PSO算法在电力系统无功优化和经济负荷分配中的应用研究
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摘要
能源是人类社会发展的必需条件,电能作为现代社会最主要的二次能源之一,在国民经济和和人民日常生活中具有极广泛的应用。随着电力技术的发展,现代电力工业进入了大系统、超高压、远距离、大容量的发展时代,电力系统运行中的各种问题日益突出,对系统的经济、安全、稳定运行具有重要的影响。电力系统无功优化和经济负荷分配是其中比较典型的两个优化问题,本文采用粒子群算法及其改进算法对这两个问题进行了相关研究。
针对电力系统无功优化问题,本文建立了一个以有功损耗最小和电压质量最好为目标函数的多目标优化模型,并采用固定权重法将多目标函数转变为单目标函数；采用了三种优化算法：粒子群算法(PSO)、自适应权重粒子群算法(AWPSO)和继承学习粒子群算法(ILPSO),对IEEE30、IEEE118节点系统进行了仿真计算,结果表明ILPSO算法可以有效地求解无功优化问题。同时,在三种粒子群算法中选取了不同的种群数及迭代次数对无功优化问题进行了计算和分析,结果表明不同的算法参数对优化结果具有较大的影响。在电力系统经济负荷分配问题中,本文以总发电成本最小为目标函数的优化模型,同时还考虑了系统传输网损,采用罚函数的形式处理功率平衡约束：采用了PSO算法、AWPSO算法和ILPSO算法三种优化算法,对3机组、6机组、15机组算例进行仿真计算,与文献结果进行了比较,表明ILPSO算法对于电力系统经济负荷分配问题的求解是有效、可行的。分析了不同的算法参数对优化结果的影响,结果表明选取正确的参数可以得到合适的优化结果。对于40机组,还考虑了阀点效应,通过ILPSO算法进行了仿真计算,获得的结果优于文献结果。
本文利用三种粒子群算法在不同参数的条件下对电力系统无功优化和经济负荷分配问题进行了研究,可以得出选取不同的算法参数设置对优化结果具有较大的影响以及ILPSO算法在求解这两个优化问题中有效性和优越性的结论。
Energy is a necessary condition for the development of human society. In the modern society, electricity is one of the most important secondary energy, which has a very wide range of applications in the national economy and people's daily life. With the development of electricity technology, modern power industry has entered the developing period of large-scale system, extra high voltage, long-distance, high-capacity, but various problems in power system operation have also become increasingly prominent, which has an great impact on economy, safe and stable operation of power system. Reactive power optimization and economic load dispatch is typical of two optimization problems. In this paper, which two problems are research by particle swarm optimization algorithm and its improved.
In reactive power optimization problem, the mathematical model of multi-objective optimization has been established in this paper. The objectives consist of real power loss and voltage quality. This paper uses fixed-weight method to transform the multi-objective functions to the single objective function. Three optimization algorithms are used:they are particle swarm optimization (PSO), adaptive weight particle swarm optimization (AWPSO) and inheritance learning particle swarm optimization (ILPSO), which has been used to solve the IEEE30, IEEE118bus system.The results show that ILPSO algorithm can effectively solve the reactive power optimization problem. Meanwhile, the different species and iterations of algorithm which are selected to calculate and analyze reactive power optimization problem. The results show that different parameters of the algorithm have a great impact on the results of optimization.
In power system economic load dispatch problem, the optimization model of total generation minimum cost has been established in this paper. Also the system transmission loss has been considered and the penalty function has been considered to handle the power balance constraints. The three optimization algorithms are used:they are particle swarm optimization (PSO), adaptive weight particle swarm optimization (AWPSO), inheritance learning particle swarm optimization (ILPSO). Three simulated examples including3-generators,6-generators and15-generators are calculated by the three optimization algorithms. The calculated results are compared with literature results; ILPSO algorithm is an effective and feasible method to solve the power system economic load dispatch problem. The impact of different algorithm parameters to optimize on the results is analyzed. The influence of different algorithm parameters on the optimization results is analyzed.The results show that selecting the correct parameters can get suitable optimization results. For40-generators, the valve point effect is considered, and the calculation results with ILPSO are better than the literature results.
In this paper, reactive power optimization and economic load dispatch are studied by three kinds of particle swarm optimization of the different parameters.It can be concluded to select the correct algorithm parameter, which has a great influence on optimization results. And ILPSO algorithm is an effective and superior algorithm for solving these two problems.
针对电力系统无功优化问题,本文建立了一个以有功损耗最小和电压质量最好为目标函数的多目标优化模型,并采用固定权重法将多目标函数转变为单目标函数；采用了三种优化算法：粒子群算法(PSO)、自适应权重粒子群算法(AWPSO)和继承学习粒子群算法(ILPSO),对IEEE30、IEEE118节点系统进行了仿真计算,结果表明ILPSO算法可以有效地求解无功优化问题。同时,在三种粒子群算法中选取了不同的种群数及迭代次数对无功优化问题进行了计算和分析,结果表明不同的算法参数对优化结果具有较大的影响。在电力系统经济负荷分配问题中,本文以总发电成本最小为目标函数的优化模型,同时还考虑了系统传输网损,采用罚函数的形式处理功率平衡约束：采用了PSO算法、AWPSO算法和ILPSO算法三种优化算法,对3机组、6机组、15机组算例进行仿真计算,与文献结果进行了比较,表明ILPSO算法对于电力系统经济负荷分配问题的求解是有效、可行的。分析了不同的算法参数对优化结果的影响,结果表明选取正确的参数可以得到合适的优化结果。对于40机组,还考虑了阀点效应,通过ILPSO算法进行了仿真计算,获得的结果优于文献结果。
本文利用三种粒子群算法在不同参数的条件下对电力系统无功优化和经济负荷分配问题进行了研究,可以得出选取不同的算法参数设置对优化结果具有较大的影响以及ILPSO算法在求解这两个优化问题中有效性和优越性的结论。
Energy is a necessary condition for the development of human society. In the modern society, electricity is one of the most important secondary energy, which has a very wide range of applications in the national economy and people's daily life. With the development of electricity technology, modern power industry has entered the developing period of large-scale system, extra high voltage, long-distance, high-capacity, but various problems in power system operation have also become increasingly prominent, which has an great impact on economy, safe and stable operation of power system. Reactive power optimization and economic load dispatch is typical of two optimization problems. In this paper, which two problems are research by particle swarm optimization algorithm and its improved.
