PREVENTIVE AND CORRECTIVE SECURITY MARKET MODEL

Transcription

1 REVENTIVE AND CORRECTIVE SECURITY MARKET MODEL Al Ahmad-hat Rachd Cheaou and Omd Alzadeh Mousav Ecole olytechnque Fédéale de Lausanne Lausanne Swzeland Abstact evous lage blacouts n Noth Ameca and Euope demonstated that powe system secuy ssues have been neglected n favo of moe fnancal concens. Whle mang decsons on geneatng un schedulng by mnmzng n the enegy esouce cost the system opeatos also must povde adequate amount of eseve to eep powe system secuy n case of unfoeseen events. Tadonally secuy contol was pefomed by peventve and coectve contol actons. In ths pape we defne peventve and coectve secuy maets coespondng to these two secuy actons. Mang a tade-off between these two maets fo eseve esouce povson s deemed to be necessay. A new SCUC poblem s poposed to model the elaton between peventve and coectve secuy maet. Bendes decomposon s employed to solve the poposed model. By solvng the SCUC poblem the optmal eseve esouces equed unde pe-contngency and post-contngency state ae detemned. Thee-bus test case s used to demonstate the pefomance of the pesented method. Keywods: Secuy constant un commment (SCUC peventve secuy maet (SM coectve secuy maet (CSM Spnnng eseve (SR NOMENCLATURE A. Vaables owe output of geneato un at tme t. I Bnay vaable whee 1 means un s onlne at tme t othewse 0. I Bnay vaable; 1 means un s accepted as gong eseve n CSM 0 othewse. I Bnay vaable; 1 means un s accepted as down-gong eseve n CSM 0 othewse. g Up-gong SR povded by un at tme t n SM. g g Down SR povded by un at tme t n SM. Up SR povded by demand j at tme t n SM. DownSR povded by demand j at tme t n SM. Up-gong eseve povded by un at tme t dung contngency n CSM. Down-gong eseve povded by un at tme t dung contngency n CSM. Up-gong eseve povded by demand j at tme t dung contngency n CSM. Down-gong eseve povded by demand j at tme t dung contngency n CSM. B. Functons F ( Cost of enegy poducton of geneato. C. Constants L djt Load of demand j at tme t. mn Mnmum capacy of geneato un. g Maxmum -gong SR that geneato can g povde at tme t n SM. Maxmum down-gong SR that geneato can povde at tme t n SM. Maxmum -gong SR that demand j can povde at tme t n SM. Maxmum down-gong SR that demand j can povde at tme t n SM. Maxmum -gong eseve that geneato can povde at tme t n CSM. Maxmum -gong eseve that demand j can povde at tme t n CSM. SD Shut down cost of geneato at tme t. SU Stat cost of geneato at tme t. on T Mnmum tme of geneato. off T Mnmum down tme of geneato. g Bd of un fo SR at tme t n SM. g g g Bd of un fo down SR at tme t n SM. Offe of demand j fo SR at tme t n SM. Offe of demand j fo down SR at tme t n SM. Bd of un fo eseve at tme t n CSM. Bd of un fo down eseve at tme t n CSM. Demand j offe fo eseve at tme t n CSM. Demand j offe fo down eseve at tme t n CSM. D. Indces b Index of buses fom 1 to NB. Index of geneatos fom 1 to NG. j Index of demands fom 1 to ND. Index of contngences unnng fom 1 to K. t Index of tme peods fom 1 to NT. 1 INTRODUCTION Secuy can be defned as the ably of an electc powe system to whstand sudden dstubances such as unantcpated loss of system components. owe system secuy s moe and moe n conflct wh economc and envonmental equements. Secuy contol ams at mang decsons n dffeent tme hozons so as to pevent the system fom undesed suatons and n patcula to avod lage catastophc outages. Tad- 17 th owe Systems Computaton Confeence Stocholm Sweden - August

