Assessing the Service Rendered by a Power Distribution Control Center

Transcription

1 1 Assessng the Servce Rendered by Power Dstrbuton Control Center C. J. Zpt, Member IEEE, J. Urre Abstrct Ths pper presents methodology bsed on queung theory for ssessng the servce rendered by the control center of power utlty. Stochstc pont process modelng s used for representng the sequence of events to be solved by the control center nd the control center opertor servce tmes. The control center servce ndexes re computed by mens of procedure of sequentl Monte Crlo smulton. Ths methodology ws ppled to the control center of Electrcrbe, lrge power dstrbuton utlty n Colomb. Results show tht:. In lmost ll the zones served by the studed control center, the nput nd servce processes re not sttonry; thus, methodology lke the proposed one, tht cn mnge sttonry nd non-sttonry processes, s necessty.. The power lw stochstc pont process model s recommended s the frst choce for representng the nput nd servce processes becuse t fts even n those cses of smples wth low tendency for whch renewl process models could not be ftted.. The trffc ntensty prmeter s very helpful becuse t shows the pttern of utlzton of the control center resources nd when they wll be totlly occuped. Index Terms Posson processes, power dstrbuton relblty, queung nlyss, relblty modelng. I. INTRODUCTION HE operton of power system s chllengng tsk Tbecuse:. It s composed by lots of components tht re dspersed over wde geogrphcl regons.. The rndom nture of the events tht ffect ts operton.. Its non-lner dynmc nture. v. It hs to operte contnuously meetng requrements of relblty, power qulty, sfety nd securty. Fortuntely, dvnces n communctons, electroncs nd computng hve llowed remotely supervsng nd controllng ts operton from control center. The hstory of power system control centers s presented n [1]; some vsons bout of ther future re gven n [1] nd [2]. Control center opertors nterct wth power system components nd others ctors of power system operton. Ths s depcted n Fg. 1. C. J. Zpt s wth Unversdd Tecnológc de Perer, Perer, Colomb. (e-ml: cjzpt@utp.edu.co). J. Urre s wth Electrcrbe, Brrnqull, Colomb. (e-ml: jurreo@electrcrbe.com). Fg. 1. Interctons of control center opertors Due to the mportnce of control centers on power system operton nd on customer servce qulty, t s necessry to ssess the servce they render. For ths purpose, methodology bsed on queung theory, stochstc pont process (SPP) modelng nd Monte Crlo smulton (MCS) s presented n ths pper. It ws prevously ppled to the repr process performed by crews n eght Colombn power dstrbuton systems [3], [4]. II. STOCHASTIC POINT PROCESSES A SPP s representton for phenomenon n whch events occur or rrve rndomly n tme. Tendency of SPP s postve f the pttern of event rrvls ncrese wth tme, negtve f t decreses wth tme nd zero f t does not ncrese or decrese; the ntensty functon λ() t controls the tendency of SPP model. A clssfcton of SPP models s shown n Fg. 2 [5]. A RP s nmed fter the dstrbuton of the nter rrvl tmes ; the most fmous RP s the exponentl one clled Homogeneous Posson Process (HPP). Whle there re mny NHPP models, the pproch here s to use the Power Lw Process (PLP) [6] becuse (). There re methods for prmeter estmton nd goodness of ft. () It cn represent process wth or wthout tendency /12/$ IEEE

