Discovering Unknown Inverter Governing Equations via Physics-Informed Sparse Machine Learning

Abstract: Discovering the unknown governing equations of grid-connected inverters from external measurements holds significant attraction for analyzing modern inverter-intensive power systems. However, existing methods struggle to balance the identification of unmodeled nonlinearities with the preservation of physical consistency. To address this, this paper proposes a Physics-Informed Sparse Machine Learning (PISML) framework. The architecture integrates a sparse symbolic backbone to capture dominant model skeletons with a neural residual branch that compensates for complex nonlinear control logic. Meanwhile, a Jacobian-regularized physics-informed training mechanism is introduced to enforce multi-scale consistency including large/small-scale behaviors. Furthermore, by performing symbolic regression on the neural residual branch, PISML achieves a tractable mapping from black-box data to explicit control equations. Experimental results on a high-fidelity Hardware-in-the-Loop platform demonstrate the framework's superior performance. It not only achieves high-resolution identification by reducing error by over 340 times compared to baselines but also realizes the compression of heavy neural networks into compact explicit forms. This restores analytical tractability for rigorous stability analysis and reduces computational complexity by orders of magnitude. It also provides a unified pathway to convert structurally inaccessible devices into explicit mathematical models, enabling stability analysis of power systems with unknown inverter governing equations.