The dynamic characteristics of the shafting and hydro-turbine governing system (HTGS) of hydropower units (HU) have not been revealed

which restricts the optimal control of HU regulation. This paper develops a nonlinear mathematical model for a shafting-HTGS coupling system in different operating modes

and examines its nonlinear dynamic response characteristics. First

the Hopf bifurcation theory is used to analyze the stable region and bifurcation characteristics of the HTGS. Then

the time-frequency dynamic response characteristics of this coupling system are simulated and analyzed for its different operating modes. The results show that supercritical Hopf bifurcation exists in HTGS of both the isolated network and grid-connected HU

and the stability region of the governor parameter under the grid-connected HU is significantly larger than that of the isolated network HU. The HTGS frequency dynamic response of the HU and the power grid in the grid-connected mode have multi-frequency characteristics

and shafting vibration causes the dynamic response of the surge tank water level to ultra-low frequency oscillation (ULFO). The dynamic response overshoot of the grid-connected HU is significantly larger than that of the isolated HU

but its adjustment time is shorter. The shafting vibrations of isolated and grid-connected HUs are multi-frequency quasi-periodic

but the dynamic characteristics of shafting vibrations of the isolated HU are more complex.