Analysis of a possible reason for oscillation phenomena in a diesel-generator set through catastrophe theory

In this paper, a possible reason for oscillation phenomena in a diesel-generator set is investigated through digital and analog network simulations. The nonlinear simulations of a swing equation show sudden deviations in the amplitude of rotor angle oscillations, provided that there exist periodic fluctuations of mechanical inputs to the generator unit. This kind of oscillation, different from the one that is identified in linear resonance, is thought to be caused by system nonlinearities and ill-combination of system parameters. The results of the analog simulations show the occurrence of bifurcation phenomenon in a electrical power mode. An approximate nonlinear model of the swing equation is found to hold the form of Duffing's equation. From the viewpoint of Duffing's equation, an instability assessment method is proposed using a catastrophe theory analogy.