Journal of Power Sources

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1 Journal of Power Sources 195 (2010) Contents lsts avalable at ScenceDrect Journal of Power Sources journal homepage: Intellgent unt commtment wth vehcle-to-grd A cost-emsson optmzaton Ahmed Yousuf Saber, Ganesh Kumar Venayagamoorthy Real-Tme Power and Intellgent Systems Laboratory, Mssour Unversty of Scence and Technology, Rolla, MO , USA artcle nfo abstract Artcle hstory: Receved 23 June 2009 Receved n revsed form 9 August 2009 Accepted 10 August 2009 Avalable onlne 20 August 2009 Keywords: Cost Emsson Grdable vehcles Partcle swarm optmzaton UC V2G A grdable vehcle (GV) can be used as a small portable power plant (S3P) to enhance the securty and relablty of utlty grds. Vehcle-to-grd (V2G) technology has drawn great nterest n the recent years and ts success depends on ntellgent schedulng of GVs or S3Ps n constraned parkng lots. V2G can reduce dependences on small expensve unts n exstng power systems, resultng n reduced operaton cost and emssons. It can also ncrease reserve and relablty of exstng power systems. Intellgent unt commtment (UC) wth V2G for cost and emsson optmzaton n power system s presented n ths paper. As number of grdable vehcles n V2G s much hgher than small unts of exstng systems, UC wth V2G s more complex than basc UC for only thermal unts. Partcle swarm optmzaton (PSO) s proposed to balance between cost and emsson reductons for UC wth V2G. PSO can relably and accurately solve ths complex constraned optmzaton problem easly and quckly. In the proposed soluton model, bnary PSO optmzes on/off states of power generatng unts easly. Vehcles are presented by nteger numbers nstead of zeros and ones to reduce the dmenson of the problem. Balanced hybrd PSO optmzes the number of grdable vehcles of V2G n the constraned parkng lots. Balanced PSO provdes a balance between local and global searchng abltes, and fnds a balance n reducng both operaton cost and emsson. Results show a consderable amount of cost and emsson reducton wth ntellgent UC wth V2G. Fnally, the practcalty of UC wth V2G s dscussed for real-world applcatons Elsever B.V. All rghts reserved. 1. Introducton The power and energy ndustry n terms of (a) economc mportance and (b) envronmental mpact s one of the most mportant sectors n the world snce nearly every aspect of ndustral productvty and daly lfe are dependent on electrcty. Unt commtment (UC) nvolves cost effcent schedulng (on/off states) of avalable generatng resources n a system. Varous numercal optmzaton technques have been employed to approach the UC problem. Prorty lst methods [1] are very fast; however, they are hghly heurstc. Branch-and-bound methods [2,3] have the danger of a defcency of storage capacty. Lagrangan relaxaton (LR) methods [4 6] concentrate on fndng an approprate co-ordnaton technque for generatng feasble prmal solutons, whle mnmzng the dualty gap. The man problem wth an LR method s the dffculty encountered n obtanng feasble solutons. The metaheurstc methods [7 18] are teratve technques that can search not only local optmal solutons but also a global optmal solu- Correspondng author at: Real-Tme Power and Intellgent Systems Laboratory ( Mssour Unversty of Scence and Technology, 240 Emerson Electrc Co. Hall, 301W. 16th St., Rolla, MO 65409, USA. Tel.: ; fax: E-mal addresses: aysaber@eee.org (A.Y. Saber), gkumar@eee.org (G.K. Venayagamoorthy). ton dependng on problem doman and executon tme lmt. In the meta-heurstc methods, the technques frequently appled to the UC problem are genetc algorthm (GA), tabu search, evolutonary programmng (EP), smulated annealng (SA), etc. They are general-purpose searchng technques. However, dffcultes are ther senstvty to the choce of parameters, balance between local and global searchng abltes, etc. There are also two popular swarm nspred methods n the feld of computatonal ntellgence: Partcle swarm optmzaton (PSO) and ant colony optmzaton (ACO). ACO was poneered by Dorgo et al. [15] from the nspraton of food-seekng behavor of real ants. It s a memory and computatonal ntensve algorthm especally when dealng wth large-scale optmzaton problems. However, PSO s smpler, and requres less memory and computatonal tme. The power and energy ndustry represents a major porton of global emsson, whch s responsble for 40% of the global CO 2 producton followed by the transportaton sector (24%) [19]. The estmated costs of an unabated clmate change are as much as 20% of the global domestc product (GDP). However, by takng the approprate measurements these costs could be lmted to around 1% of GDP [20]. Clmate change caused by greenhouse gas (GHG) emssons s now wdely accepted as a real condton that has potentally serous consequences for human socety and ndustres need to factor ths nto ther strategc plans [21]. So envronment frendly modern plannng s essental. However, power /$ see front matter 2009 Elsever B.V. All rghts reserved. do: /j.jpowsour

