Proceedngs of the th WSEAS Int. Conf. on EVOLUTIONARY COMPUTING, Lsbon, Portugal, June 1-18, 5 (pp17-175) Ant Colony Optmzaton for Economc Generator Schedulng and Load Dspatch K. S. Swarup Abstract Feasblty of applcaton of Ant Colony Optmzaton to two case studes of economc load dspatch and generaton schedulng are presented. Ant Colony Optmzaton (ACO) s a meta-heurstc approach for solvng hard combnatoral optmzaton problems. The nsprng source of ACO s the pheromone tral layng and followng behavor of real ants whch use pheromones as a communcaton medum. In analogy to the bologcal example, ACO s based on the ndrect communcaton of a colony of smple agents, called (artfcal) ants, medated by (artfcal) pheromone trals. The pheromone trals n ACO serve as dstrbuted, numercal nformaton whch the ants use to probablstcally construct solutons to the problem beng solved and whch the ants adapt durng the algorthm s executon to reflect ther search experence. The sutablty of the ant colony optmzaton algorthm for economc dspatch was carred out for two systems consstng of 3 and generatng unts. The method s further extended to generator schedulng for IEEE 14, 3 and 57 bus systems respectvely. Double brdge experment Fg 1. shows the double brdge experment to llustrate the ant behavour. Ant nest s connected to food source va two paths of dfferng length. Intally, ants move randomly and chose between shorter and longer path wth equal probablty. Whle walkng, ants deposted pheromone. When choosng a path, ants chose wth hgher probablty the path wth the hghest pheromone concentraton. Ants choosng the short path wll be frst back wth food. Therefore, tral on shorter path grows more quckly Index Terms - Power Systems, Optmzaton, Meta-heurstc, Ant Colony Optmzaton, Economc Dspatch, Generaton Schedulng. P I. INTRODUCTION ower system optmzaton s an mportant feld n the operaton, plannng and control of power systems. Many modern heurstc technques to the soluton of complex power system optmzaton problems have been proposed, each dfferng n ther method of representaton, mplementaton and soluton procedure. Ths paper presents an new meta heurstc approach to power system optmzaton problems namely economc dspatch and generaton unt commtment. II. ANT COLONY BEHAVIOR Real Ants In many ants the vsual system s very smple. Some speces are completely blnd. Communcaton between ants and between ants and ther envronment s often based on the use of chemcal sgnals. Pheromones are produced by ants and they depost them on trals when walkng n search of food. By sensng the pheromone, the followng ants can fnd food. Inspratonal source of ant colony algorthms s the double brdge experment descrbed below. K.S.Swarup s wth the Department of Electrcal Engneerng, Indan Insttute of Technology, Madras, INDIA. (e-mal: swarup@ee.tm.ac.n). Fg 1. Double Brdge Experment. Auto Catalyss: Postve feedback. It s a Self-renforcng process If no lmtng mechansm s n place, t leads to exploson. It s the central mechansm n ant algorthms. Probablty of an ant choosng a path ncreases wth the number of ants that chose the same path. It s nterestng to understand how ants, whch are almost blnd anmals wth very smple ndvdual capabltes, act together n a colony and fnd the shortest route between the ant s nest and a source of food. They are also capable of adaptng to changes n the envronment, for example, fndng a new shortest path once the old one s no longer feasble due to a new obstacle. The studes by ethnologsts reveal that such capabltes that the ants have are essentally due to what s called pheromone trals that ants use to communcate nformaton among ndvduals regardng path and decde where to go. Ants depost a certan amount of pheromone whle walkng, and each ant probablstcally prefers to follow a drecton rch n pheromone rather than a poorer one. In case of an obstacle n place, these ants that choose, by chance,
