RELIABILITY ASSESSMENT OF DEREGULATED GENERATING SYSTEMS USING RELIABILITY NETWORK EQUIVALENT AND PSEUDO-SEQUENTIAL SIMULATION TECHNIQUES

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1 RELIABILITY ASSESSMET OF DEREGULATED GEERATIG SYSTEMS USIG RELIABILITY ETWORK EQUIVALET AD PSEUDO-SEQUETIAL SIMULATIO TECHIQUES Y D, Pe Wa, Lalt Goel ad Quwe Wu Scool of Electcal ad Electoc Eee aya Tecolocal Uvety Saoe ewa@tu.edu. Abtact T ae eet a tecque to evaluate elablty of etuctued eeat ytem. Te ooed tecque baed o te combato of elablty etwok equvalet ad eudo-equetal mulato aoace. Te elablty-etwok equvalet ca be ued to educe te comutatoal bude aocated wt coduct elablty aaly ad ealy clude vaou aeemet amo maket atcat a etuctued owe ytem. Te equvalet mult-tate eeato ovde (MG) toduced to eeet eac eeato comay (Geco) u etwok equvalet tecque. Te equvalet tecque ave bee exteded t ae to deteme te elablty model of a maket atcat oe eeve aeemet wt ote maket atcat. Te eudo-equetal mulato eta te comutatoal effcecy of o-equetal mulato metod ad te ablty to model te coolocal aect. I t ae, t utlzed to clude coolocal aect of a MG elablty evaluato. Te ooed aoac ca be ealy mlemeted ad utable fo te elablty evaluato of a etuctued owe ytem. Te IEEE elablty tet ytem (RTS) ued to llutate te tecque. Keywod: elablty aemet, deeulated owe ytem, etwok equvalet, eudo-equetal mulato ITRODUCTIO Electc utlte ae exeec etuctu touout te wold. A a eult of t eoazato, wat wa te a covetoal moooly eeato utlty ow ecoomcally eaated to dffeet eeato comae (Geco). I t ew evomet, eac Geco ould ovde t elablty ad aocated ce to eue cutome atfacto ad eoal efeece. Eve tou te tecque ued to evaluate te elablty of a covetoal owe ytem ave aleady bee well develoed, te etuctu oce to a deeulated owe ytem a eeated muc eed to move tee tecque. Ref [] eet a metod to evaluate te cutome elablty a deeulated owe ytem code cutome coce o elablty. Te metod baed o te elablty etwok equvalet tecque ooed by Ref []. A eeato comay (Geco) eeeted by a equvalet mult-tate eeato ovde (MG). Tee ae two aoace to evaluate te ytem elablty dect aaly ad Mote Calo mulato [3]. Dect aaly baed o te tate eumeato ued te Ref [] to aoxmate te elablty dce a deeulated owe ytem. Howeve te ytem oeato tate ad aocated tatee uc a load ad te eeve aeemet ae tme vay atue. Te aemet of te uelablty cot dce eque kowlede of te coolocal evoluto of te ytem tate, o at leat, te coolocal evoluto of te ytem falue tate [4]. Te equetal Mote Calo metod ca mulate coolocal aect of ytem oeato, ad oduce te ecfc teuto duato [3]. Howeve te equetal Mote Calo eque moe ubtatal comutatoal effot ta te o-equetal Mote Calo ad aalytcal metod [4]. Te metod may be feable fo ome alcato lae ytem [5]. Te eudo-equetal mulato ooed [4] [6] eta te accuacy of equetal mulato wle kee te comutatoal effcecy of o-equetal mulato metod. I t metod, o-equetal aml ued to elect ytem tate ad coolocal mulato oly aled to deteme te ub-equece aocated wt falue tate tat defe te comlete teuto. Te comutatoal effcecy of te o-equetal mulato tecque ca be fute eaced [4] by comb t wt a tate tato Mote Calo tecque [7]. T ae ooe a tecque to evaluate elablty of etuctued eeat ytem. Te aoac baed o te combato of elablty etwok equvalet ad eudo-equetal mulato tecque. Te coolocal aect of a MG ca be ealy cluded te elablty evaluato by u eudo-equetal mulato. Te elablty etwok equvalet of a Geco exteded to cooate te eeve aeemet amo Geco. A ocedue to deteme a MG ad te aocated elablty dce by u eudo-equetal mulato a bee develoed. Cae tudy o te IEEE RTS [8] fo a deeulated owe ytem eeted ad dcued. 5t PSCC, Lee, -6 Auut 5 Seo 5, Pae, Pae