2 A.Y. Saber, G.K. Venayagamoorthy / Journal of Power Sources 195 (2010) systems researchers have addressed only tradtonal UC problems to mnmze cost n the exstng artcles. They have never ncluded emsson n unt commtment problems, though t s an mportant factor as mentoned above. Some researchers have ncluded emsson n economc dspatch problems only (not n unt commtment) [22,23]. Vehcle-to-grd (V2G) researchers have manly concentrated on nterconnecton of energy storage of vehcles and grd [24 30]. Ther goals are to educate about the envronmental and economc benefts of V2G and enhance the product market. However, success of V2G technology greatly depends on the effcent schedulng of grdable vehcles n lmted and restrcted parkng lots. Ideally grdable vehcles for V2G technology should be charged from renewable sources. A grdable vehcle can act as a small portable power plant (S3P). An ntellgent schedulng of S3Ps and conventonal generatng unts can reduce operaton cost and emsson. In ths paper, unt commtment wth vehcle-to-grd (UC V2G) s ntroduced where UC V2G nvolves ntellgently schedulng exstng unts and large number of grdable vehcles n lmted and restrcted parkng lots. It reduces both operaton cost and emsson wth proper and ntellgent optmzaton. In addton to fulfllng a large number of practcal constrants, the optmal UC V2G should meet the forecast load demand calculated n advance, parkng lot lmtatons, state of charge of grdable vehcles, chargng dschargng effcency, spnnng reserve requrements, etc. at every tme nterval such that the total operaton cost and emsson are mnmal. The overall objectve s to reduce bad envronmental effects such as carbon emssons and to ncrease proft. The optmzaton of UC V2G s a combnatoral optmzaton problem wth both bnary and contnuous varables. The number of combnatons of generatng unts and grdable vehcles grows exponentally n UC V2G problems. Unt commtment wth V2G s more complex than typcal UC of conventonal generatng unts, as number of varables n UC wth V2G s much hgher than typcal UC problems, and both cost and emsson are mnmzed n the objectve functon of UC V2G. The proposed PSO based soluton approach mproves balance between local and global searchng abltes, and balances reducton between operaton cost and emsson. Both cost and emsson are mnmzed for UC wth V2G; n addton, reserve and relablty of power systems s ncreased, and the negatve mpact of clmate change s decreased. Ths paper makes a brdge between UC and V2G research areas and consders UC wth grdable vehcles n V2G framework. It extends the area of unt commtment brngng n the V2G technology and makng t a success. 2. UC V2G problem formulaton 2.1. Nomenclature and acronyms The followng notatons are used n ths paper. c-s-hour cold start hour of th unt h-cost hot start-up cost of th unt c-cost cold start-up cost of th unt D(t) load demand at tme t H schedulng hours I (t) th unt status at hour t (1/0 for on/off) MU / MD mnmum up/down tme of unt N number of unts N max V2G (t) maxmum number of dschargng vehcles at hour t N V2G (t) no. of vehcles connected to the grd at hour t N max total vehcles n the system V2G P (t) output power of th unt at tme t P max/mn maxmum/mnmum output lmt of th unt P max (t) P mn (t) P v R(t) RUR RDR S3P X on (t) X off (t) FC () SC () EC () maxmum output power of unt at tme t consderng ramp rate mnmum output power of unt at tme t consderng ramp rate capacty of each vehcle system reserve requrement at hour t ramp up rate of unt ramp down rate of unt small portable power plant duraton of contnuously on of unt at tme t duraton of contnuously off of unt at tme t fuel cost functon of unt start-up cost functon of unt emsson cost functon of unt state of charge effcency 2.2. Objectve functon Usually large cheap unts are used to satsfy base load demand of a system. Most of the tme, large unts are therefore on and they have slower ramp rates. On the other hand, small unts have relatvely faster ramp rates. Besdes, each unt has dfferent cost and emsson characterstcs that depend on amount of power generaton, fuel type, generator unt sze, technology and so on. In UC wth V2G problems, man challenge s to schedule small expensve unts to mnmze cost and emsson, and to mprove system reserve and relablty. Grdable vehcles of V2G technology wll reduce dependences on small/mcro expensve unts. But number of grdable vehcles n V2G s much hgher than small/mcro unts. So proft, emsson, spnnng reserve, relablty of power systems vary on schedulng optmzaton qualty. UC wth V2G s a large-scale and complex optmzaton problem. The objectve of the UC wth V2G s to mnmze total operaton cost and emsson, where cost ncludes manly fuel cost and start-up cost. 1. Fuel cost. Fuel cost of a thermal unt s expressed as a second order functon of generated power of the unt. FC (P (t)) = a + b P (t) + c P 2 (t) (1) where a, b and c are postve fuel cost coeffcents of unt. 2. Emsson. For envronment frendly power producton, emsson effects should be consdered. Lke the fuel cost curve, the emsson curve can also be expressed as polynomal functon and order depends on desred accuracy. In ths paper, quadratc functon s consdered for the emsson curve as below [22]. EC (P (t)) = + ˇP (t) + P 2 (t) (2) where, ˇ and are emsson coeffcents of unt. 3. Start-up cost. The start-up cost for restartng a decommtted thermal unt, whch s related to the temperature of the boler, s ncluded n the model. In ths paper, smplfed start up cost s appled as follows: { h cost MD X off (t) H off SC (t) = c cost X off (t) >H off H off = MD + c s hour. (4) 4. Shut-down cost. Shut-down cost s constant and the typcal value s zero n standard systems. (3)

