Application of Shuffled Frog Leaping Algorithm to Long Term Generation Expansion Planning

Transcription

1 Inernaional Journal of Compuer and Elecrical Engineering, Vol.4, o.2, April 2012 Applicaion of Shuffled Frog Leaping Algorihm o Long Term Generaion Expansion Planning M. Jadidoleslam, E. Biami,. Amiri, A. Ebrahimi, and J. Asari Absrac This paper presens he applicaion of an efficien shuffled frog leaping algorihm (SFLA) o solve he opimal generaion expansion planning (GEP) problem. The SFLA is a mea-heurisic search mehod inspired by naural memeics. I combines he advanages of boh geneic-based memeic algorihms and social behavior based algorihm of paricle swarm opimizaion. Leas-cos GEP is concerned wih a highly consrained non-linear discree dynamic opimizaion problem. In his paper he proposed formulaion of problem, deermines he opimal invesmen plan for adding power plans over a planning horizon o mee he demand crieria, fuel mix raio, and he reliabiliy crieria. To es he proposed SFLA mehod, i is simulaed for wo es sysems in a ime horizon of 10 and 20 years respecively. The obained resuls show ha compared o he radiional mehods, he SFLA mehod can provide beer soluions for he GEP problem, especially for a longer ime horizon. Index Terms Generaion expansion planning, probabilisic producion simulaion, shuffled frog leaping algorihm. I. ITRODUCTIO The Generaion Expansion Planning (GEP) is a problem o deermine when, where, wha ype and how much capaciy of new power plans should be consruced over a long-erm planning horizon o mee forecased demand according o a pre-specified reliabiliy crieria. GEP is an imporan decision-maing aciviy for uiliy companies. The main obecive of GEP is o minimize he oal invesmen, operaing, and ouage (energy-no-served) coss of power sysem. There are generally wo deerminisic and sochasic approaches o solve he GEP problem. The Sochasic approach aes ino accoun uncerainies associaed wih he inpu daa, such as forecased demand, fuel prices, economic and echnical characerisics of new evolving generaing echnologies, consrucion lead imes, and governmenal regulaions [1]. The deerminisic approach solves he problem under differen scenarios. In his case a fas and efficien mehod is required because of grea number of simulaions needed o be run under differen scenarios. Leas-cos GEP is concerned wih a highly consrained non-linear discree dynamic opimizaion problem. The high non-lineariy of a GEP problem originaes from he naure of he producion cos and he se of non-linear consrains. The dynamic programming (DP) approach is one of he mos used algorihms in GEP. However in he generaion expansion problem, due o high dimensionaliy, he DP is no an efficien mehod for real power sysems. In commercial pacages lie WASP [2], o overcome his difficuly, heurisic unnel-based echniques are used in DP rouine, where users pre-specified configuraions and successively modified unnels are considered o arrive a local opimums. The emerging opimizaion echniques used o solve GEP problem were reviewed in [3]. In [4] he mea-heurisic echniques; such as Geneic Algorihm, Differenial Evoluion, Evoluionary Programming, Evoluionary Sraegy, An Colony Opimizaion, Paricle Swarm Opimizaion, Tabu Search, Simulaed Annealing, and Hybrid Approach, are applied o solve GEP problem and are compared wih DP. The resuls of his research show ha drawbacs of DP can be overcome by hese mea-heurisic echniques. In [5] an improved geneic algorihm (IGA) wih sochasic crossover echnique and eliism are applied o solve he GEP problem. The resuls of he IGA are compared wih hose of he convenional; such