图模型用于最优功率流
Graphical Models for Optimal Power Flow
AI总结：
本文将树状网络的最优功率流问题转化为树状图模型的推断问题，结合动态规划与区间离散化，提出了一种高效求解方法，适用于任意配电网络和混合整数优化。
摘要：
最优功率流（OPF）是电力网络中的核心优化问题。尽管在电网运行中被常规解决，但一般情况下被证明是强NP难问题，而在树状网络上为弱NP难。本文将树状网络的OPF问题建模为树状图模型的推断问题，其中节点变量为低维向量。我们适配标准的树状图模型推断动态规划算法至OPF问题。结合节点变量的区间离散化，我们开发出OPF问题的近似算法。进一步，我们利用约束编程（CP）技术进行区间计算和自适应边界传播，获得实际高效的算法。与之前使用凸松弛保证最优性的OPF算法相比，我们的方法能够处理任意配电网络和混合整数优化问题。此外，该方法可以以分布式消息传递的方式实现，具有可扩展性，适用于智能电网应用，如分布式能源资源的控制。我们在多个基准网络上评估了该技术，并展示了使用此方法可以有效解决实际OPF问题。
英文摘要：
Optimal power flow (OPF) is the central optimization problem in electric power grids. Although solved routinely in the course of power grid operations, it is known to be strongly NP-hard in general, and weakly NP-hard over tree networks. In this paper, we formulate the optimal power flow problem over tree networks as an inference problem over a tree-structured graphical model where the nodal variables are low-dimensional vectors. We adapt the standard dynamic programming algorithm for inference over a tree-structured graphical model to the OPF problem. Combining this with an interval discretization of the nodal variables, we develop an approximation algorithm for the OPF problem. Further, we use techniques from constraint programming (CP) to perform interval computations and adaptive bound propagation to obtain practically efficient algorithms. Compared to previous algorithms that solve OPF with optimality guarantees using convex relaxations, our approach is able to work for arbitrary distribution networks and handle mixed-integer optimization problems. Further, it can be implemented in a distributed message-passing fashion that is scalable and is suitable for "smart grid" applications like control of distributed energy resources. We evaluate our technique numerically on several benchmark networks and show that practical OPF problems can be solved effectively using this approach.
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