Economic Dispatch Using Firefly Algorithm

Transcription

1 ISS (Onlne) : ISS (rnt) : Internatonal Journal of Innovatve Research n Scence, Enneerng and Technology Volume 3, Specal Issue 3, March Internatonal Conference on Innovatons n Enneerng and Technology (ICIET 14) On 1 st & nd March Organzed by K.L.. College of Enneerng, Madura, Taml adu, Inda Economc Dspatch Usng Frefly Algorthm ABSTRACT Ths aper proposes a Frefly Algorthm for solvng an Economc Dspatch (ED) problem. It s the most mportant problem n power system operaton and control. Its obectve s to determne the optmal combnaton of power outputs of all generatng unts n order to mnmze the total cost satsfyng constrants and load demand n each nterval. Several conventonal and evolutonary algorthms have been employed to solve ths problem. The results obtaned by the proposed algorthm have been compared wth Genetc Algorthm (GA), Evolutonary rogrammng (E) and Gradent Search Algorthm (GSA) s already avalable n lterature. The feasblty of the proposed algorthm was verfed wth IEEE 30 bus system. KEYWORDS Economc Dspatch (ED), Frefly Algorthm (FA) and Meta-heurstc. I. ITRODUCTIO J.Merln, R.S.agaoth Assstant rofessor, Department of Electrcal & Electroncs Enneerng, K.L.. College of Enneerng, ottapalayam, Inda G Scholar, Department of Electrcal & Electroncs Enneerng, K.L.. College of Enneerng, ottapalayam, Inda Economc dspatch s an mportant problem n power system operaton and control. But t s a dffcult optmzaton problem and the purpose of ED or optmal dspatch s to reduce fuel cost for the generaton of power. By economc load schedulng, to fnd the generaton of the dfferent generators or power plants, then the fuel cost s mnmzed and at the same tme the total demand and losses at any nstant can meet by the total generaton. The economc dspatch problems nvolves n solvng of two dfferent problems,.e., unt commtment and on-lne dspatch. A large electrc network s a complcated system consstng of generators, transformers, transmsson lnes, crcut breakers, capactors, reactors, motors and other power consumng devces. The operaton, avalablty and ts contnuty n servce are very much unpredctable. Hence, the electrc demand at any nstant s a contnuously varyng factor. So the system s a dynamc one. Unless, there s some precous method to determne the behavor of the system, but t becomes dffcult to predct the power flow, lne losses, cost of generaton etc. The ob of the plannng enneer becomes very complcated n predctng and forecastng to sut the channg needs. The ncreasng energy demand from the avalable energy source, decreasng fuel sources and ncreasng cost of power generaton are another area whch necesstates the study of economc load dspatch, n early day s unscentfc method of approaches were tred for the cost effectve generaton. Even wth the transmsson losses neglected these methods faled to mnmze the cost. The soluton methods for ths problem are as follows. recedng efforts on solvng economc dspatch have employed varous conventonal methods and optmzaton technques. Ths mathematcal programmng method ncludes Lnear rogrammng, Gradent Method, Dynamc rogrammng, and Lambda teraton method and so on. The lambda teraton method s one of the mportant methods of mathematcal programmng and t s used n solvng the optmal power dspatch of generators and system lambda. Lambda s the varable ntroduced n solvng constrant optmzaton problem and called a Langranan multpler. Ths s used n Gradent method and ewton method. It s mportant to note that the lambda can also solve manually. It s used n solvng systems of equatons. Lambda teraton s ntroduced for the beneft of computng lambda and other assocated varables usng a computer. In lambda teraton method, the unknown varable lambda, gets ts next value based on ntruson. That s, there s no equaton, compares the next teraton of lambda. It s proected by nterpolatng the best possble value untl a specfed msmatch has been reached. [10] In ths algorthm, the obectve functon of a ven problem s assocated wth lght ntensty whch helps the frefles to move..e. the less brghter one wll move towards the more brghter one and more locatons n order to obtan effcent optmal solutons. In ths paper we wll show how the frefly algorthm can be used to Copyrght to IJIRSET 98 M.R. Thansekhar and. Bala (Eds.): ICIET 14

