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//To calculate secondary terminal voltage and full load efficiency at unity pf
clc;
clear;
P=4*(10^3);
E1=200;
E2=400;
// O.C Test
V=200;
Pil=70; // Iron Loss
Ioc=0.8;
R0=(V^2)/Pil;
Iw=V/R0;
Im=sqrt((Ioc^2)-(Iw^2));
X0=V/Im;
// S.C Test
Vsc=17.5;
Isc=9;
Psc=50;
R2eq=Psc/(Isc^2);
Z2eq=Vsc/Isc;
X2eq=sqrt((Z2eq^2)-(R2eq^2));
Is=P/E2; // Full load current
Pc=((Is/Isc)^2)*Psc;
fleff=(P*100)/(P+Pil+Pc);// Full load efficiency
printf('i) The Full load efficiency at unity power factor = %g percent \n \n',fleff)
// Secondary Terminal voltages cosidering full load secondary current as reference
Vs=poly([0 1],'Vs','c');
Vz=Is*(R2eq+(X2eq*%i));
// Using the characteristic equation in polar form, 'Is' as reference
// E = V/_theta + Is/_0 *(Z/_phi)
// Function to evalulate the right side of the equation in complex form
deff('a=stv(b)','a=Vs*(complex(cosd(b),sind(b)))+Vz')
case1=stv(acosd(1));
case2=stv(acosd(0.8));
case3=stv(-acosd(0.8));
// Funtion to calculate the characteristic equation of Vs
deff('x=svol(y)','x=(real(y)^2)+(imag(y)^2)-(E2^2)')
cs1=svol(case1);
cs2=svol(case2);
cs3=svol(case3);
// Roots of the characteristic equations
r1=roots(cs1);
r2=roots(cs2);
r3=roots(cs3);
// To find the positive roots
if(imag(sqrt(r1(1))))
Vs1=r1(2);
else
Vs1=r1(1);
end
if(imag(sqrt(r2(1))))
Vs2=r2(2);
else
Vs2=r2(1);
end
if(imag(sqrt(r3(1))))
Vs3=r3(2);
else
Vs3=r3(1);
end
printf('ii) The Secondary terminal voltages for various power factors are as follows \n')
printf('a) At Unity power factor, Vs = %g V \n',Vs1)
printf('b) At 0.8 power factor(Lagging), Vs = %g V \n',Vs2)
printf('c) At 0.8 power factor(Leading), Vs = %g V \n',Vs3)
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