A preprint posted on arXiv on 9 October by researchers at the University of Oslo and Xi’an University of Technology proposes a hierarchical graph neural network to estimate grid voltages and phase angles when one or two transmission lines are out of service. Called TDD-HBGNN, the method divides a grid into sub-units and voltage regions while preserving their electrical connections. It combines a physics-based linear starting estimate with a graph network that learns topology-dependent nonlinear corrections.

The authors compared the model with six methods on the IEEE 118-bus and Polish 2,746-bus test systems under N–1 and N–2 line outages not seen during training. The paper reports all-bus phase-angle errors 2.47 to 4.20 times lower than the strongest baselines; its voltage-magnitude advantage was concentrated near outaged branches. Simulations excluded load uncertainty, generator redispatch and cascading failures. These results do not constitute field validation on a live grid or proof of operational safety; the work is a preprint that has not yet undergone peer review.