#Variable declaration
P = 2.0*10**6 #Power delivered(W)
V_r = 33.0*10**3 #Receiving end voltage(V)
PF_r = 0.8 #Receiving end lagging power factor
R = 10.0 #Total resistance of the line(ohm)
X = 18.0 #Total inductive resistance of the line(ohm)
#Calculation
#Case(i)
I = P/(V_r*PF_r) #Line current(A)
sin_phi_r = (1-PF_r**2)**0.5 #Sinφ_R
V_s = V_r+I*R*PF_r+I*X*sin_phi_r #Sending end voltage(V)
reg = (V_s-V_r)/V_r*100 #Voltage regulation(%)
#Case(ii)
PF_s = (V_r*PF_r+I*R)/V_s #Sending end lagging power factor
#Case(iii)
loss = I**2*R #Losses(W)
P_s = P+loss #Sending end power(W)
n = P/P_s*100 #Transmission efficiency(%)
#Result
print('Case(i) : Percentage voltage regulation = %.3f percent' %reg)
print('Case(ii) : Sending end power factor = %.2f (lag)' %PF_s)
print('Case(iii): Transmission efficiency, η = %.2f percent' %n)
print('\nNOTE: ERROR: pf is 0.8 and not 0.9 as mentioned in the textbook problem statement')
#Variable declaration
l = 10.0 #Length(km)
V_s = 11.0*10**3 #Sending end voltage(V)
P = 1000.0*10**3 #Load delivered at receiving end(W)
PF_r = 0.8 #Receiving end lagging power factor
r = 0.5 #Resistance of each conductor(ohm/km)
x = 0.56 #Reactance of each conductor(ohm/km)
#Calculation
#Case(a)
R = r*l #Resistance per phase(ohm)
X = x*l #Reactance per phase(ohm)
E_s = V_s/3**0.5 #Phase voltage(V)
I = P/(3**0.5*V_s*PF_r) #Line current(A)
#Case(b)
sin_phi_r = (1-PF_r**2)**0.5 #Sinφ_R
E_r = E_s-I*R*PF_r-I*X*sin_phi_r #Receiving end voltage(V)
E_r_ll = 3**0.5*E_r/1000 #Receiving end line to line voltage(kV)
#Case(c)
loss = 3*I**2*R #Loss in the transmission line(W)
P_s = P+loss #Sending end power(W)
n = P/P_s*100 #Transmission efficiency(%)
#Alternate method
Z = R**2+X**2
P_A = 1.0/3*P #Load delivered(W/phase)
Q = 1.0*P*sin_phi_r/(3*PF_r) #Reactive load delivered(VAR/phase)
A = (V_s**2/3.0)-2*(P_A*R+Q*X) #Constant
B = (1/9.0)*P**2*Z/PF_r**2 #Constant
const = (A**2-4*B)**0.5 #sqrt(A^2-4B)
E_r_A = ((A+const)/2)**0.5/1000.0 #Receiving end voltage(kV/phase)
E_r_A_ll = 3**0.5*E_r_A #Receiving end line-line voltage(kV)
I_A = P/(3**0.5*E_r_A_ll*1000*PF_r) #Line current(A)
loss_A = 3*I_A**2*R #Loss in the transmission line(W)
P_s_A = P+loss_A #Sending end power(W)
n_A = P/P_s_A*100 #Transmission efficiency(%)
#Result
print('Case(a): Line current, |I| = %.1f A' %I)
print('Case(b): Receiving end voltage, E_r = %.f V (line-to-neutral) = %.2f kV (line-to-line)' %(E_r,E_r_ll))
print('Case(c): Efficiency of transmission = %.2f percent' %n)
print('\nAlternative solution by mixed condition:')
print('Case(a): Line current, |I| = %.1f A' %I_A)
print('Case(b): Receiving end voltage, E_r = %.3f kV/phase = %.2f kV (line-line)' %(E_r_A,E_r_A_ll))
print('Case(c): Efficiency of transmission = %.2f percent' %n_A)
#Variable declaration
I = 200.0 #Line current(A)
PF_r = 0.8 #Receiving end lagging power factor
R = 0.6 #Total resistance of the line(ohm)
X = 1.0 #Total inductive resistance of the line(ohm)
n = 0.93 #Efficiency(%)
#Calculation
V_r = 3*I**2*R/((3*I*PF_r/n)-3*I*PF_r) #Receiving end phase voltage(V)
sin_phi_r = (1-PF_r**2)**0.5 #Sinφ_R
V_s = V_r+I*R*PF_r+I*X*sin_phi_r #Sending end voltage(V)
V_s_ll = 3**0.5*V_s #Sending end line voltage(V)
#Result
print('Sending end voltage, V_s(line-line) = %.2f V' %V_s_ll)
#Variable declaration
P = 15.0*10**6 #Load delivered at receiving end(W)
PF_r = 0.85 #Receiving end lagging power factor
r = 0.905 #Resistance of each conductor(ohm/km)
V_r = 132.0*10**3 #Receiving end voltage(V)
loss_per = 7.5/100 #Loss
#Calculation
loss = loss_per*P #Losses in line(W)
I = P/(3**0.5*V_r*PF_r) #Line current(A)
l = loss/(3*I**2*r) #Length of line(km)
#Result
print('Distance over which load is delivered, l = %.2f km' %l)
import math
#Variable declaration
f = 50.0 #Frequency(Hz)
l = 20.0 #Length(km)
P = 5.0*10**6 #Load delivered at receiving end(W)
PF_r = 0.8 #Receiving end lagging power factor
r = 0.02 #Resistance of each conductor(ohm/km)
L = 0.65*10**-3 #Inductance of each conductor(H/km)
E_r = 10.0*10**3 #Receiving end voltage(V)
#Calculation
R = r*l #Resistance per phase(ohm)
X = 2*math.pi*f*L*l #Reactance per phase(ohm)
#Case(a)
I = P/(E_r*PF_r) #Line current(A)
sin_phi_r = (1-PF_r**2)**0.5 #Sinφ_R
E_s = E_r+I*R*PF_r+I*X*sin_phi_r #Sending end voltage(V)
E_s_kV = E_s/1000.0 #Sending end voltage(kV)
reg = (E_s-E_r)/E_r*100 #Voltage regulation(%)
#Case(b)
reg_new = reg/2 #New regulation(%)
E_s_new = (reg_new/100)*E_r+E_r #New value of sending end voltage(V)
tan_phi_r1 = ((E_s_new-E_r)*(E_r/P)-R)/X #tanφ_r1
phi_r1 = math.atan(tan_phi_r1) #φ_r1(radians)
phi_r1d = phi_r1*180/math.pi #φ_r1(degree)
PF_r1 = math.cos(phi_r1) #Lagging power factor of receiving end
sin_phi_r1 = (1-PF_r1**2)**0.5 #Sinφ_r1
I_R_new = P/(E_r*PF_r1) #New line current(A)
I_R = I_R_new*complex(PF_r1,-sin_phi_r1)
I_c = I_R-I*complex(PF_r,-sin_phi_r) #Capacitive current(A)
I_C = I_c.imag #Imaginary part of Capacitive current(A)
c = I_C/(2*math.pi*f*E_r)*10.0**6 #Capacitance(µF)
#Case(c)
loss_1 = I**2*R #Loss(W)
n_1 = P/(P+loss_1)*100 #Transmission efficiency(%)
loss_2 = I_R_new**2*R #Loss(W)
n_2 = P/(P+loss_2)*100 #Transmission efficiency(%)
#Result
print('Case(a): Sending end voltage, E_s = %.2f kV' %E_s_kV)
print(' Voltage regulation of the line = %.1f percent' %reg)
print('Case(b): Value of capacitors to be placed in parallel with load, c = %.2f µF' %c)
print('Case(c): Transmission efficiency in part(a), η_1 = %.2f percent' %n_1)
print(' Transmission efficiency in part(b), η_2 = %.1f percent' %n_2)
import math
import cmath
#Variable declaration
f = 50.0 #Frequency(Hz)
l = 10.0 #Line length(km)
Z_l = 0.5*cmath.exp(1j*60.0*math.pi/180) #Load impedance(ohm/km)
P = 316.8*10**3 #Load side power(W)
PF_r = 0.8 #Load side power factor
E_r = 3.3*10**3 #Load bus voltage(V)
#Calculation
Z_line = Z_l*l #Load impedance(ohm)
