Combined effect of upstream surge chamber and sloping ceiling tailrace tunnel on dynamic performance of turbine regulating system of hydroelectric power plant

Highlights: • Nonlinear mathematical model and Hopf bifurcation analysis of turbine regulating system are presented. • Dynamic performance of turbine regulating system under 0.5 times Thoma sectional area is analyzed and a novel dynamic performance is revealed. • Relationship between two bifurcation lines and wave superposition is studied. • Combined effect mechanisms of upstream surge chamber and sloping ceiling tailrace tunnel on stability are revealed and optimization methods are proposed. - Abstract: Based on the nonlinear mathematical model of the turbine regulating system of hydroelectric power plant with upstream surge chamber and sloping ceiling tailrace tunnel and the Hopf bifurcation theory, this paper firstly studies the dynamic performance of the turbine regulating system under 0.5 times Thoma sectional area of surge chamber, and reveals a novel dynamic performance. Then, the relationship between the two bifurcation lines and the wave superposition of upstream surge chamber and sloping ceiling tailrace tunnel is analyzed. Finally, the effect mechanisms of the wave superposition on the system stability are investigated, and the methods to improve the system stability are proposed. The results indicate that: Under the combined effect of upstream surge chamber and sloping ceiling tailrace tunnel, the dynamic performance of the turbine regulating system of hydroelectric power plant shows an obvious difference on the two sides of the critical sectional area of surge chamber. There are two bifurcation lines for the condition of 0.5 times Thoma sectional area, i.e. Bifurcation line 1 and Bifurcation line 2, which represent the stability characteristics of the flow oscillation of "penstock-sloping ceiling tailrace tunnel" and the water-level fluctuation in upstream surge chamber, respectively. The stable domain of the system is determined by Bifurcation line 2. The effect of upstream surge chamber mainly depends on its sectional area, while the effect of the sloping ceiling tailrace tunnel mainly depends on the sectional area of surge chamber, type of load disturbance and ceiling slope angle. When the stable domain is determined by Bifurcation line 1, the combined effect of upstream surge chamber and sloping ceiling tailrace tunnel on stability equals to the linear superposition of their own effects play alone. When the stable domain is determined by Bifurcation line 2, the only way to improve the system stability is to increase the sectional area of upstream surge chamber.