Exploration of Characteristic Equation Towards the Analysis of Dynamical Stability for Synchronous Generators through Swing Equation

This study reports a didactic approach on how to exploit the knowledge of the characteristic equations of any second-order system towards their stability analysis. To prove the efficacy of the method in industrial applications, the manuscript focuses on the stability study of synchronous generators. To obtain the future-ready characteristic equation, the dynamic equation of a synchronous generator is modeled via the swing equation. Literally, the swing equation describes the behavior of the rotor dynamics in the generator. By using the characteristic equation at hand, dominant parameters that affect the stability are identified. The analysis studies are then conducted to observe the stability through multifarious allowable parameters’ range that disturb the roots (or the poles) location of the equation. The outcome of this research shows that two dominant parameters, named synchronizing coefficient and per unit inertia constant, determine the damping ratio and natural frequency. As a result, these two parameters affect the stability and transient characteristics of synchronous generators.