Research Article Improved Quantum Artificial Fish Algorithm Application to Distributed Network Considering Distributed Generation

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1 Computatoal Itellgece ad Neuroscece Volume 215, Artcle ID , 13 pages Research Artcle Improved Quatum Artfcal Fsh Algorthm Applcato to Dstrbuted Network Cosderg Dstrbuted Geerato Tgsog Du, 1,2 Yag Hu, 1 ad Xatg Ke 1 1 Departmet of Mathematcs, Scece College, ChaThreeGorgesUversty,Ychag4432,Cha 2 Hube Provce Key Laboratory of System Scece Metallurgcal Process, Wuha Uversty of Scece ad Techology, Wuha 4381, Cha Correspodece should be addressed to Tgsog Du; tgsogdu@ctgu.edu.c Receved 28 May 215; Revsed 2 August 215; Accepted 1 August 215 Academc Edtor: JoséAlfredoHeradez Copyrght 215 Tgsog Du et al. Ths s a ope access artcle dstrbuted uder the Creatve Commos Attrbuto Lcese, whch permts urestrcted use, dstrbuto, ad reproducto ay medum, provded the orgal work s properly cted. A mproved quatum artfcal fsh swarm algorthm (I) for solvg dstrbuted etwork programmg cosderg dstrbuted geerato s proposed ths work. The I based o quatum computg whch has expoetal accelerato for heurstc algorthm uses quatum bts to code artfcal fsh ad quatum revolvg gate, preyg behavor, ad followg behavor ad varato of quatum artfcal fsh to update the artfcal fsh for searchg for optmal value. The, we apply the proposed ew algorthm, the quatum artfcal fsh swarm algorthm (), the basc artfcal fsh swarm algorthm (), ad the global edto artfcal fsh swarm algorthm () to the smulato expermets for some typcal test fuctos, respectvely. The smulato results demostrate that the proposed algorthm ca escape from the local extremum effectvely ad has hgher covergece speed ad better accuracy. Fally, applyg I to dstrbuted etwork problems ad the smulato results for 33-bus radal dstrbuto etwork system show that I ca get the mmum power loss after comparg wth,, ad. 1. Itroducto Dstrbuted geerato (DG) s small-scale ad radal geeratg facltes, whch are placed the vcty of the load, delverg electrcty to cosumers depedetly. Compared wth the tradtoal ad cetralzed power, DG has may advatages [1, 2] such as beg ear to the ceter of the users ad havg hgh eergy effcecy ad lower cost of costruct. Studes show that DG grd coecto has sgfcat mpact o the dstrbuted etwork, cludg power flow, voltage profle, system losses, ad relablty, the exted of whch has somethg to do wth the locato of tmately [3 5]. O the oe had, the sutable stallato posto ad capacty ca mprove the voltage qualty effectvely ad reduce the actve loss; o the other had, usutable cofguratotursouttobejusttheoppostewshad threat to the safe ad stable operato of the power etwork. There are may approaches for decdg the optmum szg ad sttg of DG uts dstrbuto systems. Some of them rely o covetoal optmzato methods ad others use artfcal tellgece-based optmzato methods [6]. The ew methods of dstrbuto etwork programmg, Geetc Algorthm (GA) [7, 8], At Coloy Algorthm (ACA) [9], Partcle Swarm Algorthm (PSA) [1], ad Chaos Algorthm (CA), have advatages ad dsadvatages, respectvely. The robustess of the GA s strog addto to ts ablty to be trapped a local mmum. Ital partcles geerated by CA have property of ergodcty but slower covergece speed. Therefore, how to effectvely combe the merts of dfferet tellget algorthms to mprove the performace amog search algorthm s a worth studyg drecto [11 13]. Basc artfcal fsh swarm algorthm () s a kd of tellgece optmzato algorthm based o amal behavor by L et al. 22 [14]. Accordg to the characterstcs of the fsh swarm ad ts amal autoomous model, t smulates behavor of fsh to acheve the purpose of the group global optmzato by each dvdual the local optmzato. The ma fsh behavors are the followg: foragg, huddlg, followg, ad beg radom. I almost all the cases, the s easy to avod fallg to local optmum ad obta the global optmum. Although the algorthm wth the merts of strog robustess ad good covergece performace

