# CHAPTER 4.9: ELECTRIC TRACTION SYSTEMS AND POWER SUPPLY¶

## Example 4.9.1, Page number 817-818¶

In :
from scipy.integrate import quad

#Variable declaration
L = 3.0           #Length of section ACB of rail(km)
L_B_A = 2.0       #Distance of B from A(km)
r_rail = 0.035    #Resistance of rail(ohm/km)
r_feed = 0.03     #Resistance of negative feeder(ohm/km)

#Calculation
def integrand(x):
ans, err = quad(integrand, 0, L_B_A)
I = ans/(L_B_A-0)                         #Current in negative feeder(A)
x = L-(I/I_load)                          #Distance from feeding point(km)
def integrand(x):
C, err = quad(integrand, 0, x)            #Voltage at point P(V)
V = r_feed*L_B_A*I                        #Voltage produced by negative booster(V)
rating = V*I/1000                         #Rating of the booster(kW)

#Result
print('Maximum potential difference between any two points of the rails, C = %.2f V' %C)
print('Rating of the booster = %.1f kW' %rating)

Maximum potential difference between any two points of the rails, C = 6.13 V
Rating of the booster = 29.4 kW


## Example 4.9.2, Page number 820¶

In :
#Variable declaration
D = 50.0    #Distance between poles(m)
w = 0.5     #Weight of trolley wire per metre(kg)
T = 520.0   #Maximum tension(kg)

#Calculation
l = D/2                              #Half distance b/w poles(m)
d = w*l**2/(2*T)                     #Sag(m)
wire_length = 2*(l+(2*d**2/(3*l)))   #Length of wire required(m)

#Result
print('Maximum sag, d = %.4f metres' %d)
print('Length of wire required = %.f metres' %wire_length)

Maximum sag, d = 0.3005 metres
Length of wire required = 50 metres