Parametric Problems in Power System Analysis: Recent Applications of Polynomial Approximation Based on Galerkin Method

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