Symbolic Explainer of Power System Dynamics

Power systems face increasing uncertainties that create nonlinear regime-dependent dynamics. Critical Clearing Time (CCT) remains a key transient stability metric, yet analytical relations with operating conditions are rarely tractable. Advanced machine learning techniques offer accurate CCT prediction and partial interpretability, but fail to uncover the governing functional dependencies. This paper introduces a Piecewise Symbolic Regression (Pc-SR) framework that automatically discovers regime-conditioned equations linking system variables to CCT. Pc-SR combines cost–complexity–pruned decision trees for task-aware partitioning with symbolic models in each region. Validation on synthetic data confirms recovery of correct partitions and equations under noise, while tests on single-machine infinite-bus variants rediscover analytical CCT equations. Applied to a modified 39-bus system with inverterbased resources, Pc-SR produces interpretable, regime-specific CCT surrogates matching black-box accuracy while exposing nonlinearities and interactions. This framework advances beyond descriptive explainability, providing transparent models to accelerate stability screening and support operator insight into complex dynamic behaviors.