Analysis and Simulation of Three-phase Induction motor using Clarke’s transformation

Call for Papers - April 2019

Download Full-Text PDF Cite this Publication

Text Only Version

Analysis and Simulation of Three-phase Induction motor using Clarke’s transformation

Analysis and Simulation of Three-phase Induction motor using Clarkes transformation


Asst.Prof. Dept of EXTC, S.S.J.C.O.E


Abstract Condition monitoring of induction motors is a fast emerging technology in the field of electrical equipment maintenance and has attracted more and more attention worldwide as the number of unexpected failure of a critical system can be avoided. Online motor diagnosis is the most efficient way to retain motors operating continuously under healthy conditions. To simplify analysis of a polyphase system, Clarkes transformation is appied. The induction motor model operation and performance is simulated using Matlab. It demonstrates the operational characteristics of faulty as well as healthy motors. This paper presents the advantages of simulation softwares such as Matlab, and use of Clarkes transformation to simplify analysis of a three-phase system.

KeywordsInduction motor, Stator and rotor faults,clarkes transform.














    Various test can be performed to investigate the steady-state and dynamic operation of electrical machines and to determine their modeling parameters. Performing such tests helps to acquire a clear understanding of the motor performance. Nevertheless, constraints in some cases make it impossible to do these tests, or only allow them to be done to a limited degree. Such constraints include: the high costs of some of the tests; the lack of appropriate measuring instruments or test rigs; the destructive nature of some of the tests. The risk of equipment damage from repeated tests in a short time period. These limitations prevent from performing some useful tests,


    Associate.Prof. Dept of EXTC, S.S.B.T.C.O.E,Bambhori, Jalgaon,India

    employed as a complement to an electrical machine performance and its practical tests [3]. Computer programshave also been used to obtain the steady-state performance of IMs under different operating conditions, using its equivalent circuit and plotting various characteristics.


    An induction motor can be represented as a generalized transformer (fig 1), with stator being fixed and behaving as the primary, while rotating rotor behaves as the secondary. Since we are dealing with a 3 phase motor therefore per phase equivalent circuit of the stator can be represented as shown below (fig 2).

    Applying KVL per phase to the equivalent circuit gives;


    Vsa = Isa Rsa + dt a (1)

    Vsa =Isa Rsa + (( Lsa Isa + Lm Isb +Lm Isc) + Lsr Ir) (2) Similarly;

    Vsb = Isb Rsb + (( Lsb Isb + Lm Isa +Lm Isc) + Lsr Ir) (3)

    Vsc = Isc Rsc + (( Lsc Isc + Lm Isa +Lm Isb) + Lsr Ir) (4)

    Using matrix notation, the above equations can be written as;

    repeating other test procedures, and employing a trial-and- error approach to get a better understanding of the machine performance. Simulations place no limitations on the duration of tests, such virtual tests are therefore perfectly cost- effective.

    The simulation of rotor bar failure and dc, no-load, of




    Lm Lsb Lm Isb + (Lsr)Ir

    { Lsa Lm Lm

    Rsa 0 0

    Isa }

    induction motors (IMs) using MATLAB/Simulink was dt proposed in [1]-[3] to improve the fundamental concepts of electric machines. Computer simulation has sometimes been


    Lm Lm Lsc


    Fig 1 Electrical equivalent circuit of IM

    Fig 2. Stator equivalent circuit

    In a more generalised form; the above equation can be written as;


    [Vs] = [Is][Rs] + dt ([Lss][Is] +[Lsr][Ir] ) (6)


    The inductance due to space fundamental component of the air gap flux produced by a stator phase current can be given as;

    i.e Vs = IsRs + dt s (7)


    s = Lss Is + Lsr Ir (8)


    Lsa =Lsb= Lsc= Ls +Lls ; and Lm = – 2


    µrrNc² Rgd


    Thus from the above equations we get;

    Ls =

    4gp² (11)



    Rsa 0 0

    Using a three phase quantity, the analysis of induction

    [Vs] = Vsb ; [Is] = Isb ; [Rs] =

    0 Rsb 0 ;

    machine becomes quiet complex. Therefore to simplify


    Lsa Lm Lm



    0 0 Rsc

    calculations Clarkes transformation also called as dqo

    transformation can be applied.

