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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 : 9.12 :
clear ; clc ; close ; // Clear the work space and console
// GIVEN DATA
z_f = 5 ; // Fault-impedance in Ω
z_g = 10 ; // Ground-impedance in Ω
kv = 230 ; // Line voltage in kV from Exa 9.9
Z_0 = 0.56*%i ; // Zero impedance in pu Ω
Z_1 = 0.2618*%i ; // Positive sequence Impedance in pu Ω
Z_2 = 0.3619*%i ; // Negative sequence Impedance in pu Ω
v = 1*exp(%i*0*180/%pi) ;
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] ;
// CALCULATIONS
// For case (b)
Z_B = kv^2/200 ; // Base impedance of 230 kV line
Z_f = z_f/Z_B ; // fault impedance in pu Ω
Z_g = z_g/Z_B ;
I_a1 = v/( (Z_1 + Z_f) + ( (Z_2 + Z_f)*(Z_0 + Z_f + 3*Z_g)/((Z_2 + Z_f)+(Z_0 + Z_f + 3*Z_g)) )) ; // Sequence current in pu A
I_a2 = -[(Z_0 + Z_f + 3*Z_g)/( (Z_2 + Z_f )+(Z_0 + Z_f + 3*Z_g) )]*I_a1 ; // Sequence current in pu A
I_a0 = -[(Z_2 + Z_f)/( (Z_2 + Z_f)+(Z_0 + Z_f + 3*Z_g) )]*I_a1 ; // Sequence current in pu A
I_f = A*[I_a0 ; I_a1 ; I_a2] ; // Phase currents in pu A
// For case (c)
V = [0 ; v ; 0] - [Z_0 0 0 ; 0 Z_1 0 ; 0 0 Z_2]*[I_a0 ; I_a1 ; I_a2] ; // Sequence Voltages in pu V
V_f = A*[V] ; // Phase voltages in pu V
// For case (d)
V_abf = V_f(1,1) - V_f(2,1) ; // Line-to-line voltages at fault points a & b
V_bcf = V_f(2,1) - V_f(3,1) ; // Line-to-line voltages at fault points b & c
V_caf = V_f(3,1) - V_f(1,1) ; // Line-to-line voltages at fault points c & a
// DISPLAY RESULTS
disp("EXAMPLE : 9.12 : SOLUTION :-") ;
printf("\n (b) Sequence currents are , \n") ;
printf("\n I_a0 = %.4f<%.2f pu A ",abs(I_a0),atand( imag(I_a0),real(I_a0) )) ;
printf("\n I_a1 = %.4f<%.2f pu A ",abs(I_a1),atand( imag(I_a1),real(I_a1) )) ;
printf("\n I_a2 = %.4f<%.2f pu A ",abs(I_a2),atand( imag(I_a2),real(I_a2) )) ;
printf("\n \n Phase currents are , [I_af ; I_bf ; I_cf] = pu A \n ") ;
printf("\n %.4f<%.1f ",abs(I_f),atand(imag(I_f),real(I_f) )) ;
printf("\n \n (c) Sequence voltages , [V_a0 ; V_a1 ; V_a2] = pu V \n ") ;
printf("\n %.4f<%.1f ",abs(V),atand(imag(V),real(V) )) ;
printf("\n \n Phase voltages , [V_af ; V_bf ; V_cf] = pu V \n ") ;
printf("\n %.4f<%.1f ",abs(V_f),atand(imag(V_f),real(V_f) )) ;
printf("\n \n (d) Line-to-line voltages at the fault points are , \n") ;
printf("\n V_abf = %.4f<%.1f pu V \n",abs(V_abf),atand( imag(V_abf),real(V_abf) )) ;
printf("\n V_bcf = %.4f<%.1f pu V \n",abs(V_bcf),atand( imag(V_bcf),real(V_bcf) )) ;
printf("\n V_caf = %.4f<%.1f pu V \n",abs(V_caf),atand( imag(V_caf),real(V_caf) )) ;
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