Graphical Models for Optimal Power Flow

TL;DR

This paper introduces a novel graphical model-based approximation algorithm for solving the optimal power flow problem in power grids, capable of handling complex network structures and mixed-integer variables efficiently.

Contribution

It formulates OPF as an inference problem over tree-structured graphical models and develops a scalable, distributed algorithm with practical efficiency for smart grid applications.

Findings

Effective solution for arbitrary distribution networks

Handles mixed-integer optimization problems

Scalable and suitable for distributed implementation

Abstract

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.