VI. MATLAB/SIMULINK RESULTS - IRD India ICEECS... · Web viewThe dynamic analysis of the symmetrical induction machines in the arbitrary reference frame has been intensively used

International Journal of Electrical, Electronics and Computer Systems (IJEECS)________________________________________________________________________________________________

Modelling &Simulation of a Three-Phase Electric Traction Induction Motor Using Matlab Simulink

1Naveed Rahaman, 2H.V. Govindraju

M-tech Student1, Associate Professor2, Dept. of EEE, Dr. AIT, Bangalore, Karnataka, India

Email: [email protected]; [email protected];

Abstract– The theory of reference frames has been effectively used as an efficient approach to analyze the performance of the induction electrical machines. This paper presents a step by step Simulink implementation of an induction machine using dq0 axis transformations of the stator and rotor variables in the arbitrary reference frame. For this purpose, the relevant equations are stated at the beginning, and then a generalized model of a three phase induction motor is developed and implemented in an easy to follow way. The obtained simulated results provide clear evidence that the reference frame theory is indeed an attractive algorithm to demonstrate the steady-state behavior of the induction machines. The designed induction motor model is then given the input supply from an IGBT 2 level inverter controlled by space vector PWM. The speed control of the designed traction induction motor is achieved by PI controller based on closed loop voltage control.

Keywords: Induction motor, D-Q transformation, Electric traction, Flux linkage, Speed, Torque, SVPWM, Inverter.

A. INDUCTION MOTOR MODELLING

I. INTRODUCTIONThe voltage and torque equations that describe the dynamic behaviour of an induction motor are time-varying. It is successfully used to solve such differential equations and it may involve some complexity. A change of variables can be used to reduce the complexity of these equations by eliminating all time-varying inductances, due to electric circuits in relative motion, from the voltage equations of the machine[1,2,3,4]. By this approach, a poly phase winding can be reduced to a set of two phase windings (q-d)with their magnetic axes formed in quad rature. In other words, the stator and rotor variables (voltages, currents and flux linkages) of an induction machine are transferred to a reference frame, which may rotate at any angular velocity or remain stationary. Such a frame of reference is commonly known in the generalized machines analysis as arbitrary reference frame[5,6, 7].

Figure1The dq0 equivalent circuit of an induction motor

The dynamic analysis of the symmetrical induction machines in the arbitrary reference frame has been intensively used as a standard simulation approach from which any particular mode of operation may then be developed.

Matlab/ Simulink has an advantage over other machine simulators in modelling the induction machine using dq0 axis transformation [8,9]. It can be a powerful techniqueinimplementingthemachineequationsastheyaretransferredto a particular reference frame. Thus, every single equation among the model equations can be easily implemented in one block so that all the machine variables can be made available for control and verification purposes. In this paper, Matlab/Simulink is used to simulate the dynamic performance of an induction motor model whose stator and rotor variables are referred to an arbitrary reference frame [1, 6, 8, 10]. The provided machine model is simulated in a way that makes it easy for the reader to follow and understand the implementation process since it gives full details about Simulink structure of each of the model equations. The equivalent circuit of the induction machine in the arbitrary reference frame is shown in figure 1 below [11, 12].

II. INDUCTION MOTOR MODELDriving the model equations can be generated from the dq0 equivalent circuit of the induction machine shown

________________________________________________________________________________________________ISSN (Online): 2347-2820, Volume -2, Issue-5, 6, 2014

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in figure 1. The flux linkages equations associated with this circuit can be found as follows:

d λqsdt

=ωb[Vqs−ωeωb λds+ RsXls ( λmq− λqs )]. . . . . . .(1)

d λdsdt

=ωb[Vds−ωeωb λqs+ RsXls ( λmd−λds )]. . . . . . .(2)

d λqrdt

=ωb [Vqr− (ω e−ωr )ωb

λdr+ RrXlr

( λ mq−λqr )]. . .(3)

d λdrdt

=ωb [Vdr− (ω e−ωr )ωb

λqr+ RrXlr

( λ mq−λdr )]. . .(4)

Where

λmq=Xml[ λqsXls + λqrXlr ]. . . . .. . . . .. . . . .. . . . . .(5)

λmd=Xml [ λdsXls + λ drXlr ]. . . . . . . . . . . . . . . . . . . . .(6)

Xml= 1

[ 1Xm

+ 1Xls

+ 1Xlr ] . .. . . . .. . . . .. . . . . . . . . . . .

