Asymptotically tight conic approximations for chance-constrained AC optimal power flow

数学优化 交流电源 高斯分布 数学 线性规划 参数统计 正态性 上下界 计算机科学 功率(物理) 量子力学 统计 物理 数学分析
作者
Abolhassan Mohammadi Fathabad,Jianqiang Cheng,Kai Pan,Boshi Yang
出处
期刊:European Journal of Operational Research [Elsevier BV]
卷期号:305 (2): 738-753 被引量:7
标识
DOI:10.1016/j.ejor.2022.06.020
摘要

The increasing penetration of renewable energy in power systems calls for secure and reliable system operations under significant uncertainty. To that end, the chance-constrained AC optimal power flow (CC-ACOPF) problem has been proposed. Most research in the literature of CC-ACOPF focuses on one-sided chance constraints; however, two-sided chance constraints (TCCs), albeit more complex, provide more accurate formulations as both upper and lower bounds of the chance constraints are enforced simultaneously. In this paper, we introduce a fully two-sided CC-ACOPF problem (TCC-ACOPF), in which the active/reactive generation, voltage, and power flow all remain within their upper/lower bounds simultaneously with a predefined probability. Instead of applying Bonferroni approximation or scenario-based approaches, we present an efficient second-order cone programming (SOCP) approximation of the TCCs under Gaussian Mixture (GM) distribution via a piecewise linear (PWL) approximation. Compared to the conventional normality assumption for forecast errors, the GM distribution adds an extra level of accuracy representing the uncertainties. Moreover, we show that our SOCP formulation has adjustable rates of accuracy and its optimal value enjoys asymptotic convergence properties. Furthermore, an algorithm is proposed to speed up the solution procedure by optimally selecting the PWL segments. Finally, we demonstrate the effectiveness of our proposed approaches with both real historical data and synthetic data on the IEEE 30-bus and 118-bus systems. We show that our formulations provide significantly more robust solutions (about 60% reduction in constraint violation) compared to other state-of-art ACOPF formulations.
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