Differential Evolution Immunized Ant Colony Optimization Technique in Solving Economic Load Dispatch Problem

Transcription

1 Engneerng, 013, 5, do:10.436/eng b09 Publshed Onlne January 013 ( Dfferental Evoluton Immunzed Ant Colony Optmzaton Technque n Solvng Economc Load Dspatch Problem N. A. Rahmat, I. Musrn Unverst Teknolog MARA, Malaysa Emal: azamrahmat@gmal.com, _musrn@yahoo.co.uk Receved 013 Abstract Snce the ntroducton of Ant Colony Optmzaton (ACO) technque n 199, the algorthm starts to gan popularty due to ts attractve features. However, several shortcomngs such as slow convergence and stagnaton motvate many researchers to stop further mplementaton of ACO. Therefore, n order to overcome these drawbacks, ACO s proposed to be combned wth Dfferental Evoluton (DE) and clonng process. Ths paper presents Dfferental Evoluton Immunzed Ant Colony Optmzaton (DEIANT) technque n solvng economc load dspatch problem. The combnaton creates a new algorthm that wll be termed as Dfferental Evoluton Immunzed Ant Colony Optmzaton (DEIANT). DEIANT was utlzed to optmze economc load dspatch problem. A comparson was made between DEIANT and classcal ACO to evaluate the performance of the new algorthm. In realzng the effectveness of the proposed technque, IEEE 57-Bus Relable Test System (RTS) has been used as the test specmen. Results obtaned from the study revealed that the proposed DEIANT has superor computaton tme. Keywords: Ant Colony Optmzaton (ACO), Dfferental Evoluton (DE), Dfferental Evoluton Immunzed Ant Colony Optmzaton (DEIANT) 1. Introducton In 199, Marco Dorgo ntroduced a probablstc algorthm known as Ant Colony Optmzaton (ACO) technque. In hs PhD thess, he descrbed that ACO resembles the natural behavor of a colony of ant durng ther random expedton to fnd the best path between ther nest and food source. The ant wll depost a chemcal trace known as pheromone. The pheromone wll act as the stmulant to attract more ants to utlze on the same path. Any less-traveled paths wll be forgotten snce ther pheromone traces has been evaporated. Marco Dorgo employed ths behavor nto hs research to solve the travellng salesmen problem (TSP) [1]. Snce, ACO has attracted many researchers to employ the algorthm nto ther research. Mohd Rozel Kall et. al successfully mplements ACO to gan maxmum loadablty n voltage control study []. Ashsh Ahuja and Anl Pahwa [3] stated n ther research that ACO sgnfcantly mnmzed the loss n a dstrbuton system. Moreover, D. Nualhong et. al utlzes ACO n hs research to solve the unt commtment problems [4]. However, further research on the algorthm ndcates that ACO suffers from several shortcomngs. H. B. Duan, et al stated n hs research that ACO may experence stagnaton due to ts postve feedback strategy. The researcher also hghlghted that the random selecton strategy of ACO makes the algorthm sluggsh [5]. Another researcher clamed that ACO has slow convergence rate [6-7]. Another attractve optmzaton technque s the Dfferental Evoluton (DE). DE was created by Storn and Prce n 1995 [8]. As a typcal Evolutonary Algorthm (EA), DE was used to solve stochastc, non-dfferentable, non-lnear, mult-dmensonal and populaton-based optmzaton problem [9]. The algorthm was also used to solve a Chebychev Polynomal Fttng Problem durng the Frst Internatonal Contest on Evolutonary Computer (1 st ICEO) n Nagoya. As a typcal Evoluton Algorthm, DE comprses of mutaton, crossover, and selecton process. In 1997, Storn and Prce stated that DE s much better than Smulated Annealng and Genetc Algorthm [10]. As such, DE has become the canddate technque to optmze Neural Network Learnng, Rado Network desgn, multprocessor synthess and gas transmsson network desgn. Therefore, ths paper presents Dfferental Copyrght 013 ScRes.

