Addressing the Primary and Subharmonic Resonances of the Swing Equation

A research investigation is undertaken to gain a more comprehensive understanding of the primary and subharmonic resonances exhibited by the swing equation. The occurrence of the primary resonance is characterised by amplified oscillatory reactions, voltage instability, and the possibility for system failure. The phenomenon of subharmonic resonance arises when the frequency of disturbance is a whole-number fraction of the natural frequency. This results in the occurrence of low-frequency oscillations and the potential for detrimental effects on equipment. The objective of this study is to expand upon the current literature regarding the impacts of primary resonance and enhance comprehension of subharmonic resonance in relation to the stability of a specific power system model. The analytical and numerical tools are utilised to investigate the fundamental principles of this resonant-related problem, aiming to provide an effective control solution. This choice is driven by the model’s complex nonlinear dynamical behaviour, which offers valuable insights for further analysis. This analysis includes the Floquet Method, the Method of strained parameters, and the concept of tangent instability in order to provide an extension to existing literature relating to primary and subharmonic resonances, taking into account the dynamic and bifurcation characteristics of the swing equation. This objective will be achieved through the utilisation of both analytical and numerical methods, enabling the identification of specific indicators of chaos that can contribute to the safe operation of real-world scenarios.