【作者】 陈吉；

【导师】 韦化；

【作者基本信息】 广西大学 ， 电力系统及其自动化， 2006， 硕士

【摘要】 电力系统最优潮流问题(OPF)研究起源于潮流计算和经典经济运行，它将经济调度和安全监控完美结合起来。OPF算法的众多研究成果中，内点法具有收敛性强、多项式时间复杂性等优点，是极具潜力的优秀算法之一。但在理论上，内点法求解非凸优化问题时的全局收敛性能受到质疑。电力系统不断发展，使得OPF算法跻身于极其困难、非凸的大规模非线性规划行列。可信域和线性搜索方法是保证最优化算法全局收敛性能的两类技术，将内点法和可信域、线性搜索方法有机结合，构造新的优化算法，是数学规划领域的研究热点。 论文在现代内点理论基础上，研究了两种OPF算法。 首先，提出一种改进的可信域内点方法。该方法无须与潮流计算配合增加算法通用性，并引入参数变量到可信域子问题模型中确保计算连续性；同时，改进可信域子问题模型以提高计算精度，调整收敛判据加快计算速度；由现代内点法求解可信域子问题，并构造简约修正方程，减少计算量。论文用该算法求解两类OPF问题，在IEEE14-300系统进行测试，表明其正确性和有效性。该方法主要缺陷是，在大规模系统中的计算速度和计算精度难以令人满意。 其次，提出一种基于线性搜索的现代内点方法，即在内点法每次迭代中，确定对应于某种评价函数的最优步长。该方法采用直角坐标OPF模型，将原问题KKT条件式的平方项相加，得到关于步长的四次多项式作为评价函数；用五点四次插值法求得评价函数解析式，并用卡丹方法求解该表达式导数值为零的点，从而确定最优步长。论文用该方法求解四种OPF问题，在IEEE4-300和N1047系统进行全面测试，取得较快的收敛速度；该方法另一优点是可以保证计算过程不发散，并通过观察最优步长值趋向于零的变化情况，提供了OPF问题在给定的计算条件下，是否存在解的一个判断标志。更多还原

【Abstract】 Study of optimal power flow problems(OPF), combining the economic dispatch with the security supervision perfectly, has resulted from power flow calculation and classical economic dispatch. The strongly convergent, polynomial-time inteior point method is a potentially powerful one among many tools for OPF. However, the global astringency of the interior point method for nonconvex problems is doubtml theoretically. With the persistent development of the power system, OPF methods are increasingly becoming difficult and nonconvex ones among the large-scale nonlinear programming algorithm.Trust-region and line-search methods are two strategies to ensure the global convergency of the optimization algorithm. Combining the inerior point method with trust-region or line-search method, has become a fashion in the mathematical programming.This paper deals with two kinds of OPF methods based on the modern interior point method.Firstly, an improved trust-region interior point method is presented. This method needn’t cooperate with power flow calculation to enhance the currency trait and introduces a parameter variable into the trust-region subproblem to insure the continuity; Meanwhile, the model of the trust-region subproblem is improved to heighten the precision of the calculation and the tolerances are adjusted to speed up the computation; The modern interior point method is used to resolve the trust-region subproblem and a reduced correction equation is derived to reduce the expenses of the computation. Two kinds of OPF problems are resolved by the improved algorithm. Numberical computation on IEEE test systems that range in size from 14 to 300, has shown the correctness and validity of the method. Main fault of the method is that both the speed and precision of the proposed mothod are not satisfactory in large scale systems.更多还原