Fast–slow dynamic behaviors of a hydraulic generating system with multi-timescales

Hydraulic generating systems are widely modeled in the literature for investigating their stability properties by means of transfer functions representing the dynamic behavior of the reservoir, penstock, surge tank, hydro-turbine, and the generator. Traditionally, in these models the electrical load is assumed constant to simplify the modeling process. This assumption can hide interesting dynamic behaviors caused by fluctuation of the load as actually occurred. Hence, in this study, the electrical load characterized with periodic excitation is introduced into a hydraulic generating system and the responses of the system show a novel dynamic behavior called the fast–slow dynamic phenomenon. To reveal the nature of this phenomenon, the effects of the three parameters (i.e., differential adjustment coefficient, amplitude, and frequency) on the dynamic behaviors of the hydraulic generating system are investigated, and the corresponding change rules are presented. The results show that the intensity of the fast–slow dynamic behaviors varies with the change of each parameter, which provides reference for the quantification of the hydraulic generating system parameters. More importantly, these results not only present rich nonlinear phenomena induced by multi-timescales, but also provide some theoretical bases for maintaining the safe and stable operation of a hydropower station.