2 tonally secuy contol has been dvded n two man categoes: peventve and coectve contol actons [1]. Theefoe two secuy maets can be defned coespondng to two secuy actons named peventve secuy maet and coectve secuy maet. In peventve secuy maet the objectve s to pepae the system when s stll n nomal opeaton n ode to mae able to face futue (uncetan events n a satsfactoy way. But n coectve secuy maet the dstubng events have aleady occued and thus the objectve becomes to contol the system n such a way the consequences ae mnmzed. Geneaton escheduln sometmes load cutalment as ntetble loads eactve compensaton and etc ae consdeed as a peventve contol actons and should be detemned n peventve secuy maet. On the othe hand the system opeato use the nvoluntay load demand and geneaton sheddn callng some fast geneatng uns shunt capaco o eacto swchn netwo spltn and etc as a coectve contol actons. The eseve sevces ae consdeed as mpotant esouces that the powe system opeatos employ to eep the system secuy n the case of unfoeseen dstubances. Thee ae two man stateges fo eseve sevce povson. The fst s the povson n a peventve secuy maet. In ths case the powe system opeatos should mantan some spnnng eseve esouces n advance to eschedule the system n ode to estoe a nomal state when a contngency occus. The second s the eseve povson n a coectve secuy maet that got moe attenton n the new competon envonment. In ths stategy the powe system opeatos povde fast eseve esouces n the eal-tme when they ae actually needed n ode to tansfe qucly the system state to a new secue opeatng pont. The eason why coectve secuy maet s used fo eseve povson can be ehe the eseve esouces povded n the peventve secuy maet ae not suffcent o the peventve secuy maet s not defned n the maet model. Note that the capalzed peventve povson can be expensve and even nfeasble fo consdeng all potental contngences. In contast although the povson of eseve esouce only n coectve secuy maet can be economcal; mght theaten the system secuy. Theefoe mang a tade-off between these two maets fo eseve povson s deemed to be necessay [2]. Secuy constaned un commment (SCUC tool s one of the ey components of standad maet desgn (SMD that can be used fo maet-cleang and eseve sevces povson poblem. Consdeable eseaches have been caed out to solve the SCUC n ode to pocue the equed eseve esouce n the last yeas. Unle the detemnstc SCUC poblem the majo pats of these studes have been ecently focused manly on the s-based SCUC poblem. Fo nstance efeences [3-4] ncopoate the s of the system scheduled n nomal state as nequaly constant nto the SCUC poblem. The soluton tes to satsfy ths constant n ode to assess the equed eseve esouce that the system opeato should mantan n advance. Moeove efeences [5-8] smulate a cost-benef analyss fo evaluaton of eseve esouces by penalzng the s ndex nto the SCUC objectve functon. Howeve the close elatons between peventve and coectve secuy maets ae not well ndcated n these leatues. Ths pape pesents a new SCUC poblem to model the elaton between peventve and coectve secuy maet. By solvng ths SCUC poblem we can compute the optmal eseve esouces equed unde pecontngency and post-contngency state. The objectve of the poblem s to mnmze the cost of opeatng the system n the nomal state and the expected cost assocated wh each of post contngency opeatng states. In othe wods the objectve of ths poblem s to mnmze the poducton costs comng fom the enegy maet and the eseve costs comng fom the peventve and coectve secuy maet n an ntegated optmzaton poblem. The poposed model s based on effectve coodnaton stategy. Bendes decomposon s employed to solve the poblem whle tang nto consdeaton ths coodnaton n an eatve pocess. 2 ROOSED MODEL FORMULATION AND METHODOLOGY A pope coodnaton between the peventve secuy maet and coectve secuy maet s vey mpeatve. One of the easons fo ths coodnaton s by acceptng some expenses n the pe-contngency state.e. peventve maet; the system opeato may save moe dung the opeaton unde post-contngency state. Ths coodnaton s obvous f the nal pedstubance opeaton set-ponts caed ove nto the eal tme opeaton ae detemned by the peventve secuy maet. Hee a new SCUC s employed to tae nto account ths coodnaton. In what follow the complete poblem fomulaton of SCUC poblem ncludng all constants ae fst povded. 2.1 Complete poblem fomulaton The fomulaton s as follows mn f ( x0 u0 e( x u u0 (1 Subject to g0 ( x0 u0 0 (2 h ( x u h (3 g ( x u u K (4 0 ( h x u u h K (5 ( u0 u K (6 f(x 0 u 0 models the SCUC objectve functon n nomal state (pe-contngency of powe system. In fact ths functon ncludes enegy maet and peventve secuy maet objectve functons. e(x u u 0 models the expected cost of secuy coectve actons unde post-contngency condon. A sngle enty named ndependent system opeato (ISO s esponsble fo management of enegy maet as well as both peven- 17 th owe Systems Computaton Confeence Stocholm Sweden - August

