3) (, r,, ),,,, N r, 0(, ) (,, ) ) ( 0(, ) ( (6) Assumng that the loads are not changed, for any confguraton, the loss s functon of all the system bus voltages s, r,,,, and, as these quanttes change wth the change n confguraton. and, are the equvalent load exponents whch may be obtaned by modelng power flows n the lnes as an aggregate of bus loads and lne losses after the consdered lne (, ). The total loss manly depends on the voltage profle, s, and the confguraton,. The total system ntake.e. the real power ntake at the r, man sub-staton (node 1) can be gven by the followng relaton. 1 1 NB 1 and NB 1 ( ) 0, N r, 0(, ) (,,, ( 0(, ) (. (7) Smlarly, the total system ntake at bus 1 can be gven by NB 1 0 ( ), N x, 0(, ) (,, ( 0(, ) ( It s observed that for a typcal dstrbuton system ( ) 0, N r, 0(, ) (,, ( 0(, ) (, N, B 0(, ) ( ( 0(, ) ( 0 ( ) r (10), 1, N Thus, the ntake and ntake are decded manly by the load exponents, and. To verfy the above sad relatons the plots were obtaned for dfferent types of loads for 50 dfferent radal confguratons of a dstrbuton system. The dfferent radal confguratons are close to each other to gve varatons n the voltages, losses, and ntake, when the loadng condtons are mantaned same. The radal confguratons are close to each other n the sense that most of the lnes are undsturbed except a few lnes. The power losses are plotted aganst average (8) (9) Department of Electrcal Engneerng, Unv. College of Engg., Osmana Unversty, Hyderabad, A., INDIA.

5 16th NATIONA OWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, voltage of sad radal confguratons n Fg 1. The average voltage has been taken to be a representatve voltage for overall system. The fgure ndcates that there s a decreasng trend n losses as the average system voltage ncreases. Ths trend s observed for all the load models. It can be observed that, compared to practcal load scenaro, the decrease n losses wth ncreasng voltage s maxmum n case of constant power loads. However, n the practcal range of p.u., behavor of all types of the loads s smlar, as far as losses are concerned. In Fg., system ntake versus average system voltage, has been plotted for the same set of 50 radal confguratons. The fgure ndcates that system ntake decreases as average system voltage ncreases for constant power ( 0 ) and ndustral ( ) loads, whereas, for commercal ( ) and resdental ( 0. 9 ) loads the trend s reverse. Thus, ncreases or decrease of ntake wth average system voltage s determned by the type of load. Ths s also vald n the practcal voltage range of (p.u). In Fg. 3, system ntake versus has been plotted for the same set of 50 radal confguratons. The fgure ndcates that system ntake ncreases as ncreases for constant power ( 0 ) and ndustral ( ) loads, whereas, for commercal ( ) and resdental ( 0. 9 ) loads the trend s reverse. Increase or decrease of ntake wth s determned by the type of load. The understandng that the ntake decreases wth decrease n does not hold n case of practcal loads. It s observed from the above dscusson that the reducton n losses mproves the voltage profle. However, the reducton n losses and mprovement n voltage profle do not necessarly result n reduced ntake at the man substaton. A smlar logc holds for ntake. The plot of versus ntake showng the reversal of behavor of practcal load ( > 1) as compared to constant load ( = 0) assumpton s depcted n Fg. 4. Ths effect s much pronounced n reactve loads normally encountered n practce due to nherently large values of. The smlar logc s also vald for S ntake. There are two scenaros for the operaton of dstrbuton systems. (1) In- House Dstrbuton System (IDS): Operator operates ts own dstrbuton systems lke organzaton/ndustral houses; the payment has to be ultmately made by the dstrbuton system owner for the usage (Intake) hence IDS would lke to mnmze the power ntake. () DISCO: The operator takes power from the ower pool or GENCO (as the case may be) and sells the power to the customers. The DISCO would mnmze losses to mnmze the Fg 1. Relatonshp between average system voltage and Fg. Relatonshp between average system voltage and ntake Fg 3. Relatonshp between and ntake Department of Electrcal Engneerng, Unv. College of Engg., Osmana Unversty, Hyderabad, A., INDIA.

