# Benders' decomposition of the unit commitment problem with semidefinite relaxation of AC power flow constraints

## TL;DR

This paper introduces a novel approach combining Benders' decomposition with semidefinite relaxation for the AC power flow in the unit commitment problem, improving convergence and solution quality.

## Contribution

It presents a new formulation integrating semidefinite programming relaxation into Benders' decomposition for AC power flow constraints in unit commitment.

## Key findings

- Improved convergence speed in numerical tests.
- Enhanced feasibility and optimality cuts.
- Effective application to 6-bus and 118-bus networks.

## Abstract

In this paper we present a formulation of the unit commitment problem with AC power flow constraints. It is solved by a Benders decomposition in which the unit commitment master problem is formulated as a mixed-integer problem with linearization of the power generation constraints for improved convergence. Semidefinite programming relaxation of the rectangular AC optimal power flow is used in the subproblem, providing somewhat conservative cuts. Numerical case studies, including a 6-bus and the IEEE 118-bus network, are provided to test the effectiveness of our proposal. We show in our numerical experiments that the use of such strategy improves the quality of feasibility and optimality cuts generated by the solution of the convex relaxation of the subproblem, therefore reducing the number of iterations required for algorithm convergence.