Determination of Maximum Allowable Load of the Buyer Bus using New Hybrid Particle Swarm Optimization

Transcription

1 Internatonal Journal of Electrcal Engneerng. ISSN Volume 4, Number 7 (2011), pp Internatonal Research Publcaton House Determnaton of Maxmum Allowable Load of the Buyer Bus usng New Hybrd Partcle Swarm Optmzaton S. Venkatesan 1 and N. Kamaraj 2 1 Department of Electrcal &Electroncs Engneerng, K.L.N. College of Engneerng, Pottapalayam , Tamlnadu, Inda E-mal: svneee@gmal.com. 2 Department of Electrcal &Electroncs Engneerng, Thagarajar College of Engneerng, Madura , Tamlnadu, Inda E-mal: nkeee@tce.edu. Abstract Ths paper descrbes a novel method to estmate mum allowable load at the buyer buses wthout volatng transmsson lne flow lmt for a wheelng transacton n a compettve electrcty market. The problem s formulated as a non-lnear optmzaton problem and the applcaton conssts of usng a developed optmal power flow based on load mzaton n each load bus by expandng the orgnal PSO. A New Hybrd Partcle Swarm Optmzaton (HPSO) s proposed to solve ths problem by addng a Cauchy mutaton on the best partcle. In the context of electrcty market, transmsson prcng s an mportant tool to acheve an effcent operaton of the electrcty system. Optmal-wheelng prce s also evaluated for the transacton under Maxmum allowable load at buyer bus. The above technque s llustrated for the consdered transacton on IEEE 30-bus system and Indan utlty 69 bus systems Keywords: Cauchy mutaton, Hybrd Partcle Swarm Optmzaton Independent Power Producer, Maxmum allowable load, wheelng prcng, Wheelng Transacton. Introducton In the deregulaton envronment, generaton, transmsson and dstrbuton are ndependent of each other. The restructured power sector ntroduces competton

2 768 S. Venkatesan and N. Kamaraj among producers and offer choces to the consumers. The regulated utltes and deregulated utltes are combned to form the concept of wheelng. Wheelng s the transmsson of electrcal energy from a seller to buyer through a transmsson network owned by thrd party [1]. Wheelng of electrcty takes place, when a customer purchases electrcty from a source other than ts own servng utlty. The utlty whose transmsson network s used for wheelng transacton has to be pad for ts servce and for meetng the losses. Electrcty wheelng has become one of the ndspensable elements of power system deregulaton. The problem of margnal costs based optmal wheelng rates consderng losses, effects of lne flow and voltage magntude constrants has been dscussed n [2,3].Caramans et al., [4] has descrbed wheelng rate evaluaton smulator, whch can be used to evaluate the margnal cost of wheelng between utltes, prvate users and prvate generators. The prncple and the mplementaton of Mw-mle methodology to evaluate the usage of transmsson network capacty for frm transmsson servces, ncludng wheelng transacton dscussed n [5]. Clayton et al., [6] descrbed the ncremental prcng concepts and ncremental loss concepts for nterchange costng and wheelng loss evaluaton. The applcaton of Optmal Power Flow (OPF) for the evaluaton of wheelng and nonutlty generaton (NUG) related optons have been dscussed n [7].Kuwahata and Hrosh [8] has explaned utlty-co generator game for prcng power sales and wheelng fees. A methodology has been proposed to access the feasblty and prcng of wheelng transactons under deregulated envronment of power ndustry. It s based on ATC and short run margnal cost as dscussed n [9]. From the feasble transactons, least cost transacton s selected whch wll help the Independent Power Producer (IPP), to choose the best locaton for sale of power and also buyer to decde from whch IPP they should buy power. Most of these models as reported n [10-16] manly focus towards power flow and the ATC lmts of power systems for total system loadablty and generally, they are not addressng the problem of estmatng mum load at buyer bus durng wheelng transactons wthout volatng lne flow lmt. An optmzaton-based scheme s proposed to solve ths problem. However, the tool of analyss belongs to the evolutonary algorthm famly. The applcaton of PSO extensvely used for some power system applcatons such as economc dspatch, OPF, and reactve Power plannng as reported n [17-19]. In ths paper, a new hybrd PSO (HPSO) s proposed. HPSO uses an dea from fast evolutonary programmng (FEP) [20, 21] to mutate the best poston by Cauchy mutaton. It s to hope that the long jump from Cauchy mutaton could get the best poston out of the local optma where t has fallen. Comparson has been conducted between HPSO wth Cauchy mutaton (HPSOCM) and other Evolutonary technque PSO. In the context of electrcty market, transmsson prcng s an mportant tool to acheve an effcent operaton of the electrcty system. Once the mum allowable load and locaton has been dentfed, optmal wheelng prce s evaluated for them by usng the methods Mw mle method, Base method(bm), Module or Use method(mou) and Zero Counter Flow(ZCF) method [22,23]. Two test systems.e., IEEE 30-bus system and Indan 69-Bus utlty bus systems wth consdered transactons used for valdate the proposed technque. Smulaton

