**Author details**

542 Induction Motors – Modelling and Control

Great differences between the magnitudes of the main spectral peak on *fl* and the sidebands

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

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*.

values and therefore *aAPL* > *aAPH* (6). The summation or averaging of *aAPL* and *aAPH* is

The processing and direct analysis of the whole stator current does not enable the

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

Dynamic rotor faults cause dynamic changes of rotor electromagnetic field and MMF and

Based on this theory, the new diagnostic method MCDA was developed. Basic properties of AM and PM at rotor faults were presented. The analyses of IM current and current signature at rotor faults together with mathematical equations for low and high autospectral magnitudes computation were derived. These equations were verified by simulation and experimentally and the possible low and high autospectral magnitudes variation due to IM

Two demodulation methods based on Hilbert transform and space transform are presented.

The phase demodulation extracts the fault PM current. PM can be used for the research of rotor magnetic field phase changes and oscillation and for the sensorless rotor magnetic

The amplitude demodulation extracts the fault AM current. The simple spectral peaks at fault frequencies *fsp* and *fr* are the dynamic rotor faults indicators almost independent on IM

field speed measurement. PM fault indicators are dependent on the motor load.

changes from zero values to negative

contribution to the *aAPL* and *aAPH* and the result is

magnitudes *aAPL, aAPH* requires the use of logarithmic or dB scale.

indicators dependences on motor load and inertia.

Great inertia or poorly fed IM causes that the angle

distinction of the individual AM, PM and

**7. Conclusion** 

inaccurate, because the equation (6) is not a linear function.

together means the low resolution both in amplitudes and frequencies.

therefore the motor current AM and PM together creating JAPM.

current nonstationarity and DSP errors were discussed.

Space transform gives the same results as Hilbert transform.

Ivan Jaksch *Technical university of Liberec, Czech Republic* 