I_r = P/(E_r*PF_r)*cmath.exp(1j*-math.acos(PF_r)) #Line current(A)
sin_phi_r = (1-PF_r**2)**0.5 #Sinφ_R
E_s = E_r+I_r*Z_line #Sending end voltage(V)
reg = (abs(E_s)-abs(E_r))/abs(E_r)*100 #Voltage regulation(%)
R = Z_line.real #Resistance of the load line(ohm)
loss = abs(I_r)**2*R #Loss in the transmission line(W)
loss_kW = loss/1000.0 #Loss in the transmission line(kW)
P_s = P+loss #Sending end power(W)
angle_Er_Es = cmath.phase(E_s)*180/math.pi #Angle between V_r and V_s(°)
angle_Er_Ir = math.acos(PF_r)*180/math.pi #Angle between V_r and I_r(°)
angle_Es_Is = angle_Er_Es+angle_Er_Ir #Angle between V_s and I_s(°)
PF_s = math.cos(angle_Es_Is*math.pi/180) #Sending end power factor
#Result
print('Voltage regulation = %.2f percent' %reg)
print('Sending end voltage, E_s = %.f∠%.1f° V' %(abs(E_s),cmath.phase(E_s)*180/math.pi))
print('Line loss = %.f kW' %loss_kW)
print('Sending end power factor = %.2f ' %PF_s)
import math
import cmath
#Variable declaration
V_s = 66.0 #Voltage(kV)
f = 50.0 #Frequency(Hz)
l = 150.0 #Line length(km)
r = 0.25 #Resistance of each conductor(ohm/km)
x = 0.5 #Inductive reactance of each conductor(ohm/km)
y = 0.04*10**-4 #Capacitive admittance(s/km)
#Calculation
#Case(a)
R = r*l #Total resistance(ohm)
X = x*l #Inductive reactance(ohm)
Y = y*l #Capacitive resistance(s)
Y_2 = Y/2 #1/2 of Capacitive resistance(s)
#Case(b)
Z = complex(R,X) #Total impedance(ohm)
A = 1+(Y*cmath.exp(1j*90.0*math.pi/180)*Z/2) #Line constant
V_R_noload = V_s/abs(A) #Receiving end voltage at no-load(kV)
#Result
print('Case(a): Total resistance, R = %.1f ohm' %R)
print(' Inductive reactance, X = %.1f ohm' %X)
print(' Capacitive resistance, Y = %.1e s' %Y)
print(' Capacitive resistance, Y/2 = %.1e s' %Y_2)
print('Case(b): Receiving end voltage at no-load, V_R = %.2f kV' %V_R_noload)
import math
import cmath
#Variable declaration
f = 50.0 #Frequency(Hz)
V_r = 132.0*10**3 #Line voltage at receiving end(V)
L = 100.0 #Line length(km)
r = 0.17 #Resistance(ohm/km/phase)
l = 1.1*10**-3 #Inductance(H/km/phase)
c = 0.0082*10**-6 #Capacitance(F/km/phase)
P_L = 70.0*10**6 #Load at receiving end(W)
PF_r = 0.8 #Lagging load power factor
#Calculation
E_r = V_r/3**0.5 #Receiving end phase voltage(V)
I_r = P_L/(3**0.5*V_r*PF_r)*cmath.exp(1j*-math.acos(PF_r)) #Receiving end current(A)
R = r*L #Total resistance(ohm/phase)
X = 2*math.pi*f*l*L #Inductive reactance(ohm/phase)
Z = complex(R,X) #Total impedance(ohm/phase)
Y = 2*math.pi*f*c*cmath.exp(1j*90.0*math.pi/180)/L #Shunt admittance of line(mho/phase)
E = E_r+I_r*(Z/2) #Voltage across shunt admittance(V/phase)
I_s = I_r+E*Y #Sending end current(A)
E_s = E+I_s*(Z/2) #Sending end voltage(V/phase)
E_s_ll = 3**0.5*abs(E_s)/1000 #Sending end line to line voltage(kV)
angle_Er_Es = cmath.phase(E_s)*180/math.pi #Angle between E_r and V_s(°)
angle_Er_Is = cmath.phase(I_s)*180/math.pi #Angle between E_r and I_s(°)
angle_Es_Is = angle_Er_Es-angle_Er_Is #Angle between E_s and I_s(°)
PF_s = math.cos(angle_Es_Is*math.pi/180) #Sending end power factor
#Result
print('Voltage at sending end, E_s = %.2f∠%.2f° V/phase = %.f kV (line-to-line)' %(abs(E_s),cmath.phase(E_s)*180/math.pi,E_s_ll))
print('Current at sending end, I_s = %.1f∠%.1f° A' %(abs(I_s),cmath.phase(I_s)*180/math.pi))
print('Sending end Power factor = %.3f (lagging)' %PF_s)
import math
import cmath
#Variable declaration
f = 50.0 #Frequency(Hz)
E_r = 66.0*10**3 #Line voltage at receiving end(V)
l = 120.0 #Line length(km)
r = 0.1 #Resistance(ohm/km/phase)
x = 0.3 #Inductive reactance(ohm/km/phase)
y = 0.04*10**-4 #Capacitive susceptance(S/km/phase)
P_L = 10.0*10**6 #Load at receiving end(W)
PF_r = 0.8 #Lagging load power factor
#Calculation
R = r*l #Total resistance(ohm/phase)
X = x*l #Inductive reactance(ohm/phase)
Y = y*l #Susceptance(mho)
Z = complex(R,X) #Total impedance(ohm/phase)
V_r = E_r/3**0.5 #Receiving end phase voltage(V)
I_r = P_L/(3**0.5*E_r*PF_r)*cmath.exp(1j*-math.acos(PF_r)) #Load current(A)
V_1 = V_r+I_r*(Z/2) #Voltage across capacitor(V)
I_c = 1j*Y*V_1 #Charging current(A)
I_s = I_r+I_c #Sending end current(A)
V_s = V_1+I_s*(Z/2) #Sending end voltage(V/phase)
V_s_ll = 3**0.5*abs(V_s)/1000.0 #Sending end line to line voltage(kV)
angle_Vr_Vs = cmath.phase(V_s)*180/math.pi #Angle between V_r and V_s(°)
angle_Vr_Is = cmath.phase(I_s)*180/math.pi #Angle between V_r and I_s(°)
angle_Vs_Is = angle_Vr_Vs-angle_Vr_Is #Angle between V_s and I_s(°)
PF_s = math.cos(angle_Vs_Is*math.pi/180) #Sending end power factor
P_s = 3*abs(V_s*I_s)*PF_s #Sending end power(W)
n = P_L/P_s*100 #Transmission efficiency(%)
#Result
print('Sending end voltage, |V_s| = %.f V/phase = %.3f V (line-to-line)' %(abs(V_s),V_s_ll))
print('Sending end current, |I_s| = %.2f A' %abs(I_s))
print('Transmission efficiency = %.2f percent' %n)
print('\nNOTE: ERROR: Calculation mistake in finding sending end power factor')
print(' Changes in the obtained answer from that of textbook is due to more precision')
import math
import cmath
#Variable declaration
f = 50.0 #Frequency(Hz)
l = 125.0 #Line length(km)
P_r = 40.0*10**6 #Load at receiving end(VA)
V_r = 110.0*10**3 #Line voltage at receiving end(V)
PF_r = 0.8 #Lagging load power factor
R = 11.0 #Resistance(ohm/phase)
X = 38.0 #Inductive reactance(ohm/phase)
Y = 3.0*10**-4 #Capacitive susceptance(S)
#Calculation
#Case(i)
E_r = V_r/3**0.5 #Receiving end phase voltage(V)
Z = complex(R,X) #Total impedance(ohm/phase)
I_c1 = E_r*(Y/2)*cmath.exp(1j*90.0*math.pi/180) #Current through shunt admittance at receiving end(A)
I_r = P_r/(3**0.5*V_r)*cmath.exp(1j*-math.acos(PF_r)) #Load current(A)
I = I_r+I_c1 #Current through series impedance(A)
E_s = I*Z+E_r #Voltage across shunt admittance at sending end(V)
E_s_ll = 3**0.5*E_s/1000.0 #Line to line voltage at sending end(kV)
I_c2 = E_s*(Y/2)*cmath.exp(1j*90.0*math.pi/180) #Current through shunt admittance at sending end(A)