3 Determnaton of Maxmum Allowable Load of the Buyer Bus 769 results has demonstrated that the proposed technque can be well used for locatng buyer wth mum capacty and ts transactons as well as a support tool for restructurng power system operaton. Hybrd Partcle Swarm Optmzaton wth Cauchy Mutaton (HPSOCM) The tradtonal PSO model was descrbed by Dr. Kennedy and Dr. Eberhart n It conssts of a number of partcles movng around n the search space, each representng a possble soluton to a numercal problem. Each partcle has a poston Vector X = ( x 1, x2,..., xn),a velocty Vector V = ( v 1, v2,..., vn).in the PSO, the collectve best poston of all the partcles taken together s termed as the global best poston gven as Glbest = (glb 1,glb 2,...,glb n) and the best poston acheved by the ndvdual partcle s termed as the local best or poston best and for th partcle gven as Pbest = ( p 1, p2,..., pn). Partcles uses both of these are nformaton to update ther postons and veloctes are gven n the followng equatons V + = ωv + C rand ( Pbest X ) + C rand ( Glbest X ) (1) k 1 k k k k k WhereV k s velocty of ndvdual at teraton k,ω s nerta weght parameters, C 1 and C 2 are two postve constants called acceleraton constants, generally C 1 =C 2 =2, k represents teraton number, rand1 and rand 2 are random values k dfferent for each partcle and each dmenson, X s poston of ndvdual at k k teraton k, Pbest s the best poston of ndvdual at teraton k, and Glbest s the best poston of group at teraton k. The poston of each partcle s updated n the each teraton. Ths s done by addng the velocty vector to the poston vector,.e. X = X + V (2) k+ 1 k k+ 1 The accuracy and rate of convergence of the algorthm depends on the approprate choce of partcle sze, mum velocty of partcle sze and the nerta constant. If the velocty s hgher than a certan lmt, called V, ths lmt wll be used as the new velocty for ths partcle n ths dmenson, thus keepng the partcle wthn the search space. The partcles have no neghborhood restrctons, meanng that each partcle can affect all other partcles. Some theoretcal results have shown that the partcle n PSO wll oscllate between ther prevous best partcle and the global best partcle found by all partcles so far, before t converges. If the searchng neghbors of the global best partcle would be added n each generaton, t would extend the search space of the best partcle. It s helpful for the whole partcles to move to the better postons. Ths can be accomplshed by havng a cauchy mutaton on the global best partcle n every

4 770 S. Venkatesan and N. Kamaraj generaton. The one dmensonal cauchy densty functon centered at the orgn s defned by t f( x) =, < x< (3) 2 2 π ( t + x ) Where t >0 s a scale parameter. The Cauchy dstrbuton functon s 1 1 x Ft ( x) = + arctan 2 π t The Cauchy mutaton operator used n HPSO s descrbed as follows: PopSze V[ j][ ] = 1 () = j W PopSze (4) (5) Where V[ j][ ] s the th velocty vector of the j th partcle n the populaton, Pop Sze s the Populaton Sze. W () s a weght vector wth n[ W, W ], and W s set to 1 n ths paper. gbest () = gbest() + W()* N( X, X ) (6) mn Where N s a Cauchy dstrbuted functon wth the scale parameter t=1, and N( Xmn, X ) s a random number wth n ( Xmn, X ), whch s a defned doman of a test functon. The Pseudo code for HPSO algorthm wth cauchy mutaton s llustrated as below, Begn Intalze Whle (not termnate-condton) Evaluate Calculate new velocty vectors Update partcle poston Update W[] f W[]>W,then W[]=W If end Mutate gbest Select gbest from the N partcles after havng N mutaton If the ftness value of gbest s better than gbest Then gbest=gbest If end Whle end End

