LAUSR

Abstract This paper aims to analyze the nonlinear dynamic characteristics of hydro-turbine governing system with downstream surge tank and sloping ceiling tailrace tunnel and reveal their combined effect mechanism on stability. First, the nonlinear mathematical model of hydro-turbine governing system is presented. Second, the Hopf bifurcation theory is adopted, and the stability performances of hydro-turbine governing system under different sectional areas of downstream surge tank are analyzed and verified. Finally, the combined effect of downstream surge tank and sloping ceiling tailrace tunnel on stability is investigated and the design methods are proposed. The results indicate that: The dynamic response process of hydro-turbine governing system shows an obvious characteristic of wave superposition. Two types of bifurcation lines reflect the critical stability characteristics of the two subsystems and constitute the boundaries of the stable domain. The sloping ceiling tailrace tunnel cannot make an obvious change of the stability performances of the subsystem of penstock - hydro-turbine unit, but it has significant effect on the stability performances of the subsystem of downstream surge tank - sloping ceiling tailrace tunnel. The larger aspect ratio or smaller ceiling slope gradient results in better stability of the subsystem of downstream surge tank - sloping ceiling tailrace tunnel.