Voltage Contingency Ranking for IEEE 39-Bus System using Newton- Raphson Method

Transcription

1 WSEAS TRANSACTIONS o OWER SSTEMS Haer m, Asma Meddeb, Souad Chebb oltage Cotgecy Rag for IEEE 39-Bus System usg Newto- Raphso Method HAER MII, ASMA MEDDEB ad SOUAD CHEBBI Natoal Hgh School of Egeers of Tus 5 Aveue Taha Husse, 1008 Motfleury, Tus TUNISIA haerm@yahoo.com, meddebasma@yahoo.fr, chebb.souad@gmal.com Abstract: - Steady state securty assessmet becomes a strget eed as t provdes the owledge about the state of the system followg a cotgecy. Ths paper presets a Newto-Raphso load flow based method for voltage securty assessmet. A voltage performace dex s computed frstly to classfy cotgeces secure, secure ad crtcal classes ad the to ra them the decreased order of severty. The proposed approach s tested o the IEEE 39-bus system by performg N-1 cotgecy for dfferet load codtos. Key-Words: - Classfcato, load flow, Newto-Raphso, N-1 cotgecy, performace dex, steady state securty assessmet. 1 Itroducto The secure power system operato s cosdered as a mportat challege for electrcty supply dustry. Thus, the eed for assessg the securty of the system s creasgly sstet [1, ]. The am of securty aalyss s to have formato about the state of the system the evet of a uscheduled cotgecy; therefore, cotrol actos for eepg the system secure operatg lmts ca be tae mmedately [3]. As a type of system securty, steady state securty assessmet SSA s cocered wth the screeg of the steady state performace of the system after beg subected to a cotgecy, terms of volato of ay operatg costrats as voltage lmts [4]. The ma fucto of the SSA s the aalyss of the cotgecy whch cludes the defto, selecto ad rag of the secure cotgeces accordg to ther severty [5]. I the lterature, varous o-le rag methods based o the estmato of the performace dex I, have bee put forward to measure the degree of severty of each cotgecy. However, the o-le applcato of these methods requres large computatoal tme addto to the hgh cost [6]. Wherefore, the offle method stll has a great mportace power system securty assessmet. Several wors have bee performed to tacle the ssue of cotgecy assessg ad rag [6-8]. The authors [9] evoed the ssue of dyamc securty assessmet DSA. They proposed a offle method based o umercal smulatos aalyses to compute two dfferet severty dces. N-1 cotgecy s performed o the IEEE 57-bus system to test the proposed method. A Newto- Raphso load flow method s proposed [10] to ra le outage. Usg a 5-bus test system, voltage performace ad actve power dces are computed for all the possble cotgeces. Ths approach s also used [11] for classfyg le outage cases for two dfferet test system. S. Gogada et al. [1] preseted a fast decoupled load flow approach to measure the actve power dex ad the voltage performace dex. The sum of the two dces s used to order le cotgeces based o ther severty. Referece [13] deals wth the aalyss of the traset stablty of the IEEE 14-bus system. The detfcato of the state of the system ad the rag of the cotgeces are carred out by applyg a heurstc method. Ths paper deals wth the statc securty assessmet of power system. The proposed method s based o Newto-Raphso load flow to compute the voltage performace dex. By performg N-1 cotgecy o the test system IEEE 39-bus system, the I dex s tested for the classfcato of the voltage securty level ad the rag of the cotgeces the decreased order of severty. The remader of the paper s orgazed as follow: secto presets the detaled methodology ad the formulato of the I. Secto 3 detals the Newto-Raphso load flow method. The case study ad the smulatos results are gve secto 4. Fally, we summarze the ma pots of ths paper the cocluso. E-ISSN: 4-350X 48 olume 1, 017