5 Determnaton of Maxmum Allowable Load of the Buyer Bus 771 Problem Formulaton Mathematcally, each blateral transacton between sellers at bus k and power purchaser at bus j satsfes the followng power balance relatonshp. The conceptual modelng of wheelng transacton s that sellers and buyers encourage the tradng between them wthout volatng the transmsson constrants, IPP Gk P P 0 = (7) dj Where P s buyer power at j th bus. dj A smultaneous wheelng transacton has been ncluded n an n bus system. Wth the seller at the bus k and the buyer wth a load at bus j, where j may be vared from 1 to n and j s not equal to k. Then, run the power flow program wth all the generators of the utlty held at fxed optmal settng of base case under these condtons. The frst objectve s to mze the allowable actve power load of each load bus and the second objectve s to determne optmum cost of generaton for the mum allowable load condton durng consdered blateral transactons Objectve 1 The mzaton of load at buyer bus s done only on load buses (j), where j s vared from 1 to N d.the mum load locaton of buyer bus has been evaluated usng HPSOCM. The objectve functon for mum allowable load at buyer bus s as follows, Maxmze actve power load appled to the buyer bus j allow Maxmze P dj (8) Where P allow dj denotes allowable load at bus j, whch represents the ncrease n the system load from base load at buyer bus wthout volatng the lne flow constrants and voltage lmt. The load at buyer bus j n steps from base case to mum loadng pont untl the system no longer has a soluton, whose load model s gven as below: The basc load-flow equatons are modfed to nclude the power generaton by IPP as follows: Let fp and f Q be two reformulated functons defned as follows, NB IPP P j=1 j j j j G Gk d NB Q j j j j G D j=1 mn G G G mn l Sl allow d j f = V Y V cos(θ +δ -δ )-(P +P )+(P + P ),k slack (9) f = V Y V sn(θ + δ - δ )-Q +Q,j slack (10) P P P (11) V V V (12) S (13) Where V and V j are the voltage magntude of bus and j,δ andδ j are the voltage

6 772 S. Venkatesan and N. Kamaraj angle of bus and j, Y and j θ j are the magntude and angle of Y j element n bus admttance matrx, P s the generated power at bus, P s the load power at bus, G D s the real power generaton of IPP at bus k, Nd s number of load buses, NB s number of buses n the system, N pq and Npv mnmum and mum voltage lmt at th mn bus, PG mn are the set of PQ, PV buses, V real power output of the generatng unt at th bus, l flow on lne l. IPP P Gk and V are the mnmum and mum and PG S s mum apparent power Objectve 2 The objectve functon to determne optmum costof generaton for consdered transacton, t s stated as follows: Mnmze n f (P G) (14) = 1 Where 2 f(p G ) = ap G + bp G + c $/hr Consder constant voltage magntude s assumed throughout the network and the constrants are as follows, IPP allow PG + PGk = Pd + Pd j mn G G G j ( j (15) P P P (16) P ) P δ (17) Transmsson Prcng Methodologes The cost of the transmsson network consders the mpact of power flow due to blateral exchange of power. Wheelng prcng s estmated usng the followng methods as dscussed below: Mw-mle method Megawatt mle prcng generally nvolves usng load flow analyss to fnd the power flows on the transmsson network to determne transmsson dstance. These dstances reflect the mpact of a transmsson agreement on the system. CT P = (18) F L