as simple geneic algorihm, he full DP and he unnel-consrained DP. The SFLA is a novel mea-heurisic opimizaion mehod inspired from he naural memeic evoluion of a group of frogs when searching for he locaion ha has he maximum amoun of available food [6]. The SFLA combines he advanages of boh geneic-based memeic algorihms and social behavior based paricle swarm opimizaion algorihms. Recenly, global opimizaion echniques using SFLA has been successfully applied o various areas of power sysem analysis such as uni commimen [7], dynamic opimal power flow [8], and opimal reacive power flow [9] problems. Because of a high capabiliy of SFLA o solve large scale opimizaion problems, in his paper i used o solve he GEP problem. Also, he efficiency of he SFLA is improved by applying he ineger encoding of soluions, mapping procedure and penaly facor approach. Since in [5], [10], [11], he prioriy of GA in solving GEP problem has been proved, GA is applied and he obained resuls by he GA are compared wih hose obained by he SFLA. This paper is organized as follows: in secion II he proposed GEP formulaion is given. An overview of he SFLA and soluion mehodology is described in secion III. Secion VI describes case sudies and provides es resuls, and secion V concludes he paper. Manuscrip received February 20, 2012; revised March 16, M. Jadidoleslam, E. Biami,. Amiri, A. Ebrahimi, and J. Asari are wih he Deparmen of Elecrical and Compuer Engineering, Isfahan Universiy of Technology, Isfahan 84156, Iran ( {m.adidoleslam, e.biami, n.amiri}@ec.iu.ac.ir, {ebrahimi, -asari}@cc.iu.ac.ir). II. GEP PROBLEM FORMULATIO Solving a leas-cos GEP problem is equivalen o deermine he opimum expansion plan over planning period 115

2 Inernaional Journal of Compuer and Elecrical Engineering, Vol.4, o.2, April 2012 ha minimizes oal cos including invesmen, operaion, and, ouage (energy-no-served) coss under several consrains inroduced as follows. A. Cos Funcion Similar o WASP mahemaical formulaion [2], he cos (obecive) funcion of he GEP problem can be represened by he following expression: min C T I ( U ) M ( X ) O ( X ) S ( U ). (1) 1 where, C is he oal cos ($), is he ime sage (1,2,...,T), T is he lengh of he sudy period (oal number of sages), U is he capaciy vecor of all candidae uni ypes in sage (MW), X is he cumulaive capaciy vecor of all exising and candidae unis in sage (MW), and X X U. (2) 1 The bar over he symbols has he meaning of discouned values o a reference dae a a given discoun rae i. Equaion (2) is sae equaion for dynamic planning problem. In order o calculae he presen values of he cos componens of (1), i is assumed ha he capial invesmen for a candidae uni added by he expansion plan is made a he beginning of he sage in which i goes ino service. Salvage value is assumed o occur a he end of he planning horizon. All he oher coss including fix and variable, operaion and mainenance (O&M) coss, and ouage cos are assumed o occur in he middle of he corresponding year. Therefore, he cos componens of (1) are calculaed as follow: I ( U ) (1 i) CI U,. (3) 1 1 s 1 y0 M ( X ) (1 i) ( 0.5 y) X VOM G. FOM (4),, 1 ( 0.5 y) O ( X ) (1 i) EES CEES. (5) where and s y0 T S ( U ) (1 i) CI U. (6) 1,, s ( 1). (7) T 0 (8) 0 s T. s number of years in each sage; 0 number of years beween he reference dae for discouning and he firs year of sudy; I ( U ) presen value of invesmen cos of he candidae unis a he sage, $; CI capial invesmen cos of h uni, $; U, capaciy vecor of candidae unis of ype in sage, MW; oal number of differen ypes of unis. M ( X ) presen value of oal fix and variable, O&M cos of