Stability and sensitivity characteristic analysis for the hydropower unit considering the sloping roof tailrace tunnel and coupling effect of the power grid

This paper focuses on the stability and dynamic characteristics of the coupled system of nonlinear hydraulic turbine regulating system (HTRS) and power grid (PG). By establishing a nonlinear mathematical model considering the downstream surge chamber and sloping roof tailrace tunnel, the coupling effect and influence mechanism between the hydropower station and power grid are revealed. First, with regard to the coupled system, HTRS considering downstream surge chamber and sloping roof tailrace tunnel and PG model is established. Then, dynamic performance of the coupled system is investigated based on the nonlinear mathematical model as well as Hopf bifurcation theory and validated by numerical simulation. Meanwhile, the impact mechanism of HTRS and PG is revealed by investigating dynamic characteristics. In addition, stability is studied by using eigenvalue method according to the Jacobian matrix of the coupled system. Finally, parameter sensitivity is investigated to quantify parameter effects on system performance. The experimental results indicate that bifurcation line divides the whole proportional-integral adjustment coefficient plane into two parts and the region at the bottom of bifurcation line is stability region. HTRS and PG possess a coupling effect on stable domain and dynamic properties of the coupled system. The variation of HTRS parameters is most significant for the coupled system, especially for the inertia time constant of the hydraulic turbine unit and penstock flow inertia time constant.