3 900 A.Y. Saber, G.K. Venayagamoorthy / Journal of Power Sources 195 (2010) Therefore, the objectve (ftness) functon for cost-emsson optmzaton of unt commtment wth V2G s mn TC = W c (Fuel + Start up) + W e Emsson N H = [W c (FC (P (t)) + SC (1 I (t 1))) =1 t=1 + W e ( EC (P (t)))]i (t) (5) subject to 6 13 constrants. s the emsson penalty factor of unt. Weght factors W c and W e are used to nclude (W = 1) or exclude (W = 0) cost and emsson n the ftness functon. It ncreases flexblty of the system. Dfferent weghts may also be possble to assgn dfferent precedence of cost and emsson n the ftness functon. Any other cost may be ncluded or any exstng type of cost may be excluded from the objectve functon accordng to the system operators demand Constrants of UC wth V2G The constrants that must be satsfed durng the optmzaton process are as follows: 1. Grdable vehcle balance n UC wth V2G. Only predefned regstered/forecasted grdable vehcles are consdered for the optmum schedulng n UC wth V2G. Total number of regstered grdable vehcles s known (fxed) and t s assumed that they are charged from renewable sources. All the vehcles dscharge to the grd durng a predefned schedulng perod (24 h). H N V2G (t) = N max V2G. (6) t=1 2. Chargng dschargng frequency. Vehcles are charged from renewable sources and dscharge to the grd. Multple chargng dschargng facltes of grdable vehcles may be consdered. It should vary dependng on lfe tme and type of batteres. For smplcty, chargng dschargng frequency s one per day n ths study. 3. System power balance. Grdable vehcles are consdered as S3Ps. Power suppled from commtted unts and selected (some percentage of total vehcles) S3Ps must satsfy the load demand and the system losses, whch s defned as N I (t) P (t) + P v N V2G (t) = D(t) + Losses. (7) =1 4. Spnnng reserve. To mantan system relablty, adequate spnnng reserves are requred. N I (t) P max (t) + P v max N V2G (t) D(t) + R(t). (8) =1 5. Generaton lmts. Each unt has generaton range, whch s represented as P mn P (t) P max. (9) 6. State of charge ( ). Each vehcle should have a desred departure state of charge level. 7. Number of dschargng vehcles lmt. All the vehcles cannot dscharge at the same tme. For relable operaton and control, lmted number of vehcles wll dscharge at a tme. Ths constrant also apples for power transfer, current lmt. N V2G (t) N max V2G (t). (10) 8. Effcency (). Chargng and nverter effcences () should be consdered. 9. Mnmum up/down tme. Once a unt s commtted/uncommtted, there s a predefned mnmum tme after t can be uncommtted/commtted respectvely. (1 I (t + 1))MU X on (t), f I (t) = 1 I (t + 1)MD X off (t), f I (t) = 0 }. (11) 10. Ramp rate. For each unt, output s lmted by ramp up/down rate at each hour as follows: P mn (t) P (t) P max (t) (12) where P mn (t) = max(p (t 1) RDR,P mn ) and P max (t) = mn(p (t 1) + RUR,P max ). 11. Prohbted operatng zone. In practcal operaton, the generaton output P of unt must avod unt operaton n the prohbted zones. The feasble operatng zones of unt can be descrbed as follows: P mn P P u,1 P l,j 1 P P u,j, j = 2, 3,...,Z. (13) P l P,Z P max where P l,j and Pu are lower and upper bounds of the jth prohbted zone of unt, and Z s the number of prohbted zones,j of unt. 12. Intal status. At the begnnng of the schedule, ntal states of all the unts and vehcles must be taken nto account. 3. Proposed soluton approach 3.1. Partcle swarm optmzaton Partcle swarm optmzaton s smlar to other swarm based evolutonary algorthms. Each potental soluton, called a partcle, fles n mult-dmensonal problem space wth a velocty, whch s dynamcally adjusted accordng to the flyng experences of ts own and ts colleagues. PSO s an ntellgent teratve method where velocty and poston of each partcle are calculated as below. v jt = w v jt + c 1 rand 1 (pbest jt x jt ) +c 2 rand 2 (gbest jt x jt ). (14) x jt = x jt + v jt. (15) In the above velocty equaton, the frst term ndcates the current velocty of the partcle (nerta); second term presents the cogntve part of the partcle where the partcle changes ts velocty based on ts own thnkng and memory; and the thrd term s the socal part of PSO where the partcle changes ts velocty based on the socalpsychologcal adaptaton of knowledge derved from the swarm.

