// Electric Machinery and Transformers // Irving L kosow // Prentice Hall of India // 2nd editiom // Chapter 14: TRANSFORMERS // Example 14-19 clear; clc; close; // Clear the work space and console. // Given data kVA = 20 ; // kVA rating of the step-down transformer S = 20000 ; // power rating of the step-down transformer in VA V_1 = 2300 ; // Primary voltage in volt V_2 = 230 ; // Secondary voltage in volt Z_e1 = 5.75 ; // Equivalent impedance w.r.t HV side in ohm R_e1 = 3.3 ; // Equivalent resistance w.r.t HV side in ohm X_e1 = 4.71 ; // Equivalent reactance w.r.t HV side in ohm // w.r.t HV side following is SC-test data P1 = 250 ; // wattmeter reading in W I1 = 8.7 ; // Input current in A V1 = 50 ; // Input voltage in V // Calculations // case a Z_e1_drop = V1 ; // High voltage impedance drop in volt // case b theta = acosd(R_e1/Z_e1) ; // PF angle in degrees R_e1_drop = I1*Z_e1*cosd(theta) ; //HV-side equivalent resistance voltage drop in volt // case c X_e1_drop = I1*Z_e1*sind(theta) ; //HV-side equivalent reactance voltage drop in volt // case d // At unity PF cos_theta1 = 1; sin_theta1 = sqrt(1 - (cos_theta1)^2); // Induced voltage when the transformer is delivering rated current to unity PF load E_1 = (V_1*cos_theta1 + I1*R_e1) + %i*(V_1*sin_theta1 + I1*X_e1); E_1_m = abs(E_1);//E_1_m=magnitude of E_1 in volt E_1_a = atan(imag(E_1) /real(E_1))*180/%pi;//E_1_a=phase angle of E_1 in degrees VR_unity_PF = ( (E_1_m - V_1) / V_1 ) * 100 ; // Transformer voltage regulation // case e // at 0.7 lagging PF cos_theta_1 = 0.7 ; // lagging PF sin_theta_1 = sqrt(1 - (cos_theta_1)^2); // Induced voltage when the transformer is delivering rated current to unity PF load E1 = (V_1*cos_theta_1 + I1*R_e1) + %i*(V_1*sin_theta_1 + I1*X_e1); E1_m = abs(E1);//E1_m=magnitude of E1 in volt E1_a = atan(imag(E1) /real(E1))*180/%pi;//E1_a=phase angle of E1 in degrees VR_lag_PF = ( (E1_m - V_1) / V_1 ) * 100 ; // Transformer voltage regulation // Display the results disp("Example 14-19 Solution : "); printf(" \n a: High voltage impedance drop :\n I_1*Z_e1 = V_1 = %d\n",Z_e1_drop); printf(" \n b: θ = %.f degrees \n",theta ); printf(" \n High voltage resistance drop :\n I_1*R_e1 = %.2f \n",R_e1_drop); printf(" \n c: High voltage reactance drop :\n I_1*X_e1 = %.2f \n",X_e1_drop); printf(" \n d: At unity PF,\n E_2 in volt = ");disp(E_1); printf(" \n E_2 = %.2f <%.2f V \n ",E_1_m , E_1_a); printf(" \n Voltage regulation at unity PF :\n VR = %.2f percent ",VR_unity_PF ); printf(" \n\n e: At 0.7 lagging PF, \n E_2 in volt = ");disp(E1); printf(" \n E_2 = %.2f <%.2f V \n ",E1_m , E1_a); printf(" \n Voltage regulation at 0.7 lagging PF :\n VR = %.2f percent ",VR_lag_PF );