Abstract: Aiming at the problem that the traditional inertia demand assessment method is difficult to accurately describe the space-time dynamic change characteristics of the system inertia demand caused by the variable operation mode of the power system with high randomness, we propose a new power system inertia demand assessment method in which the space-time characteristics and multi index constraints are taken into consideration. Firstly, by analyzing the influencing factors of system inertia demand, a frequency response model of power system considering new energy penetration and virtual inertia is established.Secondly, based on the traditional frequency response index, the recovery frequency constraint is introduced to establish the inertia demand evaluation model. Then, the influence of system parameters and node location on the inertia demand in time and space is taken into consideration, and the optimization method is used to dynamically evaluate the inertia demand of the system in different scenarios. Finally, the effectiveness and accuracy of the proposed method are verified by the example analysis of the traditional power system and the renewable energy generation system based on virtual inertia.