Sensitivity Based Optimal Real Power Rescheduling For Congestion Management Using Black Hole Algorithm

Transcription

1 Auralan Journal of Bac and Appled Scence, 0(5) Ocober 206, age: AUSTRALIAN JOURNAL OF BASIC AND ALIED SCIENCES ISSN: EISSN: Journal home page: Senvy Baed Opmal Real ower Rechedulng For Congeon Managemen Ung Black Hole Algorhm Ramachandran R and 2 Arun M &2 Aan rofeor, Deparmen of Elecrcal Engneerng, Annamala Unvery, Annamala nagar, Tamlnadu, Inda Addre For Correpondence: R.Ramachandran, Deparmen of Elecrcal Engneerng, Annamala Unvery, Annamala nagar, Taml nadu, Inda, Emal: A R T I C L E I N F O Arcle hory: Receved 26 Augu 206 Acceped 0 Ocober 206 ublhed 8 Ocober 206 Keyword: Congeon managemen; envy facor; real power rechedulng; deregulaed power yem; black hole algorhm. A B S T R A C T Tranmon congeon managemen crcal ue n he operaon of deregulaed power marke. Enurng uffcen ranmon capacy val o realze all power ranacon. Opmal power chedule correpondng o marke clearng prce may caue overloadng of ranmon lne n compeve marke. Opmal real power chedule relaed o mnmum co need o be recheduled for avodng lne overloadng. In h paper, ranmon congeon allevaon done by changng he paern of real power generaon from he dfferen generaor. The obecve of h work o mnmze he co nvolvng n rechedulng of real power for managng ranmon congeon. Tranmon congeon co he obecve and he conrol varable n h problem are he real power oupu from dfferen generaor of he yem. The generaor ha are more enve o he power flow n he congeed lne are denfed wh he help of real power envy ndex. The generaor ha are more reponble for he congeon n a lne are gven more prory n h rechedulng problem. A new opmzaon mehod baed on he recenly propoed black hole algorhm (BHA) ued for denfyng he opmal generaon paern for avodng congeon. The algorhm mmc he exence of black hole n he pace and eay o be mplemened for any opmzaon problem. The effecvene of he algorhm valdaed by eng on he modfed IEEE-30 bu yem. The reul obaned are compared wh ha of parcle warm opmzaon (SO) and bg bang bg crunch (BBBC) algorhm. The obaned numercal reul are much encouragng and valdaed. INTRODUCTION In general, deregulaed power marke are wh lmed reource of power ranferrng capably becaue of envronmenal, rgh-of-way (ROW) and oco-economc reaon. Generaon chedule correpondng o markeng clearng prce reul moly n ncreaed power lo and poe hrea o he ecury of he power yem nework (De Vre, 200) and (Lommerdal and Soder, 2003).Congeon relef neceary and varou congeon managemen approache applcable for dfferen power marke are dcued n he leraure (Lo e al., 2000) and (Raeh and Jacob Raglend, 205). Sll he necey for new approache for olvng congeon managemen problem connue forever (Shrmohammad e al., 998). In (Verma and Mukheree, 206), opmal real power re-dpach uggeed for ranmon congeon managemen. Socal welfare maxmzaon baed ranmon congeon mehod dcued n Maoud and Aref (20). Drbued power generaor are dcued for congeon relef n power yem (Sarwar and Sddqu, 205). An alernave approach baed on opology change preened n Han and apavalou (205) a an effcen way of congeon mgaon. A coordnaed approach beween generang compane and yem operaor for congeon managemen ung Bender cu dcued by Yamna and Shahdehpour (2003). Open Acce Journal ublhed BY AENSI ublcaon 206 AENSI ublher All rgh reerved Th work lcened under he Creave Common Arbuon Inernaonal Lcene (CC BY). hp://creavecommon.org/lcene/by/4.0/ To Ce Th Arcle: Ramachandran R and Arun M., Senvy Baed Opmal Real ower Rechedulng For Congeon Managemen Ung Black Hole Algorhm. Au. J. Bac & Appl. Sc., 0(5): 83-93, 206

