Physical-Informed Detailed Aggregation of Wind Farm Based on Symbolic Regression: Structure, Solution and Generalizability

Detailed aggregation of wind farms can be beneficial for efficiently simulating and analyzing the dynamic interactional behaviors with power systems. However, methods like weighted aggregation and parameter identification are inefficient and inaccurate in depicting simultaneously long-term dynamic and electromagnetic time scales. The discrepancy between the aggre gated model and the real is not guaranteed. This paper proposes a detailed aggregation method based on symbolic regression. We first set up an electromagnetic aggregation structure of the wind farm considering the dominant dynamic mode, and then the regression form of the grey-box aggregation model based on parallel physical-informed constraints and operation data is established. Then, the model is solved based on analytical optimization using the sparse-relaxed-regularized method, and the generalizability of the solution is also proved based on prox-gradient descent principles. The proposed methodology is tested on a wind farm containing 5-30 DFIGs with parameter disparities under large and small disturbances in the time and frequency domain, then tested on an HVDC-connected system for further validation. Moreover, the sensitivity of the result toward training dataset quality is further analyzed. Results show that the proposed method has high computational efficiency with stable accuracy in grasping the multi-time-scale dynamics of the system under different cases.