2 2 Computatoal Itellgece ad Neuroscece s ot sestve to tal value ad parameter selecto, t has the weakess wth search effcecy such as the poor ablty to keep balace of explorato ad developmet, late bld search, slow arthmetc speed, ad low accuracy of optmzato results. Quatum computg that s dfferet from the tradtoal calculato model of classcal physcs has comparable advatages such as quatum super parallelsm ad expoetal storage capacty [15]. The combato of quatum computg ad tellget optmzato algorthm jected ew lfe to the tellget optmzato computg source, by usg quatum computg a ew mode of represetg ad processg formato, ad so forth [16, 17]. Itellget optmzato algorthm ca be desged from aother agel to erch the theory of tellget computg ad mprove the tradtoal method of tellget search performace as awhole. I the preset paper, the mproved quatum artfcal fsh swarm algorthm (I) s proposed cosderato of the slow speed ad low accuracy of ad radomess ad bldess of quatum computg [18, 19]. The proposed algorthm mproves the codg way of the quts artfcal fsh ad uses quatum revolvg door, artfcal fsh followg, artfcal fsh preyg, ad varato of update strategy to complete self-reewal, resultg a ew artfcal fsh. I s the appled to solve hgh dmesoal ad complex ocovex programmg ad dstrbuted etwork programmg cosderg dstrbuted geerato. By smulato expermet amog, the global edto artfcal fsh swarm algorthm () has bee put forward [2] ad quatum artfcal fsh swarm algorthm (). The smulato results dcate that I has great covergece ad superorty fucto optmzato; meawhle, they llustrate the valdty ad feasbltyofiappledtooptmalcofguratoofdg dstrbuted etwork system. The rest of ths paper s orgazed as follows. We devote Secto 2 to a dscusso of those aspects of basc dea of.thedetaloquatumcomputgsthedscussed Secto 3. The update of the quatum bt eeds to make use of the trasformato of quatum gates. I Secto 4, the has bee formulated. The I gve Secto 5 s ecoded by quatum bts ad updated by quatum revolvg gate. Artfcal fsh perform preyg behavor ad followg behavor. I Secto 6, the effectveess of the algorthm compared wth those of,, ad for three multdmesoal ad box costrats programmg systems s demostrated except for oe twodmesoal box costrat programmg. Secto 7 deals wth the dstrbuted etwork modelg ad the effect of DGs o system losses. Fally, Secto 8 s devoted to drawg of the coclusos. 2. Descrpto of Artfcal fsh complete update ad obta the optmal value maly through the followg four behavors: beg radom, preyg, swarmg, ad followg the process of teratve calculato AF-Radom. Radom behavor s to radomly select a ew state x ext ts vsual feld ad the move a step the drecto. It s actually a default behavor AF-Prey. Preyg s a kd of the basc behavor of artfcal fsh, whch move to the drecto of food wth hgh cocetrato. The AF-preyg behavor s descrbed as follows: X ext { x k + Radom(step) x jk x k = { X, j X Y(X j ) s better tha Y(X ) { x k + Radom(step), else, where x jk s kth elemet of state vector; X j s kth elemets of X ; x ext s the ext step state vector; Radom(step) s a radom umber betwee ad step k=1,2,..., AF-Swarm. AF-swarm refers to the fact that every fsh moves to the ceter of the adjacet parters the process of swmmg as fast as possble ad avods overcrowdg. Suppose that X s the curret state of artfcal fsh. f s theumberofpartersadx c s the cetral posto