In reactive power optimization problem, the mathematical model of multi-objective optimization has been established in this paper. The objectives consist of real power loss and voltage quality. This paper uses fixed-weight method to transform the multi-objective functions to the single objective function. Three optimization algorithms are used:they are particle swarm optimization (PSO), adaptive weight particle swarm optimization (AWPSO) and inheritance learning particle swarm optimization (ILPSO), which has been used to solve the IEEE30, IEEE118bus system.The results show that ILPSO algorithm can effectively solve the reactive power optimization problem. Meanwhile, the different species and iterations of algorithm which are selected to calculate and analyze reactive power optimization problem. The results show that different parameters of the algorithm have a great impact on the results of optimization.
In power system economic load dispatch problem, the optimization model of total generation minimum cost has been established in this paper. Also the system transmission loss has been considered and the penalty function has been considered to handle the power balance constraints. The three optimization algorithms are used:they are particle swarm optimization (PSO), adaptive weight particle swarm optimization (AWPSO), inheritance learning particle swarm optimization (ILPSO). Three simulated examples including3-generators,6-generators and15-generators are calculated by the three optimization algorithms. The calculated results are compared with literature results; ILPSO algorithm is an effective and feasible method to solve the power system economic load dispatch problem. The impact of different algorithm parameters to optimize on the results is analyzed. The influence of different algorithm parameters on the optimization results is analyzed.The results show that selecting the correct parameters can get suitable optimization results. For40-generators, the valve point effect is considered, and the calculation results with ILPSO are better than the literature results.
In this paper, reactive power optimization and economic load dispatch are studied by three kinds of particle swarm optimization of the different parameters.It can be concluded to select the correct algorithm parameter, which has a great influence on optimization results. And ILPSO algorithm is an effective and superior algorithm for solving these two problems.
引文
[1]段金长.改进遗传算法在电力系统无功优化中的应用[J].电网与水力发电进展.2008,24(6)：15-20.
[2]Chebbo A M, Irving M R, Sterling M J H. Reactive power dispatch incorporating voltage stability[J]. IEEE Proeeedings-C, 1992, 139(3):253-260.
[3]孙东杰.电力系统经济调度和无功优化中的多目标算法研究[D].湖南大学硕士论文.2010.
[4]侯云鹤,鲁丽娟,熊信良等.改进粒子群算法及其在电力系统经济负荷分配中的应用[J].中国电机工程学报.2004,24(7)：95-100.
[5]李彩华,郭志忠,樊爱军.电力系统优化调度概述(I)—经济调度与最优潮流[J].2002,14(2)：60-63.
[6]孙伯明,陈寿孙.高等电力网络分析[M].北京：清华大学出版社,1996.
[7]陈晰.电力系统稳态分析[M].北京：中国电力出版社,1995.
[8]J Qiu, Shahidehpour S M. A New Approach for Minimizing Power Loss and Improving Voltage Profile[J]. IEEE Trans on Power system.1987,2(5):287-295.
[9]刘明波,程劲晖,陈学军.电力系统无功综合优化的线性规划内点法[J].电力系统及其自动化学报.1999,11(5-6)：87-92.
[10]Momoh J A, Adapa R, EI-Hawary M E. A review of selected optimal power flow literature to 1993. I.Nonlinear and quadratic programming approaches[J]. IEEE Transactions on Power Systems.1999,14(1):96-104.
[11]Gent M R, Lamont J W. Minimum Emission Dispatch[J]. IEEE Trans on Power Apparatus and Systems.1971,90(6):2650-2660.
[12]Delson J K. Controlled Emission Dispatch. IEEE Trans on Power Apparatus and Systems. 1974,93(6):1359-1366.
[13]Finnigan O E, Fouad A A. Economic Dispatch with Pollution Constraints[J]. IEEE Trans on power Apparatus and Systems.1974, 93(3):1734-1740.
[14]Cadogan J B, Eisenberg L. Sulfur Oxide Emissions Management for Electric Power Systems[J]. IEEE Trans on Power Apparatus and Systems.1977, 96(2):393-401.
[15]马勇飞,周任军,王献敏,邓学华.基于全局序列二次规划算法的无功优化[J].长沙电力学院学报(自然科学版).2006,21(3)：12-15.
[16]粟时平,刘桂英,甘正宁.基于动态规划的电网无功补偿综合优化法[J].长沙电力学院学报(自然科学版).2001,16(1)：39-42.
[17]《运筹学》教材编写组.运筹学(修订版).北京：清华大学出版社,1999.
