In the coming decades, the proportion of wind–solar energy in power system significantly increases, resulting to uncertainties of power fluctuation in abundant wind–solar energy regions. The flexibility operation of Pumped Storage Power Plants (PSPPs) has already been widely recognized to regulate wind–solar power fluctuations; however, less is known about the regulation reliability of the PSPP affected by them. It is a challenge, since various uncertainties exist during this regulation process. Here, a mathematical model with a solar–wind–hydro hybrid power generation system is adopted to investigate the regulation reliability of PSPP. The uncertainties and limitations of model parameters are considered during this process. Five regulation indexes, i.e., rise time, settling time, peak value, peak time and overshoot of the reactive power generator terminal voltage, guide vane opening and angular velocity, are extracted to evaluate the PSSP’s regulation quality. Finally, the PSPP reliability probability affected by parametric uncertainties is presented. The obtained results show that the inertia coefficient is the most sensitivity parameters for the settling time, peak value and peak time with sensitivity index 33.7%, 72.55% and 71.59%, respectively. The corresponding total contribution rate of the top 10 sensitive parameters are 74.45%, 93.45% and 87.15%, respectively. Despite some types of uncertainties not being considered, the results of this research are important for the regulation reliability evaluation of PSPPs in suppressing power fluctuations of wind and solar generation.