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

Abstract

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.

A Fast Parameter Identification Method for Composite Load Model Based on Jumping and Steady-State Points of Measured Data

“…Polynomial approximation method can be used to obtain a simple polynomial function that approximates a complex relationship between inputs and output of a model, which is one of the state-of-art technique in power system analysis and control [24], [31], [32].…”

“…The choice of ϕ i,ni (p i ) for each parameter p i can be related to its probability distribution. For the general parameter interval, its probability distribution can be considered as uniform distribution, and its corresponding polynomial is Legendre polynomial [24].…”

“…With the known state variables at the four points, their corresponding load powers can be easily calculated. Then, initial parameters are calculated by polynomial approximation method [24], and based on that, the optimal parameters are identified through Nelder-Mead algorithm [25]. The calculation process of this method is very simple compared with the classic measurement-based method, and hence the calculation time is less than 2.5% of that in the classic method with similar identification accuracy.…”

An optimized algorithm for optimal power flow based on deep learning

“…Traditional power system transient stability calculations use the transient stability constraint optimal power flow (TSCOPF) model Wu et al, 2021;Guangchao et al, 2017), which adds transient stability constraints based on the optimal power flow model. The purpose of the model is to solve the optimal operating point of the system when all the constraints of the power system are met so that the objective function reaches the optimal value.…”

A non-intrusive probabilistic multi-energy flow calculation method and its application in operation risk analysis of integrated energy systems

“…The intrusive methods, represented by the generalized polynomial chaos (gPC) method [24], approximate probabilistic solutions by applying expansions to differential or algebraic equations containing random input variables. Attempts have been made to apply the gPC method in the probabilistic analysis of power systems, such as probabilistic power flow calculation [25,26] and dynamic stochastic simulation with distributed generation [27,28].…”