A Scalable Fully Distributed Quantum Alternating Direction Method of Multipliers for Unit Commitment Problems

Abstract

The unit commitment problem (UCP) is a non-convex mixed-integer programming issue that is crucial in the power system. The quantum alternating direction method of multipliers (QADMM) decompose the UCP into quadratic binary optimization (QBO) subproblems and continuous optimization subproblems. Relaxing constraints reformulate the QBO into a quadratic unconstrainted binary optimization (QUBO) problem, which can be addressed using quantum algorithms. Nevertheless, this approach lacks precision for hard constraints and requires more qubits, limiting the UCP scale addressed within QADMM. To confront the aforementioned challenges, this study introduces the consensus constraint-encoded divide-and-conquer QADMM (CCDC-QADMM). As a scalable fully distributed algorithm, CCDC-QADMM decomposes the UCP into two subproblems: Subproblem 1, a QUBO problem embedded with minimum up/down constraints, and Subproblem 2, a UC problem without minimum up/down constraints. By employing variable duplication for decoupling and leveraging the principles of average consensus, CCDC-QADMM achieves fully distributed computation. Specifically, in the QUBO subproblem 1, this algorithm encodes minimum up/down constraints into a hard constraint form within the mixing Hamiltonian. Simultaneously, it employs a divide-and-conquer strategy to accommodate the current constraints posed by the limited qubit resources. The effectiveness and scalability of this algorithm are substantiated through practical validation within real-world UCP scenarios.