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

Zeynab Kaseb, Matthias Moller, Pedro P. Vergara, Peter Palensky

TL;DR

The Adiabatic Quantum Optimal Power Flow (AQOPF) algorithm is introduced, which transforms the classical optimal power flow (OPF) equations into quadratic unconstrained binary optimization (QUBO) models.

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.

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

TL;DR

The Adiabatic Quantum Optimal Power Flow (AQOPF) algorithm is introduced, which transforms the classical optimal power flow (OPF) equations into quadratic unconstrained binary optimization (QUBO) models.

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.

Paper Structure

This paper contains 19 sections, 35 equations, 2 figures, 5 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Mathematical formulation
  3. Power Flow Formulation
  4. Optimal Power Flow Formulation
  5. Combinatorial formulation
  6. Combinatorial Power Flow Formulation
  7. Combinatorial Optimal Power Flow Formulation
  8. Quantum and Digital Annealing
  9. Higher-Order Terms Handling
  10. Adiabatic Quantum Algorithm
  11. Delta Update
  12. Results
  13. Partitioned Formulation
  14. Partitioned AQPF
  15. Partitioned AQOPF
  16. ...and 4 more sections

Figures (2)

  • Figure 1: Performance comparison of the NR method, AQPF, and partitioned AQPF for the 118-bus test case using QIIO. The results are shown for (a) voltage magnitude $V_i\;\text{(p.u.)}$, (b) voltage phase angle $\delta_i\;\text{(degrees)}$, (c) net active power $P_i\;\text{(MW)}$, and (d) net reactive power $Q_i\;\text{(MVAR)}$.
  • Figure 2: Performance comparison of the NR method, AQOPF, and partitioned AQOPF for the 118-bus test case using QIIO. The results are shown for (a) voltage magnitude $V_i\;\text{(p.u.)}$, (b) voltage phase angle $\delta_i\;\text{(degrees)}$, (c) net active power $P_i\;\text{(MW)}$, and (d) net reactive power $Q_i\;\text{(MVAR)}$.