(7)

Then substituting the values of the flux linkages to find the currents;

Iqs= 1Xls

[ λqs−λmq ]. . . . . . . . . . . . . . . . . . . . . . . . .(8)

Ids= 1Xls

[ λds−λmd ]. .. . . . .. . . . .. . . . . . . . . . . . .(9)

Iqr= 1Xlr

[ λqr−λmq ]. . . . . . . . . . . . . . . . . . . . . . . .

(10)

Idr= 1Xlr

[ λdr−λmd ]. .. . . . .. . . . .. . . . . . . . . . . . (11)

Based on the above equations, the torque and rotor speed can be determined as follows:

Te=32 (P2 ) 1

ωb[ λdsIqs+λ qsIds ]. . .. . . . .. . . . . . . .

(12)

ωr=∫ P2J

(Te−Tl ). . .. . . . .. . . . . . . . . . . . . . . . . .

(13)

Where P: number of poles; J: moment of inertia (Kg/m2)

For squirrel cage induction motor, the rotor voltages Vqr

and Vdr in the flux equations are set to zero since the rotor cage bars are shorted. After driving the torque and speed equations in term of d-q flux linkages and current soft he stator, the d-q axis transformation should now be applied to the machine input(stator)voltages[1,13,14].

The three-phase stator voltages of an induction machine under balanced conditions can be expressed as:

Va=√2Vrmssin (ωt). . . . .. . . . . . . . . . . . . . . . . . (14)

Vb=√2Vrmssin (ωt−2π3

). . . . .. . . . . . . . . . . . . .

(15)

Vc=√ 2Vrms sin (ω t+ 2π3

). . . . ... . . . . . . . . . . . .

(16)

These three-phase voltages are transferred to a synchronously rotating reference frame in only two phases (d-q axis transformation). This can be done using the following two equations.

[V αV β ]=23 [1 −1

2−12

0 √32

−√32

][VaVbVc ]... . . . . . .. . . . . (17)

Then, the direct and quadrature axes voltages are

[VdVq]=[ cosθ sin θ−sin θ cosθ ][V αV β ]... . . . . . . . . . .. . . . . . .

(18)

The instant aneous values of the stator and rotor currents in three-phase system are ultimately calculated using the following transformation:


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[ I αI β ]=[cosθ −sin θsin θ cosθ ][ IdIq ]... . . . . . . . . . . . . . . . . . .

(19)

[ IaIbIc ]=23 [ 1 0

−12

√32

−12

−√32

]... . . . . . . . . .. . . . . . . . . . (20)

III MATLAB/SIMULINK IMPLEMENTATION

In this section, the three phase induction machine model is simulated by using the Matlab/Simulink. The Model is implemented using the same set of equations provided above in sections II. Figure 2 depicts the complete Simulink scheme of the described induction machine model.

Figure 2 the 3-phase induction motor Matlab/Simulink model

In this model the simulation starts with generating a three-phase stator voltages according to the equations (14, 15, 16), and then transforming these balanced voltages to two phase voltages referred to the synchronously rotating frame using Clarke and Park transformation as in equations (17, 18). After that the d-q flux linkage and current equations were implemented as to be demonstrated below. Figure 3 illustrates the internal structure of the induction machine d-q model by which the flux linkages, currents, torque and the rotor angular speed are calculated.

Figure 3 the internal structure of the 3-phase induction motor d-q model

The Matlab/Simulink model to find the Flux linkage λqs, λqr, λds, λdr, as stated in equations (1)-(4) is shown in

figure 4.

Figure 4 the internal structure of the block to calculate the flux linkages

Figures.5 show the Simulink blocks used to calculate the currents Iqs, Ids, Iqr,Idr, according to the equations (8) – (11), also λmq, λmd in equations (5), (6). Figures 6 show the implementation of torque Te and angular speed ωr as expressed in equations (12), (13) respectively.

Figure 5 the internal structure of the block to calculate the currents Iqs, Ids, Iqr,Idr, and the fluxes λmq, λmd.

Figure. 6 the implementation of the torque equation Te (12) and the angular speed equation ωr (13)

Figure.7 shows the internal structure of the blocks (1- 4) in figure 4 in which the equations (1)-(4) are implemented in Matlab/Simulink format.


