Data driven approach towards more efficient Newton-Raphson power flow calculation for distribution grids

TL;DR

This paper addresses the challenge of maintaining fast convergence for Newton-Raphson power flow calculations in distribution grids under stressed conditions. It develops three initialization strategies: an analytical basin-of-attraction bound to constrain NR’s input space, and data-driven pipelines (supervised regression and physics-informed neural networks) plus a reinforcement learning agent to steer initial guesses toward easy-converging regions. Experiments on two-bus and seven-bus benchmarks demonstrate that the analytical method bounds the basin and reduces iterations, while neural-network–based initializations and PINNs yield rapid NR convergence, and RL further accelerates convergence by actively adjusting voltages. The proposed methods promise more robust, scalable, and real-time capable PF solutions for grids with high renewable penetration and distributed generation.

Abstract

Power flow (PF) calculations are fundamental to power system analysis to ensure stable and reliable grid operation. The Newton-Raphson (NR) method is commonly used for PF analysis due to its rapid convergence when initialized properly. However, as power grids operate closer to their capacity limits, ill-conditioned cases and convergence issues pose significant challenges. This work, therefore, addresses these challenges by proposing strategies to improve NR initialization, hence minimizing iterations and avoiding divergence. We explore three approaches: (i) an analytical method that estimates the basin of attraction using mathematical bounds on voltages, (ii) Two data-driven models leveraging supervised learning or physics-informed neural networks (PINNs) to predict optimal initial guesses, and (iii) a reinforcement learning (RL) approach that incrementally adjusts voltages to accelerate convergence. These methods are tested on benchmark systems. This research is particularly relevant for modern power systems, where high penetration of renewables and decentralized generation require robust and scalable PF solutions. In experiments, all three proposed methods demonstrate a strong ability to provide an initial guess for Newton-Raphson method to converge with fewer steps. The findings provide a pathway for more efficient real-time grid operations, which, in turn, support the transition toward smarter and more resilient electricity networks.

Figures (9)

• Figure 1: Newton-Raphson method and the contrast between the initial guesses of easy-convergence case and ill-conditioned cases. The green lines and dots represent an example of the updating iterations of easy-convergence initial guess; the red is an example of the updating iterations of ill-conditioned initial guess. The cross marks the true solution, which is the target of Newton-Raphson method.
• Figure 2: Schematic of the two-bus system.
• Figure 3: Convergence map for a two-bus system. The axes show the initial values for the voltage angle $\theta_2$ and the voltage magnitude $V_2$ and the colors indicate the number of Newton-Raphson iterations until the desired solution (marked by the star) is reached up to tolerance $\epsilon$.
• Figure 4: Estimating of the basin of attraction for voltage, including the center and maximum (blue squares) and minimum (orange squares) radius of the region for a system with 7 buses. This method can be applied to grids of any size and configuration, regardless of the number of buses.
• Figure 5: Solution prediction pipeline for obtaining the power flow solution.

Theorems & Definitions (1)

• Lemma 1