中国电机工程学报2026，Vol.46Issue(3)：928-941,中插6,15.DOI:10.13334/j.0258-8013.pcsee.242015
基于随机变量二次型的配电网交流概率潮流建模和解析计算方法(一):从电量到功率量的推导
Probabilistic AC Power Flow Modeling and Analytical Calculation Methods for Distribution Networks Based on the Quadratic Form of Random Variables(Part I):Derivation From Voltage to Power
摘要
Abstract
Probabilistic load flow plays a crucial role in the uncertainty analysis of distribution networks with a high proportion of distributed renewable energy sources and highly stochastic loads.However,due to the non-linearity of flow equations and probability distributions,as well as the correlation between random variables,analytical computation of probabilistic load flow is challenging.Existing methods often derive analytical expressions for probabilistic load flow from linear flow equations.However,the high resistance-reactance ratio of distribution networks makes it difficult for linear flow equations to accurately describe the relationships between flow variables,leading to distorted probability distributions.To address this issue,this paper presents an AC probabilistic load flow model for distribution network and an analytical computation method that can consider both the non-linearity of flows and the correlation of node power injection by expressing the AC flow equations as a quadratic form of node voltages and utilizing the relationship between the normal distribution and the generalized non-central chi-squared distribution.Firstly,it is proven that when node voltages follow a multi-variate normal distribution,the power flow quantities such as node power injection,line power,and network losses,follow a generalized non-central chi-squared distribution.Secondly,accurate expressions for the mean,variance,covariance,moment generating function,and characteristic function of power flow quantities are provided.Lastly,considering the complexity of the probability distribution function of power flow quantities,which makes it difficult to solve directly,a numerical method for calculating their probability density function and cumulative distribution function is proposed.Case studies based on the IEEE 33 bus distribution networks demonstrate that the proposed AC probabilistic load flow analytical algorithm can accurately describe the probabilistic relationships between node voltages and power quantities,and is suitable for calculating the probability distribution of distribution network flows in highly stochastic environments.关键词
概率潮流/概率分布/配电网/解析计算Key words
probabilistic power flow/probability distribution/distribution network/analytical calculation分类
信息技术与安全科学引用本文复制引用
吴涵..基于随机变量二次型的配电网交流概率潮流建模和解析计算方法(一):从电量到功率量的推导[J].中国电机工程学报,2026,46(3):928-941,中插6,15.基金项目
江苏省高等学校基础科学(自然科学)研究项目(22KJD470003).Projects of Natural Science in Colleges and Universities of Jiangsu Province(22KJD470003). （自然科学）