3 tve and coectve secuy maets. x 0 s a vecto of state vaables denotng the voltage angles unde pecontngency condons. Also u 0 s a vecto of contol vaables denotng the status (on/off and the amount of powe and eseve poducton of geneatng uns unde pe-contngency condons. On the othe hand x and u ndcate the vectos of state and contol vaables unde post contngency condon espectvely. g 0 (x 0 u 0 and g (x u u 0 epesent the powe flow equatons (DC load flow and h 0 (x 0 u 0 and h (x u u 0 epesent the lne flow constants unde pe- and post-contngency condon espectvely. s feasble opeatng egon of contol vaables unde pe- and post-contngences. 2.2 oblem Fomulaton n Bendes Decomposon Bendes decomposon [9-10] s a popula optmzaton technque. In applyng the bendes decomposon algohm the ognal lage-scale optmzaton poblem wll be decomposed nto a maste poblem and subpoblem whch defnes an eatve pocedue between both levels n ode to each the optmal soluton. At the fst stage the maste poblem MI-based UC detemnng the commment and enegy and eseve dspatch of geneatng uns s solved unde nomal condon as epesented below. ( mn f ( x u (7 g ( x u 0 (8 0 h ( x u h (9 down ˆ( x0 u0 (10 whee s a contnuous vaable whch appoxmates expected coectve cost n bendes maste poblem at eaton. down s a bound that can be detemned fom physcal o economcal consdeatons petanng to the poblem unde study. It s clea that the maste poblem depends on the optmal value of the sub-poblem objectve functon and subsequently the sub-poblem depends on the optmal soluton of the maste poblem. Hence usng the soluton û 0 obtaned n the maste poblem (fst stage the sub-poblem s solved n the second stage and a new value fo s objectve functon s obtaned. Hee the coespondng sub-poblem s a combnaton of feasbly chec and optmaly chec poblems as follows. In ode to chec the maste poblem feasbly n the case of a contngency contol slac vectos ae ntoduced and the summaton of the components of these contol slac vectos ae mnmzed. The optmaly checng pat of the sub-poblem mnmzes the expected cost of the coectve secuy maet. ( 1 2 mn Z M.( s s e( x u u ( ( ( g x u u s s K (12 h x u u h K (13 u uˆ : S (14 ( 1 ( whee M s a lage enough posve constant. The last constant whch enfoces the peventve maet scheduln fxed n the maste poblem deseves specal menton. The dual vaable ( assocated wh ths constant povde the maste poblem wh elevant dual nfomaton to mpove the cuent schedule. The stoppng ceon fo the poposed poblem s as (15. s convegence toleance paamete. Z ( ( (15 ( Z Equatons (16 and (17 pesent the feasbly and the optmaly bendes cuts espectvely that ae geneated fom the subpoblem.. The feasbly bende cut s used to mgate the volatons of equaly constants (12 and the optmaly bende cut s used to gude the whole system towad the optmal soluton. Z ( u uˆ 0 (16 ( ( ( Z ( u uˆ (17 ( ( ( ( 2.3 Soluton ocedue The step-by-step pocedue of the poblem soluton s ntoduced hee. 1 Solve the maste poblem. The system state x 0 and the contol vaables u 0 n the nomal state ae detemned. Desgnate the soluton as û 0. - Inal soluton: Stat the soluton pocedue by solvng the maste poblem wh espect to the sub-poblem by gvng a guess to down. - Successve solutons: As the eatons poceed the maste poblem s solved wh espect to some constants whch ae geneated fom the sub poblem. 