This paper presents a comprehensive modeling approach for analyzing healthy and faulty conditions in Permanent Magnet Synchronous Generators (PMSGs), particularly focusing on inter-turn short circuit faults. Leveraging the finite element method (FEM) and Flux2D software, it is a step-by-step resolution over time, considering various parameters such as non-linearity, saturation, and harmonics. a comparison with an analytical model already experimentally verified validates the accuracy of the proposed model. The investigation highlights the critical importance of early-stage damage detection in PMSGs, especially concerning short-circuit faults, and underscores the significance of precise modeling for simulating and understanding machine performance. Through rigorous fault simulations and analysis, the study identifies fault indicators crucial for effective fault detection and diagnosis in PMSGs, thereby contributing to the advancement of fault detection methodologies in critical applications such as renewable energy and aerospace.