Sequential Relaxation of Unit Commitment with AC Transmission Constraints

TL;DR

This paper introduces a sequential convex relaxation approach using SOCP for solving the complex AC unit commitment problem, ensuring feasible, near-optimal solutions efficiently.

Contribution

The paper develops a novel sequential convex relaxation method with penalty terms for AC unit commitment, improving solution feasibility and optimality.

Findings

Successfully applied to IEEE benchmark systems.

Achieves near-optimal solutions with feasible points.

Demonstrates effectiveness on large-scale cases.

Abstract

This paper proposes a sequential convex relaxation method for obtaining feasible and near-globally optimal solutions for unit commitment (UC) with AC transmission constraints. First, we develop a second-order cone programming (SOCP) relaxation for AC unit commitment. To ensure that the resulting solutions are feasible for the original non-convex problem, we incorporate penalty terms into the objective of the proposed SOCP relaxation. We generalize our penalization method to a sequential algorithm which starts from an initial point (not necessarily feasible) and leads to feasible and near-optimal solutions for AC unit commitment. Once a feasible point is attained, the algorithm preserves feasibility and improves the objective value until a near optimal point is obtained. The experimental results on IEEE 57, IEEE 118, and IEEE 300 bus benchmark cases from MATPOWER demonstrate the performance of the proposed method in solving challenging instances of AC unit commitment.