exising and candidae unis in sage, $; y variable used o indicae ha he operaion and mainenance (O&M) cos is calculaed a he middle of each year; FOM fixed O&M cos of h uni, $/MW; X, cumulaive capaciy vecor of unis of ype in sage, MW; VOM variable O&M cos of h uni, $/MWh; G, expeced energy produced by h uni in sage, MWh; O ( X ) presen value of ouage cos of he exising and candidae unis, $; EES expeced energy no served, MWh; CEES cos of EES, $; S ( U ) presen value of salvage value of he candidae unis in sage, $; δ, salvage facor of h uni added in sage. B. Consrains In his paper four ypes of defined consrains are represened by he following expressions: 0 max, ( 1 Rmin ) D X, (1 Rmax M min 1 X X U U. (9), M max. ) D. (10) (11), 1 LOLP ( X ). (12) Equaion (9) reflecs he consrucion capabiliy limis in each sage, in which U max, is he maximum consrucion capaciy of unis a sage. Equaion (10) presens reserve margin consrain in which D is he pea demand in he sage, (MW). Insalled capaciy in each sage, mus lie beween he given minimum and maximum reserve margins ha represened by R min and R max, respecively. The capaciy mixes by fuel ypes are considered in (11) in which M min and M max are lower and upper bounds of h fuel ype in sage. Equaion (12) is reliabiliy crierion of he power sysem where ε is he reliabiliy crierion for maximum value of loss of load probabiliy (LOLP). Probabilisic producion simulaion is done using he Equivalen Energy Funcion (EEF) mehod [12]. Simulaing producion sysem a each sage of planning horizon calculaes he expeced energy produced by each uni in every sage of planning (G,,) o be used in variable O&M cos calculaion of (4). The reliabiliy crierion of loss of load probabiliy (LOLP), used in (12), and he expeced energy no served (EES) used in he ouage cos calculaion by (5) are also deermined by he used simulaion procedure. 116

3 Inernaional Journal of Compuer and Elecrical Engineering, Vol.4, o.2, April 2012 III. IMPLEMETATIO OF SFLA TO SOLVE THE LEAST COST GEP PROBLEM A. An Overview of SFLA The SFL algorihm is a memeic mea-heurisic mehod ha is derived from a virual populaion of frogs in which each frog represens a se of feasible soluions. Each frog is disribued o a differen subse of he whole populaion described as memeplexes. The differen memeplexes are considered as differen culure of frogs ha are posiioned a differen places in he soluion space (i.e. global search). A simulaneous independen deep local search is performed in each memeplex using a paricle swarm opimizaion lie mehod. To ensure global exploraion, a shuffled informaion exchange will occur beween memeplexes afer a defined number of evoluion seps. Infecion of a memeplex s frogs by he frogs from oher memeplexes ensures he improvemen of frog ideas qualiy and ha he culural evoluion owards any paricular ineres is unbiased. Moreover, if he local search canno find beer soluions, random virual frogs are generaed and subsiued in he populaion. Then local search and shuffling processes (global relocaion) will coninue unil defined convergence crieria are saisfied. The flowchar diagram of he SFLA is shown in Fig. 1. Then he performance of each frog is compued based on is posiion. The frogs are sored in a descending order regarding o heir finess. Then, he enire populaion is divided ino m memeplexes, each of which consising of n frogs (i.e. =n m). The division is done by disribuing he frogs one by one and in order beween he m exising memeplexes. Wihin each memeplex, he posiion of frog ih (D i ) is adused according o he difference beween he frog wih he wors finess (X w ) and he frog wih