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.
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.
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.
This paper presents an application of a novel quadratic unconstrained binary optimization (QUBO) formulation to the minimum loss problem in distribution networks. The proposed QUBO formulation was conceived to be employed in quantum annealing-a quantum computing paradigm useful for solving combinatorial optimization problems. Quantum annealing is expected to provide better and/or faster solutions to optimization problems when compared to the ones provided by classical computers. With the problem at stake, better solutions result in lower energy losses, and faster solutions contribute to the same outcome given the future need for frequent reconfiguration of distribution networks to accommodate highly volatile demand, as anticipated by recent low-carbon solutions. The paper presents the results obtained through a hybrid quantum-classical solver for a standard 33-node test network and compares them with the ones obtained from classical solvers. Our main conclusion is that quantum annealing has potential to show advantage in the near future in terms of solution quality and time-to-solution, as quantum annealers and hybrid solvers continue to improve their performance.
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.
Quantum annealing algorithms belong to the class of meta-heuristic tools, applicable for solving binary optimization problems. Hardware implementations of quantum annealing, such as the quantum processing units (QPUs) produced by D-Wave Systems, have been subject to multiple analyses in research, with the aim of characterizing the technology's usefulness for optimization and sampling tasks. In this paper, we present a real-world application that uses quantum technologies. Specifically, we show how to map certain parts of a real-world traffic flow optimization problem to be suitable for quantum annealing. We show that time-critical optimization tasks, such as continuous redistribution of position data for cars in dense road networks, are suitable candidates for quantum computing. Due to the limited size and connectivity of current-generation D-Wave QPUs, we use a hybrid quantum and classical approach to solve the traffic flow problem.
Quantum computing is rapidly advancing, harnessing the power of qubits' superposition and entanglement for computational advantages over classical systems. However, scalability poses a primary challenge for these machines. By implementing a hybrid workflow between classical and quantum computing instances, D-Wave has succeeded in pushing this boundary to the realm of industrial use. Furthermore, they have recently opened up to mixed integer linear programming (MILP) problems, expanding their applicability to many relevant problems in the field of optimisation. However, the extent of their suitability for diverse problem categories and their computational advantages remains unclear. This study conducts a comprehensive examination by applying a selection of diverse case studies to benchmark the performance of D-Wave's hybrid solver against that of industry-leading solvers such as CPLEX, Gurobi, and IPOPT. The findings indicate that D-Wave's hybrid solver is currently most advantageous for integer quadratic objective functions and shows potential for quadratic constraints. To illustrate this, we applied it to a real-world energy problem, specifically the MILP unit commitment problem. While D-Wave can solve such problems, its performance has not yet matched that of its classical counterparts.
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.