Electromagnetic transient simulations for wind farms are crucial for analyzing multi-time-scale dynamic characteristics under fault conditions or weak damping scenarios. The traditional single-machine aggregation method

widely used for its simulation efficiency in large-scale wind farm analysis

faces issues with long parameter identification times and insufficient model detail

leading to poor multi-time-scale dynamic representation. This paper uses analytical optimization to propose a complete electromagnetic transient equivalent modeling method for large-scale doubly-fed induction generator (DFIG) clusters. This method constrains the detailed structure of wind turbines

creating a data-model hybrid gray-box equivalent model of the wind farm. It employs sparse relaxation regularization and a proximal gradient algorithm for analytical solving. The proposed method is compared with traditional single-machine aggregation methods under various wind turbine scales and parameter configurations and validated for both large and small disturbances in offshore wind farms transmitted via high-voltage direct current (HVDC). Case studies demonstrate that the proposed method has low computational complexity

requires minimal operational training data

accurately reflects the multi-time-scale dynamics of the original system

and maintains better stability in equivalent accuracy amidst changes in cluster parameters and structures compared to the traditional.