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Figure 7 the implementation of the equation (1)-(4)

IV. MATLAB/SIMULINK RESULTSThe simulation results are given for the induction motor with the following specifications:

KW = 285, VL = 1140, P = 4, f = 50, Rs = 0.131, Xls = 0.589,Rr = 0.0905, Xlr = 0.589, J = 4, Xm = 19.11, rpm = 3000

Figure8 Torque speed characteristics for given induction motor

Figure9Machine variables during free acceleration of induction motor


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Figure10Torque & speed characteristics of induction motor

Finally, the machine parameters should be defined to the simulated machine system in order to complete the simulation process. There are many ways to input the required data. The method used here is the graphical user interface (GUI). The machine parameters are entered through the convenient graphical user interface (GUI) available in Matlab/Simulink, where you can

right click with your mouse and then choose parameters to be added (edit mask). Figure 11 shows the GUI of the induction machine d-q model shown earlier in figure 2. After achieving the Matlab/Simulink implementation of the described machine model using the Matlab/Simulink, a Matlab code program was assigned to the same model using the same set of equations. The code provided similar results to those obtained by Matlab/Simulink. However, it was found that Matlab/Simulink is more convenient in terms of simplicity in construction and control algorithms which may be set forth for this model. The code compilation steps can be stated by the flow chart shown below in figure 11.

Figure 11 the graphical user interface (GUI) used to define the input data to the simulated induction motor.

V. INDUCTION MOTOR WITH INVERTER CLOSED LOOP VOLTAGE CONTROL

In this section, the three phase induction machine model with inverter and closed loop voltage control system is simulated by using the Matlab/Simulink. Here the actual speed of the induction motor is compared with the reference speed; the difference between them is error. The error signal fed to the PI controller and then controlled output is then given as reference to the controlled dc voltage source for the inverter input.

Figure 12 depicts the complete Simulink scheme of the described model. Figures 13 show the 3 phase - 2 level IGBT based inverter. It also provided with the 2nd order low pass filter to get pure sine wave output from the inverter.


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Figure 12: Simulink model of PI controller based three phase Induction motor voltage control

Figure 13: Internal structure of the 3-phase igbt based inverter model

VI. MATLAB/SIMULINK RESULTSThe simulation results are given for the induction motor with the closed loop control system at different reference speed and load torque:

1. Reference speed NS = 1500 and Load Torque TL=1000:

Figure 14: Torque speed characteristics for given induction motor at NS=1500 & TL=1000

Figure 15: Torque & speed characteristics of induction motor at NS=1500 & TL=1000

Figure 16: Machine current during closed loop at NS=1500 & TL=1000

Figure 17: Inverter output voltages during closed loop at NS=1500 & TL=1000


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The figures 18 and the figure 19 show the frequency spectrum of the phase voltage and the line voltage after 2nd order low pass filter. The value of the THD for phase voltage is 54.12% while for the line voltage it is 10.88%. The value of the fundamental component of the phase voltage is 548.2 V while for the line it is 948.4 V for the dc input voltage of 1140 V.

Figure 18: THD in phase voltage Va at NS=1500 & TL=1000

Figure 19: THD in LP filter output phase voltage Va at NS=1500 & TL=1000

2. Reference speed NS = 1500 and Load Torque TL=2035:

Figure 20: Torque speed characteristics for given induction motor at NS=1500 & TL=2035

Figure 21: Torque & speed characteristics of induction motor at NS=1500 & TL=2035

Figure 22: Machine current during closed loop at NS=1500 & TL=2035

Figure 23: Inverter output voltages during closed loop at NS=1500 & TL=2035


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Figure 24: THD in phase voltage Va at NS=1500 & TL=2035

Figure 25: THD in LP filter output phase voltage Va at NS=1500 & TL=2035

The figures 24 and the figure 25 show the frequency spectrum of the phase voltage and the line voltage after 2nd order low pass filter. The value of the THD for phase voltage is 53.03% while for the line voltage it is 6.80%. The value of the fundamental component of the phase voltage is 768.8 V while for the line it is 1330 V for the dc input voltage of 1140 V.

