Development of Hybrid-Coded EPSO for Optimal Allocation of FACTS Devices in Uncertain Smart Grids

Transcription

1 Avalable ole a Proceda Compuer Scece 6 (011) Complex Adapve Sysems, Volume 1 Cha H. Dagl, Edor Chef Coferece Orgazed by ssour Uversy of Scece ad Techology 011- Chcago, IL Developme of Hybrd-Coded EPSO for Opmal Allocao of FACTS Devces Ucera Smar Grds Hroyuk or, Hajme Fuja ej Uversy,Tama-ku, Kawasak, , Japa Ths paper preses hybrd-coded EPSO (Evoluoary Parcle Swarm Opmzao) for opmal allocao of FACTS (Flexble AC Trasmsso Sysem) devces ucera smar grds. The opmal allocao of FACTS devces s oe of he mpora acks ha crease odal loadably o maxmzg he supply of acve power a specfed odes smar grds. However, s o easy o deerme he opmal locao ad he opmal varable oupu of FACTS devces due o he olear mxed eger problem. Uder such crcumsace, requres a lo of compuaoal me cosderg he uceraes due o reewable eergy. I hs paper, a hybrd-coded scheme of EPSO s proposed o reduce compuaoal me ad maa soluo accuracy. The proposed mehod has advaage o deal wh real-coded ad eger-coded varables a he same me. The proposed mehod s successfully appled o a sample sysem. 011 Publshed by Elsever B.V. Ope access uder CC BY-NC-ND lcese. Keywords FACTS Devces; Loadably; Hybrd-Coded EPSO; Opmzao; ea-heurscs; Smar Grds 1. Iroduco Ths paper preses a hybrd-coded scheme of EPSO (Evoluoary Parcle Swarm Opmzao) for opmal allocao of FACTS (Flexble AC Trasmsso Sysem) [1], [] devces. The proposed mehod s appled o he maxmzao of loadably a cera odes ha correspods o dsrbuo compaes. To maxmze he odal acve power, FACTS devces are useful for corollg power flows, odal volage magude power qualy, rasmsso capably, ec. As he devces, he followgs are well-kow: SVC, TCSC, STATCO, UPFC, ec. UPFC s more aracve due o he flexbly ha hree varables of acve ad reacve power as well as volage magude chage he power flows. However, s o easy o deerme he opmal locao ad he opmal oupu of FACTS devces due o he olear mxed eger problem. The former s expressed dscree umber whle he laer s represeed couous oe. The coveoal mehods o he opmal allocao ad he oupu opmal varables of FACTS may be classfed as follows: 1) Sesve marx mehod [3] ) ea-heurscs [4], [5] Correspodg auhor o provde phoe: ; fax: E-mal address hmor@sc.mej.ac.jp Publshed by Elsever Ld. do: /j.procs Ope access uder CC BY-NC-ND lcese.

