一种临界故障切除时间概率分布的求解方法

稳定性分析是电力系统运行与控制中必须考虑的一个以及半不变量的性质，在敏感度计算的基础上，将临界故障最基本的问题。传统稳定分析是在确定系统初始参数后进行的。由于某些原因，电力系统的初始参数，如母线负荷等，因得不到其确定值而只能知道其可能分布。这使得传统的稳定分析方法已不能适用于新的形势，为此提出了概率稳定分析这一新的课题。该文提出一种新的临界故障切除时间概率分布的求取方法，利用随机变量的Cram-Charlier级数展开式切除时间概率分布的求取转化为对初始参数的半不变量的求取。该算法在39机系统中进行了测试，与Monte-Carlo仿真结果相比，该算法不需要反复进行大量的数值仿真的采样计算，而只需在确定临界故障切除时间的灵敏度时进行一次数值仿真；计算结果能很好地描述临界故障切除时间的实际概率分布，且能显著地减少计算量，提高计算速度。利用该方法，可根据故障后临界故障切除时间的概率分布，确定临界故障切除时间分布在期望值附近某区间内的概率，为稳定分析提供了判断的依据。

A METHOD FOR COMPUTING THE PROBABILITY DISTRIBUTION OF FAULT CRITICAL CLEARING TIME

Stability analysis is a fundamental problem in power system operation and control. The traditional stability analysis methods are based on the determinate initial parameter of power system. Because of some reasons, the determinate value of initial parameter of power system, such as load, cannot be decided, and only their probability distribution can often be gotten. So the traditional stability analysis methods cannot be applied to the new condition. This paper proposed a new method to compute the probability distribution of fault critical clearing time. This method uses Gram-Charlier expansion of random variable and the property of cumulant, and on the basis of sensitivity computation, changes the computation of probability distribution of fault critical clearing time to the computation of the cumulant of initial parameters. This method was tested in 39-machine system. Compared with the Monte-Carlo simulation, the new method does not need a large mount of simulations as statistical samplings, but only need once simulation when computing the sensitivity of the fault critical clearing time; The computation results shows that the method can accurately approximate the cumulative distribution function of fault critical clearing time, and reduces computational burden and improves the speed of computation. Using this method, the probability of fault critical clearing time distributing in an interval closed to the expectation value can be determined, and it can act as an implement for stability analysis.