CLONAL SELECTION-BASED ARTIFICIAL IMMUNE SYSTEM OPTIMIZATION TECHNIQUE FOR SOLVING ECONOMIC DISPATCH IN POWER SYSTEM

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1 Proceedngs of the 6th WSEAS Int. Conf. on EVOLUTIONARY COMPUTING, Lsbon, Portugal, June 16-18, 2005 (pp ) CLONAL SELECTION-BASED ARTIFICIAL IMMUNE SYSTEM OPTIMIZATION TECHNIQUE FOR SOLVING ECONOMIC DISPATCH IN POWER SYSTEM TITIK KHAWA ABDUL RAHMAN, SAIFUL IZWAN SULIMAN, ISMAIL MUSIRIN Faculty of Electrcal Engneerng, Unverst Teknolog MARA,40450, Shah Alam, Selangor Darul Ehsan, MALAYSIA Abstract: - The man role of electrcal power utlty s to ensure that electrcal energy requrement from the customer s served. However n dong so, the power utlty has also to ensure that the electrcal power s generated wth mnmum cost. Hence, for economc operaton of the system, the total demand must be approprately shared among the generatng unts wth an objectve to mnmze the total generaton cost for the system. Economc Dspatch s a procedure to determne the electrcal power to be generated by the commtted generatng unts n a power system so that the total generaton cost of the system s mnmzed, whle satsfyng the load demand smultaneously. Ths paper presents an Artfcal Immune-based optmzaton technque for solvng the economc dspatch problem n a power system. The developed Artfcal Immune optmzaton technque adopted the Clonal Selecton algorthm and was mplemented wth several clonng, mutaton and selecton approaches. These approaches were tested and compared n order to determne the best strategy for solvng the economc dspatch problem. The feasblty of the proposed technques was demonstrated on a system wth 18 generatng unts at varous loadng condtons. The results show that Artfcal Immune System optmzaton technque that employed adaptve clonng, selectve mutaton and par-wse tournament selecton has provded the best result n terms of cost mnmzaton and least executon tme. A comparatve study wth λ-teraton optmzaton method and Genetc Algorthm was also presented. Key-Words: - Artfcal Immune System, Clonal Selecton, Optmzaton, Economc Dspatch. 1 Introducton Electrcal power system are desgned and operated to meet the contnuous varaton of power demand. The power demand s shared among the generatng unts and economc of operaton s the man consderaton n assgnng the power to be generated by each generatng unts. Therefore, Economc Dspatch(ED) s mplemented n order to ensure for economc operaton of a power system. Economc Dspatch problem s an optmzaton problem that determnes the optmal output of onlne generatng unts so as to meet the load demand wth an objectve to mnmze the total generaton cost[1]. Varous mathematcal methods and optmzaton technques have been employed to solve for ED problems. Among the conventonal methods that were prevously employed nclude lambda teraton method, base pont and partcpaton method and the gradent method. These numercal methods assumed the ncremental cost curves of the generatng unts are monotoncally ncreasng pecewse lnear functons. However, ths assumpton may cause these methods to be nfeasble because of the nonlnear characterstcs of the actual systems. In order to take nto account of the nonlnear characterstcs of the system, dynamc programmng (DP) method has been mplemented for solvng the ED problem as n reference [2]. Nevertheless, the DP method may cause the dmensons of the ED problem to be solved becomes extremely large, hence requres massve computatonal effort. In the past decade, global optmzaton technques such as smulated annealng (SA), genetc algorthms (GAs) and evolutonary programmng (EP) have been ncreasngly used to solve for power system optmzaton problems [3]. The SA method s a powerful optmzaton technque that employs probablstc approach n acceptng canddate