7 Determnaton of Maxmum Allowable Load of the Buyer Bus 773 F s Power flow n lne and L s lne Where CT s the total Cost to share ($), length (mle).the cost of transmsson per megawatt-mle s the total cost averaged over Megawatt-mles of usage. The change n power flows at every transacton s calculated. The dfference n Power s obtaned by subtractng the power flow due to transacton wth power flow due to base case. Base method(bm) In ths method, the prcng s calculated for power flow n each lne due to transacton. Here, the negatve value of power flow s also taken for fndng transmsson prcng. F (t) R(t) = C (19) F(s) s Where C s total cost n lne, F() t s power flow due to transacton t and F() s s sum of power flow transactons Module or Use method(mou) Module or Use method consders only the magntude of load flow, not the drecton of flow due to transacton. The transmsson prcng due to transacton t can be calculated as; F(t) R(t) = C (20) F(s) s Where C s total cost n lne, F (t) s the power flow due to transacton t and F (s) s the sum of power flow transactons zero counter flow method(zcf) Ths method takes only postve power flow for fndng prcng. The negatve power flows are assumed zero. The change n power flow s obtaned by addng all transacton only wth postve flows. (21) and F k(t) f F k(t) 0 FD(t) = F(t) (22) 0 C f F for k (t) F 0(t) 0 R(t) = FD (s) s 0 for F (t) 0 Where C s total cost to share n lne, F() t s power flow n lne due to transacton t, The term FD() s shows the Impacts for provokng the transacton t n lne. Ths wll ncrease the actve power flow n the lnes. Algorthm for estmatng mum allowable load at buyer bus The objectve functon s to mze allowable load at buyer bus usng HPSOCM.

8 774 S. Venkatesan and N. Kamaraj Load durng each transacton s assumed as the partcle to be optmzed. Step 1: Calculate base case values. Step 2: Set IPP at bus k. Step 3: Set load pont count j=1. Step 4: Specfy the mum and mnmum lmts of generaton power of each generaton unts and IPP, mum number of teratons to be performed. Step 5: Partcles are generated and ntalzed wth poston values and velocty. Step 6: The bndng constrants ftness values for the partcles are determned. If a partcle does not satsfy the ftness requrement, t s regenerated. Step 7: Execute the PSO operator on the partcles. Step 8: The optmal objectve ftness values are calculated for all the partcles.then the values of poston best and global best are determned. Step 9: Poston and veloctes of partcles are updated. Step 10: Perform mutaton process to replace the worst partcles. Step 11: If the mum number of teraton s exceeded or some pre specfed an ext crteron s satsfed, then goes to step 12. Else, update the tme counter. Step 12: Output the partcle wth the mum ftness values n the last generaton. Calculate the optmum value wth the objectve functon (Eq (8)) subjected to the constrants (Eq(9)-Eq(13)), usng HPSOCM. Step 13: Increment j by 1 and f j s less than or equal to number of load buses go to step 5. Otherwse, go to next step. Step 14: If all the transactons are smulated, determne the buyer bus for mum allowable load and ts locaton. Step 15: Fnd the optmal prcng as per secton 4 and optmal generaton cost (Eq (14)-Eq (17)) for the consdered transacton. Results and Dscusson For the present study, reactve power demand at load buses has been taken constant. The study has been conducted on IEEE 30-bus and Indan utlty 69-bus utlty

9 Determnaton of Maxmum Allowable Load of the Buyer Bus 775 systems, slghtly modfed to represent smultaneous of wheelng transacton n a deregulated market. For both test systems, the results are obtaned by the followng approaches: Estmatng mum Load of buyer bus by HPSOCM algorthm Optmzng transmsson prcng for consdered transacton Optmal generaton cost for consdered transacton The nfluence of the PSO parameters, the nerta weght, and populaton sze, constants C 1 & C 2, on the convergence of the algorthm has been studed. The sze of partcles has been ncreased from 10 to 100 n steps of 10 and the number of best partcle for ths problem s found to be 60, the nerta constant vared from 0.4 to 0.9 and optmal value for ths problem s found to be 0.5, Maxmum number of teraton has been taken as 100. The mnmum soluton was obtaned for 100 tral runs. Smulaton studes have been conducted on Intel(R) core 5, CPU 2.27 GHz processor under Mat Lab 7 envronment. The adopted parameters n the algorthms are gven n Table1. Table 1: Parameter values for PSO and HPSOCM for the two test systems. Parameters IEEE 30 bus INDIAN 69 Bus PSO HPSOCM PSO HPSOCM Populaton C C Inerta weght (W) W N X mn X Iteratons IEEE 30-bus system The numercal data for IEEE 30-bus system s taken from Ref. [24]. Ths system has 6 generators, 30 buses,41 transmsson lnes. The generators are connected at the buses 1,2,13,22,23 and 27. For ths system, bus 1 s slack bus and there are 24 load buses. The algorthm conducts the OPF by satsfyng all the power flow constrants and estmates the mum load at buyer buses wthout volatng transmsson constrants. In each blateral transacton, the load at buyer bus s ncreased untl the system no longer has a soluton by usng HPSOCM and ts effectveness s compared wth PSO To calculate the mum allowable real power load at buyer bus wthout volatng of the lne flow lmt, the followng methodology s used. Once the locaton and value of IPP s dentfed, the PSO and HPSOCM technques optmze the amount

