Avalable onlne at www.scencedrect.com Proceda Engneerng 7 (2010) 256 264 Proceda Engneerng 00 (2010) 000 000 Proceda Engneerng www.elsever.com/locate/proceda www.elsever.com/locate/proceda 2010 Symposum on Securty Detecton and Informaton Improved ant colony algorthm n the dstrbuton of reactve power compensaton devce and optmzaton Mng huang* School of Electrcal and Informaton Engneerng, Anhu Unversty of Scence and Technology, Huanan 232001,Anhu Abstract :Ant colony algorthm s a knd of smulaton of collaboratve optmzaton algorthm of ants foragng, mtatng ants dependence nformaton communcaton and socal behavor, showng n the agents, on the bass of the defnton of a greedy method under the gudance of the catalytc process gude each agent. Put forward mproved ant colony algorthm s appled to power system of reactve power optmzaton, to IEEE14 node system by smulaton calculaton, the optmal scheme of reactve power compensaton, the optmzaton desgn and mprovement of ant colony algorthm of the optmzaton results can be more effectvely at or near the optmal. c 2010 Publshed by Elsever Ltd. Open access under CC BY-NC-ND lcense. Keywords:Power Ant colony algorthmreactve power compensatonoptmzaton Improved ant colony algorthm 1. ntroducton In the electrc power load dstrbuton transformers, such as motor, most belongng to perceptual load, whch need to consume large amounts of reactve power, long-dstance transmsson, ncreased power loss. In the power of nstallaton shunt capactor such reactve compensaton devce, can provde the perceptual load of reactve power consumed, namely the reactve power compensaton. In Chna, the lowest level dstrbuton network loss, unversal, low voltage qualfcaton rate, n such crcumstances, the dstrbuton of reactve power optmzaton research has mportant practcal sgnfcance. The ant colony algorthm (ACA) s put forward n recent years to a new knd of smulated evolutonary algorthm, and fnally after multple teratve approxmaton problem wth mum probablty of optmal soluton. Ant colony algorthm s parallel to the postve feedback algorthm, has stronger robustness, easly wth other methods. Compared wth other ntellgent optmzaton algorthm has global searchng capablty, smple programmng, but generally takes a long tme, can use to search. Based on IEEE14 node as an expermental system smulaton system, reactve power compensaton devces to brng real utlty to power supply departments of persuasve power of reactve power compensaton wth the work. * Correspondng author. E-mal address: huangmng4852@163.com. 1877-7058 c 2010 Publshed by Elsever Ltd. do:10.1016/j.proeng.2010.11.041 Open access under CC BY-NC-ND lcense.
M. Huang / Proceda Engneerng 7 (2010) 256 264 257 2. mprovement of ant colony algorthm 2.1 ant colony algorthm Ant colony algorthm s n the smulated annealng algorthm, tabu search algorthm and genetc algorthm, the artfcal neural network algorthm and so on a seres of heurstc search algorthm and an applcaton of ntellgent optmzaton problem n the heurstc random search algorthm, show n complex optmzaton problem of ntellgent mproved ant colony algorthm has a lot of advantages. Ant colony algorthm s based on the bologcal, when the ant search for food or n the nest n the path to the land, they left chemcals, namely, make certan nformaton wthn the scope of the other ants can perceve and nfluence ts behavor. When a path through the ant, leavng the pheromone more and more, so that the choce of the path of ants later hgher probablty, and ncrease the path to attract ntensty, ant colony on the nternal mechansm of formaton of bologcal assocaton, gradually formed a pror to ther own unaware of the shortest route. Ant colony algorthm s requred n each of the search space namely ant, an ant optmzaton functon by a ftness value determned accordng to hm, the ant s how much of the nformaton surroundng the drecton of ther decson, ants and the road release nformaton, to nfluence other ants. 2.2 Smple ant colony algorthm Consder target functon: { ( ) L L L f f x xb } B {0,1} 0 f( x) Set t moments of L ant colony At ( ) { a0( t), a1( t),... ak( t)... an( t)}, ak () t B, N for ant colony optmzaton scale L defnton, X k( At ( )) ak( t). For x B, the defnton of x = 0, 1 (j j. l. - 1,...), the scope for {0,1}. Set nformaton collectonwt ( ) { w00( t), w10 ( t),... wj ( t),... w0 L1( t), w1 L1( t)}, 0,1 j 1,2... L1 (1) t = 0, constant; (2) For k 1~ N, j 1~ L1 do rj( ak( t )), Accordng to ( wj ( t)) ( Ej ) pmut probablty: Pr j ( t) (1 pmut ), Take t for 0,1, 0 p 1 ( w ( t )) ( E ) ( w ( t )) ( E ) mut. 2 0 j 0 j 1j j E0 j and E 1 j n j bts from respectvely 0 and 1 statc nspraton. (3) For 0~1, j 0~ L 1, a0 ( t) ab ( t), b {0,1,... N}, wj () t wj ()(1 t ),0 1, s attenuaton coeffcents. (4) For k 1~ N, j 0~ L 1, wr ( ( )), ( 1) ( ( )), () / ( ()) j ak t jt wr j ak t jt f