To address the challenges posed by the connection of new energy sources to the grid, pumped storage power stations (PSPSs) are required to frequently engage in transient processes to maintain load balancing and regulate grid frequency. It remains difficult, however, to evaluate the transient characteristics of the hydraulic turbine governing system (HTGS) and shafting system because of the lack of suitable models. This study seeks to address this challenge by establishing a transient turbine model based on the surface-cluster method and the shafting system transient coupling model, accounting for hydraulic-mechanical-electrical factors. HTGS and shafting systems' dynamic response characteristics are investigated under two small oscillation processes and eleven closure laws of guide vanes (CLGVs). The findings reveal that the shafting system vibration increases with the load drop during small oscillation processes. Conversely, sudden load increases reduce shafting vibration and the change of vibration is related to the force of the blade. Moreover, the study identifies that under the fast-slow two-phase CLGV, the maximum relative head and rotor radial amplitude increase with decreasing guide vanes (GV) opening of the turning point, while the change in maximum relative speed is opposite. Under the slow-fast two-phase CLGV, the maximum head and speed increase with decreasing GV opening of the turning point, while the maximum radial amplitude of the rotor is the opposite. Finally, under all the three-phase CLGVs, the transient characteristics of the head, speed, and shafting vibration under close-close-close (CCC) CLGV are the best. The innovation of this paper is to provide a method to establish the transient coupling model of HTGS and shafting, and to study the stability and transient response characteristics of HTGU.