Equilibrium points and stability of synchronous machine systems

TL;DR

This paper analyzes equilibrium points and stability in single and two-machine synchronous systems, revealing polynomial conditions for equilibrium and assessing stability through Lyapunov and eigenvalue methods.

Contribution

It derives polynomial equations characterizing equilibria and applies stability analysis techniques to understand system behavior under various parameters.

Findings

Multiple equilibria exist in both systems.

Parameter variations significantly affect stability.

Eigenvalue analysis confirms local stability conditions.

Abstract

This paper investigates equilibrium points and stability in two synchronous machine configurations: (i) a single generator with an impedance load and (ii) two interconnected machines with co-located loads. We consider both abc and dq reference frames to show that the equilibrium condition reduces to a cubic polynomial in the single-machine case and to an 18th- degree polynomial in the two-machine case. For the single-machine system, Lyapunov stability analysis and linearization based stability analysis are carried out. For the two-machine system, local stability is assessed through linearization and eigenvalue analysis. Illustrative examples confirm the existence of multiple equilibria and illustrate the impact of parameter variation on stability. Our results provide insight into the stability of synchronous machine systems.