The layout of one pipe with multiple units in a pumped storage station results in interference between each pumped storage unit, which hinders the safe and stable regulation of pumped storage units. In order to reveal the interaction characteristics of each pumped storage unit of one pipe with multiple units under gird connected of pumped storage stations. First, a novel nonlinear mathematical model for one pipe with multiple units under grid connection considering the coupling of shafting and hydro-turbine governing system (HTGS) is established. Then, the dynamic response characteristics of the coupled system are analyzed by simulation to verify the mathematical model effectiveness. These results show that the model is effective and can reveal the dynamic characteristics of the coupled system. After the disturbance, the coupled system quickly converges to stability. The generator rotor and hydro-turbine runner of each pumped storage unit are complex quasi-periodic vibrations. The smaller the \(T_{wPi}\) , the worse the nonlinear dynamic performance of the pumped storage unit.