# The three-phase, 230-V, 60-Hz, 12-kW, four-pole induction motor R2 = 0.2 Ω is to be operated from a variable-frequency, constant-volts-per-hertz motor drive whose terminal voltage is 230 V at 60 Hz. The motor is driving a load whose power can be assumed to vary as: P_load=10.5 (n/1800)^3 Kw Where n is the load speed in r/min. Motor rotational losses can be assumed to be negligible. Write a MATLAB script to find the line-to-line terminal voltage, the motor speed in r/min, the slip and the motor load in kW for (a) a source frequency of 60 Hz and (b) a source frequency of 40 Hz.

Question

The three-phase, 230-V, 60-Hz, 12-kW, four-pole induction motor R2 = 0.2 Ω is to be operated from a variable-frequency, constant-volts-per-hertz motor drive whose terminal voltage is 230 V at 60 Hz. The motor is driving a load whose power can be assumed to vary as:

Where n is the load speed in r/min. Motor rotational losses can be assumed to be negligible. Write a MATLAB script to find the line-to-line terminal voltage, the motor speed in r/min, the slip and the motor load in kW for (a) a source frequency of 60 Hz and (b) a source frequency of 40 Hz.

## (a)

clc

clear all

close all

V1  =  230/sqrt(3)  ;

N  =  3;

poles  =  4  ;

f1  =  60 ;

R1  =  0.095;

R2  =  0.2;

X1  =  0.680;

X2  =  0.672;

Xm  =  18.7;

f2  =  60 ;

X3  =  X1*(f2/f1)  ;

X4  =  X2*(f2/f1)  ;

Xm1  =  Xm*  (f2/f1)  ;

V2  =  V1*(f2/f1)  ;

ws  =  4*pi*f2/poles;

ns  =  120*f1/poles;

V3  =  abs(V2*1i*Xm/(R1  +  1i*(X1+Xm))  )  ;

Z  =  1i*Xm*(R1+1i*X1)/(R1  +  1i*(X1+Xm))  ;

R3  =  real(Z)  ;

X5  =  imag(Z)  ;

slip  =  0.0000000001 ;

error  =512;

while  error  >=  0;

slip  =  slip  +  0.00001;

nm  =  ns*(1-slip)  ;

wm  =  ws*  (1-slip)  ;

tm  =  (1/ws)*N*V3^2  *(R2/slip)  ;

tm1  =  tm/((R1+R2/slip)^2+(X3+X4)^2)  ;

pm  =  tm1*wm;

pl  =  (10.5e3*((nm/1800)^3));

error=pl-pm;

end

fprintf('\nFor fe : %g [Hz] : ',f2)

fprintf('\n Terminal voltage = %g [volt] ',V2*sqrt(3))

fprintf('\n nm = %g',nm)

fprintf('\n slip = %g [unitless] ',slip)

fprintf  ( ' \n\n' )

## The Result

For fe : 60 [Hz] :
Terminal voltage = 230 [volt]
nm = 1720.67
slip = 0.04407 [unitless]

## (b)

For fe : 60 [Hz] :
Terminal voltage = 230 [volt]
nm = 1720.67
slip = 0.04407 [unitless]

clc

clear all

close all

V1  =  230/sqrt(3)  ;

N  =  3;

poles  =  4  ;

f1  =  60 ;

R1  =  0.095;

R2  =  0.2;

X1  =  0.680;

X2  =  0.672;

Xm  =  18.7;

f2  =  40 ;

X3  =  X1*(f2/f1)  ;

X4  =  X2*(f2/f1)  ;

Xm1  =  Xm*  (f2/f1)  ;

V2  =  V1*(f2/f1)  ;

ws  =  4*pi*f2/poles;

ns  =  120*f2/poles;

V3  =  abs(V2*1i*Xm/(R1  +  1i*(X1+Xm))  )  ;

Z  =  1i*Xm*(R1+1i*X1)/(R1  +  1i*(X1+Xm))  ;

R3  =  real(Z)  ;

X5  =  imag(Z)  ;

slip  =  0.0000000001 ;

error  =512;

while  error  >=  0;

slip  =  slip  +  0.00001;

nm  =  ns*(1-slip)  ;

wm  =  ws*  (1-slip)  ;

tm  =  (1/ws)*N*V3^2  *(R2/slip)  ;

tm1  =  tm/((R1+R2/slip)^2+(X3+X4)^2)  ;

pm  =  tm1*wm;

pl  =  (10.5e3*((nm/1800)^3));

error=pl-pm;

end

fprintf('\nFor fe : %g [Hz] : ',f2)

fprintf('\n Terminal voltage = %g [volt] ',V2*sqrt(3))

fprintf('\n nm = %g',nm)

fprintf('\n slip = %g [unitless] ',slip)

fprintf  ( ' \n\n' )

## The Result

For fe : 40 [Hz] :
Terminal voltage = 153.333 [volt]
nm = 1166.39
slip = 0.02801 [unitless]

A460-V. 30-hp. 60-Hz. four-pole. Star-connected induction motor has two possible rotor designs. a single-cage rotor and a double-cage rotor. (The stator is identical for either rotor design.) The motor with the single-cage rotor may be modeled by the following impedances in ohms per phase referred to the stator circuit: R1= 0.641 Ω X1 = 0.750 Ω R2 = 0.3 Ω X2 = 0.5 Ω Xm= 26.3 Ω The motor with the double-cage rotor may be modeled as a tightly coupled. High resistance outer cage in parallel with a loosely coupled. Low resistance inner cage The stator and magnetization resistance and reactances will be identical with those in the single-cage design. The resistance and reactance of the rotor outer cage are: R2o, = 3.2 Ω X2o, = 0.5 Ω The resistance and reactance of the inner cage are R2i = 0.4 Ω X2i = 3.3 Ω Write a MATLAB script to calculate and plot the two torque-speed characteristics with the two rotor designs. How do they compare?

حجم الخط
+
16
-
تباعد السطور
+
2
-