Abstract: The existing system frequency response（SFR） model considers the synthetic inertia（SI） control of wind power in a relatively simple way, and does not adequately consider the wind speed differences in the wind farm and the rotor speed recovery stage, which is difficult to accurately reflect the system frequency characteristics. Therefore, an extended SFR model is proposed.First, the mechanism of SI control of wind power is discussed. The interaction of the wind turbine speed and system frequency in the dynamic process after disturbance is analyzed. Then, based on the dynamic model of wind turbines, the transfer functions of wind turbine at the frequency regulation stage and the rotor speed recovery stage are derived by using the small signal linearization method, and the extended SFR model containing single equivalent wind turbine is built. For the wind farm with multiple wind speeds, a prediction-modification clustering method for wind turbines based on the critical wind speed and the wind speed similarity is proposed. The wind turbines at the same stage and with similar dynamics are divided into the same group for aggregation, and the extended SFR model with multiple equivalent generators is constructed. Finally, the extended SFR model is applied in the frequency response calculation of the modified 10-generator 39-bus system. The simulation results show that the model better reflects the influence of wind power frequency regulation on frequency, and has high accuracy and high calculation speed.