Probability Efficient Point Method to Solve Joint Chance-Constrained Unit Commitment for Multi-Area Power Systems With Renewable Energy
Jinghua Li, Licheng Lin, Yifu Xu, Shuang Zhou, Dunlin Zhu, Junjie Liang
Abstract
Joint chance constraint (JCC) is a significant way to guarantee the spinning reserve in multi-area power systems with renewable energy (MAS-RE). This paper presents a novel <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> -efficient point (PEP) method to deal with the JCCs of unit commitment (UC) problems to guarantee the spinning reserve at the given confidence level. In the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> -efficient point method, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> -efficient points are used to obtain the minimum spinning reserve requirement to satisfy the given confidence level. Based on <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> -efficient points, the intractable JCCs can be converted into tractable deterministic constraints directly, which avoids the complicated calculations and approximation errors of JCCs. Furthermore, an optimal mathematical programming is formulated to directly obtain <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> -efficient points, without assumptions on the probability distribution function (PDF) of wind power. Besides, in this paper, the applicability of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> -efficient point method is extended from positive space to both positive and negative space. Simulation results demonstrate that the proposed approach has better performances in scheduling spinning reserve than the popular Sample Average Approximation (SAA), Partial Sample Average Approximation (PSAA) and the Kernel Density Estimation (KDE) combined with Boole's inequality.