## 6 Conclusions  
This paper proposes a large-scale wind farm inertia identification method based on symbolic regression with limited control information, which effectively utilizes prior model knowledge and operational data to obtain a more physically interpretable and precise estimation of inertia. The method is validated by comparing the identified values with simulation results under varying wind speeds and control parameters, leading to the following conclusions:  
1. The frequency domain analytical expression for the equivalent inertia time constant of DFIG under different control strategies is derived based on the inertia response model and the definition of the inertia time constant. The results indicate that the equivalent virtual inertia of the wind farm is influenced by its intrinsic parameters, initial operating conditions, and the inertia control strategy and parameters;
2. The proposed sparse dynamic modeling method divides the DFIG control modules and constructs input-output nonlinear feature libraries based on prior knowledge. The SR3 identification algorithm is used to estimate the model parameters. The simulation results validate the method's effectiveness in evaluating the equivalent virtual inertia of wind farms in the IEEE three-machine nine-bus system, proving its feasibility and accuracy. 3. Compared to existing methods, the method proposed in this paper is capable of handling partially known or structurally opaque control components, which is critical in practical wind turbine systems, particularly when control structures and parameters are unknown or subject to commercial confidentiality constraints. The identified models retain a symbolic, interpretable form, unlike black-box neural networks. The sparse formulation promotes the compactness and physical relevance of the derived models. Future work will focus on extending the proposed method to larger and more complex power systems, particularly heterogeneous renewable energy systems, in order to assess their inertia characteristics and frequency support capabilities, thereby contributing to the stability and security of emerging grid environments. Moreover, in response to the  
Figure 11: Simulated and evaluated inertia values at different Tf levels. structural diversity of control strategies used in real-world wind power applications, the framework will be further applied for its applicability to other forms of inertia control, such as adaptive inertia control, coordinated synthetic inertia, manufacturer-specific variants and so on. Methodology, Investigation, Formal Analysis, Validation, Writing--Original Draft and Visualization, M.S. ; Investigation, Methodology, Validation and Formal analysis, Y.L. ; Conceptualization, Resources, Project administration, Writing--review and editing, Supervision and Funding acquisition, X.S. ; Investigation, Formal analysis and Validation, D.S. ; Investigation, Formal analysis, and Visualization, M.Z. ; Data Curation, Visualization and Investigation, D.G. ; Supervision, Y.C. All authors have read and agreed to the published version of the manuscript. This work was supported by the Science and Technology Project of Central China Branch of State Grid Corporation of China (Project Number: 52140024000C). Not applicable. The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author. We would like to express our heartfelt gratitude to the Central China Branch of the State Grid Corporation of China for their generous support of this research through their Technology Project (Project Number: 52140024000C). This work would not have been possible without their invaluable assistance and commitment to advancing technological innovation. We are deeply appreciative of their support, which has been instrumental in enabling us to pursue and accomplish this research. Authors [PERSON], [PERSON] and [PERSON] were employed by the company Central China Branch of State Grid Corporation of China.