he bes finess (X b ) as shown in (13), where rand () is a random number in he range of [0,1]. During memeplex evoluion, he wors frog X w leaps oward he bes frog X b. According o he original frog leaping rule, he posiion of he wors frog is updaed as follow: Posiion change (F) rand() ( Z b Zw). (13) Z w( w max new) Z F,( F F ). (14) where D max is he maximum allowed change of frog s posiion in a single ump. If a frog wih a beer finess value is produced in his process, i replaces he wors frog, oherwise, he calculaion in (13) and (14) are repeaed wih respec o he global bes frog (X g ), (i.e. X g replaces X b ). If no improvemen becomes possible in his case, hen a new frog is randomly generaed o replace he wors frog. The evoluion process will coninue for a specific number of ieraions [6]. B. Sring Encoding and Mapping Procedure In his sudy, ineger sring srucure and mapping procedure used in [5] were applied o encode a soluion of he problem so ha, boh SFLA and GA mehods can be implemened. Sae vecor, X, and decision vecor, U, have dimension of MW, bu i can be convered ino vecors which have informaion on he number of unis in each uni ype. This mapping procedure is very useful for SFLA and GA implemenaion of a GEP problem such as encoding and reamen of inequaliy (9). The lengh of a sring is equal o he produc of he number of planning sages and he number of candidae uni s ypes. Fig. 2 illusraes a five ype, hree sage example of a sring in which each sring posiion represens he number of candidae unis in each ype o be consruced in each sage of planning horizon. For insance, he firs hree numbers, in his case, 2, 5 and 0 represens he number of candidae unis of ype1 in sages 1 hrough 3 of planning horizon. Fig. 2. A five ype, hree sage example of a sring. Fig. 1. General principle of SFLA. The SFLA begins wih an iniial populaion of frogs P={X 1, X 2,..., X } which are creaed randomly wihin he feasible space Ω. For S-dimensional problems (S variables), he posiion of he ih frog is represened as X i =[x i1,x i2,...,x is ] T. o evaluae he frog s posiion, a finess funcion is defined. C. Generaion of Iniial Sring Populaion An iniial populaion is randomly generaed so ha inequaliy (9) is saisfied. Therefore, for each sring posiion, values represening he number of candidae unis in each sage for every paricular ype, is randomly generaed using a uniform disribuion beween [0, Umax], where Umax is he upper consrucion limi of candidae unis. 117

4 Inernaional Journal of Compuer and Elecrical Engineering, Vol.4, o.2, April 2012 D. Evaluaion of finess funcion The finess funcion used here is he oal cos over he planning horizon represened by obecive funcion (1) plus penalized cos of infeasibiliy. Before evaluaion, all srings are checed for feasibiliy by consrains (10) and (11). If any sring violaes over (10) and (11), only he pars of he sring ha violae he consrains in sage are regeneraed a random unil hey saisfy he consrains. The concep of penaly funcion is used o penalize srings which fail o saisfy reliabiliy crieria of (12). The penaly funcion for nh sring is se as follows: p O ( X ) Penaly ( n) 0 LOLP oh. (15) The penaly facor, p is a large value. Consequenly, using (1), he finess value of sring n is: C( n) if n is feasible finess ( n) (16) C( n) Penaly( n) oh. The bes sring is he one ha has he minimum finess value. IV. TEST RESULTS The SFLA and GA were implemened using MATLAB code. The es sysem s descripion, parameers of GEP and SFLA and he resuls for each case sudy are presened in he following secions respecively. A. Tes Sysem Descripion The forecased pea load and oher