2 430 Hroyuk or ad Hajme Fuja / Proceda Compuer Scece 6 (011) ) Hybrd mea-heurscs [6-8] ehod 1) has he lmao ha s based o local formao. O he oher had, ehod ) s oe of opmzao mehods ha repeaedly make used of some rules or heurscs o oba beer soluos from a sadpo of global opmzao. The key po s ha mea-heurscs has a sraegy o escape from a local mmum alhough he coveoal mehods easly ge suck a local mmum. ehod 3) cosss of wo phases ha opmze he locao ad oupu of FACTS devces o evaluae he opmal soluo. The process of Layers 1 ad s repeaed o evaluae beer soluos alhough has a drawback o ake he compuaoal me. I hs paper, hybrd-coded EPSO s proposed o deal wh he uceraes of PV (Phoovolac) sysems. Ulke he coveoal mehods, hs paper hadles real ad eger varables hybrd code a he same me. To cosder he uceraes, oe Carlo Smulao (CS) s carred ou o deerme he opmal allocao of FACTS uder ucera smar grds. I s assumed ha some odes wh PV sysems brg abou probablsc varaos of geerao o smar grds. Hybrd-coded EPSO s a combao of dscree ad couous EPSO o reduce compuaoal me ad o mprove he soluo accuracy. The proposed mehod s successfully appled o a sample sysem.. EPSO.1 Oule of EPSO Ths paragraph descrbes EPSO [1, 13] ha s he mproved verso of PSO a way ha weghs are adapvely ued up o oba beer soluos. rada, e al. proposed EPSO o mprove he soluo qualy of PSO hrough roducg he evoluoary sraegy o PSO [14]. The coveoal PSO has a drawback ha ofe ges suck a local mmum. To overcome, EPSO mproves he movg rule of PSO ha makes use of replcao, muao, reproduco, ad aural seleco o modfy he weghs. The algorhm may be summarzed as follows: Sep 1: Se up he al codos for parameers such as he weghs, he maxmum erao cous, replcao rae, al ages, ec. Sep : Replcae each age. Sep 3: ove he ages ad he replcaed oes wh he movg rule of he velocy. Sep 4: Evaluae all he ages ad selec hem wh he seleco rule. Sep 5: Updae he bes soluos for each age ad he swarm. Sep 6: Sop f he algorhm reaches a he maxmum erao cous. Oherwse, reur o Sep. The movg rule of velocy may be expressed as 1 V w V w ( Pbes ) w ( Gbes S ) 0 1 w w N ( 0, 1 ) k Gbes k Gbes w 3 w 3 ' N ( 0, 1 ) S V 1 1 w 3 N ( 0, 1 ) where V : velocy of age a erao w 0 -w 3 : weghs Pbes (Gbes ): bes soluo for age (swarm) S : placeme of age a erao τ: learg raes (1) () (3) (4) (5). Bary EPSO Bary EPSO [15] s explaed hs paragraph. Bascally PSO was developed o hadle opmzao problems wh couous varables. As a resul, some geuy s requred o deal wh opmzao problems wh dscree

3 Hroyuk or ad Hajme Fuja / Proceda Compuer Scece 6 (011) varables. Keedy ad Eberhar proposed bary PSO ha modfed PSO updag he velocy ad he placeme as follows: 1 V V w Pbes x ) w ( Gbes x ) (6) 1 ) 1 exp( V ( 1 V 1 ) 1 ( rad() s( V s f ( 1 )) he x 1 1 ; 1 else x 0 where s( ): hreshold value for judgg wheher he bary value s 0 or 1 Bary PSO makes use of he sgmod fuco o rasform a couous varable o bary oe for he velocy hrough (8). The hreshold value vares wh he umber of erao cous ad coverges o a soluo. Ths paper roduces he evoluoary sraegy of EPSO o bary PSO o mprove accuracy. 3. Proposed ehod 3.1Oule of Proposed ehod I hs paragraph, he proposed mehod s ouled. As meoed before, mega solar sysems are posvely roduced o suppress he emsso of CO smar grds. To exame he fluece of he mega solar sysem o he loadably smar grds, hs paper evaluaes he characerscs of loadably uder ucera smar grds hrough CS. CS ad hybrd mea-heursc mehod are combed o solve he olear mxed eger problem of he opmal allocao of he FACTS devces so ha loadably s maxmzed a several odes. However, hey have a drawback erms of compuaoal me. Therefore, he proposed mehod makes use of hybrd-coded EPSO ha s a combao of dscree ad couous EPSO o reduce compuaoal me ad o mprove he soluo accuracy. Fg. 1 shows a cocep of hybrd-coded EPSO whch he locao ad oupu of FACTS devces are gve. The former s coded by he movg rule of dscree EPSO whle he laer s coded by couous EPSO. The key po s o rasform wo kds of codes o oe. Thus, hs paper evaluaes he fluece of erme reewable eergy o loadably a several odes wh hybrd-coded EPSO. 3. ahemacal Formulao Ths paragraph descrbes he mahemacal formulao of he opmal allocao of FACTS devces o maxmze he loadably a several specfed odes. I s assumed ha several specfed odes correspod o dsrbuo compaes ha eed acve power as much as possble. The mahemacal formulao may be wre as Cos Fuco: 1 f f ( f f f m (9) m 1 m 1 l ) 0 1 m 1 1 m 1l l 1 3 Cosras: g ( x, u ) 0 (10) m V V V (11) p p j j (1) 1k 1k k 1 k k k 1 V T T Q Q V (15) where, f 1 m l, f 1 : ILR(Icremeal Load Lae) a he specfc odes m ad l such ha (7) (8) (13) (14) (16)