2 C. Computton of Servce Indexes The servce rendered by the control center s ssessed by mens of the followng ndexes: The men wtng tme ( tw ), the men event durton ( ted ) nd the congeston ( C ). These ndexes re computed by mens of procedure of sequentl MCS. As shown n Fg. 4, smulton conssts of N relztons durng perod T of one or more yers nd sub-perods dt (week, month, etc.). 2 Fg. 2. A clssfcton of SPP models III. METHODOLOGY A. Modelng The servce rendered by control center n servce zone cn be represented s the queung system shown n Fg 3. Fg. 3. Queung model for servce zone of control center The nput to ths system s the sequence events tht control center opertors hve to solve; these nclude lrms, trps nd requests. It s represented by mens of SPP wth ntensty functon λ E () t. The servce s SPP wth ntensty functon λ S ( t ) tht represents the tmes to servce ( tts ),. e. the perods dedcted by the control center opertors to solve the events. The output of ths system s the sequence of solutons, gven by the control center opertors to the events. B. The Trffc Intensty The trffc ntensty t ( ) s defned by (1). Fg. 4. Generl procedure of the MCS procedure As depcted n Fg. 5, n ech relzton, sequence of events e ' snd solutons s ' s re generted n order to obtn smples of tw nd ted. The perod n event hs to wt untl n opertor s free to solve t s tw. The totl tme requred to solve n event s ted, the sum of tts nd tw. ( t) =λ ( t) / λ ( t ) (1) E A trffc ntensty hgher thn 1.0 (or 100%) mens events rrves fster thn the control center opertors cn solve them; thus, t hs then to be less or equl to 1.0. For the cse where the nput nd servce processes re represented by mens of PLP models: S β t () =λ t (2) λ = λe βe /( λs βs ) (3) β =β β E S The servce process performnce wll be constnt f β = 0, deterortng f β > 0 nd mprovng f β < 0. t 100 denotes the nstnt for whch t ( ) = 100%. (4) Fg. 5. A sequence of events nd solutons n relzton

3 3 After performng N relztons the servce ndexes re computed. C s obtned pplyng (5). C = tw / ted *100% (5) IV. HOW TO OBTAIN THE INPUT AND SERVICE MODELS A. Dt Smples The procedure for obtnng the smples for buldng the nput nd servce models of servce zone s: 1. For perod of t lest one yer, tke the nstnt of occurrence of ech event; ths s the smple of rrvl nstnts of the events. 2. For ech event, obtn the tme to servce; ths s the smple of tts or servce ntervls. If two events hve the sme rrvl nstnt, dsplce them ddng one mnute to one of them. If control center opertor requests the servce of n externl ctor, e. g crew, the tts ends when the request s gven. If the externl ctor clls fter to request somethng lke swtchng cton, ths request s treted s new event. B. Model Fttng Fg. 6 shows the procedure ppled for fttng SPP model to smple of sze n. x denotes n nter-rrvl ntervl nd t n rrvl tme. More detls re gven n [4]. Tendency s checked by mens of (6) nd (7), the Lplce nd Lews-Robnson sttstcs whch re normlly dstrbuted U [( t ) t ] / [ t ] (6) ( n 1) = k L n n n = 1 U = U * s / x (7) LR L x s x nd x re, respectvely, the nter-rrvl tmes stndrd devton nd men. U L nd U LR re compred to z α /2, the vlue n the stndrd norml dstrbuton for crtcl probblty α, n order to hold or reject the null hypothess of no tendency. Independency of the nter-rrvl tmes smple s checked by mens of the sctter dgrm. Goodness-of-ft to the PLP model s checked by mens the TTT-plot. Goodness-of-ft to HPP, Webull RP, Gmm RP nd the Lognorml RP s checked by mens of the Kolmogorov-Smrnov (KS) test. The prmeter of RP models s estmted before the pplcton of the KS test usng (8). λ ˆ ( t ) = n / t = 1 / x (8) n The PLP prmeters re estmted fter the pplcton of the TTT-plot test usng (9) nd (10). β= ˆ ( 2) / n n Ln( tn / t ) (9) = 1 ˆ λ= ˆ n / t β n (10) Fg. 6. Procedure for fttng SPP model

4 4 V. ELECTRICARIBE AND ITS CONTROL CENTER Electrcrbe s power dstrbuton compny tht serves the populton tht lves n the Colombn Atlntc Regon; ths regon s shown n Fg. 7. Tble I shows some dt bout ths utlty. TABLE I GENERAL DATA OF ELECTRICARIBE Electrcrbe s the thrd lrgest power dstrbuton compny n Colomb. Its control center s locted n the cty of Brrnqull, the fourth most populted cty n Colomb (Approxmtely 1 800,000 nhbtnts n ts metropoltn re). Tble II shows generl descrpton of the servce zones defned for the control center of Electrcrbe. Fg. 7. Servce terrtory of Electrcrbe TABLE II SERVICE ZONES OF ELECTRICARIBE CONTROL CENTER

