For the sake of studying the stability of the pumped storage power station, the authors focused on the mathematical modelling of the pump-turbine governing system (PTGS) at pump mode. First of all, six transfer coefficients were introduced into the model of the pump-turbine. Furthermore, utilising the internal characteristics formulas, they obtained six analytical expressions of the transfer coefficients at pump mode. Considering the elastic water-hammer model of the penstock with hydraulic friction and the second-order model of the generator, a non-linear model of the PTGS was proposed. On the basis of a real case, they obtained the curve of bifurcation points of the system by using the stability theorem, and verified the correctness of the theoretical analysis results from numerical experiments. Moreover, the stable domains of the proportional-integralderivative parameters k p and k d were identified and the non-linear dynamic behaviours of the governing system were studied. Finally, these methods and analytic results could help them improve the safety operation and performance of the pumped storage power station.
A fast-slow coupled model of the hydro-turbine governing system (HTGS) is established by introducing frequency disturbance in this paper. Based on the proposed model, the performances of two time scales for bursting oscillations in the HTGS are investigated and the effect of periodic excitation of frequency disturbance is analyzed by using the bifurcation diagrams, time waveforms and phase portraits. We find that stability and operational characteristics of the HTGS change with the value of system parameter k d . Furthermore, the comparative analyses for the effect of the bursting oscillations on the system with different amplitudes of the periodic excitation a are carried out. Meanwhile, we obtain that the relative deviation of the mechanical torque m t rises with the increase of a. These methods and results of the study, combined with the performance of two time scales and the fast-slow coupled engineering model, provide some theoretical bases for investigating interesting physical phenomena of the engineering system.
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