4 43 Hroyuk or ad Hajme Fuja / Proceda Compuer Scece 6 (011) Locao (Ieger Varables) Oupu (Couous Varables) P P k 0 Fg. 1. Cocep of Hybrd-Coded EPSO k ILR (17) 0, 1,, 3 : parameers P k0 : acve power load a Node k for orgal power sysem codos P k : acve power load a Node k for power sysem codos wh corollers f : acve power loss g (.) : power flow equao x : odal volage vecor u : corol varable vecor correspodg o he opmal allocao of UPFC m V ( V ) : upper (lower) boud of odal volage magude a Node P : hermal lmao of he le ha coecs Node wh Node j j S S ) : appare power hrough he shu (seres) verer a UPFC k m 1 ( k 1 k V : T upper boud of he appled volage magude by UPFC Q : upper boud of he jeced reacve power by UPFC The frs erm s he adjusme parameer (9). The secod shows he maxmzao of ILR a he specfed odes a way ha coeffce α s egave ad he hrd oe meas equalzg ILR a each ode. The las erm dcaes he mmzao of acve power ework loss. Also, (10)-(16) show he cosras of hs problem. 4. Smulao 4.1 Smulao Codos 1) The proposed mehod s appled o he IEEE 30-ode sysem wh 41 les. I s assumed ha he umber of UPFC devces s wo. As a resul, he umber of he UPFC locao caddaes resuls 1640 f we cosder he dreco of he UPFC devces. The proposed mehod s repeaed ul he ermao codos are sasfed. ) Ths paper makes assumpo ha he UPFC devces have he followg cosras o volage, curre ad agle: Table 1. Smulao Codos ehod A ehod B ehod C 1s Layer d Layer 1s Layer d Layer No of Parcles No of Ieraos w w Wmax Wm Replcao Rae τ τ'

5 Hroyuk or ad Hajme Fuja / Proceda Compuer Scece 6 (011) ) The parameers of he cos fuco are gve as follows: 100, 10, 15, (1) They are deermed by he prelmarly smulao. For coveece, he followg mehods are defed: ehod A: TLPSO (Two-layered PSO) ehod B: TLEPSO (Two-layered EPSO) ehod C: HCEPSO (Hybrd-Coded EPSO of Proposed ehod) Table 1 shows smulao parameers ha are deermed by he prelmarly smulao. 3) I s assumed ha Nodes ad 9 have mega solar sysems, where he capacy of mega solar a Nodes ad 9 correspod o 0% of he specfed acve power. Nodes 14 ad 30 are seleced as he arge odes maxmzg loadably. The uceray of PV sysems s smulaed CS accordg o he relaoshp bewee oupu ad frequecy. Three hudreds of scearos are used o exame he performace of ehods A ad B. 4. Smulao Resuls Table shows a comparso of each mehod, where he bes, he wors ad average cos fucos are gve. I addo, he sadard devao of he cos fucos ad compuaoal me are show. I ca be observed ha ehod B s beer ha ehod A erms of he cos fucos. Tha s because he problem o be solved has a lo of local mma ad ehod B has beer sraeges o escape from hem. I s oeworhy ha ehod B succeeded reducg 17.85% ad 19.57% of he wors cos fuco ad he sadard devao, respecvely. O he oher had, ehod B eeds more compuaoal me ha ehod A. ehod C has almos he same performace as ehod B erms of he cos fucos ad sadard devao. However, shows 45.86% mproveme erms of compuaoal mes. Fg. gves he dsrbuo of ILR. I ca be see ha ehods B ad C provde a se of soluo ses ha s far from he org. Tha mples ha he soluos more dsa from he org brg abou more capacy of loadably. Also, he reaso why he crease of loadably a Node 14 s larger ha ha a Node 30 s ha Node 30 has he les wh he hermal lmaos. To vesgae he performace of he mehods, le us defe performace dex ILR as follows: ILR' ILR Node 14 ILR () Node30 Table 3 shows he frequecy of ILR' Areas 1-4 for each mehod. I ca be observed ha ehods B ad C gve beer soluo ses ha ehod A. Table 4 shows he frequecy ad locao of allocao of UPFCs. Table. Comparso of ehods A, B ad C ehods Cos Fucos Sadard Compuaoal Bes Wors Ave Devaos Tme[s] A B C ILR 14 Fg.. Dsrbuo of ILR of Each ehod