Proceedngs of the th WSEAS Int. Conf. on EVOLUTIONARY COMPUTING, Lsbon, Portugal, June 1-18, 5 (pp17-175) the shorter path around the obstacle wll more rapdly reconsttute the nterrupted pheromone tral compared to those that choose the longer path. Hence the shorter path wll receve a hgher amount of pheromone n the tme unt and ths wll n turn cause a hgher number of ants to choose the shorter path (auto catalytc) process, very soon all the ants wll choose the shorter path. The Abstract Algorthm Colony of artfcal ants buld solutons to a gven problem by movng on the problem s graph representaton Each feasble path represents a soluton to the problem They move by employng a probablstc local decson rule that explots pheromone tral values Once an ant has bult a soluton (or whle the soluton s beng bult), the ant evaluates the qualty of the soluton, and deposts pheromone on the components t used Ths drects the search of the ants n the future Other Algorthmc Components: Evaporaton and daemon actons Evaporaton process by whch pheromone concentratons decrease over tme Needed to avod too-rapd convergence of the algorthm to a sub-optmal regon Implements a form of forgettng, favourng the exploraton of new areas of the search space Daemon actons used to mplement centralsed actvtes that are not undertaken by sngle ants Example: depost extra pheromone on the components used by the ant that bult the best overall soluton at the last teraton ( reward ) Formulaton of the approach: Explctly formulated n terms of computatonal agents Mght, n prncple, be possble to get rd of ndvdual agents and concentrate on core mechansms (renforcement and evaporaton) However, the agent-based formulaton may be more flexble, and provde a useful ad to desgnng problem solvng systems III. A SIMPLE ANT COLONY ALGORITHM Fgure shows the smple ant colony algorthm. The workng of the can be descrbed by means of the followng. 1) Intalze A(t): The problem parameters are encoded as a real number. Before each run, the ntal populaton (Nest) of the colony are generated randomly wthn the feasble regon whch wll crawl to dfferent drectons at a radus not greater than R. ) Evaluate A(t): The ftness of all ants are evaluated based on ther objectve functon. 3) Add_tral: The tral quantty s added to the partcular drectons the ants have selected n proporton to the ants ftness. 4) Send_ants A(t): Accordng to the objectve functon, ther performance wll be weghted as a ftness value whch drects nfluence to the level of tral quantty addng to the partcular drectons the ants have selected. Each ant chooses the next node to move takng nto account two parameters: the vsblty of the node and the tral ntensty of the tral prevously lad by other ants. The send_ants process sends ants by selectng drectons usng Tournament selecton based on the two parameters. 5) Evaporate: fnally, the pheromone tral secreted by an ant eventually evaporates and the startng pont(nest) s updates wth the best tour found. Start t = Intalze A(t) Evaluate A(t) No Termnate? t = t+1 End Yes Fg. A Smple Ant Colony Algorthm IV. ANT COLONY OPTIMIZATION Add Tral Send Ants Evaporate Ant Colony Optmzaton (ACO) s a recently proposed meta-heurstc approach for solvng hard combnatoral optmzaton problems. The nsprng source of ACO s the pheromone tral layng and followng behavor of real ants, whch use pheromones as a communcaton medum. In analogy to the bologcal example, ACO s based on the ndrect communcaton of a colony of smple agents, called (artfcal) ants, medated by (artfcal) pheromone trals. The pheromone trals n ACO serve as dstrbuted, numercal nformaton, whch the ants use to probablstcally construct solutons to the problem beng solved, and whch the ants adapt durng the algorthm s executon to reflect ther search experence. The frst example of such an algorthm s Ant System (AS), whch was proposed usng as example applcaton the well-known Travelng Salesman Problem (TSP). Despte encouragng ntal results, AS could not compete wth state-of-the-art algorthms for the TSP. Nevertheless, t had the mportant role of stmulatng further research on algorthmc varants, whch obtan much better computatonal performance, as well as on applcatons to a large varety of dfferent problems. In fact there exsts now a consderable amount of applcatons obtanng world class performance on problems lke the quadratc assgnment, vehcle routng, sequental orderng, schedulng, routng n Internet-lke networks, and so on. Motvated by ths success, the ACO meta-heurstc has been proposed as a common