akt, s constant. (5) to t = t + 1, f t meet beforehand, gven the mum number of teratve optmzaton s not clear when or f ( a0( t ) output current, the optmal soluton a 0 () t, Otherwse, to the second step. 2.3 Improved ant colony optmzaton algorthm The ant colony algorthm and optmzaton process has three aspects: choce mechansm, update mechansms and coordnaton mechansm. In the process of selectng mechansm, the ant colony algorthm through postve feedback optmal soluton s the prncple, strengthen f evolutonary eras to a certan degree, the premature stagnaton phenomenon, and the optmal soluton s local optmal, In the update mechansms, most ant colony algorthms are neglected to understand. In vew of ths, n the mathematcal model of conventonal by ntroducng "together" to measure the soluton, thus even the strategy decson nformaton updates every choce and the probablty of path. If you have a test on the path of ants dstrbuton s dspersve, together, thus dffcult to strengthen lesser degree, so that the optmal nformaton search slower, must strengthen the postve feedback nformaton, make a few several excellent path wth the larger probablty s selected, when only the nformaton updates, several more optmal path of nformaton can get mum enhanced. Conversely, when the test path when the ant on the dstrbuton, large cluster degrees, causng premature and stagnaton, ntellgent optmzaton s to make soluton, so you should let tend dversfcaton of path has certan probablty selected by dynamc adaptve, adjust and more nformaton on the path s mproved, and can effectvely mprove ant search speed of n the meantme also can avod local optmzaton. Therefore, we
258 M. Huang / Proceda Engneerng 7 (2010) 256 264 mproved ant colony algorthm teratve process, the choce of the path for ants weght nformaton accordng to the path of may gather to determne the degree, thus to determne the selected probablty. In the update process, mprove the mechansm of ant colony algorthm based on nformaton through the evenness of adaptve to update the nformaton, the dynamc adjustment n the path of nformaton dstrbuton, unapt too centralzed or dsperson, meanwhle enables convergence speed and prevent premature. Improved ant colony algorthm s based on the dstrbuton of each path wthn the scope of the bad or good degree and consttute soluton, dynamc update nformaton weght nformaton, a seres of teratve calculaton, and fnally acheve nformaton dstrbuton, realze adaptve optmzaton of complex problems. 2.4 Improved ant colony algorthm of adaptve range Improved ant colony algorthm of ntellgent optmzaton thought through the path to measure the dstrbuton unformty nformaton, we search process accordng to the ants were obtaned n the dstrbuton of the bad or good degree of reconclaton effectvely adjust the route nformaton updates strategy and the probablty of path choce of ants, makes the ant colony algorthm convergence and stablty are must mprove convergence speed, and solved the premature stagnaton phenomenon and the contradcton between the way, at the same tme, the soluton s more dversty, overall, sutable for large-scale complex problems. 3. Reactve power optmzaton model s establshed Reactve power optmzaton model s a very complcated problem, man features are: nonlnear, dscrete and large scale, the convergence of the ntal dependence. To make the system network loss and node voltage offset, t must be combned mnmum power reactve power optmzaton model of mult-objectve n certan constrants. Accordngly, the reactve power optmzaton mathematcal model should nclude object functon, varable constrant equatons and power constrant equatons. (1) the objectve functon The goal of the reactve power optmzaton, ncludng economc goals and performance targets. The objectve functon s satsfacton to reactve satsfacton and overall satsfacton as voltage contents, comprehensve satsfacton as the objectve functon. In 1965 Harrngton satsfacton functons, put forward the general thought s a response to all responsve varable synthess n specfc varables, and the functon of each response under the satsfacton of values between 0 ~ 1, dyd ( Y )( 1,2,... r) and dy ( ) wth the ncreasng or decreasng the correspondng satsfacton,those dy ( ) geometry average defnton as much response system overall satsfacton, realzng the functon of many response varables nto sngle response varables, then a group of controllable varable portfolo X. Based on the synthess of satsfacton: TranNum nb U O, U 1 1 S S (1 ) S S show voltage satsfacton wth adjustable transformer (near the load sde nodes), S O show reactve power balance of satsfacton (except all nodes), 0 1,the relatonshp of scale, satsfacton and reactve voltage (Voltage and reactve satsfacton), the satsfacton of actual applcaton Q Qo 1 0.6, Q o Q Q Q Qo QQo usually take 0.5. S U accordng to the followng defnton: SQ 10.6, Qmn Q Qo, Qmn Qo 0, else Q for moment reactve power; Q mn, Q s the mnmum and mum allowable reactve power. Qo s reactve expectatons. We defned target functon P S, s penalty. Accordng to the defnton of the
