Abstract
A nonlinear mathematical model of hydraulic turbine regulating system is applied to describe hydropower stations with upstream and downstream surge chambers. This model features saturation nonlinearity including pipeline system and turbine regulating system used in stability analysis. First, the existence conditions and direction of Hopf bifurcation are obtained. Second, based on the algebraic criteria for the occurrence of Hopf bifurcation, the stability domain is drawn in a coordinate system, where the proportional gain Kp is the abscissa and the integral gain Ki is the ordinate. Third, the nonlinear dynamic behaviour of a regulating system with different state parameters are analyzed, and the variations of the system stability around the two sides of the bifurcation point are numerically calculated. Based on this work we conclude that the Hopf bifurcation of system is supercritical. The bifurcation parameters that are far from the bifurcation point would be advantageous to the rapid system regulation needed to sustain equilibrium. Furthermore, it is established that using a PID controller is more conducive to stability than a PI controller. The unit stability regulation gets worse by taking into account the saturation nonlinearity.
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