#Case(ii)
I_s = I_c2+I_r #Sending end current(A)
angle_Er_Es = cmath.phase(E_s)*180/math.pi #Angle between E_r and E_s(°)
angle_Er_Is = cmath.phase(I_s)*180/math.pi #Angle between E_r and I_s(°)
angle_Es_Is = angle_Er_Es-angle_Er_Is #Angle between E_s and I_s(°)
PF_s = math.cos(angle_Es_Is*math.pi/180) #Sending end power factor
#Result
print('Case(i) : Line to line voltage at sending end, E_s = %.f kV' %(abs(E_s_ll)))
print('Case(ii): Sending end power factor = %.3f ' %PF_s)
print('\nNOTE: Answer in the textbook are incomplete')
import math
import cmath
#Variable declaration
f = 50.0 #Frequency(Hz)
R = 28.0 #Resistance(ohm/phase)
X = 63.0 #Inductive reactance(ohm/phase)
Y = 4.0*10**-4 #Capacitive susceptance(mho)
P_r = 75.0*10**6 #Load at receiving end(VA)
PF_r = 0.8 #Lagging load power factor
V_r = 132.0*10**3 #Line voltage at receiving end(V)
#Calculation
#Case(i) Nominal T method
Z = complex(R,X) #Total impedance(ohm/phase)
E_r = V_r/3**0.5 #Receiving end phase voltage(V)
I_r = P_r/(3**0.5*V_r)*cmath.exp(1j*-math.acos(PF_r)) #Line current at receiving end(A)
E = E_r+I_r*(Z/2)
I_c = 1j*Y*E #Capacitive current(A)
I_s = I_r+I_c #Sending end current(A)
v_drop = I_s*(Z/2) #Voltage drop(V)
E_s = E+I_s*(Z/2) #Sending end voltage(V)
E_s_kV = E_s/1000.0 #Sending end voltage(kV)
E_s_ll= 3**0.5*abs(E_s) #Sending end line voltage(V)
E_s_llkV = E_s_ll/1000.0 #Sending end line voltage(kV)
angle_Er_Es = cmath.phase(E_s)*180/math.pi #Angle between E_r and E_s(°)
angle_Er_Is = cmath.phase(I_s)*180/math.pi #Angle between E_r and I_s(°)
angle_Es_Is = angle_Er_Es-angle_Er_Is #Angle between E_s and I_s(°)
PF_s = math.cos(angle_Es_Is*math.pi/180) #Sending end power factor
P_s = 3**0.5*E_s_ll*abs(I_s)*PF_s #Power at sending end(W)
reg = (abs(E_s_ll)-V_r)/V_r*100 #Regulation(%)
n = (P_r*PF_r)/P_s*100 #Transmission efficiency(%)
#Case(ii) Nominal π method
I_c2 = E_r*(1j*Y/2) #Current through shunt admittance at receiving end(A)
I = I_r+I_c2 #Line current(A)
E_s_p = E_r+I*Z #Sending end voltage(V)
E_s_pkV = E_s_p/1000.0 #Sending end voltage(kV)
E_s_pll = 3**0.5*abs(E_s_p) #Sending end line voltage(V)
E_s_pllkV = E_s_pll/1000.0 #Sending end line voltage(kV)
I_c1 = E_s_p*(1j*Y/2) #Current through shunt admittance at sending end(A)
I_s_p = I+I_c1 #Sending end current(A)
angle_Er_Esp = cmath.phase(E_s)*180/math.pi #Angle between E_r and E_s(°)
angle_Er_Isp = cmath.phase(I_s)*180/math.pi #Angle between E_r and I_s(°)
angle_Es_Isp = angle_Er_Esp-angle_Er_Isp #Angle between E_s and I_s(°)
PF_s_p = math.cos(angle_Es_Isp*math.pi/180) #Sending end power factor
P_s_p = 3**0.5*E_s_pll*abs(I_s_p)*PF_s_p #Power at sending end(W)
reg_p = (abs(E_s_pll)-V_r)/V_r*100 #Regulation(%)
n_p = (P_r*PF_r)/P_s_p*100 #Transmission efficiency(%)
#Result
print('(i) Nominal T method')
print('Case(a): Voltage at sending end, E_s = %.2f∠%.2f° kV = %.1f kV (line-to-line)' %(abs(E_s_kV),cmath.phase(E_s_kV)*180/math.pi,E_s_llkV))
print('Case(b): Sending end current, I_s = %.1f∠%.2f° A' %(abs(I_s),cmath.phase(I_s)*180/math.pi))
print('Case(c): Power factor at sending end = %.4f (lagging)' %PF_s)
print('Case(d): Regulation = %.2f percent' %reg)
print('Case(e): Efficiency of transmission = %.2f percent' %n)
print('\n(ii) Nominal π method')
print('Case(a): Voltage at sending end, E_s = %.2f∠%.2f° kV = %.1f kV (line-to-line)' %(abs(E_s_pkV),cmath.phase(E_s_pkV)*180/math.pi,E_s_pllkV))
print('Case(b): Sending end current, I_s = %.1f∠%.2f° A' %(abs(I_s_p),cmath.phase(I_s_p)*180/math.pi))
print('Case(c): Power factor at sending end = %.4f (lagging)' %PF_s_p)
print('Case(d): Regulation = %.2f percent' %reg_p)
print('Case(e): Efficiency of transmission = %.2f percent' %n_p)
print('\nNOTE: Changes in the obtained answer from that of textbook is due to more precision here and more approximation in textbook')
#Variable declaration
E_s = 275.0 #Sending end voltage(kV)
f = 50.0 #Frequency(Hz)
l = 400.0 #Line length(km)
x = 0.05 #Inductive reactance(ohm/km)
y = 3.0*10**-6 #Line charging susceptance(S/km)
r = 0.0 #Lossless line
#Calculation
#Case(a)
R = r*l #Total resistance(ohm/phase)
X = x*l #Inductive reactance(ohm/phase)
Y = y*l #Susceptance(mho)
Z = complex(R,X) #Total impedance(ohm/phase)
A = 1+(Y*Z/2)*1j #Line constant
E_r = E_s/abs(A) #Receiving end voltage at no load(kV)
#case(b)
Z_0 = (X/Y)**0.5 #Load at receiving end(ohm)
#Case(c)
Z_0_new = 1.2*Z_0 #New load at receiving station(ohm)
#Result
print('Case(a): Receiving end voltage on open circuit = %.1f kV' %E_r)
print('Case(b): Load at receiving end for flat voltage profile on line, Z_0 = %.1f Ω' %Z_0)
print('Case(c): Distributed inductive reactance of the line is to be increased as, Loading for new voltage profile = %.2f Ω' %Z_0_new)
import math
import cmath
#Variable declaration
V_r = 220.0*10**3 #Receiving end voltage(V)
Z = complex(20,100) #Impedance(ohm/phase)
Y = 1j*0.0010 #Admittance(mho)
I_r = 300.0 #Receiving end current(A)
PF_r = 0.9 #Lagging power factor
#Calculation
V_2 = V_r/3**0.5 #Receiving end phase voltage(V)
I_2 = I_r*cmath.exp(1j*-math.acos(PF_r)) #Receiving end current(A)
I_C2 = (Y/2)*V_2 #Capacitive current at receiving end(A)
I = I_2+I_C2
V_1 = V_2+I*Z #Voltage across shunt admittance at sending end(V)
V_1kV = V_1/1000.0 #Voltage across shunt admittance at sending end(kV)
I_C1 = (Y/2)*V_1 #Capacitive current at sending end(A)
I_1 = I_C1+I_2 #Sending end current(A)
#Result
print('Sending end voltage, V_1 = %.2f∠%.2f° kV' %(abs(V_1kV),cmath.phase(V_1kV)*180/math.pi))
print('Sending end current, I_1 = %.3f∠%.4f° A' %(abs(I_1),cmath.phase(I_1)*180/math.pi))
import math
import cmath
#Variable declaration
f = 50.0 #Frequency(Hz)
r = 0.1 #Resistance(ohm/km)
l = 1.4*10**-3 #Inductance(H/km)
c = 8.0*10**-9 #Capacitance(F/km)
g = 4.0*10**-8 #conductance(mho/km)
V_r = 400.0 #Receiving end voltage(kV)
