Vectorized Mathematical Model of a Slip-Ring Induction Motor

Abstract

The paper deals with the modeling of a slip-ring induction motor. Induction motors are very often used in industry and their suitable model is needed to reduce control and operating costs. The identification process of self and mutual inductances of the stator and rotor, and mutual inductances between them in the function of the rotor rotation angle is presented. The dependence of each inductance on the rotor rotation angle is determined experimentally. The inductance matrix is then formulated. Taking the magnetic energy of the inductances and kinetic energy of the rotor into account, the Lagrange function is defined. Next, the motor motion equations are obtained. After making some algebraic transformations and using the dimensionless variables, the motion equations of electric circuits and of the mechanical equation are written separately in the forms facilitating their solution. The solution was obtained using the Simulink model for the stator and rotor currents in the form of vectors. The simulation was controlled by MATLAB script. The results of the simulation are presented in the form of basic variables time courses and compared with some values calculated with the use Steinmetz model of induction motor. The work is followed by two appendices, which contain procedures for determining the inverted inductance matrix.