2 Economc Dspatch Usng Frefly Algorthm solve the economc dspatch problem. [1] resented a new path for determne the economc load dspatch problem consderng valve pont constrants. The results are compared wth varous stochastc search algorthms.[] resented an artfcal bee colony optmzaton technque for solvng an economc dspatch consderng valve pont loadng and prohbted operatng zones. The results are compared wth DE and E. [3] resented a Tabu search algorthm for solvng the economc dspatch problem. The problem formulated wth base case and contngency case lne flow constrants. The results are compared wth GA and Q. [4] presented a new approach to economc dspatch problem non smooth cost functons usng SO technque. A dynamc search space reducton strategy s dscovered to step up the optmzaton process. [5] resented a new approach to clarfy the economc dspatch problem. The feasblty of the proposed algorthm s demonstrated. [6] resented a comprehensve revew of a frefly algorthm can deals wth multmodal functons effcently and naturally. [7] resented the comparatve study of FA and SO for solvng nonlnear problems. The results were nvestgated and correlated. The frefly algorthm tres to perform better for hgher level nose. resented a effcent method for solvng economc dspatch problem. By usng SO wth SQ. [8] resented a SO technque for solvng economc dspatch consderng generator constrants. The effectveness of the proposed method s demonstrated for three dfferent systems and s compared wth GA.[9] presented a GA Soluton for solvng economc dspatch consderng valve pont loadng.the formulatons of an economc dspatch computer program usng GA and these programs has two dfferent encodng technques. But these methods may not be able to fnd the accurate soluton, Because these methods reles dffcultes lke myopa for nonlnear, dscontnuous search spaces, whch leads them to a less desrable performance and these methods often use approxmatons to lmt complexty. So later modern heurstcs stochastc optmzaton technque are ntroduced. They are Smulated Annealng (SA), Genetc Algorthm (GA), Evolutonary rogram (E), Tabu Search and so on. These methods are effcent n solvng optmzaton problems. Although these methods don t guarantees that they ve the global optmum soluton, they provde soluton, whch s approxmately equal to the global optmum. These methods suffer from drawbacks such as large memory requrement, long computaton tmes or premature convergence. However, settng the control parameters n these methods s a dffcult task. Recently, n the study of nsect s behavor, scentsts have found a source for solvng the optmzaton technques..e.., the new algorthm called Frefly Algorthm s proposed. II. ROBLEM FORMULATIO The operaton of generaton facltes to produce energy at the lowest cost to relably serve consumers, recognzng any operatonal lmts of generaton and transmsson facltes. A. Obectve Functon The man goal of economc dspatch s to mnmze the followng cost functon. Where, Mn F g 1 a b c F s the total generaton cost over the dspatch perod, a, b, c are the cost coeffcents of the th generator, g s the number of generatng unts, s the real power output of the th generator. B. Constrants The equalty and nequalty constrants are as follows. 