Hybrid classical quantum approach for solving ac optimal power flows

Abstract

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.