Investigating the complex separated flows in lateral inlet/outlets of pumped-storage power stations(PSPS) is crucial for optimizing their design to ensure safe and efficient operation. In this study, Large Eddy Simulations (LES) are employed to reveal the relationship between turbulence intensity and the distribution of coherent structures in separated flows, as well as the evolution characteristics of hairpin vortices. The flow separation is notably influenced by the vertical diffusion angles α, which causes recirculation zones at the top of the inlet/outlet, leading to significant local flow velocities at the trash racks and increasing the risk of flow-induced vibration damage. Areas of high turbulence intensity exist at the top and bottom of the core flow, caused by the propagation of corresponding streams of vortical flow, which is identified as the primary cause of head loss in the inlet/outlet. Based on the average turbulence intensity, the inlet/outlet can be divided into zones of sharp turbulence increase, high turbulence intensity, and decreasing turbulence intensity. The vortical flow mainly includes three types of coherent structures: attached vortices, hairpin vortices, and quasi-streamwise vortices. Among these, the frequency of top hairpin vortices and the growth angle of hairpin vortex packets are highly susceptible to α. The growth direction of hairpin vortex packets closely aligns with the direction of turbulence intensity propagation. These findings contribute to optimizing the design of inlet/outlet of PSPS.