lAl''''C Hi KHOA IKK & C OINCJ NCJIi ( ACTRlKlNC; DAI HOC KY THUAT * SC) 7 6 2 0 1 0 NKW P A R T K L i SWARM OPTIMIZATION ALGORITHM FOR ECONOMIC LOAI) DISPA l ( II WITII VALVE POINT EFFECTS fllU,''''\T TOAN[.]
lAl'C Hi KHOA IKK & C OINCJ NCJIi ( ACTRlKlNC; DAI HOC KY THUAT * SC) - NKW P A R T K L i : SWARM OPTIMIZATION ALGORITHM FOR ECONOMIC LOAI) DISPA l ( II WITII VALVE POINT E F F E C T S fllU,'\T TOAN PS()M(')1 Df, GIAI BAI fOAN DIIU DO KINH TE \ ( i l ANH lllKiNd CUA DILM VAN CONG SUAT Le Dinh l.iion^, I'li Phan Tu, Vo Nffoc Dieu Ho Chi Minh City Universitv ofTccliiicdogv ABSTRACT 7"/i/,s paper proposes a new Particle Swarm Optimization (NPSO) method for solving the economic load dispatch (ELD) problem with valve point effects The proposed NPSO is an improvement of particle swarm optimization method with new weight parameters for better optimal solution The proposed method has been tested on 3-unit, 6-unit, 13-unit and 40-unit systems The obtained results from the proposed method are compared to those from evolutionary programming (EP) improved fast evolutionary programming (IFEP), improved particle swarm optimization (IPSO) and efficient i)jrticlc swarm optimization (EPSO) methods It is shown that the proposed method outpedorms the others in terms of total costs Therefore, the proposed NPSO is favorable for solving the ELD problem with valve point effects Keywords: particle swarm optimization, non-smooth cost functions, valve-point effects, economicload dispatch, optimal power flow TOM TA I Bai bdo di xuat phwang phap New Particle Swarm Optimization (NPSO) di giai bdi toan diiu kinh ti cdng suit (ELD) cd xet anh hwdng cua diim van cdng suit may phat Phwang phap NPSO di xuit la mot sw cai tiin cua phwang phdp PSO vdi he sd qudn tinh kieu mai giup cho kit que tinh todn toi wu Phwang phdp di xuit da dugc kiim tra tren cac mang dien nhd mdy, nha mdy, 13 nha may vd 40 nha may Kit qua dat dwgc tir phwang phap de xuit dwgc so sdnh vdi kit qua cua cac phwang phap khdc: evolutionary programming (EP), improved fast evolutionary programming (IFEP), improved particle swarm optimization (IPSO) va efficient particle swarm optimization (EPSO) Kit qua tw phwang phdp di xuit tit han nhirng phwang phap khdc vi tdng chi phi nhien lieu di phdt dien ndng nha may Do dd, phwang phdp NPSO di xuit cd Igi thi han viec giai bai todn ELD cd xet anh hwdng ciia diim van cdng suit power sv stem optimization problems such as economic dispatch [4-7], reactive power and voltage control [9-11], transient stability constrained optimal power tlow [12] and many others [5], [7] INTRODUCTION Economic Load Dispatch (I4.D) problem is an important fundamental issue in power svstem operation In essence, it is an optimization problem and its main t)biectivc is to reduce the total generation cost of units, while satisfying constraints Previous efforts on solving ELD problems have emplovcd various mathematical programming methods and optimization techniques In 1995, Ebcrhart and Kennedy suggested a Particle Swarm Optimization (PSO) based on the analogv of swarm of bird flocking and fish schooling [1] Due to its simple concept, easv implementation, and computational efficiency when compared with mathematical algorithm and other heuristic opfimization techniques, PSO has attracted many attentions and been applied in various The practical ELD problems with valvepoint effects are represented as a non smooth optimization problem with equality and inequalitv constraints To solve this problem, manv methods have been proposed such as genetic algorithm, evolutionary programming, d> namic programming, gradient method, neural network approaches In this paper, a optimization (NPSO) is economic load dispatch valve point effects The 108 new particle swanti proposed for solving (ELD) problem witli