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+// ELECTRIC POWER TRANSMISSION SYSTEM ENGINEERING ANALYSIS AND DESIGN

+// TURAN GONEN

+// CRC PRESS

+// SECOND EDITION

+

+// CHAPTER : 9 : SYMMETRICAL COMPONENTS AND FAULT ANALYSIS

+

+// EXAMPLE : 9.3 :

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

+

+// GIVEN DATA

+l = 40 ; // line length in miles

+// Conductor parameter from Table A.3

+r_a = 0.206 ; // Ohms per conductor per mile in Ω/mi

+r_b = r_a ; // r_a = r_b = r_c in Ω/mi

+D_s = 0.0311 ; // GMR in ft where D_s = D_sa = D_sb = D_sc

+D_ab = sqrt(2^2 + 8^2) ; // GMR in ft

+D_bc = sqrt(3^2 + 13^2) ; // GMR in ft

+D_ac = sqrt(5^2 + 11^2) ; // GMR in ft

+D_e = 2788.5 ; // GMR in ft since earth resistivity is zero

+r_e = 0.09528 ; // At 60 Hz in Ω/mi

+

+// CALCULATIONS

+// For case (a)

+Z_aa =[(r_a + r_e) + %i * 0.1213*log(D_e/D_s)]*l ; // Self impedance of line conductor in Ω

+Z_bb = Z_aa ;

+Z_cc = Z_bb ;

+Z_ab = [r_e + %i * 0.1213*log(D_e/D_ab)]*l ; // Mutual impedance in Ω

+Z_ba = Z_ab ;

+Z_bc = [r_e + %i * 0.1213*log(D_e/D_bc)]*l ;

+Z_cb = Z_bc ;

+Z_ac = [r_e + %i * 0.1213*log(D_e/D_ac)]*l ;

+Z_ca = Z_ac ;

+Z_abc = [Z_aa Z_ab Z_ac ; Z_ba Z_bb Z_bc ; Z_ca Z_cb Z_cc] ; // Line impedance matrix

+

+// For case (b)

+a = 1*exp(%i*120*%pi/180) ; // By symmetrical components theory to 3-Φ system

+A = [1 1 1; 1 a^2 a ;1 a a^2] ;

+Z_012 = inv(A) * Z_abc*A ; // Sequence impedance matrix

+

+// DISPLAY RESULTS

+disp("EXAMPLE : 9.3 : SOLUTION :-") ;

+printf("\n (a) Line impedance matrix , [Z_abc] = \n") ; disp(Z_abc) ;

+printf("\n (b) Sequence impedance matrix of line , [Z_012] = \n") ; disp(Z_012) ;