Nonlinear modeling and stability analysis of hydro-turbine governing system with sloping ceiling tailrace tunnel under load disturbance. (December 2015)

• Record Type: Journal Article
• Authors: Guo, Wencheng; Yang, Jiandong; Wang, Mingjiang; Lai, Xu
• Is Part Of: Energy conversion and management. Volume 106(2016)
• Page Start: 127
• Page End: 138
• Publication Date: 2015-12
• Subjects: Hydropower station -- Sloping ceiling tailrace tunnel -- Hydro-turbine governing system -- Nonlinear modeling -- Stability -- Load disturbance -- Hopf bifurcation; Direct energy conversion -- Periodicals; Energy storage -- Periodicals; Energy transfer -- Periodicals; Énergie -- Conversion directe -- Périodiques; Direct energy conversion; Periodicals; 621.3105
• DOI: 10.1016/j.enconman.2015.09.026
• Languages: English
• ISSNs: 0196-8904

Abstract

Highlights: Novel nonlinear mathematical model of hydro-turbine governing system is proposed. Hopf bifurcation analysis on the governing system is conducted. Stability of the system under load disturbance is studied. Influence of four factors on stability is analyzed. Optimization methods of improving system stability are put forward. Abstract: In order to overcome the problem of nonlinear dynamics of hydro-turbine governing system with sloping ceiling tailrace tunnel, which is caused by the interface movement of the free surface-pressurized flow in the tailrace tunnel, and the difficulty of analyzing the stability of system, this paper uses the Hopf bifurcation theory to study the stability of hydro-turbine governing system of hydropower station with sloping ceiling tailrace tunnel. Firstly, a novel and rational nonlinear mathematical model of the hydro-turbine governing system is proposed. This model contains the dynamic equation of pipeline system which can accurately describe the motion characteristics of the interface of free surface-pressurized flow in sloping ceiling tailrace tunnel. According to the nonlinear mathematical model, the existence and direction of Hopf bifurcation of the nonlinear dynamic system are analyzed. Furthermore, the algebraic criterion of the occurrence of Hopf bifurcation is derived. Then the stability domain and bifurcation diagram of hydro-turbine governing system are drawn by the algebraic criterion, and the characteristics of stability under different state parameters are investigated. Finally, the influence of step load value, ceiling slope angle and section form of tailrace tunnel and water depth at the interface in tailrace tunnel on stability are analyzed based on stable domain. The results indicate that: The Hopf bifurcation of hydro-turbine governing system with sloping ceiling tailrace tunnel is supercritical. The phase space trajectories of characteristic variables stabilize at the equilibrium points and stable limit cycles when the system state parameter point locates in the stable domain and unstable domain, respectively. Under negative disturbance and positive disturbance, the effect laws of step load value, tailrace tunnel slope angle and water depth in tailrace tunnel are inverse. Tailrace tunnel section form has significant influence on the stability under negative disturbance, while it has little influence on the stability under positive disturbance.