Proceedngs of the th WSEAS Int. Conf. on EVOLUTIONARY COMPUTING, Lsbon, Portugal, June 1-18, 5 (pp17-175) framework for the exstng applcatons and algorthmc V. ECONOMIC DISPATCH varants. WHILE termnaton condtons not meet DO ScheduleActvtes AntBasedSolutonConstructon() PheromoneUpdate() DaemonActons() {optonal} END ScheduleActvtes ENDWHILE Fg 3 Pseudo Code for ACO AntBasedSolutonConstructon(): An ant constructvely bulds a soluton to the problem by movng through nodes of the constructon graph G. Ants move by applyng a stochastc local decson polcy that makes use of the pheromone values and the heurstc values on components and/or connectons of the constructon graph. Whle movng, the ant keeps n memory the partal soluton t has bult n terms of the path t was walkng on the constructon graph. PheromoneUpdate(): When addng a component c to the current partal soluton, an ant can update the values of the pheromone trals that where used for ths constructon step. Ths knd of pheromone update s called onlne step-by-step pheromone update. Once an ant has bult a soluton, t can (by usng ts memory) retrace the same path backward and update the pheromone trals of the used components and/or connectons accordng to the qualty of the soluton t has bult. Ths s called onlne delayed pheromone update. Another mportant concept n Ant Colony Optmzaton s pheromone evaporaton. Pheromone evaporaton s the process by means of whch the pheromone tral ntensty on the components decreases over tme. From a practcal pont of vew, pheromone evaporaton s needed to avod a too rapd convergence of the algorthm toward a sub-optmal regon. It mplements a useful form of forgettng, favorng the exploraton of new areas n the search space. DaemonActons(): Daemon actons can be used to mplement centralzed actons whch cannot be performed by sngle ants. Examples are the use of a local search procedure appled to the solutons bult by the ants, or the collecton of global nformaton that can be used to decde whether t s useful or not to depost addtonal pheromone to bas the search process from a non-local perspectve. As a practcal example, the daemon can observe the path found by each ant n the colony and choose to depost extra pheromone on the components used by the ant that bult the best soluton. Pheromone updates performed by the daemon are called offlne pheromone updates. Economc dspatch n power system operaton conssts of mnmzng the operaton costs dependng on demand and subject to certan constrants. It can be formulated as follows: 1) Objectve functon: N g Mnmze Cost = F( P) (1) where Cost s the operatng cost of the power system. N g s the number of unts. F( P ) s the cost functon and P s the power output of the unt. F( P ) s usually approxmated by a quadratc functon of ts power output P as: F ( P) ap bp c = + + () where a, b and c are the cost coeffcents of the unt. Wre drawng effect occurs when each steam admsson valve n a turbne starts to open, and at the same tme a rpplng effect on the unt curve s produced. To model the effects of valve ponts a recurrng rectfed snusod contrbuton s added to the cost functon. The result s: mn F( P) = ap + bp + c+ gsn{ h( P P )} (3) mn where g and h are valve-pont coeffcents. P s the lower generaton lmt of unt. d s the ncremental cost curve value. Ignorng the valve pont effects some naccuracy would result n dspatch. ) Constrants: a. Unt operaton constrants: P P P mn = 1,,..., Ng (4) mn where P, P are the lower and upper generaton lmt of unt. b. Power Balance: N g = PL + PD P (5) = 1 where P D s the demand and P L s transmsson loss. The transmsson loss can be calculated by the B coeffcents method or power flow analyss. B coeffcents used n the power system s: T T P L P BP P B o B oo = + + ()
