Planning in the power sector has to take into account the physical laws of alternating current (AC) power flows as well as uncertainty in the data of the problems, both of which greatly complicate optimal decision making. We propose a computationally tractable framework to solve multi-stage stochastic optimal power flow (OPF) problems in AC power systems. Our approach uses recent results on dual convex semi-definite programming (SDP) relaxations of OPF problems in order to adapt the stochastic dual dynamic programming (SDDP) algorithm for problems with a Markovian structure. We show that the usual SDDP lower bound remains valid and that the algorithm converges to a globally optimal policy of the stochastic AC-OPF problem as long as the SDP relaxations are tight. To test the practical viability of our approach, we set up a case study of a storage siting, sizing, and operations problem. We show that the convex SDP relaxation of the stochastic problem is usually tight and discuss ways to obtain near-optimal physically feasible solutions when this is not the case. The algorithm finds a physically feasible policy with an optimality gap of 3% and yields a significant added value of 27% over a rolling deterministic policy, which leads to overly optimistic policies and underinvestment in flexibility. This suggests that the common industry practice of assuming direct current and deterministic problems should be reevaluated by considering models that incorporate realistic AC flows and stochastic elements in the data as potentially more realistic alternatives.

中文翻译：

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随机双动态规划，用于在不确定性下解决最佳功率流问题


电力行业的规划必须考虑交流电 （AC） 潮流的物理定律以及问题数据中的不确定性，这两者都使最佳决策变得非常复杂。我们提出了一个计算上可处理的框架来解决交流电力系统中的多级随机最佳潮流 （OPF） 问题。我们的方法使用了 OPF 问题的双凸半定规划 （SDP） 松弛的最新结果，以便将随机双动态规划 （SDDP） 算法应用于具有马尔可夫结构的问题。我们表明，通常的 SDDP 下限仍然有效，并且只要 SDP 松弛很紧，该算法就会收敛到随机 AC-OPF 问题的全局最优策略。为了测试我们方法的实际可行性，我们建立了一个存储选址、大小调整和操作问题的案例研究。我们表明随机问题的凸 SDP 松弛通常是紧密的，并讨论了在情况并非如此时获得近乎最优的物理可行解的方法。该算法找到一个物理上可行的政策，最优差距为 3%，并且比滚动确定性政策产生 27% 的显着附加值，这导致政策过于乐观和灵活性投资不足。这表明，应该通过将包含数据中实际交流流和随机元素的模型视为可能更现实的替代方案来重新评估假设直流和确定性问题的常见行业实践。