the curret feld (d j < Vsual).IfY c / f >δy, t shows that there are more food aroud the parter ad ts ot too crowded. The, the fsh moves a step forward to the cetral posto of ths parter. The AF-swarmg behavor s descrbed as follows: X +1 =X t + X c X t X c X t step Rad ( ). (2) Otherwse, the fsh performs preyg behavor AF-Follow. AF-follow llustrates that each artfcal fsh moves to the curret optmal drecto the rage of vso. Suppose that X s the curret state of artfcal fsh. Y j s the greatest parter the curret feld (d j < Vsual). If Y j / f >δy,ttursouttobethattherearemorefoodaroud X j whle beg ot too crowded. The, the fsh moves a step forward to the drecto of X j.theaf-followgbehavors descrbed as follows: X t+1 =X t + X j X t X step Rad ( ). (3) j X t Otherwse, the fsh performs preyg behavor. I the problem of fucto optmzato. Suppose that a D-dmesoal search space goal, the umber of artfcal fsh s. The state of the dvdual artfcal fsh ca be deoted by vector X=(x 1,x 2,...,x ) ad x (=1,2,...,) whch s the optmzato varable. The food cocetrato of the artfcal fsh the curret locato ca be expressed as Y = f(x),wherey deotes the objectve fucto value. d j = X X j s the dstace betwee the fsh ad the fsh j. The dea of s that t frstly talzes a swarm of artfcal fsh radomly; secodly the fsh complete update by four basc behavors metoed above. Each of the artfcal fsh explores the curret evromet codtos (cludg (1)

3 Computatoal Itellgece ad Neuroscece 3 the chage of the objectve fucto ad parters). The, select a approprate behavor ad move the drecto of optmal areas. Fally, artfcal fsh gather aroud several local optmal, especally some better optmal areas, whch are geerally able to rally more artfcal fsh, amely, the optmal value of objectve fucto. 3. Quatum Computg Physcal meda actg as the formato storage ut are a two-state quatum systems quatum computg, to be referred to as quatum bt. A quatum bt ca be a state of quatum superposto represeted by φ = α + 1, where α ad β deote quatum bt probablty ampltude. The probablty of s represeted by α 2,adtheprobablty of 1 s represeted by β 2 ;furthermore, α 2 + β 2 = 1. Each quatum state system ca be expressed as the superposto of the basc state; as α 2 ad β 2 approach to be 1 or, the quatum bt wll coverge to a specfc state. The update of the quatum bt eeds to make use of quatum gates whch clude the xor gate, the cotrolled xor gate, Hadamard trasform gate, ad the revolvg gate. The quatum revolvg gate [21, 22] was adopted ths paper to chage ts phase by terferece ad the basc state probablty ampltude. The revolvg gate s descrbed as follows: cos (θ) s (θ) U (θ) =[ ], (4) s (θ) cos (θ) where θ deotes the rotato agle of the quatum gate; the updateprocesssasfollows: [ α β ]=U(θ) [α (θ) s (θ) ]=[cos β s (θ) cos (θ) ][α ]. (5) β The rotato agle of quatum gate s adjusted dyamcallywththeevolutoaryprocess,whlstrotatoaglesset larger at the begg of the algorthm. Wth the crease of evoluto geerato, the rotato agle s gradually reduced by formula θ=k s(α,β ),wherek s a coeffcet fluecg the speed ad s(α,β ) s the drecto of rotato agle. Emphass here s o the fact that f k s very large, the search step legth wll be very bg each terato the process of calculato. It s easy to fall to local optmal value. O the other had, f the covergece speed s slow, the computato tme wll be too log. I ths paper, k=1 exp( t/t),wheret deotes the curret evoluto geerato, ad T s the bggest evoluto geerato. s(α,β ) s to make the algorthm get the optmal soluto, the prcple of whch s to use the curret soluto to approach to the best soluto best, determg the drecto of rotato of the quatum revolvg gate. A adjustg strategy