[18]Benders J F. Partitioning procedure for solving mixed-variables programming problems[J]. Numerische Mathematik 4,1962:238-252.
[19]Ramachandran K, Hariharan S. Optimal Reactive Power Allocation for Improved System Performance[J]. IEEE Transactions on Power Apparatus and System.1984,6:PAS-103.
[20]Abido M A. A new multi-objective evolutionary algorithm for environmental/economic Power dispatch[J]. In:Power engineering society Summer Meeting, New York. 2001,86-92.
[21]马晋弢,杨以涵.遗传算法在电力系统无功优化中的应用[J].中国机电工程学报.1995,15(5)：347-352.
[22]何大阔,王福利,毛志忠,李鸿儒.遗传算法在电力系统经济负荷分配中的应用[J].系统仿真学报.2007,19(4)：890-892.
[23]曾国荪,丁春玲.并行遗传算法分析[J].计算机工程.2001,27(9)：53-55.
[24]刘科研,盛万兴,李运华.基于改进免疫遗传算法的无功优化[J].电网技术.2007,31(13)：11-16.
[25]Zhuang F, Galiana F D. Unit Commitment by Simulated Annealing [J]. IEEE Trans on PWRS,1990,5(1):311-317.
[26]Annakkage U D, Numnonda T, Pahalawaththa N C. Unit Commitment by Parallel SimulatedAnnealing[J]. IEE Proc-Gener T&D,1997,142(6):595-600.
[27]顾丹珍,徐瑞德.一种地区电网多目标无功优化的新方法—改进模拟退火算法[J].电网技术.1998,22(1)：71-74.
[28]Chiang H D, Wang J C, et al. Optimal capacitor placements in distribution systems:Part 1: A new formulation and the overall problem. IEEE Trans. on Power Delivery, April 1990, 5(2):634-642.
[29]周皓,周晖.电网无功电压综合控制的改进SA算法[J].继电器.2004,32(1)：24-27.
[30]Wong K P, Fung C C. Simulated annealing based algorithm for minimum emission dispatch[J]. In:International Power Engineering Conference, Singapore.1993,49-56.
[31]王洪章,熊信银,吴耀武.基于改进Tabu搜索算法的电力系统无功优化[J].电网技术.2002,26(1)：15-18.
[32]文福栓,韩祯祥.人工神经元网络模型的无功电源最优分布及经济调度[J].中国电机工程学报.1992,12(3)：20-28.
[33]吴秀华,吕霞,罗海燕.人工神经网络在电力系统无功电压优化中的应用[J].沈阳农业大学学报.2008,39(6)：713-717.
[34]Langton CG.Artificial Life[M].redwood:Addison-Wesley.1989:1-47
[35]Millonas M M. Swarms Phase Transition and Collective Intelligence[M]. MA:Addison Wesley. 1995, 4:1942-1948.
[36]谢晓锋,张文俊,杨之廉.微粒群算法综述[J].控制与决策.2003,18(3)：129-134.
[37]刘波,王凌,金以慧等.微粒群优化算法研究进展[J].化工自动化及仪表.2005,32(3)：1-6.
[38]爱国,覃征,鲍复民,贺升平.粒子群优化算法[J].计算机工程与应用.2002,21：1-3.
[39]Shi Y, Eberhart R C. A Modified Particle Swarm Optimization[C]. Proceedings of the Congress on Evolutionary Computation, Piscataway. IEEE Press.1998:69-73.
[40]Xiao dong Li. Particle Swarm Optimization[M]. GECCO2007 Tutorial.2007,3291-3414.
[41]龚纯,王正林.精通MATLAB最优化计算[M].北京：电子工业出版社,2009.
[42]邓爱萍,王会芳.动态改变惯性权重的自适应粒子群算法[J].计算机工程与设计.2010,31(13)：3062-3065.
[43]D.Liu, Q.Y.Feng, W.B.Wang, X.Yu. Synthesis of unequally spaced antenna arrays by using inheritance learning particle swarm optimization[J]. Progress In Electromagnetics Research.2011,118:205-221.
[44]娄素华.现代电力系统优化模型及其相关算法研究[D].华中科技大学博士学位论文.2005.
[45]袁晓辉,王乘,张勇传等.粒子群优化算法在电力系统中的应用[J].电网技术.2004,28(19)：14-19.
[46]Yoshida H, Fukuyama Y, Takayama S, Nakanishi Y. A particle swarm optimization for reactive power and voltage control in electric power systems considering voltage security assessment[J]. IEEE SMC'99 Conference Proceedings.1999,6:497-502.
[47]Hirotaka Yoshida, Kenichi Kawata, Yoshikazu Fukuyama. A Particle Swarm Optimization for Reactive Power and Voltage Control Considering Voltage Security Assessment[J]. IEEE Transaction on Power Systems. 2000,15(4):1232-1239.
[48]Yoshikazu Fukuyama, Hirotaka Yoshida. A particle swarm optimization for reactive power and voltage control in electric power system[J]. Evolutionary Computation.2001, 1:87-93.
[49]赵波,曹一家.电力系统无功优化的多智能体粒子群优化算法[J].中国电机工程学报.2005,25(5)：1-7.
[50]何佳,吴耀武,娄素华,熊信艮.基于微粒群优化算法的电力系统动态无功优化[J].电网技术.2007,31(2)：47-51.
[51]Hirotaka Yoshida, Kenichi Kawata. A Particle Swarm Optimization for Reactive Power and Voltage Control Considering Voltage Security Assessment[J]. IEEE Trans on Power Systems.2000,15(4):1232-1239.
