Fast Frequency Stability Prediction Using Physics-Informed Neural Networks

This paper proposes an ultra-fast frequency deviation prediction model for power systems based on Physics-Informed Neural Networks (PINN) and systematically compares three learning configurations distinguished by the source of physics inputs and label availability: supervised learning with dynamic-simulation inputs, supervised learning with static power-flow inputs and unsupervised learning with static power-flow inputs. The proposed model embeds the swing equation as a physics constraint in the loss function, enabling simultaneous data-driven learning and physical consistency. The supervised model utilizes the mechanical-electrical power imbalance obtainable only through dynamic simulation, while the static power-flow based supervised model employs a generation-load imbalance derivable from static power flow calculations with a learnable scale correction parameter. The unsupervised model attempts to learn solely from the physics loss without labeled data. Experiments on the KPG-193 bus system, a reduced Korean power grid model, use 180,768 samples from 2,152 operating conditions generated via PSSⓇE 33. The supervised model achieves an R-squared of 0.9989 and a plus-minus five percent accuracy of 95.22 percent, while the static power-flow based supervised model attains 0.9973 and 90.97 percent using only static power flow inputs. The unsupervised model minimizes the physics loss yet fails to identify the absolute scale parameter, and five-percent weak supervision reaches only an R-squared of 0.51, confirming that labels are the sole identification signal for the absolute magnitude. Ensemble learning with Monte Carlo (MC) Dropout quantifies the prediction uncertainty as the dispersion of ensemble predictions, which serves as a relative reliability indicator and the basis of the 95 percent confidence intervals. The proposed models achieve prediction times under one millisecond, representing over a thousand-fold speedup compared to conventional dynamic simulations.