ANALYTICAL ANALYSIS OF ROTOR SLOT HARMONICS IN THE LINE CURRENT OF SQUIRREL CAGE INDUCTION MOTORS

This paper describes a new approach for analysing the effect of the space distribution of rotor bars in squirrel cage induction machines on the generation of rotor slot harmonics (RSH). An analytical expression of the stator current has been developed. The proposed expression is based on the linkage inductance expression derived using the winding function approach (WFA) and its decomposition into Fourier series. This approach describes the necessary relationship required for the presence of rotor slot harmonics and explains how the stator current is influenced by voltage unbalance. Simulations results have shown excellent match with theoretically predicted harmonic components. K e y w o r d s: induction motor, rotor slot harmonics, voltage unbalance, Fourier series, diagnostics The squirrel cage induction motor has been used in all kinds of electric drives more often than other electric motors because of its reliability, robustness and simplicity of its construction. The classical theory of this electromechanical component is based on the assumption that the rotating mmf produced by stator winding excitation is sinusoidally distributed in space and that the rotor mmf due to the slip frequency induced currents is similarly distributed. This condition would only exist, however, if the surfaces of the stator and rotor were both smooth, and the windings were sinusoidally distributed on them. In the real machine the windings are placed in slots and therefore the resulting mmf and flux density distributions are not sinusoidal but contain, apart from the fundamental wave, a series of space harmonics. The space harmonics effects must be considered precisely during the design process of the induction machine to achieve good motor performance. These effects are of many kinds: asynchronous crawling, locking and synchronous crawling, magnetic noise, vibration and speed ripples. On the other hand the space harmonics have also a great influence on the harmonic content of stator currents. Several authors [1-3] have shown that, as a result of the nature of the rotor cage winding, all space harmonics from the stator side will be reflected by the rotor and occur only at high frequencies in the stator current spectrum. These harmonics known as rotor slot harmonics (RSH) have found application in modern speed estimation techniques [4–6]; in addition, recent works have shown that it is possible to use them to monitor some mechanical and electrical faults. Toliyat et al [7] have proposed the detection of air gap eccentricity in induction machines by measuring the harmonic content in the stator current spectrum. By means of the winding function approach all the space harmonics were taken into account. Vas [3] has presented a formula for computing the frequency components in the stator current which is due to air gap eccentricity. The frequency components are found to be function of the fundamental stator frequency, number of rotor slots, slip, type of eccentricity and stator mmf time harmonics.