Abstract
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.
Similar content being viewed by others
Abbreviations
- 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.
- ν:
-
Order of spatial harmonic.
- u 1Sρ :
-
First symmetrical component of stator voltages transformed into rotor coordinate system.
- ρ :
-
Angle between stator and rotor coordinate systems.
- i 1Sρ :
-
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.
- ω:
-
Synchronous angular frequency.
- T :
-
Machine torque.
- T l :
-
Load torque.
- J :
-
Moment of inertia.
References
Bacha K, Gossa M, Capolino GA (2004) Diagnosis of induction motor rotor broken bars. In: IEEE international conference on industrial technology, vol. 2. pp 799–982
Williamson S, Smith AC (1982) Steady-state analysis of 3-phase cage motors with rotor-bar and end-rings faults. In: IEEE proceedings vol 129 no. 3, pp 91–100
Manolas SJ, Tegopoulos JA (1999) Analysis of squirrel cage motors with broken bars and rings. IEEE Trans Energy Convers 14(4):1300–1305
Martinez J, Belahcen A, Arkkio A (2013) Broken bar indicators for cage induction motors and their relationship with the number of consecutive broken bars. IET Electr Power Appl 7(8):633–642
Ouachtouk I, El Hani S, Guedira S, Sadiki L, Dahi K (2015) Modeling of squirrel cage induction motor: a view to detection broken rotor bars faults. In: 1st International conference on electrical and information technologies (ICEIT), pp 347–352
Romashykhina Z, Kalinov A, Qawaqzeh M (2017) Analysis of the electromagnetic field of an induction motor with broken rotor bars. In: International conference on modern electrical and energy systems, pp 112–115
Spyropoulos D, Gyftakis K, Kappatou J, Epaminodas D (2012) The influence of the broken bar fault on the magnetic field and electromagnetic torque in 3-phase induction motors. In: 2012 XXth international conference on electrical machines, pp 1868–1874
Mingxing Y, Xiumei T, Dazhi X, Ziyuan X (2017) Fault diagnosis and numerical simulation of broken rotor bars for small cage induction motors. In: Chinese automation congress (CAC), pp 5355–5359
Yazidi A, Henao H, Capolino GA (2005) Broken rotor bars fault detection in squirrel cage induction machines. In: IEEE international conference on electric machines and drives, pp 741–747
Karnavas Y, Chasiotis I, Vrangas A (2017) Fault diagnosis of squirrel-cage induction motor bars based on a model identification method with subtractive clustering. In: 11th International symposium on diagnostics for electrical machines, power electronics and drives, pp 304–410
Zhu H, Mao Z, Jiang B, Liu H (2017) Fault diagnosis for induction motor with rotor broken bar fault based on multiple-model estimation. In: 36th Chinese control conference, pp 7459–7464
Sridhar S, Uma Rao K, Jade S (2015) Detection of broken rotor bar fault in induction motor at various load conditions using wavelet transforms. In: International conference on recent developments in control, automation and power engineering, pp 77–82
Garcia-Calva TA, Morinigo-Sotelo D, Romero-Troncoso RJ (2017) Non-uniform time resampling for diagnosis broken rotor bars in inverter-fed induction machines. IEEE Trans Indus Electron 64(3):2306–2315
Ünsal A, Kara Ö (2013) Modeling of broken rotor bars in a squirrel-cage induction motor. In: 4th International conference on power engineering, energy and electrical drives, pp 1597–1602
Stepina J (1968) Fundamental equations of the space vector analysis of electrical machines. Acta Technica CSAV 2:184–198
Stepina J (1986) Matrix calculation of inductances for the general theory of electrical machines. Electric Mach Power Syst 11(1):53–63
Stepina J (1990) Complex equations for electrical machines. In: International conference on electrical machines, pp 43–47
Schreier L, Bendl J, Chomat M (2017) Operation of five-phase induction motor after loss of one phase of feeding source. Electr Eng 99:9–18
Schreier L, Bendl J, Chomat M (2015) Analysis of fault-tolerance of five-phase induction machine with various configurations of stator winding. In: 18th International conference on electrical drives and power electronics (EDPE), pp 196–203
Schreier L, Bendl J, Chomat M (2011) Mathematical model of five-phase induction machine. Acta Technica CSAV 56:141–157
L. Schreier and M. Chomat (2019) Investigation of induction machine with rotor-bar faults. In: International conference on electrical drives & power electronics (EDPE), pp 12–17
Acknowledgment
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Dr. Jiri Bendl passed away on February 19, 2019.
Rights and permissions
About this article
Cite this article
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). https://doi.org/10.1007/s00202-020-01096-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00202-020-01096-2