An Investigation into the Primary and Subharmonic Resonances of the Swing Equation

A study is conducted to obtain a deeper insight into the primary and subharmonic resonances of the swing equation. The primary resonance, which can result in increased oscillatory responses, voltage instability, and potential system collapse, happens when the external disturbance frequency coincides with the natural frequency of the system. Subharmonic resonance occurs when the disturbance frequency is an integer fraction of the natural frequency, leading to low-frequency oscillations and possible equipment damage. The purpose of this study is to provide an extension of the existing literature of the effects of primary resonance and further provide a thorough understanding of subharmonic resonance on the stability of a certain power system paradigm. Motivated by the rich nonlinear dynamical behaviour exhibited by this evergreen model, analytical and numerical techniques are employed to examine the underlying principles, creating an efficient control solution for this resonant-related problem. The main objective of this research is to provide a comprehensive understanding of the primary and subharmonic resonances considering the dynamical and bifurcational behaviour of the underlying swing equation, whereby both analytical and numerical techniques are employed, allowing for an identification of certain precursors to chaos that may lead and cater for the safe operation of practical problems.