Stability analysis and estimation of domain of attraction for hydropower station with surge tank

Abstract

The surge tank is extensively used pressure reduction facility in the hydropower station, and its stability of the water level oscillation (WLO) has always been a significant issue in academia and engineering. The stability of the WLO in the nonlinear hydropower station with surge tank (HSST) system is closely related to the external disturbance. This paper aims to study the stability and domain of attraction in the HSST system. Firstly, the nonlinear mathematical model of the HSST system is established. The critical stable cross-sectional area (CSCA) of surge tanks is investigated based on Lyapunov's first method. Subsequently, the estimation of domain of attraction is conducted based on Lyapunov's second method. Finally, the global asymptotic stability of the HSST system under Thoma stable area is analyzed. of surge tanks. The results show that when the surge tank area is smaller than Thoma stable area, the HSST system is unstable, so the CSCA is large than Thoma stable area. When the surge tank area is larger than Thoma stable area, the HSST system is locally asymptotically stable. The general method for constructing Lyapunov function is presented. The domain of attraction of the WLO is drawn, which defines the disturbance range of asymptotic stability of the HSST system. The domain of attraction rises with the increase of the surge tank area. When the surge tank area is taken as Thoma stable area, the system is not asymptotically stable under any disturbance. The proposed conclusions can provide theoretical reference for the design of surge tanks in practical engineering.