M. Huang / Proceda Engneerng 7 (2010) 256 264 259 1, followng ways: Node voltage n qualfed for 1, wthn the lmts for when the node voltages for,,here s small postve. Here we take 0.000000001, n the lmted power nodes, punsh, correct results wthout effect. (2) Varable constrant equaton To make the safety of the electrcty system operaton, need certan constrants can guarantee, generally make power voltage of blast V G, Reactve power compensaton equpment capacty Q C, adjustable transformer onload tap postons T as the control varables. Select node voltage ampltude V and reactve power generators QG as state varables. Lst nequalty constrants: VG mn VG VG, T mn T T, QC mn Q QC,Power voltage of blast upper and lower lmts: V G, V G mn.adjustable transformer on-load tap postons upper and lower lmts: T, T mn.reactve power compensaton equpment capacty upper and lower lmts: Q C, Q C mn. State varable constrant nequalty: QG mn QG QG, Vmn V V.Node voltage ampltude upper and lower lmts: V, V mn.reactve power generators upper and lower lmts: Q G, Q G mn. (3) Power constrant equaton: P V Vj( Gj cosj Bjsn j), Q V Vj( Gjsnj Bjcos j), jh jh PG PL P 0, QG QC Q QL 0.In the equaton V, Q, P as node of voltage, njected nto reactve and actve; j as node I and node j voltage phase dfference, G j, B j as node admttance matrx elements of the magnary part and real part. H s drectly connected wth node all the nodes ponts. 4. Improved ant colony algorthm s appled to optmal dstrbuton of reactve power compensaton scheme The mproved ant colony algorthm s appled to reactve power optmzaton, need to have the followng: the defnton of adaptve ant colony, pheromones weght and transton probablty, transfer strategy, adaptve pheromones and teratve end condtons. 4.1 The defnton of adaptve ant colony optmzaton (1) Gather degrees: We have ants n m only as I startng r path, the unform dstrbuton n every road s m/r ant, we defne the r m 2 cluster nodes : jd() ( ak ) 0, when m ant focused on startng wth nodes n the path of r a certan, k 1 r r1 m 2 m 2 1 the gather degrees n node : jd( ) ( ) ( ) m 1. k 1 r r r (2) Optonal path: For the gather degrees n node jd() n the current node determne the ant choce of the path to step n, such as mproved ant search speed can also avod local optmzaton, take jd() pathselectnumber() [ ( r 1) 0.5] 1. jd ( ) (3)Vst degrees
260 M. Huang / Proceda Engneerng 7 (2010) 256 264 Vst degrees expressed ant colony optmzaton path constrant, the ratonalzaton of transfer n HengZuoBao I ( r path( k, j) j ) can vst, ncludng j expressed as kj. r 4.2 Transton probablty and pheromone weght We have to start wth I r path by pheromone strength, the seral order n stored n the array xnxsuorder smply speakng, array xnxsuorder( j) element s the path ( j ) to the value of the concentraton of pheromone arranged seral number, pathselectnumber() s the path of pheromone strength pathselectnumber() arranged smply, the sequence of array element s value,set q,as r xnxsuorder[ j] q 1, xnxsuorder[ j] pathselectnumber( ) j 0, otherwse j s the path ( j ) s pheromone weght. Rely on pheromone weght, the probablty of ants under by node I choose j jj, k j allowed k node j. Pj K allowed j j k 0, otherwse 4.3 Path transfer strategy: Due to the convergence speed and the optmal soluton of the problem, we put the adaptve factors n each tme the ant transfer from dstance, transfer, the volume s small ponts, whereas larger. Choose transfer ponts n 1, pos lastpos probablty of pos, last lastpos ponts for each step, the volume for: poschange, thus n 1, pos lastpos the convergence speed and stagnaton of balance, realze adaptve optmal selecton of the path. 4.4 Adaptve pheromone refresh strategy and calculaton method Because nformaton evenness can adaptvely updated nformaton, so can dynamcally adjustng the path of nformaton dstrbuton, can accelerate convergence, and can avod precocous, thus not overly dspersed or excessve concentraton. Accordng to the followng strategy update nformaton of the whole: m j ( t1) (1 ) j () t lj () t l1, FL s The L ant the path length. Q/ F l L j () t 0 Ant colony algorthm (mnmum value s, the paper dstrbuton of reactve power optmzaton objectve functon s the mum functon. Thus we should ask the objectve functon s mnmum mappng, so as to solve the problem of the optmzaton of reactve power compensaton. 4.5 Iteratve end condtons In the cycle N, N N and 3/4 above the ants on a path, or when N N end the teraton. Through the whole process from the start, a seres of operatons ntalzed to end, acheve optmal parameters, concrete process can partcpate.
