基于自适应混沌粒子群算法的多目标无功优化研究
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摘要
电力系统的无功优化控制,不仅能有效地降低系统的有功功率损耗,而且还可以改善电网的电压质量,对系统的安全稳定、经济运行具有非常重要意义。根据系统运行的要求,无功优化问题可以分为单目标无功优化和多目标无功优化。多目标无功优化顺应电力系统运行的经济性和安全性的要求。本文将有功功率损耗最小、节点电压偏移量最小和静态电压稳定裕度最大整合为无功优化的目标函数。
分析粒子群算法的构成及寻优原理,指出基本粒子群优化算法由于随机生成代表控制变量值的粒子,使得在优化迭代过程中易陷入局部最优解,而且后期收敛速度慢等问题,将混沌优化算法融合到粒子群算法中,提出了自适应混沌粒子群算法求解多目标无功优化问题。该算法在初始化粒子即无功优化控制变量值时,采用混沌思想,增加控制变量取值的多样性;通过粒子群无功优化算法计算各个粒子对应的适应值即无功优化目标函数值,并按照其大小择优选取控制变量值进行混沌优化以帮助无功优化控制变量跳出局部极值区域;并根据无功优化目标函数值自适应地调整其惯性权重系数以提高全局与局部搜索能力。
将自适应混沌粒子群算法应用到多目标无功优化中,通过MATLAB编制程序对IEEE14和IEEE30节点系统进行无功优化计算,并与基本粒子群算法和遗传算法比较,结果表明本文提出的算法具有很好的全局寻优能力和较快的收敛速度,能够有效地进行无功优化。按优化的结果进行的系统运行控制,能达到降低网损,提高电压质量水平和静态电压稳定性的目的。
The control of reactive power optimization in electric power system can not only reduce power loss,but also improve voltage quality. Consequently it is of great importance to security and economic operation of power system.
According to the requirements of power system operation, reactive power optimization problem can be divided into single-objective reactive power optimization and multi-objective one. To meet the needs of economic and safe operation of power system, this paper establishes the minimum set of system power loss, the minimum node voltage offset and the largest static voltage stability margin in the multi-objective reactive power optimization model.
The Particle Swarm Optimization Algorithm is mainly studied in the paper. And the composition of particle swarm optimization algorithm and the optimization principle were analyzed deeply. In particle swarm reactive power optimization it is easily falls into the local optimal solution in the iterative process of optimization due to the particles randomly generated on behalf of variable values and the slow convergence problem finally. Consequently, in this paper the chaotic particle swarm algorithm produced by the chaotic optimization algorithm integrated into the particle swarm algorithm is proposed to solve the problem of multi-objective reactive power optimization. The chaotic method is adopted to increase the diversity of control variable value in the initialization of the algorithm, that the value of reactive power optimization of control variables. The particle swarm algorithm is used to calculate the fitness of each particle that corresponds to reactive power optimization of the objective function value and merit-based selection in accordance with its size control variable values of chaos optimization to help optimize the reactive power control variables out of local optimum area. In accordance with the objective function value of reactive power optimization, it is adaptively adjusted its coefficient of inertia weight to enhance the global and local search capabilities.
The chaotic particle swarm algorithm is applied to reactive power optimization,through MATLAB programming right IEEE14-bus and IEEE30-bus system reactive power optimization calculation,and with elementary particle swarm optimization and genetic algorithm comparison, the results show that the algorithm proposed in this paper effectively reduces the system power loss and improves system voltage quality level,and has a better ability of global optimization and faster convergence speed.
