配电网无功优化方法的研究
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摘要
简单遗传算法(SGA)存在着收敛速度慢、易“早熟”等缺陷，针对这些缺陷，本文设计出改进遗传算法（IGA）。动态调节种群大小，去掉遗传算法在迭代后期搜索产生的过多相似个体，达到减少计算时间的目的；按照解的优劣程度给适应度函数增加一个在GA搜索过程中动态改变的可变罚函数，给搜索最优解创造一个梯度，使遗传算法收敛到可行的较优解或最优解；根据适应度值最大和最小个体的差修正适应度函数，使适应度函数值适中不容易造成收敛太快、局部收敛或根本不收敛而变成随机搜索；为了避免“近亲繁殖”采用竞争择优的交叉操作；利用并行遗传算法的思想，提出一种自适应多子种群进化策略；提出人口汰新政策来解决类似甚至相同的个体的情况发生。
为了提高配电网无功优化的收敛速度，结合配电网的特点，提出采用简单可行的灵敏度公式选择无功电容补偿器的安装地点，并用灵敏度分析变异变压器分接头，使变异算子的选取更符合配电网无功优化问题中关于调节变压器分接头的实际情况，减少了一些不必要的变异运算，使适应性和鲁棒性加强；根据实际情况采用无功补偿电容器的启发式变异，使变异算子的选取更符合无功优化问题中关于补偿电容器的实际。本文利用一定的专家系统知识综合调节变压器分接头和补偿电容器组数，来帮助遗传算法搜索问题的最优解。
对配电网电压无功优化问题中负荷的非概率性的不确定性问题、多目标问题、约束不可行性问题进行了研究，用模糊区间来描述实际的负荷情况，并用负荷的模糊区间值计算配电网的潮流，得到有功功率损耗和电压的模糊区间值，使网损率和节点电压最大偏移量的隶属函数更接近实际情况；将改进遗传算法与模糊集理论相结合，通过求解多目标函数和约束条件的模糊集合的交集，得出网损率和节点电压最大偏移量最小的最优运行状态。
SGA has defects of slow convergence and being prone to immature convergence. In order to eliminate the defects, an improved GA is proposed in this thesis. This thesis suggests a process considered minimizes the population size as similar individuals occur in the fitter members of the population, which helps reduce the execution times for GA by removing the redundancy associated with the saturation effect found in the later generation. This thesis uses a method that adds dynamic penalty terms to the fitness function according to the optimal degree of solutions, so as to create a gradient toward a feasible suboptimal or even optimal solutions. On the basis of the difference of the biggest and the smallest of Fitness of individual, modifying the fitness function in order to convergence is a satisfaction. In order to avoid inbreeding, competitive crossover is used. Making use of the idea of the parallel genetic algorithms, presenting the adaptive multiple subpopulation evolutive strategy. presenting extinction and immigration strategy in order to avoid the similar or even same individuals appear.
In order to enhance convergence velocity of reactive power optimization of the radial distribution system, combining the characteristic of the radial distribution system, a sensitivity analysis approach was build up for optimal selection of capacitors and mutation of transformer tap changer. Heuristic mutation capacitors basing on practice are proposed.
Taking load uncertainties, infeasibility problem and multiple objection of the reactive power optimization in the radial distribution system into consideration, loads are modeled as fuzzy interval numbers. Fuzzy power flow is proposed based on fuzzy interval load for the more practical membership function of line losses rate and maximal voltages offset. This thesis presents multiple objection model of the reactive power optimization considering uncertainties using the fuzzy set theory. The model is do by IGA and fuzzy set. The optimal solution is the one with maximum value of the satisfaction parameter.
