Chaotic behavior of turbine regulating system for hydropower station under effect of nonlinear turbine characteristics

Abstract

This paper studies the chaotic behavior of turbine regulating system (TRS) for hydropower station under effect of nonlinear turbine characteristics (NTC). Firstly, the nonlinear fourth-order state equation that describes the dynamic behavior of TRS under effect of NTC is established and verified. Then, the chaotic behaviors of TRS, i.e. existence of chaotic motion and path to chaotic motion, are studied. The effects of sensitivity parameters on the chaotic behavior of TRS are analyzed. Finally, the effect mechanism of NTC on chaotic behavior of TRS is revealed. The guidance for practical applications is clarified. The results show that, with the change of governor parameters, the dynamic behavior of TRS transforms among damped oscillation, persistent oscillation, frequency division and chaos phenomenon. The chaotic motion only appears under the particular value ranges of governor parameters. The path to chaotic motion of TRS is period doubling bifurcation. The chaotic motion is more likely to appear when the stability of TRS is worse. The reasonable selection of sensitivity parameters can eliminate or weaken the chaotic motion. The chaos phenomenon is caused by the nonlinear speed characteristics (NSC), not the nonlinear head characteristics. The effect of NSC is related to the values of governor parameters.