2 158 N. A. RAHMAT, I. MUSIRI Evoluton Immunzed Ant Colony Optmzaton (DEIANT) technque n solvng economc load dspatch problem. The am of the proposed technque s to allevate the slow convergence, and stagnaton experenced n the tradtonal ACO through the applcaton of DE. The performance of DEIANT wll be evaluated by usng the algorthm to solve and optmze economc load dspatch problems. Performance evaluaton of the proposed DEIANT revealed that the proposed technque s superor than the tradtonal ACO n terms of achevng optmal soluton and computaton tme.. Dfferental Evoluton Immunzed Ant Colony Optmzaton Formulaton The capablty to acheve fast convergence has been dentfed as the attractve feature of DE [10]. Ths feature wll be used to compensate the stagnaton of ACO algorthm. The modfcaton of ACO algorthm wll be focusng on the pheromone updatng rule whch s subjected to clonng, mutaton, crossover, and selecton process. Fgure 1 depcts the overall structure and processes of Dfferental Evoluton Immunzed Ant Colony Optmzaton (DEIANT) algorthm. DEIANT s confgured from the combnaton of orgnal ACO, combned wth DE and clonng process. ACO search agent wll ntalze random tours and depost pheromone layers. The algorthm wll update the pheromone level at each teraton. Clonng process wll ncrease the pheromone amount by generatng the exact copes of the pheromone layer. To enhance the pheromone layer, DE wll mutate and crossover the pheromone layer, thus ncreasng the dversty of the pheromone. ACO wll evaluate the ftness of the pheromone layer. ACO Clonng process DE Ant colony depost pheromone layer Increases pheromone quantty Mutaton and crossover process enhance pheromone dversty Fgure 1. Structural dagram of DEIANT.1. Intalzaton DEIANT DEIANT consst of several classcal ACO parameters. Therefore, smlar to ACO technque, the ntal number of ant, nodes, pheromone decay parameter, α, and the ntal pheromone level, τ 0 wll be heurstcally ntalzed. The maxmum dstance travelled by each ant, d max, s subjected to a constrant n order to avod large computaton tme. d max s obtaned by calculatng the longest dstance travelled by the ants. Each ant wll tour and select the next unvsted node untl all nodes have been vsted... Apply State Transton Rule The next unvsted node s chosen accordng to the state transton rule, s. Each node can only be vsted once. The ant that was postoned at node(r) wll go to the next node(s). β [ τ( r,s )] [ η( r.s ) ] P ( r,s ) = k µεj k( r ).3. Apply Local Updatng Rule β [ τ( r,u )] [ η( r.u ) ] Alterng the level of pheromone deposton s done durng the constructon of soluton. The amount of pheromone s ether ncreased or decreased to vary the attractveness of the route va the evaporaton rate, ρ. Dorgo stated that parameter ρ s needed to avod the algorthm converge pre-maturely. The parameter ρ act as a multpler and s set between 0 to 1. In ths research, the evaporaton rate s set to 0.7, meanng that at every teraton; the pheromone wll be reduced by Pheromone Clonng The clonng process from Artfcal Immune System s mplemented nto DEIANT. The pheromone level wll be duplcated to ncrease pheromone populaton and dversty. Fgure below depcts the clonng of the orgnal pheromone level. [ r s] υω Where υ represents the set of pheromone that wll be cloned, and ω represents the cloned pheromone set. Both υ and ω can be wrtten as υ = 1,,V and ω = 1, W, respectvely..5. Pheromone Mutaton [ r s] 11 [ r s] 1 Fgure. Pheromone clonng process The pheromone mutaton process s used to enhance the pheromone layer over the vsted node durng ant exploraton. The Gaussan Dstrbuton Equaton was utlzed to mutate the pheromone level as n (): (1) Copyrght 013 ScRes.

3 N. A. RAHMAT, I. MUSIRI 159 f ( ) X j max X j mn f max X + m, j = X, j + N 0, β () Where : Pheromone mutaton functon X + m, j X j mn : Smallest vsted node X j max : Largest vsted node f max : Dstance travelled by ant f : Longest dstance travelled by ant.6. Crossover Crossover operaton s mplemented to emphasze the dversfcaton vector of the pheromone tral. The mutated pheromone tral and the orgnal one wll merge together by applyng a bnomal dstrbuton known as the crossover operaton. In ths algorthm, the orgnal and mutated pheromone level wll be resorted wthn the same matrx. The crossover matrx, X g s sorted n descendng order, as shown below: X g Where n s the hghest pheromone level for the tour, and n-m s the lowest pheromone level..8 Selecton n = n 1 Tral pheromone tral, ρ t s the product of the crossover process. The algorthm wll now select the requred tral accordng to ths rule: ρt,f ρ t = n 1 n m pheromone level, ρ α ρ,otherwse Where α s the pheromone decay parameter. Bascally, the selecton process wll specfy the acceptable condton to accept the pheromone level. The tral wth a hgher pheromone level wll be selected. The tral wth fewer pheromone levels wll be dscarded..9 Control Varable Calculaton (3) (4) The control varable x, s computed by applyng the followng equaton: Where: d : dstance for every ants tour d max : maxmum dstance for every ants tour x max : maxmum of x Varable x wll become the multpler to calculate the objectve functon. In ths research, varable x s multpled wth the cost functon (7)..10 Global Updatng Rule After all ants have fnshed performng ther random exploraton, the best ant of the colony wll be selected. The best ant s carryng the data of the best tour, and thus, the data wll be stored. The followng equaton s appled to update the pheromone level globally: ( r,s) ( 1 α ) τ ( r,s) α. τ( r,s ) τ + (6) The globally best tour wll be selected as the frst node of the next teraton..11 End Condton d x = xmax (5) d max The DEACO algorthm wll halt the teraton when the maxmum number of teraton (t max ) has been reached and all ants have completed ther tours. If a better path s dscovered, t wll be used as the reference. Only one ant wll fnd the optmal path. 3. Economc Load Dspatch Formulaton Economc load dspatch s the operaton of determnng the optmal output that must be produced by the generaton facltes to feasbly satsfy the load demand [1]. Therefore, the key objectve of economc load dspatch s to reduce the operatng cost of each generatng unt n the power system. The operaton cost can be calculated by utlzng equaton (7): Ng cost = F ( P ) (7) Where Ng s the number of generatng unt. F (P ) s the cost functon, and P s the real power output of the unt I, measured n MW. F (P ) s usually approxmated by a quadratc functon: F ( P ) = a P + b P c (8) + Copyrght 013 ScRes.

