Parallel Dual Dynamic Integer Programming for Large-Scale Hydrothermal Unit-Commitment

Unit commitment has been at the center of power system operations for over 50 years. Yet, this problem cannot be considered solved due to its size and complexity. Today, operators rely on off-the-shelf optimization solvers to tackle it, and often resort to simplifications to make the problem tractable and solvable in reasonable times. Nonetheless, despite the simplifications and advancements in commercial optimization solvers, solving the unit commitment in a timely manner is still a challenge. In this work, we propose a parallel dual dynamic integer programming approach for solving this problem. Different from what can be currently found in the literature, our parallel approach is applied to a deterministic problem and thus requires induced parallelization. Our strategy is assessed on 20 cases of a hydrothermal system with over 7,000 buses and it is able to solve all instances to a 0.1% gap in less than two hours with speed-ups up to 9.2 compared to a sequential strategy. We also apply our strategy to a purely thermal, large-scale academic system with 9,241 buses, 16,049 transmission lines and 1,445 generating units, for which our strategy returns a 0.1% solution in less than 30 min.

I. Introduction

Over the years, the management of electrical energy resources has seen significant changes and, because of recent technological developments and economic and environmental concerns, it continues to require intensive research. In particular, a problem that remains computationally challenging after more than 50 years of research is the unit-commitment (UC) problem. In its most complete form, this problem is an uncertain mixed-integer nonlinear optimization problem that is computationally intractable. As such, the UC problem is usually simplified to a deterministic mixed-integer linear programming (MILP) problem, both to facilitate its solution and also to comply with current market practices. However, the resulting MILP is still computationally challenging due to its size and combinatorial nature. Consequently, researchers have turned to decomposition approaches to overcome tractability limits. Different from directly solving a UC instance with a optimization solver which will try to find solutions to the entire optimization, decomposition approaches are based on a divide-and-conquer philosophy: they work by dividing the optimization model into smaller chunks that are easier to solve separately and whose solutions can later be combined into a solution to the original problem.