[52]Amita Mahor, Vishnu Prasad, Saroj Rangnekar. Economic dispatch using particle swarm optimization:A review [J]. Renewable and Sustainable Energy Reviews.2009, 13:2134-2141.
[53]El-Gallad A, El-Hawary M. Particle swarm optimizer for constrained economic dispatch with prohibited operating zones[A]. Canadian Conference on Electrical and Computer Engineering Manitoba, Canada. 2002:78-81.
[54]Cohelo SL, Lee SC. Solving economic load dispatch problems in power system using chaotic and Guassian particle swarm optimization approaches[J]. Electrical Power and Energy Systems.2008,30:297-307.
[55]Jiejin C, Xiaoqian M, Lixiang L, Haipeng P. Chaotic particle swarm optimization for economic load dispatch considering the generator constraints[J]. Energy Conversion & Management. 2007,48:645-653.
[56]Chen P H, Chang H C. Large scale economic dispatch by genetic algorithm[J]. IEEE Transaction on Power Systems.1995,10(4):1919-1926.
[57]Yuan X, Wang L, Yuan Y. Application of enhanced PSO approach to optimal scheduling of hydro system[J]. Energy Conversion and Management. 2008,49(11):2966-2972.
[58]Talaq J H, Ferial, EI-Hawary M E. A summary of environmental/economic dispatch algorithms[J]. IEEE Transaction on Power System.1994, 9(3):1508-1516.
[59]Abido MA. Multi-objective particle swarm optimization for environmental/economic dispatch problem[J]. Electric Power System Research.2009, 79(7):1105-1113.
[60]Bo Z, Guo C, Cao Y. Dynamic economic dispatch in electricity market using particle swarm optimization algorithm[J]. IEEE International Conference on Intelligent Control and Automation.2004,6:5050-5054.
[61]Wang L, Singh C. Reserve constrained multi-area environmental/economic dispatch using enhanced particle swarm optimization[J]. IEEE Systems and Information Engineering Design Symposium.2006,1:96-100.
[62]蒋秀洁,徐满清,龚学会,陈林.计及阀点效应负荷经济分配的杂交粒子群算法[J].电力系统保护与控制.2009,37(8)：10-13.
[63]Zwe-Lee Gaing. Particle swarm optimization to solving the economic dispatch considering the generator constraints[J]. IEEE Trans on Power Systems.2003, 18(3):1187-1195.
[64]卢有麟,周建中,覃晖等.差分进化算法在电力系统环境经济调度中的应用[J].华中科技大学学报(自然科学版).2010,38(8)：121-124.
[65]袁晓辉,王乘,张勇传等.粒子群优化算法在电力系统中的应用[J].电网技术.2004,28(19)：14-19.
[66]张振宇,葛少云,刘自发.粒子群优化算法及其在机组优化组合中应用[J].电力自动化设备.2006,26(5)：28-31.
[67]王剑,刘天琪,刘学平.基于优先级排序和内点法的机组优化组合[J].电力系统保护与控制.2010,38(13)：55-60.
[68]萧国泉,徐生均.电力规划[M].北京：水利电力出版社,1993.
[69]顾永东,金义雄.粒子群算法及其在电网规划中的应用[J].电气应用.2007,26(2)：37-42.
[70]牛东晓,凌云鹏,赵奇,赵庆营.一种适用于电网扩展规划问题的边界搜索粒子群优化算法[J].华北电力大学学报.2007,34(4)：80-84.
[71]陈建华,李先允,邓东华等.粒子群优化算法在电力系统中的应用综述[J].继电器.2007,35(23)：77-84
[72]Abido M A. Optimal power flow using particle swarm optimization[J]. Int J.Elect.Power Energy Syst. 2002,24(7):563-571.
[73]B Zhao, C X Guo, Y J Cao. Improved particle swam optimization algorithm for OPF problems[J]. In Proc IEEE/PES Power System Conference Expo.2004, 233-238.
[74]Abido A. A Particle swarm optimization for multimachine power system stabilizer design[J]. In Proc.IEEE Power Eng Soc. Summer Meeting. 2001,3:1346-1351.
[75]Abido M A. Optimal Design of Power System Stabilizers Using Particle Swarm Optimization[J]. IEEE Trans on Energy Conversion. 2002,17 (3):406-413.
[76]L Chun Feng, J Chia Feng. Evolutionary fuzzy control of flexible AC transmission system[J]. Inst. Elect. Eng. Proc. Generation Transmission Distrib.2005,152(4):441-448.
[77]龙云,王建全.基于粒子群游算法的同步发电机参数辨识[J].大电机技术.2003,1：8-11.
[78]胡家声,郭创新,曹一家.基于扩展粒子群优化算法的同步发电机参数辨识[J].电力系统自动化.2004,28(6)：32-35.
[79]Shigenori Naka, Yoshikazu Fukuyama. Practical Distribution State Estimation Using Hybrid Particle Swarm Optimization[A]. IEEE Power Engineering Society Winter Meeting.2001,815-820.
[80]Fukuyama Y. State estimation and optimal setting of voltage regulator in distribution systems[J]. IEEE Power Engineering Society Winter Meeting. 2001,2:930-935.
[81]Gonen T. Electrical Power Distribution System Engineering[M]. New York: McGraw-Hill.
[82]吕干云,方奇品,蔡秀珊.一种基于粒子群优化算法的间谐波分析方法[J].电工技术学报.2009,24(12)：156-161.