2 Solve the sub-poblem accodng to the nfomaton obtaned fom the maste poblem. Then a new value fo the sub-poblem objectve functon Z ( and the dual vaable of bundle constant ( assocated wh eaton ae obtaned. - Bendes feasbly cut: If the sub-poblem s nfeasble an nfeasbly bendes cut s geneated usng (16 and s etuned to the maste poblem. - Bendes optmaly cut: As the eatons poceed the bendes optmaly cut s geneated usng (17 and s etuned to the maste poblem. 3 Chec the stoppng cea (15. If ths condon s not met add the bendes cuts to the maste poblem and solve agan (go to step e-contngency Objectve Functon The pe-contngency objectve functon f(x 0 u 0 ncludes the cost of enegy poducton (enegy maet and the cost of povdng the eseve sevces n the peventve secuy maet. Ths objectve functon s fomulated n detal as (18. NT NG f ( x0 u0 ( F ( g SU SD I t1 1 NG 1 ( ND ( j1 (18 The fst lne of (18 epesents the enegy poducton cost of geneatng uns as well as the stat- and the shut-down costs. The enegy poducton s estcted 17 th owe Systems Computaton Confeence Stocholm Sweden - August

4 by a typcal set of constants ncludng powe balance constant mnmum and mum capacy of the geneatng uns ampng /down ates constants stat/shutdown amp lm of geneatos mnmum /down tme constants and etc [11]. Fo the sae of concseness the mathematcal fomulaton of these constants s omted hee. The second lne of (18 s the cost of geneaton sde spnnng eseve scheduln -gong and down-gong spnnng eseves n the peventve secuy maet. These two tems ae estcted by the pe lms on the - and down- spnnng eseve as follows. 0 I t (19 0 I t (20 The thd lne of (18 s the cost of povdng the demand sde -gong and down-gong spnnng eseve n the peventve secuy maet. In ths espect mples beng eady to voluntaly decease o ncease the level of consumpton f equed. Smlaly these tems ae estcted by the lms on demands whch ae wllng to ncease o decease the consumpton. 0 j t (21 0 j t (22 In addon the powe balance constant at each bus and the DC netwo secuy constant at nomal state ae lsted as (23 - (25. g L Llt 0 b t (23 Jb jdb lhb mt nt Llt ( m nl l (24 X mn L l Llt Ll l t (25 J b s the set of geneatng uns connected to bus b and D b s the set of load demands connected to bus b. Set H b ncludes the lnes connected to bus b whch ae labeled as ehe the ''to bus'' o the ''fom bus'' n the set. 2.5 ost-contngency Objectve Functon The post-contngency objectve functon e(x u u 0 s the expected cost of deployng the coectve actons whch ae specfed n the coectve secuy maet. Ths objectve functon s fomulated n detal as follows. NT K NG e( x u u0 ( ( g SU I t1 1 1 K NG ( ( SD I ( K ND ( ( 1 j1 ( s the pobably of the contngency (ncludng geneatng uns and tansmsson lnes occung dung the tme nteval. As shown n the Appendx unde small tme nteval ths can be well appoxmated by equaton (27. ( (27 The fst lne of (26 epesents the expected cost of callng the quc geneatng uns to be tuned on and to pc the load n the case of contngency. Ths quc stat geneatng un s lmed by ampng- constant as lsted below n addon of the feasble opeatng egon lmatons. mn I g g I t (28 The elatonshp between un status ndcato n nomal state and un status ndcato when contngency occus s I ˆ I 1 t (29 Equaton (29 enfoces that ths sevce can be povded only by off lne geneatos I =0. They should be capable of beng tuned on when the system opeatos call them dung the contngency. The second lne of (26 s the cost appled to a geneatng uns aleady onlne ( I =1 and geneatng g when the system opeato ass fo them to be qucly tuned off whn the contngency occuence duaton. Hence the down-gong eseve that povded by these geneatng uns n the coectve secuy maet s estcted by the followng constants. ˆ ˆ I I t (30 I Iˆ 0 t (31 The last lne of (26 s the nvoluntay load addng and load sheddng costs espectvely. They ae n fact the costs mposed to the load demands when the system opeato ass them to abtly ncease o decease the consumpton level whn the occuence of contngency. The -gong and down-gong eseves povded by the load demands n the coectve secuy maet ae constaned by the followng nequales. 