4 A.Y. Saber, G.K. Venayagamoorthy / Journal of Power Sources 195 (2010) Data structure In the proposed method, each PSO partcle has the followng felds for the V2G schedulng problem, Partcle P {Generatng unt: An N H bnary matrx X ; Vehcle: An H 1 nteger column vector Y ; Velocty: An (N + 1) H real-valued matrx V ; Ftness: A realvalued cost TC;}. PSO can easly optmze an N H bnary matrx for generatng unts because possble state of a generatng unt s ether 1 or 0 only. On the other hand, basc PSO has less balance between local and global searchng abltes for the optmzaton of an H 1 nteger column vector for grdable vehcles, as possble number of connected grdable vehcles vares from 0 to N max (t) at hour t. The V2G authors have used bnary PSO for the optmzaton of generatng unts and balanced (regulated) PSO for the optmzaton of grdable vehcles of V2G. Besdes, some extra storage s needed for pbest, gbest and temporary varables, whch s acceptable and under typcal computer memory lmt. For the UC wth V2G problem, dmenson of a partcle P s (N + 1) H. Dmensons of locaton and velocty are presented by three ndces as x jt and v jt, respectvely n the rest of the paper for smplcty where = partcle number, j = generatng unt/no. of vehcles and t = tme Bnary PSO for generatng unts Schedulng of thermal unts s a bnary optmzaton problem. A contnuous searchng space can be converted to a vald bnary searchng space by a probablty dstrbuton. To extend the realvalued PSO to bnary space, the authors calculate probablty from the velocty to determne whether x jt wll be n on or off (0/1) state. In (18), U(0, 1) generates a real number between 0 and 1. v jt = 4.0, f v jt > 4.0. (16) 1 Pr(v jt ) = 1 + exp( v jt ). (17) { 1, f U(0, 1) <Pr(v x jt = jt ) (18) 0, otherwse Balanced PSO for V2G vehcles Number of connected vehcles to grd s presented by an nteger number nstead of zero or one for each vehcle to reduce the dmenson of the problem. At each hour, optmal number of grdable vehcles s needed to determne so that the operatng cost and emsson are mnmum. In the proposed balanced PSO, changes of velocty depend on teraton. To make a fne tunng (balance) n complex searchng space, ntally velocty changes rapdly for global search and then velocty changes slowly for local search. A balancng factor s ncluded n velocty calculaton (the last term of (19)). Integer number of vehcles s formulated by roundng off the real value of a new partcle locaton n balanced PSO. v jt = [v jt + c 1 rand 1 (pbest jt x jt ) + c 2 rand 2 [ (gbest jt x jt )] 1 + Range ] Max Ite (Ite 1). (19) x jt = x jt + v jt. (20) x jt = round (x jt ). (21) x jt = N max V2G (t), f x jt >N max V2G (t). (22) x jt = 0, f x jt < 0. (23) 3.5. Proposed algorthm for UC wth V2G In the same algorthm, bnary PSO s appled for the optmzaton of generatng unts and balanced PSO s appled for the optmzaton of grdable vehcles as below. Flowchart of the proposed method s shown n Fg. 1. (1) Intalze. Intalze a (N + 1) H matrx for each partcle randomly. Set parameters of bnary PSO and balanced PSO. Select pbest and gbest locatons. Take some temporary varables. (2) Move. For each partcle n the current swarm, calculate velocty and locaton n all dmensons. Apply bnary PSO (14, 16 18) on N H bnary matrx for generatng unts and balanced PSO (19 23) on H 1 column vector for grdable vehcles n the same model. Merge the outputs of bnary PSO and balanced PSO. (3) Repar and calculate economc dspatch. Check each partcle for all the constrants (6 13). Repar each partcle locaton f any constrant s volated there. Then, calculate economc dspatch (see Secton 3.7) of feasble partcle locatons (solutons) only. It accelerates the process. (4) Evaluate ftness. Evaluate each feasble locaton n the swarm usng the objectve functon. Accordng to the operators demand, prce and (or) emsson are consdered n the ftness functon. Update pbest and gbest locatons. (5) Check and stop/contnue. Prnt the gbest soluton and stop f maxmum number of teratons (Max Ite) s reached; otherwse ncrease current teraton number and go back to Step (2) Constrants management Stochastc random PSO partcles (solutons) do not always satsfy all the constrants. Constrants are handled n two ways drect repar and ndrect penalty methods [8]. A drect repar for the constrants of UC wth V2G s gven below. () If total number of vehcles s not satsfed, dfference between left and rght sdes of (6) s randomly dstrbuted among 24 h. () System power balance, generaton lmt and ramp rate constrants are satsfed n ED of UC wth V2G. () Nearest (upper/lower) vald lmt s assgned for nequalty constrants. The above repar accelerates convergence. If solutons are stll nvald after repar, penalty s added to dscourage the nvald solutons ED calculaton Load demand s dstrbuted among generatng unts and selected number of grdable vehcles. It s the most computatonal ntensve part of UC wth V2G. Capacty of each vehcle s constant (P v ). At hour t, f schedule s [I 1 (t),i 2 (t),...,i N (t),n V2G (t)] T then power from vehcles s N V2G (t) P v (1 ) and the remanng demand [D(t) N V2G (t) P v (1 )] s fulflled by runnng unts of schedule [I 1 (t),i 2 (t),...,i N (t)] T. Lambda teraton s used to calculate economc dspatch (ED) here. An ntellgent method may be used to mprove the soluton qualty. 4. Results and dscusson All calculatons have been run on Intel(R) Core(TM)2 Duo 2.66 GHz CPU, 3 GB RAM, Mcrosoft Wndows XP OS and Vsual C++ compler. A 10-unt system s consdered for smulaton wth 50,000 grdable vehcles, whch are charged from renewable sources. Veh-

