Optimal Power Flow (OPF) is a fundamental optimisation problem in power systems, aiming to minimize the generation cost dispatch while satisfying operational constraints. Traditional optimisation methods, especially the AC-OPF formulation, struggle to converge or find optimal solutions due tothenon-linear andnon-convexnatureoftheproblem. Thisstudyaddressesthe AC-OPF using a hybrid iterative algorithm that combines classical and quantum computing, where Quantum Annealing assists in optimizing decision variables. ThemethodologysplitstheAC-OPFintotwointerrelatedproblems. Thefirstsub-problemisthe classical OPFformulation, whichincorporatesallelectricalnetworkcomponentsandminimizes the objective function under technical and operational constraints. The second sub-problem, also known as the master problem, is a binary problem that assumes activation states of the generators, while minimizingcostsofgenerationandstart-upcostsfordifferenttimesteps. This forms aBinary Integer Linear Programming (BILP) problem, which is well-suited for quantum computing due to its discrete structure and combinatorial complexity. Once the BILP is defined, it is converted into a Hamiltonian and evolved using Quantum Annealing throughtheQiboframework. Theresultingoptimalbinarycombinationisthenapplied to the network model and solved classically. If the solution is feasible and optimal, the process ends. If not, the combination is excluded from the BILP and added as a constraint to guide the search for the next best feasible solution. This methodology is tested on two IEEE networks of 9 to evaluate computational speedup and assess the limitations of actual quantum hardware. Once this is done, future work will explore the use of Quantum Machine Learning to generate 24-hour load and generation profiles, while in this work, an LSTM is used, enabling the AC-OPF solutions.
Optimal Power Flow (OPF) is a fundamental optimisation problem in power systems, aiming to minimize the generation cost dispatch while satisfying operational constraints. Traditional optimisation methods, especially the AC-OPF formulation, struggle to converge or find optimal solutions due tothenon-linear andnon-convexnatureoftheproblem. Thisstudyaddressesthe AC-OPF using a hybrid iterative algorithm that combines classical and quantum computing, where Quantum Annealing assists in optimizing decision variables. ThemethodologysplitstheAC-OPFintotwointerrelatedproblems. Thefirstsub-problemisthe classical OPFformulation, whichincorporatesallelectricalnetworkcomponentsandminimizes the objective function under technical and operational constraints. The second sub-problem, also known as the master problem, is a binary problem that assumes activation states of the generators, while minimizingcostsofgenerationandstart-upcostsfordifferenttimesteps. This forms aBinary Integer Linear Programming (BILP) problem, which is well-suited for quantum computing due to its discrete structure and combinatorial complexity. Once the BILP is defined, it is converted into a Hamiltonian and evolved using Quantum Annealing throughtheQiboframework. Theresultingoptimalbinarycombinationisthenapplied to the network model and solved classically. If the solution is feasible and optimal, the process ends. If not, the combination is excluded from the BILP and added as a constraint to guide the search for the next best feasible solution. This methodology is tested on two IEEE networks of 9 to evaluate computational speedup and assess the limitations of actual quantum hardware. Once this is done, future work will explore the use of Quantum Machine Learning to generate 24-hour load and generation profiles, while in this work, an LSTM is used, enabling the AC-OPF solutions.
Alternating Current Optimal Power Flow Unit Commitment (AC-OPF-UC) is a difficult mixed-integer nonlinear optimization problem that combines binary generator commitment decisions with nonconvex continuous AC power-flow constraints. In this work, we investigate whether hybrid quantum-classical variational algorithms can improve the solution of single-period AC-OPF-UC relative to classical approaches. To the best of our knowledge, this is the first study to directly evaluate quantum or hybrid quantum-classical algorithms for the full AC-OPF-UC problem. We consider two candidate algorithms for improving AC-OPF-UC solution quality relative to purely classical methods on ideal quantum hardware. The first applies QAOA directly to a fully discretized formulation of the problem, with equality and inequality constraints incorporated through penalty terms and slack variables. Although conceptually straightforward, this approach requires a prohibitively large number of qubits even for small instances. The second, qubit-efficient approach encodes only the binary generator status variables on a quantum computer, while optimizing the continuous power-flow variables classically for each sampled bitstring. We benchmark this method on randomly generated AC-OPF-UC instances with 5 to 13 generators and compare it against SCIP, SMAC, and uniform random sampling. Our simulations show that the qubit-efficient hybrid method does not outperform uniform sampling. These results suggest that in order to establish potential advantage of the variational hybrid strategy considered here over the best classical algorithms, if any, much larger system sizes (25+ generators) need to be tested, which is beyond our computational capacity. Alternatively, different approaches, such as quantum versions of branch-and-bound methods, may be more promising.