2 84 Ramachandran R and Arun M, 206 Auralan Journal of Bac and Appled Scence, 0(5) Ocober 206, age: Locaonal Margnal rce (LM) ued a a gnal for congeon managemen (Kumar and Mohan, 206) by adung he generaor power oupu. Flexble AC ranmon yem (FACTS) devce are ued for congeon managemen by changng he power flow paern n a power yem nework. Th approach uable only when he level of congeon mall. Some of he FACTS devce ued for ranmon congeon allevaon are: Thyror-Conrolled Sere Compenaor (TCSC) and Thyror Conrolled hae Angle Regulaor (TCAR) (ael and alwal, 205) and (Hoohmand e al., 205). Congeon caued by volage nably and hermal overload aken n (Suganh e al., 205). Real power rechedulng baed on relave elecrcal dance adoped o allevae lne overload n (Yeuranam and Thukaram, 2007). Th mehod doe no ake no accoun he opmzaon of co when he generaor have dfferen co funcon. Srvaava and Kumar (2000) followed load curalmen mehod for managng congeon n a nework. Recenly, evoluonary algorhm are propoed o opmze he rechedulng co of real power oupu from ynchronou generaor. Evoluonary rogrammng (E) algorhm ued for rechedulng of real power generaon for congeon managemen preened Ramaubramanan e al. (202). Opmal congeon managemen n an elecrcy marke ung baceral foragng opmzaon (BFA) done by angrah and and (2009). Valakh and Bakar (20) ued a modfed NSGA II algorhm baed model for he decenralzed congeon managemen problem n he deregulaed forward power marke. Bo geography algorhm baed loadably lm enhancemen preened n (Arunachalam and Logaman, 205) for congeon allevaon. In he preen work, he recenly developed naure npred mple and effcen echnque of BHA aken for mnmzng oal congeon co by he rechedulng of real power for congeon managemen. In h congeon managemen cheme by real power rechedulng n a generaor, he amoun of rechedulng of power decded by he envy of ha generaor o he power flow n he congeed lne. aern of changng he real power chedule no done n a random manner only he parcpang generaor are aken. Th mnmze he oal congeon co. The algorhm eay o mplemen and wh le number of parameer o be uned n obanng he nearly global be oluon. Black Hole henomenon: John Mchell and erre Laplace denfed he abence of ar by negrang Newon law bu he abence of ar wa no called a black hole n hoe day. John Wheeler, an Amercan phyc fr named he phenomenon of ma collapng or abence of ar a a black hole. A black hole n he pace lef when a ar or mave zed plane ge collaped. Black hole wallow and vanhe any obec ha come nearer o boundary. The phere-haped boundary of a black hole called a he even horzon whoe radu named a he Schwarzchld radu. The Schwarzchld radu calculaed by he followng equaon: 2GM R () 2 C Where, G he gravaonal conan, M he ma of he black hole, and C he velocy of lgh. Black Hole Algorhm (BHA) Haamlou, (203): Lke he oher mea-heurc algorhm, a populaon of randomly drbued canddae oluon are creaed n he problem pace. opulaon-baed algorhm ue dfferen echnque o move he ndvdual oward he global be oluon by a ceran echnque. For nance, muaon and croover are he echnque ued n GA. SO ake he ndvdual be and global be oluon for movng he nal oluon o he global be oluon. In BHA, he evoluon of he populaon acheved by movng all he canddae oward he be canddae n each eraon namely, he black hole and replacng hoe canddae ha ener whn he range of he black hole by newly generaed canddae n he oluon pace. In BHA he be canddae among all he canddae a each eraon eleced a a black hole. Then, all he canddae are moved oward he black hole baed on her curren locaon and a random number. The earchng mechanm of BHA a under: A randomly generaed populaon of oluon aken a he nalzaon proce. Then he fne value of he populaon are evaluaed and he be oluon whoe fne value he be one he black hole. Afer nalzng he black hole and ar, he black hole ar aborbng he ar around and all he ar ar movng oward he black hole. The aborpon of ar by he black hole mahemacally formulaed a follow: x x rand(0,)( xbh, x ( )) (2) Where, x and x are he locaon of he h ar a eraon and, repecvely. x he locaon BH of he black hole n he earch pace. rand a random number n he nerval (0, ). N he number of ar (canddae oluon).whle movng oward he black hole, a ar may reach a locaon wh lower co han he black hole. In uch a cae, he black hole move o he locaon of ha ar and vce vera. Then he BHA wll