为了提高配电网无功优化的收敛速度，结合配电网的特点，提出采用简单可行的灵敏度公式选择无功电容补偿器的安装地点，并用灵敏度分析变异变压器分接头，使变异算子的选取更符合配电网无功优化问题中关于调节变压器分接头的实际情况，减少了一些不必要的变异运算，使适应性和鲁棒性加强；根据实际情况采用无功补偿电容器的启发式变异，使变异算子的选取更符合无功优化问题中关于补偿电容器的实际。本文利用一定的专家系统知识综合调节变压器分接头和补偿电容器组数，来帮助遗传算法搜索问题的最优解。
对配电网电压无功优化问题中负荷的非概率性的不确定性问题、多目标问题、约束不可行性问题进行了研究，用模糊区间来描述实际的负荷情况，并用负荷的模糊区间值计算配电网的潮流，得到有功功率损耗和电压的模糊区间值，使网损率和节点电压最大偏移量的隶属函数更接近实际情况；将改进遗传算法与模糊集理论相结合，通过求解多目标函数和约束条件的模糊集合的交集，得出网损率和节点电压最大偏移量最小的最优运行状态。
SGA has defects of slow convergence and being prone to immature convergence. In order to eliminate the defects, an improved GA is proposed in this thesis. This thesis suggests a process considered minimizes the population size as similar individuals occur in the fitter members of the population, which helps reduce the execution times for GA by removing the redundancy associated with the saturation effect found in the later generation. This thesis uses a method that adds dynamic penalty terms to the fitness function according to the optimal degree of solutions, so as to create a gradient toward a feasible suboptimal or even optimal solutions. On the basis of the difference of the biggest and the smallest of Fitness of individual, modifying the fitness function in order to convergence is a satisfaction. In order to avoid inbreeding, competitive crossover is used. Making use of the idea of the parallel genetic algorithms, presenting the adaptive multiple subpopulation evolutive strategy. presenting extinction and immigration strategy in order to avoid the similar or even same individuals appear.
In order to enhance convergence velocity of reactive power optimization of the radial distribution system, combining the characteristic of the radial distribution system, a sensitivity analysis approach was build up for optimal selection of capacitors and mutation of transformer tap changer. Heuristic mutation capacitors basing on practice are proposed.
Taking load uncertainties, infeasibility problem and multiple objection of the reactive power optimization in the radial distribution system into consideration, loads are modeled as fuzzy interval numbers. Fuzzy power flow is proposed based on fuzzy interval load for the more practical membership function of line losses rate and maximal voltages offset. This thesis presents multiple objection model of the reactive power optimization considering uncertainties using the fuzzy set theory. The model is do by IGA and fuzzy set. The optimal solution is the one with maximum value of the satisfaction parameter.
引文
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[3] 罗铸，电力系统无功和电压的优化调节，电力系统自动化，1988，34-38
[4] 刘龙瑞， 电力系统无功优化的经典法与线性规划相结合方法， 重庆大学硕士论文，重庆大学电气工程学院图书室，1993，9-10
[5] Hano. Real Time Control of System Voltage and Reactive Power. IEEE PAS-88,No1,1969，267-272
[6] 赵尤新,徐国禹. 用敏感度方法分析计算系统无功和电压最优控制问题. 重庆大学学报,1985，25-30
[7] Mamandur.K.P.C. Optimal Control of Reactive Power Flow for Improvements in Voltage Profiles and Real Power Loss Minmization. IEEE PAS-100,No.7,1981 267-271
[8] 朱继忠, 徐国禹,秦翼鸿， 二滩电站接入系统四川电网无功优化配置研究. 重庆大学研究报告，Jan 1995，28-30
[9] John.Preschon. Optimal Control of Reactive Power Flow. IEEE PAS-87,No.1,1968，234-240
[10] Hughts.A,Jee.G,Hsiang.P,Shoults.R.R,Chen.M.S. Optimal Reactive Power Planning. IEEE PAS-100,No.5,1981，121-126
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[12] Sun.D.I,Ashley.B. Optimal Power Flow by Newton Approach. IEEE PAS-103,No.10,1984，26-31
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[23] GHOSE T ,GOS WAMI S K,BASU S K. Energy loss reduction in distribution system by capacitor placement through combined GA-SA technique. IEEE TENCON98,1998,1234-1243
[24] SUNDHARARA JANS,PAHWA A. Optimal capacitor placement on radial distribution system. IEEE Trans on PD,1989,4(1),725-734.
[25] YOSHIDA H,KAWATA K,FUKUYAMA Y,etal. A partical swarm optimization for reactive power and voltage control considering voltage stability .ISAP99,1999.126-131.
[26] 李亚男，张粒子，舒隽等，结合专家知识的遗传算法在无功规划优化中的应用，电网技术，2001,25(7),14-17
[27] Tomsovic K. A Fuzzy Linear Programming Approach to Reactive Power /Voltage Control Problem. TEEE Trans on power system,V7 N1 February 1992,287-293
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[32] Jwo W S,Liu C W,Liu C C,etal. Hybrid Expert System and Simulated Annealing Approach to Optimal Reactive Power Planning. IEE Proceedings Generation, Transmission & Distribution,1995,142(4):381-385
[33] Ponnambakam K,Quintana V H,VannelliA.A fast algorithm for power system optimization problem using an interior point method .IEEE Trans on PS,1992,7(2),872-878
[34] Momoh JA ,Guo SX ,Ogbuobiri EC etal . The quadratic interior point method solving power system optimization problems .IEEE Trans on PS,1994,9(3),1236-1242.
