Solving Economic Emissions Load Dispatch problem by using Hybrid ACO-MSM approach

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1 Th Ol Joual o ow ad Egy Egg (OJEE) Vol. () No. () Solvg Eoo Essos oad Dspath pobl by usg Hybd ACO-MSM appoah a Wal.F. Abd El-Wahd a A.A.Mousa b M.A.Elssy Faulty of Coputs ad Ifoato, Shb El-Ko, Mufya Uvsty, Egypt. b Faulty of Egg, Shb El-Ko, Mufya Uvsty, Egypt. Bha Hgh Isttut of Thology, Bha Uvsty, Egypt. Abstat- Ths pap todus a soluto of th oo ssos load dspath (EED) pobl usg a hybd appoah of at oloy optzato (ACO) ad odfd spl thod (MSM). Th poposd appoah obs ad tds th attatv fatus of both ACO ad MSM, wh t s basd o ACO to gt appoat odoatd st of th pobl followd by MSM to pov th soluto. Th poposd appoah has b appld two tst apls ad th soluto s th opad wth that obtad by so oth thqus to pov th supoty ad fftvss of th poposd algoth. Kywods- Multobtv Dso Mag pobl, ato optal, At Coloy Optzato, Modfd Spl thod, oo ssos load dspath pobl. I. INTRODUCTION Th obtv of th Eoo Esso oad Dspath (EED) pobl of lt pow gato s to shdul th ottd gatg uts outputs to t th qud load dad at u opatg ost wth u sso whl satsfyg all uts ad syst qualty ad qualty ostats. EED pobl s o of th athatal optzato ssus pow syst opato attatg ay sahs tsts. EED pobl s a ultobtv athatal pogag pobl whh s od wth th attpt to obta th optal soluto whh sultaously optzs two ofltg obtvs. May appoahs ad thods w poposd to solv ultobtv oo sso load dspath pobls [4, 7, ]. Th us ad dvlopt of tahusts-basd ultobtv optzato thqus hav sgfatly gow. atal swa algoth s o of tahust algoths that hav b appld optzato tass suh as EED pobl [3, 7,, 3]. At oloy optzato (ACO) s o of th ost t tahust thqus fo appoat optzato so w usd t to solv ths pobl. Th fst ACO algoths w todud by Mao Dogo ad ollagus as a ovl atu-spd tahust fo th soluto of had obatoal optzato (CO) pobls th aly 99 s [,5,6]. ACO blogs to th lass of tahusts [], whh a appoat algoths usd to obta good ough solutos to had CO pobls a asoabl aout of oputato t. It s spd by th ats foagg bhavo, at th o of ths bhavo s th dt ouato btw th ats by as of hal phoo tals, whh abls th to fd shot paths btw th st ad food sous. II. MUTIOBJECTIVE DECISION MAKING ROBEM FORMUATION A ultobtv dso ag pobl (MODM) a b dfd as th pobl of fdg a vto of dso vaabls whh satsfs ostats ad optzs (z o az) a vto futo whos lts pst th obtv futos. Th athatal foulato of a MODM pobl s to optz dfft obtv futos -usually oflt wth ah oth- subt to a st of syst ostats [9]. optz f()=((),(),...,()) f f f subt to (,,...,) T G(),,..., J wh s a dsoal vto of dso vaabls ad also s alld th dso spa o sah spa, G,,,..., J a qualty ostats. Fo a pobl havg o tha o obtv futo (say, { f,,,...,, } ), ay two solutos ad a hav o of two possblts, o doats th oth o odoats th oth. A soluto s sad to doat th oth soluto, f both th followg odto a tu:. Th soluto s o wos tha all obtvs, o f ()() f fo all,,..., obtvs.. Th soluto s sttly btt tha at last o obtv, o f ()() f fo at last o {,,..., }. Dfto [9]: (ato optal soluto): s sad to b a ato optal soluto of ultobtv optzato pobl f th sts o oth fasbl (.., ) suh that, f ()() f fo all,,...,, ad f ()() f fo at last o obtv. III. ECONOMIC EMISSION OAD DISATCH Th oo sso load dspath hav two obtv futo ful ost ad sso obtvs whh a ofltg os. Th pobl a b foulatd as dsbd blow: T () Rf Nub: W9-8 3