2 WSEAS TRANSACTIONS o OWER SSTEMS Haer m, Asma Meddeb, Souad Chebb Methodology We propose a offle method to ra all the probable cotgeces to detfy those that may lead to secure state. The approach s based o the resoluto of the o-lear load flow equatos to obta the post-cotgecy buses voltages. These values are used for computg the performace dex I. A cosderable umber of operatg codtos s geerated by modfyg the total load of the power system large rage ad for each load patter; a three-phase short crcut s appled at each trasmsso le usg AC load flow. The cotgeces are raed the decreased order of severty.e., hgher the I severe s the cotgecy. Table 1 shows the dfferet classes of the cotgeces correspodg to the I rage. Whe the I value s below 0., the system s sad a secure state ad the cotgeces are the least severe. The secod class correspods to the secure state where the I value s above 0.8 ad the cotgeces are the most severe. Whle f 0. <I<0.8, the state of the system s deemed crtcal [14]. Table 1 Classes of oltage erformace Idex Class Secure Isecure Crtcal I rage < 0. > < I< The dex of voltage performace I ths paper the performace dex I, represeted by equato 1, s used to classfy the voltage securty codto ad to ra the cotgeces from a well-defed lst. Oly the voltage volated buses are cosdered the computato of the I. w I f M f S M f s a fucto defed as follows: max m, for >, for < max m 1 : the umber of the bus whch belogs to the set of the volated buses oly. : the post-cotgecy voltage at the th bus. bus. max : the upper lmt of the voltage at the th m bus. M ad : the lower lmt of the voltage at the th w are the order of the expoet ad the weghg coeffcet respectvely. We started the I computato by arbtrary usg w =1 ad M=4. Tag to accout that 0<I<1, t was observed after repeated smulatos, that the approprate values of w ad M to obta reasoable results are: w =1 ad M=6. Table summarzes the ma results of the smulatos the base case o load crease. Table Idex I alue Fucto of M Trasmsso I le M=4 M=5 M= oltage cotgecy rag The followg steps summarze the proposed method for voltage securty rag: - Geerate varous operatg codtos by perturbg the load of all the buses wde rage; - For each case of load crease, perform N-1 cotgecy for all the trasmsso les by AC load flow; - Compute the voltage Is usg equato 1 for all the cotgeces; - The cotgeces havg I value <0. are ot cosdered to be raed; - Ra the selected cotgeces the decreased order of severty. 3 Newto-Raphso Method The Newto-Raphso method s the most used teratve algorthm for solvg load flow problem. Based o Taylor's seres, t approxmates o-lear equatos to lear equatos. To express the process of the NR method, a -bus system wth bus 1 as a slac bus s cosdered [15-17]. The comg curret to a gve bus of a power system ca be wrtte as follows: I 1 for =1,,..., I : the ected curret at bus ; E-ISSN: 4-350X 49 olume 1, 017

3 : a elemet of the admttace matrx; : the ected voltage at bus ; : umber of the buses the system. I polar form, the equato ca be expressed as follows: I 1 3 : the dfferece betwee voltage phase agles of buses ad ; : voltage agle at bus. The complex power delvered to the bus s gve by equato 4: I * 4 : the ected actve power at bus ; : the ected reactve power at bus ; : the ected voltage at bus. By substtutg the expresso of I equato 4, we obta: 1 5 From equato 5, the real ad reactve powers are gve by: cos 1 6 s 1 7 Equatos 6 ad 7 represet the olear algebrac equatos whch deped upo the voltage ad the phase agle. By expadg these two equatos Taylor's seres cocerg the tal estmate, we obta the set of lear equatos 8. From equato 8, the acoba matrx presets a learzed relatoshp betwee o the oe had, the small chages voltage magtude ad voltage agle ad o the other had, the small chages real ad reactve power ad. The acoba matrx elemets, except for those of the slac bus whch are ow, are the partal dervatves of real ad reactve power equatos. I the matrx form, the equato 8 ca be expressed as: The terms ad are called power resduals, they represet the dfferece betwee the calculated ad the scheduled values ad are expressed by equatos 10 ad 11. sched 10 sched 11 sched ad sched : scheduled actve ad reactve power at bus. The estmates of the voltages ad the phase agles are therefore wrtte as follows: WSEAS TRANSACTIONS o OWER SSTEMS Haer m, Asma Meddeb, Souad Chebb E-ISSN: 4-350X 50 olume 1, 017

4 WSEAS TRANSACTIONS o OWER SSTEMS Haer m, Asma Meddeb, Souad Chebb 4 Case Study ad Results The proposed approach s tested for voltage cotgecy classfcato ad rag of IEEE 39- bus New Eglad system [18]. Ths test system cossts of 46 trasmsso les, 1 trasformers, 19 loads ad t has 10 geerators. 30 smulato cases were geerated correspodg to 5 operatg codtos: base case, 10%, 30%, 50% ad 70% of load crease. A three-phase short crcut s cosdered as the cotgecy ad s appled for each load patter, at all the trasmsso les wth the followg characterstcs: fault resstace r = 0.01Ω ad fault durato t= 100ms. I each case, the severty of the cotgecy s evaluated by computg the I. The test results of oly some scearos are show Tables 3 ad 4, because of the lmted space. Table 3 presets the classfcato of the cotgeces secure, secure ad crtcal classes. Durg the dfferet load patters, the I value case of a fault at le 1-39 s uder 0., so the state of the system s classfed as secure. However, a short-crcut at le 8-7 leads to secure state. I other cases, for example le 14-15, the cotgecy s crtcal durg the base case ad 10% of load crease, but t belogs to secure class uder heavy load codtos. f The rag phase cosders oly the cotgeces belogg to secure ad crtcal classes. Thus, after assessg the I value of all the 46 cotgeces, t was foud that the system operates a secure maer for the followg cotgeces: le 1-39, le 9-39, le 11-1, le 6-9, le 13-1 ad le 5-6. Therefore, these fault cases are fltered out from the lst of credble cotgeces.e. are ot cosdered to be raed. Table 4 shows the frst te most severe cotgeces. The trasmsso les 8-5, 8-7 ad 9-8 gave the hghest I values ad hece are deemed the most crtcal les the test system. However, les 11-10, 16-4, ad gave the least performace severty levels. From the smulato results for all the load patters, t s foud that the proposed method s able to classfy all the cotgeces three classes ad to ra them accordg to ther severtes. However, a short-crcut at le 8-7 leads to secure state. I other cases, for example le 14-15, the cotgecy s crtcal durg the base case ad 10% of load crease, but t belogs to secure class uder heavy load codtos. Table 3 Cotgecy Classfcato for 5 Operatg Codtos Base case 10% 30% 50% 70% Le I State Le I State Le I State Le I State Le I State S S S S S S S S S S C C C C C C C I I I S S S S S C C C C C C C C C C C C C C C S S S S S S S S S S S S S S S I I I I I C C C C C I I I I I I I I I I S: Secure; C: Crtcal; I: Isecure E-ISSN: 4-350X 51 olume 1, 017

