Abstract: With the large-scale integration of renewable energy generation, power systems are exhibiting characteristics such as power electronics dominance and low inertia. Consequently, the system frequency dynamic response intensifies, making the accurate calculation of the frequency nadir and the derivation of the full-process frequency expression critical issues in frequency security analysis. To address the shortcomings of traditional frequency equivalent models, which overlook the dynamic characteristics of renewable energy stations, and the insufficient generalization ability of artificial intelligence methods, this paper builds upon the open-loop model of the first-order equivalent governor frequency response (FASF) model. It introduces a generic frequency response model for renewable energy stations and improves the linear feedback input of the governor into a quadratic function form, thereby achieving the derivation of an analytical expression for the entire frequency variation process. Furthermore, the calculation results of the proposed model are compared and validated against PSCAD time-domain simulation results in terms of both frequency nadir calculation accuracy and frequency dynamic curve matching. Case studies are conducted under scenarios with varying inertia levels and renewable energy penetration rates. The results demonstrate that the proposed method significantly reduces computational complexity while ensuring calculation accuracy, enables fast online frequency calculation, and possesses good generalization ability and engineering applicability. The research findings can provide theoretical support for frequency security assessment and dispatch optimization of renewable energy power systems.