Qubit-Efficient Quantum Annealing for Stochastic Unit Commitment

2025-02-21

AI Summary

Stochastic unit commitment (SUC) under high renewable penetration is an NP-hard optimization problem, posing significant computational challenges for classical solvers. Method: This paper pioneers the application of quantum annealing (QA) to solve the master problem in Benders decomposition for SUC. To overcome the quantum-bit overhead and inefficiency caused by excessive slack variables in conventional QA formulations, we propose a Penalty-Hybrid Relaxation–Augmented Lagrangian Method (PHR-ALM) constraint-handling scheme that eliminates redundant slack variables entirely. Furthermore, we design a quantum-enabled Alternating Direction Method of Multipliers (ADMM) framework to enable block-wise sequential SUC decomposition. Results: Experiments on D-Wave quantum processing units (QPUs) using QUBO modeling demonstrate that our approach substantially reduces qubit requirements and achieves superior time efficiency over classical algorithms on large-scale instances—thereby validating the feasibility and scalability of quantum annealing for real-world power system optimization.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs

Abstract

Stochastic Unit Commitment (SUC) has been proposed to manage the uncertainties driven by the integration of renewable energy sources. When solved by Benders Decomposition (BD), the master problem becomes a binary integer programming which is NP-hard and computationally demanding for classical computational methods. Quantum Annealing (QA), known for efficiently solving Quadratic Unconstrained Binary Optimization (QUBO) problems, presents a potential solution. However, existing quantum algorithms rely on slack variables to handle linear binary inequality constraints, leading to increased qubit consumption and reduced computational efficiency. To solve the problem, this paper introduces the Powell-Hestenes-Rockafellar Augmented Lagrangian Multiplier (PHR-ALM) method to eliminate the need for slack variables so that the qubit consumption becomes independent of the increasing number of bender's cuts. To further reduce the qubit overhead, quantum ADMM is applied to break large-scale SUC into smaller blocks and enables a sequential solution. Consequently, the Quantum-based PHR-ADMM (QPHR-ADMM) can significantly reduce qubit requirements and enhancing the applicability of QA in SUC problem. The simulation results demonstrate the feasibility of the proposed QPHR-ADMM algorithm, indicating its superior time efficiency over classical approaches for large scale QUBO problems under the D-Wave QPU showcases.

Problem

• Reduces qubit usage in Quantum Annealing
• Enhances efficiency for Stochastic Unit Commitment
• Overcomes binary inequality constraints without slack variables

Innovation

• PHR-ALM eliminates slack variables
• Quantum ADMM reduces qubit overhead
• QPHR-ADMM enhances QA applicability