x = 200.0 #Length of line(km)
#Calculation
V_2 = V_r/3**0.5 #Receiving end phase voltage(kV)
z = r+1j*2*math.pi*f*l #Total impedance(ohm/km)
y = g+1j*2*math.pi*f*c #Total susceptance(mho/km)
Z_c = (z/y)**0.5 #Surge impedance(ohm)
gamma = (z*y)**0.5 #γ
#Case(i)
V_0_plus = V_2/2 #Incident voltage to neutral at receiving end(kV)
#Case(ii)
V_0_minus = V_2/2 #Reflected voltage to neutral at receiving end(kV)
#Case(iii)
gamma_l = gamma*x #γl
V_1_plus = (V_2/2)*cmath.exp(gamma_l) #Incident voltage to neutral at 200 km from receiving end(kV)
V_1_minus = (V_2/2)*cmath.exp(-gamma_l) #Reflected voltage to neutral at 200 km from receiving end(kV)
#Case(iv)
V_1 = V_1_plus+V_1_minus #Resultant voltage to neutral(kV)
V_L = abs(V_1) #Resultant voltage to neutral(kV)
V_L_ll = 3**0.5*V_L #Line to line voltage at 200 km from receiving end(kV)
#Result
print('Case(i) : Incident voltage to neutral at receiving end, V_0_plus = %.1f∠%.f° kV' %(abs(V_0_plus),cmath.phase(V_0_plus)*180/math.pi))
print('Case(ii) : Reflected voltage to neutral at receiving end, V_0_minus = %.1f∠%.f° kV' %(abs(V_0_minus),cmath.phase(V_0_minus)*180/math.pi))
print('Case(iii): Incident voltage to neutral at 200 km from receiving end, V_1_plus = (%.3f+%.2fj) kV' %(V_1_plus.real,V_1_plus.imag))
print('Case(iv) : Resultant voltage to neutral at 200 km from receiving end, V_L = %.2f kV' %V_L)
print(' Line to line voltage at 200 km from receiving end = %.2f kV' %V_L_ll)
import math
import cmath
#Variable declaration
f = 50.0 #Frequency(Hz)
L = 200.0 #Line length(km)
l = 1.20*10**-3 #Inductance(H/km)
c = 8.0*10**-9 #Capacitance(F/km)
r = 0.15 #Resistance(ohm/km)
g = 0.0 #Conductance(mho/km)
#Calculation
z = r+1j*2*math.pi*f*l #Total impedance(ohm/km)
Z = z*L #Total impedance(ohm)
y = g+1j*2*math.pi*f*c #Total susceptance(mho/km)
Y = y*L #Total susceptance(mho/km)
gamma_l = (Z*Y)**0.5 #γl
alpha_l = gamma_l.real #αl
beta_l = gamma_l.imag #βl
Z_c = (Z/Y)**0.5 #Surge impedance(ohm)
A = cmath.cosh(gamma_l) #Constant
B = Z_c*cmath.sinh(gamma_l) #Constant(ohm)
C = (1/Z_c)*cmath.sinh(gamma_l) #Constant(S)
D = A #Constant
#Result
print('A = D = %.3f∠%.2f° ' %(abs(A),cmath.phase(A)*180/math.pi))
print('B = %.2f∠%.3f° Ω' %(abs(B),cmath.phase(B)*180/math.pi))
print('C = %.2e∠%.3f° S' %(abs(C),cmath.phase(C)*180/math.pi))
import math
import cmath
#Variable declaration
V_r = 132.0*10**3 #Receiving end voltage(V)
f = 50.0 #Frequency(Hz)
L = 200.0 #Line length(km)
l = 1.3*10**-3 #Inductance(H/km)
c = 9.0*10**-9 #Capacitance(F/km)
r = 0.2 #Resistance(ohm/km)
g = 0.0 #Conductance(mho/km)
P_r = 50.0*10**6 #Power received(VA)
PF_r = 0.8 #Lagging power factor at receiving end
#Calculation
z = r+1j*2*math.pi*f*l #Total impedance(ohm/km)
y = g+1j*2*math.pi*f*c #Total susceptance(mho/km)
Z_c = (z/y)**0.5 #Surge impedance(ohm)
gamma = (z*y)**0.5 #γ
gamma_l = gamma*L #γl
cosh_gl = cmath.cosh(gamma_l) #cosh γl
sinh_gl = cmath.sinh(gamma_l) #sinh γl
V_2 = V_r/(3**0.5) #Receiving end phase voltage(V)
I_2 = P_r/(3*V_2)*cmath.exp(1j*-math.acos(PF_r)) #Line current(A)
V_1 = V_2*cosh_gl+I_2*Z_c*sinh_gl #Sending end voltage(V)
V_1kV = V_1/1000.0 #Sending end voltage(kV)
I_1 = (V_2/Z_c)*sinh_gl+I_2*cosh_gl #Sending end current(A)
angle_V2_V1 = cmath.phase(V_1)*180/math.pi #Angle between V_2 and V_1(°)
angle_V2_I1 = cmath.phase(I_1)*180/math.pi #Angle between V_2 and I_1(°)
angle_V1_I1 = angle_V2_V1-angle_V2_I1 #Angle between V_1 and I_1(°)
PF_s = math.cos(angle_V1_I1*math.pi/180) #Sending end power factor
P_1 = 3*abs(V_1*I_1)*PF_s #Sending end power(W)
P_2 = P_r*PF_r #Receiving end power(W)
n = P_2/P_1*100 #Efficiency
#Result
print('Sending end voltage, V_1 = %.3f∠%.4f° kV per phase' %(abs(V_1kV),cmath.phase(V_1kV)*180/math.pi))
print('Sending end current, I_1 = %.3f∠%.2f° A' %(abs(I_1),cmath.phase(I_1)*180/math.pi))
print('Power factor = %.3f ' %PF_s)
print('Efficiency, η = %.2f percent' %n)
import math
import cmath
#Variable declaration
f = 50.0 #Frequency(Hz)
L = 160.0 #Line length(km)
r = 0.15 #Resistance(ohm/km/phase)
l = 1.2*10**-3 #Inductance(H/km/phase)
c = 0.008*10**-6 #Capacitance(F/km/phase)
g = 0.0 #Conductance(mho/km/phase)
#Calculation
#Case(i) Using convergent series(Complex angles) method
z = r+1j*2*math.pi*f*l #Impedance(ohm/km)
Z = z*L #Total series impedance(ohm)
y = g+1j*2*math.pi*f*c #Shunt admittance(S/km)
Y = y*L #Total shunt admittance(S)
A = 1+(Y*Z/2)+((Y*Z)**2/24) #Constant
B = Z*(1+(Y*Z/6)+((Y*Z)**2/120)) #Constant(ohm)
C = Y*(1+(Y*Z/6)+((Y*Z)**2/120)) #Constant(mho)
D = A #Constant
#Case(ii) Using convergent series(Real angles) method
gamma_l = (Z*Y)**0.5 #γl
alpha_l = gamma_l.real #αl
beta_l = gamma_l.imag #βl
Z_c = (Z/Y)**0.5 #Surge impedance(ohm)
A_2 = cmath.cosh(gamma_l) #Constant
B_2 = Z_c*cmath.sinh(gamma_l) #Constant(ohm)
C_2 = (1/Z_c)*cmath.sinh(gamma_l) #Constant(mho)
D_2 = A_2 #Constant
#Result
print('Case(i): Using convergent series(Complex Angles) method')
print('A = D = %.3f∠%.1f° ' %(abs(A),cmath.phase(A)*180/math.pi))
print('B = %.f∠%.1f° ohm' %(abs(B),cmath.phase(B)*180/math.pi))
print('C = %.4f∠%.1f° mho' %(abs(C),cmath.phase(C)*180/math.pi))
print('\nCase(ii): Using convergent series(Real Angles) method')
print('A = D = %.3f∠%.1f° ' %(abs(A_2),cmath.phase(A_2)*180/math.pi))
print('B = %.1f∠%.1f° ohm' %(abs(B_2),cmath.phase(B_2)*180/math.pi))
print('C = %.4f∠%.1f° S' %(abs(C_2),cmath.phase(C_2)*180/math.pi))
print('\nNOTE: Slight change in obtained answer from that of textbook is due to more precision')
import math
import cmath
#Variable declaration
V_r = 220.0*10**3 #Line voltage at receiving end(V)
Z = complex(40,200) #Impedance per phase(ohm)
Y = 1j*0.0015 #Admittance(mho)
I_r = 200.0 #Receiving end current(A)
PF_r = 0.95 #Lagging power factor
#Calculation
#Case(a)
A = 1+(Y*Z/2)+((Y*Z)**2/24) #Constant
B = Z*(1+(Y*Z/6)+((Y*Z)**2/120)+((Y*Z)**3/5040)) #Constant(ohm)
