simulation of three-phase

Simulation of three-phase induction motor in Scilab

Mgr inż. Madejski Rafał

Politechnika Częstochowska,

Wydział Inżynierii Procesowej, Materiałowej i Fizyki Stosowanej Instytut Przeróbki Plastycznej Inżynierii Bezpieczeństwa

Zakład Automatyzacji Procesów Przemysłowych.

Position: PhD student

City, Country- Poland

e-mail address [email protected]

Abstract - The paper presents the structure of the model used to

simulate processes in a three-phase induction motor.

Considerations are implemented in Scilab environment and

apply the induction motor with a power PN = 75kW and input

parameters for the model 5AM280S6 electric motor. Computer

simulation shows the results of the engine at idle and short

circuit.

Keywords-component; model; silnik indukcyjny; scilab.

I. INTRODUCTION.

At present, simulation programs are an essential tool for research and engineering in the field of electric drive and power electronics. Over the last ten years there have been many universal simulation packages (eg SCILAB, MATLAB / Simulink), containing models of electric machines and power electronics components, significantly accelerating and facilitating the process of modeling and simulation of complex drive systems, which include the induction motor drive system . The literature on modeling of induction motor drives and use of certain mathematical methods, due to the specific characteristics and properties of induction motors, electrical machines (non-linear mathematical models of electric machines leading to the description of the motor drive systems with a rigid, non-linear differential equations) is very poor. Especially descriptions of the methods of analysis and simulation of induction motors such as high power 75kW. Due to the scope and objectives of this Article and the complexity of the mathematical model of induction motor mathematical modeling of induction motor systems was carried out in the Scilab library using this program.

II. A MATHEMATICAL MODEL OF DIFFERENTIAL EQUATIONS

FOR INDUCTION MOTOR IN D Q SYSTEM.

One of the most popular models of induction motors from the system dq Model Krause is described in detail in the book [1]

According to the model Kraus differential equation of motion for the induction motor in dq system has the following form:

……….(1)

…….…(2)

……….(3)

………....(4)

………………………………(5)

………………………………(6)

……………………………...(7)

Figure1. Dynamic or d-q equivalent circuit of an induction machine.

Current equation::

……………………………...... (8)

……………………………... (8.1)

……………………………... (8.2)

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…………………………….. (8.3)

Xlr = eLlr - rotor leakage reactance,

Xls = eLls- stator leakage reactance,

Rs – stator resistance,

Rr – rotor resistance,

e = stator angular electrical frequency,

e = 4/p – prędkość kątowa pola elektrycznego stojana,

r = rotor angular electrical speed,

b = motor angular electrical base frequency,

Electromechanical equation:

…………………………..(12)

……………………………..(13)

,

,

The transition from the system voltage in 3-phase abc to

the dq in a stationary coordinate system using the

transformation Park'a:

…(14)

where:

The transition from the dq to abc coordinate system for the stator currents

III. IMPLEMENTATION OF DIFFERENTIAL EQUATIONS IN

SCILABIE.

The differential equations are implemented in the function Vdqfun (), in which the input parameters are:

t - vector time,

x - vector of state variables x=[Fqs;Fds;Fqr;Fdr;wr]

Vm- voltage amplitude,

fHz – the frequency of supply voltage,

TABLE 1. Listing function Vdqfun

Listing f function Vdqfun 1. function [xdot]=Vdqfun(t, x, Vm, fHz)

2. xdot=zeros(5,1);

3. *********************************

4. // MACHINE PARAMETERS INDUCTOR

5. *********************************

6. // Stator resistance [Ohm]

7. Rs=0.435;

8. // Rotor resistance [Ohm]

9. Rr=0.64;

10. // Stator winding inductance [H]

11. Ls=0.0477;

12. // Rotor winding inductance [H]