[35] Granville S . Optimal reactive dispatch through interior point methods. IEEE Trans on PS,1994,9(1),38-42
[36] WuYu-Chi,Debs AS,Marsten RE.A direct nonlinear predictor-corrector primal-dual interior point algorithm for optimal power flows .IEEE Trans on PS,1994,9(2),163-167
[37] 张元明，王晓东，李乃湖，基于原对偶内点法的电压无功功率优化，电网技术，1998，22(6),42-45
[38] Chang SK ,Marks GE, Kato K.Optimal real-time voltage control .IEEE Trans on PS ,1990,5(3),462-467
[39] Alsac O,Bright J, Prais Me tal .Further development in LP-based optimal power flow .IEEE Trans on PS，1990，5(3)，421-427
[40] 刘宝碇，赵瑞清，随机规划与模糊规划，北京，清华大学出版社，第一版，1998.6，23
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[42] 周帅，遗传算法改进及其在配电网规划中的应用研究，硕士毕业论文，2000.6，14-15
[43] 唐加福等，一种求解非线性规划问题的改进遗传算法，东北大学学报，1997.11，490-493
[44] 严卫，朱兆达，一种遗传-梯度混合算法，信号处理，1998.12，42-45
[45] M.Srinivas,L.M.Patnaik, Apaptive probabilities of Crossover and Mutation in Genetic Algorithm, IEEE Trans on SMC，vol24，No4，April 1994.
[46] 周明，孙树栋，遗传算法原理及应用，北京，国防工业出版社，第一版，1999年6月，47
[47] 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，电网技术，2001，25(3)，22-25
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[2] 杨毅刚等，电力系统无功最优补偿与无功电源优化的数学模型和计算方法，湖南大学学报，38-43
[3] 罗铸，电力系统无功和电压的优化调节，电力系统自动化，1988，34-38
[4] 刘龙瑞， 电力系统无功优化的经典法与线性规划相结合方法， 重庆大学硕士论文，重庆大学电气工程学院图书室，1993，9-10
[5] Hano. Real Time Control of System Voltage and Reactive Power. IEEE PAS-88,No1,1969，267-272
[6] 赵尤新,徐国禹. 用敏感度方法分析计算系统无功和电压最优控制问题. 重庆大学学报,1985，25-30
[7] Mamandur.K.P.C. Optimal Control of Reactive Power Flow for Improvements in Voltage Profiles and Real Power Loss Minmization. IEEE PAS-100,No.7,1981 267-271
[8] 朱继忠, 徐国禹,秦翼鸿， 二滩电站接入系统四川电网无功优化配置研究. 重庆大学研究报告，Jan 1995，28-30
[9] John.Preschon. Optimal Control of Reactive Power Flow. IEEE PAS-87,No.1,1968，234-240
[10] Hughts.A,Jee.G,Hsiang.P,Shoults.R.R,Chen.M.S. Optimal Reactive Power Planning. IEEE PAS-100,No.5,1981，121-126
[11] 汤建民，电力系统无功补偿综合规划，重庆大学硕士论文，重庆大学电气工程学院图书室，1995，18-21
[12] Sun.D.I,Ashley.B. Optimal Power Flow by Newton Approach. IEEE PAS-103,No.10,1984，26-31
[13] 张力民，何大愚，朱太秀， 牛顿法最优潮流和最优无功补偿， 中国电机工程学报，1992，18（9），34-39
[14] 周双喜，杨彬，实现无功优化的新算法--遗传算法，电力系统自动化，1995，19(11)，19-23
[15] Wu Q H,Cao Y J,Wen J Y .Optimal Reactive Power Dispatch Using an Adaptive Genetic Algorithm. Int J of Electrical Power & Energy Systems, 1998, 20(8):563-569
[16] KenjiIba. Reactive Power Optimization by Genetic Algorithm. IEEE Transon Power Systems,1994,9(2):685-692
[17] 范明天，相年德，张祖平等，基于遗传算法技术的离散无功优化，电网技术，1995，19(5),40-45
[18] 文劲宇，江振华，姜霞等，基于遗传算法的无功优化在鄂州电网中的实现，电力系统自动化，2000，24(2),45-47,60
[19] 周双喜，蔡虎，应用于电力系统无功优化的改进遗传算法，电网技术，1997，21(12),1-3,11
[20] 赵登福，周文华，张伏生等，遗传算法在无功优化应用中的改进，电网技术，1998，22(10),34-38,43
[21] 韩祯祥，文福拴，模拟进化优化方法及其应用，人工智能学术讨论会，1988，56-62
[22] LEE K Y,BAI X,PARK Y.M. Optimization method for reactive power planning by using a modified simple genetic algorithm. IEEE Trans on power systems.1995,10(4),1843-1850.