2 Th Ol Joual o ow ad Egy Egg (OJEE) Vol. () No. () Obtv Futos Ful ost obtv: Th lassal oo dspath pobl of fdg th optal obato of pow gato, whh zs th total ful ost whl satsfyg th total qud dad a b athatally statd as follows: f ()()() $ / C a b h G G G () wh C : Ful ost of gato. a, b, : Ful ost offts of gato. : Out pow (p.u) by gato. : ub of gato. G Esso obtv: Th sso futo a b pstd as th su of all typs of sso osdd, suh as NO, SO thal sso, t., wth sutabl pg o wghtg o ah pollutat ttd. I th pst study, oly o typ of sso NO s ta to aout wthout loss of galty. Th aout of NO sso s gv as a futo of gato output, that s, th su of a quadat ad potal futo: () [ () p( G )] G / G () f to h wh,,,, : offts of th th gato's NO sso haatst. Costats: ow bala ostat: th total pow gatd ust supply th total dad ad th tassso losss wh (3) G D loss D s load dad, loss loss a alulatd by wh s tassso losss. B loss B a th lts of loss offt at B. Gato apaty ostat: Fo stabl opato al pow output of ah gato s sttd by low ad upp lts as follows: a,..., N (4) G G G Suty ostats: A athatal foulato of th suty ostad EED pobl would qu a vy lag ub of ostats to b osdd. Howv, fo su opato th tassso l loadg S s sttd by ts upp lt as: a S S (5)... : Th ub of tassso ls. IV. THE ROOSED AGORITHM I ths sto, w pst th poposd algoth. Fstly ACO was pltd to gt appoat odoatd st ND(). Sodly, odfd spl thod MSM was usd as a ghbohood sah g to pov th soluto qualty. Th poposd algoth s plad as follows. ACO Algoth Th ACO algoth has b usd to fd appoat odoatd soluto st of MODM. Th a haatst fatus of ths appoah sulats paalll dpdt us statgy [], wh w apply a squ of M olos osttutg a ha o followd th oth ad ah of th has ow paats. Also, t dffs fo oth appoahs slto podu whh, ah at oloy ostut ts solutos basd o a wght su of ultobtv ta, wh th wght attahd to ultobtv ta s ot ostat but adoly gatd. ado (.) w,,,.., (6) ado (.) wh ado (.) s a o-gatv ado ub. Fo quato (6) w a s that s a al ub th losd tval, ad w w (.). Evy at oloy ostuts ts solutos basd o dfft wght valus wly gatd by quato (6). Th obd ftss futo s dfd as: f w f () (7) Sav all th odoatd soluto podud by all M t olos tally th ahv A ND (). Updat ahv, Algoth s usd to updat th ahv. Tll ths ot w gt a appoat ato soluto, w s to pov th soluto qualty by gttg solutos o los to th tu ato optal soluto; w plt loal sah thqu as a ghbohood sah g. Th podu of MSM s dsbd th followg substo. Algoth : Ahv Updat. INUT A,. If ' A ' f th 3. A 4. ls f ' A f ' th 5. A { }\{ D} 6. ls f A ' f th 7. A { } 8. d f 9. OUTUT : A Modfd Spl Algoth Ths sto s otat dsbg o of loal sah thqu usd ola pogag [9] ad ts odfd fo to b sutabl to ultobtv optzato pobls. Th bas da th spl thod s to opa th valus of th obtv futo at th ( + ) vts of a gal spl ad ov th spl gadually towad th optu dug th tatv poss. Th a th opatos, ow as flto, otato, ad paso. Ou thod ts to pov a st of pots to gt odoatd soluto Rf Nub: W9-8 3