2 RELIABILITY EQUIVALETS OF GEERATIO COMPAIES Te eeato fucto of a etuctued owe ytem ovded by may dffeet deedet Geco. A Geco uually ow oe o moe eeat ut ad ovde electcty ad eeve to t cutome. A Geco wt may eeat ut ca be eeeted by a equvalet mult-tate eeato ovde (MG) []. Te tate of a MG ca be detemed baed o te falue ate ad ea ate of eac eeat ut te Geco u te equato []. Te elablty of a Geco ca ceae we t a eeve aeemet wt ote Geco. Te eeve aeemet ca be blateal o multlateal. A etuctued eeat ytem, wc a Geco ad bulk load ot eeeted by equvalet mult-tate eeato ovde MG, MG ) a ow F.. ( Ay load model a aoxmato of te actual load. Te accuacy of a load model deed o te amout ad qualty of data avalable [4]. Te aveae load oly a aoxmate eeetato of te actual load. A elatve accuate eeetato te ouly tme vay load ued [9]. A detaled cutome load ofle vae wt te cutome locato, tme of te day, te day of te week ad te week of te yea. Te tme equetal mulato tecque (TSST) ae uually ued to calculate elablty dce code te coolocal load model. Howeve te comutatoal ce u TSST ue fo lae owe ytem. A multlevel o-aeate Makov load model (ML) ow F. wa ooed [4] to educe te comut tme. T model code a et of multlevel load tate equetally coected te ame coolocal ode a tey aeaed te tocal equece. A cotat load tato ate of L, wc oce a ou, ued te ML. L T ( A ) eeet te load level of at ou T. If a load tato occu fom T to T+, te load level all wll be caed fom L T ( A ) to L T + ( A ). L L L L L L LT LT L L L L Fue : Mult-level o-aeated Makov load model T Fue : Relablty equvalet of eeato comae 4 MARKOV MODELS FOR RESTRUCTURED GEERATIG SYSTEMS MG combed wt t ML to fom a equvalet mult-tate eeato ovde wt ML (MGML). If a MG a m tate ad ML a H tate, te umbe of MGML tate ca be detemed a: M m H () Te obablte, fequece ad ote tattcal dce fo te MGML tate ca be detemed u bac elablty tecque. Te tate-ace daam fo te MGML ow F. 3. ate fom te tate to te tate tato ate fom te tate eectvely. te tato, ad to te tate te, 3 TIME VARYIG LOAD MODELS M,,, M, M,, M, M,, M,,, M Fue 3: State-ace daam fo MGML 5t PSCC, Lee, -6 Auut 5 Seo 5, Pae, Pae

3 A MG uually a eeve aeemet wt ote MG. Te MGML wc ued a te eeve ovde of aote MGML deated a a equvalet multtate eeve ovde wt ML (MRML). Te MGML tat a eeve aeemet wt ote MGML ca be eeeted a a MGML wt eeve aeemet (MGMLWR). Te tate of a MGMLWR te combato of te elated MGML ad MRML tate. If te eeve ovde of a MRML a tate, te te aocated MGMLWR wll ave M tate. Code all te M tate te mulato vey tme-coum ad maybe moble fo a lae owe ytem. Fotuately te comutatoal bude ca be educed by code oly falue tate of te MGML. If te MGML a c falue tate, te umbe of te tate fo te MGMLWR educed to c + ( M c ). Te tate-ace daam ow F. 4. te tato ate fom te, tate to te tate ad, te tato ate fom te tate to te tate eectvely.,, () (3),, wee, te tato ate fom te tate to te tate, te tato ate fom te tate, to te tate ad, eectvely. te obablty te tate te tato ate fom te, tate to te tate ad te tato, ate fom te tate to te tate eectvely. (4),, (5),, wee, te tato ate fom te tate to te tate,, te tato ate fom te tate to