Parametric Transient Stability Constrained Optimal Power Flow Solved by Polynomial Approximation Based on the Stochastic Collocation Method

Bingqing Xia, Hao Wu, Wenbin Yang, Lu Cao and Yonghua Song
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Bingqing Xia: The PowerChina Huadong Engineering Corporation Limited, Hangzhou 311122, China
Hao Wu: The College of Electrical Engineering, Zhejiang University, Hangzhou 310027, China
Wenbin Yang: The PowerChina Huadong Engineering Corporation Limited, Hangzhou 311122, China
Lu Cao: The Huadong Branch of State Grid, Shanghai 200120, China
Yonghua Song: The Department of Electrical and Computer Engineering, University of Macau, Macau, China

Energies, 2022, vol. 15, issue 11, 1-20

Abstract: To better respond to the impact of power system-uncertain parameters on transient stability, a novel model named the parametric transient stability constrained optimal power flow (parametric TSCOPF) is proposed. It seeks the optimal control scheme of transient stability constrained optimal power flow (TSCOPF) expressed by the function of uncertain parameters in power systems. The key difficulty to solve this model lies in that the relationship between the parametric TSCOPF solution and uncertain parameters is implicit, which is hard to derive generally. To this end, this paper approximates the optimal solution of parametric TSCOPF by polynomial expressions of uncertain parameters based on the stochastic collocation method. First, the parametric TSCOPF model includes both uncertain parameters and transient stability constraints, in which the transient stability constraint is constructed as a set of polynomial expressions using the SCM. Then, to derive the relationship between the parametric TSCOPF solution and uncertain parameters, the SCM is applied to the parametric Karush–Kuhn–Tucker (KKT) conditions of the parametric TSCOPF model, so that the optimal solution of the parametric TSCOPF is approximated by using polynomial expressions with respect to uncertain parameters. The proposed parametric TSCOPF model has been tested on a 3-machine, 9-bus system, and the IEEE 145-bus system, which verifies the effectiveness of the proposed method.

Keywords: transient stability constrained optimal power flow; uncertain parameters; stochastic collocation method; polynomial approximation (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2022
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