C = Y*(1+(Y*Z/6)+((Y*Z)**2/120)+((Y*Z)**3/5040)) #Constant(mho)
D = A #Constant
E_r = V_r/3**0.5 #Receiving end phase voltage(V)
I_r1 = I_r*cmath.exp(1j*-math.acos(PF_r)) #Line current(A)
E_s = A*E_r+B*I_r1 #Sending end voltage(V)
E_s_ll = 3**0.5*E_s/1000.0 #Sending end line voltage(kV)
#Case(b)
I_s = C*E_r+D*I_r1 #Sending end current(A)
#Result
print('Case(a): Sending end voltage, E_s = %.1f∠%.2f° kV (line-to-line)' %(abs(E_s_ll),cmath.phase(E_s_ll)*180/math.pi))
print('Case(b): Sending end current, I_s = %.1f∠%.2f° A' %(abs(I_s),cmath.phase(I_s)*180/math.pi))
print('\nNOTE: ERROR: Z = (40+j200)Ω, not Z=(60+j200)Ω as given in problem statement')
print(' Changes in obtained answer from that of textbook is due to more precision')
import math
import cmath
#Variable declaration
V_r = 220.0*10**3 #Line voltage at receiving end(V)
Z = complex(40,200) #Impedance per phase(ohm)
Y = 1j*0.0015 #Admittance(S)
I_R = 200.0 #Receiving end current(A)
PF_r = 0.95 #Lagging power factor
#Calculation
#Case(i) Nominal π method
#Case(a)
E_r = V_r/3**0.5 #Receiving end phase voltage(V)
I_r = I_R*cmath.exp(1j*-math.acos(PF_r)) #Line current(A)
Y_2 = Y/2.0 #Admittance(S)
I_c2 = Y_2*E_r #Current through shunt admittance at receiving end(A)
I = I_r+I_c2 #Current through impedance(A)
IZ_drop = I*Z #Voltage drop(V)
E_s = E_r+IZ_drop #Sending end voltage(V)
E_s_kV = E_s/1000.0 #Sending end voltage(kV)
#Case(b)
I_c1 = E_s*Y_2 #Current through shunt admittance at sending end(A)
I_s = I+I_c1 #Sending end current(A)
#Case(ii) Nominal T method
#Case(a)
I_r_Z2 = I_r*Z/2 #Voltage drop at receiving end(V)
E = E_r+I_r_Z2 #Voltage(V)
I_c = Y*E #Current through shunt admittance(A)
I_s_2 = I_c+I_r #Sending end current(A)
I_s_Z2 = I_s_2*(Z/2) #Voltage drop at sending end(V)
E_s_2 = I_s_Z2+E #Sending end voltage(V)
E_s_2kV = E_s_2/1000.0 #Sending end voltage(kV)
#Result
print('Case(i): Nominal π method')
print(' Case(a): Sending end voltage, E_s = %.1f∠%.2f° kV' %(abs(E_s_kV),cmath.phase(E_s_kV)*180/math.pi))
print(' Case(b): Sending end current, I_s = %.1f∠%.2f° A' %(abs(I_s),cmath.phase(I_s)*180/math.pi))
print('Case(ii): Nominal T method')
print(' Case(a): Sending end voltage, E_s = %.1f∠%.2f° kV' %(abs(E_s_2kV),cmath.phase(E_s_2kV)*180/math.pi))
print(' Case(b): Sending end current, I_s = %.1f∠%.2f° A' %(abs(I_s_2),cmath.phase(I_s_2)*180/math.pi))
print('\nThe results are tabulated below')
print('________________________________________________________')
print('METHOD E_s(kV) I_s(A)')
print('________________________________________________________')
print('Rigorous √3*132.6∠16.46° 209.8∠39.42°')
print('Nominal π √3*%.1f∠%.2f° %.1f∠%.2f°' %(abs(E_s_kV),cmath.phase(E_s_kV)*180/math.pi,abs(I_s),cmath.phase(I_s)*180/math.pi))
print('Nominal T √3*%.1f∠%.2f° %.1f∠%.2f°' %(abs(E_s_2kV),cmath.phase(E_s_2kV)*180/math.pi,abs(I_s_2),cmath.phase(I_s_2)*180/math.pi))
import math
import cmath
#Variable declaration
f = 50.0 #Frequency(Hz)
L = 280.0 #Line length(km)
Z = complex(35,140) #Series impedance(ohm)
Y = 1j*930.0*10**-6 #Shunt admittance(S)
P_r = 40.0*10**6 #Power delivered(W)
V_r = 220.0*10**3 #Voltage at receiving end(V)
PF_r = 0.9 #Lagging power factor
#Calculation
R = Z.real #Resistance of the line(ohm)
#Case(a)
I_r_a = P_r/(3**0.5*V_r*PF_r)*cmath.exp(1j*-math.acos(PF_r)) #Receiving end current(A)
I_s_a = I_r_a #Sending end current(A)
V_r_a = V_r/3**0.5 #Phase voltage at receiving end(V)
V_s_a = V_r_a+I_r_a*Z #Sending end voltage(V)
V_s_a_ll = 3**0.5*V_s_a #Sending end line voltage(V)
V_s_a_llkv = V_s_a_ll/1000.0 #Sending end line voltage(kV)
reg_a = (abs(V_s_a_ll)-V_r)/V_r*100 #Voltage regulation(%)
loss_a = 3*abs(I_r_a)**2*R #Line loss(W)
input_a = P_r+loss_a #Input to line(W)
n_a = P_r/input_a*100 #Efficiency of transmission(%)
A_a = 1.0 #Constant
B_a = Z #Constant(ohm)
C_a = 0 #Constant(mho)
D_a = A_a #Constant
#Case(b)
V_b = V_r_a+I_r_a*Z/2 #Voltage drop across shunt admittance(V)
I_c_b = Y*V_b #Current through shunt admittance(A)
I_s_b = I_r_a+I_c_b #Sending end current(A)
V_s_b = V_b+I_s_b*Z/2 #Sending end voltage(V)
V_s_b_ll = 3**0.5*V_s_b #Sending end line voltage(V)
V_s_b_llkv = V_s_b_ll/1000.0 #Sending end line voltage(kV)
angle_V_Is_b = cmath.phase(I_s_b)*180/math.pi #Angle between V_r and I_s_b(°)
angle_V_Vs_b = cmath.phase(V_s_b)*180/math.pi #Angle between V_r and V_s_b(°)
angle_Is_Vs_b = angle_V_Is_b-angle_V_Vs_b #Angle between V_s_b and I_s_b(°)
PF_s_b = math.cos(angle_Is_Vs_b*math.pi/180) #Sending end power factor
P_s_b = 3**0.5*abs(V_s_b_ll*I_s_b)*PF_s_b #Sending end power(W)
n_b = P_r/P_s_b*100 #Efficiency of transmission(%)
reg_b = (abs(V_s_b_ll)-V_r)/V_r*100 #Voltage regulation(%)
A_b = 1+(1.0/2)*Y*Z #Constant
B_b = Z*(1+(1.0/4)*Y*Z) #Constant(ohm)
C_b =Y #Constant(mho)
D_b = A_b #Constant
#Alternative solution for case(b)
V_s_ba = A_b*V_r_a+B_b*I_r_a #Sending end voltage(V)
V_s_ba_ll = 3**0.5*V_s_ba #Sending end line voltage(V)
V_s_ba_llkv = V_s_ba_ll/1000.0 #Sending end line voltage(kV)
I_s_ba = C_b*V_r_a+D_b*I_r_a #Sending end current(A)
angle_V_Is_ba = cmath.phase(I_s_ba)*180/math.pi #Angle between V_r and I_s_b(°)
angle_V_Vs_ba = cmath.phase(V_s_ba)*180/math.pi #Angle between V_r and V_s_b(°)
angle_Is_Vs_ba = angle_V_Is_ba-angle_V_Vs_ba #Angle between V_s_b and I_s_b(°)
PF_s_ba = math.cos(angle_Is_Vs_ba*math.pi/180) #Sending end power factor
P_s_ba = 3**0.5*abs(V_s_ba_ll*I_s_ba)*PF_s_ba #Sending end power(W)
n_ba = P_r/P_s_ba*100 #Efficiency of transmission(%)
reg_ba = (abs(V_s_ba_ll)-V_r)/V_r*100 #Voltage regulation(%)
#Case(c)
I_c2_c = Y/2.0*V_r_a #Current through shunt admittance at receiving end(A)
I_c = I_r_a+I_c2_c #Current through impedance(A)
V_s_c = V_r_a+I_c*Z #Sending end voltage(V)
V_s_c_ll = 3**0.5*V_s_c #Sending end line voltage(V)
V_s_c_llkv = V_s_c_ll/1000.0 #Sending end line voltage(kV)