[83]覃思师,刘前进.基于粒子群与神经网络的间谐波测量算法研究[J].电力系统保护与控制.2011,39(2)：18-22.
[84]Koay C, Srinivasan D. Particle swarm optimization-based approach for generator maintenance scheduling[J]. IEEE Swarm Intell.Symp.2003,167-173.
[85]许文超,郭伟.电力系统无功优化的模型及算法综述[J].电力系统及其自动化学报.2003,15(1)：100-104.
[86]宋军英,刘涤尘,陈允平.电力系统模糊无功优化的建模及算法[J].电网技术.2001,25(3)：22-25.
[87]李亚男,张粒子,杨以涵.考虑电压约束裕度的无功优化及其内点解法[J].中国电机工程学报.2001,21(9)：1-4
[88]韩新华,赵琰,邓玮.电力系统无功优化模型与算法的研究与发展[J].东北电力技术.2010,4：17-21.
[89]Granville S. Optimal Reactive Dispatch Through Interior Point Methods [J], IEEE Trans on Power Systems.1994,19(1):136-142.
[90]娄素华,李研,吴耀武,熊信银.多目标电网无功优化的量子遗传算法[J].高电压技术.2005,31(9)：69-72.
[91]宋军英,刘涤尘,陈允平.电力系统模糊无功优化的建模及算法[J].电网技术.2001,25(3)：22-25.
[92]刘述奎.基于自适应聚焦粒子群算法的电力系统无功优化[D].西南交通大学硕士学位论文.2009.
[93]宋明曙.电力系统无功优化分析[D].山东大学硕士学位论文.2008.
[94]张伯明,陈寿孙,严正.高等电力网络分析(第2版)[M].北京：清华大学出版社,2007.
[95]吴际舜,侯志俭.电力系统潮流计算的计算机方法[M].上海：上海交通大学出版社,2000.
[96]Immanuel Selvakumar A, Thanushkodi K. A New Particle Swarm Optimization Solutionto Nonconvex Economic Dispatch Problems[J]. IEEE TRANSACTIONS ON POWER SYSTEMS.2007,22(1):42-51.
[97]Ross D W, Kim S. Dynamic economic dispatch of generation[J]. IEEE Trans. Power App.Syst. 1980,99(6):2060-2068.
[98]Irina Ciornei, Elias Kyriakides. A GA-API Solution for the Economic Dispatch of Generation in Power System Operation[J]. IEEE TRANSACTIONS ON POWER SYSTEMS.2012,27(1):233-242.
[99]Amjady N. Economic dispatch using an efficient real-coded genetic algorithm [J]. IET Generation, Transmission & Distribution. 2009,3(3):266-278.
[100]Chaturvedi K T, Manjaree Pandit and Laxmi Srivastava. Self-Organizing Hierarchical Particle Swarm Optimization for Nonconvex Economic Dispatch[J]. IEEE TRANSACTIONS ON POWER SYSTEMS.2008,23(3):1079-1087.
[101]Nidul Sinha, Chakrabarti R, Chattopadhyay P K. Evolutionary Programming Techniques for Economic Load Dispatch[J]. IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION.2003,7(1):83-94.
[102]Immanuel Selvakumar A, Thanushkodi K. A New Particle Swarm Optimization Solution to Nonconvex Economic Dispatch Problems[J]. IEEE TRANSACTIONS ON POWER SYSTEMS.2007,22(1):42-51.
[103]王凌,黄付卓,李灵坡.基于混合双种群差分进化的电力系统经济负荷分配[J].控制与决策.2009,24(8)：1156-1160.
[104]王瑜,李斌,袁博.混合SQP的基于完全学习的粒子群优化算法的电力系统中经济分配问题的应用[J].中国科学,2010,40(3)：403-411.
[105]Meng K, Wang G, Dong Z, Wong K. Quantum-inspired particle swarm optimization for vale-point economic load dispatch[J]. IEEE Transactions on Power Systems.2010, 25(1):215-222.
[106]Nasimul Nomana, Hitoshi Iba. Differential evolution for economic load dispatch problems[J]. Electric Power Systems Research.2008,78(8):1322-1331.
[107]唐巍,李殿璞.电力系统经济负荷分配的混沌优化方法[J].中国电机工程学报.2000,20(10)：36-40
[2]Chebbo A M, Irving M R, Sterling M J H. Reactive power dispatch incorporating voltage stability[J]. IEEE Proeeedings-C, 1992, 139(3):253-260.
[3]孙东杰.电力系统经济调度和无功优化中的多目标算法研究[D].湖南大学硕士论文.2010.
[4]侯云鹤,鲁丽娟,熊信良等.改进粒子群算法及其在电力系统经济负荷分配中的应用[J].中国电机工程学报.2004,24(7)：95-100.
[5]李彩华,郭志忠,樊爱军.电力系统优化调度概述(I)—经济调度与最优潮流[J].2002,14(2)：60-63.
[6]孙伯明,陈寿孙.高等电力网络分析[M].北京：清华大学出版社,1996.
[7]陈晰.电力系统稳态分析[M].北京：中国电力出版社,1995.
[8]J Qiu, Shahidehpour S M. A New Approach for Minimizing Power Loss and Improving Voltage Profile[J]. IEEE Trans on Power system.1987,2(5):287-295.
[9]刘明波,程劲晖,陈学军.电力系统无功综合优化的线性规划内点法[J].电力系统及其自动化学报.1999,11(5-6)：87-92.
[10]Momoh J A, Adapa R, EI-Hawary M E. A review of selected optimal power flow literature to 1993. I.Nonlinear and quadratic programming approaches[J]. IEEE Transactions on Power Systems.1999,14(1):96-104.
