The equivalent circuit used for obtaining the mathematical model of the induction motor is shown in the Fig. 2.
Fig. 2 : Equivalent circuit of induction motor in d - q frame
An induction motor model is then used to predict the voltage required to drive the flux, torque & the speed to the demanded values. This calculated voltage is then synthesized using the space vector modulation. The stator & rotor voltage equations are given by [56].where Vsd and Vsq, Vrd and Vrq are the direct axes & quadrature axes stator and rotor voltages [56]. The squirrel-cage induction motor considered for the simulation study in this paper, has the d and q-axis components of the rotor voltage zero. The flux linkages to the currents are related by the
Eq. (5) The electrical part of an induction motor can thus be described by a fourth-order state space model which is given in Eq. (6), by
combining equations (1) - (5) as [56], (6) where s is the laplacian operator. By superposition, i.e., adding the torques acting on the d-axis and the q-axis of the rotor windings, the instantaneous torque produced in the electromechanical interaction is given by. (8)
The electromagnetic torque expressed in terms of inductances is given by (9) The mechanical part of the motor is modeled by the equation [56]., (10)where,Jeq Equivalent Moment of Inertia,