PISR: Physics-Informed Symbolic Regression for Predicting Power System Voltage

The ongoing transition from centralized power systems to renewable and decentral power systems introduces significant variability in generation and demand patterns. This leads to additional challenges in grid operation due to the large number of controllable units - especially in distribution grids with poor sensor measurement feedback. Our research addresses the challenge of improving the prediction of voltage profiles in electrical grids using machine-learning (ML) techniques. If these techniques become reliable and fast enough, they could become a key to solving complex control tasks. We propose and evaluate a novel physics-based ML method based on Symbolic Regression (SR) to predict the voltage at individual grid buses. SR generates equations fitted to data using genetic algorithms based on predefined operators. Previous research on ML-based voltage prediction focused on the use of neural networks. While these methods show good performance, safety considerations of grid operators hinder the deployment of pure black-box models in actual control applications. Physics-based ML models attempt to increase robustness by incorporating physical laws into the model structure. We follow this line of research by developing custom physics-based SR operators reflecting line current and voltage drop. We evaluate the proposed physics-informed Symbolic Regression (PISR) method by performing experiments using the IEEE-14 test grid to investigate power transmission applications and a rural test grid from SimBench to investigate power distribution applications. Our results show that the mean error of PISR is on par with an optimally configured and tuned multilayer perceptron (MLP) model in sparse training data situations. The consistency of PISR precision across multiple training runs is higher, while the results remain interpretable. Our results indicate that PISR could be a viable and more robust alternative to NN-based models and could thus play a major role in increasing the resilience of future power systems.