10 776 S. Venkatesan and N. Kamaraj of real power load at buyer buses durng wheelng transacton. However, a feasble transacton has been executed by optmum value of IPP wth mum allowable load wthout volatng lne flow lmt. Two cases has been outlned below for detaled results dscusson. Case 1 deals wth the problem of mum allowable load of buyer buses as per objectve, whch s gven n secton3. Case 2 explans the effectveness of wheelng transacton f t crosses the mum allowable load of buyer bus. For both cases, a transmsson-prcng methodology has been ntroduced for consdered transacton and fnds the optmum wheelng cost. Case 1: Let us connect that ndependent Power producer of IPP of MW s connected at bus 10. All other generators of the system are held at optmal poston. Therefore, 7 generator buses and 23 load buses n the system Note that only MW overloadng of transmsson lnes are consdered. IPP s nterested to have a wheelng transacton of all load buses of 30-bus system. The algorthm conducts the OPF by satsfyng all the power flow constrants and fnds the mum MW load of buyer buses. Fgure.1 presents the mum allowable load that can be suppled by IPP through varous wheelng transactons at dfferent load ponts wthout volatng transmsson lne flow lmt. The mum allowable load MW has been found at bus 5 at 17 th teraton by usng HPSOCM. However, t s only 97.88MW wth PSO and the results are obtaned only n the 24 th teraton. 100 Maxmum allowable load (Mw) PSO HPSO bus number Fgure 1: Estmaton of Maxmum allowable load suppled by IPP through wheelng transacton for IEEE 30-bus system. Case 2: The load at buyer bus s slghtly ncreased to MW at bus 5. Fgure 2 shows summary of the transmsson lnes overloadng for the transacton. Lne 13 (.e., between buses 10 and 6 ) s congested and t exceeds about 107.7% of ther respectve MVA lmt. Ths overload can be allevated by load curtalment or by generator reschedulng.

11 Determnaton of Maxmum Allowable Load of the Buyer Bus 777 Fgure 2: Percentage of over loadng for the Transacton 10-5 for case 2. The wheelng charges for the transactons are calculated by dfferent methods as dscussed n secton 4 and t has been presented n Table 2. The change n the magntude of power flow on the system caused by the wheelng transacton s taken nto consderaton n order to assst n the allocaton of the wheelng cost to each of the wheelng transacton. Table 2: Comparson Of Prcng Methods for case 1-IEEE 30 Bus System. Transactons Mw-mle Base Method Module Or Use Zero Counter Flow Total cost ($/hr)

