Optimal Reactive Power Dispatch using Bacterial Foraging Algorithm

Transcription

1 Internatonal Journal of Electrcal Engneerng. ISSN Volume 5, Number 2 (2012), pp Internatonal Research Publcaton House Optmal Reactve Power Dspatch usng Bacteral Foragng Algorthm 1 M. Ettappan M.E., 2 B. Padmanabhan and 3 Dr. M. Rajaram 1 Head of Department and Assocate Professor, Department of Electrcal Engneerng, Sardar Raja College of Engneerng, runelvel Dst, amlnadu, Inda E-mal: ettappanm@redffmal.com 2 M.E. Student, Power Systems Engneerng, Sardar Raja College of Engneerng, runelvel Dst, amlnadu Inda E-mal: padmanabhan_balu@yahoo.co.n 3 Vce Chancellor of Anna Unversty of echnology, runelvel, Inda. Abstract Reactve power plays crucal roles n power systems relablty and securty. hs paper proposes the Bacteral Foragng Algorthm(BFA) appled to optmal reactve power dspatch (ORPD). Optmal reactve power dspatch s a mxed nteger, nonlnear optmzaton problem whch ncludes both contnuous and dscrete control varables. he proposed algorthm s used to fnd the settngs of control varables such as generator voltages, tap postons of tap changng transformers and the amount of reactve compensaton devces to be swtched for real power loss mnmzaton and mprove the voltage profle n the transmsson system. he proposed algorthm s evaluated on an IEEE 30-bus power system, Smulaton results show that the proposed approach converges to better solutons much faster than the earler reported approaches. he optmzaton strategy s general and can be used to solve other power system optmzaton problems as well. Keywords: Reactve Power dspatch; Bacteral Foragng Algorthm; ransmsson Open Access Introducton Reactve Power Dspatch for mprovng economy and securty of power system operaton has receved much attenton at present. he man objectve of optmal reactve power control s to mprove the voltage profle and mnmzng system real power losses va redstrbuton of reactve power n the system. In addton, the

2 222 M. Ettappan M.E. et al voltage stablty can be enhanced by reallocatng reactve power generatons. herefore, the problem of the RPD can be optmzed to enhance the voltage stablty, mprove voltage profle and mnmze the system losses as well. he reactve power dspatch problem has a sgnfcant nfluence on secure and economc operaton of power systems. Reactve power optmzaton s a sub problem of the optmal powerflow (OPF) calculaton, whch determnes reactve power outputs of generators, control voltages of PV-buses and tap settngs of the under-load tap changng transformers to mnmze network power loss. Solvng these problems s subject to a number of constrants, such as lmts on bus voltages, tap settngs of transformers, and number of controllable varables, etc [1]. he reactve power dspatch problem has a sgnfcant nfluence on secure and economc operaton of power systems. Reactve power optmzaton s a sub problem of the optmal power-flow (OPF) calculaton[4], whch determnes all knds of controllable varables, such as reactve-power outputs of generators and statc reactve power compensators, tap ratos of transformers, outputs of shunt capactors/reactors, etc., and mnmzes transmsson losses or other approprate objectve functons, whle satsfyng a gven set of physcal and operatng constrants. Snce transformer tap ratos and outputs of shunt capactors/reactors have a dscrete nature, whle reactve power outputs of generators and statc VAR compensators, bus-voltage magntudes, and angles are, on the other hand, contnuous varables, the reactve power optmzaton problem can be exactly formulated usng a Bacteral Foragng Algorthm,.e., cast as a nonlnear optmzaton problem wth a mxture of dscrete and contnuous varables. Up to now, a number of technques rangng from classcal technques lke gradent-based optmzaton algorthms to varous mathematcal programmng technques have been appled to solve ths problem [2]-[6]. Recently, due to the basc effcency of nteror-pont methods, whch offer fast convergence and convenence n handlng nequalty constrants n comparson wth other methods, nteror-pont lnear programmng [7], quadratc programmng [8], and nonlnear programmng [9] methods have been wdely used to solve the OPF problem of large-scale power systems. However, these technques have severe lmtatons n handlng nonlnear, dscontnuous functons and constrants, and functon havng multple local mnma. Unfortunately, the orgnal reactve power problem does have these propertes. In all these efforts some or the other smplfcaton has been done to get over the nherent lmtatons of the soluton technque. Recently, agent-based computaton has been studed n the feld of dstrbuted artfcal ntellgence [10] and has been wdely used n other branches of computer scence [11]. Problem solvng s an area that many multagent-based applcatons are concerned wth. Lu et al. [12] ntroduced an applcaton of dstrbuted technques for solvng constrant satsfacton problem. hs paper proposes an effcent BFA Algorthm for solvng the reactve power optmzaton problem. he rest of ths paper s organzed as follows: Secton II descrbes the formulaton of an Reactve power dspatch problem; whle secton III explans the standards n BFA. Secton IV then detals the procedure of handlng the BFA. Secton V gves the smulaton results. Secton VI outlnes our concluson.

