With the large-scale grid connection of power electronic power sources, the power system gradually exhibits the characteristics of ‘low inertia’, and the indexes of frequency characteristics are getting closer to the safety critical value, which seriously affects the frequency safety of the system operation. To quantitatively analyze the minimum inertia requirement of the power electronic power system under the condition of multi-resource participation in frequency regulation (FR) when it is disturbed by active power, based on the improved frequency response model of the multi-machine system, this paper proposes a minimum inertia estimation method of the power system considering the frequency response characteristics. The theoretical inertia of each FR unit is represented in the form of rotor kinetic energy, and the calculated inertia of the power system is quantified based on the Rate of Change of Frequency (RoCoF). The sliding window technique is used to select the data set with the smallest variance and obtain the final calculated inertia of the system. The proposed estimation method takes the initial RoCoF, the maximum frequency deviation, and the steady-state frequency deviation as the frequency change constraint indicators, and adds the minimum inertia improvement measures to reduce the demand for the minimum inertia. Finally, the PSD-BPA software is used to verify the accuracy of the proposed model. And based on the improved frequency response model of the multi-machine system, MATLAB/Simulink is used to verify the proposed minimum inertia estimation method.