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IET conference proceedings.

Data-driven fitting of the minimum electricity power purchase cost function to enable quantum market clearing

Xiaodong Zheng, Peile Lin, Haoyong Chen

Published Jul 1, 2026• 0 citations
Publisher

Abstract

At present, the construction of the electricity spot market is becoming increasingly sophisticated. Security constrained unit commitment (SCUC) can effectively reduce power procurement costs. However, as the system scale expands, the computational complexity of solving the SCUC problem increases significantly. This paper focuses on transforming the SCUC into a quadratic unconstrained binary optimization (QUBO) model suitable for quantum computers, with the aim of leveraging quantum computing technologies to accelerate the solution of the unit commitment problem. Based on the Benders decomposition framework, the SCUC model is decomposed to generate a set of unit commitment samples together with the corresponding optimal values of their Benders subproblems. To establish the functional relationship between unit commitment and the optimal cost (i.e., the SCUC value function) in a manner compatible with quantum computing technologies, a high-dimensional quadratic function is employed to fit the obtained unit commitment samples and their corresponding optimal cost values, based on the value function theory of mixed-integer programming. The fitted high-dimensional quadratic function is then solved using both commercial solvers and quantum computing platforms. The results indicate that the QUBO can provide high-quality suboptimal solutions to the original SCUC problem.

DOI
10.1049/icp.2026.1621

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At present, the construction of the electricity spot market is becoming increasingly sophisticated. Security constrained unit commitment (SCUC) can effectively reduce power procurement costs. However, as the system scale expands, the computational complexity of solving the SCUC problem increases significantly. This paper focuses on transforming the SCUC into a quadratic unconstrained binary optimization (QUBO) model suitable for quantum computers, with the aim of leveraging quantum computing technologies to accelerate the solution of the unit commitment problem. Based on the Benders decomposition framework, the SCUC model is decomposed to generate a set of unit commitment samples together with the corresponding optimal values of their Benders subproblems. To establish the functional relationship between unit commitment and the optimal cost (i.e., the SCUC value function) in a manner compatible with quantum computing technologies, a high-dimensional quadratic function is employed to fit the obtained unit commitment samples and their corresponding optimal cost values, based on the value function theory of mixed-integer programming. The fitted high-dimensional quadratic function is then solved using both commercial solvers and quantum computing platforms. The results indicate that the QUBO can provide high-quality suboptimal solutions to the original SCUC problem.
Mixed-integer linear programs (MILPs) are fundamental to power system operations but are challenging to solve due to their NP-hard nature. Quantum annealing, which seeks to find the ground state of an Ising model–a minimization of a quadratic binary function–offers potential speedups for solving combinatorial optimization problems. However, converting MILPs into quadratic unconstrained binary optimization (QUBO) problems often requires lots of slack variables, leading to significant qubit overhead and limiting the capability of quantum annealers. In this work, we propose an efficient formulation approach that generates a QUBO representation of a targeted MILP without introducing auxiliary binary variables. Geometrically, our method approximates the value function of the MILP with a quadratic binary function leveraging a simple convex optimization subroutine. We prove the existence of the QUBO representation, which preserves the MILP’s optimal solution and objective value with the same number of binary variables. The proposed approach is validated on several instances of the security-constrained unit commitment (SCUC) problem, with test cases featuring up to 288 binary variables, demonstrating its efficacy in reducing qubit overhead for quantum-classical hybrid Benders decomposition frameworks.
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.
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.
This paper proposes a learning-based quantum-classical Benders decomposition method for solving large-scale two-stage stochastic unit commitment (UC) problems. The approach integrates a long short-term memory (LSTM) network to approximate subproblem costs and a support vector machine (SVM) classifier to filter dominant Benders cuts, thereby reducing problem size, facilitating quantum computing implementation, and improving scalability. The master problem is reformulated into a quadratic unconstrained binary optimization (QUBO) problem, enabling its solution on quantum hardware. The key contributions are: (i) a quantum-classical decomposition framework tailored for stochastic UC, (ii) an LSTM-based subproblem proxy to facilitate iterations, (iii) an SVM-based cut filtering method to retain only dominant cuts, and (iv) a QUBO reformulation suitable for quantum solvers. Numerical experiments demonstrate that the proposed method significantly reduces computational overhead and quantum resource requirements compared with conventional approaches.
Stochastic Unit Commitment (SUC) has been proposed to manage the uncertainties driven by renewable integration, but it leads to significant computational complexity. When accelerated by Benders Decomposition (BD), the master problem becomes binary integer programming, which is still NP-hard and computationally demanding for classical 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, making qubit consumption independent of the increasing number of Benders cuts. To further reduce the qubit overhead, quantum ADMM is applied to break large-scale SUC into smaller blocks for sequential solutions, which does not scale with the number of generators. Finally, the simulation results on both 4-generator and the IEEE bus-118 systems demonstrate the feasibility and scalability of the proposed algorithm, indicating its superior qubit and runtime efficiency over classical and baseline quantum approaches on the D-Wave QPU platform.
This paper proposes a hybrid quantum-classical algorithm to solve a fundamental power system problem called unit commitment (UC). The UC problem is decomposed into a quadratic subproblem, a quadratic unconstrained binary optimization (QUBO) subproblem, and an unconstrained quadratic subproblem. A classical optimization solver solves the first and third subproblems, while the QUBO subproblem is solved by a quantum algorithm called quantum approximate optimization algorithm (QAOA). The three subproblems are then coordinated iteratively using a three-block alternating direction method of multipliers algorithm. Using Qiskit on the IBM Q system as the simulation environment, simulation results demonstrate the validity of the proposed algorithm to solve the UC problem.