A Hybrid GNN-IZR Framework for Fast and Empirically Robust AC Power Flow Analysis in Radial Distribution Systems

The Alternating Current Power Flow (ACPF) problem forces a trade-off between the speed of data-driven models and the reliability of analytical solvers. This paper introduces a hybrid framework that synergizes a Graph Neural Network (GNN) with the Implicit Z-Bus Recursive (IZR) method, a robust, non-iterative solver for radial distribution networks. The framework employs a physics-informed GNN for rapid initial predictions and invokes the IZR solver as a failsafe for stressed cases identified by a two-stage trigger. A failure is defined as any solution with a maximum power mismatch exceeding 0.1 p.u., a significant operational deviation. On a challenging test set of 7,500 stressed scenarios for the IEEE 33-bus system, the GNN-only model failed on 13.11 % of cases. In contrast, the hybrid framework identified all potential failures, delegating them to the IZR solver to achieve a 0.00 % failure rate, empirically matching the 100 % success rate of the analytical solver on this specific test set. An expanded ablation study confirms that both physics-informed training and Z-bus sensitivity features are critical, collaboratively reducing the GNN's failure rate from 98.72 % (data-only) to 13.11 %. The hybrid approach demonstrates a pragmatic path to achieving the empirical reliability of an analytical solver while leveraging GNN speed, enabling a significant increase in the number of scenarios analyzable in near real-time.