3 85 Ramachandran R and Arun M, 206 Auralan Journal of Bac and Appled Scence, 0(5) Ocober 206, age: connue wh he black hole n he new locaon and hen ar ar movng oward h new locaon. In addon, here he probably of crong he even horzon durng movng ar oward he black hole. Every canddae oluon ha croe he even horzon of he black hole wll be ucked by he black hole. Every me a canddae ar de and anoher canddae oluon born and drbued randomly n he earch pace and ar for a new earch. Th done o keep he number of populaon ze conan. The nex eraon ake place afer all he ar have been moved. The radu of he even horzon n he black hole algorhm calculaed ung he followng equaon: f BH R (3) N f Where, f he fne value of he black hole and BH f he fne value of he h ar. N he number of canddae oluon. When he dance beween a canddae oluon and he black hole le han R, ha canddae collaped and a new canddae creaed and drbued randomly n he earch pace. Baed on he above decrpon he flow char for BHA hown n fgure () Fg. : flow char for Black Hole Algorhm

4 86 Ramachandran R and Arun M, 206 Auralan Journal of Bac and Appled Scence, 0(5) Ocober 206, age: Implemenaon of BHA for congeon managemen: Sep : Inalze he algorhm parameer lke populaon ze, maxmum number of eraon and black hole. Sep 2: Each ndvdual a vecor of he conrol varable..e. X ]. N he number of [ g, g 2, g3, gn agen are generaed by repecng he lm of conrol parameer. Sep 3: Calculae he fne funcon value of all canddae oluon by runnng he NR load flow. Sep 4: Deermne he cener of ma whch ha global be fne ung equaon (3). Sep 5: Generae new canddae ung he cener of ma, parcle be and global be by addng/ubracng a normal random number accordng o equaon (2). Sep 6: Repea ep ep 2 o ep 5 unl oppng crera ha no been acheved. Mahemacal roblem Formulaon: 2. Formulaon of generaor envy ndex: The generaor n he yem have dfferen enve o he power flow hrough he congeed lne. A change n real power flow n a ranmon lne k conneced beween bue and due o change n real power generaon by generaor g can be ermed a generaor envy o congeed lne (GS) whch can be wren mahemacally a (Dua and Sngh, 2008) and (Venkaah and Kumar, 20). GS GS g (4) Gg Where he real power flow on congeed lne-k; h he real power generaed by he g generaor. Gg The real power flow hrough he congeed lne can be wren a: 2 V G VV G co( ) VV B n( ) (5) The fr erm of he wo produc n (6) are obaned by dfferenang (5) a follow: g Gg Gg (6) VV G n( ) VV B co( ) (7) VV G n( ) VV B co( ) (9) S S V The acve power neced a a bu- can be repreened a: (0) GS DS Where he acve load a bu-. DS V 2 n G can be expreed a S (( G co( ) B n( )) V ) V n {( G co( ) B n( )) V } () Where, n he number of bue n he yem. Dfferenang () w.r.. and S, he followng relaon can be obaned: (8)

5 87 Ramachandran R and Arun M, 206 Auralan Journal of Bac and Appled Scence, 0(5) Ocober 206, age: V V V { G n( ) B co( )} n {( G n( ) B co( )) V } Neglecng -V couplng, he relaon beween ncremenal change n acve power a yem bue and he phae angle of volage can be wren n marx form a: H (4) n nn n Where, 2 n 2 2 n 2 n H. (5) nn n n n 2 n Thu H M n n (6) (7) Where, M H (8) To fnd he value of / and / Gg Gg n (6), he marx M need o be deermned. However, [H] a ngular marx of rank one defcency. So no drecly nverble. The lack bu n he preen work ha been condered a he reference node and agned a bu number. The elemen of fr row and fr column of [H] can be elmnaed o oban a marx [ H ] whch can be nvered o oban marx [ M ], where (.) repreen a marx whoe fr row and column are deleed. Ung hee relaon he followng equaon can be obaned: M (9) The acual vecor [ ] can be found by mply addng he elemen o (9) a hown by he followng relaon: n 0 0 nn 0 M n (20) n The econd erm of he um n (20) vanhe a, beng he change n phae angle of lack bu zero. Accordngly, (20) reduce o: (2) (3)

