**6. Demodulation analysis versus direct analysis**

540 Induction Motors – Modelling and Control

on *fload* in MCDA spectrum –lower window.

small ripple from *fr* is clearly visible.

**5.5. IM energized from inverters** 

time varying load.

at a stable motor load.

PM was completely opposite.

Experimental results are depicted in Fig.10. Additional two new spectral sidebands appear on frequencies *fl ± fload* in MCSA spectrum-upper window and one new spectral peak appears

The time course of amplitude demodulated current, so the time course of amplitude modulating (i.e. fault) current is depicted in the middle window. The sum of three harmonic with the fundamental amplitudes *Ispa, Iload* and *Ir* and corresponding frequencies *fsp, fload* and

The broken bar fault indicator *Ispa* did not change its amplitude (compare with Fig.7). The important conclusion is that the size of MCDA fault indicator *Ispa* is not influenced by the

The last experiment examined two-pole IM with 2 broken bars energized from inverters. Two PWM open-loop inverters were used. The measurements were made at low inertia and

In the first measurement, an inverter was properly rated. In this case, the results correspond to the results for IMs energized from line. The MCS *aAPL* = *aAPH* and time course of AM and

> *aAPL*


*aAPH, at φ<0*

**Figure 11.** Inverter fed IM, low DC-link and overloaded, low inertia, 75% of full load, MCS, time course

In the second measurement another inverter was not properly rated and its DC-link voltage was only 400V. IM was fed by lower voltage apps. 185V and therefore was overloaded. In

of amplitude and phase demodulated current, PM delays *-ϕ* behind AM.

The presented MCDA and following AM and PM synthesis to the full IM current fault indicators *aAPL*, *aAPH* (6) enables the comparison of the demodulation analysis to the direct full IM current analysis.

The IM stator current demodulation analysis enables to find out the complex changes in the rotor electromagnetic field and MMF. Based on this analysis the new method MCDA was introduced. MCDA comes from the basic fundamental which occurs at dynamic rotor faults – JAPM. MCDA senses the whole stator current, but before the further evaluation as spectral analysis, it extracts time courses of fault currents directly induced by dynamic rotor faults. Anything more accurate than the extraction and direct processing of fault currents cannot exist.

The phase demodulation extracts PM current and can be used for the research of rotor magnetic field changes and oscillation and for the sensorless speed measurement. PM is not very suitable for rotor fault diagnostics, because the fault indicators are dependent on motor load.

The amplitude demodulation extracts AM fault current. AM is from 20% of full load almost independent of motor load and it is the base for rotor fault diagnostics not dependent on different load and inertia. Broken bar and dynamic eccentricity fault indicators are simple spectral peaks at direct fault frequencies *fsp, fr* (no sidebands). The amplitude demodulation can be easily implemented continually in a real time.

MCDA is a clear, very simple and reliable method and it is very useful for industrial application both for diagnostics and also for IM continual monitoring.

Methods of the direct analysis of IM current sense and subsequently process the full IM current. The great disadvantage of the direct IM current analysis is that its fault indicators *aAPL, aAPH* are dependent on IM load and inertia moment. The second disadvantage is that fault frequencies cannot be determined directly, but as a difference from *fl*, which can change. The third disadvantage is the lower resolution both in frequency and amplitude.

Great differences between the magnitudes of the main spectral peak on *fl* and the sidebands magnitudes *aAPL, aAPH* requires the use of logarithmic or dB scale.

Rotor Cage Fault Detection in Induction Motors by Motor Current Demodulation Analysis 543

load and inertia. It was also proved that MCDA fault indicators are not influenced by the

The presented diagnostic method is very clear and can be easily used for a reliable rotor

The author gratefully acknowledges the contributions of the Grant Agency of Czech

faults diagnostics in a real time or for continual IM monitoring.

*Technical university of Liberec, Czech Republic* 

AM Amplitude Modulation PM Phase Modulation

IM Induction motor

*fsp* Slip pole frequency – *2sfl fr* Motor rotation frequency *fl* Motor supply frequency *fload* Time varying load frequency

JAPM Joint Amplitude Phase Modulation MCDA Motor Current Demodulation Analysis MCS Motor Current Signature -*aAPL, aAPH*

*aAL, aAH* Low and high spectral magnitudes of AM *aPL, aPH* Low and high spectral magnitudes of PM

*fL, H* Low and high spectral sidebands frequencies *H(t*) Analytical signal created by Hilbert transform

*Inom* Induction motor nominal current amplitude *id(t), iq(t)* Real and imaginary part of space vector

*Il* Induction motor current amplitude

*Ispp* PM current amplitude at *fsp* frequency

*aAPL, aAPH* Low and high spec. mag. of MCS at JAPM –real motor state

*Ispa* AM current amplitude at *fsp* frequency, **broken bars fault indicator** 

time varying load.

**Author details** 

**Acknowledgement** 

Ivan Jaksch

Republic.

**Appendix** 

**Nomenclature** 

The presented demodulation analysis of IM current proved that IM current at dynamic rotor faults is not so simple and inwardly contains JAPM. Simply to say stator current consists of 3 parts - stator current of health motor, amplitude modulating current and phase modulating current (12). Just JAPM is the main reason for of the full current based fault indicators dependences on motor load and inertia.

The demodulation analysis exactly established the reasons for *aAPL* and *aAPH* formation and developed equations for their computation (5), (6). Consequently the MCDA has allowed a complete explanation of both MCS load and inertia dependences: MCS fault indicators *aAPL, aAPH* actually consist of 3 variables - AM, PM and *ϕ,* (6). PM increases with the increasing load (Fig.7-9, Table 4) and therefore causes the increase of both *aAPL* and *aAPH*. Great inertia or poorly fed IM causes that the angle changes from zero values to negative values and therefore *aAPL* > *aAPH* (6). The summation or averaging of *aAPL* and *aAPH* is inaccurate, because the equation (6) is not a linear function.

The processing and direct analysis of the whole stator current does not enable the distinction of the individual AM, PM and contribution to the *aAPL* and *aAPH* and the result is the continual dependence of MCSA *aAPL* and *aAPH* fault indicators on IM load and inertia. No improvements and sophistication of the measurement and evaluation methods can reduce this dependence. Logarithmic or dB scale has to be used for *aAPL* and *aAPH* displaying. It together means the low resolution both in amplitudes and frequencies.
