基于改进降维法的概率潮流计算

Probabilistic Load Flow Calculation Based on Improved Dimension Reduction Method

旨在建立一种高效、准确的概率潮流算法。在处理潮流方程中的相关随机变量时,选用高斯Copula和秩相关系数来建模,将相关随机变量表示成独立的标准正态随机变量,从而将概率潮流输出量的统计矩表示成关于独立标准正态随机变量的多维积分。沿用单维降维法的思想,提出了一种改进的降维模型,将概率潮流输出量的统计矩近似成多个低维积分之和,并基于容积量法求解积分权重和节点,用以计算低维积分。此外,文中方法也可与基于单维降维模型的点估计法相结合,用于求解概率潮流问题。对IEEE 30-节点和IEEE 118-节点系统的计算结果表明：与Hong的点估计和基于单维降维法的点估计相比,文中算法更加灵活,在提高精度的同时也可减小计算量。

This paper aims to develop an efficient and accurate algorithm for probabilistic load flow（PLF） calculation. When correlated random variables are included in power flow equations, Gaussian Copula and rank correlation coefficient are employed, and the correlated random variables are expressed as a function of independent standard normal variables, and statistic moments of PLF outputs are represented with a multiple integral of independent standard normal variables. Following the idea of univariate dimension reduction（UDR） method, an improved dimension reduction model is proposed, whereby the statistic moments of PLF outputs are approximated with a sum of integrals of lower dimension, calculated with quadrature weights and nodes from cubature rule. The proposed method can be combined with point estimate method（PEM） based on UDR model for PLF calculation. Testing on an IEEE 30-bus system and an IEEE 118-bus system, results indicate that the proposed method is more flexible, accurate and efficient than Hong’s PEM and PEM based on UDR model.