3 Optmal Reactve Power Dspatch usng Bacteral Foragng Algorthm 223 Problem Formulaton he objectve of the reactve power dspatch s to mnmze the actve power loss n the transmsson networ whch can be descrbed as follows: 2 2 f = P = g ( V + V 2V V cosθ ) (1) kloss k k N E k N E j where k = (, j); N B; j N he symbols of the above equaton and n the followng context are gven n the Nomenclature secton. he mnmzaton of the above functon s subject to a number of constrants: P P V V ( G cosθ + B snθ ) = 0 N (2) and G D j j N j j j j j V V ( G snθ + B cosθ ) = 0 N (3) V S G mn mn k mn G mn C l D S V l j j N k V G C j k G C j j N N l N l j N k N where power flow equatons are used as equalty constrants, reactve power source nstallaton restrctons, reactve generaton restrctons, transformer tap-settng restrctons, bus voltage restrctons and power flow of each branch are used as nequalty constrants. In the most of the nonlnear optmzaton problems, the constrants are consdered by generalzng the objectve functon usng penalty terms. In the reactve power dspatch problem, the generator bus voltages V PV and V S, the tap poston of transformer, and the amount of the reactve power source nstallaton C are control varables whch are self-constraned. Voltages of P bus VP and njected reactve power of PV bus G are constraned by addng them as penalty terms to the objectve functon (1). he above problem s generalzed as follows: lm 2 lm 2 F = f + λ ( V V ) + λ ( ) (9) Where postve constants; B G C V G lm lm N V N λ V and λ G are the penalty factors, and both penalty factors are large V lm lm V and lm G are defned as, j G V ; V > V = (10) mn mn V ; V < V O P G (4) (5) (6) (7) (8)

4 224 M. Ettappan M.E. et al lm = G ; G > G G (11) mn ; < mn G G G Bacteral Foragng Algorthm BFA method was nvented by Kevn M. Passno motvated by the natural selecton whch tends to elmnate the anmals wth poor foragng strateges and favor those havng successful foragng strateges [13]. Durng foragng of the real bactera, locomoton s acheved by a set of tensle flagella. E.col bactera s behavor and movement comes from a set of sx rgd spnnng ( r.p.s) flagella, each drven as a bologcal motor. An E. col bacterum alternates through runnng and tumblng. Runnng speed s μm/s, but they cannot swm straght. Flagella help an E.col bacterum to tumble or swm, whch are two basc operatons performed by a bacterum at the tme of foragng. After many generatons, poor foragng strateges are ether elmnated or reshaped nto good ones. he foragng strategy s governed bascally by four processes namely Chemotaxs, Swarmng, Reproducton, Elmnaton and Dspersal. Chemotaxs Chemotaxs process s the characterstcs of movement of bactera n search of food and conssts of two processes namely swmmng and tumblng. A bacterum s sad to be 'swmmng' f t moves n a predefned drecton, and 'tumblng' f movng n an altogether dfferent drecton. Suppose θ ( represents th bacterum at j th chemotactc, k th reproductve and l th elmnaton dspersal step. C() s the sze of the step taken n the random drecton specfed by the tumble (run length unt). hen n computatonal chemotaxs the movement of the bacterum may be represented by Δ ( ) θ ( j + 1, = θ ( + C( ) (12) Δ ( ) Δ ( ) where Δ ndcates a vector n the random drecton whose elements le n [ 1, 1]. Swarmng It s always desred that the bacterum whch has searched optmum path of food search should try to attract other bactera so that they reach the desred that the bacterum whch has searched optmum path of food search should try to attract other bactera so that they reach the desred place more rapdly. Swarmng makes the bactera congregate nto groups and hence move a concentrc pattern of groups wth hgh bacteral densty. Mathematcally, swarmng can be represented by J S CC CC = 1 S p 2 [ dattract exp( ωattract ( θm θm) )] = 1 m= 1 ( θ, P( ) = J ( θ, θ ( ) = +