2 Proceedngs of the 6th WSEAS Int. Conf. on EVOLUTIONARY COMPUTING, Lsbon, Portugal, June 16-18, 2005 (pp ) solutons n ts search process so that t can jump out from the local optmal solutons to approach the near global soluton [4]. However, t s dffcult to approprately set the control parameters of the SA based algorthm and n addton, the speed of the algorthm s slow when appled to real power system problems [5]. Snce ts ntroducton n late 1980 s, GAs has been used to solve many power system optmzaton problems. It has been successfully employed to solve for economc dspatch problem due ts ablty to model any knd of constrants usng varous chromosome-codng schemes accordng to specfc problem [6]. On the other hand, long executon tme and non-guaranteed n convergence to the global optmal soluton contrbute the man dsadvantages of GAs. Another bologcally nspred optmzaton-technque, the evolutonary programmng has also receved ncreasng attenton by many researchers due to ts ablty to look for near global optmal soluton. It has been successfully appled to solve optmzaton problems n power system such as economc dspatch, unt commtment, optmal power flow and many others. However, ts long executon tme posed ts man dsadvantage [7]. Artfcal mmune systems can be defned as metaphorcal systems developed usng deas, theores and components, extracted from the natural mmune system [8]. The natural mmune system s a very complex system wth several mechansms for defense aganst pathogenc organsms. The man purpose of the mmune system s to recognze all cells wthn the body and categores those cells as ether self or nonself. The mmune system learns through evoluton to dstngush between dangerous foregn antgens and the body s own cells or molecules. From an nformaton-processng perspectve, the mmune system s a remarkable parallel and dstrbuted adaptve system. It uses learnng, memory and assocatve retreval to solve recognton, classfcaton and optmzaton tasks [9]. A few computatonal models have been developed based several prncples of the mmune system such as mmune network model, negatve selecton algorthm, postve selecton algorthm and clonal selecton prncple [10,11]. In ths paper, a new method for solvng ED problem based on the Artfcal Immune System (AIS) s presented. The developed AIS adopted the Clonal Selecton algorthm n determnng the optmal actve power to be generated by the generatng unts n a power generaton system. The am of the clonal operator s to produce a varaton n the populaton around the parents accordng the affnty [12]. Hence, the searchng area s enlarged and premature convergence can be avoded. The feasblty study of the proposed technque was conducted on a practcal system havng 18 generatng unts. Several loadng scenaros wth a number of equalty and n equalty constrants were tested n order to demonstrate the effectveness of the proposed technque. The results obtaned from the proposed technque were also compared wth those obtaned from the GA optmzaton methods n order to assess the soluton qualty and computatonal effcency. 2 Economc Dspatch Mathematcal Formulaton Solvng the Economc Dspatch problem s to solve an optmzaton problem wth an objectve to mnmze the total cost of generaton. The soluton gves the optmal generaton output of the onlne generatng unts that satsfy the system s power balance equaton under varous system and operatonal constrants. The Economc Dspatch problem can be formulated mathematcally as follows: Equaton 1 s the total generaton cost to be mnmzed and therefore the objectve functon to the problem. Its value s taken to be the affnty to antbody n the AIS optmzaton technque. F = N T F (P ) (1) = 1 F p 2 (P ) = a + b P + c (2) The cost of power generaton for each generatng unt s gven by equaton 2. Parameters a, b, c n the equaton symbolzes constants on the Input- Output Curve of a generatng unt. The ED problem consdered n ths paper s the classc ED, whereby the losses are neglected. Hence, the power balance equaton s gven by equaton 3 and t s the equalty constrant that has to be satsfed. Whle equaton 4 s the nequalty constrant, ndcatng the generaton lmts for each generatng unt n the system. P 1 + P 2 + P P N = P D (3) P mn <= P <= P max (4) P D s the total load demand (Megawatts). P s the