分析粒子群算法的构成及寻优原理,指出基本粒子群优化算法由于随机生成代表控制变量值的粒子,使得在优化迭代过程中易陷入局部最优解,而且后期收敛速度慢等问题,将混沌优化算法融合到粒子群算法中,提出了自适应混沌粒子群算法求解多目标无功优化问题。该算法在初始化粒子即无功优化控制变量值时,采用混沌思想,增加控制变量取值的多样性;通过粒子群无功优化算法计算各个粒子对应的适应值即无功优化目标函数值,并按照其大小择优选取控制变量值进行混沌优化以帮助无功优化控制变量跳出局部极值区域;并根据无功优化目标函数值自适应地调整其惯性权重系数以提高全局与局部搜索能力。
将自适应混沌粒子群算法应用到多目标无功优化中,通过MATLAB编制程序对IEEE14和IEEE30节点系统进行无功优化计算,并与基本粒子群算法和遗传算法比较,结果表明本文提出的算法具有很好的全局寻优能力和较快的收敛速度,能够有效地进行无功优化。按优化的结果进行的系统运行控制,能达到降低网损,提高电压质量水平和静态电压稳定性的目的。
The control of reactive power optimization in electric power system can not only reduce power loss,but also improve voltage quality. Consequently it is of great importance to security and economic operation of power system.
According to the requirements of power system operation, reactive power optimization problem can be divided into single-objective reactive power optimization and multi-objective one. To meet the needs of economic and safe operation of power system, this paper establishes the minimum set of system power loss, the minimum node voltage offset and the largest static voltage stability margin in the multi-objective reactive power optimization model.
The Particle Swarm Optimization Algorithm is mainly studied in the paper. And the composition of particle swarm optimization algorithm and the optimization principle were analyzed deeply. In particle swarm reactive power optimization it is easily falls into the local optimal solution in the iterative process of optimization due to the particles randomly generated on behalf of variable values and the slow convergence problem finally. Consequently, in this paper the chaotic particle swarm algorithm produced by the chaotic optimization algorithm integrated into the particle swarm algorithm is proposed to solve the problem of multi-objective reactive power optimization. The chaotic method is adopted to increase the diversity of control variable value in the initialization of the algorithm, that the value of reactive power optimization of control variables. The particle swarm algorithm is used to calculate the fitness of each particle that corresponds to reactive power optimization of the objective function value and merit-based selection in accordance with its size control variable values of chaos optimization to help optimize the reactive power control variables out of local optimum area. In accordance with the objective function value of reactive power optimization, it is adaptively adjusted its coefficient of inertia weight to enhance the global and local search capabilities.
