Physics-Informed Graph Neural Networks for Multi-Energy Systems

Reliable state estimates are the foundation for every downstream decision in grid operations: load dispatch, contingency analysis, and anomaly detection. In practice, however, two classes of measurement degradation challenge the reliability of classical estimators: measurements that are simply missing or sparse due to sensor outages and communication failures, and measurements that are sign-corrupted, meaning the polarity of a power-flow or power-injection reading is inverted. Both failure modes can silently degrade the estimated operating picture in ways that conventional methods do not handle well.
This research program, conducted in collaboration with Noga, addresses both challenges through two complementary.

Part I – State Estimation Under Sparse and Missing Measurements (ProxGNSE)

In real transmission networks, a significant fraction of measurements may be unavailable at any given time. Classical weighted least-squares (WLS) solvers become unreliable in such low-observability regimes, while purely data-driven AI approaches trained on fixed measurement configurations tend to break down when the set of available sensors changes. We developed ProxGNSE — a hybrid estimator that combines the physics-based Levenberg–Marquardt (LM) solver with a Graph Neural Network (GNN) acting as a learned regularizer. The key idea is that the GNN does not replace the classical solver; instead, it operates alongside it at each iteration, applying learned corrections to the estimated voltage state that reflect patterns drawn from historical grid operating data. Because the GNN works directly on the voltage state rather than on the raw measurement vector, it naturally adapts to whatever measurements happen to be available — no retraining is needed when sensor coverage changes.
The method was tested on the IEEE 118-bus and 300-bus benchmark systems under severe measurement loss of 70% and 90%. ProxGNSE consistently outperformed both classical regularized LM and the leading data-driven baseline (GAEN), reducing estimation error by up to 37% at 70% missing data on the 118-bus system. Notably, the model trains in under 20 epochs, compared to over 100 epochs for the purely data-driven alternative — a direct consequence of its physics-based initialization that starts from a sensible operating point rather than random weights.

Part II – State Estimation Under Sign-Corrupted Measurements


A subtler but equally dangerous fault class arises when the polarity of a measurement is inverted, for example, due to a wiring mistake, sensor calibration error, communication glitch, or adversarial manipulation. A sign-flipped power-flow reading does not show up as an unusually large number; it appears physically plausible in magnitude while conveying the exact opposite direction of power flow. Standard bad-data detection (BDD) schemes, which flag measurements based on residual magnitude, are poorly suited to catch this type of fault and may instead compensate for the flip by distorting the estimated voltage state.
We developed a joint estimation framework that simultaneously reconstructs the system state and identifies which measurements carry a sign error. The algorithm alternates between two steps: a WLS-type state update using sign-corrected measurements, and a Newton-type sign-vector update guided by a Bayesian prior encoding the expectation that sign faults are rare. A key innovation is a Sign Change Alert (SCA) mechanism that prevents the state solver from inadvertently absorbing a true sign flip into the voltage estimate, a masking failure mode that naive alternating approaches are susceptible to. The framework additionally supports a Huber loss to handle large-magnitude outliers alongside sign corruptions, and allows a protected set of measurements (those from physically verified or trusted channels) to be exempted from sign correction.
Simulations on the IEEE 118-bus system across a wide range of sign-flip rates show that the proposed algorithm substantially outperforms classical WLS with BDD, both in voltage estimation accuracy and in sign-flip detection rate. At low-to-moderate flip rates, the classical BDD approach achieves detection F-scores between 47% and 61%, while the proposed method exceeds 93%.

Summary

Together, these two contributions advance the state of the art in physics-informed machine learning for power grid monitoring, directly addressing two distinct and practically important failure modes that the current generation of estimation tools does not handle well. The first equips the estimator to remain accurate when measurement coverage is degraded; the second equips it to detect and correct a class of polarity faults that can otherwise silently corrupt the grid's operational picture. Both methods are grounded in the physical laws governing power flow, ensuring that the AI components reinforce rather than override the established engineering models that Noga's operations depend on.