Widely used in many industrial applications, the induction motors represent the starting point when
an electrical drive system has to be designed. In modern control theory, the induction motor is
described by different mathematical models, according to the employed control method. In the
symmetrical three-phase version or in the unsymmetrical two-phase version, this electrical motor
type can be associated with vector control strategy. Through this control method, the induction
motor operation can be analysed in a similar way to a DC motor. The goal of this research is to
summarize the existing models and to develop new models, in order to obtain a unified approach on
modelling of the induction machines for vector control purposes. Starting from vector control
principles, the work suggests the d-q axes unified approach for all types of the induction motors.
However, the space vector analysis is presented as a strong tool in modelling of the symmetrical
induction machines. When an electrical motor is viewed as a mathematical system, with inputs and
outputs, it can be analysed and described in multiple ways, considering different reference frames
and state-space variables. All the mathematical possible models are illustrated in this report. The
suggestions for what model is suitable for what application, are defined as well. As the practical
implementation of the vector control strategies require digital signal processors (DSP), from the
continuos time domain models are derived the discrete time domain models. The discrete models
permit the implementation of the mathematical model of the induction motors, in order to obtain
high efficiency sensorless drives. The stability of these various models is analysed.