The chaotic particle swarm algorithm is applied to reactive power optimization,through MATLAB programming right IEEE14-bus and IEEE30-bus system reactive power optimization calculation,and with elementary particle swarm optimization and genetic algorithm comparison, the results show that the algorithm proposed in this paper effectively reduces the system power loss and improves system voltage quality level,and has a better ability of global optimization and faster convergence speed.
引文
[1]骆济寿.电力系统优化运行.武汉:华中理工大学出版社,1989
[2]李婧,李俊儒,刘玲.电力系统无功优化的模型及算法的综述.中国电力教育,2007年研究综述与技术论坛专刊,131～133
[3]许文超,郭伟.电力系统无功优化的模型及算法综述.电力系统及其自动化学报,2003,Vol.15(1):100～105
[4]翟海保,程浩忠,陈春霖,等.输电网络优化规划研究综述.电力系统及其白动化学报,2004,Vol.16(2):17～23
[5] I. J. Ken.Reactive Power Optimization by Genetic Algorithm.IEEE Trans on Power System,1994,Vol.9(2):685～691
[6]刘科研,盛万兴,李运华.基于改进遗传模拟退火算法的无功优化.电网技术,2007,Vol.31(3):13～17
[7]任晓莉,程红丽,刘健.基于禁忌搜索算法的变电站电压无功优化控制.继电器2008,Vol.36(8):31～35
[8]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.中国电机工程学报,2001,Vol.21(9):136～142
[9] J. Shu,L. Z. Zhang,Y. Liu,et al.An improved genetic algorithm for dynamic reactive power optimization in electricity market.Power System Technology,2004,PowerCon 2004
[10] L. Furong,J. D. Pilgrim,C. Dabeedin,et al.Genetic algorithms for optimal reactive power compensation on the national grid system.IEEE Transactions on Power Systems,2005,Vol.20(1):493～500
[11]戴彦,倪以信,文福栓,韩帧祥.电力市场下的无功电价研究.电力系统自动化,2000,Vol.24(3):9～14
[12]黄志刚,李林川,杨理,等.电力市场环境下的无功优化模型及其求解方法.中国电机工程学报,2003,Vol.23(12):79～83
[13]刘明波,朱春明,钱康龄,等.计及控制设备动作次数约束的动态无功优化算法.中国电机工程学报,2004,Vol.24(3):34～40
[14]赵尤新,徐国禹.用敏感度方法分析计算电力系统无功和电压最优控制问题.重庆大学学报,1985,Vol.(4):1～11
[15]姚诸香,涂惠亚,徐国禹.基于灵敏度分析的无功优化潮流.电力系统自动化,1997,Vol.21(11):19～21
[16]张伯明著.高等电力网络分析.清华大学出版社,2000
[17]朱太秀.电力系统优化潮流与无功优化.电网技术,1990,45(4):13～16
[18]王永刚,柳悼.牛顿法优化潮流的实用化研究.继电器,1999,Vol.27(5):6～8
[19]徐建亭,王秀英,李兴源.电力系统电压无功的序列二次规划算法.电力系统自动化,2001,Vol.25(23):4～8
[20]李乃湖.计及整型控制变量的电压-无功功率优化.电力系统自动化,1994,Vol.18(12):5～11
[21]刘方,颜伟,Y. C. David.基于遗传算法和内点法的无功优化混合策略.中国电机工程学报,2005,Vol.25(15):67～72
[22]向铁元,周青山,李富鹏,等.小生境遗传算法在无功优化中的应用研究.中国电机工程学报,2005,Vol.25(17):45～51
[23]莫宏伟,金鸿章.免疫算法原理与应用.航空计算技术,2002,Vol.32(4):49～51
[24]钟红梅,任震,张勇军,等.免疫算法及其在电力系统无功优化中的应用.电网技术,2004,Vol.28(3):16～19
[25]贾德香,唐国庆,韩净.基于改进模拟退火算法的电网无功优化.继电器,2004,Vol.32(4):32～35
[26]王洪章,熊信良,吴耀武.基于改进Tabu搜索算法的电力系统无功优化.电网技术,2002,Vol.26(l):15～18
[27]朱向阳.基于改进禁忌搜索算法的配电网电压无功优化控制.继电器,2006,Vol.34(14):35～37
[28] H. Y. Su.Voltage control using a combined integer linear programming and arule-based approach.IEEE Trans on Power Systems,2002,Vol.7(2):744～748