3 Proceedngs of the 6th WSEAS Int. Conf. on EVOLUTIONARY COMPUTING, Lsbon, Portugal, June 16-18, 2005 (pp ) output of generatng unt. P,mn and P,max are the lower and upper lmts of power generated by unt. N s the number of generators n the power generaton system. 3 Artfcal Immune System The natural mmune system s a complex pattern recognton system that defends the body from foregn pathogens. In a smple manner, t recognzes all the body s own cells wthn the body as the selfcells and the foregn dsease causng elements or the antgens as the non-self-cells. The non-self cells are further characterzed n order to actvate the sutable defense mechansm whch s unque wth respect to a partcular antgen. At the same tme, the mmune system also developed a memory to enable more effcent responses n case of further nfecton by the smlar antgen. The process taken place n the mmune system can be looked as a dstrbuted task force that has the ntellgence to take acton from a local and global perspectve usng a network of chemcal messengers for communcaton [11]. when exposed to a second antgenc stmulus, they wll dfferentate nto large lymphocytes that are capable to produce hgh affnty antbodes to fght aganst the same antgens that stmulated the frst response [13]. Fgure 1 shows the mechansm of the mmune system [11]. The fgure shows that after the selectve actvaton through the bndng of antgens, the lymphocytes wll duplcate themselves through clonal prolferaton and maturate nto plasma cells and also long-lved memory cells. The plasma cells then secrete antbodes that are smlar to the receptor of the B-lymphocytes and they are ready to bnd the antgens. Durng the process, T cells are responsble n regulatng the B cells response to produce antbodes. In order to understand the theoretcal concept of AIS, the bologcal process of the mmune system need to be apprecated. B-lymphocytes and T- lymphocytes are the two man components n the lymphocyte structure responsble for the defense mechansm n the body mmune system. The B- lymphocytes are cells produced by the bone marrow and the T-lymphocytes are cells produced by the thymus. B-lymphocyte wll produce only one antbody that s placed on ts outer surface that acts as a receptor. When our body s exposed to an antgen, B-lymphocytes would respond to secrete antbodes specfc to the partcular antgen. The porton on the antgen recognzed by the antbody s called eptope that acts as an antgen determnant. Hence, each type of antbody has ts specfc antgen dentfer called dotope. The matchng antbody-antgen are bounded and a second sgnal from the T-helper cells, would then stmulates the B-lymphocyte to prolferate and maturate formng a large clone of the plasma cells. Plasma cells are non-dvdng cells that secrete large amount of antbodes. Snce the lymphocytes can only make only one antbody, therefore the antbodes secreted by the plasma cell wll be dentcal to that whch was orgnally acted as the lymphocyte receptor [11]. Besdes maturng nto plasma cells, the lymphocytes also dfferentate nto long-lved B-memory cells. These memory cells crculate through the blood, lymph and tssue, so that Fg. 1 Mechansm of Immune System 3.1 Clonal Selecton Algorthm The mmune process descrbed n secton 3.0 s known as Clonal Selecton Algorthm. Only only those cells that recognzed the specfc antgens would be selected to prolferate and thus go through the process of affnty maturaton depct ths. The man features of the clonal selecton prncple are as follows [10] :- a) New cells are copes of ther parents (clone) subjected to a mutaton mechansm. b) Elmnaton of newly dfferentated lymphocytes carryng self-reactng receptors.

4 Proceedngs of the 6th WSEAS Int. Conf. on EVOLUTIONARY COMPUTING, Lsbon, Portugal, June 16-18, 2005 (pp ) c) Prolferaton and dfferentaton on contact of mature cells wth antgens d) The persstence of forbdden clones provdes resstant to early elmnaton by self-antgens as the bass of autommune dseases. In the selecton stage of the clonal selecton algorthm, B cells wth hgh affnty wth respect to an antgen would be able to recognzed the antgen. They are then actvated and stmulated to prolferate producng a large number of clones. In the maturaton process, these clones mutate and turn nto plasma cells whch then that secrete large number of antbodes. Some of the B cells clones maturate nto memory cells that have the memory of the antgenc pattern for future nfectons. The antbodes secreted from the second response would have hgher affnty than those of the earler response. In the computatonal pont of vew, ths strategy suggests that the process perform a greedy search, where the ndvdual wll be locally optmzed and the newcomers would yeld a broader exploraton of the search space. Ths characterstcs makes the clonal selecton algorthm s sutable for solvng multmodal optmzaton problems[14]. When the clonal selecton algorthm s mplemented for solvng optmzaton problem, a few adaptatons have to be made as follows [11] :- a) There s no explct antgen to be recognzed, but an objectve functon s to be optmzed. Therefore the affnty of an antbody refers to the evaluaton of the objectve functon. b) All antbodes are to be selected for clonng. c) The number clones generated by the antbodes are equal. However, ths study nvestgated the effect of varyng the number of clones accordng to the affnty and the results were compared to that obtaned from standard clonng process. 