12 778 S. Venkatesan and N. Kamaraj The total transmsson system cost s then the sum of all the power flow-mle and ths provdes a measure of how much each transacton uses the transmsson system, the prce s proportonal to the transmsson usage by respectve transactons. The power flow mles of each transmsson lne are totalled up to represent the amount of the transmsson resources used by the correspondng transacton. All the lne lengths are assumed to be 100 mles and the Transmsson cost s taken to be 50$/MW-Mleannum. Fgure 3 shows the percentage of cost contrbuton to the consdered transacton 10-5 under mum allowable load at buyer bus 5 for case 1and case 2. It s evdent that module or use (MOU) method has shown the mnmum contrbuton of cost for the transmsson servce n both cases. % of cost contrbuton case1 Methods of prcng case2 Mw -Mle Base method MOU ZCF Fgure 3: Wheelng cost allocaton to transactons for IEEE 30 bus system. Indan-69 Bus Utlty System Indan utlty 69-bus system has 13 generators and 99 transmsson lnes. The bus data for ths system has been taken from TamlNadu Electrcty Board report ( ) [25]. Taml nadu s one of the southern states of Inda and ths system s under the control of Taml Nadu electrcty Board, a state government owned Power Corporaton. The One lne dagram of Indan utlty-69 bus system s shown n fgure 4.

13 Determnaton of Maxmum Allowable Load of the Buyer Bus 779 Fgure 4: One lne dagram of Indan utlty-69 bus system. Case 1: Let us connect IPP of MW at bus no 7. Fgure 5 presents the mum allowable load that can be suppled by IPP through varous wheelng transactons at dfferent load ponts wthout volatng transmsson lne flow lmt. In addton, the mum allowable load has been dentfed at bus no 2 and ts value s MW usng HPSOCM. Maxmum allowable load ( MW) PSO HPSO Bus Number Fgure 5: Estmaton of Maxmum allowable load suppled by IPP through wheelng transacton for Indan-69 bus utlty system.

14 780 S. Venkatesan and N. Kamaraj Case 2: The load at buyer bus s slghtly ncreased to MW at bus 2. Lne 17 (.e., between buses 10 and 9) and lne 18 (.e., between buses 11 and 9 ) are congested and t exceeds about 108 % and 117.5% of ther respectve MVA lmt. Let us assume all the lne lengths100 mles. Transmsson cost s 50 $/MW-Mleannum. Fgure 6 presents a graph that shows the percentage of cost contrbuton to the transacton 7-2 under mum allowable load at bus 2. The total transacton cost s obtaned about 4800 $/hr. It s mportant to menton that Module or Use (MOU) method has shown the mnmum contrbuton of cost for transmsson servce. % of cost contrbuton case1 Methods of prcng case2 Mw-Mle Base method MOU ZCF Fgure 6: wheelng cost allocaton to transactons for Indan utlty-69 bus system. Optmal generaton cost for the consdered transacton The HPSOCM lke the orgnal PSO algorthm was orgnally proposed for contnuous problems. HPSOCM has been tested for convergence on smple generaton cost optmzaton problems. Generator bus data for Indan 69 bus utlty system and cost coeffcent for IPP are gven n Appendx 1 and 2. Fgure 7, Fgure 8 and Table 3 shows the evoluton process of the functon values for HPSOCM and PSO employed for IEEE 30 bus and Indan 69 bus utlty system. Fgure 7: Comparson between PSO and HPSO for IEEE 30 bus system.

15 Determnaton of Maxmum Allowable Load of the Buyer Bus 781 Fgure 8: Comparson between PSO and HPSO for Indan utlty 69-bus system. Table 3: Optmum cost of generaton for test systems usng HPSOCM and PSO. Test system IEEE 30 bus system Indan utlty69 bus Algorthm PSO HPSOCM PSO HPSOCM Total cost of generaton n $/hr Convergence Iteraton Computaton tme n sec For the smple fuel cost functons, HPSOCM and PSO performed equally well at the begnnng because the partcles at that tme are not good enough so that both methods could mprove well. Once the partcles n the populatons are close to the best partcle, the convergence of PSO becomes slower because the search steps n PSO become smaller. Wth the help of cauchy mutaton on the best partcles, HPSOCM could move the best partcle away from the rest of partcles n the populaton so that the fast speed could reman through the whole evoluton process. Because of such mutatons made on the best partcle, HPSOCM could successfully fnd better solutons whle mantanng fast search speed. On the other hand, PSO could be easly tracked nto local mnma wthout the mutaton done on the best partcle. Concluson The proposed algorthm hybrd partcle swarm optmzaton ncorporatng cauchy mutaton operator nto Partcle Swarm Optmzaton has been successfully appled to estmate the mum allowable load of buyer bus. From the result obtaned, t s proved that HPSOCM s havng faster convergence and better global search ablty on those mum allowable loads and total fuel cost of buyer buses compared to the