13. Lr=0.0577;

14. Lm =0.012;

15. // Coefficient of drag

16. D=0.001;

17. // Moment of inertia

18. J=0.28;

19. // Number of pole pairs

20. p=6;

21. // Stator angular electrical frequency

22. we=4*%pi*fHz/p;

23. // Motor angular electrical base frequency

24. wb=2*%pi*50

25. // Load torque

26. Tl=0;

27. Xls=wb*Ls;

28. Xlr=wb*Lr;

29. Xm=wb*Lm;

30. Xml=1/(1/Xls+1/Xm+1/Xlr);

31. //x=[Fqs;Fds;Fqr;Fdr;wr]

32. // Stream Fqs

33. Fqs=x(1);

34. // Stream Fds

35. Fds=x(2);

36. //Strumień Fqr

37. Fqr=x(3);

38. // Stream Fdr

39. Fdr=x(4);

40. // Rotor angular electrical speed [rad/sek]

41. wr=x(5);

42. // q and d-axis stator currents

43. iqs=(Fqs-Xml*(Fqs/Xls+Fqr/Xlr))/Xls;

44. ids=(Fds-Xml*(Fds/Xls+Fdr/Xlr))/Xls;

45. iqrr=(Fqr-Xml*(Fqs/Xls+Fqr/Xlr))/Xlr;

46. idrr=(Fdr-Xml*(Fds/Xls+Fdr/Xlr))/Xlr;

47. // Electrical output torque

48. Te=3/4*p*(Fds*iqs-Fqs*ids)/wb;

49. // q and d-axis stator voltages

50. Va=Vm*sin(2*%pi*fHz*t);

51. Vb=Vm*sin(2*%pi*fHz*t-2*%pi/3);

52. Vc=Vm*sin(2*%pi*fHz*t+2*%pi/3);

53. *********************************

54. //MODELOWANIE STANU ZWARCIA

55. //if t>=3 then

56. //Va=0;

57. //Vb=0;

58. //Vc=0;

59. //end

60. fi=2*%pi*fHz*t;

61. // The transformation of the voltage to the d-q

62. [Vab]=2/3*[1,0.5,-0.5;0,sqrt(3)/2,-sqrt(3)/2]*[Va;Vb;Vc]

63. [Vdq]=[cos(fi),sin(fi);-sin(fi),cos(fi)]*Vab;

64. // Vdq(1)=Vq Vdq(2)=Vd



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65. Fmq=Xml*(Fqs/Xls+Fqr/Xlr);

66. Fmd=Xml*(Fds/Xls+Fdr/Xlr);

67. // Differential equations:

68. xdot(1)=wb*(Vdq(1)-

we/wb*Fds+Rs/Xls*(Xml/Xlr*Fqr+(Xml/Xls-1)*Fqs));

69. xdot(2)=wb*(Vdq(2)+we/wb*Fqs+Rs/Xls*(Xml/Xlr*Fdr+(Xm

l/Xls-1)*Fds));

70. xdot(3)=wb*(-(we-

wr)/wb*Fdr+Rr/Xlr*(Xml/Xls*Fqs+(Xml/Xlr-1)*Fqr));

71. xdot(4)=wb*((we-

wr)/wb*Fqr+Rr/Xlr*(Xml/Xls*Fds+(Xml/Xlr-1)*Fdr));

72. xdot(5)=p/(2*J)*(Te-wr*D-Tl);

73. endfunction

Differential equations (1 ... 4) are implemented in lines {68th .. 71}. Equation (13) is implemented in line {72}.

Before the differential equations were implemented equations determine the value of the parameters and variables. In line {62 and 63} Park'a implemented transformations (equation (14)).

The value of current IQS, ids, idr, IQR were determined from equations (8 ... 8.4) and have been implemented in the lines {43.46}.

TABLE 2.Currents.