5 902 A.Y. Saber, G.K. Venayagamoorthy / Journal of Power Sources 195 (2010) Fg. 1. Algorthmc flowchart of the proposed bnary PSO and balanced PSO for UC wth V2G. cles are charged from renewable sources and they dscharge to the grd so that the total runnng cost and emsson are mnmal; however, the load demand and constrants are fulflled. Load demand and unt characterstcs of the 10-unt system are collected from Ref. [14]. Emsson coeffcents and penalty factor equaton are gven n Appendx A. In order to perform smulatons on the same condton of Refs. [7,9 11,14], the spnnng reserve requrement s assumed to be 10% of the load demand, cold start-up cost s double of hot start-up cost, and total schedulng perod s 24 h. The proposed method s stochastc and convergence depends on proper settng of parameter values. Parameter values are SwarmSze = 30; MaxIteratons=1000; trust parameters c 1 =1.5, c 2 =2.5; total number of vehcles = 50,000; balance of search, Range = 0.6; maxmum battery capacty = 25 kwh; mnmum battery capacty = 10 kwh; average battery capacty, P v = 15 kwh; maxmum number of dschargng vehcles at each hour, N max (t) = 10% of total vehcles; total number of grdable vehcles n the system, N max = 50, 000; chargng dschargng V2G V2G frequency = 1 per day; schedulng perod = 24 h; departure state of charge, = 50%; effcency, = 85%. In ftness functon, both cost and emsson are consdered (.e., W c = 1 and W e = 1) and randomly selected results wth and wthout grdable vehcles are shown n Tables 1 and 2, respectvely. Runnng cost s $559, (fuel cost plus startup cost) and emsson s 257, tons when 50,000 grdable vehcles are consdered n the 10-unt system durng 24 h (Table 1). On the other hand, runnng cost and emsson are $565, and 260, tons, respectvely when grdable vehcles are not consdered n the same system (Table 2). Thus V2G saves ($565, $559,367.06=) $ and reduces (260, , tons=) tons emsson per day n the 10-unt small system. Effect of both cost and emsson n ftness functon of UC wth V2G s shown n Fg. 2. Though value of ftness functon s contnuously decreasng, ndvdual cost and emsson are frequently fluctuatng (both ncreasng and decreasng) up to 200 teratons. In the proposed method, varatons of cost and emsson are small, and fnally both producton cost and emsson are moderate after program executon. From Fg. 2, emsson varaton s hgher than cost varaton because values of second order emsson coeffcents are much hgher than that of fuel cost coeffcents. Accordng to Tables 1 and 2, emsson s always lower; however, maxmum capacty of the system and reserve are always hgher (except at 4th hour) when grdable vehcles are consdered n unt commtment wth V2G. Only at 4th hour, reserve s lower and emsson s hgher, whch are tolerable, as spnnng reserve (10%) s satsfed; however, t s happened because the method s stochastc and t makes balance between cost and emsson optmzaton. Mnmum reserve s MW at 24th hour usng grdable vehcles n V2G technology and t s MW at the same hour wthout usng V2G. Average reserve s MW usng V2G technology and t s only MW wthout usng V2G. Fgs. 3 5 gve a detaled descrpton vsually. So V2G ncreases relablty of the system as well. Cost and emsson are also tested separately as a ftness functon of the same system. Table 3 shows the results when only cost (fuel cost plus start-up cost) s consdered n the ftness Fg. 2. Cost plus emsson n ftness functon of UC wth V2G. Fg. 3. Maxmum capacty wth and wthout V2G.

6 Table 1 Schedule and dspatch of generatng unts and grdable vehcles for 10-unt system wth 50,000 grdable vehcles (both cost and emsson are consdered n the ftness functon). Tme (h) U-1 U-2 U-3 U-4 U-5 U-6 U-7 U-8 U-9 U , , , , , , , , , , , , , , , , , , , , , , , , Total emsson = 257, ton. Total runnng cost = $559, (fuel cost plus start-up cost). V2G/S3P No. of vehcles Emsson (ton) Maxmum capacty Demand Reserve A.Y. Saber, G.K. Venayagamoorthy / Journal of Power Sources 195 (2010)

7 Table 2 Schedule and dspatch of generatng unts wthout grdable vehcles for 10-unt system (both cost and emsson are consdered n the ftness functon). Tme (h) U-1 U-2 U-3 U-4 U-5 U-6 U-7 U-8 U-9 U-10 V2G/S3P Emsson (ton) , , , , , , , , , , , , , , , , , , , , , , , , Total emsson = 260, ton. Total runnng cost = $565, (fuel cost plus start-up cost). Maxmum capacty Demand Reserve 904 A.Y. Saber, G.K. Venayagamoorthy / Journal of Power Sources 195 (2010)

8 Table 3 Schedule and dspatch of generatng unts and grdable vehcles for 10-unt system wth 50,000 grdable vehcles (only cost s consdered n the ftness functon). Tme (h) U-1 U-2 U-3 U-4 U-5 U-6 U-7 U-8 U-9 U-10 V2G/S3P , , , , , , , , , , , , , , , , , , , , , , , , Total runnng cost = $558, (fuel cost plus start-up cost). Total emsson = 260, ton. No. of vehcles Emsson (ton) Maxmum capacty Demand Reserve A.Y. Saber, G.K. Venayagamoorthy / Journal of Power Sources 195 (2010)