16 782 S. Venkatesan and N. Kamaraj standard PSO. It also suggests that a cauchy mutaton on the best partcle alone mght not be enough to prevent the search from fallng n the local optma. It s evdent from the smulaton studes that ths approach s smple, easy to mplement, converges at a faster rate, and can be used to other optmzaton problems as fne. Also, transmssonprcng methodologes are ntroduced and optmum prce s determned for the transactons under mum allowable load at buyer bus. The valdty of the proposed method has been llustrated wth IEEE 30 and Indan utlty 69 bus test systems. The proposed method s completely free from complex mathematcal formulaton and provdes qute encouragng results whch wll be useful for deregulated envronment Acknowledgement The authors are grateful to the prncpal and management of Thagarajar College of Engneerng, Madura and K.L.N college of Engneerng, Madura for provdng all facltes for the research work. References [1] Yog Raj Sood, Narayana Prasad Padhy and H.O. Gupta, Wheelng of Power Under Deregulated Envronment of Power System-A Bblographcal Survey, IEEE Transactons on Power Systems, Vol. 17, No. 3, August 2004, pp [2] Hyde M. Merrll, Bruce W.Erckson, Wheelng Rates Based on Margnal Cost Theory, IEEE Transacton on Power Systems, Vol 4, No. 4, October 1989, pp [3] Caramans Mchael C., Bohn Roger E., Schweppes Fred C., "The costs of wheelng and optmal Wheelng rates", IEEE Transacton. on Power System, Vol. PWRS-1, No.1, February 1986, pp [4] M.C.Caramans, N.Roukos, F.C.Schweppe, WRATES: A Tool for Evaluatng the Margnal Cost of Wheelng, IEEE Transacton on Power Systems, Vol 4, No. 2, May 1989, pp [5] Darush Shrmohammad, Paul R.Grbk, ErcT.K.Law, JamesH.Malnowsk, Rchard E.O Donnell, Evaluaton of Transmsson Network Capacty Use for Wheelng Transacton, IEEE Transacton on Power Systems, Vol 4, No. 4, October 1989, pp [6] J.Scott Clayton, Charles A.Gbson, Interchange Costng and Wheelng Loss Evaluaton By means of Incremental, IEEE Transacton on Power Systems, Vol 5, No. 3, August 1990, pp [7] Rana mukerj, Wendell Neugabeur, RchardP.Ludorf, Armand Catell, Evaluaton of Wheelng and Non-Utlty Generaton (NUG) Optons usng Optmal Power Flows, IEEE Transacton on Power Systems, Vol 7, No.1, February 1992, pp