3 Th Ol Joual o ow ad Egy Egg (OJEE) Vol. () No. () los to tu ato optal soluto. Assu th obtad appoat odoatd st s pstd by ND(). Rflto: To pla ths thod, assu th a th pots,, 3 ND ad assu ths pots a aagd aodg to o of th obtv futos,,. A w pot obtad by fltg th pot (subspt dat th ddl pot) th oppost fa to hav w valu. Mathatally, th fltd pot s gv by () (8) s th tod of all pots pt 3 (9) s alld th flto offt.copag th gatd pot wth th st of pots,, 3. s plad by f F () doats F () ad psv ts fasblty, ls f F () ad F () a odoatd to ah oth, th a addd to th st,, 3 podug th st,, 3,. I th oth had f F () was doatd by F (), th otato poss wll b usd to gat a w pot. Algoth dsbs th a fatu of th flto poss. Algoth : Rflto poss. INUT ND (),. If () ND th f 3. ND}\{ U} ad go to Epaso poss 4. ls f () ND th f 6. ad ND go to Cotato poss 7. ls () f ND f th 8. ND () { U } 9. d f. OUTUT : A Epaso: If a flto poss gvs a pot fo whh F () doat F ().., th sultat st s th pots assu t s aly as,, 3 so w a gally pt to gt o aptd pots by ovg alog th dto potg fo to. H w pad to usg th lato: () () Algoth 3: Epaso poss. INUT ND (),. If () ND th f 3. ND}\{ U} 4. ls f () ND th f 6. go ND ba to Rflto poss 7. ls () f ND f th 8. ND} U 9. d f. OUTUT : A wh s alld th paso offt. Algoth 3 dsbs th a fatu of th paso poss. Cotato: If a flto poss gvs a pot fo whh a doatd by ay pot th st,, 3. I ths as w pot a gatd as follows: () () wh s alld th otato offt ( ). Algoth 4 dsbs th a fatu of th otato poss. Algoth 4: Cotato poss. INUT (), ND. If () ND th f 3. () ND}\{ U} 4. ls f () ND f 6. () ND 7.Rpla all () by( ND )/ 8. () ls f ND f th 9. () ND} U. d f. OUTUT : A Th psudo od of th poposd algoth s show fgu (). ACO Costut M olos. Italz th paats fo ah ACO, Italz ahv A t b Fo =: M Whl (Stop to has ot b satsfd) do Soluto Costuto ( ) hoo Updat ( ) Nodoatd solutos of oloy() t t A Updat ( A,) ND Ed Ed Ahv A ota all gatd appoatd odoatd solutos, MSM Fo =:sz( A,)- (,,) (),(),()a A f dsdg f f.. ay w t f Whl (th algoth do ot podu w pots) do Gat If (Rflto poss s sudd) Epaso poss If ls (Cotato poss s sudd) If (Rflto poss s sudd) Epaso poss Ed Gat w st of pots (,,) Ed Ed Fgu (): Th psudo od of th poposd algoth V. IMEMENTATION OF THE ROOSED AROACH Th thqus ad all sulatos dvlopd ths study w pltd o 3. GHz C usg MATAB laguag. Rf Nub: W9-8 33

4 Th Ol Joual o ow ad Egy Egg (OJEE) Vol. () No. () Th algoth dvlopd th pvous sto has b pltd to th stadad IEEE 3-bus 6-gato tst syst. Th valus of ful ost ad sso offts a gv Tabl (). To dostat th pottal of th poposd appoah fo dfft pobl oplts ad tad-off sufas, two dfft ass hav b osdd as follows. Cas ( A), fo opaso puposs wth th potd sults, th syst s osdd as losslss ad th suty osta s lasd. Covg of ful ost ad sso obtvs a show fgu (3). Cas ( B), ths as, th pow loss has b ta to aout. Th tassso loss B-offts a spfd [3]. Covg of ful ost ad sso obtvs wh optzd a show fgu (4). Th valus of th bst ost ad th bst sso obtvs wth th poposd appoah a gv Tabls (). ost Esso pow G G G3 G4 G5 G6 a b E-4 5E-4 E-6 E-3 E-6 E a Tabl (): Gato ost, apats ad sso offts of tst syst B= oposd algoth [3] Cas(A) Cas(B) Cas(B) G G G G G G Cost Esso osss Tabl (): Solutos oposg u ful ost ad sso Th sod tst syst ossts of th plats ad s gatos. Th tst syst osdd was dvd fo [7].Th gato data