An alternating direction method of multipliers approach for the reconfiguration of radial electrical distribution systems

Abstract

The electrical network reconfiguration problem aims to minimize losses in a distribution system by adjusting switches while ensuring the radiality (tree structure) of the network. Although this problem can be formulated as a mixed integer nonlinear program, solving the resulting optimization problem requires significant time and resources. A carefully selected initial solution, which can be identified by appropriate heuristics, reduces the search space, accelerates convergence, and ensures feasibility. This paper introduces two heuristic algorithms based on the Alternating Direction Method of Multipliers (ADMM) to address this problem. These heuristics break down the problem into smaller, more manageable subproblems that can be solved efficiently. Two algorithms are developed: one relies on natural variable substitution, and the other on a previously used relaxation technique. The challenge encountered in previous studies of incorporating radial constraints with ADMM is addressed by redefining the combinatorial subproblem in the projection step of ADMM as a minimum weight rooted arborescence problem, whose solutions are guaranteed to be radial. Convex optimization techniques can then handle the remaining subproblems. The performance of both heuristics is evaluated through numerical experiments on the 33-bus and 70-bus systems, as well as on a real-world electrical network.