Proceedngs of the th WSEAS Int. Conf. on EVOLUTIONARY COMPUTING, Lsbon, Portugal, June 1-18, 5 (pp17-175) where P s an Ng dmensonal column vector of the power where σ ( K) s the penalty factor made on teraton K. a s output of the unts. T a postve parameter. P s an assocate matrx of P. B s an Ng X Ng coeffcent matrx. T s the upper lmt of teratve tmes. σ s the upper lmt of B s an Ng dmensonal coeffcent column vector. B o oo s a σ ( K ) coeffcent. We can also get the transmsson loss by power VI. ECONOMIC DISPATCH USING ANT COLONY flow analyss. Lne flow constrants and system stablty OPTIMIZATION constrants can be expressed as follows: Soluton Codng: c. Lne Flow Constrants: Let X = ( x 1, x,..., xng) be a vector denotng the th ndvdual of the ant colony, where Ng s the number of unts Lf Lf = 1,... NL (7) and x s the generated power output of unt. At ntalzaton phrase, X s selected randomly from the where Lf s the MW lne flow, Lf s the allowable selected regon S. mum flow of lne (lne capacty), and N L s the number of transmsson lnes subject to lne capacty constrants. d. System Stablty Constrants: j j, 1,,... D j = N and j (8) where, are voltage angle of bus and j j. j s the allowable mum voltage angle. N s the number of D buses subject to system stablty constrants. Generalzed Ant Colony Optmzaton (GACO) It has the characterstcs of postve feedback, dstrbuted computaton, and the use of constructve greedy heurstc, the GACO can be used to solve the non-convex, nonlnear constraned optmzaton problems. When an objectve functon f() X s mnmzed n a compact set, t must be subject to lnear/nonlnear, nequalty/equalty constrants. We can transform those constrants, whch s dffcult to be dealt wth n feasble regon by usng the penalty functon. l u 1 σ { j } = 1 j= 1 mn FX ( ) = f( X) + σ ( hx ( )) +, gx ( ) h( X) =, = 1,,..., l l (9) gj( X), j= 1,,..., u u where f() X s the orgnal objectve X ( xx xn) T = s a functon. 1,,..., are the numbers of equalty and nequalty constrants of orgnal problem. σ 1 and σ are the penalty factors. σk ( ) = 1 σ = 1, (1) ak 1+ exp ( ) T n-dmensonal vector. l, u Objectve functon and Feasble regon: In order to mnmze the objectve functon of ED the constrants have to be obeyed. We can use penalty functon to transform those constrants dffcult to deal wth n the feasble regon ncludng power balance, etc. the feasble regon S s determned by the unt operaton constrants. Parameter Settng: The parameters used here are N=1-5, 1. γ1 λ 1 τ =, = =,T=4-1, a=1-5, r=.8-.5,.9 ρ =, NI=1. Upper lmt of vsblty s 5 and penalty factor s 15. VII. ACO ALGORITHM FOR ECONOMIC DISPATCH The Ant Colony Optmzaton Algorthm for economc dspatch conssts of the followng steps. Step 1: Intalzaton: An ntal populaton of ant colony ndvduals s selected randomly from the feasble regon S. Typcally; the dstrbuton of ntal trals s unform. Vsblty s defned and ths quantty s modfed durng the run of the program. At the begnnng, the ants can search on a large scale. Wth the runnng of the program the vsblty decreases and the exacttude of the search ncreases gradually. Step : A set s defned. If A s not equal to ph, whch s an empty set, then go to Step 3, else go to Step 4. Step 3: Let m be the quantty of elements n A and transtonal probablty s defned. Po s the probablty of the neghborhood search. If the selecton result s Pj then update rule 1 s carred out. Update rule 1: Movng an ant from pont to j. Go to Step 5 If the selecton result s Po then update rule s carred out. Update rule : Carryng out a search n the neghborhood of X. Go to Step 5. Step 4: Searchng n neghborhood. Let the result be Y.
