A Low-Rank Rounding Heuristic for Semidefinite Relaxation of Hydro Unit Commitment Problems

TL;DR

This paper introduces a low-rank rounding heuristic for semidefinite relaxation of hydro unit commitment problems, improving solution efficiency while considering operational constraints and transmission models.

Contribution

It proposes a novel heuristic combining semidefinite programming relaxation with rank reduction for hydro unit commitment, addressing computational challenges in large systems.

Findings

Heuristic achieves solutions close to branch-and-bound methods.

Method reduces computational time for large-scale problems.

Effective in handling complex operational and transmission constraints.

Abstract

Hydro unit commitment is the problem of maximizing water use efficiency while minimizing start-up costs in the daily operation of multiple hydro plants, subject to constraints on short-term reservoir operation, and long-term goals. A low-rank rounding heuristic is presented for the semidefinite relaxation of the mixed-integer quadratic-constrained formulation of this problem. In addition to limits on reservoir and generator operation, transmission constraints are represented by an approximate AC power flow model. In our proposed method, the mathematical program is equivalently formulated as a QCQP problem solved by convex relaxation based on semidefinite programming, followed by a MILP solution of undefined unit commitment schedules. Finally, a rank reduction procedure is applied. Effectiveness of the proposed heuristic is compared to branch-and-bound solutions for numerical case studies of varying sizes of the generation and transmission systems.