a gv Tabls (3). Th syst load was 9 w. Two dfft ass hav b osdd as tst syst. Covg of ful ost ad sso obtvs a show fgu (5) fo as (A) ad fgu (6) fo as (B). Th valus of th bst ost ad th bst sso obtvs wth th poposd appoah a gv Tabls (4) Fgu (3): Cas (A), Rsults of tst syst Fgu (4): Cas (B), Rsults of tst syst I ths substo, a opaatv study has b ad out to assss th poposd appoah og qualty of th ato st. O th fst had, volutoay thqus suff fo th qualty of th ato st. Thfo th poposd appoah has b usd to as th soluto qualty by obg th two ts of two hust algoths. Howv, th goal s ot oly to as th soluto qualty, but also to gat a pstatv subst, whh atas th haatsts of th gal st ad ta th soluto dvsty to osdato. O th oth had, lassal thqus a to gv sgl pot at ah tato of pobl solvg by ovtg th ultobtv pobl to a sgl obtv pobl by la obato of dfft obtvs as a wghtd su. O th otay, th poposd appoah s a husts-basd ultobtv optzato thqu wh, t uss a populato of solutos th sah, ultpl ato-optal solutos a, ppl, b foud o sgl u. ost Esso pow G G G3 G4 G5 G6 a b a Tabl (3): Gato ost, apats ad sso offts of tst syst. Rf Nub: W9-8 34

5 Th Ol Joual o ow ad Egy Egg (OJEE) Vol. () No. () B oposd algoth [7] Cas(A) Cas(B) Cas(A) Cas(B) G G G G G G Cost Esso osss Tabl 4: Solutos oposg u ful ost ad sso Fgu (5): Cas (A), Rsults fo tst syst Fgu (6): Cas (B), Rsults of tst syst V. CONCUSION I ths pap, w pst a w appoah fo solvg EED. Th thodology obs ad tds th attatv fatus of both ACO ad MS. Th algoth psts a w slto podu basd o a obd ftss futo ad pal sults show that ou appoah s vy fft to fd th tu ato optal solutos fo EED ad ay b vy hlpful studyg optzato pobls pow systs. 4 REFERENCES [] C. Blu, At oloy optzato: Itoduto ad t tds, hyss of f Rvws , 5. [] C. Blu ad A. Rol, Mtahusts obatoal optzato: ovvw ad optual opaso, ACM Coput., Suvys 35 (3) 68 38, 3 [3] Ca,. Ma, Q.,. ad H. g, A ultobtv haot patl swa optzato fo votal/oo dspath, Egy Covso ad Maagt, atl pss 9. [4] K. T. Chatuvd, M. adt,. Svastava, Modfd o-fuzzy uo-basd appoah fo oo ad votal optal pow dspath, Appld Soft Coputg 8, ,8 [5] M. Dogo ad T. Stützl, At Coloy optzato, Cabdg, MA: MIT ss, 4. [6] M. Dogo,V. Mazzo,A. Colo, ostv fdba as a sah statgy. Thal Rpot 9-6, Dpatto d Elttoa, olto d Mlao, Italy, 99. [7] C. alahay, N. S. Babu, Aalytal soluto fo obd oo ad ssos dspath, Elt ow Systs Rsah 78, 9 37, 8. [8] B.K. agah, V. Ravua ad, Saoy Das, Adaptv patl swa optzato appoah fo stat ad dya oo load dspath, Egy Covso ad Maagt 49, 47 45, 8. [9] S.S. RAO, Egg optzato Thoy ad at, Thd dto, Joh Wly & Sos, I., Wly East td, ublshs, ad Nw Ag Itatoal ublshs, td,996. [].K. Hota, R. Chaabat,.K. Chattopadhyay, Eoo sso load dspath though a tatv fuzzy satsfyg thod, Elt ow Systs Rsah 54,5 57,. [] T. Stützl, aalllzato statgs fo at oloy optzato,,odgs of aalll obl Solvg fo Natu, A. El, T. B.a, M. Shoau, ad H. Shwfl (Eds.), tu Nots Coput S, Vol. 498, pp. 7 74, Spg-Vlag, Bl,998. []. Wag, C. Sgh, Rsv-ostad ult aa votal/ oo dspath basd o patl swa optzato wth loal sah, Egg Applatos of Atfal Itllg, 98 37,9. [3]. Wag ad C. Sgh, Stohast oo sso load dspath though a odfd patl swa optzato algoth, Elt ow Systs Rsah 78, ,8. Rf Nub: W9-8 35