With the grid-connection of large-scale new energy and other power electronic devices, the inertia level of power system is gradually reduced. Also the demand for rotational inertia of the system brings new changes, so the frequency support capability of the load side becomes more and more important. To solve the inertia problem, the frequency response characteristics of an induction machine are analyzed systematically. Based on small signal analysis, a modeling method for the induction machine in mechanical and electrical transient state is proposed, and the frequency response model of the power system is constructed in a way which takes the frequency response of the induction machine into account. Based on the in-depth analysis of the inertia characteristics of the new power system, and considering the frequency safety constraints such as frequency change rate, maximum frequency deviation and reserve capacity limit, the evaluation model of the minimum inertia of the power system is constructed and analysed by genetic algorithm. Finally, an example is simulated and analyzed on the Matlab and PSASP platform to verify the correctness and validity of the proposed frequency response model and the lowest inertia evaluation results. This work is supported by the National Key Research and Development Program of China (No. 2016YFB0900602).