This paper presents a detailed fifth-order mathematical model of a three-phase induction motor, used in the WECC (Western Electricity Coordinating Council) composite load model. The main objective is to analyze the dynamic behavior of three-phase induction motors during fault-induced delayed voltage recovery (FIDVR) events, a critical phenomenon in power system voltage stability. The model is implemented in MATLAB/Simulink and validated by comparing its results with previous studies, demonstrating its ability to capture transient and subtransient responses under voltage disturbances. Different types of motors (A, B, and C) are analyzed, and variations in load and voltage disturbance magnitudes are studied. The results show that the model is accurate and robust, making it useful for voltage stability studies in systems with high induction motor penetration. However, the model has limitations, such as the lack of consideration for frequency drives and protection systems, suggesting areas for future research.

This paper presents a detailed mathematical procedure for implementing a three-phase induction motor model. Induction motors are crucial components in electric power systems. Therefore, several investigations have been conducted on the three-phase motor model. However, the mathematical representations for model development are complex due to nonlinearity and complicated structure. In this case, a composite load model is used to provide a block diagram based on the fifth-order analytical method in polar coordinates to calculate the transient and subtransient responses of a three-phase motor. Specifically, the behavior of a three-phase deep-slot squirrel cage motor is represented using parameters to describe its response from start-up to the voltage sag. Simulation was used to calculate the responses of the electromechanical variables after disturbances, in order to better understand the dynamic behavior of motor loads in voltage stability in electrical systems. The results were compared with those in the literature to verify the performance of the model.