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// A Texbook on POWER SYSTEM ENGINEERING
// A.Chakrabarti, M.L.Soni, P.V.Gupta, U.S.Bhatnagar
// DHANPAT RAI & Co.
// SECOND EDITION
// PART II : TRANSMISSION AND DISTRIBUTION
// CHAPTER 11: LOAD FREQUENCY CONTROL AND LOAD SHARING OF POWER GENERATING SOURCES
// EXAMPLE : 11.13 :
// Page number 337-338
clear ; clc ; close ; // Clear the work space and console
// Given data
l = 20.0 // Length of cable(km)
r = 0.248 // Resistance(ohm/km)
x = 0.50*10**-3 // Inductance(H/m)
V_gen = 6600.0 // Generation voltage(V)
f = 50.0 // Frequency(Hz)
V = 33000.0 // Transmission voltage(V)
rating = 10.0 // Transformer rating(MVA)
loss_cu = 100.0 // Copper loss at full load(kW)
x_tr = 2.5/100 // Transformer reactance
load = 7.5 // Load to be transmitted(MW)
PF = 0.71 // Lagging power factor
// Calculations
R = l*r // Resistance of the cable(ohm)
I_fl = rating*10**6/(3**0.5*V) // Transformer current at full load(A)
R_eq = loss_cu*1000/(3*I_fl**2) // Equivalent resistance per phase of transformer(ohm)
R_total_hv = R+2.0*R_eq // Total resistance per conductor in terms of hv side(ohm)
X = 2.0*%pi*f*l*x // Reactance of cable per conductor(ohm)
per_X_tr = V/3**0.5*x_tr/I_fl // % reactance of transformer(ohm)
X_total_hv = X+2.0*per_X_tr // Total reactance per conductor in terms of hv side(ohm)
I = load*10**6/(3**0.5*V*PF) // Line current at receiving end(A)
IR = I*R_total_hv // IR drop(V)
IX = I*X_total_hv // IX drop(V)
E_r = V/3**0.5 // Phase voltage at station B(V)
cos_phi_r = PF
sin_phi_r = (1-PF**2)**0.5
E_s = ((E_r*cos_phi_r+IR)**2+(E_r*sin_phi_r+IX)**2)**0.5/1000 // Sending end voltage(kV)
E_s_ll = 3**0.5*E_s // Sending end line voltage(kV)
V_booster = 3**0.5*(E_s-E_r/1000) // Booster voltage between lines(kV)
tan_phi_s = (E_r*sin_phi_r+IX)/(E_r*cos_phi_r+IR) // tanΦ_s
phi_s = atand(tan_phi_s) // Φ_s(°)
cos_phi_s = cosd(phi_s) // cosΦ_s
P_s = 3.0*E_s*I*cos_phi_s // Power at sending end(kW)
loss = P_s-load*1000 // Loss(kW)
loss_per = loss/(load*1000)*100 // loss percentage
// Results
disp("PART II - EXAMPLE : 11.13 : SOLUTION :-")
printf("\nLoss in the interconnector as a percentage of power received = %.3f percent", loss_per)
printf("\nRequired voltage of the booster = %.3f kV (in terms of H.V) \n", V_booster)
printf("\nNOTE: Changes in the obtained answer from that of textbook is due to more precision here")
printf("\n kVA rating of booster is not calculated in textbook and here")
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