Global Solution Strategies for the Network-Constrained Unit Commitment Problem with AC Transmission Constraints

TL;DR

This paper introduces a new global optimization algorithm for the complex unit commitment problem with AC transmission constraints, ensuring globally optimal solutions through advanced mathematical techniques.

Contribution

The paper presents a novel multi-tree global optimization algorithm tailored for the nonconvex UC-AC problem, integrating bounds tightening, relaxations, and approximations.

Findings

Effective convergence demonstrated on benchmark problems

Achieved high-quality globally optimal solutions

Improved solution times compared to existing methods

Abstract

We propose a novel global solution algorithm for the network-constrained unit commitment problem incorporating a nonlinear alternating current model of the transmission network, which is a nonconvex mixed-integer nonlinear programming (MINLP) problem. Our algorithm is based on the multi-tree global optimization methodology, which iterates between a mixed-integer lower-bounding problem and a nonlinear upper-bounding problem. We exploit the mathematical structure of the unit commitment problem with AC power flow constraints (UC-AC) and leverage optimization-based bounds tightening, second-order cone relaxations, and piecewise outer approximations to guarantee a globally optimal solution at convergence. Numerical results on four benchmark problems illustrate the effectiveness of our algorithm, both in terms of convergence rate and solution quality.