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// Example 8.3
// Determine (a) System active power (b) Power factor of the synchronous motor
// (c) System power factor (d) Percent change in synchronous field current
// required to adjust the system power factor to unity (e) Power angle of the
// synchronous motor for the conditions in (d)
// Page No. 324
clc;
clear;
close;
// Given data
Php=400; // Power in hp
eta=0.958; // Efficiency
Pheater=50000; // Resistance heater power
Vs=300; // Synchronous motor voltage
eta2=0.96; // Synchronous motor efficiency
Xs=0.667; // Synchronous reactnace
VT=460; // 3-Phase supply voltage
delta=-16.4; // Power angle
// (a) System active power
Pindmot=Php*0.75*746/(eta); // Motor operating at three quarter rated load
Psynmot=Vs*0.5*746/(eta2); // Synchronous motor power
Psys=Pindmot+Pheater+Psynmot;
Psysk=Psys/1000;
// (b) Power factor of the synchronous motor
Pin=Psynmot; // Power input
Vtph=VT/sqrt(3); // Voltage per phase
Ef=-(Pin*Xs)/(3*Vtph*sind(delta));
// Complex to Polar form...
Ef_Mag=Ef; // Magnitude part
Ef_Ang=delta; // Angle part
Vtph_Mag=Vtph;
Vtph_Ang=0;
////////////
N01=Ef_Mag+%i*Ef_Ang; // Ef in polar form
N02=Vtph_Mag+%i*Vtph_Ang; // Vt in polar for
N01_R=Ef_Mag*cos(-Ef_Ang*%pi/180); // Real part of complex number Ef
N01_I=Ef_Mag*sin(Ef_Ang*%pi/180); //Imaginary part of complex number Ef
N02_R=Vtph_Mag*cos(-Vtph_Ang*%pi/180); // Real part of complex number Vt
N02_I=Vtph_Mag*sin(Vtph_Ang*%pi/180); //Imaginary part of complex number Vt
FinalNo_R=N01_R-N02_R;
FinalNo_I=N01_I-N02_I;
FinNum=FinalNo_R+%i*FinalNo_I;
// Complex to Polar form...
FN_M=sqrt(real(FinNum)^2+imag(FinNum)^2); // Magnitude part
FN_A = atan(imag(FinNum),real(FinNum))*180/%pi;// Angle part
Ia_Mag=FN_M/Xs; // Magnitude of Ia
Ia_Ang=FN_A-(-90); // Angle of Ia
Theta=0-Ia_Ang;
FP=cosd(Theta); // Power factor
// (c) System power factor
ThetaIndMot=acosd(0.891); // Induction motor power factor
Thetaheat=acosd(1); // Heater power factor
ThetaSyncMot=-34.06; // Synchronous motor power factor
Qindmot=tand(27)*Pindmot;
Qsynmot=tand(ThetaSyncMot)*Psynmot;
Qsys=Qindmot+Qsynmot;
Ssys=Psys+%i*Qsys; // System variable in complex form
// Complex to Polar form...
Ssys_Mag=sqrt(real(Ssys)^2+imag(Ssys)^2); // Magnitude part
Ssys_Ang = atan(imag(Ssys),real(Ssys))*180/%pi; // Angle part
FPsys=cosd(Ssys_Ang); // System power factor
// (d) Percent change in synchronous field current required to adjust the
// system power factor to unity
Ssynmot=Psynmot-(%i*(-Qsynmot+Qsys)); // Synchronous motor system
// Complex to Polar form...
Ssynmot_Mag=sqrt(real(Ssynmot)^2+imag(Ssynmot)^2); // Magnitude part
Ssynmot_Ang=atan(imag(Ssynmot),real(Ssynmot))*180/%pi; // Angle part
Ssynmot1ph_Mag=Ssynmot_Mag/3; // For single phase magnitude
Ssynmot1ph_Ang=Ssynmot_Ang; // For single phase angle
Iastar_Mag=Ssynmot1ph_Mag/Vtph; // Current magnitude
Iastar_Ang=Ssynmot1ph_Ang-0; // Current angle
IaNew_Mag=Iastar_Mag;
IaNew_Ang=-Iastar_Ang;
IaXs_Mag=IaNew_Mag*Xs;
IaXs_Ang=IaNew_Ang-90;
// Convert these number into complex and then perform addition
// Polar to Complex form
// Y=29.416<-62.3043 //Polar form number
IaXs_R=IaXs_Mag*cos(-IaXs_Ang*%pi/180); // Real part of complex number
IaXs_I=IaXs_Mag*sin(IaXs_Ang*%pi/180); // Imaginary part of complex number
Efnew=Vtph+IaXs_R+%i*IaXs_I;
// Complex to Polar form...
Efnew_Mag=sqrt(real(Efnew)^2+imag(Efnew)^2); // Magnitude part
Efnew_Ang=atan(imag(Efnew),real(Efnew))*180/%pi; // Angle part
DeltaEf=(Efnew_Mag-Ef)/Ef;
// (e) Power angle of the synchronous motor
deltasynmot=Efnew_Ang;
// Display result on command window
printf("\n System active power = %0.1f kW ",Psysk);
printf("\n Power factor of the synchronous motor = %0.3f leading ",FP);
printf("\n System power factor = %0.3f lagging ",FPsys);
printf("\n Percent change in synchronous field current = %0.2f Percent ",DeltaEf*100);
printf("\n Power angle of the synchronous motor = %0.2f deg ",deltasynmot);
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