6 88 Ramachandran R and Arun M, 206 Auralan Journal of Bac and Appled Scence, 0(5) Ocober 206, age: n 0 nn 0 M (2) n Thu requred elemen of / and / Gg Gg are found ou from (2). I o be noed ha he generaor envy value hu obaned are wh repec o he lack bu a he reference. So he envy of he lack bu generaor o any congeed lne n he yem alway zero. GS denoe how much acve power flow over a ranmon lne connecng bu and bu would g change due o acve power necon by generaor g. The yem operaor elec he generaor havng non unform and large magnude of envy value a he one mo enve o he power flow on he congeed lne and o parcpae n congeon managemen by rechedulng her power oupu. 3.2 The obecve funcon: The man am of h work o fnd he opmal rechedulng of acve power generaon baed on real power envy ndex of he generaor o a o mnmze he congeon co whle afyng he yem equaly and nequaly conran. The obecve funcon of h congeon managemen problem can be wren mahemacally a (andya and Joh, 203) and Gao e al. (205). ng mn TC ( C D ) $/hr (22) k G Where, TC he oal congeon co n $/hr C he ncremenal bdng co k D he decremened bdng co k k G G he amoun of acve power ncremen n he generaor. G he amoun of acve power decremen n he generaor. Equaly conran: Real power balance: g d N V V Y co( ) 0 (23) Reacve power balance: Q g Q d N V V Y n( ) 0 (24) c g g g g ;,2,3... ng (25) c dk dk ; k,2,3... Nd (26) Inequaly conran: Real power generaon lm: mn max ng (27) G G G,... Reacve power generaon lm: mn max Q Q Q ng (28) G G G,... Incremened or decremened real power lm: mn mn max max ( ) ( ) (29) g g g g g g g 0; 0 (30) g g

7 89 Ramachandran R and Arun M, 206 Auralan Journal of Bac and Appled Scence, 0(5) Ocober 206, age: RESULTS AND DISCUSSIONS The performance of he propoed algorhm n congeon co mnmzaon problem eed n he modfed IEEE-30 yem. The modfcaon dne n he andard IEEE -30 bu yem ha he generaor bue are numbered fr and he load bue follow. The modfed IEEE-30 bu yem con of 4 ranmon lne, 24 load bue and 6 generaor bue wh a bae load of MW real power and 26.2 MVAR reacve power. Lne daa and bu daa for boh he e cae yem aken from he (Balaraman and Kamara, 200). Here, wo cae congeon have been aken Cae A Ouage of lne -2 and Cae B a Load a all he bue are raed by 20%. 4. Cae: A Ouage of lne -2: Ouage of ranmon lne and conequen congeon condered n h cae. Lne ouage conngency creenng and rankng how ha lne -2 he mo crcal one n IEEE-30 bu yem. ower flow hrough he congeed lne (lne.e.-7 lne 7-8) and correpondng generaor envy ndce are gven n able.when lne -7 and 7-8 are congeed, generaor 3 conrbung more han he oher generaor n congeon. However, can be oberved ha almo all he generaor are conrbung conderably. Th becaue of he cloe nerconnecon among he yem componen. Table : Generaor Senvy facor (cae A) Congeed lne G G2 Lne Lne G3 Real power oupu of generaor 3 adued by large amoun for relevng congeon due o he ouage of he lne -2. erformance we BHA beer han he BBBC and SO algorhm. Toal congeon co uggeed by BHA only $ whle $ by SO and $ by BBBC. The co obaned by BHA, hown n able 2 much low and mprove he rengh of he algorhm. Table 2: Opmal rechedulng Recheduled power BBBC Technque SO Technque BHA Technque G G G G G G6 Congeon Co Lo I obvou from able 3 ha BBBC and BHA are behavng n he ame manner n adung he generaon for reducng congeon co. They ugge decremenal change n generaor and 5 and ncremenal change n he remanng hree generaor. For mnmum congeon co, BHA how relavely large change a generaor 2 han ha hown by. Table 3: Opmal change of real power Technque U/DOWN adumen of parcpang generaor (MW) G G2 G3 G4 G4 G5 G5 G6 G6 BBBC SO BHA ower flow n he lne of he yem under dfferen condon are compared n fgure 2. Ouage of lne - 2 reul n overflow n lne -7 and 7-8. The congeed flow n hee wo lne are removed by rechedulng of generaor power. I obvou from he fgure ha all he hree algorhm are ucceeded n congeon managemen.