1) Equalty Constrants Snce only the real power generaton s consdered n ths proect work for the Economc Dspatch problem, the real power balance equaton alone s consdered for the equalty constrants. The power balance equaton s as follows: ) ower Balance Equatons Where, l =Actve Load of the th bus G = Transfer conductance between bus and B = Transfer susceptance between bus and =Voltage angle dfference between bus and ) Inequalty Constrants: In a power system components and devces have operatng lmts, & these lmts are created for the securty constrants. Thus the requred obectve functon can be mnmzed by mantanng the network components wthn the securty lmts. Ths brngs the concept of nequalty constrants. The most usual type of nequalty constrants are the upper bus voltage lmts at generaton at load buses, lower bus voltage lmts at generaton at load buses, lower bus voltages lmts at some generators and mum lne loadng lmts, upper bounds of real power generaton at generator buses, lower bounds of real power generaton at generator buses. ) Real ower Operatng Lmt Q mn l l V V 1 1 V ( G V ( G cos B sn B sn ) 0 cos ) 0 Copyrght to IJIRSET 99 M.R. Thansekhar and. Bala (Eds.): ICIET 14

3 Economc Dspatch Usng Frefly Algorthm ) Reactve ower Operatng Lmt Q mn ) Bus Voltage Lmt V mn V V v) Lne Flow Constrant S S III. FIREFLY ALGORITHM A. Introducton to Frefly Frefly Algorthm s one of the recent swarm ntellgence method developed by Xn She Yang n 008. It s a knd of stochastc nature nspred meta-heurstc algorthm that can be appled for solvng the hardest optmzaton problems. The stochastc algorthm means that t uses as a knd of randomzaton by searchng for a set of solutons. It s nspred by the flashng lghts of the frefles n nature. Heurstc means to fnd or to dscover solutons by tral and error. In ths algorthm lower level means Heurstc and hgher level means Meta-Heurstc. The lower level concentrates on the generaton of new soluton wthn a search space and thus selects the best soluton for survval. On the other hand, randomzaton enables the search process to avod the soluton beng trapped nto local optma. Also, FA s populaton based. The populaton-based algorthm has the advantages when compared to other algorthm. [6][7] B. Bolocal Foundatons Frefles (Coleoptera: Lampyrdae) are among the most enchantment of all nsects, and ther spectacular courtshp dsplays have nspred poets and scentsts alke. owadays, more that 000speces exst worldwde. Usually, frefles lve n a warm envronment and they are most actve n summer nghts. A lot of researchers have studed frefly phenomena n nature and there exst numerous papers researchng frefles, Frefles are characterzed by ther flashng lght produced by bochemcal process bo-lumnescence. Such flashng lght may serve as the prmary courtshp sgnals formattng. Besdes attractng matng partners, the flashng lght may also serve to warn off potental predators. ote that n some frefly speces some adults are n capable of bo-lumnescence. The subspeces attract ther mates due to pheromone, smlarly to ants. In frefles, bolumnescent tractons take place from lghtproducng organs called lanterns. The most bolumnescent organsms provde only slowly modulated flashes (also glows).in contrast, adults n many frefly speces are able to control ther bolumnescence n order to emt hgh and dscrete flashes. The lanterns' lghtproducton s ntalzed by sgnals ornatng wthn the central nervous system of frefly. Most frefly speces rely on bolumnescent courtshp sgnals. Typcally, the frst sgnalers are flyng males, who try to attract flghtless females on the ground. In response to these sgnals, the females emt contnuous or flashng lghts. Both matng partners produce dstnct flash sgnal patterns that are precsely tmed n order to encode nformaton lke speces dentty and sex. Females are attracted accordng to the behavoral dfferences n the courtshp sgnal. Typcally, females prefer brghter male flashes. It s well known that the flash ntensty vares wth the dstance from the source. Fortunately, n some frefly speces females cannot dscrmnate between more dstant flashes produced by stronger lght source and closer flashes produced by weaker lght sources. Two features are characterstcs for swarm ntellgence are self-organzaton and decentralzed decson makng. Here, autonomous ndvduals lve together n a common place as, for example, bees n hves, ants n anthlls, etc. In order to lve n harmony, some nteracton or communcaton s needed among group members who lve together. In fact, ndvduals wthn a group cannot behave as f they are soltary, but must adapt to the overall goals wthn a groups. The socal lfe of frefly s not ust