0 d t (32 0 d t (33 In addon the equaly constant assocated wh nodal powe balance usng DC load flow n case of contngency s as (34. g L Llt 0 b t (34 Jb jdb lhb (35 d jt d jt d jt d jt L L (36 mt nt Llt ( m nl l t (37 X mn Equaton (35 states the powe outputs of geneatng uns esult fom the powe poductons settled n the enegy maet plus the dffeent types of eseves n peventve and coectve secuy maets deployed to accommodate system n contngency. An analogous ntepetaton can be caed out fo the powe consumed by each load demand as addessed n (36. The amount of eseve sevces whch wee povded n the peventve secuy maet as a esponse to the contngency must be unde the followng lms. 0 ˆ 0 ˆ t (38 17 th owe Systems Computaton Confeence Stocholm Sweden - August

5 1 (MW 2 (MW Tme t (h 3 (MW 4 (MW 5 (MW dt ($/MWh dt ($/MWh D 1l D 2l D 3l Table 1: Load data. Fgue 1: Thee-bus test system. p ˆ p p ˆ p d jt d jt d jt d jt 0 0 j t (39 The tansmsson lne lm n the case of contngency s as L l Llt Ll l t (40 Note that f unde contngency a patcula geneatng un s out of sevce then the coespondng status (I the dspatch of ths geneatng un ( and all the eseve sevce lms ae set to zeo. Moeove f a patcula lne s out of sevce unde contngency then the coespondng lne flow lm (L l s set to zeo. 3 NUMERICAL EXAMLE The poposed model s appled to a thee-bus test system ove a fve-hou hozon to llustate the pefomance of the new SCUC wh the peventve and coectve secuy maets. As depcted n fg.1 ths case has thee geneaton uns thee tansmsson lnes and thee demands. Ths case s smple enough so that the coectness of the esults can be eadly vefed. The lne eactances ae all 0.3 p.u on a base of 100 MVA and 138 V. The capaces of lnes ae 100 MVA. Also falue ate ( of lnes s 1/500 (f/h. Thee demands ae allocated at each bus and vay houly accodng to the gven patten n table 1. In addon each consume offes to 40% of s houly load as an ntetble load to the peventve secuy maet. Besdes each consume patcpates n the coectve secuy maet whle offe the value of lost load assocated wh nvoluntay cutalment of s load. The geneatng uns data ae gven n table 2. It s assumed that geneato poduce enegy wh stat cost SD and ncemental cost a n the ange of [g mn g ]. Hee the pe bounds on amp and down ate ae the same fo peventve and coectve secuy maets. In ths example fo the sae of smplcy s assumed that: a all the gven load and geneato data eman unchanged ove all hous of the scheduled hozon b demand don t offe n -gong eseve n peventve and coectve secuy maet c geneatng un don t patcpates n coectve secuy maet as down-gong eseve d all the geneatng uns except geneatng un 3 wee off fo thee hous at the tme t=0 and geneatng un 3 was tuned on fo thee hous at the tme t=0. The poposed model s n a lnea fom and s solved usng CLEX 12 unde GAMS [13]. Geneato g (MW mn g (MW a ($/MWh SD ($/h (MW (MW on T (h off T (h ($/MWh p ($/MWh p ($/MWh c (f/h Table 2: Geneaton data. Note that to second ode contngences ae consdeed hee and the analyses ae caed out ove fve consecutve hous. Thee dffeent scenaos ae conducted to demonstate the pefomance of the poposed models. The fst scenao s chaactezed only wh peventve secuy maet. That s the system opeato has to schedule the system n the pe-contngency state n such a way that she s able to estoe the system to the nomal state only wh the assstance of peventve actons (load and geneaton eschedulng when a contngency happens. Consequently the second and thd scenaos consde both the peventve and coectve secuy maets. The second scenao taes nto account the nvoluntay load cutalment as the coectve acton whle n the thd one both nvoluntay load cutalment and quc geneatng uns ae taen nto consdeaton n the coectve secuy maet. The esults fo the mentoned scenaos ae summazed n tables 3-6. Table 3 outlnes the optmal geneaton and eseve schedule n enegy and peventve secuy maet assocated wh scenao 1. All geneatng uns ae commted at all the fve hous n the esult of secuy constants and geneatng uns techncal constants such as amp /down ates and mnmum /down tmes. It s wothwhle to be mentoned that n the only peventve secuy maet case the system has to be peposoned n such a way that all the possble contngences would be coveed by the peventve contol actons. Snce dung the heavy loads peods the system s unde moe stess the load demands ae scheduled to patcpate n the peventve maet as an ntetble load. 17 th owe Systems Computaton Confeence Stocholm Sweden - August