    Lss = Lm Lsb Lm ; s = <Psb ; (9)

    Lm Lm Lsb <Psc

    It is to be noted that [Lsr] and [Ir] are also in the form of matrices, which is derived during the analysis of rotor circuit.


    Clarkes transformation is a mathematical transformation to simplify analysis of a three-phase circuit; given as;


    Xdqo= j2/3* Xb * u ; where


    cos 0 cos(0 – 2rr/3) cos(0 + 2rr/3)

    Generally the value X0 is used to indicate the amount of

    U = -sin0 -sin (0 – 2rr/3) – sin (0 + 2rr/3)

    1 1 1

    2 2 2

    imbalance in a 3 system. Since the system is balanced

    ,therefore Xo tends to zero, indicating that the system is perfectly balanced.

    Thus we will be implementing the clarkes transformation

    Thus ;

    Xd= j2/3 [ cos * Xa + cos(0 – 2rr/3)* Xb + cos(0 +

    only to derive the d and q axis, which are referred as the direct and quadrature axis.

    2rr/3) * Xc]


    Dq transformation can be applied to any 3 phase quantity e.g.

    voltage, current, flux linkage, etc. Thus to convert 3 supply to dq-axis the converter (transformation circuit ) can be

    Xq = – j2/3 [ sin * Xa + sin(0 – 2rr/3)* Xb + sin(0 +

    implemented as shown in fig 3.

    2rr/3) * Xc]

    X0 = j2/3 [ Xa+Xb+Xc ]



    Thus Vd or Vq represents Vs. The value of stator flux can be calculated if Vs, Is and Rs are known. In the same way stator current for a 3 system, can be converted to a 2 quantity

    j2 using the same



    Fig 3. Clarkes transformer

    Fig 4 Internal blocks of Clarkes transformet


The use of clarkes transformation helps to convert a

three phase quantity into a two abbrievated as direct and quadrature

phase quantity quantities. The

observations for each scope is presented to justify the clarkes transformer. Fig 5 represents a three phase supply which is converted to two phase (in quadrature to each other) using clarkes transformation as depicted in fig 6.

Fig 5 Three phase supply

Fig 6 Two phase quantity

This analysis can be further extended to calculate the values of stator and rotor currents by making using of the clarkes transformation. Fig 7 and fig 8 represent the equivalent matlab models for estimating stator and rotor currents in a three phase induction motor by the application of clarkes transformation. Fig 9 depicts the two currents represented as single phase quantities

Fig 7 Estimating stator and rotor current per phase

Fig 8 Internal blocks for measurement of stator and rotor currents



Phase (deg)






















6 wb/m





Fig 9 Representation of stator and rotor currents as single phase quantities


  1. Amar Bentounsi, Hind Djeghloud, Hocine Benalla, Tahar Birem, and Hamza Amiar Computer-Aided Teaching Using MATLAB/Simulink for Enhancing an IM Course With Laboratory Tests. Ieee transactions on education, vol. 54, no. 3, august 2011 .

  2. Mansour Ojaghi, Jawad Faiz, Majid Kazemi, and Mohsen Rezaei. Performance Analysis of Saturated Induction Motorsby Virtual Tests .

    Ieee transactions on education, vol. 55, no. 3, august 2012

  3. K K pandey, Dr. P.H. Zope Estimating parameters of a three phase induction motor using Matlab/simulink. International Journal of Scientific & Engineering Research, Volume 4, Issue 12,December-2013 ISSN 2229-5518

  4. Bashir Mahdi Ebrahimi, Amir Masoud Takbash, and Jawad Faiz. Losses Calculation in Line-Start and Inverter-Fed Induction Motors Under Broken Bar Fault Ieee transactions on instrumentation and measurement, vol. 62, no. 1, january 2013.

