摘要
最优潮流是一类典型的非线性规划问题，最优潮流计算上的困难限制了它在电力系统运行中的应用，在过去的30年中，人们提出了各种优化方法来解决此问题，至今未能取得公认的满意的成果。
本文总结了国内外关于最优潮流算法的研究现状，介绍了求解最优潮流的经典算法，现代优化方法以及其它算法，对各类优化方法进行了比较和讨论。
本文提出了一种混沌搜索与模糊集理论相结合求解电力系统最优潮流问题的新方法。该方法用模糊集理论将多目标函数和可伸缩约束条件模糊化，把多目标最优潮流问题转化为单目标非线性规划问题；利用混沌变量的随机性、规律性、遍历性进行寻优，克服了基于导数优化方法对于梯度信息的高度依赖性而造成的困难。
本文提出了一种复杂函数的混合优化策略，将混沌搜索与单纯形法相结合，首先利用混沌的遍历性特点进行全局搜索，同时为单纯形法生成较好的初始点，然后用单纯形法进行局部优化，避免了单一算法的弱点。
Optimal Power Flow (OPF) can be defined as a typical nonlinear programming problem. The computational difficulties in solving the OPF problem have limited its use in power system operations. In the past three decades, various optimization techniques were proposed to solve the problem. But people fail to make the generally acknowledged satisfied achievement so far.
This paper has summarized the research in recent advances about the OPF algorithm both at home and abroad, recommended the classical algorithms of OPF, the modern optimization methods and other algorithms. This paper compared and discussed the method of these kinds of optimization.
A new method that the chaos optimization combines with fuzzy set was proposed and applied to OPF problems. Object functions and soft constraints of multi-objective OPF problem are modeled using fuzzy sets, and then this multi-objective fuzzy OPF model is reformulated as a single objective non-linear programming problem. Chaotic variables are used in the searching, which takes advantage of their propriety of randomicity, regularity and ergodicity. The method overcomes the difficulties in traditional gradient search.
Combining the simplex method with the chaos optimization method, a hybrid optimization strategy is proposed to solve the optimization problems of complex functions. The hybrid optimization strategy utilizes the ergodicity of chaos to find the global optimal solution, at the same time the initial points that are needed in simplex method are formed, then use simplex method to perform local optimization, which avoid the weakness of single method.
引文
[1] 诸骏伟主编. 电力系统分析（上册）. 北京：中国电力出版社，1995
[2] 于尔铿等. 能量管理系统. 北京：科学出版社，1998:281~291
[3] 张伯明等. 高等电力网络分析. 北京：清华大学出版社，1996:241~253
[4] 钟德成等. 柔性交流输电系统潮流计算中改进的遗传算法. 电力系统自动化，2000，24(2):48~50
[5] 段刚等. 电力系统NP难问题全局优化算法的研究. 电力系统自动化，2001，25(5):14~18
[6] 赵晋泉等. 改进最优潮流牛顿算法有效性的对策研究. 中国电机工程学报，1999，19(12):70~75
[7] 赵晋泉等. 牛顿最优潮流算法中离散控制量处理的新方法. 电力系统自动化，1999，23(23):37~40
[8] 刘明波等. 内点法在求解电力系统优化问题中的应用综述. 电网技术，1999，23(8):61~64
[9] 刘明波等. 一种求解多目标最优潮流的模糊优化算法. 电网技术，1999，23(9):23~26,31
[10] 石立宝等. 自适应进化规划及其在多目标最优潮流中的应用——基于自适应进化规划的多目标最优潮流. 电力系统自动化，2000，24(8):33~36
[11] Chen L, Suzuki H, Katou K. Mean field theory for optimal power flow. IEEE Trans on PS, 1997 ,12(4):1481~1486
[12] Baldick R, Kim B H, Chase C, Luo Y. A Fast distributed implementation of optimal power flow. IEEE Trans on PS, 1999 ,14(3):858~864
