Induction machines are a crucial type of electrical equipment utilized as motors in various industries and single-phase forms in household applications. They make up more than 80% of the industrial motors used today. This paper presents a dynamic simulation of three-phase induction machines based on the (d-q) model, providing a clear and easy-to-understand explanation of the behavior of the induction motor in the synchronous reference frame. The simulation is implemented using SIMULINK/MATLAB software, and full-order model analysis is conducted for transient analysis. However, modeling induction machines as part of power system analysis can be done with a less detailed model than the full-order one. In this paper, a reduced-order model is employed to simulate the induction motor using MATLAB/SIMULINK. The results of the reduced-order system and the full-order framework are compared to investigate the model's limits, and the computational benefits of saving time during large power system simulations justify the relative decrease in accuracy. The use of a reduced-order model results in a significant reduction in computation time when simulating large and very large-scale power systems, with a much higher accuracy in transient analysis than the conventional steady-state model.