daa of a es sysem wih 15 exising power plans and five ypes of candidae opions are aen from [5]. The SFLA and GA mehods have been applied o his sysem wih 2 planning horizons: case 1 wih a 10-year planning period and case 2 for a real-scale sysem wih a 20-year planning period. Each planning horizon consiss of wo-year sages, maing hem o be five and en sages in case1 and case 2, respecively. umber of years beween he reference dae of cos calculaions and he firs year of sudy (0) is assumed o be 2 years. The forecased pea demand over he sudy period is shown in Table I. Technical and economical daa of exising and candidae plan opions for fuure addiion is given in Tables II and III, respecively. B. Parameer for GEP and SFLA In his paper, we use 8.5% as discoun rae, 1 day per year (0.27%) as LOLP crieria in each sage, and he lower and upper bounds for reserve margin are se a 20% and 50% respecively. EES cos is assumed o be 0.05 $/Wh. The lower and upper bounds of capaciy mixes by fuel ypes are 0% and 30% for oil-fired power plans, 0% and 40% for LG-fired, 20% and 60% for coal-fired, and 30% and 60% for nuclear, respecively. Salvage facor (δ) is calculaed by sining fund depreciaion mehod [2]. Since he SFLA parameers have significan effec on he qualiy of soluion, hey were evaluaed before commencing his experimen for he suiable parameer values of populaion size, number of ieraions, number of memeplexes, and Dmax. As a resul, in Table IV heir seleced values o be used in our SFLA experimen are shown. Moreover, based on many rials, he penaly facor, p of 1,000,000 is used o ensure ha he infeasible soluions are penalized. TABLE I: FORECASTED PEAK DEMAD [5] Sage (year) 0 (2010) 1 (2012) 2 (2014) (2016) (2018) (2020) Pea Demand (MW) Sage (year) - 6 (2022) 7 (2024) (2026) (2028) (2030) Pea Demand(MW) TABLE II: TECHICAL AD ECOOMICAL DATA OF EXISTIG PLATS [5] ame o. of Uni (fuel Type) Unis Capaciy FOR Operaing Fixed O&M (MW) (%) Cos Cos ($/Wh) ($/W-Mon) Oil #1 (Heavy Oil) Oil #2 (Heavy Oil) Oil #3 (Heavy Oil) LG G/T #1 (LG) LG C/C #1 (LG) LG C/C #3 (LG) LG C/C #4 (LG) Coal #1 (Anhracie) Coal #2 (Biuminous) Coal #3 (Biuminous) uclear #1 (PWR) uclear #2 (PWR) TABLE III: TECHICAL AD ECOOMICAL DATA OF CADIDATE PLATS [5] Candidae Cons. Upper Capa- Type Limi ciy FOR Operaing Fixed Capial Life (MW) (%) Cos O&M Cos Time ($/Wh) Cos ($/W) (yrs) Oil LG C/C Coal (Bi.) uc. (PWR) uc.(phwr) TABLE IV: BEST PARAMETERS FOR SFLA IMPLEMETATIO SFLA Parameers Populaion size o. of Ieraions Memplexes D max Values Inf. C. umerical Resuls Since he SFLA mehod is random-based, each run may yield a differen soluion. Therefore, each case sudy is solved in en runs and he bes soluion is hen chosen beween hem. This soluion for each case sudy is shown in Table V. For comparison, each case sudy is similarly solved by GA mehod and is resuls are also repored in Table V. Comparing he resuls shows he soluion qualiy and accuracy in SFLA are beer han GA in boh cases. In case 1 and case 2, SFLA has achieved a 0.031% and 0.15% improvemen in coss over GA, respecively. I should be noed ha, he resuls of he GA mehod are obained over 500 ieraions. In case 2, performance of SFLA is more eviden wih incremen of decision variables. Since a long-erm GEP problem deal wih a grea amoun of invesmen, a sligh improvemen in expansion plan cos by he proposed SFLA mehod can resul in considerable cos saving for elecric uiliies. Fig. 3 and Fig. 4, illusrae he convergence characerisics of SFLA and GA mehods in case 1 and case 2, respecively. In hese figures, he mean values of 10 run characerisics are depiced for 100 ieraions for boh mehods. The SFLA shows beer performance han GA in boh cases. Table VI summarizes he opimal resuls obained by SFLA mehod for generaion expansion plans of case 1 and case 2 which are he 118