whch s geeral ad has othg to do wth the problem [23] s adopted ths paper. These strateges are descrbed Table Descrpto of The artfcal fsh s ecoded wth quatum bts. It maly uses update strategy of quatum revolvg gate for self-reewal to get ew artfcal fsh. Compared wth, the dversty of ts fsh becomes rcher. Despte the small scale of the fsh, t does ot affect the covergece of the algorthm. Atthesametme,thealgorthmhasfastercovergecespeed as well as hgher accuracy. Suppose that there s a quatum of artfcal fsh Q(t) = {q t 1,qt 2,...,qt },where deotes the populato sze, t s evoluto geerato, ad q t j represets a quatum artfcal fsh, whch s ecoded by quatum bt as follows: q t j =[αt 1 α t 2 α t m ], j=1,2,...,, (6) β t 1 β t 2 β t m where m deotes the quatum umber. A artfcal fsh ecodg wth multple quatum bts ca be represeted as [19] q t j =[αt 11 α t 12 α t 1k αt 21 α t 22 α t 2k αt m1 α t m2 α t mk β t 11 β t 12 β t 1k βt 21 β t 22 β t 2k ], (7) βt m1 β t m2 β t mk where m s varable dmeso of artfcal fsh optmal cotrol, k s quatum bt umber of optmal cotrol varables, α xy ad β xy (1 x m,1 y k)are complex costats, ad α xy 2 + β xy 2 =1. The quatum bts codg (α, β) of each dvdual s talzedto (1/ 2, 1/ 2). A measuremet s carred out for the talzato of the artfcal fsh order to obta a set of defte soluto P(t) = p t 1,pt 2,...,pt,wherept j s jth soluto tth geerato populato, whch s performed by bary strg of legth m, eachofwhchsor1ad gotte by the probablty of quatum bts. The measuremet process s radomly geeratg a umber betwee ad 1. If ths umber s greater tha α t 2, the result value s 1, otherwse.ieachterato,frstly,measurethepopulato to get a set of determate solutos P(t), ad the calculate the ftess value of each soluto. Usg quatum revolvg gate to adjust dvdual the populato to obta the updated populato, record the curret optmal soluto, ad compare wth the curret target value. If t s better tha the curret target, let the ew optmal soluto be a target for the ext terato. Otherwse, keep the curret target value the same.

4 4 Computatoal Itellgece ad Neuroscece Table 1: Chagg the agle value. s(α best,β ) α β > α β < α = β = ± ± ± ± Descrpto of I Despte the fact that ca reach hgh precso ad covergece speed, t may get some feror solutos whle producg better oe. The fsh dversty s ot very rch ad the covergece speed ca be further mproved. Therefore, the I gve ths paper s ecoded by quatum bts ad updated by quatum revolvg gate. Make t perform preyg behavor ad followg behavor. Ad swap quatum probabltyampltudeofartfcalfshhavgpoorresults ca realze the varato, ad the the optmal soluto s obtaed [24]. At the early stage of the quatum artfcal fsh optmzato, each tme the artfcal fsh has acheved a update, t wll tur to the mplemetato of the talgatg behavor of AFSA, whch ca mprove the covergece speed of artfcal fsh. At the late stage of the artfcal fsh quatum optmzato, each tme the artfcal fsh has realzed a update, t wll tur to the mplemetato of the preyg behavor of AFSA, whch ca mprove the accuracy of optmzato. Havg bee updated by quatum revolvg gate, preyg behavor, ad followg behavor, for those artfcal fsh havg poor optmzato results, t ca erch the dversty of the artfcal fsh by swappg the quatum bt probablty ampltude value, amely, (α, β), ad reversg the dvdual evolutoary drecto as a whole, whch ca prevet the dvdual evoluto fallg to a local optmum. Fally, the varato of artfcal fsh s brought about. Here a pot that should be stressed s that the Paul-X gate s used below to realze mutato operato: [ 1 1 ][α β ]=[β ]. (8) α Because the qualty of preyg ad followg behavor has close relato wth vso ad step of artfcal fsh. The results the