[29] K. H. Abdul,S. M. Shahide,M. Daneshdoost.An approach to optimal VAR control with fuzzy reactive loads.IEEE Transactions on Power Systems,2005,Vol.10(1):88～97
[30]谭涛亮,张尧.基于遗传禁忌混合算法的电力系统无功优化.电网技术,2003,Vol.28(11):57～61
[31] Y. Liu,L. Ma,J. J. Zhang.GA/SA/TS hybrid algorithms for reactive power optimization.IEEE Power Engineering Society Summer Meeting,2000,l:245～249
[32] H. Song,B. Lee,Y. H. Moon.Reactive optimal power flow incorporating margin enhancement constraints with nonlinear interior point method.IEE Proceedings:Generation,Transmission and Distribution,2005,Vol.152(6):961～968
[33]刘钰玉.计算排序法及其应用.计算机技术,1998,Vol.11(4):24～28
[34] J. Kennedy,R. Eberhart.Particle Swarm Optimization.Proceedings of IEEE International Conference on Neural Networks,2001:1942～1948
[35] J. J. Liang,A. K. Qin,S. Baker.Comprehensive learning particle swarm optimizer for global optimization of multimodal function.IEEE trans on evolutionary computation,2006,Vol.10(3):281～295
[36]李洪亮,侯朝桢,周绍生.一种高效的改进粒子群优化算法.计算机工程与应用,2008,Vol.44(1):14～16
[37]曾传华,申元霞.新型分阶段粒子群优化算法.计算机工程与应用,2008,Vol.44(24):81～82
[38]丁玉凤,文劲宇.基于改进PSO算法的电力系统无功优化研究.继电器,2005,Vol.33(6):20～24
[39]虞斌能,连志刚,焦斌.动态惯性权重粒子群优化算法.上海电机学院学报,2008,Vol.11(3):170～176
[40]莫宏伟,金鸿章.免疫算法原理与应用.航空计算技术,2002,Vol.32(4):49～51
[41]王凌.智能优化算法及其应用.北京:清华大学出版社,2001
[42]李兵,蒋慰孙.混沌优化方法及其应用.控制理论与应用,1997,Vol.14(4):613~615
[43]蒙文川,邱家驹.电力系统经济负荷分配的混沌粒子群优化算法.电力系统及其自动化学报,2007,Vol.19(2):114～119
[44]刘自发,葛少云,余贻鑫.基于混沌粒子群优化方法的电力系统无功最优潮流.电力系统自动化,2005,Vol.29(7):53～57
[45]赵涛,熊信银,吴耀武.基于混沌优化算法的电力系统无功优化.继电器,2003,Vol.31(3):20～25
[46]褚美茹,崔明勇.混沌遗传算法在配电网无功优化中的应用.信息技术,2004,Vol.28(10):48～50
[2]李婧,李俊儒,刘玲.电力系统无功优化的模型及算法的综述.中国电力教育,2007年研究综述与技术论坛专刊,131～133
[3]许文超,郭伟.电力系统无功优化的模型及算法综述.电力系统及其自动化学报,2003,Vol.15(1):100～105
[4]翟海保,程浩忠,陈春霖,等.输电网络优化规划研究综述.电力系统及其白动化学报,2004,Vol.16(2):17～23
[5] I. J. Ken.Reactive Power Optimization by Genetic Algorithm.IEEE Trans on Power System,1994,Vol.9(2):685～691
[6]刘科研,盛万兴,李运华.基于改进遗传模拟退火算法的无功优化.电网技术,2007,Vol.31(3):13～17
[7]任晓莉,程红丽,刘健.基于禁忌搜索算法的变电站电压无功优化控制.继电器2008,Vol.36(8):31～35
[8]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.中国电机工程学报,2001,Vol.21(9):136～142
[9] J. Shu,L. Z. Zhang,Y. Liu,et al.An improved genetic algorithm for dynamic reactive power optimization in electricity market.Power System Technology,2004,PowerCon 2004
[10] L. Furong,J. D. Pilgrim,C. Dabeedin,et al.Genetic algorithms for optimal reactive power compensation on the national grid system.IEEE Transactions on Power Systems,2005,Vol.20(1):493～500
[11]戴彦,倪以信,文福栓,韩帧祥.电力市场下的无功电价研究.电力系统自动化,2000,Vol.24(3):9～14
[12]黄志刚,李林川,杨理,等.电力市场环境下的无功优化模型及其求解方法.中国电机工程学报,2003,Vol.23(12):79～83
[13]刘明波,朱春明,钱康龄,等.计及控制设备动作次数约束的动态无功优化算法.中国电机工程学报,2004,Vol.24(3):34～40