Proceedngs of the th WSEAS Int. Conf. on EVOLUTIONARY COMPUTING, Lsbon, Portugal, June 1-18, 5 (pp17-175) Step 5: Updatng the tral ntensty matrx. Step : After teraton all the ants have completed one move, calculate the results. 1) If convergence s not acheved, cancel the result from step to step 4 and go to step. ) If the results are not changed after NI teratons, dsturb the ant colony by ncreasng the vsblty and neghborhood search. NI s a coeffcent. VIII. SIMULATION RESULTS FOR ANT COLONY OPTIMIZATION Case Study I: 3 Generator System. A computer program mplementng the proposed algorthm was frst prepared and run for a 3 generator system. A comparson wth Lambda method and Genetc Algorthm (GA) s provded n table. In ACO the followng parameters are chosen heurstcally. No of ants=5, No of cycles=1, Alpha=.5, Beta=.5, Forget factor=.9, Q=5 Cost coeffcents and power range for calculatng the operaton cost s gven n table 1. Fg. 4. Cost optmzaton for 3 generator system TABLE 3: COMPARISON OF RESULTS FOR 5MW LOAD FOR A 3 UNIT SYSTEM CONSIDERING LOSSES. Case Study Unt1 Unt Unt3 Losses Cost ($/h) GA 3.1 17. 1.1 7.99 5745.11 ACO 99.4 171.93 99.84 71. 5735.74 CO 99.4 17 98.84 7.4 5735.93 Un t TABLE 1: GENERATOR COST COEFFICIENTS FOR A 3 UNIT SYSTEM P Pmn a b c d g h 1 1.15 7.9 51.314 3.315 4 1.194 7.85 31.388.4 3 5.48 7.97 78.94 15.3 The load demand here s 85MW w/o losses. TABLE : RESULTS FOR 85MW LOAD FOR A 3UNIT SYSTEM Case Study Unt1 Unt Unt3 Cost ($/h) Lambda 393.198 334.38 1.4 8194.37 Method ACO 394.11 333.1 1.3 8195.1 GA 3 4 15 837. The B-Loss coeffcents for computng the losses are gven below.7.953.57 [ B ] =.953.51.91.57.91.94.7 B =.34.189 B =.4357 Table 3 shows the comparson of the ACO for 3 generatng unt system wth other methods lke Genetc Algorthm, and constraned optmzaton. Case Study Case Study II: Generator System. Table 4 shows the Generator cost coeffcents for a unt system. Load demand s 18MW. Transmsson Losses are gnored. Table 4: Data for generator system Unt P Pmn a b c d g h 1 1.15 7.9 5 1.31 4 3.31 5 4 1.194 7.8 31.388.4 5 3 5.48 7.9 7 78.94 15.3 4 59 14.139 7. 5 44 11.184 7.4 44 11.184 7.4 5 9 5 9 5.78.38 5.38 5.54.. The followng parameters are chosen heurstcally for the ACO. No of ants=5; No of cycles=; Alpha=.5; Beta=.5; Forget factor=.9; Q=5. Table 5 and fgure 5 show the result and the cost optmzaton for the generator unt system TABLE 5: RESULTS FOR GENERATOR SYSTEM UNIT1 UNIT UNIT3 UNIT4 UNIT5 UNIT Fuel Cost ($/h) NEWTON 184 1. 54.4 59 4.7 4.7 19.57 ACO 48. 17.3 74.94 588.3 335.7 335. 1579.33 7 7 8 8 GA 5.4 9 15.4 3 19.9 57.8 4 35. 35. 1585.85
Proceedngs of the th WSEAS Int. Conf. on EVOLUTIONARY COMPUTING, Lsbon, Portugal, June 1-18, 5 (pp17-175) Fg. 5. Cost optmzaton for generator system The ACO approach to economc dspatch ahs been further tested for the IEEE 14, 3 and 57 bus systems respectvely. The comparsons of the results are shown n table. Case study IEEE 14 Bus System IEEE 3 Bus System IEEE 57 Bus System TABLE : RESULTS FOR IEEE 14, 3, 57 BUS SYSTEMS Base case Optmum Load Optmum Cost generaton generaton (n $/h) P1=1. P1=159.44 1134.98 P=4 P=7.89 59. P= P=39.9 Losses=11. Losses=8. P1=38.48 P=4 P11= Losses=15.8 P1=478.57 P3=4 P8=45 P1=31 Losses=7.857 P1=14.33 P=73.98 P11=54.34 Losses=9.9 P1=411.15 P3=99.5 P8=45.78 P1=358.45 Losses=.8 83.4 15.8 144.7 517.87 Tables 7 8 and 9 show the comparson of the ACO wth conventonal methods for the standard IEEE 14, 3 and 57 bus systems. Fg.. Fuel Cost Optmzaton for IEEE 14 Bus system Fg. 7. Fuel Cost Optmzaton for IEEE 3 Bus system TABLE 7: COST OF GENERATION OBTAINED BY DIFFERENT TECHNIQUES FOR IEEE 14 BUS SYSTEM: S. no Technques used Total cost of generaton (n $/h) 1 QP method 1134.77 GA 113.4 3 ACO 1134.98 TABLE 8: COST OF GENERATION OBTAINED BY DIFFERENT