lterature [22] show that the larger rage of vso s, the stroger global search ablty of artfcal fsh s ad faster covergece speed s. O the cotrary, the smaller rage of vso s, the stroger local search ablty of artfcal fsh s. Whlst the larger sze of step s, the faster covergece speed s; however, t wll tur out to be a oscllato pheomeo. O the other had, the smaller sze of step s, the faster covergece speed s, but there wll be the hgh precso of the soluto. Cosequetly, the dyamc adjustmets of artfcal fsh vso ad step sze are as follows: I steps are as follows. vsual = vsual a+vsual m, step = step a+step m, a=exp [ 3 ( t T )s ]. Step 1. Italze the quatum of artfcal fsh Q(t ) = q t 1,q t 2,...,q t the feasble rego, ad all optmal cotrol varables (α t,β t ) of the artfcal fsh populatos are talzed to (1/ 2, 1/ 2). Set up parameters such as the artfcal fsh vso, step legth, crowded degree, maxmum attempts, ad evoluto geerato. Step 2. Calculate the ftess of each artfcal fsh the populatoq(t); the determate soluto P(t) ca be calculated. Step 3. Coduct ftess evaluato for the determate solutos ad put the optmal artfcal fsh ad ts ftess value the bullet board. Step 4. Othebassoftheaboveadjustmetstrategy,frstly use the quatum revolvg gate U(θ) ad the correspodg rotato agle adjustmet polcy to update quatum bt of artfcal fsh Q(t + 1), ad perform preyg behavor ad followg behavor for artfcal fsh through the fsh evoluto process. Fally, ew artfcal fsh s gotte. Step 5. Perform mutato for artfcal fsh, choose q(q < ) artfcal fsh havg mmum ftess, ad update ts quatum bt probablty ampltude by usg formula (6). Step 6. If evoluto geerato acheves the maxmum, the outputtheresultothebulletboardasthefaloptmal soluto;otherwse,creasetheteratoumberbyg=g+1 ad go back to Step Smulato Expermet ad Aalyss I order to verfy the feasblty ad effectveess of I, four typcal fucto smulatos are proposed compared wth,, ad the lterature [2]: E.g. 1 [2]: m f 1 (x) = =1 s.t. 1 < x <1 E.g. 2 [2]: m f 2 (x) = 1 x 2 4 [x 2 1cos (2Πx )+1] =1 s.t. 1 < x < 1 =1 cos ( x )+1 (9) (1) (11)

5 Computatoal Itellgece ad Neuroscece 5 Table 2: (a) Results of smulato wth ad. (b) Results of smulato wth ad I. (a) fu dm max T A m G m σ A m G m σ f e e f e 2 4e 3 2.5e e e 4 4e 3 8.5e e 1 7e f e e e e f e e 15.5 (b) fu dm max T I A m G m σ A m G m σ f e e e e e e f e 3 1.e e 3 1.e e e e e e f e 8 3.7e e 8 3.7e e 8 3.7e e 8 3.7e e f e 1 1.6e e e 16 E.g.3[25]: m f 3 (x) = 2exp (.2 1 exp ( 1 =1 s.t. 32 < x <32 E.g. 4 [2]: =1 x 2 ) cos (2Πx )) e m f 4 (x 1,x 2 ) =.5 + s2 x 2 1 +x2 2.5 s.t. 1 < x 1,x 2 < 1. [1 +.1 (x 2 1 +x2 2 )]2 (12) (13) We ca fd the optmal value to be through the aalyss for fucto expresso ad the fucto mage showfgures1,2,3,ad4.thetheoretcalmmum value of these four multdmesoal fuctos are actually, where f 4 (x) s a two-dmesoal fucto; other fuctos are all multdmesoal fuctos. Use,,, ad I to get mmum value of four dfferet fuctos, respectvely. Parameter settgs are set as follows: fshum = 4, try-umber = 9, vsual = 1, δ =.618, step m =.2, s=2,step =.5,advsual m =.1. The maxmum terato s set to be 1 tmes ad 15 tmes. All algorthms ru 5 tmes from dfferet radom tal populato, respectvely. The global average mmum value, the global mmum value, ad stadard devato are to be as a measuremet of the performace of algorthm, ad the results are show from Tables 2(a) ad 2(b), where fu deotes fucto ad dm deotes dmeso; max T s maxmum evoluto geerato, A m s average mmum, G m s global mmum value, ad δ s stadard devato, respectvely. Ths paper uses,,, ad I for 5 tmes ad obtas the average of the evolutoary curve ad draws Fgures 5 14 of dfferet dmeso fuctos f 1, f 2, f 3,adf 4. I Table 2, the average mmum value, the global mmum value, ad the global mmum of the four fuctos have bee obtaed uder dfferet dmesos ad umber of teratos by usg,,, ad I. I each fgure, the ordate s expressed by atural logarthm of optmal average of the fucto (.e., l(f)), ad the abscssa s expressed by evoluto geerato; four dfferet kds of les show the chagg tedecy of