I_c1_c = V_s_c*Y/2.0 #Current through shunt admittance at sending end(A)
I_s_c = I_c+I_c1_c #Sending end current(A)
angle_V_Is_c = cmath.phase(I_s_c)*180/math.pi #Angle between V_r and I_s_c(°)
angle_V_Vs_c = cmath.phase(V_s_c)*180/math.pi #Angle between V_r and V_s_c(°)
angle_Is_Vs_c = angle_V_Is_c-angle_V_Vs_c #Angle between V_s_c and I_s_c(°)
PF_s_c = math.cos(angle_Is_Vs_c*math.pi/180) #Sending end power factor
P_s_c = 3**0.5*abs(V_s_c_ll*I_s_c)*PF_s_c #Sending end power(W)
n_c = P_r/P_s_c*100 #Efficiency of transmission(%)
reg_c = (abs(V_s_c_ll)-V_r)/V_r*100 #Voltage regulation(%)
A_c = 1+(1.0/2)*Y*Z #Constant
B_c = Z #Constant(ohm)
C_c =Y*(1+(1.0/4)*Y*Z) #Constant(mho)
D_c = A_c #Constant
#Alternative solution for case(c)
V_s_ca = A_c*V_r_a+B_c*I_r_a #Sending end voltage(V)
V_s_ca_ll = 3**0.5*V_s_ca #Sending end line voltage(V)
V_s_ca_llkv = V_s_ca_ll/1000.0 #Sending end line voltage(kV)
I_s_ca = C_c*V_r_a+D_c*I_r_a #Sending end current(A)
angle_V_Is_ca = cmath.phase(I_s_ca)*180/math.pi #Angle between V_r and I_s_c(°)
angle_V_Vs_ca = cmath.phase(V_s_ca)*180/math.pi #Angle between V_r and V_s_c(°)
angle_Is_Vs_ca = angle_V_Is_ca-angle_V_Vs_ca #Angle between V_s_b and I_s_c(°)
PF_s_ca = math.cos(angle_Is_Vs_ca*math.pi/180) #Sending end power factor
P_s_ca = 3**0.5*abs(V_s_ca_ll*I_s_ca)*PF_s_ca #Sending end power(W)
n_ca = P_r/P_s_ca*100 #Efficiency of transmission(%)
reg_ca = (abs(V_s_ca_ll)-V_r)/V_r*100 #Voltage regulation(%)
#Case(d).(i)
gamma_l = (Y*Z)**0.5 #γl
Z_c = (Z/Y)**0.5 #Surge impedance(ohm)
V_s_d1 = V_r_a*cmath.cosh(gamma_l)+I_r_a*Z_c*cmath.sinh(gamma_l) #Sending end voltage(V)
V_s_d1_ll = 3**0.5*V_s_d1 #Sending end line voltage(V)
V_s_d1_llkv = V_s_d1_ll/1000.0 #Sending end line voltage(kV)
I_s_d1 = V_r_a/Z_c*cmath.sinh(gamma_l)+I_r_a*cmath.cosh(gamma_l) #Sending end current(A)
angle_V_Is_d1 = cmath.phase(I_s_d1)*180/math.pi #Angle between V_r and I_s_d(°)
angle_V_Vs_d1 = cmath.phase(V_s_d1)*180/math.pi #Angle between V_r and V_s_d(°)
angle_Is_Vs_d1 = angle_V_Is_d1-angle_V_Vs_d1 #Angle between V_s_d and I_s_d(°)
PF_s_d1 = math.cos(angle_Is_Vs_d1*math.pi/180) #Sending end power factor
P_s_d1 = 3**0.5*abs(V_s_d1_ll*I_s_d1)*PF_s_d1 #Sending end power(W)
n_d1 = P_r/P_s_d1*100 #Efficiency of transmission(%)
reg_d1 = (abs(V_s_d1_ll)-V_r)/V_r*100 #Voltage regulation(%)
A_d1 = cmath.cosh(gamma_l) #Constant
B_d1 = Z_c*cmath.sinh(gamma_l) #Constant(ohm)
C_d1 = (1/Z_c)*cmath.sinh(gamma_l) #Constant(mho)
D_d1 = A_d1 #Constant
#Case(d).(ii)
A_d2 = (1+(Y*Z/2)+((Y*Z)**2/24.0)) #Constant
B_d2 = Z*(1+(Y*Z/6)+((Y*Z)**2/120)) #Constant(ohm)
C_d2 = Y*(1+(Y*Z/6)+((Y*Z)**2/120)) #Constant(mho)
D_d2 = A_d2 #Constant
V_s_d2 = A_d2*V_r_a+B_d2*I_r_a #Sending end voltage(V)
V_s_d2_ll = 3**0.5*V_s_d2 #Sending end line voltage(V)
V_s_d2_llkv = V_s_d2_ll/1000.0 #Sending end line voltage(kV)
I_s_d2 = C_d2*V_r_a+D_d2*I_r_a #Sending end current(A)
angle_V_Is_d2 = cmath.phase(I_s_d2)*180/math.pi #Angle between V_r and I_s_d(°)
angle_V_Vs_d2 = cmath.phase(V_s_d2)*180/math.pi #Angle between V_r and V_s_d(°)
angle_Is_Vs_d2 = angle_V_Is_d2-angle_V_Vs_d2 #Angle between V_s_d and I_s_d(°)
PF_s_d2 = math.cos(angle_Is_Vs_d2*math.pi/180) #Sending end power factor
P_s_d2 = 3**0.5*abs(V_s_d2_ll*I_s_d2)*PF_s_d2 #Sending end power(W)
n_d2 = P_r/P_s_d2*100 #Efficiency of transmission(%)
reg_d2 = (abs(V_s_d2_ll)-V_r)/V_r*100 #Voltage regulation(%)
#Result
print('Case(a): Short line approximation')
print('Sending end voltage, V_s = %.1f∠%.1f° kV (line-to-line)' %(abs(V_s_a_llkv),cmath.phase(V_s_a_llkv)*180/math.pi))
print('Voltage regulation = %.1f percent' %reg_a)
print('Transmission efficiency, η = %.1f percent' %n_a)
print('A = D = %.f ' %A_a)
print('B = %.1f∠%.1f° ohm' %(abs(B_a),cmath.phase(B_a)*180/math.pi))
print('C = %.f ' %C_a)
print('\nCase(b): Nominal T method approximation')
print('Sending end voltage, V_s = %.1f∠%.1f° kV (line-to-line)' %(abs(V_s_b_llkv),cmath.phase(V_s_b_llkv)*180/math.pi))
print('Voltage regulation = %.2f percent' %reg_b)
print('Transmission efficiency, η = %.1f percent' %n_b)
print('A = D = %.3f∠%.2f° ' %(abs(A_b),cmath.phase(A_b)*180/math.pi))
print('B = %.1f∠%.1f° ohm' %(abs(B_b),cmath.phase(B_b)*180/math.pi))
print('C = %.2e∠%.f° S' %(abs(C_b),cmath.phase(C_b)*180/math.pi))
print('\tALTERNATIVE SOLUTION:')
print('\tSending end voltage, V_s = %.1f∠%.1f° kV (line-to-line)' %(abs(V_s_ba_llkv),cmath.phase(V_s_ba_llkv)*180/math.pi))
print('\tVoltage regulation = %.2f percent' %reg_ba)
print('\tTransmission efficiency, η = %.1f percent' %n_ba)
print('\tA = D = %.3f∠%.2f° ' %(abs(A_b),cmath.phase(A_b)*180/math.pi))
print('\tB = %.1f∠%.1f° ohm' %(abs(B_b),cmath.phase(B_b)*180/math.pi))
print('\tC = %.2e∠%.f° S' %(abs(C_b),cmath.phase(C_b)*180/math.pi))
print('\nCase(c): Nominal π method approximation')
print('Sending end voltage, V_s = %.f∠%.1f° kV (line-to-line)' %(abs(V_s_c_llkv),cmath.phase(V_s_c_llkv)*180/math.pi))
print('Voltage regulation = %.2f percent' %reg_c)
print('Transmission efficiency, η = %.1f percent' %n_c)
print('A = D = %.3f∠%.2f° ' %(abs(A_c),cmath.phase(A_c)*180/math.pi))
print('B = %.1f∠%.1f° ohm' %(abs(B_c),cmath.phase(B_c)*180/math.pi))
print('C = %.2e∠%.1f° mho' %(abs(C_c),cmath.phase(C_c)*180/math.pi))
print('\tALTERNATIVE SOLUTION:')
print('\tSending end voltage, V_s = %.1f∠%.1f° kV (line-to-line)' %(abs(V_s_ca_llkv),cmath.phase(V_s_ca_llkv)*180/math.pi))
print('\tVoltage regulation = %.2f percent' %reg_ca)
print('\tTransmission efficiency, η = %.1f percent' %n_ca)
print('\tA = D = %.3f∠%.2f° ' %(abs(A_c),cmath.phase(A_c)*180/math.pi))
print('\tB = %.1f∠%.1f° ohm' %(abs(B_c),cmath.phase(B_c)*180/math.pi))
print('\tC = %.2e∠%.f° S' %(abs(C_c),cmath.phase(C_c)*180/math.pi))
print('\nCase(d): Long Line Rigorous Solution')
print(' Case(i): Using Convergent Series (Real Angles) Method')
