Power flow and optimal power flow using quantum and digital annealers: a computational scalability analysis

TL;DR

This paper explores reformulating power flow and optimal power flow problems as combinatorial optimization tasks solvable by quantum and digital annealers, demonstrating promising scalability and robustness on large test cases.

Contribution

Introduces the AQOPF algorithm transforming classical OPF into QUBO models for quantum and digital annealers, expanding the computational tools for power system optimization.

Findings

Algorithms reproduce feasible power flow solutions

Demonstrated scalability on large test cases up to 1354-bus systems

Showed robustness in ill-conditioned scenarios

Abstract

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.