5 Implementaton of Clonal Selecton- Based AIS for Economc Dspatch The developed AIS optmzaton technque adoptng Clonal Selecton algorthm was mplemented to solve the economc dspatch problem on a practcal system havng 18 generatng unts [6]. Real number was used to represent the attrbutes of the antbodes. Each antbody attrbute wll be n a form of a par of real valued vector (x, η ), { 1,, µ }, where η s a strategy parameter[15]. Each antbody wll go through the mutaton process accordng to the expresson gven by equatons 5 and 6. η (j) = η (j) exp(τ N(0,1) + τn j (0,1)), (5) x (j) = x (j) + η (j) N j (0,1), (6) where, N(0,1) s a normally dstrbuted random number wth zero mean and standard devaton equals to one. τ = ((2(n) 1/2 ) 1/2 ) -1 (7) τ = ((2n) 1/2 ) -1 (8) n = number of attrbute for an antbody The clonal selecton was mplemented accordng to the followng procedures :- a) Intal populaton s formed by a set of randomly generated real numbers. Each antbody was tested for any constrant volaton usng equatons (3) and (4). Only antbodes that satsfy the constrant are ncluded n the populaton set. b) The affnty value of each antbody n the populaton set s evaluated usng equaton (1). c) Clone the ndvduals n the populaton, gvng rse to a temporary populaton of clones. d) The populaton of clones undergoes maturaton process through genetc operaton.e mutaton. The ftness of the mutated clones are evaluated. e) A new populaton of the same sze as the ntal populaton s selected from the mutated clones based on ther affnty. f) The new populaton wll undergo the same process as stated n steps a e. g) The process s repeated untl the soluton converged to an optmum value. Two other mutaton technques were also tested namely Cauchy mutaton and selectve mutaton. Cauchy mutaton scheme used Cauchy dstrbuted random number to generate mutated the ndvduals and selectve mutaton selects the best ndvdual resulted from Gaussan and Cauchy mutaton schemes. Fnally, two selecton strateges namely rankng and par-wse tournament were mplemented for comparson. As other optmzaton technque, several parameters have to be determned before ts mplementaton such as the populaton sze, number of clones generated by each antbody (for fxed clones sze) and mutaton rate. Based on the smulaton results, the followng parameters are found to be sutable: 20

5 Proceedngs of the 6th WSEAS Int. Conf. on EVOLUTIONARY COMPUTING, Lsbon, Portugal, June 16-18, 2005 (pp ) members n a populaton pool, the number of prolferated clones s 10 and the mutaton probablty s Results Table 1 gves the generator operatng lmts and quadratc cost functon coeffcents for the 18 generators n the test system. The maxmum total power output Ρ of the generators s MW. Varous tests were made wth varyng percentage of the maxmum power as the power demand. Table 1. Generator operatng lmts and quadratc cost functon coeffcents. No. P max P mn a b c (MW) (MW) $/hr S/MWhr $/MW 2 hr The results from the smulaton are summarzed n Table 2. Ths table shows the mnmum generaton cost obtaned by each AIS technque mplementng dfferent strateges of clonng, mutaton and selecton. The smulaton was done when the demand s 70% of the total maxmum power output. It can be observed that the mnmum generatng cost s obtaned by the real number AIS technque that mplemented adaptve clonng, selectve mutaton strategy and tournament selecton wth total generaton cost of $ The average executon tme for all of AIS technques s 2 s. Table 2. Mnmum Generaton Cost From the Smulaton Clonng Mutaton Selecton Ftness (Mnmum Generaton Cost) /$h -1 Gaussan Rankng Tournament Standard Adaptve Cauchy Selectve Gaussan Cauchy Selectve Rankng Tournament Rankng Tournament Rankng Tournament Rankng Tournament Rankng Tournament The results obtaned from the proposed real number AIS technque mplementng adaptve clonng, selectve mutaton strategy and tournament selecton were compared wth those obtaned from the classcal optmzaton technque namely λ-teraton method and Genetc Algorthm technque as shown n Table 3. From these results, t shows that the proposed technque has performed much better than the classcal optmzaton technque, bnary-coded GA and also real-coded GA for varous power demands. The proposed AIS optmzaton technque was much faster than the other technques. It takes only 2 seconds to provde the optmal soluton. The tests were carred out a Pentum IV personal computer. Table 3. Comparson n Mnmum Generaton Cost Obtaned From Varous Optmzaton technque Demand λ-teraton Bnary GA Real GA Real AIS 95% P % P % P % P Executon tme (s)

