A Galerkin Method-Based Polynomial Approximation for Parametric Problems in Power System Transient Analysis

Parametric problems in the transient analysis refer to the investigations of the relationship between parameters and dynamic behavior. To solve parametric problems, we propose a Galerkin method-based polynomial approximation. The proposed method uses a series of polynomials combined with coefficient...

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Bibliographic Details
Published in:IEEE transactions on power systems 2019-03, Vol.34 (2), p.1620-1629
Main Authors: Xia, Bingqing, Wu, Hao, Qiu, Yiwei, Lou, Boliang, Song, Yonghua
Format: Article
Language:English
Subjects:
Analytical models
Approximation
Differential equations
Galerkin method
Linearity
Mathematical model
Method of moments
Parameter uncertainty
Parameterization
parametric problems
polynomial approximation
Polynomials
Power system dynamics
Power system transient analysis
State variable
Trajectories
Transient analysis
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Summary:Parametric problems in the transient analysis refer to the investigations of the relationship between parameters and dynamic behavior. To solve parametric problems, we propose a Galerkin method-based polynomial approximation. The proposed method uses a series of polynomials combined with coefficients to approximately represent state variables with parameters, where the Galerkin method is introduced to determine the coefficients. Thereby, the relationship between parameters and dynamic behavior is established through the polynomial expressions. Because models in power system transient analysis are a set of complicated differential-algebraic equations, practical issues related to the non-polynomial model terms, parameterization of initial operation point are discussed in this paper. The proposed method is tested on a three-machine system and the IEEE 145-bus test system. The case studies show that compared to trajectory sensitivities, the proposed method can maintain high accuracy in cases of large parameter variations and strong non-linearity. We also illustrate that the validity of the proposed method for parametric problems like trajectory approximation, finding the critical parameter values and uncertainty quantification.
ISSN:0885-8950
1558-0679
DOI:10.1109/TPWRS.2018.2879367