6 6 Computatoal Itellgece ad Neuroscece Fgure 1: Image of fucto f 1 (x). Fgure 3: Image of fucto f 3 (x) Fgure 2: Image of fucto f 2 (x). mmum value obtaed by,,, ad I wth the crease of the umber of teratos. From Table 2, t s clearly see that the average optmzato results ad the optmal results of I are much better tha those of,, ad dfferet dmesos adumberofteratosofeachfucto.meawhle,the precso of the optmzato results s greater tha,, ad. Furthermore, most of stadard devatos of I are almost. I addto, from each fgure, t s qute evdet that stablty of I s better tha those of,, ad by comparg the stadard devato. Wth the crease of the dmeso, the effect becomes more obvous compared wth other algorthms. For example, the stadard devato of fucto f 1 wth 3D s obtaed by I, but the others are usually bgger tha. At the same tme, all fgures, each optmal value s the form of a logarthm order to broade the dffereces Fgure 4: Image of fucto f 4 (x). betwee dfferet algorthms. From each fgure, t s easly see that covergece speed ad optmzato precso of I are obvously better tha those of,, ad. For example, Fgure 8 shows that the optmal values obtaed the quckest way by I are better tha ay other optmal values by other algorthms. 7. Dstrbuted Network Cosderg DG 7.1. Formulato of Objectve Fucto. The optmal cofgurato of the dstrbuto etworks wth DG uts s a olear optmzato problem. I ths paper, the objectve fucto of the olear model s formulated wth the am of fdg the mmum power loss. Thus, o the codto that the costrats below are cosdered, the objectve fucto of the recostructo s defed as mf = =1 P 2 +Q 2 U R, (14)

7 Computatoal Itellgece ad Neuroscece l(f 1 ) l(f 1 ) I I Fgure 5: Average m evoluto curve 3D fucto of f 1 (x). Fgure 7: Average m evoluto curve 1D fucto of f 1 (x). 5 l(f 1 ) 1 l(f 2 ) I Fgure 6: Average m evoluto curve 5D fucto of f 1 (x). where P s real power load ad Q s reactve power load of the ode, respectvely.u s voltage of ode, adr s resstace of brach,whlst s the umber of braches I Fgure 8: Average m evoluto curve 3D fucto of f 2 (x). (b)actvepoweradreactvepowercostratsofthe DG uts are 7.2. Costrats (a) Voltage ampltude costrats are U m U U max. (15) P m P DG P max, Q m Q DG Q max. (16)

8 8 Computatoal Itellgece ad Neuroscece.5 l(f 2 ) l(f 2 ) I Fgure 9: Average m evoluto curve 5D fucto of f 2 (x) I Fgure 1: Average m evoluto curve 1D fucto of f 2 (x). (c) Curret costrats are I m (d) Power flow equato costrats are I I max. (17) 4 2 P =V V j (G j cos δ j +B j s δ j ), j=1 Q =V V j (G j cos δ j B j s δ j ), j=1 (18) l(f 3 ) where U s voltage of ode, U m s the mmum, ad U max sthemaxmumoftheodevoltage,respectvely.p DG s actve power ad Q DG s reactve power of,respectvely; P m s the mmum ad P max s the maxmum of the actve power of,whlstq m s mmum of the reactve power of ad Q max s the maxmum. I s the curret of the ode, I m s the mmum, ad I max s the maxmum of ode curret separately. G j s coductace ad B j s susceptace betwee ode ad ode j. δ j s the voltage phase agle dfferece Hadg of the Calculatg Load Flow. DG stalled o the radal power dstrbuto etwork ca be smplfed to a PV ode, PQ ode, or PI ode. I ths paper, s cosdered as a PQ ode whch has costat power factor. The characterstc of DG makes t a optoal ad alteratve power supply ormally so that t s usually stalled o the locato of the load. Assume that placemets of all DG uts are the eghborhood of the load stead of le the preset paper. So, the basc cofgurato of I Fgure 11: Average m evoluto curve 3D fucto of f 3 (x). the dstrbuto etwork after stallg s show Fgure 15. Accordg to the comparso of actve powers from the loadaddg,therearethreekdsofstuatosbetweeload ad dstrbuted etwork whe t comes to actve power flow. (1) If P DG s greater tha P L, the load of the ode ca be cosdered as power supply outputtg P DG P L

