论文标题
瓦斯尔斯坦的两步方法在分配上有牢固的机会和安全约束的调度
A two-step approach to Wasserstein distributionally robust chance- and security-constrained dispatch
论文作者
论文摘要
本文考虑了在可再生生成的存在下，涉及发电和线突变的安全性限制性调度问题。可再生能源引起的不确定性是使用关节机会约束建模的，并使用储备金处理了因素和可再生能源而引起的不匹配。我们考虑了一种解决偶然受限计划的分配强大的方法。我们假设不确定性的样本可用。使用它们，我们构建了一组分布，称为歧义集，其中包含所有与Wasserstein指标下经验分布接近的分布。对于歧义性设置中的所有分布而施加的机会约束是为了形成分布强大的优化问题。这个问题是非概念的，并且在计算上很重，无法准确解决。我们采用两步方法来找到近似解决方案。在第一步中，我们在不确定性空间中构建了一个多面体集，该集合包含歧义集中所有分布的足够质量。该集合是通过解决几个二维分布在鲁棒的问题上构建的。在第二步中，我们解决了一个线性鲁棒优化问题，其中对位于多面体集合中的所有不确定性值施加了不确定的约束。我们使用数值实验证明了方法的可伸缩性和鲁棒性。
This paper considers a security constrained dispatch problem involving generation and line contingencies in the presence of the renewable generation. The uncertainty due to renewables is modeled using joint chance-constraint and the mismatch caused by contingencies and renewables are handled using reserves. We consider a distributionally robust approach to solve the chance-constrained program. We assume that samples of the uncertainty are available. Using them, we construct a set of distributions, termed ambiguity set, containing all distributions that are close to the empirical distribution under the Wasserstein metric. The chance constraint is imposed for all distributions in the ambiguity set to form the distributionally robust optimization problem. This problem is nonconvex and computationally heavy to solve exactly. We adopt a two-step approach to find an approximate solution. In the first step, we construct a polyhedral set in the space of uncertainty that contains enough mass under all distributions in the ambiguity set. This set is constructed by solving several two-dimensional distributionally robust problems. In the second step, we solve a linear robust optimization problem where the uncertain constraint is imposed for all uncertainty values lying in the polyhedral set. We demonstrate the scalability and robustness of our method using numerical experiments.
