Abstract: For the complex hydraulic system including single penstock multi-machine with surge, due to the great influence of hydraulic coupling and the computational difficulty, it is quite difficult to design the controller and analyze stability of the hydro turbine generating unit（HTGS）with hydraulic coupling. In this paper, the transient changes of head and flow in the tunnel and surge were analyzed. It is found that the hydraulic transient satisfies the superposition principle. Accordingly, the transient changes of the head and flow in the tunnel and surge were expressed as a function of the flow of the single HTGS that is the multi-machine form. A differential algebraic model of multi-machine of hydro turbine with surge was further constructed. The model can be directly connected with the classical differential equation model of multi-machine, to constitute the local multi HTGS system model of hydropower station. Finally, a case study of a hydraulic system was carried out. The simulation results show that the proposed model has high computational accuracy and meets the requirements of transient analysis and control design of the HTGS.