9 Computatoal Itellgece ad Neuroscece l(f 3 ) 4 l(f 4 ) I I Fgure 12: Average m evoluto curve 5D fucto of f 3 (x). Fgure 14: Average m evoluto curve 3D fucto of f 4 (x) Table 3: Sutable sze for. Locato of DG Actve power of DG/kW Sze of DG/kW l(f 3 ) I Fgure 13: Average m evoluto curve 1D fucto of f 3 (x). to dstrbuted etwork, amely, to form reverse power flow. (2) If P DG s equal to P L, there s o actve flow betwee dstrbuted etwork ad load. (3) If P DG s less tha P L, the dstrbuted etwork provdes load wth the actve power of P L P DG. The route s show Fgure Smulato. IEEE33 odes dstrbuted etwork system [26] s adopted to take a smulato test our work as show Fgure17.Theratedvoltage,totalactvepower,adreactve power of system are kv, 3715 kw, ad 23 kvar [27], respectvely. Cocurretly the actve power loss s kw ad reactve power loss s kw wthout DG uts. The voltage ampltude of the system s show Fgure 18. To verfy feasblty ad stablty of I ad compare wth,, ad, t s assumed that locatos of DG uts are fxed due to certa costrats such as power resourcesstablty;buses16,17,ad32whosevoltagequaltes are the lower are selected as DG locato, ad all of them are operated a costat power factor mode, also kow as the PQ ode. It s equal to egatve load whch s stalled the eghborhood of the load. Cosderg that decrease total power loss depeds oszeadlocatoofdgthspaper,fourkdsof algorthms were used to determe the optmal sze of DG o the codto that power loss of system s mmum. Fally, results were compared wth each other. Some parameters are set as follows: fshum = 4, try-umber = 9, vsual = 1, δ =.618, step =.5, vsual m =.1, step m =.2, s=2.themaxevolutoalgeeratosweresetto5tmes ad results were gotte Tables 3 7. Tables 3, 4, 5, ad 6 provde smulato results carred out o the test etwork gve Fgure 17, usg,,, ad I algorthms, respectvely. Smulato

10 1 Computatoal Itellgece ad Neuroscece P L P DG S Q L Q DG DG P DG,Q DG P L,Q L Fgure 15: Basc cofgurato of dstrbuto etwork after stallg DG. Iput data cludg etwork cofgurato ad max terato Italze populato ad use forward-backward sweep to calculate the ftess value Select optmal soluto from the values ad keep t Update the behavor ad calculate objectve fucto Record the pbest ad gbest Yes Mutate the populato based o equato (6) Check the stop crtero No Stop ad prt out the results Fgure 16: Flowchart of the proposed I cosderg DG. Table 4: Sutable sze for. Locato of DG Actve power of DG/kW Sze of DG/kW Table 5: Sutable sze for. Locato of DG Actve power of DG/kW Sze of DG/kW Table 6: Sutable sze for I. Locato of DG Actve power of DG/kW Sze of DG/kW results are obtaed from MATLAB ad clude the best solutos, as provded Table 7. It ca be observed from Table 7: Power losses ad processg tme. I Power loss/kw Processg tme/s Tables 3 6 that the szes of DG uts are mataed wth permtted rage of tolerace. Table 7 gves the system losses ad processg tme wth four kds of algorthms, ad the mmum obtaed by I after comparg results wth each other. Therefore, the mmum system loss ad processg tme are 45. kw ad.2 s correspodg to the fact that outputs of buses 16, 17, ad 32 are kw, 25 kw, 1 kw, respectvely. It s show that the optmal placemet ofdgutssystemcausedalargerreductopower losses ad less tme wth I. I cosderato of realstc factors, the szes of buses 16, 17, ad 32 were set to 5 kw, 3 kw, ad 1 kw. Covergece curves for four algorthms ca also be used to show the capablty ad the speed of algorthm obtag