5 Optmal Reactve Power Dspatch usng Bacteral Foragng Algorthm 225 S p 2 [ hrepellant exp( ωrepellant ( θm θm) )] = 1 m= 1 (13) where, J CC s the penalty added to the orgnal cost functon. J CC s bascally the relatve dstances of each bacterum from the fttest bacterum. S s the number of bacterum, p represents number of parameters to be optmzed, θ m s the poston of the fttest bacterum, d attract, h repellant, ω attract and ω repellant are dfferent coeffcents. Reproducton In reproducton, populaton members who have had suffcent nutrents wll reproduce and the least healthy bactera wll de. he healther half of the populaton replaces wth the other half of bactera whch gets elmnated, owng to ther poorer foragng abltes. hs makes the populaton of bactera constant n the evoluton process. Elmnaton and Dspersal A sudden unforeseen event may drastcally alter the evoluton and may cause the elmnaton and/or dsperson to a new envronment. hey have the effect of possbly destroyng the chemotactc progress, but they also have the effect of assstng n chemotaxs, snce dspersal may place bactera near good food sources. Elmnaton and dspersal helps n reducng the behavor of stagnaton.e. beng trapped n a premature soluton pont or local optma. Algorthm For Bfa Method Step he followng varables are ntalzed. 1 Number of bactera (S) to be used n the search. Number of parameter (P) to be optmzed. Swmmng length N s. N c the number of teraton n a chemotactc loop. (N c > N s ). N re the no of reproducton. N ed the no of elmnaton and dspersal events. Locaton of each bacterum P(p, S,.e. random numbers on [0-1]. he values of d attract, h repellant, ω attract and ω repellant. Step Elmnaton-dspersal loop: l=l+1 2 Step Reproducton loop: k=k+1 3 Step 4 Chemotaxs loop: j=j+1 Calculate [a] For = 1,2 S take a chemotactc step for bacterum as follows. [b] Compute the ftness functon, J (,. Let, J (, = J (, + J CC ( θ (, P( ) (.e.

