The stability of power system operation is often related to the access of the converter, and the time scale of a converter device is not consistent with the traditional power system. In order to reveal the interaction of stability occuring between devices with different time scales, a calculation and analysis method of a stability bound is established. This paper considers a converter connecting to a power system, and based on singular perturbation theory, establishes an analysis model of multi-time scale system stability bound. A theoretical method for obtaining the system stability bound is given, and the method is proved by mathematical theory. It uses Matlab time domain simulation to carry out quantitative analysis and verification. The results show that the system with fast and slow variables can accurately describe the stability and dynamic response characteristics. Singular perturbation analysis can accurately describe the stability bound of a power system composed of variables with different time scales. In addition, the numerical simulation results validate the accuracy of the proposed model and stability bound analysis method.