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// Example 6.2
// Determine (a) Capacitance required in series with the auxillary winding
// in order to obtain a 90 degree phase displacement between the current in
// the main winding and the current in the auxillary winding at locked rotor
// (b) Locked rotor torque in terms of the machine constant
// Page No. 265
clc;
clear;
close;
// Given data
Zmw=2.00+%i*3.50 // Main winding impedance
Zaw=9.15+%i*8.40 // Auxillary winding impedance
VT=120; // Transformer voltage
Xaw=8.40; // Auxillary winding reactance
Raw=9.15; // Auxillary winding resistance
f=60; // Frequency
Tlr=107.1; // Original torque
// (a) Capacitance required in series with the auxillary winding
// Main winding impedance in polar form
// Complex to Polar form...
Zmw_Mag=sqrt(real(Zmw)^2+imag(Zmw)^2); // Magnitude part
Zmw_Ang=atan(imag(Zmw),real(Zmw))*180/%pi; // Angle part
// Auxillary winding impedance in polar form
// Complex to Polar form...
Zaw_Mag=sqrt(real(Zaw)^2+imag(Zaw)^2); // Magnitude part
Zaw_Ang=atan(imag(Zaw),real(Zaw))*180/%pi; // Angle part
// Main winding current
Imw_Mag=VT/Zmw_Mag; // Main winding current magnitude
Imw_Ang=0-Zmw_Ang; // Main winding current angle
// Auxillary winding current
Iaw_Mag=VT/Zaw_Mag; // Auxillary winding current magnitude
Iaw_Ang=0-Zaw_Ang; // Auxillary winding current angle
Theta_awi=90-60.26; // Required phase angle
Theta_awz=-Theta_awi;
Xc=Xaw-Raw*tand(Theta_awz); // Capacitive reactance
C=1/2*%pi*f*Xc; // Required capacitance
// (b) Locked rotor torque in terms of the machine constant
Zawnew=Raw+%i*Xaw-%i*Xc; // Auxillary winding impedance
// Complex to Polar form...
Zawnew_Mag=sqrt(real(Zawnew)^2+imag(Zawnew)^2); // Magnitude part
Zawnew_Ang=atan(imag(Zawnew),real(Zawnew))*180/%pi; // Angle part
Iawnew_Mag=VT/Zawnew_Mag; // Auxillary winding current magnitude
Iawnew_Ang=0-Zawnew_Ang; // Auxillary winding current magnitude
Tlenew=Imw_Mag*Iawnew_Mag*sind(90);
// Percent change increase in locked rotor torque
PI=(Tlenew-Tlr)/Tlr*100;
// Display result on command window
printf("\n Required capacitance = %0.1f microF ",C);
printf("\n Percent increase in locked rotor torque = %0.0f Percent",PI);
//Note: Capacitor computation is wrong in the book
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