Analysing the Swing Equation using MATLAB Simulink for Primary Resonance, Subharmonic Resonance and for the case of Quasiperiodicity

Abstract

The swing equation plays a significant role in the analysis of stability and frequency response various power systems and mechanical systems. MATLAB Simulink simulates and analyses different systems, including synchronous generators with various excitation methods. This research aims to study the swing equation by modelling the system in Simulink. Swing equation analysis can be applied to tackle power instabilities in the electrical grid, to avoid power outages by monitoring the small disturbances that occur within the system. This paper shows the time series, phase portraits, and Poincar´e maps generated using data from the simulated model. It highlights the occurrence of period doublings which lead to loss of synchronisation and the resulting instability in the system that descends into chaos when the variables are changed in the Simulink model. The integrity diagrams were also identified for primary resonance, subharmonic resonance, and quasiperiodicity, offering valuable information to understand the system’s nonlinear behaviour. Using the swing equation in MATLAB Simulink provides a robust tool for analysing, simulating, and optimising systems. Hence this study provides an enhanced understanding of the system’s behaviour in Simulink for primary resonance, subharmonic resonance and for the case of quasiperiodicity. Additionally, it validates the analytical and numerical findings from prior works by the same authors.