New efficient ADMM algorithm for the Unit Commitment Problem

TL;DR

This paper presents a novel, efficient ADMM-based algorithm for solving the non-convex Unit Commitment Problem, achieving high-quality solutions with faster computation times compared to traditional MILP methods, especially for longer time horizons.

Contribution

The paper introduces a new ADMM algorithm that relaxes constraints and iteratively enforces feasibility, improving solution speed and quality for the UC problem over existing methods.

Findings

Algorithm produces high-quality solutions on benchmark instances.

Computation time grows linearly with the time horizon length.

Outperforms MILP approaches in speed and scalability for large instances.

Abstract

The unit commitment problem (UC) is an optimization problem concerning the operation of electrical generators. Many algorithms have been proposed for the UC and in recent years a more decentralized approach, by solving the UC with alternating direction method of multipliers (ADMM), has been investigated. For convex problems ADMM is guaranteed to find an optimal solution. However, because UC is non-convex additional steps need to be taken in order to ensure convergence to a feasible solution of high quality. Therefore, solving UC by a MIL(Q)P formulation and running an off-the-shelf solver like Gurobi until now seems to be the most efficient approach to obtain high quality solutions. In this paper, we introduce a new and efficient way to solve the UC with ADMM to near optimality. We relax the supply-demand balance constraint and deal with the non-convexity by iteratively increasing a penalty coefficient until we eventually force convergence and feasibility. At each iteration the subproblems are solved by our efficient algorithm for the single UC subproblem developed in earlier work and our new ADMM algorithm for the transmission subproblems. Computational experiments on benchmark instances demonstrated that our algorithm produces high-quality solutions. The computation time seems to grow practically linear with the length of the time horizon. For the case with quadratic generation cost our algorithm is significantly faster than solving the problem by a state-of-the-art MIL(Q)P formulation. For the case of linear generation cost, it outperforms the MILP approach for longer time horizons.