This paper presents the generator's internal fault modeling and analysis based on the one-machine infinite-bus power system for the simulation of internal faults in a synchronous generator. The model applied is a low-order synchronous generator model, and is based on the so-called fourth-order representation with the mechanical mode from the second-order system and the electrical mode from the second-order system. The test cases for internal faults demonstrates the output waveforms for id, iq, vd, vq, ω, Efd, Vt, Te, ia, ib, ic, va, vb, and vc using the MATLAB tool. Furthermore, the fault perturbations for internal windings and for an exciter terminal are also carried out and are compared by the results of four cases of simulations.