A hybrid classical-quantum approach to highly constrained Unit Commitment problems

TL;DR

This paper presents a hybrid quantum-classical algorithm for solving the NP-hard unit commitment problem in power systems, incorporating real-world constraints and demonstrating near-classical solution accuracy with polynomial efficiency.

Contribution

It introduces a novel hybrid quantum-classical approach using QAOA for the UC problem, including spinning reserve constraints and warm-start optimization, achieving efficient approximate solutions.

Findings

Hybrid solutions within 5.1% of classical solutions

Reduced QAOA convergence iterations with warm-start

Polynomial time complexity for large instances

Abstract

The unit commitment (UC) problem stands as a critical optimization challenge in the electrical power industry. It is classified as NP-hard, placing it among the most intractable problems to solve. This paper introduces a novel hybrid quantum-classical algorithm designed to efficiently (approximately) solve the UC problem in polynomial time. In this approach, the UC problem is decomposed into two subproblems: a QUBO (Quadratic Unconstrained Binary Optimization) problem and a quadratic optimization problem. The algorithm employs the Quantum Approximate Optimization Algorithm (QAOA) to identify the optimal unit combination and classical methods to determine individual unit powers. The proposed hybrid algorithm is the first to include both the spinning reserve constraint (thus improving its applicability to real-world scenarios) and to explore QAOA warm-start optimization in this context. The effectiveness of this optimization was illustrated for specific instances of the UC problem, not only in terms of solution accuracy but also by reducing the number of iterations required for QAOA convergence. Hybrid solutions achieved using a single-layer warm-start QAOA (p=1) are within a 5.1 % margin of the reference (approximate) classical solution, while guaranteeing polynomial time complexity on the number of power generation units and time intervals.