8 90 Ramachandran R and Arun M, 206 Auralan Journal of Bac and Appled Scence, 0(5) Ocober 206, age: Fg. 2: ower flow hrough he lne (Cae A) Srengh of he propoed algorhm analyzed by he number of eraon ake for fndng he global be oluon. The algorhm manan he be oluon over dfferen eraon and converge o he global be oluon a abou he 8 h eraon hown n fgure 3. Tha whn 0 eraon be oluon reached. Th prove he rengh and relably of he algorhm. Fg. 3: Convergence behavour of BHA n cae A 4.2 Cae B: Load a all he bue are raed by 20%.: In h cae, congeon due o ncreaed load aken. Load a all he 24 load bue are ncreaed by 20%. The oal real and reacve power demand are ncreaed o MW and 5.44 MVAR.A a reul, lne -2 ge congeed. For rechedulng of real power, he generaor whoe generaon are more nfluencng he power flow hrough he congeed lne are denfed fr. The generaor envy ndce of all he x generaor are calculaed and gven n able 4. Senvy ndex of generaor 2 he greae among he ndce howng large nfluencng on he power flow n he congeed lne. Amoun of real power oupu from he generaor are adued accordng o he value of envy ndex. The more he value of he ndex he more he amoun of power adued. Table 4: Generaor Senvy facor of congeed lne (cae B) Congeed lne G G2 G3 Lne The new mehod uggeed run for mnmzng he oal congeon co. Congeon co opmal power oupu repored he hree mehod are compared n able 5. Congeon co found by BHA algorhm beer han he co repored by SO and BBBC algorhm. G4 G5 G6

9 9 Ramachandran R and Arun M, 206 Auralan Journal of Bac and Appled Scence, 0(5) Ocober 206, age: Table 5: Opmal rechedulng Recheduled power BBBC Technque SO Technque BHA Technque G G G G G G6 Congeon Co Lo In rechedulng of real power, all he hree algorhm are behavng n he ame manner. The change n power ncremenal a all he generaor bue. Becaue of hgh envy, amoun of power changed n generaor 2 he hghe one a hown n able 6. Table 6: Change n power Technque U/DOWN adumen of parcpang generaor (MW) G G2 BBBC SO BHA G3 For clear underandng of he congeon relef, power flow hrough he congeed lne -2 depced n fgure 4. BBBC ouperform he oher wo algorhm of SO and BHA n relevng he lne from exceve power flow. However, he obecve of mnmum co for removng congeon acheved only by he propoed BHA algorhm. G4 G5 G6 Fg. 4: ower flow hrough he lne (Cae B) Convergence characerc of BHA n h cae hown n fgure 5. The number of eraon aken o reach he be reul only 30. The number of eraon aken much encouragng and prove he effcency of he algorhm. Fg. 5: Convergence behavor of BHA n cae B