dedcated to forang, but more to reproducton. These collectve decsons are closely connected wth the flashng lght behavor that served as the man bolocal foundaton for developng the frefly algorthm [6]. C. Behavors of Frefly The azure flled wth the lghts of frefles. It s a marvelous sght n the summer season. There are two thousand frefly speces, and most of the frefly produces a rhythmc flashes. The pattern of the flashes, amount of flashng and the rate of tme for the flashes whch are observed together formng a knd of a prototype that attracts both the males and females to each other. Female s speces act n response wth ndvdual prototype of the male speces. The ntensty of lght at a certan dstance(r) from the lght source conforms to the nverse square law. It s the ntensty of the lght I goes on decreasng as the dstance r wll ncrease n terms of I =1/r. Addtonally, the ar keeps absorbng the lght whch becomes weaker wth the ncrease n the dstance. These two factors when combned make most frefles vsble at a lmted dstance, normally to a few hundred meters at nght, whch s qute enough for frefles to communcate wth each other.[6][7] D. Concept ow we can specalze some of the flashng characterstcs of frefles so as to develop frefly-nspred algorthms. Flashng characterstcs of frefles s used to develop frefly-nspred algorthm. Frefly algorthm works on the bass of three rules and three man factors. The man factors are lght ntensty and attractveness, dstance and movement of the frefles. The rules are as follows: Copyrght to IJIRSET M.R. Thansekhar and. Bala (Eds.): ICIET 14

4 Economc Dspatch Usng Frefly Algorthm All the frefles are unsex so t means that one frefly s attracted to other frefles rrespectve of ther sex. Attractvty and lumnosty are recprocal to one another, the lesser brght one wll move towards the brghter one. If one of the frefles s brghter than other frefly, t wll move randomly. The brghtness of a frefly s determned by the vew of the obectve functon. For mzaton problem, the brghtness s smply proportonal to the value of the obectve functon. Other forms of the brghtness could be defned n an dentcal way to the ftness functon n genetc algorthms [6]. 1.) Lght ntensty and Attractveness: Lght s absorbed by the meda, so we should allow the attractveness to vary wth the varyng degree of absorpton. Lght ntensty I(r) vares accordng to the nverse square law. l I( r) (3.1) r Step 4: Evaluate FA functon.e.t evaluates the qualty of the soluton. The mplementaton of a ftness functon f(s) s performed nsde. Step 5: Order FA functon sorts the populaton of frefles accordng to ther ftness values. Step 6: Fnd The Best FA functons, and then selects the best ndvduals n the populaton. Step 7: Fnally, Move FA functon performs a moves the frefly postons and Stop the program. Overvew of roposed Algorthm Where I s the ntensty at the source. For a stated medum wth a fxed lght absorpton coeffcent, the lght ntensty I vary wth the dstance r. I r I o e (3.) Where I o s the ntal lght ntensty, smlarly for attractveness s proportonal to the lght ntensty. ow we can defne the attractveness of a frefly as o e r (3.3).) Dstance: The dstance between the two frefles and at x and x respectvely s the Cartesan dstance. r, ( x x ) ( y y ) (3.4) 3.) Movement: The movement of the frefly whch s attracted by the more brghter one s determned by x x r, ( x x ) 1 e o (3.5) IV. STES FOR FIREFLY ALGORITHM The steps nvolved n frefly algorthm are as follows: Step 1: Intalze the generaton counter, best soluton and attractveness value. Step : Intalze populaton and parameters value. The frefly process comprses nsde of the whle loop and s composed of followng steps. Step 3: The alpha new functon s dedcated to modfy the ntal value of parameter IV. RESULTS AD DISCUSSIO The proposed FA algorthm has been tested on IEEE 30 bus system. The computatonal work was performed on Intel Core Duo wth a.93 GHz mcroprocessor n MATLAB 7.0 platform. The frefly algorthm result s compared wth Genetc Algorthm, Gradent Based Approach, and Evolutonary rogrammng already avalable n lterature. A. IEEE 30 Bus System IEEE 30 bus test system conssts of sx generators at buses 1,,5,8,11,13 and four transformers wth offnomnal tap raton at lnes 6-9, 6-10,4-1 and 8-7.To demonstrate the effectveness of the proposed approach. I Copyrght to IJIRSET M.R. Thansekhar and. Bala (Eds.): ICIET 14

