Solid-Rotor Induction Motor Modeling Based on Circuit Model Utilizing Fractional-Order Derivatives

Abstract

This paper presents the Park model of a solid-rotor induction motor. In this model, the dynamic state of the motor is described by integer and noninteger order differential equations. The skin effect in the solid rotor was represented by resistance and inductance with lumped constants, and the fractional inductance was dependent on the frequency of the eddy current induced in the rotor. The parameters of the equivalent circuit were determined by the standstill frequency response test with the stationary machine on the basis of the finite element method analysis of the electromagnetic field. A simulation of the dynamic states of the induction motor with a solid rotor was carried out based on the calculated parameters. The simulation was carried out using a program written in the Matlab environment. The simulations show that the electromagnetic moment during the motor start-up is about 2 times greater than the initial torque in the steady state. On the other hand, the maximum value of the stator current during the start-up is about 1.5 times greater than the effective value of the inrush current in the steady state. A good agreement was obtained between the results calculated from the distribution of the magnetic field by the finite element method and the results obtained on the basis of the equivalent circuit and, in the case of the electromagnetic torque, with the results obtained from the transient state during motor reversal.

Identification of Fractional Models of an Induction Motor with Errors in Variables

“…The use of integer-order dynamical models leads to significant errors between the measured signals and the results obtained from simulations [13]. The greatest discrepancies are high-power squirrel cage induction machines, in which there is a skin effect in the rotor cage bars and in induction and synchronous machines with a solid rotor [14].…”

“…There are far fewer articles devoted to modeling and identification of induction motors by fractional-order models. In [14,[22][23][24], the researchers represented the skin effect in a solid rotor by means of resistance and inductance with fixed values and fractional-order inductance, depending on the frequency of induced eddy currents.…”