te tate ad te obablty te tate, eectvely. Te ooed Makov model fo te MGMLWR te exteo of te Makov model ow F.3. Te ma advatae of te ooed Makov model vey flexble ad make te elablty evaluato fo te eeat ytem wt eeve ovde qute ealy. 5 SIMULATIO PROCEDURES I eudo-equetal mulato tecque, oequetal mulato ued to elect falue tate, ad equetal mulato aled oly to deteme te teuto equece of ebo tate ad te falue duato. A tecque amed te fowadbackwad mulato ued te equetal mulato [4]. Te fowad mulato a oce to detfy a equece of falue tate afte leav te elected falue tate, utl t fd a ucceful tate. Te backwad mulato a oce to detfy a equece of falue tate befoe av at te elected falue tate, utl t fd a ucceful tate. Te moved eudo-equetal mulato ocedue fo evaluat elablty dce of a MGMLWR code multle eeve aeemet cot of te follow te: M,,, M,,,,, M, M,, M,, M,,,,,,, M, M, M, M,, Fue 4: State-ace daam fo a MGMLWR Ste: Samle te MGML tate baed o t dtbuto. Ste: Evaluate te efomace of te amled tate. If te tate a ucce tate etu to te ; f te tate a cotecy tate, o to te ext te. Ste3: Samle a tate fom te eeve ovde baed o t dtbuto. Ste4: Combe te tate ad te tate to te tate. If te tate a ucce tate etu to te ; f te tate a falue tate, o to te ext te. Ste5: Obta a teuto equece ad duato D u te ub-te: (). cay out a fowadbackwad mulato tat fom te elected tate ; (). obta te teuto equece ad calculate te total duato D. Ste6: Etmate te elablty dce Ste7: If te cofdece teval fo te etmate atfed, calculate te elablty dce; otewe etu to te. 6 RELIABILITY IDICES Te elablty dce ued t ae ae: te lo of load obablty ( LOLP ), te lo of load fequecy ( LOLF ), te exected eey ot uled ( EES ) ad exected cutome teuto cot ( ). 5t PSCC, Lee, -6 Auut 5 Seo 5, Pae, Pae 3

4 Tee dce ca be etmated u te follow equato du te mulato ocedue. LOLP LOLP (6) f Succe tate wee LOLP (7) f Falue tate ad te umbe of mulato amle. EES EES (8) f Succe tate wee EES (9) LS T f Falue tate ad LS te load edd te falue tate, T te eod of aaly. () wee f Succe tate () K E( D) f Falue tate S ad K te cutome ecto teuto cot ad ve by: K CDF ( D ) D LS, I ad I te equece of falue tate, () CDF te aocated cutome damae fucto [3], D te duato of te tate ad LS, te load edd of cutome ecto te falue tate. E (D) te exected value of te total duato fo te equece I ad ve by: wee I E ( D) E( ) (3) D E( D ) T ( ) (4) ad te tato ate betwee te tate ad te dectly coected tate. LOLF LOLF (5) f Succe tate wee LOLF (6) E( D) f Falue tate Te ucetate of te elablty dce ae uually eeeted a te coeffcet of vaato: β V ( LOLC) LOLC (7) LOLC β V ( EES) EES (8) EES β V ( ) (9) β V ( LOLF ) LOLF () LOLF wee V (LOLC), V (EES), V () V (LOLF) ae te vaace of LOLP, EES, ad LOLF eectvely. 7 SYSTEM STUDIES Te ooed tecque ave bee ued to aalyze te IEEE-RTS [8]. Te IEEE-RTS eeato ytem etuctued to tee Geco. Geco ow lat at bue 5, 6, 8, ad. Te eleve eeat ut coected to bue, ad 7 belo to Geco. Geco 3 ow x lat at bue 3 ad 3. It aumed tat 4 6 ad 8 elect Geco a te eeato ovde,,, 4, 5 ad 7 cooe Geco a te eeato ovde ad 3, 6, 8 ad 3 elect Geco 3 a te eeato ovde. Te coolocal load cuve fo te RTS a bee ued. A yea eeeted t load cuve by tee eao: wte, fall ad umme. Te aual ouly load cuve ca be develoed afte te aual eak load, weekly ecetae, daly ecetae ad 4 ou load ofle ae detemed. Te RTS load model a 8736 ou ad eeeted a 8736 coolocal tate. Fou cae ae tuded to