基于广义多项式混沌方法的电力系统时域仿真不确定性分析

Uncertainty Analysis of Time-domain Simulation for Power System Based on Generalized Polynomial Chaos Method

电力系统时域仿真不确定性分析主要研究电力系统中不确定性因素对时域仿真结果的影响,为分析不确定情况下系统的暂态稳定性提供重要依据。提出一种基于广义多项式混沌方法的时域仿真不确定性分析方法。该方法近似认为变量在任一时刻与随机因素之间存在多项式关系。求解时首先获取最优的正交多项式基函数,对随机输入变量及待求变量实施多项式逼近,并基于Galerkin法,通过投影运算将描述系统暂态过程的随机方程转变为相应的确定性方程。求解该方程,可得待求变量的多项式逼近系数,进而获得相关变量在任一时刻的统计特征及概率分布。单机无穷大系统和IEEE 9节点系统算例验证了所提方法的有效性。

Uncertainty analysis of power system time-domain simulation is mainly concerned with the study of the influence of uncertainty factors in power system on time-domain simulation results.It provides an important reference for analyzing the transient stability of power system under uncertain conditions.A method based on generalized polynomial chaos（gPC）is proposed for uncertainty analysis of time-domain simulation.Approximately,the method assumes that there exists a polynomial relationship between variables and random factors at any time.The solution procedure is as follows.Firstly,the optimal orthogonal polynomial basis function is acquired to approximate the random input variables and unknown variables.Then,by Galerkin method,the stochastic equations which describe the system＇s transient process are transformed into the corresponding deterministic equations.Finally,by solving these equations,the polynomial approximation coefficients of unknown variables are obtained,which can be used to calculate the statistical results and probability distribution of relevant variables at any time.Case study results from a single-machine infinite bus（SMIB）system and IEEE 9-bus system show the effectiveness of our method.