Dynamic Simulation of a ThreePhae Induction Motor Uing Matlab Simulink Adel Aktaibi & Daw Ghanim, graduate tudent member, IEEE, M. A. Rahman, life fellow, IEEE, Faculty of Engineering and Applied Science, Memorial Univerity of Newfoundland St. John, NL, Canada, AB X5 aama8@.mun.ca, dfg@.mun.ca, arahman@mun.ca; Abtract The theory of reference frame ha been effectively ued a an efficient approach to analyze the performance of the induction electrical machine. Thi paper preent a tep by tep Simulink implementation of an induction machine uing dq axi tranformation of the tator and rotor variable in the arbitrary reference frame. For thi purpoe, the relevant equation are tated at the beginning, and then a generalized model of a threephae induction motor i developed and implemented in an eay to follow way. The obtained imulated reult provide clear evidence that the reference frame theory i indeed an attractive algorithm to demontrate the teadytate behavior of the induction machine. I. INTRODUCTION The voltage and torque equation that decribe the dynamic behavior of an induction motor are timevarying. It i uccefully ued to olve uch differential equation and it may involve ome complexity. A change of variable can be ued to reduce the complexity of thee equation by eliminating all timevarying inductance, due to electric circuit in relative motion, from the voltage equation of the machine [,,, ]. By thi approach, a poly phae winding can be reduced to a et of two phae winding (qd) with their magnetic axe formed in quadrature. In other word, the tator and rotor variable (voltage, current and flux linkage) of an induction machine are tranferred to a reference frame, which may rotate at any angular velocity or remain tationary. Such a frame of reference i commonly known in the generalized machine analyi a arbitrary reference frame [5, 6, 7]. Figure The dq equivalent circuit of an induction motor The dynamic analyi of the ymmetrical induction machine in the arbitrary reference frame ha been intenively ued a a tandard imulation approach from which any particular mode of operation may then be developed. Matlab/Simulink ha an advantage over other machine imulator in modeling the induction machine uing dq axi tranformation [8, 9]. It can be a porful technique in implementing the machine equation a they are tranferred to a particular reference frame. Thu, every ingle equation among the model equation can be eaily implemented in one block o that all the machine variable can be made available for control and verification purpoe. In thi paper, Matlab/Simulink i ued to imulate the dynamic performance of an induction motor model whoe tator and rotor variable are referred to an arbitrary reference frame [, 6, 8, ]. The provided machine model i imulated in a way that make it eay for the reader to follow and undertand the implementation proce ince it give full detail about Simulink tructure of each of the model equation. The equivalent circuit of the induction machine in the arbitrary reference frame i hown in figure below [, ]. II. INDUCTION MOTOR MODEL Driving the model equation can be generated from the dq equivalent circuit of the induction machine hown in figure. The flux linkage equation aociated with thi circuit can be found a follow: Where. ().... (). (). (). (5). (6).. (7) Then ubtituting the value of the flux linkage to find the current;. (8)... (9). ()... () Baed on the above equation, the torque and rotor can be determined a follow:. (). () Where P: number of pole; J: moment of inertia (Kg/m ). For quirrel cage induction motor, the rotor voltage V qr and V dr in the flux equation are et to zero ince the rotor cage
