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+clc;
+v=6600; // rated voltage of motor
+xs=20 ; // per phase synchronous reactance
+p=500000; // VA rating of motor
+il=p/(sqrt(3)*v); // rated armature current
+vt=v/sqrt(3); // per phase rated voltage
+disp('case a');
+de=10; // load angle
+c1=1;
+c2=-2*vt*cosd(de);
+c3=vt^2-(il*xs)^2; // coefficients of quadratic equation in Ef
+p= [ c1 c2 c3 ];
+Ef=roots(p);
+printf('Per phase excitation EMF at lagging pf is %f v\n',Ef(2));
+printf('Excitation line EMF at lagging pf is %f v\n',sqrt(3)*Ef(2));
+printf('Per phase excitation EMF at leading pf is %f v\n',Ef(1));
+printf('Excitation line EMF at leading pf is %f v\n',sqrt(3)*Ef(1));
+disp('case b');
+disp('For lagging pf');
+pd=(3*vt*Ef(2)*sind(de))/xs;
+pf=pd/(sqrt(3)*v*il);
+printf('Mechanical power developed is %f W\n',pd);
+printf('Power factor is %f lagging\n',pf);
+disp('For leading pf');
+pd=(3*vt*Ef(1)*sind(de))/xs;
+pf=pd/(sqrt(3)*v*il);
+printf('Mechanical power developed is %f W\n',pd);
+printf('Power factor is %f leading\n',pf);
+disp('case c');
+p=200000; // delivered power
+de=90; // load angle for falling out of step
+// motor falls out of step at de= 90 degrees
+Ef=(p*xs)/(3*sind(de)*vt);
+printf('Minimum excitation voltage per phase is %f v',Ef);
+
+