5 Fuel Cost ($/hr) Economc Dspatch Usng Frefly Algorthm Table 1 represents the optmal settngs of the control varable usng frefly algorthm. From the obtaned results generaton satsfes the demand and also t satsfes the constrants..e. bus voltage, real power operatng lmts are wthn the range. TABLE.1: Optmal Settngs of Control Varables for IEEE 30 Bus system Usng FA DESCRITIO 1 (MW) (MW) (MW) (MW) (MW) (MW) Fuel Cost($/hr) Losses Frefly Algorthm In ths curve, X-axs represents the no of teratons and Y-axs represents the fuel cost. The curve explans the convergence rate of the proposed algorthm o. of Iteratons Fg. 1 Convergence Characterstcs Curve Table represents the comparson of fuel cost for dfferent methods. The proposed algorthm has been compared wth GA, E and Gradent approach whch s already avalable n lterature. TABLE.: Comparson of fuel cost for dfferent methods for IEEE 30 bus system METHOD GA[11] Gradent based approach[1] Evolutonary rogrammng[13] Frefly Algorthm FUEL COST($/hr) Based on the above results t s clear that the proposed algorthm for solvng the Economc Dspatch better result than other approaches. V. COCLUSIO In ths work, an attempt has been made to revew varous optmzaton methods used to solve ED problems. Even though, excellent new trals have been made n classcal methods, but they suffer from the followng dsadvantages. In several cases, mathematcal formulatons have to be smplfed to get the solutons because of the extremely lmted capablty to solve realtme hard power system problems. They are weak n handlng qualtatve constrants. They have premature convergence rate, so they may get struck at mnmum optmum. Hence n ths work, Frefly Algorthm has been mplemented to solve the economc dspatch problem. The proposed algorthm s tested on IEEE 30 bus system and the results obtaned show the effectveness of the proposed algorthm compared to those technques avalable n lterature. REFERECES [1] G. ryanka Roy, rtam Roy, Modfed Shuffled Frog Leapng Algorthm Wth Genetc Algorthm Crossover For Solvng Economc Load Dspatch roblem Wth Valve-ont Effect, Appled Soft Computng, July 013. [] M.Basu, Artfcal Bee Colony Optmzaton for Mult-area Economc Dspatch, Electrcal ower and Energy Systems, February 013. [3] Bakhta aama, Solvng The Economc Dspatch roblem By Tabu Search Algorthm, Energy roceda, January 013. [4] Jong-Bae ark, A artcle Swarm Optmzaton For Economc Dspatch Wth on-smooth Cost Functons, IEEE Transactons on ower Systems, February 005.Vol.0, o 1 [5] anchol, artcle Swarm Optmzaton For Securty Constraned Economc Dspatch, Intellgent Sensng and Informaton rocessng, August 004. [6] Xn-She Yang, A Comprehensve Revew of Frefly Algorthms, Swarm and Evolutonary Computaton, June 013. [7] Sabal K.al, Comparatve Study of Frefly Algorthm and artcle Swarm Optmzaton for osy on-lnear Optmzaton roblems, Intellgent Systems and Applcatons, September 01. [8] T.Aruldas Albert Vctore, Hybrd SO-SQ for Economc Dspatch wth Valve-ont Effect, Electrc ower Systems Research 71, December 004.pp [9] Walters D.C., Genetc Algorthm Soluton for Economc Dspatch wth Valve ont Loadng,IEEE Transactons on ower Systems, August 00. [10] Allen J Wood, Bruce E.Wollen Berg, ower Generaton Operaton and control, copyrght@1984,1996 by ohn wlsey & sons,inc. [11] Tarek Bouktr, Lnda slman, A Genetc Algorthm for Solvng the Optmal ower Flow roblem, Leonardo Journal of Scences, 004,pp [1] Lee.K.Y., ark.y.m, A Unted Approach to Optmal Real and Reactve ower Dspatch, IEEE Transactons on ower Apparatus and Systems, May 1985.Vol.AS-104,o.5. [13] Jason Yurvevch, Kt o Wong, Evolutonary rogrammng Base Optmal ower Flow Algorthm, IEEE Transactons on ower Systems,1999, Vol.14,o.4, pp Copyrght to IJIRSET 30 M.R. Thansekhar and. Bala (Eds.): ICIET 14