Graphical Models for Optimal Power Flow
This provides a scalable, distributed method for solving OPF in arbitrary distribution networks, including mixed-integer problems, which is incremental for smart grid applications like controlling distributed energy resources.
The authors tackled the NP-hard optimal power flow problem over tree networks by formulating it as an inference problem on a tree-structured graphical model and developing an approximation algorithm using dynamic programming, interval discretization, and constraint programming techniques, showing that practical OPF problems can be solved effectively in evaluations on benchmark networks.
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.