proposed NPSO is TAP CHI KHOA HOC & CONG NGHE CAC TRUONG DAI HOC KY TIIUAT * SO 76 - 2010 improvement of particle swarm optimization method with new weight parameter for better optimal solution The proposed method has been tested on 3-unit, 6-unit, 13-unit and 40unit systems The obtain results from the proposed method are compared to those from Evolutionary Programming (EP), classical Evolutionary Programming (CEP) and Improved Fast Evolutionary Programming (IFEP) [4], improved particle swarm optimization (IPSO) [6] and efficient particle swarm optimization (EPSO) [5] methods XL ECONOMIC LOAD DISPATCH PROBLEM Smooth quadratic function approximations of the generating unit inputoutput characteristics provide the basis for most classical economic load dispatch techniques Thus, the valve-point effects are ignored The generating units with multi-valve steam turbines exhibit a greater variation in the fuelcost functions Since the valve point results in thc ripples, a cost function contains higher order nonlinearity Therefore, the equation (4) should be replaced as (5) to consider the valvepoint effects lere, the sinusoidal functions are thus added to the quadratic cost functions as follows [6] The economic load dispatch problem can be described as an optimization (minimization) process with the following objective function F(P) = c7 +l->f' + r / ' ' +\e xs'inif x(P c = t.p.(P.) (6) where a, /', c, are the fuel cost coefficients of the /""' unit and c, and / are the fuel cost coefficients of the /"' unit with valve point effects (1) where FfPJ is the fuel cost function of the /""' unit and P, is the power generated by the /"' unit , f without point valve Subject to power balance constraints / ' " ^ Z Z P =P - P 6\/ ^ ^' a ^Y^PC,B„+B,, /=! /=! J=\ Fig Example cost function with valves f5] III SOLUTION METHODOLOGY (3) A Overview of the PSO where 5,„ B,o, BQO are known as the losses or Bcoefficients and generating capacity constrains ' constraints Table 17 Optimal dispatch and corresponding cost in 40-unit svstem I'nil : - 28 29 30 ' ' 3'l the (icncration Cost CS) ' i.nun ' i.min (MW) 11 l" 110.7998 92 s 0964 II 110.7998' 92s ()i)6 30 120 1190 S.ISS 97.i999| ^7.0 ' 190 2143.5503 [79.7.^,0 80 706.5001 87779991 97 47 142.7998 1604.7 128 140 08 259 S99() ^612.88 15 " ^ 300 no 2S 599f) 2779.8 366 135 300 2Sl 5996 ,2798 2i()2 300 135 130.0000 2'^0"• 0650 300 130 93 99981 '1893.3043 94 375 93.994 11 1908.1362 94 375 30 1.5 [95 n 0.2971 500 125 51497)989 500 304.5195 125 6436,5862 125 394.2793 500 394.2793 6436,5862 500 125 489.2793 5296.7107 220 500 220 489.2793 5288.7651 500 5540.9292 242 550 511.2793 5627.7512 242 550 505.0000 5071.2897 254 523,2793 550 5071,2896 254 550 523.2793 ' 254 5057,2231 523.2793 550 550 254 523.2793 5057.2230 254 523.2793 5275,0885 550 60 33 60 'I 90 90 90 25 25 25 35 36 37 38 39 11 12 L^ 14 15 16 17 18 19 20 21 22 23 24 25 47 60 32 ^ 10 254 10 10 10 550 150 150 150 97 190 190 190 200 200 200 no no no 242 550 40 lotal (icncration & Cosl 523.2793 11,0000 10.0000 10.0000 95.0000 197,9999 197.9999 197.9999 180.0000 164.7998 205.683 109.9995 108.0000 100.0000 503,2792 5275.0885 1164.0309 1140.5240 1140.5240 823.19774 1658.9037 1658.9037 1658,9037 1841.2934 1539.8703 2091.6657 1220,1637 1207.1644 1126.5035 5534.6712 10500.000 121416.42 V CONCLUSION In this paper, the new Particle Swarm Optimization method has been presented to solve the non-smooth ELD problems The results show that the proposed algorithms have thc capabilitv to obtain better solutions than cvolutionarv programming modified evolutionary programming and modified particle swarm optimization methods in terms of total costs for test sv stems from to 40 units Therefore, the proposed algorithm is effective and efficient solving large scale ELD problems with valve point etTccts