Flux linkage calculation bar are horted. After driving the torque and equation in term of dq flux linkage and current of the tator, the dq axi tranformation hould now be applied to the machine input (tator) voltage [,, ]. The threephae tator voltage of an induction machine under balanced condition can be expreed a: () (5) (6) Thee threephae voltage are tranferred to a ynchronouly rotating reference frame in only two phae (dq axi tranformation). Thi can be done uing the following two equation. Then, the direct and quadrature axe voltage are.(7).(8) The intantaneou value of the tator and rotor current in threephae ytem are ultimately calculated uing the following tranformation:..(9).() III MAAB/SIMULINK IMPLEMENTATION In thi ection, the three phae induction machine model i imulated by uing the Matlab/Simulink. The Model i implemented uing the ame et of equation provided above in ection II. Figure depict the complete Simulink cheme of the decribed induction machine model. VA VB VC phae upply Va Vb Vc Vq Vd tranformation from abc to dq Figure the phae induction motor Matlab/Simulink model In thi model the imulation tart with generating a threephae tator voltage according to the equation (, 5, 6), and then tranforming thee balanced voltage to two phae voltage referred to the ynchronouly rotating frame uing Clarke and Park tranformation a in equation (7, 8). After that the dq flux linkage and current equation re implemented a to be demontrated below. Figure illutrate the internal tructure of the induction machine dq model by which the flux linkage, current, torque and the rotor angular are calculated. induction motor dq model Iq Id Iqr Idr ia ib ic current calculation current calculation Figure the internal tructure of the phae induction motor dq model The Matlab/Simulink model to find the flux linkage,,, a tated in equation ()() i hown in figure. Figure the internal tructure of the block to calculate the flux linkage Figure.5 how the Simulink block ued to calculate the current,,, according to the equation (8) (), alo, in equation (5),(6). Figure 6 & 7 how the implementation of torque T e and angular a expreed in equation (), () repectively. 5 Figure 5 the internal tructure of the block to calculate the current,,,, and the fluxe. calculation 5 calculation 6
.5*P/(*) Figure. 6 the implementation of the torque equation () Figure.9 preent the implementation of the flux linkage, found in figure. 5. Alo, figure. depict how the current,,, are contructed. /Xl /Xlr /((/Xm)(/Xl)(/Xlr)) P/(*J) Figure. 7 the implementation of the angular equation () /Xl /((/Xm)(/Xl)(/Xlr)) /Xlr Figure 9 the calculation of the flux linkage, Figure.8 how the internal tructure of the block ( ) in figure in which the equation ()() are implemented in Matlab/Simulink format. / r/xl /Xl /Xlr / r/xl /Xl /Xlr (c) (d) Figure the implementation of the dq current equation IV. MAAB/SIMULINK RESULTS / rr/xlr (c) Two induction motor; hp and 5 hp re teted in thi imulated model. The reult of the imulation are given for the firt induction motor with the following pecification: Hp = VL = f = 6 R =.5 Xl =.75 P = Rr =.86 Xlr =.75 J =.89 Xm = 6. rpm = 7 (d) / rr/xlr 8 6 Figure 8 the implementation of the equation ()() 6 8 6 8 Figure characteritic for the hp induction motor
ic ic ib ib ia ia.....5.6.7.....5.6.7.....5.6.7.....5.6.7.....5.6.7.....5.6.7.....5.6.7.....5.6.7 time Figure Machine variable during free acceleration of a hp induction motor The reult of the imulation are alo given for the other induction motor with the following pecification: Hp = 5 VL = f = 6 R =.9 Xl =.6 P = Rr =. Xlr =.6 J = 6.87 Xm =. rpm = 786 x 6 8 6 8 Figure characteritic for the 5 hp induction motor x x.5.5.5.5 x.5.5.5.5 x x 5 5.5.5.5.5 x 5 5 x.5.5.5.5 x.5.5.5.5 x x.5.5.5.5 5 x x 5.5.5.5.5 x 5 5 5.5.5.5.5 time x Figure Machine variable during free acceleration of a 5hp induction motor Finally, the machine parameter hould be defined to the imulated machine ytem in order to complete the imulation proce. There are many way to input the required data. The method ued here i the graphical uer interface (GUI). The machine parameter are entered through the convenient graphical uer interface (GUI) available in Matlab/Simulink, where you can right click with your moue and chooe (edit mak) then chooe parameter to be added. Figure 5 how the GUI of the induction machine dq model hown earlier in figure. After achieving the Matlab/Simulink implementation of the decribed machine model uing the Matlab/Simulink, a Matlab code program wa aigned to the ame model uing the ame et of equation. The code provided imilar reult to thoe obtained by Matlab/Simulink. Hover, it wa found that Matlab/Simulink i more convenient in term of implicity in contruction and control algorithm which may be et forth for thi model by the cholar in the future. The code compilation tep can be tated by the flow chart hown below in figure 6.
