Abstract: From the perspective of stability equivalence, nominal performance and robustness, the qualitative principles and quantitative evaluation index of stability criterion adaptation are proposed in Part Ⅰ. In addition, the adaptation of the existing stability criteria and the physical interpretation of instability corresponding to the suitable stability criterion are analyzed for the typical equipment in power system, such as synchronous machines, doubly-fed induction generators (DFIG) and converters in Part II. Thereby the stability classification of the renewable power system is discussed based on dominant output variable. Firstly, aiming at low-frequency and sub-synchronous oscillation/resonance (SSO/SSR) of synchronous machine, the rationality of the existing stability analysis methods and physical interpretation was verified by using the proposed evaluation index. Secondly, the proposed evaluation index was used to analyzed the oscillation of converters and DFIG, and the suitable stability criterion, derivation mechanism and dominant output variable werre further discussed. Finally, a novel idea of equipment stability classification based on physical mechanism and dominant output variables were proposed, which classifies equipment stability from the vector perspective into three categories: phase-dominated synchronous stability, amplitude-dominated voltage stability, and electrical resonance formed by their special combination. Issues such as the concept of wide-band oscillation, the distinction between equipment stability and system stability, and the extensibility of their classification were further explored.