Graphical models for optimal power flow

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• 作者：Krishnamurthy Dvijotham ; Michael Chertkov ; Pascal Van Hentenryck…
• 关键词：Constraint programming ; Graphical models ; Power systems
• 刊名：Constraints
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：22
• 期：1
• 页码：24-49
• 全文大小：
• 刊物类别：Computer Science
• 刊物主题：Artificial Intelligence (incl. Robotics); Optimization; Computing Methodologies; Operation Research/Decision Theory;
• 出版者：Springer US
• ISSN：1572-9354
• 卷排序：22

文摘

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 tree-structured 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. Numerical evaluations on several benchmark networks show that practical OPF problems can be solved effectively using this approach.