6 Hou un G G G G G G G1 1 0 G D D D Table 3: Scenao 1 esults. (GD and C ae fo geneaton dspatch n enegy maet peventve maet and coectve maet espectvely. GD GD C Hou un G G G G G1 2 0 G D L 10-4 Table 4: Scenao 2 esults. D D D Table 4 summazes the esults fo scenao 2 n whch the peventve and coectve secuy maets ae employed fo system peposonng. As can be seen fom ths table the geneatng un G2 beng ncementally the most expensve one s not commted n ths case. Moeove only the load demand D3 povdes the eseve dung pea hou fo the peventve maet. Lewse as seen n the last thee ows of ths table the optmum maet schedulng call fo the load demand patcpaton fo all the peods n the coectve secuy maet. We measue the expected amount of patcpaton assocated wh each load demand dung the peod t n the coectve secuy maet usng the followng ndex. K L ( t. (41 1 The values of ths ndex fo each load demand n dffeent tme peods ae pesented n the table 4. As mentoned eale besdes the load demands povdng the eseve n coectve secuy maet the quc geneatng uns can effectvely patcpate n ths maet and mpove the maet effcency. Table 5 shows the maet schedulng n the case whee both quc geneatng uns and load demands ae called fo to act as a coectve acton. It s obvous that the ole of each load demand n coectve secuy maet s educed athe than scenao 2. The eason s the less expensve coectve acton s povded by quc stat geneaton un G2. So ths geneaton un effectvely patcpates n coectve secuy maet n all the peods as shown GD C L 10-4 G Hou un G G G G G1 6 G D D G Table 5: Scenao 3 esults. Scenao [$] Runnng Cost eventve Cost Coectve Cost Total Cost Table 6: Compason between each cost fo each scenao. n the last ow of table 5. The expected amount of geneaton un patcpaton dung the peod t n the coectve secuy maet s evaluated usng the followng equaton: K G ( t. (42 1 Now we show how ths two secuy maets nteact togethe to estoe the system to the nomal state when a contngency occus. It s assumed that the outages of lnes 1 and 3 occu smultaneously at pea hou (tme t=3 such that the bus 2 s solated fom the whole system. Wh egad to the nfomaton n table 3 n scenao 1 the system opeato deploys 23 MW -gong spnnng eseve n bus 2 10 MW and 13 MW downgong spnnng eseve n bus 1 and bus 3 espectvely n ode to deal wh ths contngency. Whle n scenao 2 system opeato deploys 20 MW and 13 MW down-gong eseve fom the peventve secuy maet n bus 1 and bus 3 espectvely to sply load demands n these two buses. Addonally he ass fo the load demand n bus 2 to shed 33 MW loads as coectve acton to ovecome the contngency. In the thd scenao the system opeato domnates ths contngency by usng the followng pe-specfed eseves n peventve and coectve maets: deployng 6 MW and 27 MW down-gong spnnng eseve n bus 1 and bus 3 espectvely whch ae povded n peventve secuy maet as well as callng 33 MW -gong eseves whch s povded by fast geneatng un G2 n coectve secuy maet. What maes the esults of ths model nteestng s the 36% educton of the system total cost n scenao 1 by sacfcng only 2% of ths cost n the coectve secuy maet n scenao 2 (34% net benef. These esults ae demonstated n table 6. Moeove can be deduced fom the compason between scenao 2 and 3 n ths table that f the numbe of sevces n coectve secuy maet ncease the system schedulng cost n 17 th owe Systems Computaton Confeence Stocholm Sweden - August

