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.
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.
Power flow (PF) analysis is a foundational computational method to study the flow of power in an electrical network. This analysis involves solving a set of non-linear and non-convex differential-algebraic equations. State-of-the-art solvers for PF analysis, therefore, face challenges with scalability and convergence, specifically for large-scale and/or ill-conditioned cases characterized by high penetration of renewable energy sources, among others. The adiabatic quantum computing paradigm has been proven to efficiently find solutions for combinatorial problems in the noisy intermediate-scale quantum (NISQ) era, and it can potentially address the limitations posed by state-of-the-art PF solvers. For the first time, we propose a novel adiabatic quantum computing approach for efficient PF analysis. Our key contributions are (i) a combinatorial PF algorithm and a modified version that aligns with the principles of PF analysis, termed the adiabatic quantum PF algorithm (AQPF), both of which use Quadratic Unconstrained Binary Optimization (QUBO) and Ising model formulations; (ii) a scalability study of the AQPF algorithm; and (iii) an extension of the AQPF algorithm to handle larger problem sizes using a partitioned approach. Numerical experiments are conducted using different test system sizes on D-Wave's Advantage™ quantum annealer, Fujitsu's digital annealer V3, D-Wave's quantum-classical hybrid annealer, and two simulated annealers running on classical computer hardware. The reported results demonstrate the effectiveness and high accuracy of the proposed AQPF algorithm and its potential to speed up the PF analysis process while handling ill-conditioned cases using quantum and quantum-inspired algorithms.
We present the first direct comparison between gate-based quantum computing (GQC) and adiabatic quantum computing (AQC) paradigms for solving the AC power flow (PF) equations. The PF problem is reformulated as a combinatorial optimization problem. For the GQC approach, the Quantum Approximate Optimization Algorithm (QAOA) is employed, while for the AQC approach, the problem is formulated as an Ising model. Numerical experiments on a 4-bus test system evaluate solution accuracy and computational performance. Results obtained using QAOA are benchmarked against those produced by D-Wave's Advantage system and Fujitsu's latest-generation Digital Annealer, implemented through the Quantum-Inspired Integrated Optimization (QIIO) software. The findings provide quantitative insights into the performance trade-offs, scalability, and practical viability of GQC and AQC paradigms for PF analysis, highlighting the potential of quantum optimization algorithms to address the computational challenges associated with the operation of modern electricity grids in the fault-tolerant era.
We investigate the performance of different annealers for power flow analysis. The annealers are D-Wave’s simulated annealer Neal, D-Wave’s quantum-classical hybrid annealer, D-Wave’s Advantage™ system (QA), Fujitsu’s simulated annealer, and Fujitsu’s digital annealer V3 (DA). We implement Quadratic Unconstrained Binary Optimization (QUBO) and Ising model formulations, with the latter offering finer control over complex voltage adjustments. We also propose a new method for the iterative and adaptive updating of complex voltages for the QUBO and Ising model formulations. Six different test systems are experimented with. QA and DA show superior performance over classical annealers. DA effectively manages the 15-bus system, whereas QA encounters difficulties in embedding the problem graph onto the hardware graph because of the limited qubit connectivity. This constraint confines QA to the 14-bus system with the QUBO formulation and the 4-bus system with the Ising model formulation. The best performance is associated with different annealers across different test systems, which suggests that adjusting the threshold can improve precision if the compiler and annealer are capable of handling the variables involved.
We investigate the performance of different annealers for power flow analysis using adiabatic computing. The annealers include D-Wave's simulated annealer Neal, D-Wave's quantum-classical hybrid annealer, D-Wave's Advantages system (QA), Fujitsu's classical simulated annealer, and Fujitsu's digital annealer V3 (DA). We implement Quadratic Unconstrained Binary Optimization (QUBO) and Ising model formulations, with the latter offering finer control over complex voltage adjustments. Different test systems are experimented with to systematically evaluate the annealers. The evaluation is based on the accuracy, the annealer's capability to handle the decision variables, and the computational time needed. QA and DA show superior performance over classical annealers for our application. DA effectively manages larger test systems, whereas QA encounters difficulties embedding the problem graph onto the hardware graph because of the limited qubit connectivity. This constraint confines QA to the 14-bus system with the QUBO formulation and the 4-bus system with the Ising model formulation. The best performance is associated with different annealers across different test systems, which suggests that adjusting the threshold can improve precision if the compiler and annealer are capable of handling the number of variables involved.
This paper proposes the use of annealing-based quantum computing for solving combinatorial optimal power flow problems. Quantum annealers provide a physical computing platform which utilises quantum phase transitions to solve specific classes of combinatorial problems. These devices have seen rapid increases in scale and performance, and are now approaching the point where they could be valuable for industrial applications. This paper shows how an optimal power flow problem incorporating linear multiphase network modelling, discrete sources of energy flexibility, renewable generation placement/sizing and network upgrade decisions can be formulated as a quadratic unconstrained binary optimisation problem, which can be solved by quantum annealing. Case studies with these components integrated with the IEEE European Low Voltage Test Feeder are implemented using D-Wave Systems’ 5,760 qubit Advantage quantum processing unit and hybrid quantum-classical solver.
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.