基于点估计和Gram-Charlier展开的含风电电力系统概率潮流实用算法

A Practical Algorithm Based on Point Estimate Method and Gram-Charlier Expansion for Probabilistic Load Flow Calculation of Power Systems Incorporating Wind Power

概率潮流(probabilistic load flow,PLF)计算是评估风电并网影响的基础。风电功率具有随机性和波动性,其分布特征难以用常见的概率密度函数进行拟合,而且潮流计算的输出变量与输入变量之间是非线性关系。针对上述特点,提出一种基于点估计(point estimate method,PEM)和Gram-Charlier展开的概率潮流实用算法(PG算法),无需知道输入随机变量的概率密度函数,仅根据其样本数据,在有n个输入随机变量的情况下仅需计算2n+1次潮流便可估计出输出随机变量的期望、方差、累积分布等统计信息。对IEEE 16机系统的仿真结果表明:该方法精度高,计算量小。此外,本文提出的PG算法还可用于分析其他考虑不确定因素但其概率密度函数未知的电力系统问题。

Probabilistic load flow （PLF） calculation is the first step to evaluate the impact of the integrated wind power to the power system. The wind power is featured with stochastic and variable property. It is hard to fit its distribution characteristics to any common probability density function （PDF）. At the same time, the relationship between the input and output variables of load flow calculation is nonlinear. In view of the two characteristics, a new practical algorithm based on point estimate method and Gram-Charlier expansion （PG algorithm） was proposed for PLF calculation of power system incorporating wind power. Based only on the sample data of the wind power, the expectation, variance and cumulative distribution of the output variables can be estimated with PG algorithm by 2n＋l times of load flow calculation where n is the number of input stochastic variables, exempting the need for distribution of the input variables. The digital simulation results of the IEEE 16-generator system show that the algorithm provides high precision with small computation. The algorithm can also be applied to solve other problems with uncertainty factors whose distribution is unknown in power systems.