6 16th NATIONA OWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, Fg 4. Relatonshp between and ntake operatonal overheads (to the customers) to reman compettve by reducng overall charges to the customers. Earler reconfguraton studes show that, n case of constant power loads, the reducton n losses (real, reactve and MA) s equvalent to reducton of system ntakes (ntake, ntake, and Sntake) and thus DISCO and IDS utltes were same as far as payments were concerned. Ths relatonshp between reduced losses and reduced system ntake does not hold n case of voltage dependent practcal loads. In ths case when the losses are reduced (through reconfguraton) the bus voltages ncrease; ths ncrease n the bus voltages leads to ncrease n the bus loads, and therefore whle the losses decrease the total load demand ncreases. In most of the cases, the ncrease n the total demand over-weghs the reducton n losses and results n ncreased cost due to ncreased ntakes. As loss mnmzaton s not equvalent to ntake mnmzaton, DISCO, whch pays for losses, would mnmze losses and IDS, whch pays for ntake would mnmze ntake(s). Ths phenomenon makes dfference n the payment crteron for DISCO and IDS. Thus, n case of IDS, and other cases where mnmzaton of ntake s obectve, more approprate formulatons for reconfguraton would be to mnmze the overall system ntake n terms of ntake, ntake, or S ntak, as requred, at the man substaton, as opposed to mnmzng or. Also, t s mportant to note that the voltage profle may be a competng constrant rather than beng supportve to system ntake. Thus, t s evdent that dfferent formulatons for reconfguraton problem may be gven as follows for IDS. Mnmze N B N B 1 1 ( ) 0 Mnmze 0 ( ) ntake ntake 1 (, 0, 0, α, β), N, N r, x, 0(, ) 0(, ) ( ) 1 (, 0, 0, α, β) ( ),, ) ( 0(, ) ( (11),, ) ( 0(, ) ( ) ) Mnmze S ntake ntake ntake (1) (13) Each of the above obectves s subect to the followng set of constrants N B G B )] 0 ( ) [ cos( ) sn ( 1 for 1 to N B (14) NB 0 ( ) [ G sn( ) B 1 ( N B cos( )] for 1 to (15) 0(, ) for 0(, ) for [ ( ), N ) G G cos B sn, (16) ( ), N ) B G sn B cos, (17),, 1/ 0 (, ) ( ( 0(, ) ( ] for N MA (, )max, (18) max for 1 to N B (19) mn for 1 to (0) N B where (14) - (17) are usual power flow equatons and (18) (0) are the operatonal system constrants. I. CONCUSIONS From the analyss carred out n the present work, t s establshed that omsson of load models could lead to erroneous formulaton of reconfguraton problem. Mnmzng the system losses s not same as mnmzng the system ntakes from the man substaton and therefore, may not be approprate crtera n many practcal cases such as IDS. It has also been shown that a system confguraton may result yeldng hgher system ntakes f load models are omtted. Thus, concept of loss reducton as measure of system cost effcency may change n some cases when load models are taken nto account. The quanttatve sgnfcance of mpact of load models s nvestgated n part II of ths paper. REFERENCES [1] C. Concorda and S. Ihara, oad representaton n power systems stablty studes, IEEE Trans. ower App. Syst., vol. AS-101, no. 4, pp , Apr [] IEEE Task Force on oad Representaton for Dynamc erformance, Bblography on load models for power flow and dynamc performance smulaton, IEEE Trans. ower Syst., vol. 10, no. 1, pp , Feb [3] IEEE Task Force on oad Representaton for Dynamc erformance, oad representaton for dynamc performance analyss, IEEE Trans. ower Syst., vol. 8, no., pp , May [4] IEEE Task Force on oad Representaton for Dynamc erformance, Standard load models for power flow and dynamc performance smulaton, IEEE Trans. ower Syst., vol. 10, no. 3, pp , Aug [5] D.T. Rzy, J.S. awler, J.B. atten, and W.R. Nelson, Measurng and analyzng the mpact of voltage and capactor control wth hgh speed data acquston, IEEE Trans. on ower Delvery, vol.4, no. 1, pp , Jan Department of Electrcal Engneerng, Unv. College of Engg., Osmana Unversty, Hyderabad, A., INDIA.

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