Unit commitment (UC) problems faced by Independent System Operators on a daily basis are becoming increasingly complex due to the recent push for renewables and the consideration of sub-hourly UC to accommodate the increasing variability in the net load. A disruptive solution methodology to address the growing complexity is therefore required. Quantum computing offers a promise to overcome the combinatorial complexity through the use of the so-called “qubits.” To make the best use of near-term quantum computers to solve UC problems with a much larger number of binary variables than the number of qubits available, this paper devises a novel solution methodology based on a synergistic combination of quantum computing and Surrogate Lagrangian Relaxation (SLR) to solve UC problems. Our new contributions include: 1) A Quantum-SLR (QSLR) algorithm incorporating quantum approximate optimization algorithm (QAOA) into the SLR method, which overcomes the fundamental difficulties of previous LR-based quantum methods such as zigzagging of multipliers and the need to know or estimate the optimal dual value for convergence; 2) A Distributed QSLR framework (D-QSLR) capable of coordinating local quantum/classical computing resources with those within neighborhoods and, in the meantime, protecting data privacy; 3) A Quantized UC model to obtain accurate commitment unit subproblems decision by using a quantum machine; and 4) A time-unit-decomposed quantum UC approach to overcoming the quantum resources’ limitations. Promising quantum test results validate the effectiveness of QSLR and the scalability of the UC-oriented D-QSLR algorithm, which demonstrate QSLR’s enormous potential in UC optimization.
Unit commitment (UC) problems faced by Independent System Operators on a daily basis are becoming increasingly complex due to the recent push for renewables and the consideration of sub-hourly UC to accommodate the increasing variability in the net load. A disruptive solution methodology to address the growing complexity is therefore required. Quantum computing offers a promise to overcome the combinatorial complexity through the use of the so-called “qubits.” To make the best use of near-term quantum computers to solve UC problems with a much larger number of binary variables than the number of qubits available, this paper devises a novel solution methodology based on a synergistic combination of quantum computing and Surrogate Lagrangian Relaxation (SLR) to solve UC problems. Our new contributions include: 1) A Quantum-SLR (QSLR) algorithm incorporating quantum approximate optimization algorithm (QAOA) into the SLR method, which overcomes the fundamental difficulties of previous LR-based quantum methods such as zigzagging of multipliers and the need to know or estimate the optimal dual value for convergence; 2) A Distributed QSLR framework (D-QSLR) capable of coordinating local quantum/classical computing resources with those within neighborhoods and, in the meantime, protecting data privacy; 3) A Quantized UC model to obtain accurate commitment unit subproblems decision by using a quantum machine; and 4) A time-unit-decomposed quantum UC approach to overcoming the quantum resources’ limitations. Promising quantum test results validate the effectiveness of QSLR and the scalability of the UC-oriented D-QSLR algorithm, which demonstrate QSLR’s enormous potential in UC optimization.
The penetration of distributed energy resources (DERs) within the microgrids (MGs) increases the complexity of Unit Commitment (UC) problem. In this paper, the idea of quantum computing (QC) is introduced in power system distributed optimization to solve the combinatorially complex UC problem. To take advantage of QC, the quantum-amenable model of UC problem is innovatively developed. Then, by using the hybrid nature of quantum-inspired alternate direction method of multipliers (ADMM) and by exploiting the superposition and entanglement of quantum bits (qubits), the classical ADMM coordinates the subproblems to obtain feasible solutions. Additionally, this paper uses a decomposition and coordination-supported framework for quantum optimization, which allows to solve problems larger that currently available quantum computers are capable of solving. The quantum distributed UC results are compared with those from its classical counterpart, which validate the efficacy of quantum computing,
The dawn of quantum computing brings on a revolution in the way combinatorially complex power system problems such as Unit Commitment are solved. The Unit Commitment problem complexity is expected to increase in the future because of the trend toward the increase of penetration of intermittent renewables. Even though quantum computing has proven effective for solving a host of problems, its applications for power systems’ problems have been rather limited. In this paper, a quantum unit commitment is innovatively formulated and the quantum version of the decomposition and coordination alternate direction method of multipliers (ADMM) is established. The above is achieved by devising quantum algorithms and by exploiting the superposition and entanglement of quantum bits (qubits) for solving subproblems, which are then coordinated through ADMM to obtain feasible solutions. The main contributions of this paper include: 1) the innovative development of a quantum model for Unit Commitment; 2) development of decomposition and coordination-supported framework which paves the way for the utilization of limited quantum resources to potentially solve the large-scale discrete optimization problems; 3) devising the novel quantum distributed unit commitment (QDUC) to solve the problem in a larger scale than currently available quantum computers are capable of solving. The QDUC results are compared with those from its classical counterpart, which validate the efficacy of quantum computing.
