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+// Electric Machinery and Transformers

+// Irving L kosow 

+// Prentice Hall of India

+// 2nd editiom

+

+// Chapter 6: AC DYNAMO VOLTAGE RELATIONS-ALTERNATORS

+// Example 6-5

+

+clear; clc; close; // Clear the work space and console.

+

+// Given data

+kVA = 100 ; // kVA rating of the 3-phase alternator

+V_L = 1100 ; // Line voltage of the 3-phase alternator in volt

+

+// dc-resistance test data

+E_gp1 = 6 ; // generated phase voltage in volt 

+V_l = E_gp1 ; // generated line voltage in volt

+I_a1 = 10 ; // full-load current per phase in A

+cos_theta_b1 = 0.8 ; // 0.8 PF lagging (case b)

+cos_theta_b2 = 0.8 ; // 0.8 PF leading (case b)

+sin_theta_b1 = sqrt( 1 - (cos_theta_b1)^2 ); // (case b)

+sin_theta_b2 = sqrt( 1 - (cos_theta_b2)^2 ); // (case b)

+

+// open-circuit test data

+E_gp2 = 420 ; // generated phase voltage in volt 

+I_f2 = 12.5 ; // Field current in A

+

+// short-circuit test data

+I_f3 = 12.5 ; // Field current in A

+// Line current I_l = rated value   in A

+

+// Calculations

+// Assuming that the alternator is delta-connected

+// case a :

+I_a_rated = (kVA*1000)/(V_L*sqrt(3)); // Rated current per phase in A

+I_L = I_a_rated ; // Line current in A 

+

+V_p = E_gp2 ; // Phase voltage in volt

+V_l = V_p ; // Line voltage in volt (from short circuit data)

+

+I_p = I_L / sqrt(3) ; // Phase current in A (delta connection)

+I_a = I_p ; // Rated current in A

+

+Z_s = V_l / I_p ; // Synchronous impedance per phase

+R_dc = E_gp1/(2*I_a1); // effective dc armature resistance in ohm/winding

+R_ac = R_dc * 1.5 ; // effective ac armature resistance in ohm.phase

+

+// R_eff in delta = 3 * R_eff in Y

+R_eff = 3 * R_ac ; // Effective armature resistance in ohm

+R_a = R_eff ; // effective ac armature resistance in ohm.phase from dc resistance test

+

+X_s = sqrt( Z_s^2 - R_a^2 ); // Synchronous reactance per phase

+

+V_p = V_L ; // Phase voltage in volt (delta-connection)

+

+// At 0.8 PF lagging

+E_gp1 = ( V_p*cos_theta_b1 + I_a * R_a ) + %i*( V_p*sin_theta_b1 + I_a*X_s);

+E_gp1_m=abs(E_gp1);//E_gp1_m=magnitude of E_gp1 in volt

+E_gp1_a=atan(imag(E_gp1) /real(E_gp1))*180/%pi;//E_gp1_a=phase angle of E_gp1 in degrees

+V_n1 = E_gp1_m ; // No-load voltage in volt

+V_f1 = V_p ; // Full-load voltage in volt

+VR1 = ( V_n1 - V_f1 )/ V_f1 * 100; // percent voltage regulation at 0.8 PF lagging 

+

+

+// At 0.8 PF leading

+E_gp2 = ( V_p*cos_theta_b2 + I_a * R_a ) + %i*( V_p*sin_theta_b2 - I_a*X_s);

+E_gp2_m=abs(E_gp2);//E_gp2_m=magnitude of E_gp2 in volt

+E_gp2_a=atan(imag(E_gp2) /real(E_gp2))*180/%pi;//E_gp2_a=phase angle of E_gp2 in degrees

+V_n2 = E_gp2_m ; // No-load voltage in volt

+V_f2 = V_p ; // Full-load voltage in volt

+VR2 = ( V_n2 - V_f2 )/V_f2 * 100 ; // percent voltage regulation at 0.8 PF leading 

+

+// Display the results

+disp("Example 6-5 Solution : ");

+printf(" \n Assuming that the alternator is delta-connected : \n ");

+printf(" \n a: I_p = %.3f A ", I_p );

+printf(" \n    Z_s = %.2f ohm/phase ", Z_s );

+printf(" \n    R_eff in delta = %.2f ohm/phase ", R_eff );

+printf(" \n    X_s = %.1f ohm/phase \n", X_s );

+printf(" \n    R_eff, reactance and impedance per phase in delta is 3 times")

+printf(" \n    the value when connected in Y. \n")

+

+printf(" \n b: At 0.8 PF lagging ");

+printf(" \n    Percent voltage regulation = %.1f percent \n", VR1 );

+

+printf(" \n    At 0.8 PF leading ");

+printf(" \n    Percent voltage regulation = %.1f percent \n", VR2 );

+printf(" \n    Percentage voltage regulation remains the same both in Y and delta connection.");