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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 : 9.4 :

+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_s =[(r_a + r_e) + %i*0.1213*log(D_e/D_s)]*l ; // Self impedance of line conductor in Ω . From equ 9.49

+D_eq = (D_ab * D_bc * D_ac)^(1/3) ; // Equ GMR

+Z_m = [r_e + %i*0.1213*log(D_e/D_eq)]*l ; // From equ 9.50

+Z_abc = [Z_s Z_m Z_m ; Z_m Z_s Z_m ; Z_m Z_m Z_s] ; // Line impedance matrix

+

+// For case (b)

+Z_012 = [(Z_s+2*Z_m) 0 0 ; 0 (Z_s-Z_m) 0 ; 0 0 (Z_s-Z_m)] ; // Sequence impedance matrix . From equ 9.54

+

+// DISPLAY RESULTS

+disp("EXAMPLE : 9.4 : SOLUTION :-") ;

+printf("\n (a) Line impedance matrix when line is completely transposed , [Z_abc] = \n") ; disp(Z_abc) ;

+printf("\n (b) Sequence impedance matrix when line is completely transposed , [Z_012] = \n") ; disp(Z_012) ;