5 5 VI. RESULTS A. Input nd servce models Tble III shows the nput nd servce models tht were bult usng opertng dt of yer For confdence level of 95% (Crtcl probblty α= 5% ), z α /2 = s the reference vlue to ccept or reject the null hypothess of no tendency. As cn be observed, lmost ll nput nd servce processes re non sttonry. The PLP model could be ftted for ll smples, even for those wth low tendency. In ll cses, t 100 s very lrge wht mens tht the trffc ntensty prmeter wll never be 1.0,. e. the resources wll never be 100% occuped. TABLE III POWER LAW MODELS FOR INPUT AND SERVICE B. Servce Indexes Tble IV shows the servce ndexes for T = 1.0 yer. As cn be seen, the wtng tme s very low n ll servce zones. TABLE VI REQUIRED COMPUTATIONAL TIME FOR ASSESSING THE SERVICE INDEXES TABLE IV SERVICE INDEXES FOR T = 1.0 YEAR VII. REQUIRED COMPUTATIONAL TIME An mportnt spect of every smulton method s to hve n de of the requred computtonl tme. Tble V shows requred computtonl tme for ssessng the performnce ndexes of the servce zones. Fg. 8 shows how the requred computtonl tme grows exponentlly wth the number of events to be processed. Ths s dsdvntge of ll ssessment methods bsed on MCS; however, t s mtgted by the fct tht every dy computers wth hgher performnce re more ffordble.

6 6 X. BIOGRAPHIES Crlos J. Zpt obtned hs BScEE degree from the Unversdd Tecnológc de Perer, Perer, Colomb, n 1991 nd hs MSc nd PhD degrees from the Unversdd de Los Andes, Bogotá, Colomb, n 1996 nd 2010, respectvely. From 1991 to 2001 he worked for Concol S. A, Bogotá, Colomb, where he prtcpted n projects of power system studes, electrcl desgns nd softwre development. Snce 2001, he hs worked for the Unversdd Tecnológc de Perer. John Urre obtned hs BScEE from the Unversdd Nconl de Colomb, Medellín, Colomb, n 1999 nd the degree of speclst n trnsmsson nd dstrbuton power systems from the Unversdd de los Andes, Bogotá, Colomb, n Snce 2000 he hs worked for Electrcrbe S. A. Fg. 8. Requred computtonl tme VIII. CONCLUSIONS 1. In lmost ll the servce zones served by the control center of Electrcrbe the nput nd servce processes re not sttonry; thus, methodology lke the proposed one, tht cn mnge sttonry nd non-sttonry processes, s necessty. 2. The power lw stochstc pont process model s recommended s the frst choce for representng the nput nd servce processes becuse t fts even n those cses of smples wth low tendency for whch renewl process models could not be ftted. 3. The trffc ntensty prmeter s very helpful becuse t shows the pttern of utlzton of the control center resources nd when they wll be totlly occuped. IX. REFERENCES [1] F. F. Wu, K. Mosleh, A. Bose, Power system control centers: pst, present nd future, Proceedngs of the IEEE, Vol. 93, No. 11, November, [2] P. Zhng, F. L, N. Bhtt, Next-generton montorng, nlyss, nd control for the future smrt control center, IEEE Trnsctons on Smrt Grd, Vol. 1, No. 2, September, [3] C. J. Zpt, S. C. Slv, H. I. Gonzles, O. L. Burbno, J. A. Hernández, Modelng the repr process of power dstrbuton system, IEEE Trnsmsson & Dstrbuton Ltn Amerc Conference & Exhbton, [4] C. J. Zpt, J. Díz, M. L. Ocmpo, J. D. Mrrg, J. U. Ptño, A. F. Gllego, The repr process of fve Colombn power dstrbuton systems, IEEE Trnsmsson & Dstrbuton Ltn Amerc Conference & Exhbton, [5] C. J. Zpt, A. Torres, D. S. Krschen, M. Ros, Some msconceptons bout the modelng of reprble components, IEEE PES Generl Meetng, [6] IEC Power lw model Goodness-of-ft test nd estmton methods, IEC Stndrd 61710, [7] J. Urre, Model of event rrvls nd the servce n the control center of Electrcrbe S. A. E. S. P, Unversdd de los Andes, (In Spnsh). [8] Brown R. E, Electrc Power Dstrbuton Relblty, Mrcel Dekker, 2002.