The unit commitment (UC) problem is essential to operating the power system in an efficient and reliable manner. However, modern power systems are growing increasingly complex with the growing penetration of distributed energy resources, making classical approaches to the UC problem computationally inefficient. Quantum computing approaches have been investigated for the UC problem due to the potential to outperform classical solutions. In many quantum models, including quadratic unconstrained binary optimization, or QUBO, the problem must be reformulated by discretizing continuous variables into "bins" or "segments" to ensure compatibility with the quantum processing unit (QPU). This would increase the number of variables due to discretization and lead to sub-optimal solutions. In this paper, we propose a new reformulation strategy for converting optimization problems into QPU-compatible binary quadratic models while creating significantly fewer binary variables, resulting in faster computation, increased efficiency, and further scalability. The performance of this approach is examined in terms of computation time and solution optimality to demonstrate its advantages and to illustrate the potential capability to solve the UC problem more efficiently than classical solutions.
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.
This paper introduces D2-UC, a quantum-ready framework for the unit commitment (UC) problem that prepares UC for near-term hybrid quantum-classical solvers by combining distributed classical decomposition with distributed quantum execution. We reformulate deterministic and stochastic UC into a three-block alternating direction method of multipliers (ADMM): (i) a convex quadratic subproblem for dispatch and reserves, (ii) a binary subproblem expressed as a quadratic unconstrained binary optimization (QUBO), and (iii) a proximal slack update for consensus. The core contributions are fivefold. First, we demonstrate how the full UC problem can be expressed as a single monolithic QUBO, establishing a direct interface to quantum solvers. Second, we decompose this large binary block into three type-specific QUBOs for commitment, startup, and shutdown, making the problem more tractable but revealing slower ADMM convergence. Third, we restore local logical couplings through per-unit-time micro-QUBOs, which accelerate convergence. Fourth, we batch micro-QUBOs into K non-overlapping block-diagonal problems, reducing many subproblems to a fixed number of solver-ready QUBOs per iteration, compatible with distributed variational quantum eigensolvers (DVQE). Fifth, we integrate an accept-if-better safeguard with DVQE to stabilize hybrid updates and prevent oscillations. Case studies confirm that the proposed methods deliver feasible schedules, faster convergence, and QUBO sizes aligned with current and near-term quantum hardware capabilities. All detailed data, codes, and parameter values are available at https://github.com/LSU-RAISE-LAB/3B-ADMM-UC-DVQE .
• We propose a new hybrid quantum-classical algorithm for solving the UC problem. • The hybrid model successfully optimizes 24-hour UC systems from 10 to 1000 units. • The model outperforms classical metaheuristics (GA and SA) and classical MINLP. • This represents an improvement over previous QCUC methods, a step to real-world use. Resource scheduling is critical in many industries, especially in power systems where the Unit Commitment (UC) problem determines the on/off status and output levels of generators under physical and economic constraints. Traditional exact methods, such as Branch‑and‑Bound, Branch‑and‑Cut, dynamic programming and mixed‑integer linear programming (MILP), remain the backbone of UC solution techniques, but they often rely on linear approximations or exhaustive search, leading to high computational burdens as system size grows. Metaheuristic approaches, such as genetic algorithms, particle swarm optimization, and other evolutionary methods, have been explored to mitigate this complexity; however, they typically lack optimality guarantees, exhibit sensitivity to initial conditions, and can become prohibitively time‑consuming for large‑scale systems. In this paper, we introduce a quantum‑classical hybrid algorithm for UC, and other resource scheduling problems by extension, that leverages Benders decomposition to decouple binary commitment decisions from continuous economic dispatch. The binary “master problem” is formulated as a quadratic unconstrained binary optimization (QUBO) model and solved on a quantum annealer. The continuous “subproblem,” which minimizes generation costs, with Lagrangian cuts feeding back to the master until convergence. We evaluate our hybrid framework on systems scaled from 10 to 1,000 generation units. Compared against a classical mixed‑integer nonlinear programming (MINLP) baseline, the hybrid algorithm achieves a consistently lower computation‑time growth rate and maintains an absolute optimality gap below 1.63%. These results demonstrate that integrating quantum annealing within a hybrid quantum-classical Benders decomposition loop can significantly accelerate large‑scale resource scheduling without sacrificing solution quality, pointing toward a viable path for addressing the escalating complexity of modern power grids.