**2. The analysis of IM current and current signature at rotor faults**

522 Induction Motors – Modelling and Control

Zhang et. al., 2011).

models (Lebaroud & Clerc, 2008), pendulous oscillation of rotor magnetic field (Mirafzal & Demerdash, 2005), vibration analysis (Dorrell et al., 1977) etc. A review of diagnostic techniques has been presented in several publications (Nandi et. al., 2005; Bellini et. al., 2008;

We can see that today it is not a problem to find rotor faults. What still remains a problem is to exactly and unambiguously determine fault indicator and its fault severity with a defined measurement uncertainty under changing motor parameters - various loads and inertia. Ideally the fault indicator should be independent on IM load. The examination of the various load influence on the fault indicator changes is very important especially in the industrial applications, where the keeping the same motor loads is often difficult. It has to be known what range of parameter changes are allowed for the keeping of the fault indicator constancy. As it is not known, at repeated measurements with different fault indicators, it is not clear, if the reason is due to the varied (deteriorating) IM faults or due to IM changing parameters. What is also important is the repeatability of the measurement with the same result. The third problem is a preferably simplicity and easy implementation of the methods for practical use in

industry. Introduced new demodulation methods fulfill most of these requirements.

load, inertia and also on IM working conditions.

use in industrial diagnostics.

Dynamic rotor faults of IM, namely rotor broken bars and dynamic or combined eccentricity, cause a distortion of the rotor bars current distribution, and thus they cause periodical dynamic changes related to IM rotation frequency *fr* in the rotor magnetic field and consequently torque oscillation and therefore stator current modulation. The complex stator current analysis and experiments based on simultaneous amplitude and phase demodulation techniques proved that the stator current at rotor faults consists both of amplitude modulation (AM) and phase modulation (PM). AM and PM are combined into the Joint Amplitude Phase Modulation (JAPM). Amplitude and phase modulating currents are in certain relations, both in their amplitudes and mutual phases, dependent on motor

Motor Current Demodulation Analysis - MCDA comes out from the fundamental principle which arises at dynamic rotor faults - IM stator current modulation. The basic idea of MCDA is to extract only those currents from the whole stator current which are directly induced and caused by rotor faults, and to investigate only these fault currents in the time and frequency domain. At health IM these currents do not exist, practically are near zero.

The demodulation is a process, how to gain back the information about the time course of modulating signal from modulated signal. Outputs of demodulation methods are, therefore, the direct time courses of modulating i.e. fault currents. The spectrum of a fault current does not contain any sideband components, fault frequencies are determined directly and only one spectral peak represents the fault indicator. The great advantage of MCDA is its easy

Most of the present diagnostic methods, both for stationary and non-stationary (Joint Time-Frequency Analysis) IM working conditions, use full IM current analysis methods for rotor fault detection. Just MCDA proved the complexity of the IM current at dynamic rotor faults and therefore the dependence of fault indicators based on full IM current on IM The widely used rotor fault detection technique - MCSA is presented in a large number of publications. This approach analyses whole IM stator current uses the spectral low and high slip pole frequency *2sfl* sidebands *aAPL*, *aAPH* around the supply frequency *fl* for broken bars detection (Bellini et. al., 2001). According to this theory, magnetic rotor asymmetry causes a backward rotating field and formation of a current component *aAPL* at the low sideband frequency *fl-fsp*. The consequent torque and speed oscillation cause the occurrence of a new component *aAPH* at the high sideband frequency *fl+fsp.* First, the only low sideband spectral magnitude was taken as a fault indicator for broken bars. Later a new diagnostic index was introduced as a sum of the two spectral sideband components *aAPL*+*aAPH.* 

Presented theory of the spectral low *aAPL* and high *aAPH* sidebands origination and formation and broken bars detection is quite different from MCSA theory. The theory comes from general modulation principles and exactly determinates both sidebands origination including the equations for *aAPL*, *aAPH* computation.

An exact detailed analysis of the stator current content at broken bars from the view of the complex air-gap rotor electromagnetic field analysis representing simultaneous stator current AM and PM, their mutual relation and changes at different load and inertia moment, and their formation to the MCS *aAPL* and *aAPH* magnitudes has been missing so far.