4 160 N. A. RAHMAT, I. MUSIRI Where a, b, and c are the cost coeffcents of generator. The above equaton s subjected to both the equalty and nequalty constrants. The system power loss can be calculated by usng the power flow equaton below (19): L N N j j j N P = P B P + B P + B Where B j, B o, and B oo are the B-loss coeffcent. The cost functon s gven by equaton (6): n n o n oo (9) C = a + bp + cp (10) The followngs are the generators operatng costs for IEEE 57-Bus System. These equatons are derved from equaton (10): C = P P1 = P P C 3 = P P3 6 = P P6 8 = P P8 9 = P P P P1 C = + (11) Where C 1, C, C 3, C 6, C 8, C 9 and C 1 are the operatng cost functons for generator 1, generator, generator 3, generator 6, generator 8, generator 9, and generator 1 respectvely. The total operatng cost, C T can be formulated as: C T = C1 + C + C3 + C6 + C8 + C9 + C1 (1) The total operatng cost s the objectve functon for ths research. The objectve s to cut-down the total operatng cost, whle preservng the system constrants wthn the permssble lmts. Whle mnmzng the operatng cost, t was ntally estmated that the power loss wll be reduced as well. Power loss s the margnal dfference between the power produced, and the power sold to the consumer [13]. 4. Results and Dscusson The DEIANT algorthm was developed by usng MATLAB. The algorthm was used to optmze economc load dspatch problem. The research was conducted on IEEE-57 bus system. The system contans seven generatng unts. The load was vared to assess the performance of the proposed algorthm. The objectves are to mnmze the total generatng cost, to reduce transmsson loss, and to reduce the computaton tme. Comparsons were made between DEIANT and the orgnal ACO. Table 1 tabulates the smulaton results of classcal ACO algorthm. Table tabulates the smulaton results of the newly developed DEIANT algorthm. Note that the load, desgnated by Q d at Bus 10 was vared between 0 to 5MVAR to see the performance of DEIANT n solvng economc load dspatch problem. The comparson of DEIANT and classcal ACO undoubtedly ponts out that the new algorthm successfully outperforms the classcal ACO. Varyng the load gves less mpact to the performance of DEIANT. For example, when Q d s set to 0MVAR, DEIANT generates the total operatng cost of $/h. The cost s economcal than the one calculated by classcal ACO (4186 $/h), gvng a prce drop of %. If the load was set to 15MVAR, the dea s the same; DEIANT only generates lower power loss. Table 1. Smulaton results of classcal ACO Q d (MVAR) P 1 (MW) P (MW) P 3 (MW) P 6 (MW) P 8 (MW) P 9 (MW) P 1 (MW) P loss (MW) Total Cost ($/h) Tme (s) Table. Smulaton results of DEIANT Copyrght 013 ScRes.