5 Average Finess Value ($) Average Finess Value ($) Inernaional Journal of Compuer and Elecrical Engineering, Vol.4, o.2, April 2012 number of each ype of power plans in each sage of planning periods. The resuls obained by GA are shown in Table VII for comparison. Coal (Bi.)-500MW 2(1) 2(3) 0(0) 0(0) 1(1) uc. (PWR)-1000MW 2(2) 0(0) 1(1) 1(1) 0(0) uc.(phwr)-700mw 0(0) 0(0) 0(0) 0(0) 0(0) *The figures wihin parenhesis denoe he resul of SFLA in case 1. V. COCLUSIOS This paper proposed a new approach based on he shuffled frog leaping algorihm (SFLA) o solve long-erm leas-cos generaion expansion planning problem in power sysems. Incorporaion of ineger encoding, mapping procedure and penaly facor approach improved he proposed mehod. Ineger encoding and mapping procedure made easier implemenaion of SFLA o he GEP problem especially for consrucion capabiliy limis o be aen ino accoun. Also, he penaly facor approach, improved effeciveness and efficiency of he SFLA searches where inequaliy consrains are involved. The SFLA has been successfully applied o long-erm GEP problem wih resuls ha ouperform GA in erm of success rae and soluion qualiy. The proposed SFLA could also achieve an order of magniude of improvemen, especially in larger scale GEP problems. Therefore, i can be employed as a planning ool for long-erm generaion expansion planning in a real-sysem scale. TABLE V: COST OF BEST SOLUTIOS OBTAIED BY SFLA AD GA Cumulaive Discouned Cos (Million $) Soluion Mehod Case 1 (10-year sudy Period) Case 2 (20-year sudy Period) SFLA GA x GA SFLA Generaion Fig. 3. Convergence characerisics of SFLA and GA mehods in Case 1 sysem x Generaion GA SFLA Fig. 4. Convergence characerisics of SFLA and GA mehods in Case 2 sysem. TABLE VI: UMBER OF EWLY ITRODUCED PLATS I CASE 1 AD CASE 2 BY SFLA METHOD Candidae Type umber of Uni Seleced Sage I II III IV V VI VII VIII IX X Oil-200MW 0(2)* 1(1) 1(1) 4(4) 1(1) LG C/C-450MW 3(3) 2(1) 0(0) 1(1) 1(1) TABLE VII: UMBER OF EWLY ITRODUCED PLATS I CASE 1 AD CASE 2 BY GA METHOD Candidae Type umber of Uni Seleced Sage I II III IV V VI VII VIII IX X Oil-200MW 0(2)* 1(1) 1(1) 0(4) 2(1) LG C/C-450MW 3(3) 2(1) 1(0) 1(1) 0(1) Coal (Bi.)-500MW 2(3) 2(1) 1(0) 2(0) 1(1) uc. (PWR)-1000MW 2(1) 0(1) 0(1) 1(1) 0(0) uc.(phwr)-700mw 0(0) 0(0) 0(0) 0(0) 0(0) *The figures wihin parenhesis denoe he resul of GA in case 1. REFERECES [1] A. G. Kagiannas, D. T. Asounis, and J. Psarras, Power generaion planning:a survey from monopoly o compeiion, In. J. Elec. Power Energy Sys. vol. 26, no. 6, pp , [2] Inernainal Aomic Energy Agency, Wien Auomaic Sysem Planning (WASP) pacage - A compuer code for power generaing sysem expansion planning, version WASP-IV user s manual, IAEA, Vienna, [3] J. Zhu and M. Y. Chow, A review of emerging echniques on generaion expansion planning, IEEE Trans. Power Sysems, vol. 12, no. 4, pp , ov [4] S. Kannan, S. M. R. Slochanal, and. P. Padhy, Applicaion and comparison of meaheurisic echniques o generaion expansion planning problem, IEEE Trans. on Power Sysems, vol. 20, no. 1, pp , Feb [5] J. B. Par, Y. M. Par, J. R. Won, and K. Y. Lee, An improved geneic algorihm for generaion expansion planning, IEEE Trans. on Power sysems, vol. 15, no. 3, pp , Aug [6] M. M. Eusuff, K. Lansey, and F. Pasha, Shuffled frog-leaping algorihm: a memeic mea-heurisic for discree opimizaion, Engineering Opimizaion, vol. 38, no. 2, pp , [7] J. Ebrahimi, S. H. Hosseinian, and