Quantum-Enhanced Reinforcement Learning for Accelerating Newton-Raphson Convergence with Ising Machines: A Case Study for Power Flow Analysis

TL;DR

This paper introduces a quantum-enhanced reinforcement learning approach to optimize the initialization of the Newton-Raphson method for power flow analysis, significantly improving convergence speed and robustness.

Contribution

It presents a novel quantum-enhanced RL framework that accelerates Newton-Raphson convergence by optimizing initialization using quantum annealers within a power flow context.

Findings

Reduced number of NR iterations

Faster convergence under challenging conditions

Enhanced robustness of power flow solutions

Abstract

The Newton-Raphson (NR) method is widely used for solving power flow (PF) equations due to its quadratic convergence. However, its performance deteriorates under poor initialization or extreme operating scenarios, e.g., high levels of renewable energy penetration. Traditional NR initialization strategies often fail to address these challenges, resulting in slow convergence or even divergence. We propose the use of reinforcement learning (RL) to optimize the initialization of NR, and introduce a novel quantum-enhanced RL environment update mechanism to mitigate the significant computational cost of evaluating power system states over a combinatorially large action space at each RL timestep by formulating the voltage adjustment task as a quadratic unconstrained binary optimization problem. Specifically, quantum/digital annealers are integrated into the RL environment update to evaluate state transitions using a problem Hamiltonian designed for PF. Results demonstrate significant improvements in convergence speed, a reduction in NR iteration counts, and enhanced robustness under different operating conditions.