A Physics-Informed Deep Learning Method for Wind Turbine Impedance Modeling

Accurate impedance modeling of wind turbines (WTs) is essential for assessing the small-signal stability of power systems with high penetration of renewable energy. Existing approaches face a fundamental trade-off: physics-based “white-box” models require proprietary manufacturer parameters that are rarely disclosed, while purely data-driven “black-box” models often lack physical interpretability and exhibit poor generalization under unseen operating conditions. To address this gap, this paper proposes a gray-box framework—the Physics-Informed Hybrid Model (PIHM)—that integrates a simplified physical impedance branch with a Bidirectional Long Short-Term Memory (Bi-LSTM) network in a novel parallel architecture. The physical branch, systematically parameterized via a constrained phase-error minimization method, captures the dominant baseline dynamics and decouples the learning task, allowing the Bi-LSTM to focus exclusively on the complex nonlinear residual. The framework is validated on a high-fidelity simulation platform of a doubly fed induction generator (DFIG) wind farm. Quantitative results demonstrate that the PIHM achieves an average coefficient of determination (R2) of 0.989 and a mean squared error (MSE) of 1.24×10−4 on unseen test data, while producing smooth, physically consistent impedance profiles that generalize across four distinct wind speed conditions. These results establish the PIHM as a reliable, parameter-free tool for impedance-based stability analysis of modern wind power systems.