6 226 M. Ettappan M.E. et al umble Swm add on the cell to cell attractant-repellant profle to smulate the swarmng behavor) Where, JCC s defned n (11). [c] Let J last = J(, to save ths value snce we may fnd a better cost va a run. [d] p Generate a random vector Δ() R wth each element Δ m (), m=1,2,,p, a random number on [-1, 1]. [e] Move : Let Δ ( ) θ ( j + 1, = θ ( + C( ) Δ ( ) Δ ( ) hs results n a step of sze C() n the drecton of the tumble for bacterum. [f] Compute J (, j + 1, and let J (, j + 1, = J (, + J CC ( θ ( j + 1,, P( j + 1,. [g] Let m=0 (counter for swm length). Whle m<n s (f have not clmbed down too long). Let m=m+1. If J (, j + 1, < J last (f dong better), let J last = J(, j + 1, and let Δ ( ) θ ( j + 1, = θ ( + C( ) Δ ( ) Δ ( ) And use ths θ ( j + 1, to compute the new J (, j + 1, as we dd n [f] Else, let m=n S. hs s the end of the whle statement. [h] Go to next bacterum (+1) f S (.e., go to [b] to process the next bacterum). Step 5 Step 6 If j<n c, go to step 4. In ths case contnue chemotaxs snce the lfe of the bactera s not over. Reproducton [a] For the gven k and l, and for each =1,2,,S, let J health = N + C 1 j= 1 J (, be the health of the bacterum ( a measure of how many nutrents t got over ts lfetme and how successful t was at avodng noxous substances). Sort bactera and chemotactc parameters C() n order of ascendng cost J health (hgher cost means lower health). [b] he S r bactera wth the hghest J health values de and the remanng S r bactera wth the best values splt (ths process s performed by the copes that are made are placed at the same

7 Optmal Reactve Power Dspatch usng Bacteral Foragng Algorthm 227 locaton as ther parent). Step If k < N re, go to step 3. In ths case, we have not reached the number of specfed 7 reproducton steps, so we start next generaton of the chemotactc loop. Step Elmnaton For = 1,2,,S wth probablty P ed, elmnate and dsperse each 8 dspersal bacterum (ths keeps the number of bactera n the populaton constant). o do ths, f a bacterum s elmnated, smply dsperse another one to a random locaton on the optmzaton doman. If l<n ed, then go to step 2; otherwse end. Smulaton Results o verfy the effectveness and effcency of the proposed BFA Algorthm based reactve power optmzaton approach, the IEEE 30-bus power system are used as the test system. he BFA has been mplemented n Matlab programmng language and numercal tests are carred on a Intel(R) Core(M) 2.53 GHz computer. IEEE 30-BUS Power System he IEEE 30-bus system data and operatng condtons are gven n the [1]. he network conssts of 48 branches, sx generator-buses, and 22 load-buses. After mplementng the BFA to the ORPD problem for dfferent objectve functons the results are presented. able 2 compares optmal transmsson loss for the 30-bus IEEE network for dfferent methods after ten runs for each method. he table also shows percentage of power loss decrease wth respect to the case that all generator voltages and transformer taps are set to 1 p.u. and reactve compensaton devces are set to zero. able I: Values of control varables after optmzaton by HSA, SGA, PSO and BFA Control Devce HSA SGA PSO BFA V V V V V V

8 228 M. Ettappan M.E. et al he results obtaned from BFA for power loss reducton are compared wth other algorthms such as n [14] HSA, [15] whch a DE method s used to solve the optmzaton problem or CLPSO n [16]. In all of these references some of the constrants and ntal settngs of the problem are dfferent wth the assumed values and constrants. able II: Results of ransmsson Loss Compared Wth Results Of [17] Method Power Loss (MW) CGA AGA CLPSO L-DE L-SaDE SOA HSA BFA he results presented by the Harmony search algorthm and some other algorthms are better than the result obtaned from BFA but t should be regarded that the operatons mplemented to the data n the search process are very smple. In the future studes modfyng the operatons used n BFA wth other technques n the form of hybrdzaton for achevng better results than the mentoned algorthms n able II wll be nvestgated. Concluson he proposed BFA method obtans lesser loss reducton compared to other technques PSO, SGA, and HSA wth less number of populaton szes. he mnmum loss obtaned by BFA s lesser than the mnmum loss obtaned by other algorthms. he mnmum loss value obtaned by the proposed BFA s always closer to the average loss value for the test systems. It s observed from the repeated tral runs that BFA converges to near optmal soluton wth hgh success rate. he computatonal results show that the BFA Algorthm can be used for solvng the ORPD problems successfully. References [1] B.Zhao, C.X.Guo and Y.J.Cao., 2005, "A multagent-based partcle swarm optmzaton approach for optmal reactve power dspatch," IEEE ransactons on power systems, 20(2), pp

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