7 oweed by TCDF ( nomal state would be effcently deceased (fom $ n scenao 2 to $ n scenao 3. Hence the maet effcency s mpoved. 4 CONCLUSION The peventve and coectve contol actons ae the man tools wh whch the system opeato eeps the system secuy n s allowed bounday. Ths pape pesents a peventve and coectve secuy maet model coespondng to these two outne contol actons. A new SCUC poblem s fomulated to model the elaton between peventve and coectve secuy maet. The objectve of ths ntegated optmzaton poblem s to mnmze the poducton costs comng fom the enegy maet and the eseve costs comng fom the peventve and coectve secuy maet. Hee -gong and down-gong spnnng eseve povded by synchonzed geneatng uns (geneatng uns accepted n enegy maet and load demands can be consdeed as eseve esouces n the peventve secuy maet. Moeove callng the quc geneatng uns to be tuned on asng some synchonzed geneatng uns to be tuned off addng some loads and sheddng some nvoluntay load n the case of contngency can be consdeed as eseve esouces n coectve secuy maet. Bende decomposon algohm s appled to solve the poposed SCUC poblem. The poposed appoach s appled to a thee-bus test system and the esults show that system opeato can manage the system moe effcently usng both secuy maets athe than usng one of them. AENDIX CONTINGENCY ROBABILITY Consde that the nteval of tme ( s dvded nto n vey small ntevals of ncement. If s assumed to be the mean ate of occuence contngency then the expected of occuence n nteval s gven by. Let denote the pobably of havng zeo occuences n (0 by (. In expessng (+ we note that 0 event may occu dung (0 + n only one way: 0 event occu n (0 and 0 events occu n ( +. 0( 0( 0( 0( * (1 0( (43 If s small.e. goes to zeo then: 0 ( 0( (44 By ntegatn we have ln 0 ( C (45 If at we assume that no event has occued (.e. the devce s opeable then ( =1 whch foces C=0 so that ( e 0 (46 Theefoe pobably of havng an occuence named n the nteval ( s ( 1 e (47 If <<1 whch s geneally tue fo the opeaton peod ( to seveal hous then ( (48 It can be easly shown usng the osson dstbuton [14] that the occuence of havng moe than one contngency n the shot tme nteval s nealy the same of havng one contngency n ths nteval. That means the tme fo epang the components n ths contngency s so shot and s neglected. Theefoe equaton (48 epesents the pobably that contngency occus and the faled elements ae not eplaced dung the nteval. Some efeences [12] named ths nteval as lead tme. REFERENCES [1] M. Shahdehpou W. F. Tnney Y. Fu Impact of Secuy on owe System Opeaton IEEE o Vol. 93 No.11 Nov 2005 [2] Y. Fu M. Shahdehpou Z. L AC Contngency Dspatch Based on Secuy-Constaned Un Commment IEEE Tans. owe Syst Vol. 21 No. 2 May 2006 [3] F. Bouffad F. D. Galana An Electcy Maet wh a obablstc Spnnng Reseve Ceon IEEE Tans. on owe Syst Vol. 19 No. 1 pp Feb 2004 [4] M. A. Otega-Vazquez D. S. Kschen D. udjanto Optmsaton the Schedulng of Spnnng Reseve Consdeng the Cost of Intetons IEEE oc Gene. Tansm. Dstb Vol. 153 No. 5 pp Dec 2006 [5] F. Bouffad F. D. Galana A. Conejo Maet Cleang wh Stochastc Secuy-at I: Fomulaton IEEE Tans. owe Syst Vol. 20 pp Nov 2005 [6] F. Bouffad F. D. Galana A. Conejo Maet Cleang wh Stochastc Secuy-at II: Case Studes IEEE Tans. owe Syst Vol. 20 pp Nov 2005 [7] M. A. Otega-Vazquez D. S. Kschen Optmzng the Spnnng Reseve Requements Usng a Cost-Benef Analyss IEEE Tans. owe Syst Vol. 22 No. 1 pp Feb 2007 [8] A. Ahmad-Khat R. Cheaou A obablstc Jont Enegy and Spnnng Reseve Maet Model IEEE ES Geneal Meetn 2010 [9] M. Shahdehpou Y. Fu Bendes Decomposon- Applyng Bendes Decomposons to owe Systems IEEE owe Enegy Mag. Vol. 3 pp [10] A. J. Conejo E. Castllo R. Mnguez R. G. Betand Decomposon Technques n Mathematcal ogammng Spnge 2006 [11] A. J. Wood B. F. Wollenbe owe Geneaton Opeaton and Contol John Wley 1996 [12] R. Bllnton R. N. Allan Relably Evaluaton of owe Systems 2nd Edon 1996 lenum ess USA [13] R. E. Rosenthal GAMS: A Use's Gude GAMS Development Copoaton Washngton DC USA 2010 [14] R. Bllnton R. N. Allan Relably Evaluaton of Engneeng System 2nd Edon 1993 lenum ess USA 17 th owe Systems Computaton Confeence Stocholm Sweden - August