【摘要】 机组的经济目标函数以多段或二次项系数小于零的单段二次函数表示时,负荷分配问题就呈现出非凸、非线性特性,给高效求取全局最优解或具有较高性能的局部最优解带来了较大困难。该文提出了一种最陡增/减变量对寻优法,此方法每次迭代过程只有两个变量(变量对)发生变化,其中一个增大,另一个进行同等量值的减小,增/减的步长按照一定的规则动态控制,并确保满足约束条件;同时,从原目标函数关于增/减变量对的偏导数和最小的变量对中动态地选择变量对,以确保每次迭代都能够按照使原目标函数最陡下降的变量对方向进行。此方法可快速求得凸二次规划问题的全局最优解和非凸二次规划问题的局部最优解。进一步地,该文结合问题的特点引入一种简捷的进化策略,使最陡增/减变量对寻优法在进化规划的框架下获得了能够求得非凸二次规划问题全局最优解的能力,并在很大程度上保留了原方法快速寻优的优点。算例表明,该文方法和策略为非凸二次规划负荷分配问题提供了一种高效实用的分析工具。更多还原

【Abstract】 The mathematical model for economic dispatch of power system is a non-convex and nonlinear mathematical programming when some of units’ cost functions are piecewise quadratic or have a negative quadratic coefficient, which gives rise to more difficulties on searching for the local/global optimum. This paper proposes a steepest descent optimization method based on increasing/decreasing variable pair. In each iterating, only one pair of state variables will be modified: one variable will increase, and the other will decrease with an identical step length. The step length is controlled dynamically under a set of principles to satisfy all the constraints; meanwhile, the increasing/decreasing variable pair is selected dynamically from all variable pairs and it has the smallest partial derivative sum to insure every iterating is along the deepest decent direction. The partial derivative is of the original objective function to variable. The method could get a global optimum for a convex programming and a local optimum for a non-convex one. In addition, an improved steepest descent optimization method based on increasing/decreasing variable pair that combines evolutionary strategy is proposed. The improved method can keep rapidness of original algorithm and get the global optimal solution. The results of sample systems indicate the practicability and effectiveness of these two methods.更多还原