With the large-scale grid connection of power electronic power sources, the new power system（NPS）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 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, a minimum inertia estimation method of the power system considering frequency response characteristics is proposed. 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 the improvement measures when the system inertia is insufficient are added to calculate the minimum inertia of the NPS under the multi-resource participation in FR. Finally, the feasibility of the NPS minimum inertia demand estimation method proposed is verified by using simulation software, which provides a guiding basis for the rationalized allocation of NPS FR resources.