VII. CONCLUSIONSIn this paper, an implementation and dynamic modeling of a three-phase induction motor using Matlab/Simulink are presented in a step-by-step manner and its speed control is achieved using voltage control by closed loop PI control system. The parameters are obtained from the testing done on the electrical traction induction motor. The model was tested at three different load torque of a small and large induction motors. The simulated machine has given a satisfactory response in terms of the torque and speed characteristics. Also, the model was controlled from an IGBT based 2 level inverter at different load torque conditions. Both physical and simulation methods have given almost same results for the three phase induction motors used for traction purpose. There is appreciable improvement in THD in inverter line and phase voltage as the modulation index is increased and close to unity. From the analysis we

conclude that as the modulation index increased. This concludes that the Matlab/Simulink is a reliable and sophisticated way to analyse and predict the behaviour of induction motors using the theory of reference frames. Total harmonic distortion THD in line and phase voltage decreases as the value of load torque increased. The value of fundamental component in line and phase voltage is increased with the increase in load torque.

REFERENCES[1] P. C. Krause, O. Wasynczuk, S. D. Sudhoff

“Analysis of Electric Machinery and Drive Systems”, IEEE Press, A John Wiley & Sons, Inc. Publication Second Edition, 2002.

[2] M. L. de Aguiar, M. M. Cad, “The concept of complex transfer functions applied to the modeling of induction motors”, Power Engineering Society Winter Meeting, 2000, pp. 387–391.

[3] S. Wade, M. W. Dunnigan, B. W. Williams, “Modeling and simulation of induction machine vector control with rotor resistance identification”, IEEE Transactions on Power Electronics, vol. 12, No. 3, May 1997, pp. 495–506.

[4] B. Ozpineci, L. M. Tolbert, “Simulink implementation of induction machine model – A Modular approach”, Ieee, 2003, pp 728-734.

[5] H. C. Stanley, “An Analysis of the Induction Motor”, AIEE Transactions, Vol. 57(Supplement), 1938, pp. 751-755.

[6] H. C. Stanley, “An Analysis of the Induction Motor”, AIEE Transactions, Vol. 57 (Supplement), 1938, pp. 751-755.

[7] G. McPherson and R. D. Laramore, “an Introduction to Electrical Machines and Transformers”, 2rd ed., John Wiley and Sons, New York, 1990.

[8] J. O. P. Pinto, B. K. Bose, L. E. B. Silva, M. P. Kazmierkowski, “A neural-network-based space-vector PWM controller for voltage-fed inverter induction motor drive,” IEEE Transactions on Industry Applications, vol. 36, no. 6, Nov./Dec. 2000, pp. 1628–1636.

[9] Bose B.K., Power Electronics and AC Drives, Englewood Cliffs, NJ: Prentice Hall, 1986

[10]. Frede Blaabjerg,, Sigurdur Freysson, Hans-Henrik Hansen, and S. Hansen “A New Optimized Space-Vector Modulation Strategy for a Component-Minimized Voltage Source Inverter ” IEEE Trans. on Power Electronics, Vol. 12, No. 4, July 1997, pp 704-710.

[11] Scott Wade, Matthew W. Dunnigan, and Barry W. Williams, “Modelling and Simulation of Induction Machine Vector Control with Rotor


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Resistance Identification”, IEEE transactions on power electronics, vol. 12, no. 3, may 1997.

[12] Ramon Blasco Blasco Gimenez, “High Performance Sensorless Vector Control of Induction Motor Drives”, The University of Nottingham, December 1995

[13] Adel Aktaibi, Daw Ghanim, and M. A. Rahman, “Dynamic Simulation of a Three-Phase Induction Motor using Matlab Simulink”.

[14] S. Senthilkumar and S. Vijayan, “Simulation of High Performance PID Controller for Induction Motor Speed Control with Mathematical Modelling”, Research Journal of Applied Sciences, Engineering and Technology 6(18): 3343-3348, 2013. ISSN: 2040-7459.

[15] Amit Kumar Sharma, Tushar Deep Saxena, Shirazul Islam, Arunkumar Yadav, “Performance Analysis of Three Phase PWM Voltage Source Inverter Fed Three Phase Induction Motor Drive”, IJAEEE, ISSN : 2278-8948, Volume-2, Issue-2, 2013.


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VI. MATLAB/SIMULINK RESULTS - IRD India ICEECS... · Web viewThe dynamic analysis of the symmetrical induction machines in the arbitrary reference frame has been intensively used