Pumped-storage power stations (PSPSs) are vital for grid stability, yet pump-turbines (PTs) operating in the S-shaped region often induce severe hydraulic instability. To reveal the mechanism of these self-excited oscillations, this study establishes a nonlinear mathematical model based on rigid water column theory and a cubic polynomial approximation of the PT’s nonlinear characteristics. Both analytical derivations and numerical simulations were conducted. Analytical results indicate that, in the absence of surge tanks, self-excited oscillations occur when the PT’s negative hydraulic impedance modulus exceeds the pipeline impedance. With a single surge tank, the system behaves analogously to the Van der Pol oscillator, exhibiting oscillations that converge to a stable limit cycle governed by system parameters. Numerical simulations for a dual-surge-tank system further reveal that, due to initial negative damping, the PT transitions to alternative stable equilibria. Crucially, the transition direction is governed by the polarity of the initial disturbance: negative perturbations lead to the regular turbine region, while positive ones lead to the reverse pump region. Additionally, pipe friction causes the steady-state discharge to deviate slightly from the theoretical static value, with deviations remaining below 2.96%. This work provides a theoretical basis for stability prediction in PSPSs.
Mao et al. (Wed,) studied this question.
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