[11]Gent M R, Lamont J W. Minimum Emission Dispatch[J]. IEEE Trans on Power Apparatus and Systems.1971,90(6):2650-2660.
[12]Delson J K. Controlled Emission Dispatch. IEEE Trans on Power Apparatus and Systems. 1974,93(6):1359-1366.
[13]Finnigan O E, Fouad A A. Economic Dispatch with Pollution Constraints[J]. IEEE Trans on power Apparatus and Systems.1974, 93(3):1734-1740.
[14]Cadogan J B, Eisenberg L. Sulfur Oxide Emissions Management for Electric Power Systems[J]. IEEE Trans on Power Apparatus and Systems.1977, 96(2):393-401.
[15]马勇飞,周任军,王献敏,邓学华.基于全局序列二次规划算法的无功优化[J].长沙电力学院学报(自然科学版).2006,21(3)：12-15.
[16]粟时平,刘桂英,甘正宁.基于动态规划的电网无功补偿综合优化法[J].长沙电力学院学报(自然科学版).2001,16(1)：39-42.
[17]《运筹学》教材编写组.运筹学(修订版).北京：清华大学出版社,1999.
[18]Benders J F. Partitioning procedure for solving mixed-variables programming problems[J]. Numerische Mathematik 4,1962:238-252.
[19]Ramachandran K, Hariharan S. Optimal Reactive Power Allocation for Improved System Performance[J]. IEEE Transactions on Power Apparatus and System.1984,6:PAS-103.
[20]Abido M A. A new multi-objective evolutionary algorithm for environmental/economic Power dispatch[J]. In:Power engineering society Summer Meeting, New York. 2001,86-92.
[21]马晋弢,杨以涵.遗传算法在电力系统无功优化中的应用[J].中国机电工程学报.1995,15(5)：347-352.
[22]何大阔,王福利,毛志忠,李鸿儒.遗传算法在电力系统经济负荷分配中的应用[J].系统仿真学报.2007,19(4)：890-892.
[23]曾国荪,丁春玲.并行遗传算法分析[J].计算机工程.2001,27(9)：53-55.
[24]刘科研,盛万兴,李运华.基于改进免疫遗传算法的无功优化[J].电网技术.2007,31(13)：11-16.
[25]Zhuang F, Galiana F D. Unit Commitment by Simulated Annealing [J]. IEEE Trans on PWRS,1990,5(1):311-317.
[26]Annakkage U D, Numnonda T, Pahalawaththa N C. Unit Commitment by Parallel SimulatedAnnealing[J]. IEE Proc-Gener T&D,1997,142(6):595-600.
[27]顾丹珍,徐瑞德.一种地区电网多目标无功优化的新方法—改进模拟退火算法[J].电网技术.1998,22(1)：71-74.
[28]Chiang H D, Wang J C, et al. Optimal capacitor placements in distribution systems:Part 1: A new formulation and the overall problem. IEEE Trans. on Power Delivery, April 1990, 5(2):634-642.
[29]周皓,周晖.电网无功电压综合控制的改进SA算法[J].继电器.2004,32(1)：24-27.
[30]Wong K P, Fung C C. Simulated annealing based algorithm for minimum emission dispatch[J]. In:International Power Engineering Conference, Singapore.1993,49-56.
[31]王洪章,熊信银,吴耀武.基于改进Tabu搜索算法的电力系统无功优化[J].电网技术.2002,26(1)：15-18.
[32]文福栓,韩祯祥.人工神经元网络模型的无功电源最优分布及经济调度[J].中国电机工程学报.1992,12(3)：20-28.
[33]吴秀华,吕霞,罗海燕.人工神经网络在电力系统无功电压优化中的应用[J].沈阳农业大学学报.2008,39(6)：713-717.
[34]Langton CG.Artificial Life[M].redwood:Addison-Wesley.1989:1-47
[35]Millonas M M. Swarms Phase Transition and Collective Intelligence[M]. MA:Addison Wesley. 1995, 4:1942-1948.
[36]谢晓锋,张文俊,杨之廉.微粒群算法综述[J].控制与决策.2003,18(3)：129-134.
[37]刘波,王凌,金以慧等.微粒群优化算法研究进展[J].化工自动化及仪表.2005,32(3)：1-6.
[38]爱国,覃征,鲍复民,贺升平.粒子群优化算法[J].计算机工程与应用.2002,21：1-3.
[39]Shi Y, Eberhart R C. A Modified Particle Swarm Optimization[C]. Proceedings of the Congress on Evolutionary Computation, Piscataway. IEEE Press.1998:69-73.
[40]Xiao dong Li. Particle Swarm Optimization[M]. GECCO2007 Tutorial.2007,3291-3414.
[41]龚纯,王正林.精通MATLAB最优化计算[M].北京：电子工业出版社,2009.
[42]邓爱萍,王会芳.动态改变惯性权重的自适应粒子群算法[J].计算机工程与设计.2010,31(13)：3062-3065.
[43]D.Liu, Q.Y.Feng, W.B.Wang, X.Yu. Synthesis of unequally spaced antenna arrays by using inheritance learning particle swarm optimization[J]. Progress In Electromagnetics Research.2011,118:205-221.
[44]娄素华.现代电力系统优化模型及其相关算法研究[D].华中科技大学博士学位论文.2005.
[45]袁晓辉,王乘,张勇传等.粒子群优化算法在电力系统中的应用[J].电网技术.2004,28(19)：14-19.