TECHNIQUES FOR IEEE 3 BUS SYSTEM: S. no Technques used Total cost of generaton (n $/h) 1 QP method 144.4 GA 145.81 3 ACO 144.7 TABLE 9: COST OF GENERATION OBTAINED BY DIFFERENT TECHNIQUES FOR IEEE 57 BUS SYSTEM: S. no Technques used Total cost of generaton (n $/h) 1 QP 53.47 ACO 517.87 Fgures, 7 and 8 show the Fuel cost optmzaton of the ACO for the standard IEEE 14, 3 and 57 bus systems. Fg. 8. Fuel Cost Optmzaton for IEEE 57 Bus system IX. SHORT TERM GENERATION SCHEDULING USING ANT COLONY SEARCH ALGORITHM (ACSA) To supply a hgh qualty of electrc energy to the consumer n a secure and economc manner, electrc utltes face many economcal and techncal problems n operaton, plannng and control of electrc energy systems. One of the most mportant problems s to determne the most economc and secure way of short-term generaton schedulng and dspatch such that the constrants are satsfed smultaneously. Here a novel co-operatng agents approach, ant colony search algorthm(acsa)- based scheme, for solvng a short-term generaton schedulng problem of thermal power systems. In the ACSA, the state transton rule, global and local updatng rules are also ntroduced to ensure an optmal soluton. Once
Proceedngs of the th WSEAS Int. Conf. on EVOLUTIONARY COMPUTING, Lsbon, Portugal, June 1-18, 5 (pp17-175) β all the ants have completed ther tours, a global pheromone τ (, j) η (, j) updatng rule s then appled and the process s terated untl pk(, j) =, j Jk() β τ ( u, ) η ( u, ) the stop condton s satsfed. The effectveness of the u Jk () (17) proposed scheme has been demonstrated on the daly generaton schedulng problem of model power systems. = otherwse Constrants Consdered Spnnng reserve constrants: G j Dj / Dj up P P.1, j T (11) = 1 where, uj s the status ndex of the unt at the j stage( 1 for up and for down) Mnmum up tme of unts: ( j j )( j τ ) where, τh w = uj( w j 1 + 1) u u 1 w 1 h, G, j T (1) s the mnmum up tme of the unt and Mnmum down tme of unts: ( )( ) uj uj 1 qj 1 τl, G, j T τ l j = ( 1 j)( j 1 + 1) where, (13) s the mnmum down tme of the unt and q u q Maxmum operatng tme of unts: uj, vj 1 τ u, G, j T (14) ( ) τu where s the mum operatng tme of th unt and vj = uj ( vj 1 + 1) The objectve functon to be mnmzed s gven as n (15) f ( π ) tc( sπ () sπ ( + 1) ) = = 1 where (, j) tc s s s the total transton cost between state and state j that s gven and π () for =1, n defnes a permutaton. Let m be the number of ants, then n m = b t (1) = 1 () where b () t s the number of ants n state at tme t. There s also a global structure that represents the nest neghborhood. In terms of GSP t represents the transton cost between each par of states and the tral left by the ants n the course of the algorthm executon. When the ant system, s appled to symmetrc nstances of he travelng salesman problem, each ant generates a complete tour by choosng the ctes accordng to a probablstc state transton rule to buld a soluton and a local pheromone updatng rule wll be followed. Once all the ants have completed ther tours a global pheromone updatng rule s then appled and the process s terated untl the end condton s satsfed. The state transton rule used by the ant system s called random proportonal rule gven by whch gves the probablty wth whch ant k n cty, chooses to move to the state j. Here τ s the pheromone, =1/ s the nverse of the dstance. Whle constructng ts tour, an ant also modfes the amount of pheromone on the vsted edges by applyng the local updatng rule gven by ( j, ) ( 1 ) ( j, ) ( j, ) τ ρ τ + ρ τ (18) where < ρ <1 s a parameter. The global updatng rule s fnally mplemented as follows. Once all the ants have bult ther tours, the pheromone s updated on all the edges accordng to m τ (, j) ( 1 α) τ (, j) + τ k (, j) (19) k = 1 where <α <1 s a pheromone decay parameter. m s number of ants. ACSA ALGORITHM: The ACSA algorthm shown n fgure 9 conssts of the followng mportant steps. 