A precise simulation of the internal faults of synchronous generators is very important for designing the main protection scheme; therefore, it is necessary to propose an accurate model. The time-step finite element method is quite qualified for analysing problems related to the transient electromagnetic field, including the internal faults of synchronous generators. This paper presents a new time-step method, which employs a rotation coupling technique to handle rotor motion. By using this technique, the rotor remains stationary during the process of the simulation, and the motion problem becomes simple and can be conveniently implemented with a programming process. Simulation and experimental results for the internal faults of an experimental machine are compared to verify the accuracy of the rotation coupling time-step method. Moreover, a 300 MW salient pole synchronous generator is used as an example, and the transient process of this generator during internal faults is simulated. The air gap flux density, fault currents, damper windings eddy current losses, and core dynamic electromagnetic force are investigated in detail to reveal the fault characteristics more clearly and provide a basis for designing protection schemes. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.