9 906 A.Y. Saber, G.K. Venayagamoorthy / Journal of Power Sources 195 (2010) Fg. 4. Reserve power wth and wthout V2G. Fg. 7. Emsson n ftness functon of UC wth V2G. Fg. 5. Emsson wth and wthout V2G. functon (.e., W c = 1 and W e = 0). Usng the proposed method, runnng cost s $558, where all the constrants are satsfed and for ths runnng cost, emsson s 260, tons. Therefore the cost s reduced by ($559, $558,003.01=) $ and for the $ cost reducton, emsson s ncreased by (260, , tons =) tons. Accordng to Table 3, most of the tme large cheap unts are runnng; large amount of power s delvered from V2G at peak load hours; emsson s always hgh; and reserve, cost are low. Effect of only cost n ftness functon of UC wth V2G s shown n Fg. 6. Cost s contnuously decreasng; however, emsson s fluctuatng up to 200 teratons. From Fg. 6, varatons of emsson and total cost are hgh when only fuel cost s consdered n the ftness functon and as the cost s low, emsson s very hgh, whch s not tolerable for envronment. Smlarly Table 4 shows the results when only emsson s consdered n the ftness functon (.e., W c = 0 and W e = 1). Usng the proposed method, emsson s 249, tons, where only emsson s the ftness functon and all constrants are fulflled; however, runnng cost s $570, Therefore emsson s reduced by (257, , tons=) tons; however, cost s ncreased by ($570, $559,367.06=) $11, for the small system. From Table 4, sometmes small expensve unts are also commtted even at off-peak load; power delvered from V2G does not vary greatly between peak and off-peak loads; emsson s always low; and reserve, cost are hgh. Effect of only emsson n ftness functon of UC wth V2G s shown n Fg. 7. Emsson s rapdly decreasng; however, cost fluctuates slowly up to 500 teratons. As emsson s low, the cost s hgh, whch may not be acceptable when only emsson s consdered n the ftness functon of UC wth V2G. Load curve of the 10-unt system has both peaks and valleys (Fg. 3). Emsson comparson s shown n Fg. 8. Emsson s always hgh when only prce s consdered n the ftness functon to generate low cost schedule. On the other hand, emsson s always low and cost s very hgh when only emsson s consdered n the ftness functon to generate envronmental frendly schedule. However, dfference s small at peaks (12th and 20th h) and valleys (16th and 17th h) of the load for the optmzaton method. From Tables 3 and 4, total emsson s reduced by (260, , tons=) 10, tons per day or 3,828,390.1 tons per year and cost s ncreased by ($570, $558,003.01=) $12, per day or $4,654, per year for dfferent ftness functons. In the proposed method, ftness functon (5) s flexble usng weghts W c and W e for gvng precedence of cost and emsson, respectvely. For practcal use, values of W c and W e should be chosen carefully consderng prce, envronmental effects, consumers and system operators demand. So there s a trade-off between cost and emsson. However, ftness functon of unt commtment wth V2G, consderng both cost and emsson, can make a balance between the cost and emsson where both cost and emsson are moderate (Tables 1 and 2 and Fg. 2). Besdes, V2G helps to reduce both cost and emsson n power systems (Tables 1 and 2). Therefore ntellgent unt commtment wth V2G, for both cost and emsson optmzaton, s essental n power systems. The man challenge of unt commtment s to properly schedule small expensve unts, as large cheap unts are always on. Operators expect that large cheap unts wll manly satsfy base load and other small expensve unts wll fulfll fluctuatng, peak loads. Grdable vehcles of V2G reduce dependences on small expensve unts. Table 5 shows the effect of V2G on each unt consderng both cost and emsson n the ftness functon. Usually a negatve value of V2G effect ndcates a relatvely expensve (or more pollutng) unt Fg. 6. Cost n ftness functon of UC wth V2G. Fg. 8. Emsson comparson.

10 Table 4 Schedule and dspatch of generatng unts and grdable vehcles for 10-unt system wth 50,000 grdable vehcles (only emsson s consdered n the ftness functon). Tme (h) U-1 U-2 U-3 U-4 U-5 U-6 U-7 U-8 U-9 U-10 V2G/S3P , , , , , , , , , , , , , , , , , , , , , , , , Total emsson = 249, ton. Total runnng cost = $570, (fuel cost plus start-up cost). No. of vehcles Emsson (ton) Maxmum capacty Demand Reserve A.Y. Saber, G.K. Venayagamoorthy / Journal of Power Sources 195 (2010)

11 908 A.Y. Saber, G.K. Venayagamoorthy / Journal of Power Sources 195 (2010) Table 5 Power from generatng unts durng 24 h consderng 50,000 grdable vehcles. U-1 U-2 U-3 U-4 U-5 U-6 U-7 U-8 U-9 U-10 V2G/S3P Wth V2G 10, Wthout V2G 10, V2G effect Notes: V2G effect = results wth V2G results wthout V2G. Usually a negatve value of V2G effect ndcates an expensve or more pollutng unt. n the system. In ths nstance U-1, U-7, U-9 and U-10 produce same constant powers, as U-1 s the cheapest unt and t always generates maxmum power; however, U-7, U-9 and U-10 are expensve and they generate mnmum power whenever they are commtted. U-2, U-3, U-5, U-6 and U-8 generate less power (negatve value of V2G effect) when V2G s consdered, because they are ether (relatvely) costly or more pollutng unts. In ths nstance U-4 generates more power (postve value of V2G effect) when V2G s consdered, because the proposed method makes balance between the cost and emsson, and t satsfes all the constrants of the system. Number of vehcles connected to grd s not drectly proportonal to the load demand. Schedule of vehcles (amount of power delvered from