M. Huang / Proceda Engneerng 7 (2010) 256 264 261 5. Examples analyss Accordng to ths reactve power optmzaton s based on mproved ant colony algorthm, we IEEE14 accordng to the followng steps to node smulaton: (1) the assumpton of reactve power compensaton devces on the entre network load node, (2) gve the dsturbance, reactve power optmzaton scheme, reactve compensaton devce s prohbted. (3) compared to the pont where the acton of reactve power compensaton, by comparng the movement, the less node reactve power compensaton devces, If (4) n the current reactve compensaton devces nstalled, under the ste to step (2) contnue, (5) n steps (2), n a node n the restrcton condton, voltage, mmedately stop judgng here should be nstalled reactve compensaton devces. In step (3) process for the next few node, return to step (2), When all the voltage s the voltage dsturbance condton, here permanently elmnate restrcted node reactve power compensaton devces nstalled. (6) completed the crculaton, get out successve optmal reactve power compensaton equpment nstallaton locaton. Through smulaton, the fgure 2, reactve power compensaton devce at each node, the voltage fluctuaton on expectatons of 1.0 slghtly, t explans n proper place nstallaton reactve power compensaton devces, accordng to mprove qualty of voltage dstrbuton expectaton, thus, method s feasble.
262 M. Huang / Proceda Engneerng 7 (2010) 256 264 START Intalzaton (read cycle parameters, the grd number, ant number etc.) Random generaton m path Intalzaton parameter =1 The adaptve probablty calculaton and transfer of ants =+1 <TN+nb+1 Y N Update matrx bus and matrx lne Calculaton of adaptve updatng the pont pheromone strength Calculate target functon, select the optmal parameters Update sequence tab and c N=N+1 Y N<N N The optmal parameters extracton END Fgure1. Improved ant colony algorthm reactve power optmzaton flow
M. Huang / Proceda Engneerng 7 (2010) 256 264 263 Fgure 2. Not have reactve compensaton devce voltage curve Fgure 3. have reactve power compensaton devce voltage curve
264 M. Huang / Proceda Engneerng 7 (2010) 256 264 6. concluson Based on a new ntellgent optmzaton algorthm mproved ant colony algorthm s used to optmze the reactve power compensaton devces, establshed mult-objectve nonlnear optmzaton model of reactve power, through the use of MATLAB language IEEE14 node system smulaton, through the smulaton dagram can see, ths s based on mproved ant colony algorthm of reactve power optmzaton allocaton scheme can better determne the locaton of reactve power compensaton devces, mproved ant colony algorthm of general ntellgent optmzaton algorthm s robust and hgher n solvng large-scale optmzaton problem, can have a better soluton actual applcaton prospect n the current dstrbuton of reactve power compensaton equpment nstallaton, to study the optmzaton of reactve power compensaton devce confguraton s of far-reachng sgnfcance. References [1] XongXn slver, WuYaoWu. genetc algorthm and ts applcaton n power system, [M], wuhan huazhong unversty press, 2002. [2] HuangYouRu, ntellgent optmzaton algorthm and ts applcaton [M], Bejng, and defense ndustry press. 2008; 119-138. [3] LuKeYan, ChengWanXng, LYunHua. based on the mproved genetc smulated annealng method, the reactve power optmzaton [J], the grd technology 2007. [4] YangJanJun, red, LuChengJe, reactve power compensaton dstrbuton crcut on the optmzaton of genetc algorthm, the mproved [J], power system protecton and control. 2010; 1. [5] based on LuoWenGuang cppga mproved nche genetc algorthm, the power system reactve power optmzaton [J] electromechancal 2009; 6. [6]XongHu, ChengHaoZhong, WangJaXan, GeChangHong, based on mmune algorthm of multobjectve programmng, reactve power compensaton [J]. hydropower scence 2007; 4. [7] n Asa to compensate the genetc algorthm to realze postonng pont dstrbuton network, reactve power optmzaton [J], journal of engneerng nsttute of scence and technology, xan, 200; 12. [8] LuJunHua, square pgeons fly, LvYanYan, based on the senstvty of reactve power compensaton method s used to determne locaton, power system and ts automaton [J], journal 2006. [9] Dorgo M, Manezzo V, Colorn A, Ant system: optmzaton by acolony of cooperatngagents,ieee Trans on Systems, Man, and Cyber netcs-part B, Cybernetcs, 1996.