74. // Simulation parameters

75. t=0:0.001:4;

76. t0=0;

77. fHz=50;

78. Vm=380;

79. // Initial conditions

80. y0=[0;0;0;0;0]

81. // Calling the function ode

82. y=ode(y0,t0,t,list(Vdqfun,Vm,fHz));

Before calling the function in lines {75 ... 80} are defined values: simulation time, amplitude, frequency and initial conditions (assuming zero initial conditions).

The values of the motor parameters such as winding resistance and inductance, mutual inductance, coefficient of drag bearings are defined inside a function VdqFun ().

Since the function returns the value streams, and angular velocity, for the determination of the electromagnetic torque and currents auxiliary variables and parameters must be re-calculated [2].

IV. SIMULATION OF INDUCTION MOTOR IN SCILABIE.

1) Simulation of start-up and idle

The induction machine - a compact induction motor with the

following parameters: Rs=0.435 - stator resistance [Ohm];

Rr=0.64 - rotor resistance [Ohm];

Ls=0.0477 -stator winding inductance [H] ;

Lr=0.0577 - rotor winding inductance [H];

Lm =0.012;

D=0.001 - coefficient of drag;

J=0.28 - moment of inertia;

p=6 - number of pole pairs;

fHz=50; Vm=380;

Figure 2. Mileage angular velocity wr [rpm].

Figure 3Mileage electromagnetic torque Te.

Figure 4. Current waveform ia [A].

Figure 5. Current waveform ib[A].

Figure 6. Current waveform ic [A].

Figure 2 shows the course of the rotor speed at the time of start-up and operation sterile induction machine. Speed is set at about 985 rev / min. In Figures 4, 5, 6 show the course of the phase currents. Figure 3 shows the course of the electromagnetic torque during start-up and idle.[3]

2.) 3-phase fault simulation engine.

Simulation of a short circuit in the power supply circuit is modeled in the lines {40 ..... 45}:



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Condition if t> = 3 then determines the second stator windings

short to ground. For modeling faults at different stages of the

parameters should be set in the environment. After calling the function from () displays the results of the

simulation.

Figure 7. Speed stages, power supply circuit w 3 sek.

Figure 8. Mileage electromagnetic torque.

Figure 9. Current waveform ia[A].

Figure 10. Current waveform ib[A].

Figure 11. Current waveform ic [A].

Short circuit (short circuit 3 phase) of power induction machine is modeled in 3 seconds.

V. SUMMARY

From the analysis of velocity waveforms to the rotation of the machine to determine the value of the electromagnetic torque should decrease, while the average value of the results set point is set at a value greater than the values occurring during start-up..

To validate the model, the model was built in the environment maltab / Simulink, which is implemented exactly the same structure equations. Figure 12 shows a time course of the electromagnetic environment of the model matlab/simulink.[4].

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-10

-5

0

5

10

15

Figure 12. Mileage electromagnetic torque at start-up - model in the environment Matlab

Because the model is implemented in an environment like

Scilab and Matlab are identical (in terms of mathematical

equations, and the implementation of the program itself), the

differences between the results are not the result of the

mathematical model is not correct, but the difference and computational capabilities of both environments. For Scilab

environment simulations were carried out for different time

periods and different solvers sampling. A further analysis of the induction machine operation

should be carried out on a model made in Matlab or implement equations describing the motion of the machine in a different form, because due to the error introduced by Scilab environment does not allow for the correct analysis of the results.

REFERENCES

[1] P.C. Krause, Analysis of Electric Machinery ,McGraw-Hill Book

Company, 1986.

[2] Akpinar E., Pillay P.: A Computer program to predict the performance of slip energy recorery induction motor drire, IEEE Trans, on Energy

Conv.. 5. 2. 1990. 357-265

[3] Pasek W., Dynamics of AC machines, Publisher HELION, Gliwice, 1998.

[4] Zalas P., Zawilak J., Influence of the excitation current control system for the synchronization process synchronous motor, operating problems

of electric machines and drives: BOBRME "Komel" 2006, 83–88.



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