G. B. Gharehpeian, Uni commimen problem soluion using shuffled frog leaping algorihm, IEEE Trans. on Power sysems, vol. 26, no. 2, pp , [8] G. Chen, J. Chen, and X. Duan, Power flow and dynamic opimal power flow including wind farms, in Proc. 1h Inernaional Conference on Susainable Power Generaion and Supply, aning, China, 2009, pp [9] Q. Li, Shuffled frog leaping algorihm based opimal reacive power flow, presened a he Inernaional Symposium on Compuer ewor and Mulimedia Technology, Wuhan, China, December 18-20, [10] Y. Fuuyama and H. D. Chiang, A parallel geneic algorihm for generaion expansion planning, IEEE Trans. on Power Sysems, vol. 11, no. 2, pp , [11] J. Sirium and A. Techaniisawad, Power generaion expansion planning wih emission conrol: a nonlinear model and a GA-based heurisic approach, In. J. Energy Res. vol. 30, pp , [12] X. Wang and J. R. McDonald, Modern power sysem planning, McGraw-Hill, 1994, ch. 3, pp Moreza Jadidoleslam received he B.Sc. degree in Elecrical Engineering from Kerman Universiy, Kerman, Iran in He received he M.Sc. degree from Isfahan Universiy of Technology (IUT), Isfahan, Iran in Currenly, he is pursuing his Ph.D. a he Isfahan Universiy of Technology (IUT), Isfahan, Iran. His research ineress include power sysem operaion and planning, generaion expansion planning, compuaional inelligence and heir applicaions o power sysems. Ehsan Biami received his B.S. degree in Elecrical Engineering from Kerman Universiy, Iran in From 2008 o 2010 he was as posgraduae suden in Isfahan Universiy of Technology, Isfahan, Iran, where he received M.Sc. degree on Conrol Engineering. He is currenly spending he miliary Servisce period. His ineress include power sysem conrol and sabiliy, sof compuing, renewable energy, robus conrol and model predicive conrol. 119

6 Inernaional Journal of Compuer and Elecrical Engineering, Vol.4, o.2, April 2012 avid Amiri received he B.Sc. and he M.Sc. degrees in elecrical engineering from Isfahan Universiy of Technology (IUT), Isfahan, Iran, in 2008 and 2011, respecively. Currenly, he is pursuing his Ph.D. a he Iran Universiy of Science and Technology Tehran, Iran. His research ineress include nonlinear conrol, faul diagnosis in elecromechanical sysems, power elecronics, and variable-speed ac drives. Abar Ebrahimi received he B.Sc. degree from Amir Kabir Universiy, Tehran, Iran, in 1979, M.Sc. degree from Universiy of Mancheser, Insiue of Science and Technology (UMIST), Mancheser, U.K., in 1985, and Ph.D. Degree from Tarbia Modares Universiy, Tehran, in 1994, all in elecrical power engineering. Currenly, he is an assisan professor a Isfahan Universiy of Technology, Isfahan, Iran. His research ineress are power sysem operaion, reliabiliy evaluaion, and planning wih applicaions of arificial inelligence and Bayesian analysis. Javad Asari-Marnani received he B.Sc. and M.Sc. degrees in elecrical engineering from Isfahan Universiy of Technology in 1987 and from Universiy of Tehran in 1993, respecively. He received also Ph.D degrees in elecrical engineering from Universiy of Tehran in From 1999 o 2001, he received a gran from DAAD and oined Conrol Engineering deparmen a Technical Universiy Hamburg Harburg in Germany, where he complees his Ph.D. wih Professor Lunze s research group. He is currenly an assisan professor a conrol engineering deparmen of Isfahan Universiy of Technology. His curren research ineress are in conrol heory, paricularly in he field of Hybrid Dynamical Sysems and Faul-Toleran Conrol, Idenificaion, Discree-Even Sysems, Graph Theory and Elecrical Engineering Curriculum. 120