[13] Wu Y C, Debs A S, Marsten R E. A directnonlinear predictor-correcter primal-dual interior pointalgorithm for optimal power
flows. IEEE Trans on PS, 1 994, 9(2):876~883
[14] Xihui Y, Quintana V H. Improving an interior-point-based OPF by dynamic adjustments of step sizes and tolerances. IEEE Trans on PS, 1999 ,14(2):709~717
[15] Wei H, Sasaki H.,Kubokawa J, Yokoyama R. Large scale hydrothermal optimal power flow problems based on interior point nonlinear programming. IEEE Trans on PS，2000，15(1):396~403
[16] Kim B H, Baldick R. A comparison of distributed optimal power flow algorithms. IEEE Trans on PS，2000，15(2):599~604
[17] Nejdawi I M, Clements K A, Davis, P.W. An efficient interior point method for sequential quadratic programming based optimal power flow. IEEE Trans on PS，2000，15(4):1179~1183
[18] Tognola G, Bacher R. Unlimited point algorithm for OPF problems. IEEE Trans on PS, 1999 ,14(3):1046~1054
[19] Torres G L, Quintana V H. On a nonlinear multiple-centrality-corrections interior-point method for optimal power flow. IEEE Trans on PS，2001，16(2):222~228
[20] Wu Y-C. Fuzzy second correction on complementarity condition for optimal power flows. IEEE Trans on PS，2001，16(3):360~366
[21] Lin C-H, Lin S-Y. A new dual-type method used in solving optimal power flow problems. IEEE Trans on PS, 1997 ,12(4):1667~1675
[22] Momoh J A，Zhu J Z. Improved interior point method for OPF problems. IEEE Trans on PS, 1999 ,14(3): 1114~1120
[23] Chen L, Matoba S, Inabe H, Okabe T. Surrogate constraint method for optimal power flow. IEEE Trans on PS, 1998 ,13(3):1084~1089
[24] Yuryevich J, Wong K P. Evolutionary programming based optimal power flow algoriththm. IEEE Trans On PS,1999,14(4):1245~1250
[25] Rahli M, Pirotte P. Optimal load flow using sequential unconstrained
minimization technique(SUMT) method under power transmission losses minimization. Electric Power Systems research.1999,52(1):61~64
[26] 李兵, 蒋慰孙. 混沌优化方法及其应用. 控制理论与应用, 1997, 14（4）: 613~615
[27] 唐巍, 李殿璞. 电力系统经济负荷分配的混沌优化方法. 中国电机工程学报, 2000, 20（10）: 36~40
[28] 吴际舜, 侯志俭. 电力系统潮流计算的计算机方法. 上海: 上海交通大学出版社, 2000
[29] 唐巍, 李殿璞, 陈学允. 混沌理论及其应用研究. 电力系统自动化, 2000, 24（7）: 67~70
[30] 王凌. 智能优化算法及其应用. 北京: 清华大学出版社, 2001
[31] D. M. 希梅尔布劳. 实用非线性规划. 北京: 科学出版社, 1981
[32] 谢巍, 方康玲. 一种求解不可微非线性函数的全局解的混合遗传算法. 控制理论与应用, 2000, 17 (2) : 180~183
[33] 叶庆凯, 王肇明. 优化与最优控制中的计算方法. 北京. 科学出版社, 1986
[34] 丁晓莺, 王锡凡. 最优潮流在电力市场环境下的最新发展. 电力系统自动化, 2002, 26（13）: 1~7
[35] 欧阳红兵，汪希萱. 电磁式在线自动平衡头结构参数的混沌优化. 中国机械工程, 2000, 11（5）: 557~560
[36] 唐巍，郭镇明，李殿璞. 混沌优化用于电力系统静态负荷模型参数辨识. 电力系统自动化, 2000, 24（13）: 27~30
[37] 唐巍, 李殿璞, 陈学允. 模糊电力系统稳定器的混沌优化方法. 电力系统自动化, 2000, 24（9）: 28~31
[38] 李祥飞，邹恩，张泰山. 一种模糊神经网络控制器参数的混沌优化设计. 控制与决策, 2002, 17（3）: 320~323
[39] 张春慨,邵惠鹤. 混沌优化方法在甲醛生产过程中在线优化的应用. 信息与控制, 2000, 29（6）: 570~574