REFF.RKNCES J Kennedy and R C Eberhart; "Particle swarm optinfi/ation," Proceedings cf IEEE International Ccmference on \ewcil Networks (IC\'\"95); Vol IV Perth, Australia 1995 pp 1942-1948 Yuhui Shi and Russell F^berhart; "'A Modified Particle Swarm Optimi/er," Proceedings of IEEE International Conference on Evolutionary Computation: Anchorage 4-9 Mav 1998, pp 69 - 73 Russell C Eberhart and Yuhui Shi; "Particle Swarm Optimization: Developments Applications and Resources"; Proceedings of IEEE International Conference on Evolutionarv Computation, Volume 1,2001, pp 81-86 Nidul Sinha, R Chakrabarti, and P K Chattopadhyay; "1-volutionary Programming Techniques for Economic Load Dispatch"; lEEli Transactions cm Evoluticmary Computation, Vol No.l, February 2003, pp 83-94 Dr K Thanushkodi, S Muthu Vijaya Pandian, R.S.Dhivy Apragash, M Jothikumar, S.sriramnivas and K.Vindoh; "An Efficient Particle Swarm Optimization for Economic Dispatch Problems With Non-smooth cost functions"; WSEAS Transactions on Power Systems, Issue Volume 3, April 2008, pp 257-266 Jong-Bae Park, Member, IEEE, Yun-Won Jeong, Woo-Nam Lee, and Joong-Rin Shin; "An Improved Particle Swarm Optimization for Economic Dispatch Problems with Non-Smooth Cost Functions"; IEEE Power Engineering Society General Meeting, 2006 114 TAP CHI KHOA HOC & COINU NGHE CAC TRUONG DAI HOC KY i H U A T * SO 76 - 2010 C H Chen, and S N Yeh; ''Particle Swarm Optimization for Economic Power Dispatch with Valve-Point Effects"; 2006 IEEE PES Transmissicm and Distribution ('oiiference and Expo.sition Latin America, Venezuela, 15-18 Aug 2006 K S Swarup; "Swarm intelligence approach to thc solution of optimal power fiow"; hidian Institute of Science, Oct 2006, pp 439-455 K T Chaturvedi Manjaree Pandit Member 11 f l ' and laxmi Srivaslava Member II-1,1-,; "SelfOrganizing Flierarchical Particle Swarm Optimi/ation for Nonconve.x f.conomic Dispatch"; IEEE Transactions on Pcnver Systems Vol, 23 No 3, August 2008, pp 1079-1087 10 Hirotaka Yoshida, Kenichi Kawata ^'oshika/u Fukuvania Yosukc Nakanishi; "A Particle Swarm Optimization for Reactive Power and Voltage control considering Voltage security assessment"; IEEE Trans, on Power Svsiems Vol.15, No.4 November 2001 pp 1232-1239 11 G Krost G K Venavaganioorthv, L Grant; "Swarm Intelligence and F.volutionary Approaches for Reactive Power and Voltage Control"; 200S IEEE Swarm Intelligence Symposium September 21-23,2008 12 N Mo, Z.^' Zou K.W Chan and T.^^(i Pong; " ransient stabilitv constrained optimal power fiow using particle swarm optimisation"; lETGener Transm Distrib., 2007, 1, (3), pp 476-483 13 Bo Zhao, Quanyuan Hang Chuangxin Guo, Yijia Cao; "A novel particle swarm optimization approach for optimal reactive power dispatch"; 15tli PSCC Liege, Session 21, 22-26 August 2005 14 Adel AH ,Abou El-Ela Ragab Abdcl-A/i/ I-4-Schiem>'; "Optimized Generation Costs Using Modified Particle Swarm Optimization Version"; IVseas Transacticms on Power Systems Issue 10, Volume October 2007 pp 225-232 Dia chi lien lgc: Le Dinh Luong fel: (+84) 989.888.996; Email: ledinhluong@gmail.com Ho Chi Minh City Universitv of Technology - Vietnam 144/24 Dien Bien Phu Str., Binh Thanh District, Tp Ho Chi Minh 15 ... Opfimizafion (EPSO) [5], Improved Particle Swarm Optimization (IPSO) [6], Mean personal-best oriented PSO (MPPSO) [7], Adaptive personal-best oriented PSO (APPSO) [7], Decisive personal-best oriented PSO. .. IPSO 300.27 400.00 149.73 850,00 8234.07 APPSO 18014.61 18291.92 17978.89 EPSO 300.26 400.00 149.73 850,00 8234.073 DPPSO 18084.99 18310.43 r976.31 NPSO 300.26 399.99 149.73 850.00 8234.071 NPSO... 122624.35 APPSO DPPSO PSO NPSO 123985.15 126259.11 122044.63 123647.81 125295.98 122159.99 NA NA 124577.27 121467.99 121773.89 121416.42 400 700 Mean cost Method Fig Convergence nature of \PSO in