Abstract: As the traditional synchronous generators are gradually replaced by renewable energy generators, the inertia of the power system is constantly reduced, and the temporal-spatio inertia evaluation is more and more important to ensure the safe and stable operation of the system. Firstly, the temporal-spatio inertia perception method of global power grid based on adaptive variable-order fitting of second-order penalty function is proposed. Secondly, the rate of change of frequency and power change of each spatial node of the system are accurately estimated based on the phasor measurement unit（PMU）. The second-order penalty function is adopted for the preprocessing of PMU monitoring data and the adaptive variable-order fitting is applied to the processing process of each segment of the fitting data. Finally, through the combination of the two methods, the temporal-spatio perception of the generalized node inertia of the power system can be realized. The accuracy and applicability of the proposed method for the temporal-spatio inertia evaluation under the condition of large or small disturbances are verified through the simulation case analysis.