17 Determnaton of Maxmum Allowable Load of the Buyer Bus 783 [8] Akeo kuwahata, Hrosh Asano, Utlty-Generator Game for Prcng Power Sales and Wheelng Fees IEEE Transacton on Power Systems, Vol 9, No.4, November pp [9] Yog Raj Sood, Narayana Prasad Padhy and H.O.Gupta, Assessment for feasblty and prcng of wheelng transactons under deregulated envronment of power ndustry, Electrc Power and Energy Systems, Vol 26, Issue 3, March 2004, pp [10] Yoshhko Kataoka, An Approach For The Regularzaton of a Power Flow Soluton Around the Maxmum Loadng Pont, IEEE Transacton on Power Systems, Vol 7,No.3, August 1992,pp [11] Y.R. Sood, S. Verma, N.P. Padhy, H.O. Gupta, Evolutonary programmng based algorthm for selecton of wheelng optons, Proceedngs of the IEEE Power Engneerng Socety Wnter Meetng,Columbus, OH, USA, 28 January-1 February [12] Y.R. Sood, N.P. Padhy, H.O. Gupta, S. Verma, Analyss and Management of wheelng transactons based on AI technque under Deregulated Envronment of Power System, Water and Energy Internatonal Journal, January-March 2001, CBIP, New Delh, Inda. [13] Y.R. Sood, N.P. Padhy, H.O. Gupta, Assessment of feasble transacton under deregulated envronment of power ndustry, n: Proceedngs of the Internatonal Conference on Energy, Automaton and Informaton Technology, Indan Insttute of Technology, Kharagpur,Inda, December 2001, pp [14] Zechun Hu, Xfan Wang, Effcent Computaton of Maxmum Loadng Pont by Load Flow Method wth Optmal Multpler, IEEE Transacton on Power Systems, Vol:23,No.2, May 2008, pp [15] ManfredF.Bedrnana, Carlos A.Castro, Maxmum Loadng Pont Computaton based on Load Flow wth Step Sze Optmzaton, IEEE Transacton on Power Systems, 20-24,July 2008,pp 1-8. [16] C.H.Fujsawa, C.A.Castro, Smple Method for Computng Power Systems Maxmum Loadng Condtons, IEEE Power Tech Conference, June 28-July 2, 2009.pp 1-6. [17] M.A.Abdo, Optmal power flow usng Partcle swarm optmzaton, Electrcal power and energy systems,vol 24, ssue 7,Oct 2002,pp [18] D.N.Jeya Kumar, T.Jeyabarath, T.Raghunathan, Partcle swarm Optmzaton for varous types of economc dspatch problems, Electrcal Power and energy systems, Vol 28, ssue 1, Jan 2006, pp [19] Ahmed A.A.Esmn, Antono C.Zambron de Souza, Hybrd Partcle Swarm Optmzaton Appled to Loss Power Mnmzaton, IEEE Transactons on Power Systems, Vol 20, No.2, May 2005,pp [20] X. Yao, Y. Lu and G. Ln, Evolutonary Programmng Made Faster, IEEE Transactons on Evolutonary Computaton,Vol 3, No 2, July 1999, pp [21] Hu Wang, Yong Lu, A Hybrd Partcle Swarm Optmzaton Algorthm wth Cauchy Mutaton, IEEE Swarm Intellgence Symposum 2007, pp

18 784 S. Venkatesan and N. Kamaraj [22] Ferrera J, Vale Z and Puga, Nodal Prce Smulaton n Compettve Electrcty Markets, Proceedngs of 6th Internatonal Conference on the European Electrcty Market, EEM 09,Leuven, Belgum [23] Ferrera j, Vale Z, Vale A and Puga, Cost of Transmsson Transacton: Comparson and Dscusson of Used Methods, Internatonal Conference on Renewable Energes and Power Qualty (ICREPQ 03), Vgo,2003 [24] pstca. [25] Taml Nadu Electrcty Board Statstcs at a Glance , Plannng Wng of TamlNadu Electrcty Board, Chenna, Inda. Authors Informatonn S. Venkatesan receved the B.E. degree n Electrcal and Electroncs Engneerng and M.E. degree n Power System Engneerng from Madura Kamarajar Unversty n 1990 and 1992 respectvely. He s currently pursung the PhD degree at Anna Unversty, Chenna. At present, he s workng as Professor n Electrcal and Electroncs Engneerng Department, K.L.N.College of Engneerng, Madura.Taml nadu, Inda. Hs areas of nterest are Transmsson Congeston Management and Bddng Strateges Dr. N. Kamaraj receved the B.E. degree n Electrcal and Electroncs Engneerng n the year of 1988, M.E. degree n Power Systems Engneerng from Thagarajar College of Engneerng, Madura. He has done hs PhD n Madura Kamarajar Unversty durng the year At present he s workng as Head of the Department n Electrcal & Electroncs Department, Thagarajar college of Engneerng, Madura, Taml nadu, Inda. Hs research area of nterest s Electrcal Power System Securty usng ANN and Fuzzy logc. Appendx. 1: Generator bus data for Indan 69 bus utlty system. Q mn Q Bus No. P mn P (MW) (MW) (MVAR) (MVAR) $/MW 2 -h $/MW-h a b c $/h

19 Determnaton of Maxmum Allowable Load of the Buyer Bus Appendx 2: IPPs-Generator Data. Test Systems P (MW) a $/MW 2 -h b $/MW-h c $/h IEEE 30-bus system INDIAN 69-bus utlty system