Abstract: Influenced by the nonlinear dynamics of mathematical models found in power systems, an analysis of the dynamical behaviour of the coupled swing equation is performed. The coupled formulation explains the interactions between interconnected synchronous machines, which play a critical role in modern power systems. This paper examines analytically and numerically the emergence and evolution of oscillatory periodic solutions under primary resonance. As the control parameter is altered, the system undergoes a cascade of period-doubling bifurcations, which leads to loss of stability and the onset of complex dynamical behaviour can be observed. Phase portraits, time series and Poincaré maps are used to characterise the transition between different dynamical patterns to identify the precursors to instability. A thorough understanding of the system’s behaviour shows valuable insights into bifurcation with the appearance of the initial period doubling phenomena, depicting early indicators of adverse effects that can occur within an interconnected power system.

Keywords: nonlinear dynamics, power system, swing equation, coupling, bifurcation, chaos

Pages: 25-34