Analytical Inertia Identification of Doubly Fed Wind Farm with Limited Control Information Based on Symbolic Regression  
[PERSON]  
1 Central China Branch of State Grid Corporation of China, Wuhan 430077, China; [EMAIL_ADDRESS] (M.S. ); [EMAIL_ADDRESS] (M.Z.) [PERSON]  
2 State Key Laboratory of Disaster Prevention and Reduction for Power Grid, School of Electrical and Information Engineering, Changsha University of Science and Technology, Changsha 410114, China; [EMAIL_ADDRESS] (Y.L. ); [EMAIL_ADDRESS] (X.S. ); 22105010925@csust. farms' equivalent virtual inertia under diverse control strategies [20; 21] has emerged as a pivotal enabler for deploying effective frequency stability countermeasures in low-inertia systems [22; 23]. A considerable number of researchers have investigated the inertia characteristics of wind farms, grounded in physical principles and data-driven methodologies. Ref. [24] formulated the voltage phase angle motion equation for DFIGs, thereby providing a representation of the equivalent virtual inertia of the wind farms. It has been noted that the equivalent virtual inertia of a wind farm is a variable quantity that changes over time, and its magnitude is associated with the control parameters employed; Ref. [25] represented the equivalent inertia time constant of a wind turbine as a function of the wind rotor inertia, the initial operating point of the turbine, and rotor speed variations, while the equivalent virtual inertia time constant is expressed as a piecewise linear function of wind speed. It also emphasizes that the wind farm inertia response is closely tied to the turbine's operating conditions. These studies derived the equivalent virtual inertia of wind farms from a physical mechanism perspective and further deepened our understanding of wind farm equivalent virtual inertia. Nevertheless, these methods require precise knowledge of each wind turbine's control parameters and structure, making them challenging to apply when the information is unavailable. Recent advancements in wide-area measurement technologies and artificial intelligence algorithms have facilitated the widespread adoption of data-driven methodologies for assessing wind farm inertia [26; 27; 28]. In the process of selecting an identification model, the detailed ontology-based modeling approach based on physical mechanisms establishes explicit mathematical relationships between inertial response characteristics and control parameters through the integration of prior knowledge, providing a theoretical foundation for quantifying equivalent virtual inertia characteristics in wind farms. Studies such as ref. [29] utilized the Kalman filter to identify the control parameters within wind turbine structures, integrating this with inertia calculations to evaluate the inertia of the wind farm. Ref. [30] derived the active power-frequency transfer function of wind power based on the physical connections of various control modules within the wind farm. Using measured active power-frequency curves, the parameters of the transfer function are identified through the least squares method, thereby obtaining the equivalent inertia coefficient. Due to commercial confidentiality, manufacturers of renewable energy equipment typically provide only black-box models, which delineate input-output characteristics. The internal control structure is generally considered proprietary and is not readily accessible. Consequently, the development of a polynomial model to delineate the input-output relationship is a widely adopted methodology for addressing this concern. Ref. [31] established a polynomial model based on measured active power-frequency disturbance data and, combined with the swing equation principle, derived the equivalent virtual inertia of the wind farm. Ref. [32] developed a controlled autoregressive model, employing recursive least squares to estimate the time-varying inertia of DFIGs.