10 92 Ramachandran R and Arun M, 206 Auralan Journal of Bac and Appled Scence, 0(5) Ocober 206, age: Concluon: In h work, he new naure npred BHA algorhm adoped for he congeon managemen problem. The algorhm found o be wh le number of parameer need ha are o be uned and can be realzed n Malab codng wh lle effor. The man challenge n he operaon of rerucured power marke managng congeon and h work well addreed ung he propoed algorhm. To keep he congeon co mnmum, he parcpang generaor are more mporance for real power generaon adumen Senvy baed rechedulng of real power generaon followed n h work for congeon managemen. Tranmon congeon caued by lne ouage and overload are condered here. Three dfferen algorhm of BBBC, SO and BHA are ued for congeon managemen hrough real power rechedulng. The performance of he BHA eed on Modfed IEEE-30 bu yem. I obvou from he numercal reul ha he BHA algorhm perform beer han he oher wo algorhm. Congeon co repored by he propoed algorhm beer han ha by he oher wo opmzaon mehod. The algorhm relable wh regard o convergence qualy. The algorhm converge o he global be reul and ake le number of eraon. The preen work can be red ung oher conemporary algorhm or he ame work may be exended for addreng he ame problem wh dfferen caue of ranmon congeon. The caue congeon can be due o blaeral and mullaeral ranacon. REFERENCES Arunachalam, R.K. and. Logaman, 205. Enhancemen of Loadably Lm of Deregulaed ower Syem va Adapve Real Coded Bogeography-Baed Opmzaon. Auralan Journal of Bac and Appled Scence, 9(): Balaraman, S. and N. Kamara, 200. Congeon managemen n deregulaed power yem ung real coded genec algorhm. Inernaonal Journal of Engneerng Scence and Technology, 2(): De Vre, L.J., 200. Capacy allocaon n a rerucured elecrcy marke: echncal and economc evaluaon of congeon managemen mehod on nerconnecor. IEEE oro ower ech proceedng, : 6-. Dua, S., and S.. Sngh, Opmal rechedulng of generaor for congeon managemen baed on parcle warm opmzaon. IEEE Tranacon on ower Syem, 23(4): Gao, B., T. Ma and Y. Tang, 205. ower Tranmon Schedulng for Generaor n a Deregulaed Envronmen Baed on a Game-Theorec Approach. Energe, 8(2): Han, J., and A. apavalou, 205. Congeon managemen hrough opologcal correcon: A cae udy of Cenral Weern Europe. Energy olcy, 86: Haamlou, A., 203. Black hole: A new heurc opmzaon approach for daa cluerng. Informaon cence, 22(2): Hoohmand, R.A., M.J. Morhed and M. araegar, 205. Congeon managemen by deermnng opmal locaon of ere FACTS devce ung hybrd baceral foragng and Nelder Mead algorhm. Appled Sof Compung, 28: Kumar, K.R. and S.C. Mohan, 206. LM Congeon Managemen Ung Enhanced STF-LODF n Deregulaed ower Syem. Crcu and Syem, 7(09): Lo, K.L., Y.S. Yuen and L.A. Snder, Congeon managemen n deregulaed elecrcy marke. Inernaonal Conference on Elecrc Uly Deregulaon and Rerucurng and ower Technologe, DRT: Lommerdal, M., and L. Soder, Smulaon of congeon managemen mehod. In IEEE ower Tech. Maoud, M.R.F. and J.I. Aref, 20. Tranmon Congeon Managemen n Elecrcy Marke Rerucured and Increae he Socal Welfare on he Syem IEEE 4-Bu. Auralan Journal of Bac and Appled Scence, 5(2): andya, K.S., and S.K. Joh, 203. Senvy and parcle warm opmzaon-baed congeon managemen. Elecrc ower Componen and Syem, 4(4): angrah, B.K. and V.R. and, Congeon managemen ung adapve baceral foragng algorhm. Energy Converon and Managemen, 50(5): ael, H., and R. alwal, 205. Congeon managemen n deregulaed power yem ung fac devce. Inernaonal Journal of Advance n Engneerng & Technology, 8(2): Raeh, R and Dr. I. Jacob Raglend, 205. Mul-Obecve Congeon Managemen n a Deregulaed ower Syem - A Revew Auralan Journal of Bac and Appled Scence, 9(6): Ramaubramanan,., G.U. raana and K. Sumah, 202. Opmal locaon of FACTS devce by evoluonary programmng baed OF n deregulaed power yem. Brh Journal of Mahemac & Compuer Scence, 2(): Sarwar, M. and A.S. Sddqu, 205. Congeon managemen n deregulaed elecrcy marke ung drbued generaon. Annual IEEE Inda Conference (INDICON): -5

11 93 Ramachandran R and Arun M, 206 Auralan Journal of Bac and Appled Scence, 0(5) Ocober 206, age: Shrmohammad, D., B. Wollenberg, A. Vodan,. Sandrn, M. erera, F. Rahm and B. So, 998. Tranmon dpach and congeon managemen n he emergng energy marke rucure. IEEE Tranacon on ower Syem, 3(4): Srvaava, S.C. and. Kumar, Opmal power dpach n deregulaed marke conderng congeon managemen. Inernaonal Conference on Elecrc Uly Deregulaon and Rerucurng and ower Technologe, pp: Suganh, S.T., D. Devara and S.H. Thlagar, 205. An Improved Dfferenal Evoluon Algorhm for Congeon Managemen Conderng Volage Sably. Indan Journal of Scence and Technology, 8(24): -9. Venkaah, C., and D.V. Kumar, 20. Fuzzy adapve baceral foragng congeon managemen ung envy baed opmal acve power re-chedulng of generaor. Appled Sof Compung, (8): Verma, S., and V. Mukheree, 206. Opmal real power rechedulng of generaor for congeon managemen ung a novel an lon opmer. IET Generaon, Tranmon & Drbuon, 0(0): Valakh, S., and S. Bakar, 20. Mulobecve decenralzed congeon managemen ung modfed NSGA-II. Araban Journal for Scence and Engneerng, 36(5): Yamna, H.Y. and S.M. Shahdehpour, Congeon managemen coordnaon n he deregulaed power marke. Elecrc ower Syem Reearch, 65(2): Yeuranam, G. and D. Thukaram, Congeon managemen n open acce baed on relave elecrcal dance ung volage ably crera. Elecrc power yem reearch, 77(2):