In power systems, there are many uncertainty factors such as power outputs of distributed generations and fluctuations of loads. It is very beneficial to power system analysis to acquire an explicit function describing the relationship between these factors (namely parameters) and power system states (or performances). This problem, termed as parametric problem (PP) in this paper, can be solved by Galerkin method, which is a powerful and mathematically rigorous method aiming to seek an accurate explicit approximate function by projection techniques. This paper provides a review of the applications of polynomial approximation based on Galerkin method in power system PPs as well as stochastic problems. First, the fundamentals of polynomial approximation and Galerkin method are introduced. Then, the process of solving three types of typical PPs by polynomial approximation based on Galerkin method is elaborated. Finally, some application examples as well as several potential applications of power system PPs solved by Galerkin method are presented, namely the probabilistic power flow, approximation of static voltage stability region boundary, and parametric time-domain dynamic simulation.

中文翻译：

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电力系统分析中的参数问题：基于Galerkin方法的多项式逼近的最新应用

在电力系统中，存在许多不确定因素，例如分布式发电的功率输出和负载波动。获得描述这些因素（即参数）和电力系统状态（或性能）之间关系的显式函数对电力系统分析非常有益。这个问题在本文中称为参数问题（PP），可以通过Galerkin方法解决，Galerkin方法是一种功能强大且数学上严格的方法，旨在通过投影技术寻求精确的显式近似函数。本文综述了基于Galerkin方法的多项式逼近在电力系统PP中的应用以及随机问题。首先，介绍了多项式逼近和Galerkin方法的基本原理。然后，阐述了基于Galerkin方法的多项式逼近求解三种典型PP的过程。最后，给出了通过Galerkin方法求解的电力系统PP的一些应用实例以及一些潜在的应用，即概率潮流，静态电压稳定区域边界的逼近以及参数时域动态仿真。