aalyze elablte fo te cutome of Geco at dffeet ceao. It aumed tat te load ote fo te of Geco ae te ame. I Cae, tee ae o eeve aeemet amo Geco, Geco ad Geco 3. I t cae, Geco wt tme vay load eeeted a MGML. I Cae, tee a eeve aeemet betwee Geco ad Geco fo a eeve cotecy tate. I Cae3, tee a eeve aeemet betwee Geco ad Geco 3 fo a eeve cotecy tate. I Cae4, Geco, Geco ad Geco 3 ca ae eeve cotecy tate tou a multlateal eeve aeemet a ow F. 5. Te MGML wt eeve ovde eeeted a te MGMLWR Fue 5: Relablty model of te etuctued RTS 5t PSCC, Lee, -6 Auut 5 Seo 5, Pae, Pae 4

5 Te LOLP, EES ad LOLF fo te Geco ave bee evaluated ad eeted Table. It ca be ee fom te Table te cutome of te Geco wll be eved wt te maxmum elablty cae 4 weea wt te lowet elablty cae. Te eeve aeemet amo Geco ca eatly affect te cutome elablte. LOLP EES LOLF (MWy) (occy) Cae Cae Cae Cae Table : Te elablty dce of te Geco fo fou cae Te EES ad fo te of te Geco fo Cae ad ae ow Table. It ca be ee fom te Table tat te elablte ceae fcatly. Cae Cae EES EES (MWy)) (k$y)) (MWy)) (k$y)) Table : Te elablty dce fo cae ad cae Te EES ad fo te of te MGMLWR fo Cae 3 ad 4 ae ow Table 3. Coma te elablty dce of cae 3 wt toe cae 4, t ca be ee fom tat te elablte ceae wt u te multlateal eeve aeemet. Cae 3 Cae 4 EES EES (MWy)) (k$y)) (MWy)) (k$y)) Table 3: Te elablty dce fo cae 3 ad cae 4 8 COCLUSIOS A tecque to obta elablty dce fo deeulated owe ytem by code eeve aeemet amo Geco ad tme vay load eeted ad llutated t ae. Te elablty etwok equvalet ad eudo-equetal mulato aoace ae te foudato of t tecque. Te tecque eta te comutatoal effcecy of o-equetal mulato ad accuacy of equetal mulato. By u elablty etwok equvalet t ealy to clude vaou aeemet amo maket atcat. A ew Makov model ooed fo te eeetato of te eeat ytem code eeve ovde t ae. Te tecque ovde flexblty ad accuacy evaluat elablte te ew evomet. Te ooed tecque ca be ealy ued to ae te elablty, ad to maae ad ce ytem eeve of lae-cale ad actcal ytem. Te mulato oam wa wtte by Matlab. All mulato eult wee obted by a 3G MHz PC. Te exectuto tme fo Cae 4 6 mute ad 37 ecod. REFERECES [] P. Wa, R. Bllto, Relablty Aemet of a Retuctued Powe Sytem U Relablty etwok Equvalet Tecque, IEE Poc.-Gee. Tam. Dtb., vol. 5, o. 5, , 3 [] P. Wa, R. Bllto ad L.Goel, Uelablty cot aemet of a electc owe ytem u elablty etwok equvalet aoace, IEEE Ta. o Powe Sytem, vol. 7, o. 3, ,. [3] R. Bllto, R.. Alla Relablty Evaluato of Powe Sytem, Pleum Pe,.Y. ad Lodo 996. [4] A. M. Lete da Slva, L. A. da Foeca Mao, J. C. de Olvea Mello ad R. Bllto, Peudo- Coolocal Smulato fo Comote Relablty Aaly wt Tme Vay Load, IEEE Ta. o Powe Sytem, vol. 5, o.,. 73 8,. [5] O. Betold, L. Salvade ad S. Scalco, Mote Calo Aoac Pla Stude: a Alcato to IEEE RTS, IEEE Ta. o Powe Sytem, vol. 3, o. 3, , 988. [6] J. C. de Olvea Mello, M. V. F. Peea ad A. M. Lete da Slva Evaluato of Relablty Wot Comote Sytem baed o Peudo-Sequetal Mote Calo Smulato, IEEE Ta. o Powe Sytem, vol. 9, o. 3, , 994. [7] R. Bllto, W. L A Sytem State Tato Saml Metod fo Comote Sytem Relablty Evaluato, IEEE Ta. o Powe Sytem, vol. 8, o. 3, , 993. [8] IEEE Tak Foce, IEEE Relablty Tet Sytem, IEEE Ta. o Powe Aaatu ad Sytem, PAS- 98,.47-54, ovdec 979 [9] P. Wa, R. Bllto, Tme Sequetal Dtbuto Sytem Relablty Wot Aaly Code Tme Vay Load ad Cot Model, IEEE Ta. o Powe Delvey, vol. 4, o. 3,. 46 5, t PSCC, Lee, -6 Auut 5 Seo 5, Pae, Pae 5