6 434 Hroyuk or ad Hajme Fuja / Proceda Compuer Scece 6 (011) Table 3. Frequecy of ILR of Each ehod Areas ehod A ehod B ehod C Table 4. Frequecy ad Locao of Allocao of UPFCs Paers Frequecy [%] UPFC 1 UPFC Cocluso Ths paper has proposed a hybrd-coded EPSO mehod for he opmal allocao of FACTS devces ucera smar grds. The proposed mehod s based o he combao of dscree ad couous EPSO o reduce he compuaoal me ad o mprove he soluo accuracy. As he hybrd-code, eger-codes are merged wh couous oes o express he opmal allocao ad oupu of FACTS devces. I was compared wh wo-layered PSO ad wo-layered EPSO he IEEE 30-ode sysem wh wo mega solar sysems. The smulao resuls have show ha he proposed mehod ouperforms he coveoal mehods erms of he cos fucos ad compuaoal mes. Therefore, he proposed mehod allows ework plaers o evaluae loadably ucera smar grds adequaely. Refereces 1 L. Gyugy, A Ufed Power Flow Corol Cocep for Flexble AC Trasmsso Sysems, IEE Proceedgs-C, Vol. 139, No. 4 (199) L. Gyugy, C. D. Schauder, S. L. Wllams, T. R. Rema, D. R. Torgerso ad A. Edrs, The Ufed Power Flow Coroller: A New Approach o Power Trasmsso Corol, IEEE Tras. o Power Delvery, (1995) C. Huag, H. Saoh ad J. Toyoda, Feaure Exraco for corollable Area of Power Flows Depedg o Phase Shfer Allocaos, Tras. IEE Japa, (1998) P. Paer, e al., Opmal Locao of Phase Shfers he Frech Nework by Geec Algorhm, IEEE Tras. o Power Sysem, (1999) Y. auo ad A. Yokoyama, Opmzao of Isallao of FACTS Devce Power Sysem Plag by Boh Tabu Search ad Nolear Programmg ehods, Proc. of IEEE ISAP 99, (1999) H. or ad Y. Goo, A Parallel Tabu Search Based ehod for Deermg Opmal Allocao of FACTS Power Sysems, Proc. of IEEE PowerCo 000, (000) H. or ad Y. aeda, Applcao of Two-Layered Tabu Search o Opmal Allocao of UPFC for axmzg Trasmsso Capably, Proc. of IEEE ISCAS 006, (006) H. or ad Y. aeda, A Hybrd ehod of EPSO ad TS for FACTS Opmal Allocao Power Sysems, Proc. of IEEE Ieraoal Cof. o SC 006, (006) S.N. Sgh, ad I. Erlch, Locag Ufed Power Flow Coroller for Ehacg Power Sysem Loadably, Proc. of 005 IEEE Ieraoal Cof. Fuure Power Sysems (CD), (005) 5 pages. 10 J.G. Sgh, S.N. Sgh, ad S. C. Srvasavah, Placeme of FACTS Coroller for Ehacg Power Sysem Loadably, Proc. of 006 IEEE Power Ida Cof.(CD), (006) 7 pages. 11 W Fag ad H.W. Nga, A Robus Load Flow Techque for Use Power Sysem wh Ufed Power Flow Corollers, Elecrc Power Sysems Research (000) V. rada ad N. Foseca, EPSO-Bes-of-Two-Worlds ea-heursc Appled o Power Sysem Problems, Proc. of IEEE Cogress o Evoluoary Compuao, Vol. (00) V. rada ad N. Foseca, EPSO-Evoluoary Parcle Swarm Opmzao, Proc. of 005 IEEE EBS 005, (006) J. Keedy ad R. Eberhar, Parcle Swarm Opmzao, Proc. of IEEE Ieraoal Jo Cof. o Neural Neworks, (1995) J. Keedy ad R. C. Eberhar, A Dscree Bary Verso of he Parcle Swarm Algorhm, Proc. of IEEE 1997 Ieraoal Cof. o SC (1997)