Analytical Inertia Identification of Doubly Fed Wind Farm with Limited Control Information Based on Symbolic Regression

The integration of large-scale wind power clusters significantly reduces the inertia level of the power system, increasing the risk of frequency instability. Accurately assessing the equivalent virtual inertia of wind farms is critical for grid stability. Addressing the dual bottlenecks in existing inertia assessment methods, where physics-based modeling requires full control transparency and data-driven approaches lack interpretability for inertia response analysis, thus failing to reconcile commercial confidentiality constraints with analytical needs, this paper proposes a symbolic regression framework for inertia evaluation in doubly fed wind farms with limited control information constraints. First, a dynamic model for the inertia response of DFIG wind farms is established, and a mathematical expression for the equivalent virtual inertia time constant under different control strategies is derived. Based on this, a nonlinear function library reflecting frequency-active power dynamic is constructed, and a symbolic regression model representing the system’s inertia response characteristics is established by correlating operational data. Then, sparse relaxation optimization is applied to identify unknown parameters, allowing for the quantification of the wind farm’s equivalent virtual inertia. Finally, the effectiveness of the proposed method is validated in an IEEE three-machine nine-bus system containing a doubly fed wind power cluster. Case studies show that the proposed method can fully utilize prior model knowledge and operational data to accurately assess the system’s inertia level with low computational complexity.