[23] GHOSE T ,GOS WAMI S K,BASU S K. Energy loss reduction in distribution system by capacitor placement through combined GA-SA technique. IEEE TENCON98,1998,1234-1243
[24] SUNDHARARA JANS,PAHWA A. Optimal capacitor placement on radial distribution system. IEEE Trans on PD,1989,4(1),725-734.
[25] YOSHIDA H,KAWATA K,FUKUYAMA Y,etal. A partical swarm optimization for reactive power and voltage control considering voltage stability .ISAP99,1999.126-131.
[26] 李亚男，张粒子，舒隽等，结合专家知识的遗传算法在无功规划优化中的应用，电网技术，2001,25(7),14-17
[27] Tomsovic K. A Fuzzy Linear Programming Approach to Reactive Power /Voltage Control Problem. TEEE Trans on power system,V7 N1 February 1992,287-293
[28] Abdul-Rahman K H. A Fuzzy-based Optimal Reactive Power Control. TEEE Trans on power system,V8 N2 May 1993,662-670
[29] 谭建成等，电力系统无功结合优化的模糊数学解决，中国电机工程学报，第10卷增刊，1990年11月，32-36
[30] Tomosovice K evin. Fuzzy Linear Programming for Reactive Power Control. Proc of the 5th IEEE Internation Symposium on intelligent control,1990,245-251
[31] Abdul RahmanK H,ShahidehpourS M,DaneshdoostM. AI Approach to Optimal VAR Control with Fuzzy Reactive Loads .IEEE Transon Power Systems, 1995, 10(1):88-97
[32] Jwo W S,Liu C W,Liu C C,etal. Hybrid Expert System and Simulated Annealing Approach to Optimal Reactive Power Planning. IEE Proceedings Generation, Transmission & Distribution,1995,142(4):381-385
[33] Ponnambakam K,Quintana V H,VannelliA.A fast algorithm for power system optimization problem using an interior point method .IEEE Trans on PS,1992,7(2),872-878
[34] Momoh JA ,Guo SX ,Ogbuobiri EC etal . The quadratic interior point method solving power system optimization problems .IEEE Trans on PS,1994,9(3),1236-1242.
[35] Granville S . Optimal reactive dispatch through interior point methods. IEEE Trans on PS,1994,9(1),38-42
[36] WuYu-Chi,Debs AS,Marsten RE.A direct nonlinear predictor-corrector primal-dual interior point algorithm for optimal power flows .IEEE Trans on PS,1994,9(2),163-167
[37] 张元明，王晓东，李乃湖，基于原对偶内点法的电压无功功率优化，电网技术，1998，22(6),42-45
[38] Chang SK ,Marks GE, Kato K.Optimal real-time voltage control .IEEE Trans on PS ,1990,5(3),462-467
[39] Alsac O,Bright J, Prais Me tal .Further development in LP-based optimal power flow .IEEE Trans on PS，1990，5(3)，421-427
[40] 刘宝碇，赵瑞清，随机规划与模糊规划，北京，清华大学出版社，第一版，1998.6，23
[41] 邢文训，谢金星，现代优化计算方法，北京，清华大学出版社，第一版，1999.8，32-33
[42] 周帅，遗传算法改进及其在配电网规划中的应用研究，硕士毕业论文，2000.6，14-15
[43] 唐加福等，一种求解非线性规划问题的改进遗传算法，东北大学学报，1997.11，490-493
[44] 严卫，朱兆达，一种遗传-梯度混合算法，信号处理，1998.12，42-45
[45] M.Srinivas,L.M.Patnaik, Apaptive probabilities of Crossover and Mutation in Genetic Algorithm, IEEE Trans on SMC，vol24，No4，April 1994.
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