Newtonian Mechanics Based Transient Stability PART VI: Machine Transformation

TL;DR

This paper analyzes machine transformations in transient stability analysis, showing that trajectory correction enables valid transformation from individual to equivalent machines, while energy correction is physically meaningless.

Contribution

It introduces two types of machine transformations based on energy and trajectory corrections, clarifying their validity and limitations in transient stability analysis.

Findings

Trajectory correction enables valid machine transformation.

Energy correction is mathematically valid but physically meaningless.

Simulation confirms trajectory correction as the feasible approach.

Abstract

This paper focuses on the transformations from the individual machine to the equivalent machine through the "correction" perspective of the inner-group machine. The machines are first classified as the real machine with equation of motion and the pseudo machine without equation of motion. Then, it is clarified that both individual machine and equivalent machine are real machines, while the superimposed machine is a pseudo machine. Based on the classifications of the machines, two types of machine transformations are provided. The two types of machine transformations are based on the "energy correction" and "trajectory correction" of the inner-group machine, respectively. For the energy correction case, it is clarified that the trajectory transformation completely fails, while the energy transformation mathematically holds yet it is physically meaningless. For the trajectory correction case, it is clarified that both energy transformation and trajectory transformation are established. The reason is that each trajectory-correction based individual machine has the same equation of motion, i.e., the motion of the equivalent Machine-CR. Simulation results show that the machine transformation from the individual machine to the equivalent machine can be realized only through trajectory correction.