6 Proceedngs of the 6th WSEAS Int. Conf. on EVOLUTIONARY COMPUTING, Lsbon, Portugal, June 16-18, 2005 (pp ) 7 Concluson A new approach of usng clonal selecton based AIS to solve for economc dspatch n power system s presented. The developed AIS technque s capable to determne the power to be generated by each generatng unt n power system so that the cost of generaton could be mnmzed whle satsfyng the operatng constrants. Several modfcatons were made on the clonng, mutaton and selecton schemes of the developed AIS optmzaton technque. The results obtaned from varous combnatons of schemes were compared. It was found that the developed AIS optmzaton technque employng adaptve clonng scheme, selectve mutaton and tournament selecton gves the best result. A comparatve study was carred out between the proposed technque, the λ-teraton method and also Genetc Algorthm technque. The results has shown that the proposed real number AIS optmzaton technque wth adaptve clonng scheme, selectve mutaton and tournament selecton s also capable to provde better results wth reduced computaton tme. Ths study also shows that AIS could be a promsng technque for solvng complcated optmzaton problems n power system operaton. References: [1] J. Tppayacha, W. Ongsakul and I. Ngamroo, Parallel Mcro Genetc Algorthm for Constraned Economc Dspatch, IEEE Trans. Power Syst., vol.17, pp , Aug [2] F.N. Lee and A.M Brepohl, Reserved Constraned Economc Dspatch Wth Prohbtve Operatng Zones, IEEE Trans. Power Syst., vol.8, pp , Feb [3] K.P. Wong and Y.W. Wong, Genetc and Genetc/Smulated Annealng Approaches to Economc Dspatch, Proc. IEE Gen. Trans. Dst., vol.141, no. 5, pp , Sept [4] P. Attavryanupp, H. Kta, T. Tanaka and J. Hasegawa, A Hybrd EP and SQP for Dynamc Economc Dspatch Wth Nonsmooth Fuel Cost Functon, IEEE Trans. Power Syst., vol.17, pp , May [5] A.G. Bakrtzs, V. Petrds and S. Kazarls, Genetc Algorthm Soluton to The Economc Dspatch Problem, Proc. IEE Gen. Trans. Dst., vol.141, no. 4, pp , July [6] J. G. Damouss, A.G. Bakrtzs and P.S. Dokopoulos, Network-Constraned Economc Dspatch Usng Real-Coded Genetc Algorthm, IEEE Trans. Power Syst., vol.18, pp , Feb [7] B. N. S. Rahmullah, E.I. Ramlan and T.K.A. Rahman, Evolutonary Approach for Solvng Economc Dspatch n Power System, In Proceedngs of the IEEE/PES Natonal Power Engneerng Conference, vol.1, pp , Dec [8] L. N. de Castro and J. Tmms, Artfcal Immune Systems : A Novel paradgm to Pattern Recognton, In Artfcal Neural Networks n Pattern Recognton, SOCO-2002, Unversty of Pasley, UK, pp , [9] D. Dasgupta and N. A. Okne, Immunty-Based Systems: A Survey, In Proceedngs of the IEEE Internatonal Conference on Systems, Man and Cybernetcs, vol.1, pp , Oct [10] L.N. de Castro and F.J. Von Zuben. Learnng and Optmsaton Usng the Clonal Selecton Prncple, IEEE Trans. Evolutonary Computaton., vol.6, pp , June [11] L.N. de Castro and F.J. Von Zuben. Artfcal Immune System : Part 1 Basc Theory and Applcatons, Techncal report, TR-DCA 01/99, Dec [12]H. F. Du, L.C. Jao and S. A. Wang, Clonal Operator and Antbody Clone Algorthms, In Proceedngs of the Frst Internatonal Conference on Machne Learnng and Cybernetcs, Bejng, pp , Nov [13]D. Dasgupta and N. A. Okne, Immunty-Based Systems: A Survey, In Proceedngs of the IEEE Internatonal Conference on Systems, Man and Cybernatcs, vol.1, pp , Oct [13]J. A. Whte and S. M. Garrett, Improved pattern Recognton wth Artfcal Clonal Selecton, Dept. of Computer Scence, Unversty of Wales, June aper.pdf [14]Y. Matsumura, K. Okhura and K. Ueda, Evolutonary Programmng wth Non-Codng Segments for Real Valued Functon Optmzaton, In Proceedngs of the IEEE Internatonal Conference on Systems, Man and Cybernatcs 1999, vol.4, pp , Oct 1999.