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This paper details how the equations describing the magnetic field inside the motor and the equations of its electric circuit can be integrated in one only system, which can be solved using the Finite Element Method (FEM). When a model of a circuit is used, the solution of the magnetic field equation is the input to calculate the currents of the machine windings. As the magnetic field depends on these currents, it is necessary to follow an iterative process until initial and final currents match. With the technique proposed in this paper, because both magnetic field equations and electric circuit equations are integrated in the system, just in one step, the currents and induced voltages can be obtained with high accuracy and considerable time saving.

Electrical machine slots cause an undesirable effect on the m.m.f. wave in the airgap. This effect consists of the occurrence of high frequency harmonics. When the rotor turns, the movement of rotor slots in relation to the stator slots produces cycle variations in the magnetic circuit reluctance. This effect results in high frequency harmonics in the current wave spectrum. Simultaneously high frequency harmonics torques appear. These are known as slot harmonics. To avoid slot harmonics, both in the rotor and in the stator slots, the slots are skewed. When this technique is used, the simplified hypothesis of the finite element model (FEM) in 2D cannot be employed, as it is based on the concept that the magnetic field possesses translational symmetry along the machine shaft. In this paper a method for analysing electrical machines with skewed slots is presented without using the 3D analysis.

The purpose of this paper is to present a detailed advanced dynamical model of induction machine (IM) with unskewed rotor bars, including rotor slot harmonics.

Procedure of IM modeling using results from finite element analysis (FEA). Series of magneto-static FEA simulations are used to obtain matrix of IM inductances as a function of rotor angular position and geometry. Each element in this matrix is represented by Fourier series (FS) and incorporated in proposed dynamical model. Using or neglecting various elements in FS of inductance matrix may be useful for determining which component of the series has dominant influence on harmonic content of stator currents, torque ripple or speed variation. The usefulness of application of presented model is verified comparing with time-stepping FEA simulations.

Although the model is not suitable for usage in on-line regulation of IM drives, but the results of simulations may be used to thoroughly explain origins of higher order harmonics in stator currents of IM and help improve sensorless speed estimation algorithms and fault diagnostics.

This paper shows an approach to the modeling of IM which includes effects of non-uniform air gap and non-sinusoidal distributions of magneto-motive forces. Inductance matrix elements are complex functions of rotor position, geometry and winding distributions and it gives an opportunity for detail analysis of IM behavior in numerous applications.