Induction motors are the horsepower in the industrial environment, and among them, 3-phase induction motors (3PIMs) stand out for their robustness and standard 3-phase power supply. In the literature, there are many approaches to diagnose faults for the nonlinear 3PIM model, and the vast majority focus on a single motor fault, although others address more faults but at the cost of greater computational complexity. In this sense, one of the methods with less computational load and early detection is the parity equation approach, which is based on analyzing the discrepancy between the input and output signals of a real process and a linear mathematical model to generate a residual signal, which contains important information about the fault and is obtained through a suitable selection of a weighting matrix W to isolate the faults as much as possible. The problem in this case study is that the 3PIM model is a nonlinear system. In this work, the fault detection method based on the parity equations approach applied in the 3PIM is explored using a simplified and proposed model of the 3PIM working in the D-Q synchronous reference frame, which is matched with the direct current motor model to guarantee both the existence of the parity space and to ensure a large set of detectable faults in the 3PIM parameters. Simulation and experimental results validate the proposed scheme and confirm a very simple set of residual equations to guarantee both early detection and a large set of detectable faults in: Stator and rotor resistances, stator and rotor inductances, as well as current, voltage, and speed sensors. Additionally, development of human machine interface (HMI) is implemented to validate the proposed scheme.