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Analysis of stator and rotor currents and torque of induction machine with rotor-bar faults

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The paper analyzes a case of the induction motor in which one or more rotor bars in the rotor cage are broken. The method of space vectors and symmetrical components of instantaneous values of currents and voltages is used in the analysis. The solution obtained makes it possible to determine the currents in each of the healthy rotor bars, the stator currents, and the electromagnetic torque of the machine for any number and arbitrary combination of broken rotor bars. The calculations are made for an induction motor with 17 rotor bars. The theoretical results are compared with experimental measurements.

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m :

Number of phases.

n :

Index of symmetrical component.

i n :

Symmetrical component of currents with index n.

i A, i B, i C, … i M :

Currents in rotor bars.

a m :

Complex operator.


Order of spatial harmonic.

u 1 :

First symmetrical component of stator voltages transformed into rotor coordinate system.

ρ :

Angle between stator and rotor coordinate systems.

i 1 :

First symmetrical component of stator currents transformed into rotor coordinate system.

i 1R :

First symmetrical component of rotor currents.

u 1S :

First symmetrical component of stator voltages.

R S :

Stator resistance.

L σS :

Stator leakage inductance.

L σR :

Rotor leakage inductance.

L 1R :

Main inductance for fundamental spatial harmonic.

L 1 :

Inductance of single conductor for fundamental harmonic.

\(\chi_{1S}\) :

Stator winding factor for first harmonic.

N S :

Number of conductors of single-phase stator winding.

\(\chi_{1R}\) :

Rotor winding factor for first harmonic

N R :

Number of conductors of single-phase rotor winding.

R B :

Resistance of single rotor bar.

R R :

Resistance of single rotor bar rated to stator number of conductors.

i 1B :

First symmetrical component of rotor bar currents.

L σB :

Leakage inductance of rotor bar.

A, B, C, … M :

Denotation of rotor bars.

p :

Number of pole pairs.

ωm :

Mechanical angular frequency.


Synchronous angular frequency.

T :

Machine torque.

T l :

Load torque.

J :

Moment of inertia.


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This work was supported by the Czech Science Foundation under research Grant 16–07795S and by the institutional support RVO 61388998. The authors would like to thank the company ATAS elektromotory Nachod, a.s. for cooperation and manufacturing the experimental machine and the rotor with a broken bar.

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Correspondence to M. Chomat.

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Dr. Jiri Bendl passed away on February 19, 2019.

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Schreier, L., Bendl, J. & Chomat, M. Analysis of stator and rotor currents and torque of induction machine with rotor-bar faults. Electr Eng 103, 519–528 (2021).

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