V. CONCLUSIONS In thi paper, an implementation and dynamic modeling of a threephae induction motor uing Matlab/Simulink are preented in a tepbytep manner. The model wa teted by two different rating of a mall and large induction motor. The two imulated machine have given a atifactory repone in term of the torque and characteritic. Alo, the model wa evaluated by Matlab mfile coding program. Both method have given the ame reult for the ame pecification of the three phae induction motor ued in thi imulation. Thi conclude that the Matlab/Simulink i a reliable and ophiticated way to analyze and predict the behavior of induction motor uing the theory of reference frame. REFERENCES t = t t Figure 5 the graphical uer interface (GUI) ued to define the input data to the imulated machine. tart Reading the Initial value and aigned value of the variable Generating and then Solving the differential equation ()() to find the flux linkage,,,,, Calculating the current,,,, uing the equation (8) () Calculating the and the angular uing the equation () and () repectively t > T end Figure 6 the flow of the induction machine imulation model [] P. C. Kraue, O. Waynczuk, S. D. Sudhoff Analyi of Electric Machinery and Drive Sytem, IEEE Pre, A John Wiley & Son, Inc. Publication Second Edition,. [] P.C. Kraue and C. H. Thoma, Simulation of Symmetrical Induction Machinery, IEEE Tranaction on Por Apparatu and Sytem, Vol. 8, November 965, pp. 85. [] P. C. Kraue, Analyi of Electric Machinery, McGrawHill Book Company, 986. [] D. C. White and H. H. Woodon, Electromechanical Energy Converion, John Wiley and Son, New York, 959. [] M. L. de Agu, M. M. Cad, The concept of complex tranfer function applied to the modeling of induction motor, Por Engineering Society Winter Meeting,, pp. 87 9. [5] S. Wade, M. W. Dunnigan, B. W. William, Modeling and imulation of induction machine vector control with rotor reitance identification, IEEE Tranaction on Por Electronic, vol., No., May 997, pp. 95 56. [6] B. Ozpineci, L. M. Tolbert, Simulink implementation of induction machine model A Modular approach, Ieee,, pp 787. [7] H. C. Stanley, An Analyi of the Induction Motor, AIEE Tranaction, Vol. 57(Supplement), 98, pp. 75755. [8] R. H. Park, TwoReaction Theory of Synchronou MachineGeneralized Method of Analyi, Part I, AIEE Tranaction, Vol. 8, July 99, pp. 7677. [9] D. S. Brereton, D. G. Lewi, and C. G. Young, Repreentation of Induction Motor Load During Por Sytem Stability Studie, AIEE Tranaction, Vol. 76, Augut 957, pp.56. [] E. Clarke, Circuit Analyi of AC Por Sytem, Vol. ISymmetrical and Related Component, John Wiley and Son, New York, 9. [] H. C. Stanley, An Analyi of the Induction Motor, AIEE Tranaction, Vol. 57 (Supplement), 98, pp. 75755. [] G. Kron, Equivalent Circuit of Electric Machinery, John Wiley and Son, New York, 95. [) D. S. Brereton, D. G. Lewi, and C. G. Young, Repreentation of Induction Motor Load During Por Sytem Stability Studie, AIEE Tranaction, Vol.76, Augut 957, pp.56. [] G.Kron, Equivalent Circuit of Electric Machinery, John Wiley and Son, New York, 95. [5] O. Waynczuk and S. D. Sudhoff, Automated State Model Generation Algorithm for Por Circuit and Sytem, IEEE Tranaction on Por Sytem, Vol., No., November 996, pp. 95956. [6] G. McPheron and R. D. Laramore, an Introduction to Electrical Machine and Tranformer, rd ed., John Wiley and Son, New York, 99. [7] J. J. Cathey, R. K. Calvin, III, and A. K. Ayoub, Tranient Load Model of an Induction Machine, IEEE Tranaction on Por Apparatu and Sytem, Vol. 9, July/Augut 97, pp. 996. [8] J. O. P. Pinto, B. K. Boe, L. E. B. Silva, M. P. Kazmierkowki, A neuralnetworkbaed pacevector PWM controller for voltagefed inverter induction motor drive, IEEE Tranaction on Indutry Application, vol. 6, no. 6, Nov./Dec., pp. 68 66.