[46]Yoshida H, Fukuyama Y, Takayama S, Nakanishi Y. A particle swarm optimization for reactive power and voltage control in electric power systems considering voltage security assessment[J]. IEEE SMC'99 Conference Proceedings.1999,6:497-502.
[47]Hirotaka Yoshida, Kenichi Kawata, Yoshikazu Fukuyama. A Particle Swarm Optimization for Reactive Power and Voltage Control Considering Voltage Security Assessment[J]. IEEE Transaction on Power Systems. 2000,15(4):1232-1239.
[48]Yoshikazu Fukuyama, Hirotaka Yoshida. A particle swarm optimization for reactive power and voltage control in electric power system[J]. Evolutionary Computation.2001, 1:87-93.
[49]赵波,曹一家.电力系统无功优化的多智能体粒子群优化算法[J].中国电机工程学报.2005,25(5)：1-7.
[50]何佳,吴耀武,娄素华,熊信艮.基于微粒群优化算法的电力系统动态无功优化[J].电网技术.2007,31(2)：47-51.
[51]Hirotaka Yoshida, Kenichi Kawata. A Particle Swarm Optimization for Reactive Power and Voltage Control Considering Voltage Security Assessment[J]. IEEE Trans on Power Systems.2000,15(4):1232-1239.
[52]Amita Mahor, Vishnu Prasad, Saroj Rangnekar. Economic dispatch using particle swarm optimization:A review [J]. Renewable and Sustainable Energy Reviews.2009, 13:2134-2141.
[53]El-Gallad A, El-Hawary M. Particle swarm optimizer for constrained economic dispatch with prohibited operating zones[A]. Canadian Conference on Electrical and Computer Engineering Manitoba, Canada. 2002:78-81.
[54]Cohelo SL, Lee SC. Solving economic load dispatch problems in power system using chaotic and Guassian particle swarm optimization approaches[J]. Electrical Power and Energy Systems.2008,30:297-307.
[55]Jiejin C, Xiaoqian M, Lixiang L, Haipeng P. Chaotic particle swarm optimization for economic load dispatch considering the generator constraints[J]. Energy Conversion & Management. 2007,48:645-653.
[56]Chen P H, Chang H C. Large scale economic dispatch by genetic algorithm[J]. IEEE Transaction on Power Systems.1995,10(4):1919-1926.
[57]Yuan X, Wang L, Yuan Y. Application of enhanced PSO approach to optimal scheduling of hydro system[J]. Energy Conversion and Management. 2008,49(11):2966-2972.
[58]Talaq J H, Ferial, EI-Hawary M E. A summary of environmental/economic dispatch algorithms[J]. IEEE Transaction on Power System.1994, 9(3):1508-1516.
[59]Abido MA. Multi-objective particle swarm optimization for environmental/economic dispatch problem[J]. Electric Power System Research.2009, 79(7):1105-1113.
[60]Bo Z, Guo C, Cao Y. Dynamic economic dispatch in electricity market using particle swarm optimization algorithm[J]. IEEE International Conference on Intelligent Control and Automation.2004,6:5050-5054.
[61]Wang L, Singh C. Reserve constrained multi-area environmental/economic dispatch using enhanced particle swarm optimization[J]. IEEE Systems and Information Engineering Design Symposium.2006,1:96-100.
[62]蒋秀洁,徐满清,龚学会,陈林.计及阀点效应负荷经济分配的杂交粒子群算法[J].电力系统保护与控制.2009,37(8)：10-13.
[63]Zwe-Lee Gaing. Particle swarm optimization to solving the economic dispatch considering the generator constraints[J]. IEEE Trans on Power Systems.2003, 18(3):1187-1195.
[64]卢有麟,周建中,覃晖等.差分进化算法在电力系统环境经济调度中的应用[J].华中科技大学学报(自然科学版).2010,38(8)：121-124.
[65]袁晓辉,王乘,张勇传等.粒子群优化算法在电力系统中的应用[J].电网技术.2004,28(19)：14-19.
[66]张振宇,葛少云,刘自发.粒子群优化算法及其在机组优化组合中应用[J].电力自动化设备.2006,26(5)：28-31.
[67]王剑,刘天琪,刘学平.基于优先级排序和内点法的机组优化组合[J].电力系统保护与控制.2010,38(13)：55-60.
[68]萧国泉,徐生均.电力规划[M].北京：水利电力出版社,1993.
[69]顾永东,金义雄.粒子群算法及其在电网规划中的应用[J].电气应用.2007,26(2)：37-42.
[70]牛东晓,凌云鹏,赵奇,赵庆营.一种适用于电网扩展规划问题的边界搜索粒子群优化算法[J].华北电力大学学报.2007,34(4)：80-84.
[71]陈建华,李先允,邓东华等.粒子群优化算法在电力系统中的应用综述[J].继电器.2007,35(23)：77-84
[72]Abido M A. Optimal power flow using particle swarm optimization[J]. Int J.Elect.Power Energy Syst. 2002,24(7):563-571.
[73]B Zhao, C X Guo, Y J Cao. Improved particle swam optimization algorithm for OPF problems[J]. In Proc IEEE/PES Power System Conference Expo.2004, 233-238.
[74]Abido A. A Particle swarm optimization for multimachine power system stabilizer design[J]. In Proc.IEEE Power Eng Soc. Summer Meeting. 2001,3:1346-1351.
[75]Abido M A. Optimal Design of Power System Stabilizers Using Particle Swarm Optimization[J]. IEEE Trans on Energy Conversion. 2002,17 (3):406-413.