  5. Andrian Ceban, Remus Pusca, and Raphaël Romary.Study of Rotor Faults in Induction Motors Using External Magnetic Field Analysis

    Ieee transactions on industrial electronics, vol. 59, no. 5, may 2012

  6. Tarek AROUI, Yassine KOUBAA* and Ahmed TOUMI Magnetic Coupled Circuits Modeling of Induction Machines Oriented to Diagnostics Research Unity of Industrial Process Control (UCPI) National Engineering School of Sfax (ENIS), B.P.: W 3038 Sfax- Tunisia.

  7. Saffet Ayasun,, and Chika O. Nwankpa Induction Motor Tests Using MATLAB/Simulink and Their Integration Into Undergraduate Electric Machinery Courses Ieee transactions on education, vol. 48, no. 1, february 2005

  8. P.H.Zope, Dr. Prashant Sonare, Development of Single Phase Z-source Inverter Using ARM7 for Speed Control of Induction Motor, Second International Conference on Control, Communication and Power Engineering 2011-CCPE Nov-2011, Proc. published by Springer, V.V. Das and N. Thankachan (Eds.): CIIT 2011, CCIS 250, pp. 440443, 2011, © Springer-Verlag Berlin Heidelberg 2011

  9. Reza Kianinezhad, Babak Nahid-Mobarakeh, Lotfi Baghli, Franck Betin, and Gérard-André Capolino.Modeling and Control of Six-Phase Symmetrical Induction Machine Under Fault Condition Due to Open

    Phases Ieee transactions on industrial electronics, vol. 55, no. 5, may 2008

  10. Masahiro Ikeda and Takashi Hiyama Simulation Studies of the Transients of Squirrel-Cage Induction Motors Ieee transactions on energy conversion, vol. 22, no. 2, june 2007

  11. Jee-Hoon Jung and Bong-Hwan Kwon Corrosion Model of a Rotor- Bar-Under-Fault Progress in Induction Motors Ieee transactions on industrial electronics, vol. 53, no. 6, december 2006

  12. Smail Bachir, Slim Tnani, Jean-Claude Trigeassou, and Gérard Champenois Diagnosis by Parameter Estimation of Stator and Rotor Faults Occurring in Induction Machines ieee transactions on industrial electronics, vol. 53, no. 3, june 2006.

  13. Carlo Concari, Giovanni Franceschini, Carla Tassoni, and Andrea Toscani. Validation of a Faulted Rotor Induction Machine Model With an Insightful Geometrical Interpretation of Physical Quantities Ieee transactions on industrial electronics, vol. 60, no. 9, september 2012

  14. Munoz A.R. and Lipo T.A. Complex vector model of the squirrel-cage induction machine including instantaneous rotor bar currents, IEEE-

    IAP, vol. 35, N°6, 1999

  15. Nandi S. and Toliyat H.A., Condition monitoring and fault diagnosis of electrical machinesA review, in Conf. Rec. IEEE-IAS Annu.

    Meeting, vol. 1, Phoenix, AZ, pp. 197204. 1999

  16. Razik H.and Gaëtan D., Sur la détection dun défaut au rotor des moteurs asynchrones, La revue 3EI n° 27, Décembre 2001 .

[17 ]Toliyat H.A. and Lipo T.A., Transient analysis of cage induction machines under stator, rotor bar and end-ring faults, IEEE Transaction on Energy Conversion, vol. 10, N° 2, pp 241-247, June 1995.

  1. P.H.Zope, Performance and Simulation Analysis of Single-Phase Grid Connected PV System Based on Z-Source Inverter, 2010 IEEE Conference PEDES-2010-Power India, Digital Object Identifier: 10.1109/PEDES.2010.5712436, Print ISBN: 978-1-4244-7782-1.

  2. P.H.Zope, Dr. Prashant Sonare, Simulation and Implementation of control strategy for Z-source inverter in the speed control of Induction Motor International Journal of Electrical Engineering & Technology (IJEET) (JULY 2011) ISSN 0976-6553 (online), Volume 2

  3. K K Pandey, P H Zope, Review on fault diagnosis in a three phase induction motor, International journal on computer applications, sept. 2012

Leave a Reply

Your email address will not be published. Required fields are marked *