Abstract: Part I of this paper introduces the multi-timescale analysis and control theory of power electronics hybrid systems, while its applications are further illustrated in Part Ⅱ. First, the opportunities and challenges of power electronic technologies are analyzed from the aspect of the actual demands of high-power and large-scale converters. Secondly, the discreet state event-driven (DSED) modeling and simulation method based on the numerical convex lens theory is introduced and analyzed. Furthermore, the multi-timescale control methods including active control and energy balancing control approaches are presented. These simulation and control methods are applied to a megawatt multi-port multi-functional power electronics transformer (PET) case to show their efficiency. Finally, the future developments of the multi-timescale analysis and control methods are prospected.