[76]L Chun Feng, J Chia Feng. Evolutionary fuzzy control of flexible AC transmission system[J]. Inst. Elect. Eng. Proc. Generation Transmission Distrib.2005,152(4):441-448.
[77]龙云,王建全.基于粒子群游算法的同步发电机参数辨识[J].大电机技术.2003,1：8-11.
[78]胡家声,郭创新,曹一家.基于扩展粒子群优化算法的同步发电机参数辨识[J].电力系统自动化.2004,28(6)：32-35.
[79]Shigenori Naka, Yoshikazu Fukuyama. Practical Distribution State Estimation Using Hybrid Particle Swarm Optimization[A]. IEEE Power Engineering Society Winter Meeting.2001,815-820.
[80]Fukuyama Y. State estimation and optimal setting of voltage regulator in distribution systems[J]. IEEE Power Engineering Society Winter Meeting. 2001,2:930-935.
[81]Gonen T. Electrical Power Distribution System Engineering[M]. New York: McGraw-Hill.
[82]吕干云,方奇品,蔡秀珊.一种基于粒子群优化算法的间谐波分析方法[J].电工技术学报.2009,24(12)：156-161.
[83]覃思师,刘前进.基于粒子群与神经网络的间谐波测量算法研究[J].电力系统保护与控制.2011,39(2)：18-22.
[84]Koay C, Srinivasan D. Particle swarm optimization-based approach for generator maintenance scheduling[J]. IEEE Swarm Intell.Symp.2003,167-173.
[85]许文超,郭伟.电力系统无功优化的模型及算法综述[J].电力系统及其自动化学报.2003,15(1)：100-104.
[86]宋军英,刘涤尘,陈允平.电力系统模糊无功优化的建模及算法[J].电网技术.2001,25(3)：22-25.
[87]李亚男,张粒子,杨以涵.考虑电压约束裕度的无功优化及其内点解法[J].中国电机工程学报.2001,21(9)：1-4
[88]韩新华,赵琰,邓玮.电力系统无功优化模型与算法的研究与发展[J].东北电力技术.2010,4：17-21.
[89]Granville S. Optimal Reactive Dispatch Through Interior Point Methods [J], IEEE Trans on Power Systems.1994,19(1):136-142.
[90]娄素华,李研,吴耀武,熊信银.多目标电网无功优化的量子遗传算法[J].高电压技术.2005,31(9)：69-72.
[91]宋军英,刘涤尘,陈允平.电力系统模糊无功优化的建模及算法[J].电网技术.2001,25(3)：22-25.
[92]刘述奎.基于自适应聚焦粒子群算法的电力系统无功优化[D].西南交通大学硕士学位论文.2009.
[93]宋明曙.电力系统无功优化分析[D].山东大学硕士学位论文.2008.
[94]张伯明,陈寿孙,严正.高等电力网络分析(第2版)[M].北京：清华大学出版社,2007.
[95]吴际舜,侯志俭.电力系统潮流计算的计算机方法[M].上海：上海交通大学出版社,2000.
[96]Immanuel Selvakumar A, Thanushkodi K. A New Particle Swarm Optimization Solutionto Nonconvex Economic Dispatch Problems[J]. IEEE TRANSACTIONS ON POWER SYSTEMS.2007,22(1):42-51.
[97]Ross D W, Kim S. Dynamic economic dispatch of generation[J]. IEEE Trans. Power App.Syst. 1980,99(6):2060-2068.
[98]Irina Ciornei, Elias Kyriakides. A GA-API Solution for the Economic Dispatch of Generation in Power System Operation[J]. IEEE TRANSACTIONS ON POWER SYSTEMS.2012,27(1):233-242.
[99]Amjady N. Economic dispatch using an efficient real-coded genetic algorithm [J]. IET Generation, Transmission & Distribution. 2009,3(3):266-278.
[100]Chaturvedi K T, Manjaree Pandit and Laxmi Srivastava. Self-Organizing Hierarchical Particle Swarm Optimization for Nonconvex Economic Dispatch[J]. IEEE TRANSACTIONS ON POWER SYSTEMS.2008,23(3):1079-1087.
[101]Nidul Sinha, Chakrabarti R, Chattopadhyay P K. Evolutionary Programming Techniques for Economic Load Dispatch[J]. IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION.2003,7(1):83-94.
[102]Immanuel Selvakumar A, Thanushkodi K. A New Particle Swarm Optimization Solution to Nonconvex Economic Dispatch Problems[J]. IEEE TRANSACTIONS ON POWER SYSTEMS.2007,22(1):42-51.
[103]王凌,黄付卓,李灵坡.基于混合双种群差分进化的电力系统经济负荷分配[J].控制与决策.2009,24(8)：1156-1160.
[104]王瑜,李斌,袁博.混合SQP的基于完全学习的粒子群优化算法的电力系统中经济分配问题的应用[J].中国科学,2010,40(3)：403-411.
[105]Meng K, Wang G, Dong Z, Wong K. Quantum-inspired particle swarm optimization for vale-point economic load dispatch[J]. IEEE Transactions on Power Systems.2010, 25(1):215-222.
[106]Nasimul Nomana, Hitoshi Iba. Differential evolution for economic load dispatch problems[J]. Electric Power Systems Research.2008,78(8):1322-1331.
[107]唐巍,李殿璞.电力系统经济负荷分配的混沌优化方法[J].中国电机工程学报.2000,20(10)：36-40