V2G) depends on non-lnear prce curves, emsson curves, load demand, constrants, ftness functon and balance between cost and emsson. The proposed method can handle these factors effcently and results are shown n Tables 1, 3 and 4. When only cost s consdered, most of the vehcles are connected at peak loads or concentrated at peak hours (see Table 3) where hgh correlaton between load demand and delvered power from V2G s However, vehcles are ntellgently dstrbuted (not concentrated) durng 24-h schedulng perod where load demand and delvered power from V2G are weakly correlated ( ) to make balance between cost and emsson (see Table 1). Fg. 9 shows ths fact vsually where both cost and emsson are mnmzed. Regardng the optmzaton algorthm, the proposed method solves UC wth V2G problem effcently. Stochastc results are shown n Table 6. The best, worst, and average fndngs of the proposed method from 10 runs are reported together. Two sets of data are gven at each entry of the tables, as both cost and emsson are consdered n the ftness functon. Frst set s for cost and second set s for emsson. In each set, frst element s the producton cost and second element s emsson for the producton cost. For 10-unt system wth 50,000 vehcles and 10% spnnng reserve, best results s $559,685 producton cost wth 255,764 tons emsson or $560,254 producton cost wth 255,206 tons emsson. Both are consdered as best because frst one s the lowest producton cost and second one s the lowest emsson. Results of dfferent systems are also ncluded n Table 6. For 20-unt system, the base 10-unt system s duplcated (coped 2 tmes) and the load demand s multpled by two. The system converges for both small and large unts. Accordng to Table 6, a system wth 5% spnnng reserve needs less producton cost than the same system wth 10% spnnng reserve; however, emsson s near about the same and sometmes t s even hgher because emsson coeffcents of U-3 and U-4 are much hgher than others. The system wth lower spnnng reserve (e.g., 5%) has lower Fg. 9. Power delvered from V2G. runnng cost; however, t s less relable. The proposed method s a generalzed optmzaton method for UC wth V2G. Thus t can handle a new UC V2G system of dfferent nput characterstcs and constrants. So the system always converges. In the begnnng, t converges faster, then converges slowly at the mddle of generaton and then very slowly or steady from the near fnal teratons (see Fgs. 2, 6 and 7). Therefore, the proposed PSO holds the above fnetunng characterstc of a good optmzaton method. The method s stochastc; however, varaton of results at dfferent tme s tolerable and results are not based. These facts strongly demonstrate the robustness of the proposed method for optmzaton of both cost and emsson n UC wth V2G. Table 7 shows the comparson of the proposed method to recent methods, e.g., nteger-coded GA (ICGA) reported n Ref. [7], Lagrangan relaxaton and genetc algorthm (LRGA) reported n Ref. [9], genetc algorthm (GA), dynamc programmng (DP) and Lagrangan relaxaton (LR) reported n Ref. [10], evolutonary programmng (EP) reported n Ref. [11], and hybrd partcle swarm optmzaton (HPSO) reported n Ref. [14] wth respect to the total cost. ndcates that no result s reported n the correspondng artcle. The proposed method s workng properly, as results are comparable wth exstng methods when only number of grdable vehcles s assgned to zero n the algorthm keepng all other resources and constrants the same. The proposed method s superor to other mentoned methods n Table 7, because (a) the DP cannot search all the states of the V2G schedulng; (b) t s very dffcult to obtan feasble solutons and to mnmze the dualty gap n LR for V2G schedulng; (c) most of the cases, SA generates random nfeasble solutons n each teraton by a random bt flppng operaton from the huge matrx of UC wth V2G; (d) PSO shares many common parts of GA, EP, etc.; however, () t has better nformaton sharng and conveyng mechansms than GA, EP; () t needs less memory and smple calculatons; () t has no dmenson lmtaton; (v) t s easy to mplement. The proposed PSO generates lttle bt better results than HPSO just for proper parameter settngs, swarm sze (n the proposed method, swarm sze s 30 nstead of 20 n HPSO), ED calculatons and effcent programmng. Table 6 shows executon tme of the proposed method. Executon tme depends on algorthm, computer confguraton and effcent program codng. The proposed method s mplemented effcently n Vsual C++ and run on a modern (moderate speed) system. Executon tme s acceptable, as t s n second. Executon tme does not vary too much because swarm sze and number of teratons are the same for all the systems. However, t s faster when grdable vehcles are consdered because ED s the most computatonal expensve part of UC wth V2G and less amount of power wll be dspatched from generatng unts whch s usually faster to calculate when grdable vehcles are connected. Executon tme s not exponentally growng wth respect to the number of grdable vehcles of V2G, as vehcles are treated as a cluster of nteger number of vehcles n the proposed method. Battery sze of an EV s larger than that of a HEV/PHEV. Performance of each EV and HEV/PHEV affects the results of UC wth V2G. Results consderng EVs (25 kwh each for around 100 mles drve) or HEVs/PHEVs (average 10 kwh) are shown n Table 8. Emsson

