In a small power grid, frequency stability is one of the most important issues. The hydro-turbine and its speed governor model directly affect the accuracy of frequency stability results in a high hydro-ratio power grid. To examine this issue, the frequency dynamic characteristics of a power grid using ideal, operation point change and transfer coefficient models are compared and analyzed. Based on the transfer function of hydropower units, the oscillation frequency and damping characteristics of different water head and units with different output are quantitatively analyzed. Through transient simulation, the frequency oscillation characteristics of different models at different operating points of the unit are studied. Finally, some suggestions are made for a turbine simulation model suitable for engineering calculation. This work is supported by the National Key Research and Development Program of China (No. 2018YFB0905200).