基于拉格朗日插值法的概率建模方法及其在概率潮流分析中的应用
摘要：大规模可再生能源并网给电力系统带来大量概率不确定源，这会极大地增加电力系统概率潮流分析中对不确定源概率建模的计算负担。Nataf变换能够有效完成对皮尔森相关随机变量的概率建模，其关键在于标准正态分布域的相关系数求解。然而传统的基于辛普森数值积分法和二分法的相关系数求解法，使Nataf变换的过程耗时严重，难以达到实时计算的要求。为此，采用拉格朗日插值法和简化牛顿法实现相关系数的高效计算，以加快概率建模的过程，提高概率潮流分析的效率。基于改进的IEEE 118节点算例，测试了所提相关系数求解法的计算精度与速度，并进一步测试了其误差对整个概率潮流计算结果精度的影响。结果表明，所提方法能够高效而精确地完成Nataf变换中标准正态分布域相关系数的求解，从而在保证概率潮流结果精度前提下，提高概率潮流分析的效率。
Abstract:Grid-connection of vast renewable energy sources brings a lot of probabilistic uncertain sources to power system, so it tremendously increases computational burden in probabilistic modeling for uncertain sources during probabilistic power flow (PPF) analysis of power system. In practical application, the Nataf transformation is an effective approach to achieve the probabilistic modeling for such Pearson correlated random variables, where the core step is to determine the Pearson correlation coefficients (PCC) in standard normal distribution scope. However, traditional correlation coefficient solving method, which combines the Simpson’s numerical integration with the bisection method, is so time-consuming that the whole procedure of Nataf transformation is hard to satisfy the demand of realtime computation. To address this issue, an approach based on Lagrange interpolation and simplified Newton method was adopted to implement efficient computation of correlation coefficients to speed up the process of probabilistic modeling, thus the efficiency of PPF analysis could be further improved. Based on the modified IEEE118-bus system, the accuracy and efficiency of the proposed method is tested, and the influence of calculation error on the accuracy of total PPF calculation results was further tested. Test results show that utilizing the proposed method the solution of correlation coefficients of standard normal distribution field in Nataf transformation can be completed efficiently and accurately, thus, on the premise of ensuring the accuracy of PPF results, the efficiency of PPF analysis can be improved.
标题：基于拉格朗日插值法的概率建模方法及其在概率潮流分析中的应用
英文标题：A Lagrange Interpolation Based Probabilistic Modeling Method and Its Application in Probabilistic Power Flow Analysis
作者：杨少瑜, 黄国栋, 林星宇, 乐彦婷, 唐俊杰,
关键词：可再生能源并网, 概率建模, Nataf变换, 拉格朗日插值, 概率潮流,
发表日期：2021-08-10
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