Load shedding processes are widespread in hydropower stations, which has great influence on the safe and stable operation of the hydro-turbine governing system. In order to study the dynamic characteristics of the hydro-turbine governing system during the load shedding process, a novel nonlinear mathematical model of the hydro-turbine governing system is established considering the hydro-turbine system, the generator system and the governor system. In particular, a novel nonlinear mathematical model of the six hydro-turbine transfer coefficients is presented based on the definitions and hydro-turbine internal characteristics. After that, from the viewpoint of nonlinear dynamics and the practical engineering, the dynamic characteristics of the hydro-turbine governing system are investigated utilizing bifurcation diagrams, time series, Poincare maps, power spectrums and phase planes. Some meaningful results are found. The advantages of the novel nonlinear mathematical model are illustrated and commented in detail in comparison with the previous model. Finally, these models and analysis results will provide some theoretical references for the operation of hydropower stations in the load shedding transient.Energies 2018, 11, 1244 2 of 17 to optimizing the control of the HTGS. Based on the polynomial robust H ∞ optimization method, Eker [16] presented a robust single-input multi-output design approach for governors for speed control of hydro-turbines. Khodabakhshian and Hooshmand [17] put forward a new robust proportionalintegral-derivative (PID) controller for automatic generation control of hydro-turbine power systems, which is designed mainly based on a maximum peak resonance specification. Ren et al. [18] proposed an improved cascade control strategy for hydro-turbine speed governors, which can effectively decrease fluctuations of the rotational speed under non-Gaussian disturbance conditions in practical hydropower plants. Chen et al. [19] focused on designing the fractional-order PID controller using a chaotic non-dominated sorting genetic algorithm II for the HTGS, which has a better performance than traditional integer PID controllers. Zhang et al.[20] created a brand new non-linear predictive control method using the Takagi-Sugeno (T-S) fuzzy method and the generalized predictive control, which can govern a non-linear system more effectively. Chen et al.[21] established a new nonlinear mathematical model of the HTGS with a surge tank, and then, the nonlinear dynamical behaviors of the system in small fluctuation process were studied in detail. Guo et al. [22] studied the stability of the HTGS of the hydropower station with sloping ceiling tailrace tunnel utilizing the Hopf bifurcation theory, and also got the algebraic criterion of the occurrence of Hopf bifurcation. Xu et al. [23] built the Hamiltonian mathematical model of the multi-hydro-turbine governing system with a sharing common penstock under the excitation of stochastic and shock load, and then, discussed the stability of the system by comparing ...