5 N. A. RAHMAT, I. MUSIRI 161 Q d (MVAR) P 1 (MW) P (MW) P 3 (MW) P 6 (MW) P 8 (MW) P 9 (MW) P 1 (MW) P loss (MW) Total Cost ($/h) Tme (s) Moreover, at 0MVAR load adjustment, the classcal ACO computed power loss of MW. However, DEIANT effectvely reduces t to 19.87MW, wth a sgnfcant dfference of 17.5kW. Furthermore, DEIANT possesses faster computaton tme than the classcal ACO. For nstance, classcal ACO requres about 35 seconds to optmze the objectve functon, but DEIANT optmze the objectve functon n just fve seconds. Ths mples that DEIANT can acheve optmal soluton at a faster rate, although the algorthm s more complex and sophstcated than the classcal ACO. 5. Concluson Ths study demonstrates the development of a new algorthm termed as Dfferental Evoluton Immunzed Ant Colony Optmzaton (DEIANT). Through the combnaton of DE, ACO and clonng process, ths new algorthm has successfully overcome the drawbacks of classcal ACO algorthm. The good performance of DEIANT was verfed by optmzng economc load dspatch problem. Comparsons wth classcal ACO mply that DEIANT effectvely cuts-down the operatng cost whle reducng the power loss. The optmzaton process was performed wth a faster speed than the classcal ACO. Future development wll be focusng on the modfcaton to ncrease the convergence speed of the algorthm. 6. Acknowledgement The authors would lke to acknowledge The Research Management Insttute (RMI) UTM, Shah Alam and Mnstry of Hgher Educaton Malaysa (MOHE) for the fnancal support of ths research. Ths research s supported MOHE under the Fundamental Research Grant Scheme (FRGS) wth project code: 600-RMI/ST/FRGS 5/3/Fst (163/010). REFERENCES [1] Yng-Tung Hsao, Cheng-LongChuang and Cheng- Chh Chen, Ant Colony Optmzaton for Best Path Plannng, Internatonal Symposum on Communcatons and Informaton Technologes 004 (ISCIT 004), Sapporo, Japan, 6-9 October 004, pp [] Mohd Rozely Kall, Ismal Musrn, Muhammad Murtadha Othman, Maxmum Loadablty n Voltage Control Study Usng Ant Colony Optmzaton Technque, IEEE Frst Internatonal Power and Energy Conference (PECon007), 8-9 Nov. 006, pp [3] Ashsh Ahuja and Anl Pahwa, Usng Ant Colony Optmzaton for Loss Mnmzaton n Dstrbuton Networks, 37th Annual North Amercan Power Symposum, 005, 3-5 Oct. 005, pp [4] D. Nualhong, et al., "Dversty Control Approach to Ant Colony Optmzaton for Unt Commtment Problem," n TENCON IEEE Regon 10 Conference, 004, pp Vol. 3. [5] H.B. Duan and D.B. Wang, a novel mproved ant colony algorthm wth fast global optmzaton and ts smulaton, Informaton and Control, vol.33, pp , Aprl 004. [6] Lnda Slman and Tarek Bouktr, Economc Power Dspatch of Power System wth Polluton Control usng Multobjectve Ant Colony Optmzaton, Internatonal Journal of Computatonal Intellgence Research (IJCIR) 007, Vol. 3, No., pp [7] R. Bhavan, G. Sudha Sadasvam, and R. Kumaran, "A novel parallel hybrd K-means-DE-ACO clusterng approach for genomc clusterng usng MapReduce," n Informaton and Communcaton Technologes (WICT), 011 World Congress on, 011, pp [8] R. Storn and K. Prce, Dfferental Evoluton A Smple and Effcent Adaptve Scheme for Global Optmzaton Over Contnuous Spaces, Techncal Report TR-95-01, ICSI, March [9] K.P. Wong and Z.Y. Dong, Dfferental Evoluton, an AlternatveApproach to Evolutonary Algorthm, n K.Y. Lee edt. Copyrght 013 ScRes.

6 16 N. A. RAHMAT, I. MUSIRI Intellgent Optmzaton and Control for Power Systems, IEEE Publshng, nvted chapter, Nov [10] Storn R., Prce K.: Dfferental Evoluton A Smple and Effcent Adaptve Scheme For Global Optmzaton Over Contnuous Space, Journal of Global Optmzaton, [11] N. A. Rahmat, I. Musrn (01). Dfferental Evoluton Ant Colony Optmzaton Technque (DEACO) In Solvng Economc Load Dspatch Problem. IEEE Internaton Power Engneerng and Optmzaton. [1] S. M. V. Pandan and K. Thanushkod, "Solvng Economc Load Dspatch Problem Consderng Transmsson Losses by Hybrd EP-EPSO Algorthm for Solvng Both Smooth and Non-Smooth Cost Functon," Internatonal Journal of Computer and Electrcal Engneerng, vol., 010 [13] M. Basu, Artfcal Immune System for Dynamc Economc dspatch, Electrcal Power and Energy System, vol. 33, pp , 7 June 010 Copyrght 013 ScRes.