Asymptotically tight conic approximations for chance-constrained AC optimal power flow
Asymptotically tight conic approximations for chance-constrained AC optimal power flow
复制标题
机会约束交流最优功率流的渐近紧圆锥曲线近似
DOI：
10.1016/j.ejor.2022.06.020
复制
发表时间：
2023
影响因子：
6.4
通讯作者：
Yang, Boshi
中科院分区：
文献类型：
--
作者：
Mohammadi Fathabad, Abolhassan;Cheng, Jianqiang;Pan, Kai;Yang, Boshi
随着可再生能源在电力系统中的日益普及，需要在重大不确定性下实现安全可靠的系统运行。为此，提出了机会约束的交流最优潮流问题（CC-ACOPF）。文献中对CC-ACOPF的研究大多集中在单侧机会约束上；然而，双边机会约束（tcc）虽然更复杂，但提供了更准确的公式，因为机会约束的上界和下界是同时实施的。在本文中，我们引入了一个完全双边CC-ACOPF问题（TCC-ACOPF），其中有功/无功发电量、电压和潮流同时保持在给定概率的上/下界内。我们没有采用Bonferroni近似或基于场景的方法，而是通过分段线性（PWL）近似提出了高斯混合（GM）分布下tcc的有效二阶锥规划（SOCP）近似。与传统的预测误差正态性假设相比，GM分布增加了代表不确定性的额外精度水平。此外，我们还证明了我们的SOCP公式具有可调的准确率，其最优值具有渐近收敛性。在此基础上，提出了一种通过优化选择PWL段来加快求解过程的算法。最后，我们用IEEE 30总线和118总线系统上的真实历史数据和综合数据证明了我们所提出方法的有效性。我们表明，与其他最先进的ACOPF配方相比，我们的配方提供了显着更健壮的解决方案（约减少60%的约束违反）。
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.