print(' Sending end voltage, V_s = %.f∠%.1f° kV (line-to-line)' %(abs(V_s_d1_llkv),cmath.phase(V_s_d1_llkv)*180/math.pi))
print(' Voltage regulation = %.2f percent' %reg_d1)
print(' Transmission efficiency, η = %.1f percent' %n_d1)
print(' A = D = %.3f∠%.2f° ' %(abs(A_d1),cmath.phase(A_d1)*180/math.pi))
print(' B = %.f∠%.1f° ohm' %(abs(B_d1),cmath.phase(B_d1)*180/math.pi))
print(' C = %.2e∠%.1f° mho' %(abs(C_d1),cmath.phase(C_d1)*180/math.pi))
print('\n Case(ii): Using Convergent Series (Complex Angles) Method')
print(' Sending end voltage, V_s = %.f∠%.1f° kV (line-to-line)' %(abs(V_s_d2_llkv),cmath.phase(V_s_d2_llkv)*180/math.pi))
print(' Voltage regulation = %.2f percent' %reg_d2)
print(' Transmission efficiency, η = %.1f percent' %n_d2)
print(' A = D = %.3f∠%.2f° ' %(abs(A_d2),cmath.phase(A_d2)*180/math.pi))
print(' B = %.1f∠%.1f° ohm' %(abs(B_d2),cmath.phase(B_d2)*180/math.pi))
print(' C = %.2e∠%.1f° mho' %(abs(C_d2),cmath.phase(C_d2)*180/math.pi))
print('\nNOTE: Changes in obtained answer from that of textbook is due to more precision')
import math
import cmath
#Variable declaration
V_r = 132.0*10**3 #Line voltage at receiving end(V)
P_L = 45.0*10**6 #Load delivered(VA)
PF_r = 0.8 #Lagging power factor
A = 0.99*cmath.exp(1j*0.3*math.pi/180) #Constant
B = 70.0*cmath.exp(1j*69.0*math.pi/180) #Constant(ohms)
C = A #Constant
D = 4.0*10**-4*cmath.exp(1j*90.0*math.pi/180) #Constant
#Calculation
E_r = V_r/3**0.5 #Receiving end phase voltage(V)
I_r = P_L/(3**0.5*V_r)*cmath.exp(1j*-math.acos(PF_r)) #Line current(A)
E_s = A*E_r+B*I_r #Sending end voltage(V)
E_s_llkV = 3**0.5*E_s/1000.0 #Sending end line voltage(kV)
I_s = C*I_r+D*E_r #Sending end current(A)
angle_Er_Es = cmath.phase(E_s)*180/math.pi #Angle between E_r and E_s(°)
angle_Er_Is = cmath.phase(I_s)*180/math.pi #Angle between E_r and I_s(°)
angle_Es_Is = angle_Er_Es-angle_Er_Is #Angle between E_s and I_s(°)
PF_s = math.cos(angle_Es_Is*math.pi/180) #Sending end power factor
P_s = 3*abs(E_s*I_s)*PF_s #Sending end power(W)
P_skW = P_s/1000.0 #Sending end power(kW)
P_r = P_L*PF_r #Receiving end power(W)
n = P_r/P_s*100 #Transmission efficiency(%)
#Result
print('Case(i) : Sending end voltage, E_s = %.1f∠%.f° kV (line-to-line)' %(abs(E_s_llkV),cmath.phase(E_s_llkV)*180/math.pi))
print('Case(ii) : Sending end current, I_s = %.1f∠%.1f° A' %(abs(I_s),cmath.phase(I_s)*180/math.pi))
print('Case(iii): Sending end power, P_s = %.f kW' %(P_skW))
print('Case(iv) : Efficiency of transmission = %.2f percent' %n)
print('\nNOTE: Changes in obtained answer from that textbook is due to more precision')
import math
import cmath
#Variable declaration
A_1 = 0.98*cmath.exp(1j*2.0*math.pi/180) #Constant of 1st line
B_1 = 28.0*cmath.exp(1j*69.0*math.pi/180) #Constant of 1st line(ohms)
C_1 = 0.0002*cmath.exp(1j*88.0*math.pi/180) #Constant of 1st line(mho)
D_1 = A_1 #Constant of 1st line
A_2 = 0.95*cmath.exp(1j*3.0*math.pi/180) #Constant of 2nd line
B_2 = 40.0*cmath.exp(1j*85.0*math.pi/180) #Constant of 2nd line(ohms)
C_2 = 0.0004*cmath.exp(1j*90.0*math.pi/180) #Constant of 2nd line(mho)
D_2 = A_2 #Constant of 2nd line
#Calculation
A = A_1*A_2+B_1*C_2 #Constant
B = A_1*B_2+B_1*D_2 #Constant(ohm)
C = C_1*A_2+D_1*C_2 #Constant(mho)
D = C_1*B_2+D_1*D_2 #Constant
#Result
print('A = %.3f∠%.1f° ' %(abs(A),cmath.phase(A)*180/math.pi))
print('B = %.1f∠%.f° ohm' %(abs(B),cmath.phase(B)*180/math.pi))
print('C = %.6f∠%.1f° mho' %(abs(C),cmath.phase(C)*180/math.pi))
print('D = %.3f∠%.1f° ' %(abs(D),cmath.phase(D)*180/math.pi))
import math
import cmath
#Variable declaration
A = 0.94*cmath.exp(1j*1.5*math.pi/180) #Constant
B = 150.0*cmath.exp(1j*67.2*math.pi/180) #Constant(ohm)
D = A #Constant
Y_t = 0.00025*cmath.exp(1j*-75.0*math.pi/180) #Shunt admittance(mho)
Z_t = 100.0*cmath.exp(1j*70.0*math.pi/180) #Series impedance(ohm)
#Calculation
C = (A*D-1)/B #Constant(mho)
A_0 = A*(1+Y_t*Z_t)+B*Y_t #Constant
B_0 = A*Z_t+B #Constant(ohm)
C_0 = C*(1+Y_t*Z_t)+D*Y_t #Constant(mho)
D_0 = C*Z_t+D #Constant
#Result
print('A_0 = %.3f∠%.f° ' %(abs(A_0),cmath.phase(A_0)*180/math.pi))
print('B_0 = %.f∠%.1f° ohm' %(abs(B_0),cmath.phase(B_0)*180/math.pi))
print('C_0 = %.6f∠%.1f° mho' %(abs(C_0),cmath.phase(C_0)*180/math.pi))
print('D_0 = %.3f∠%.1f° ' %(abs(D_0),cmath.phase(D_0)*180/math.pi))
print('\nNOTE: Changes in obtained answer from that of textbook is due to more precision')
import math
#Variable declaration
z = complex(0.2,0.6) #Per phase impedance(ohm)
V_r = 6351.0 #Receiving end voltage per phase(V)
reg = 7.5/100.0 #Voltage regulation
#Calculation
V_s = (1+reg)*V_r #Sending end voltage per phase(V)
R = z.real #Resistance of the line(ohm)
X = z.imag #Reactance of the line(ohm)
Z = (R**2+X**2)**0.5 #Impedance per phase(ohm)
P_m = (V_r**2/Z)*((Z*V_s/V_r)-R) #Maximum power transmitted through line(W/phase)
P_m_MW = P_m/10**6 #Maximum power transmitted through line(MW/phase)
P_m_MWtotal = 3*P_m_MW #Total maximum power(MW)
Q = -(V_r**2*X)/Z**2 #Reactive power per phase(Var)
Q_MW = Q/10**6 #Reactive power per phase(MVAR)
phi_r = math.atan(abs(Q_MW/P_m_MW))*180/math.pi #Φ_r(°)
PF_r = math.cos(phi_r*math.pi/180) #Receiving end lagging PF
I = P_m/(V_r*PF_r) #Current delivered(A)
I_KA = I/1000.0 #Current delivered(KA)
loss = 3*I**2*R #Total line loss(W)
loss_MW = loss/10**6 #Total line loss(MW)
#Result
print('Maximum power transmitted through the line, P_m = %.1f MW' %P_m_MWtotal)
print('Receiving end power factor = %.2f (lagging)' %PF_r)
print('Total line loss = %.2f MW' %loss_MW)
import math
import cmath
#Variable declaration
L = 100.0 #Length of line(km)
PF_r = 1.0 #Receiving end Power factor
Z_c = 400.0 #Characteristic impedance(ohm)
beta = 1.2*10**-3 #Propagation constant(rad/km)
V_s = 230.0 #Sending end voltage(kV)
#Calculation
beta_L = beta*L #(rad)
beta_L_d = beta_L*180/math.pi #(°)
A = math.cos(beta_L) #Constant