11 Computatoal Itellgece ad Neuroscece Fgure 17: A 33-bus radal dstrbuto etwork system. Voltage ampltude Bus Fgure 18: Voltage ampltude of IEEE33 odes system. Voltage profle Node 9 I Power losses (kw) I Fgure 19: Covergece curves for four algorthms. the optmal results. By takg the best results that are gve byfouralgorthmsadplottgtherbestftessvaluethe populato for each terato as show Fgure 19, I gves the faster results reachg the global optmal soluto ad stayed there tll the ed of teratos. Furthermore, other Fgure 2: Voltage level comparso o IEEE33 odes system. algorthms faled to provde the global mmum ad oly reach the local mmum. Hece, t ca be cocluded that theproposedmethodthspaperresultsasuperor performace as compared to the exstg methods such as ad ad also umercally coverges more quckly tha the tradtoal methods. Fgure 2 shows the mprovemet voltage profle uder load models. As show Fgure 2, the voltage at all buses after sertg DG uts system s hgher tha before, especallytheplaceofthebuswheredgslocated. 8. Cocluso I ths paper, quatum computg s troduced o bass of artfcal fsh algorthm, ad the mproved quatum artfcal fsh algorthm s put forward. I the early stage of the artfcal fsh optmzato, followg behavor ad preyg behavor of artfcal fsh are added the late stage, whch mprove covergece speed ad optmzato precso ad ehace the dversty of populato by mplemetato of the mutato after each terato. Smulato results show that compared wth,, ad, I s more sutable for solvg hgh dmesoal ad complex

12 12 Computatoal Itellgece ad Neuroscece ocovex programmg. So the algorthm s more coverget. Fally, I s appled to optmal cofgurato of dstrbuted etwork system ad smulato results dcate that I has great valdty ad feasblty. The theory research of I s stll ts facy. I the future, usg more test fuctos wth hgher dmeso to verfy performace of the proposed method s ecessary. Covergece ad stablty of the algorthm remas to be prove so that more detaled work ad further research from the theory are eeded to expad. Coflct of Iterests The authors declare o coflct of terests. Ackowledgmets Ths work was supported by the Natoal Natural Scece foudato of Cha uder Grat , Hube Provce Key Laboratory of Systems Scece Metallurgcal Process of Cha uder Grat Z2142, ad the Natural Scece Foudato of Hube Provce, Cha, uder Grat 213CFA131. The authors scerely apprecate the revewers for ther careful readg ad sgfcat commets whch have resulted the preset mproved verso of the orgal paper. 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13 Computatoal Itellgece ad Neuroscece 13 [23] T. Radtke ad S. Frtzsche, Smulato of -qubt quatum systems. I. Quatum regsters ad quatum gates, Computer Physcs Commucatos,vol.173,o.1-2,pp ,25. [24] M. J. Q ad P. Y. Wag, Quatum artfcal fsh algorthm, Ahu Agrcultural Sceces, Cha,vol.4,pp ,212. [25] Y. Ta ad G. Z. Ta, A chaotc local search strategy of dfferetal evoluto algorthm for global optmzato, Computer Egeerg ad Its Applcato,vol.45,o.14,pp.15 17,29. [26] E. B. Mesut ad F. W. Felx, Network recofgurato dstrbuto systems for loss reducto ad load balacg, IEEE Trasactos o Power Delvery,vol.4,o.2,pp , [27]D.Ye,Z.He,adT.Zag, Stgadszgofdstrbuted geerato plag based o adaptve mutato partcle swarm optmzato algorthm, Power System Techology, vol. 35, o. 6, pp , 211.

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