1) Form the search space. ) m ants are ntally postoned n n states. 3) Each ant bulds a tour by repeatedly applyng the state transton rule 4) By applyng the local updatng rule, amount of pheromone s changed. Once all ants have termnated ther tour, the amount of pheromone s modfed agan by applyng global rule. 5) Seek the best tour usng the soluton process. ) Pheromone updatng rules are so desgned so that they gve more pheromone to edges whch should be vsted by ants. 7) The overall flow of the ACSA based technque s gven n the algorthm below. Generator Schedulng Data: The method dscussed n the prevous secton deals wth 4h generaton schedulng or allocaton problem. The general and fuel characterstcs of unts of the model system (UNITS) are gven below n table 1 below. TABLE 1: FUEL CHARACTERISTICS OF UNIT SYSTEM No Name P Pmn a b c Cost PF mn λ λ 1 UT1 15.51.34 15 11 1 5.9 3.97 UT 7.39 1.911 5 11 1.8 7.18 3 UT3 3.48 1.9 1 11 1 1.1 5.3 4 UT4 5 9.1 1.5354 7 11 1 18.35. 5 UT5 5 19.193 1.818 1 9 1 11.473 1.3 UT.171 1.543 1 9 1 11.335 15.5 The numerc parameters are set to the followng 1 values. L s the α = ρ =.1, β =, τ =, where nn Lnn tour length produced by the nearest neghbor heurstc and n s the number of states, and the number of ant s heurstcally chosen to be 5.
Proceedngs of the th WSEAS Int. Conf. on EVOLUTIONARY COMPUTING, Lsbon, Portugal, June 1-18, 5 (pp17-175) terms of both economy and optmalty, the proposed ACSAbased optmzaton technque s applcable to the short term Start generaton problem of thermal power systems. Form the search space Set parameters and ntalze ants Ants buld ther tours Further studes should be done to nvestgate the feasblty of the algorthm n large systems wth more complcated constrants. TABLE 11: GENERATION SCHEDULING OVER 4 HRS FOR THE GENERATOR SYSTEM Tme 1 3 4 5 7 8 9 1 11 1 Unt1 15 1 15 15 15 1 Unt 8 5 1 31 Unt3 5 5 34 4 38 5 Unt4 8 89 9 Unt5 1 155 1 153 157 17 189 188 19 191 19 19 Unt 198 187 185 17 183 198 1 Apply local updatng rule No Last Ant? Yes Tme 13 14 15 1 17 18 19 1 3 4 Unt1 15 14 15 15 1 1 1 1 15 Unt 1 8 1 54 38 33 45 31 Unt3 35 45 38 7 58 54 31 51 47 3 Unt4 89 9 8 Unt5 19 19 19 19 19 19 19 19 19 19 19 18 Unt Apply global updatng rule Comparson of scheduled capacty Yes Last Strategy? No 8 7 5 No Seek the best tour End condton? Prnt Results Yes Load Load 4 ACSA 3 1 1 3 4 5 7 8 9 11111314151171819134 t[hours] Fg. 1. Generaton Schedulng obtaned by ACO. Fg 9. Flow Chart of Generaton Schedulng usng ACSA X. SCHEDULING RESULTS Table 11 shows the schedulng of unts obtaned by the ACO. In the generaton schedulng we have decded dependng on the cost of generaton that whch unts should be swtched on and whch should be kept off n the 4 hr perod accordng to the varyng load. In ED the unts were kept on all the tme and the generaton was decded to mnmze the cost. Hence by usng ths technque we should see a dfference n the cost ncurred n generaton. Fgure 1 shows the generaton schedulng obtaned by the ACO. Ths method gves us $ 18484.3 whereas just ED gves us $ 18715.9 for the same case. The study results ndcate that, n VII CONCLUSIONS The feld of ACO algorthms s very lvely, as testfed for example by the successful bannual workshop, where researchers meet to dscuss the propertes of ACO and other ant algorthms, both theoretcally and expermentally. From the theory sde, researchers are tryng ether to extend the scope of exstng theoretcal results, or to fnd prncpled ways to set parameters values. From the expermental sde, most of the current research s n the drecton of ncreasng the number of problems that are successfully solved by ACO algorthms, ncludng real-world, ndustral applcatons.