12 A.Y. Saber, G.K. Venayagamoorthy / Journal of Power Sources 195 (2010) Table 6 Test results of the proposed PSO for UC wth V2G. System Total cost/emsson Executon tme Best (cost, emsson) Worst (cost, emsson) Average (cost, emsson) Std. dev. (cost, emsson) Maxmum (s) Mnmum (s) Average (s) 10% spnnng reserve 10-unt wth 50,000 vehcles ($559,685, 255,764 ton) a ($560,254, 255,206 ton) ($560,094, 255,448 ton) ($213.2, ton) ($560,254, 255,206 ton) b ($559,685, 255,764 ton) 10-unt wthout vehcles ($565,356, 260,735 ton) ($565,949, 259,711 ton) ($565,740, 260,097 ton) ($277, ton) ($565,949, 259,711 ton) ($565,888, 260,666 ton) 20-unt wth 100,000 vehcles ($1,115,572, 516,563 ton) ($1,116,724, 514,050 ton) ($1,116,111, 515,111 ton) ($452, 1138 ton) ($1,116,486, 513,695 ton) ($1,115,572, 516,563 ton) 20-unt wthout vehcles ($1,128,196, 523,035 ton) ($1,129,042, 521,243 ton) ($1,128,720, 522,173 ton) ($395, 986 ton) ($1,129,042, 521,243 ton) ($1,128,667, 523,443 ton) 5% spnnng reserve 10-unt wth 50,000 vehcles ($553,090, 255,760 ton) ($553,636, 255,186 ton) ($553,385, 255,594 ton) ($241.1, ton) ($553,636, 255,186 ton) ($553,090, 255,760 ton) 10-unt wthout vehcles ($558,757, 259,867 ton) ($559,568, 259,086 ton) ($559,131, 259,677 ton) ($358, 488 ton) ($559,568, 259,086 ton) ($559,070, 259,870 ton) 20-unt wth 100,000 vehcles ($1,102,742, 516,045 ton) ($1,103,188, 510,581 ton) ($1,103,077, 514,574 ton) ($274.7, ton) ($1,103,188, 510,581 ton) ($1,103,302, 517,098 ton) 20-unt wthout vehcles ($1,112,294, 526,909 ton) ($1,112,942, 521,308 ton) ($1,112,610, 523,742 ton) ($290.1, ton) ($1,112,942, 521,308 ton) ($1,112,294, 526,909 ton) a Best value for cost. b Best value for emsson. and operaton cost are lower; and maxmum system capacty and average reserve are hgher when EVs are consdered n the system. However, EVs are more costly than HEVs. 5. Practcalty of V2G for UC For future practcal applcatons, number of grdable vehcles n an electrc power network can be estmated analytcally based on number of electrcty clents (customers) n that network. An estmate of grdable vehcles from resdental electrcty clents may be computed as follows: N GV = NV UC V2G V REC N REC = NV UC V2GV REC X RL L mn AV HLD (24) AV HLD = AV MEC (25) where N GV s the number of grdable vehcles (GVs), NV UC V2G s the percentage of the number of regstered GVs for partcpaton n UC wth V2G, V REC s the average number of grdable vehcles per resdental electrcty clent, N REC s the number of resdental electrcty clents, X RL s the percentage of resdental loads n the power network, L mn s the mnmum load n the power network at gven tme, AV HLD s the average hourly load demand per resdental electrcty clent (kw), and AV MEC s the average monthly electrcty consumpton per resdental electrcty clent (kwh). For example: the mnmum load, L mn, n the 10-unt benchmark system consdered n ths paper s 700 MW [14]. It can be taken that the average monthly electrcty consumpton, AV MEC,of a domestc home s about 1500 kwh [31]. Thus average hourly electrcty load of a resdental clent, AV HLD, s kw. If we assume that X RL = 30%, the total number of clents n the regon N REC,s 100,801.6 and t can be rounded to 100,000 for smplcty. It s reasonable to assume that n the future, n Unted States, V REC = 1,.e., on average there wll be one grdable vehcle per resdental electrcty clent, and NV UC V2G = 50%,.e., 50% regster to partcpant n UC wth V2G. Thus, N GV from (24) s 50,000 and there are a reasonable number of vehcles to be consdered on the 10-unt benchmark system for our smulaton studes. Lkewse, the 20- unt system (double the sze of the 10-unt system) wth 100,000 grdable vehcles s consdered n ths paper to show scalablty. The average dstance drven wth a vehcle s about 20,000 km per year [32], thus each day a vehcle covers an average dstance of km (20,000/365) and takes roughly less than 2 h of travel tme. Therefore, t can be sad that on average a vehcle s on the road less than 10% of a day and t s parked more than 90% of a day, ether n a parkng lot or n a home garage. Vehcles can be controlled n UC wth V2G durng the 90% tme of a day usng an automatc ntellgent agent when they are parked. It s dffcult to determne whether a partcular vehcle wll be parked or on the road at a partcular tme. Thus n ths model, an ndvdual vehcle s not scheduled. However, UC wth V2G determnes number of vehcles that need to be connected every hour for 24 h. It s logcal that most of the vehcles are parked and dependng on the UC wth V2G schedule, commtted number of vehcles (not specfc vehcles) s dscharged usng an ntellgent autonomous agent, as enough number of grdable vehcles s n parkng lots or n home garages. Instead of consderng ndvdual vehcle, aggregaton of vehcles can solve the dschargng control problem of mass number of vehcles n UC wth V2G. For relable control operatons, maxmum number of dschargng vehcles lmt constrant, gven n (10), s mposed so that number of scheduled vehcles at each hour s not too hgh wth respect to the total number of vehcles n the system, whch s easy to control. In order to llustrate the concept n ths paper, maxmum 10% of the vehcles are scheduled for dschargng at each hour. Ths percentage can be made to vary every hour dependng on system,