Scheduled-Asynchronous Distributed Algorithm for Optimal Power Flow

TL;DR

This paper introduces a scheduled-asynchronous distributed algorithm for solving large-scale, non-convex optimal power flow problems in power networks, ensuring convergence without clock synchronization.

Contribution

It proposes a novel asynchronous algorithm with a specific network orientation and a distributed graph coloring method to improve convergence in power flow optimization.

Findings

Algorithm converges asymptotically to the optimal solution.

Distributed graph coloring achieves orientation with diameter at most five.

Simulations validate effectiveness on IEEE bus test cases.

Abstract

Optimal power flow (OPF) problems are non-convex and large-scale optimization problems with important applications in power networks. This paper proposes the scheduled-asynchronous algorithm to solve a distributed semidefinite programming (SDP) formulation of the OPF problem. In this formulation, every agent seeks to solve a local optimization with its own cost function, physical constraints on its nodal power injection, voltage, and power flow of the lines it is connected to, and decision constraints on variables shared with neighbors to ensure consistency of the obtained solution. In the scheduled-asynchronous algorithm, every pair of connected nodes in the electrical network update their local variables in an alternating fashion. This strategy is asynchronous, in the sense that no clock synchronization is required, and relies on an orientation of the electrical network that prescribes the precise ordering of node updates. We establish the asymptotic convergence properties to the primal-dual optimizer when the orientation is acyclic. Given the dependence of the convergence rate on the network orientation, we also develop a distributed graph coloring algorithm that finds an orientation with diameter at most five for electrical networks with geometric degree distribution. Simulations illustrate our results on various IEEE bus test cases.