Transient Energy of an Individual Machine PART III: Newtonian Energy Conversion

Abstract

In this third paper, the fundamental mechanism of individual-machine transient stability is explained through Newtonian mechanics. The original Newtonian system with variant gravity is developed. This system is formed by a ball and the Earth. It is found that the Newtonian energy conversion strictly holds inside the system, and the equal area criterion can be considered a reflection of the Newtonian work. Based on these features, the stability characterizations of the system are given. Then, the original Newtonian system is extended to a generalized Newtonian system with multiple balls. It is found that this generalized Newtonian system can be decomposed into each two-ball-based subsystem, and the Newtonian energy conversion inside each subsystem is unique and different. This decomposition also ensures the independent parallel stability characterization of the generalized system. Finally, the strict mappings between Newtonian system stability and individual-machine transient stability are systematically analyzed. All these strict mappings fully reveal that the theoretical foundation of the individual-machine transient stability should be Newtonian mechanics.