5 WSEAS TRANSACTIONS o OWER SSTEMS Haer m, Asma Meddeb, Souad Chebb Table 4 Cotgecy Rag for 5 Operatg Codtos Base case 10% 30% 50% 70% Ra Le I Ra Le I Ra Le I Ra Le I Ra Le I Cocluso Ths paper has preseted a offle method to ra selected cotgeces the decreased order of severty, accurate maer. The approach s based o the computato of the voltage performace dex I usg Newto-Raphso load flow method. The hghest values of the dex correspod to the most severe cotgeces whch lead to the volato of voltage lmts. Durg the dfferet load codtos, the rag of the cotgeces are the same, however, there are some msrag due to the fact that the I values are so close ad the varato degree s ot always the same. Further wors wll troduce others methods for comparso purpose. Refereces: [1] E.Capesso, D.Cro, S.Massucco, A.Mor, A.tto ad F.Slvestro, Rs-Based Dyamc Securty Assessmet for ower System Operato ad Operatoal lag, Eerges oural, 017. [] A.Sharfa, ad S.Sharfa, A ew power system traset stablty assessmet method based o Type- fuzzy eural etwor estmato, Electrcal ower ad Eergy Systems, pp , 015. [3] M. D Sato, N. Raaldo, D.llacc, ad E. Zmeo, erformg Securty Aalyss of Large Scale ower Systems wth a Broer-based Computatoal Grd, Iteratoal Coferece o Iformato Techology, 004. [4] K.Sh.Swarup, Artfcal eural etwor usg patter recogto for securty assessmet ad aalyss, Scece Drect, pp , 008. [5] D. Devara,.. Rosely, ad R. U. Ra, Artfcal eural etwor model for voltage securty based cotgecy rag, Scece Drect, pp 7-77, 007 [6] N. Amady, Dyamc voltage securty assessmet by a eural etwor based method, Electrc ower Systems Research, pp 15-6, 003. [7] K.Sa, ad A.Saxea, Ole ower System Cotgecy Screeg ad Rag Methods usg Radal Bass Neural Networs, Iteratoal oural of Electrcal ad Electrocs Egeerg Research, vol. 6, ssue 3, pp 9-16, 016. E-ISSN: 4-350X 5 olume 1, 017

6 WSEAS TRANSACTIONS o OWER SSTEMS Haer m, Asma Meddeb, Souad Chebb [8] T.a, L.Srvastava, ad SN.Sgh, Fast oltage Cotgecy Screeg usg Radal Bass Fucto Neural Networ, IEEE trasactos o power systems, vol. 18, 003. [9] W.A.Oyeam, G.Radma ad T.O.Aewole, Traset stablty based dyamc securty assessmet dces, Electrcal & Electroc Egeerg, 017. [10].Sehar, ad S.Mohaty, ower system cotgecy rag usg Newto Raphso load flow method, IEEE Ida Coferece, 013 [11] S. Burada, D. osh, ad K.D. Mstry, Cotgecy Aalyss of ower System by usg oltage ad Actve ower erformace Idex, 1st IEEE Iteratoal Coferece o ower Electrocs, Itellget Cotrol ad Eergy Systems, 016. [1] S.r. Gogada,T.S. Rao,.Mallarua rao, S. Salma, ower System Cotgecy Rag usg Fast Decoupled Load Flow Method, Iteratoal Coferece o Electrcal, Electrocs, ad Optmzato Techques, 016. [13] A. Meddeb, H. m, ad S. Chebb, Heurstc aalyss ad cotgeces classfcato of case Study IEEE 14-bus, 7th Iteratoal Coferece o Sceces of Electrocs, Techologes of Iformato ad Telecommucatos SETIT, pp , 017. [14] L. Srvastava, S.N. Sgh, ad. Sharma, A hybrd eural etwor model for fast voltage cotgecy screeg ad rag, Electrcal ower ad Eergy Systems, pp 35 4, 000. [15] O.A. Afolab, W.H. Al,.Cofe,.Fuller,.Obomo, ad E.S. Kolawole, Aalyss of the Load Flow roblem ower System lag Studes, Eergy ad ower Egeerg, pp , 015. [16] T. Kulworawachpog, Smplfed Newto Raphso power-flow soluto method, Electrcal ower ad Eergy Systems, pp , 010. [17] X.-F. Wag et al., Moder ower Systems Aalyss, Sprger Scece ad Busess Meda, 008 [18] L.Leor, Automatc Operator of Electrcal Networ, hd. thess, Uv. uebec, ue 009. E-ISSN: 4-350X 53 olume 1, 017