Proceedngs of the th WSEAS Int. Conf. on EVOLUTIONARY COMPUTING, Lsbon, Portugal, June 1-18, 5 (pp17-175) Currently, the great majorty of problems attacked by ACO are statc and well-defned combnatoral optmzaton problems, that s, problems for whch all the necessary nformaton s avalable and does not change durng problem soluton. For ths knd of problems ACO algorthms must compete wth very well establshed algorthms, often specalzed for the gven problem. Also, very often the role played by local search s extremely mportant to obtan good results. Although rather successful on these problems, t s beleved that ACO algorthms wll really prove ther strength when they wll be systematcally appled to ll-structured problems for whch t s not clear how to apply local search, or to hghly dynamc domans wth only local nformaton avalable. A frst step n ths drecton has already been done wth the applcaton to telecommuncatons networks routng, but more research s necessary. More refnement n nfeasblty detecton s requred. The problem can be extended to further dspatch problems wth prohbtng operatng zones and envronmental constrants. It can also be appled to other large scale power system optmzaton problems lke Optmal Power Flow, etc. Important Contrbutons In the case of Economc dspatch, GACO s able to solve complcated, non convex, nonlnear problems. It acheves good convergence and provdes accurate dspatch solutons n reasonable tme. The results show that GACO s robust, accurate and effcent. Further work s requred for searchng the neghborhood, and present more effcacous suffcent condtons for convergence. Varous practcal applcatons of new method wat for further development as well. The effectveness of the ACSA has been demonstrated on the daly generaton schedulng problems of model power systems and n terms of both economy and optmalty, t s applcable. Further studes are beng conducted to nvestgate the feasblty of the algorthm n large systems wth more complcated constrants. [] M. Dorgo, G. D Caro and L. M. Gambardella, 1999. Ant algorthms for dscrete optmzaton. Artfcal Lfe, 5,, pages 137-17. [3] M. Dorgo, V. Manezzo and A. Colorn, 199. Ant System: Optmzaton by a colony of cooperatng agents. IEEE Transactons on Systems, Man and Cybernetcs - Part B,, 1, pages 9-41. [4] M. Dorgo and T. Stützle,. The ant colony optmzaton metaheurstc: Algorthms, applcatons and advances. In F. Glover and G. Kochenberger edtors, Handbook of Metaheurstcs, volume 57 of Internatonal Seres n Operatons Research & Management Scence, pages 51-85. Kluwer Academc Publshers, Norwell, MA. [5] M. Dorgo and T. Stützle, 3. Ant Colony Optmzaton. MIT Press, Boston, MA. [] Colon A, Dorgo M, Manezzo V. An Investgaton of some propertes of Ant Algorthm. Proceedngs of the parallel problem solvng from nature 199; Conference(PPSN9): 59-. [7] Modern optmzaton technques n power systems. In: Song Y H, edtor. Dordrecht: Kluwer, 1999 [8] Yu IK, Song Y H. Short term generaton schedulng of thermal unts wth envronmental constrants. Proceedng of IEE-Generaton Transmsson and Dstrbuton, part C 1997; 144(5): 49-7 [9] Song Y H, Chou C S. Applcaton of ant colony search algorthms n power system optmzaton. IEEE Power Engneerng Revew 1998;18(1):3-4. VIII REFERENCES [1]M. Dorgo and G. D Caro, 1999. The Ant Colony Optmzaton meta-heurstc. In D. Corne, M. Dorgo, and F. Glover edtors, New Ideas n Optmzaton}, pages 11-3. McGraw-Hll.