Quantum computing provides alternative algorithmic approaches to solve computationally challenging problems and has shown potential advantages compared to classical methods for specific problem classes. This thesis explores variational quantum algorithms (VQAs) for solving the alternating current optimal power flow (AC OPF) problem and the AC power flow (PF) problem. Both tasks are fundamental to power system analysis, operation, and planning, but they become increasingly challenging as grid size and complexity grow. The first main contribution of the thesis introduces a variational quantum framework for solving the OPF problem, formulated as a nonconvex quadratically constrained quadratic program. The proposed method encodes primal and dual optimization variables using two parameterized quantum circuits (PQCs), allowing the OPF Lagrangian to be expressed as expectations over quantum observables. An OPF solution can be found by minimizing the Lagrangian over the parameters of the first PQC and maximizing it over the parameters of the second PQC. The proposed framework seeks saddle points of the Lagrangian in a hybrid fashion. The gradients of the Lagrangian are estimated using the two PQCs, and PQC parameters are updated classically using a primal-dual method. A key innovation is to permute the primal variables of the original problem, so the corresponding quantum observables adhere to a banded form that facilitates a novel qubit-efficient quantum measurement protocol. The second main contribution presents a quantum machine learning (QML) approach for learning AC PF solutions using a data-embedded PQC. The method first poses a single PF instance as a nonlinear least-squares problem over PQC parameters. Second, the PF specifications are embedded as features into another PQC, and the resultant QML model is trained to learn the PF mapping. Once presented with a new problem instance, the trained QML model can perform the prediction step efficiently in real-time operation. Third, a novel protocol is devised to efficiently measure PF observables by leveraging the graph structure of a power network. The proposed quantum AC PF/OPF framework sets the foundations for addressing more elaborate grid tasks via quantum computing. More broadly, the proposed quantum paradigms can be used to achieve safe QML as PQCs are trained to comply with data-dependent constraints.
Alternative Current Optimal Power Flow (AC-OPF) is essential for efficient power system planning and real-time operation but remains an NP-hard and non-convex optimization problem with significant computational challenges. This paper proposes a novel hybrid classical-quantum deep learning framework for AC-OPF problem, integrating parameterized quantum circuits (PQCs) for feature extraction with classical deep learning for data encoding and decoding. The proposed framework integrates two types of residual connection structures to mitigate the ``barren plateau" problem in quantum circuits, enhancing training stability and convergence. Furthermore, a physics-informed neural network (PINN) module is incorporated to guarantee tolerable constraint violation, improving the physical consistency and reliability of AC-OPF solutions. Experimental evaluations on multiple IEEE test systems demonstrate that the proposed approach achieves superior accuracy, generalization, and robustness to quantum noise while requiring minimal quantum resources.
• 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.
Mixed Integer Linear Programming (MILP) can be considered the backbone of the modern power system optimization process, with a large application spectrum, from Unit Commitment and Optimal Transmission Switching to verifying Neural Networks for power system applications. The main issue of these formulations is the computational complexity of the solution algorithms, as they are considered NP-Hard problems. Quantum computing can give a direct solution to this problem, as it has been experimentally shown that it can provide significant speedups in solving MILPs. In this work, we present a general framework for solving power system optimization problems with a Quantum Computer (QC), which leverages mathematical tools and QCs’ sampling ability to provide accelerated solutions. Our guiding applications are the optimal transmission switching and the verification of neural networks trained to solve a DC Optimal Power Flow. Specifically, using an accelerated version of Benders Decomposition , we split a given MILP into an Integer Master Problem and a linear Subproblem and solve it through a hybrid “quantum-classical” approach, getting the best of both worlds. We provide 2 use cases, and benchmark the developed framework against other classical and hybrid methodologies, to demonstrate the opportunities and challenges of hybrid quantum-classical algorithms for power system mixed integer optimization problems.
This study further explores reformulating power flow (PF) analysis as a discrete combinatorial optimization problem, proposed in our earlier study using the Adiabatic Quantum Power Flow (AQPF) algorithm, which can be executed on Ising machines, including quantum and quantum-inspired hardware. This approach provides a new representation of the underlying equations, analogous to how neural networks approximate complex functions using simple operations. While the resulting combinatorial optimization problem is NP-hard, it is compatible with emerging quantum hardware designed to address such complexity. We introduce the Adiabatic Quantum Optimal Power Flow (AQOPF) algorithm, which transforms the classical optimal power flow (OPF) equations into quadratic unconstrained binary optimization (QUBO) models. Furthermore, the AQPF and AQOPF algorithms are evaluated on standard test cases ranging from 4- to 1354-bus systems using D-Wave's Advantage\texttrademark\ system (QA), its hybrid quantum-classical solver (HA), and Fujitsu's third-generation Digital Annealer (DAv3) and Quantum-Inspired Integrated Optimization (QIIO) platform. Both full and partitioned formulations are investigated, with particular attention to scalability and robustness in ill-conditioned scenarios. The results demonstrate that the algorithms can reproduce feasible PF and OPF solutions and exhibit promising computational scalability when supported by scalable hardware.