Fast-slow bursting behaviors of hydroelectric governing system with double periodic excitations

Abstract

ABSTRACT In this article, we integrate the nonelastic water column model of the hydro-turbine with the third-order nonlinear generator model. Further, we introduce the periodic functions of the hydraulic derivative coefficient and the electric field voltage. Based on the novel integrated nonlinear mathematical model of the hydroelectric governing system and the double periodic excitations claimed from the fast-slow analysis method, the fast-slow bursting behaviors of the system are found. The nonlinear dynamic behaviors of the system regarding the derivative gain, excitation frequency, and excitation amplitude are illustrated via bifurcation diagrams, time waveforms, phase trajectories, and power spectrums. The results show that the governing system sustains distinct kinds of nonlinear dynamic behaviors depending on the sensitive parameter values. The system can escape from the fast-slow bursting phenomena when grows larger. The increase of leads the system to the stable state. However, the increase of leads the system to the robust fast-slow bursting state. Finally, the analytical method and the results of this article provide principal references for the sensitive parameter setting to guard the hydroelectric governing system from the fast-slow bursting behaviors and ensure the safe and stable operation of hydroelectric power stations.