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OA
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
潮流的概率分布在高比例分布式可再生能源和强随机性负荷接入后的配电网不确定性分析中发挥着重要作用.但受限于交流潮流方程和概率分布函数的非线性、随机变量的相关性等问题,现有概率潮流计算方法存在精度低、解析性较差、无法给出高保真度的概率分布闭式解等问题,难以适用于高精度的配电网分析.为了在原始交流潮流模型的基础上得到解析的概率分布表达式,解决传统概率潮流计算方法依赖线性化潮流方程带来的概率潮流精度较低等问题,该文探索一种基于随机变量二次型的概率潮流建模和解析求解方法.该方法能够同时考虑潮流非线性和节点注入功率相关性,且具有良好的解析性质和较高的计算精度.首先,证明当节点电压服从多维正态分布时节点注入功率、线路功率、网损等潮流功率量服从广义非中心卡方分布;其次,给出当节点电压服从多维正态分布时潮流功率量的均值、方差、协方差、矩生成函数和特征函数的准确表达式.考虑到潮流功率量的概率分布函数形式较为复杂,难以直接求解,提出概率密度函数和累积概率分布函数的数值计算方法.基于IEEE 33 节点配电网的算例分析表明,提出的交流概率潮流模型和解析计算方法能够准确描述节点电压和功率量概率分布间的关系,适用于强随机性环境下配电网潮流概率分布的计算.
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.
吴涵
智能电网产业技术研究院(南京工程学院),江苏省 南京市 211167
信息技术与安全科学
概率潮流概率分布配电网解析计算
probabilistic power flowprobability distributiondistribution networkanalytical calculation
《中国电机工程学报》 2026 (3)
928-941,中插6,15
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).
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