Warm-Startable Progressive Integrality Outer-Inner Approximation for AC Unit Commitment with Conic Formulation

Abstract

The alternating-current unit commitment problem provides a realistic representation of power system operations, which is a nonconvex mixed-integer nonlinear programming problem and hence is computationally intractable. A common relaxation to the alternating-current unit commitment problem is based on the second-order cone, which results in a mixed-integer second-order cone program and remains computationally challenging. In this paper, we propose a warm-startable outer-inner approximation framework that alternatively solves a mixed-integer linear programming (MILP) as an outer approximation and a convex second-order cone programming as an inner approximation to find a (near-)optimal solution to the second-order cone-based alternating-current unit commitment problem. To improve computational efficiency, we introduce a progressive integrality strategy that gradually enforces integrality, reducing the reliance on expensive MILP solutions in early iterations. In addition, time-block Benders cuts are incorporated to strengthen the outer approximation and accelerate convergence. Computational experiments on large-scale test systems, including 200-bus and 500-bus networks, demonstrate that the proposed framework significantly improves both efficiency and robustness compared to state-of-the-art commercial solvers.