[14]赵尤新,徐国禹.用敏感度方法分析计算电力系统无功和电压最优控制问题.重庆大学学报,1985,Vol.(4):1～11
[15]姚诸香,涂惠亚,徐国禹.基于灵敏度分析的无功优化潮流.电力系统自动化,1997,Vol.21(11):19～21
[16]张伯明著.高等电力网络分析.清华大学出版社,2000
[17]朱太秀.电力系统优化潮流与无功优化.电网技术,1990,45(4):13～16
[18]王永刚,柳悼.牛顿法优化潮流的实用化研究.继电器,1999,Vol.27(5):6～8
[19]徐建亭,王秀英,李兴源.电力系统电压无功的序列二次规划算法.电力系统自动化,2001,Vol.25(23):4～8
[20]李乃湖.计及整型控制变量的电压-无功功率优化.电力系统自动化,1994,Vol.18(12):5～11
[21]刘方,颜伟,Y. C. David.基于遗传算法和内点法的无功优化混合策略.中国电机工程学报,2005,Vol.25(15):67～72
[22]向铁元,周青山,李富鹏,等.小生境遗传算法在无功优化中的应用研究.中国电机工程学报,2005,Vol.25(17):45～51
[23]莫宏伟,金鸿章.免疫算法原理与应用.航空计算技术,2002,Vol.32(4):49～51
[24]钟红梅,任震,张勇军,等.免疫算法及其在电力系统无功优化中的应用.电网技术,2004,Vol.28(3):16～19
[25]贾德香,唐国庆,韩净.基于改进模拟退火算法的电网无功优化.继电器,2004,Vol.32(4):32～35
[26]王洪章,熊信良,吴耀武.基于改进Tabu搜索算法的电力系统无功优化.电网技术,2002,Vol.26(l):15～18
[27]朱向阳.基于改进禁忌搜索算法的配电网电压无功优化控制.继电器,2006,Vol.34(14):35～37
[28] H. Y. Su.Voltage control using a combined integer linear programming and arule-based approach.IEEE Trans on Power Systems,2002,Vol.7(2):744～748
[29] K. H. Abdul,S. M. Shahide,M. Daneshdoost.An approach to optimal VAR control with fuzzy reactive loads.IEEE Transactions on Power Systems,2005,Vol.10(1):88～97
[30]谭涛亮,张尧.基于遗传禁忌混合算法的电力系统无功优化.电网技术,2003,Vol.28(11):57～61
[31] Y. Liu,L. Ma,J. J. Zhang.GA/SA/TS hybrid algorithms for reactive power optimization.IEEE Power Engineering Society Summer Meeting,2000,l:245～249
[32] H. Song,B. Lee,Y. H. Moon.Reactive optimal power flow incorporating margin enhancement constraints with nonlinear interior point method.IEE Proceedings:Generation,Transmission and Distribution,2005,Vol.152(6):961～968
[33]刘钰玉.计算排序法及其应用.计算机技术,1998,Vol.11(4):24～28
[34] J. Kennedy,R. Eberhart.Particle Swarm Optimization.Proceedings of IEEE International Conference on Neural Networks,2001:1942～1948
[35] J. J. Liang,A. K. Qin,S. Baker.Comprehensive learning particle swarm optimizer for global optimization of multimodal function.IEEE trans on evolutionary computation,2006,Vol.10(3):281～295
[36]李洪亮,侯朝桢,周绍生.一种高效的改进粒子群优化算法.计算机工程与应用,2008,Vol.44(1):14～16
[37]曾传华,申元霞.新型分阶段粒子群优化算法.计算机工程与应用,2008,Vol.44(24):81～82
[38]丁玉凤,文劲宇.基于改进PSO算法的电力系统无功优化研究.继电器,2005,Vol.33(6):20～24
[39]虞斌能,连志刚,焦斌.动态惯性权重粒子群优化算法.上海电机学院学报,2008,Vol.11(3):170～176
[40]莫宏伟,金鸿章.免疫算法原理与应用.航空计算技术,2002,Vol.32(4):49～51
[41]王凌.智能优化算法及其应用.北京:清华大学出版社,2001
[42]李兵,蒋慰孙.混沌优化方法及其应用.控制理论与应用,1997,Vol.14(4):613~615
[43]蒙文川,邱家驹.电力系统经济负荷分配的混沌粒子群优化算法.电力系统及其自动化学报,2007,Vol.19(2):114～119
[44]刘自发,葛少云,余贻鑫.基于混沌粒子群优化方法的电力系统无功最优潮流.电力系统自动化,2005,Vol.29(7):53～57
[45]赵涛,熊信银,吴耀武.基于混沌优化算法的电力系统无功优化.继电器,2003,Vol.31(3):20～25
[46]褚美茹,崔明勇.混沌遗传算法在配电网无功优化中的应用.信息技术,2004,Vol.28(10):48～50