B = 1j*Z_c*math.sin(beta_L) #Constant
alpha_angle = cmath.phase(A)*180/math.pi #α(°)
beta_angle = cmath.phase(B)*180/math.pi #β(°)
V_r = V_s #Receiving end voltage due to lossless line(kV)
P_max = (V_s*V_r/abs(B))-(abs(A)*V_r**2/abs(B))*math.cos((beta_angle-alpha_angle)*math.pi/180) #Maximum power transferred(MW)
#Result
print('Maximum power that can be transferred to the load at receiving end, P_max = %.f MW' %P_max)
print('\nNOTE: Changes in obtained answer from that of textbook is due to more precision')
import math
import cmath
#Variable declaration
L = 160.0 #Length of line(km)
P_r = 90.0*10**6 #Load(W)
PF_r = 0.85 #Receiving end lagging power factor
E_r = 230.0*10**3 #Receiving end voltage(V)
A = 0.9785*cmath.exp(1j*0.3*math.pi/180) #Constant
B = 85.2*cmath.exp(1j*77.47*math.pi/180) #Constant(ohm)
C = 0.000503*cmath.exp(1j*90.1*math.pi/180) #Constant(mho)
D = A #Constant
load_c = 120.0 #Load(MW). At case(c)
#Calculation
V_r = E_r/3**0.5 #Receiving end phase voltage(V)
I_r = P_r/(3**0.5*E_r*PF_r) #Line current(A)
#Case(a)
V_s_ph = E_r*85.2/V_r #Sending end voltage per phase(kV)
V_s = 3**0.5*V_s_ph #Sending end line voltage(kV)
I_s = 36.0*10**6/(V_s_ph*10**3) #Sending end current(A)
theta_s = 27.0 #θ_s(°)
PF_s = math.cos(theta_s*math.pi/180) #Sending end power factor
regulation = (V_s-(E_r/1000.0))/(E_r/1000.0)*100 #Regulation
P_s = 3*V_s_ph*I_s*PF_s*1000.0 #Sending end power(W)
n = P_r/P_s*100 #Efficiency(%)
#Case(b)
load_b = 25.0*3 #Load carried for 8% regulation(MW)
#Case(c)
power_phase = load_c/3.0 #Power per phase(MW)
V_s_c = 238*85.2/(V_r/1000) #Voltage(kV)
drop_phase_c = V_s_c-133.0 #Drop per phase(kV)
MVAR_phase_c = 16.0 #MVAR per phase
MVAR_c = 3*MVAR_phase_c #Total MVAR required
#Case(d)
MVAR_leading = 11.5*20 #Leading MVAR per phase
MVAR_3_d = 3*MVAR_leading #Leading MVAR for all 3 diagram
#Case(e)
P_e = 8.15*20 #Maximum power for one phase(MW)
P_e_total = 3*P_e #Maximum power for all three phases(MW)
theta_e = 50.5 #θ_r(°)
PF_e = math.cos(theta_e*math.pi/180) #Power factor
#Result
print('Case(a): Sending end voltage = %.f kV (line-to-line)' %V_s)
print(' Sending end current, |I_s| = %.f A' %I_s)
print(' Sending end power factor = %.2f ' %PF_s)
print(' Regulation = %.1f percent' %regulation)
print(' Efficiency of transmission line = %.1f percent' %n)
print('Case(b): Load carried at 8 percent regulation = %.f MW' %load_b)
print('Case(c): Voltage drop per phase = %.1f kV' %drop_phase_c)
print(' Total MVAR required = %.f MVAR' %MVAR_c)
print('Case(d): Leading MVAR = %.f MVAR' %MVAR_3_d)
print('Case(e): Maximum power transmitted = %.f MW' %P_e_total)
print(' Corresponding power factor = %.3f (leading)' %PF_e)
print('\nNOTE: ERROR: PF = 0.85, not PF = 0.8 as given in textbook statement')
print(' All values are taken directly from textbook circle diagram')
import math
import cmath
#Variable declaration
E_r = 220.0 #Receiving end voltage(kV)
P_r = 75.0 #Load(MW)
PF_r = 0.8 #Receiving end lagging power factor
A = 0.9055*cmath.exp(1j*0.6*math.pi/180) #Constant
B = 156.0*cmath.exp(1j*84.5*math.pi/180) #Constant(ohm)
C = 0.00116*cmath.exp(1j*90.2*math.pi/180) #Constant(mho)
D = A #Constant
#Calculation
#Case(i)
P_base = E_r**2/abs(B) #Base power(MW)
V_s_pu = 1.135 #Sending end voltage(p.u)
V_s = V_s_pu*E_r #Sending end voltage(kV)
delta = 11.8 #Phase shift between sending & receiving end voltage(°)
#Case(ii)
P_s_real = 0.249*P_base #Sending end real power(MW)
P_s_reactive = 0.035*P_base #Sending end reactive power(MW)
line_loss = P_s_real-P_r #Line loss(MW)
#Case(iii)
P_s_max = 1.26*P_base #Sending end maximum power(MW)
P_r_max = 1.035*P_base #Receiving end maximum power(MW)
#Case(iv)
SPM_cap = 0.03*P_base #SPM capacity to improve pf(MVAR)
#Case(v)
V_s_5 = 1.105*E_r #Sending end voltage(kV)
reg = (V_s_5-E_r)/E_r*100 #Voltage regulation(%)
reg_noSPM = (V_s-E_r)/E_r*100 #Voltage regulation without SPM(%)
#Result
print('Case(i) : Sending end voltage = %.f kV' %V_s)
print(' Phase shift between sending end & receiving end voltage, δ = %.1f° ' %delta)
print('Case(ii) : Sending end real power = %.1f MW' %P_s_real)
print(' Sending end reactive power = %.2f MVAR' %P_s_reactive)
print(' Line loss = %.1f MW' %line_loss)
print('Case(iii): Maximum power transmitted from sending end = %.f MW' %P_s_max)
print(' Maximum power received at receiving end = %.2f MW' %P_r_max)
print('Case(iv) : SPM capacity to improve power factor = %.1f MVAR' %SPM_cap)
print('Case(v) : Voltage regulation with SPM = %.1f percent' %reg)
print(' Voltage regulation without SPM = %.1f percent' %reg_noSPM)
print(' Regulation is improved from %.1f to %.1f percent with SPM installation' %(reg_noSPM,reg))
print('\nNOTE: Some values are taken directly from textbook circle diagram')
import math
import cmath
#Variable declaration
V_s = 250.0 #Sending end voltage(kV)
V_r = 230.0 #Receiving end voltage(kV)
A = 0.9785*cmath.exp(1j*0.3*math.pi/180) #Constant
B = 85.2*cmath.exp(1j*77.47*math.pi/180) #Constant(ohm)
D = A #Constant
#Calculation
cos_beta = math.cos(cmath.phase(B)) #cosβ
line_loss_1 = 0.2*20*2*cos_beta #Line loss when 90MW is supplied(MW/phase)
line_loss_1_total = 3*line_loss_1 #Total line loss(MW)
line_loss_2 = 0.13*20*2*cos_beta #Minimum line loss(MW/phase)
line_loss_2_total = 3*line_loss_2 #Total minimum line loss(MW)
power = 3*0.2*20 #Receiving end power(MW)
PF = 0.174 #Power factor
#Result
print('Line loss when 90MW is supplied to load at receiving end = %.2f MW/phase = %.2f MW (total)' %(line_loss_1,line_loss_1_total))
print('Minimum line loss = %.3f MW/phase = %.3f MW (total)' %(line_loss_2,line_loss_2_total))
print('Receiving end power = %.f MW' %power)
print('Power factor = %.3f ' %PF)
print('\nNOTE: Changes in obtained answer from that of textbook is due to more precision')
print(' Some values are taken directly from textbook circle diagram')