# Chapter 9: Electrical Design of Overhead Lines¶

### Example 9.1, Page Number: 214¶

In :
from __future__ import division
import math

#Variable declaration:
d = 200                     #Spacing of conductors(cm)
r = 1.2/2                   #Radius of conductor(cm)

#Calculation:
L = 10**-7*(1+4*math.log(d/r))*10**3  #Loop inductance per m length of the line(H)

#Result:
print " The loop inductance per km of the line is",round(L*1000,3),"mH"

 The loop inductance per km of the line is 2.424 mH


### Example 9.2, Page Number: 214¶

In :
from __future__ import division
import math

#Variable declaration:
d = 300                     #Spacing of conductors(cm)
r = 1                      #Radius of conductor(cm)
u1 = 1                     #relative permeability of copper
u2 = 100                    #relative permeability of steel

#Calculation:
#(i) With copper conductors,
Lc = 10**-7*(u1+4*math.log(d/r))*10**3     #Loop inductance/km

#(ii) With steel conductors,
Ls = 10**-7*(u2+4*math.log(d/r))*10**3      ##Loop inductance/km

#Result:
print "The loop inductance per km length of the line are:"
print "(i) for copper, Lc",round(Lc*1000,2),"mH and"
print "(ii) for steel line, Ls =",round(Ls*1000,2),"mH"

The loop inductance per km length of the line are:
(i) for copper, Lc 2.38 mH and
(ii) for steel line, Ls = 12.28 mH


### Example 9.3, Page Number: 214¶

In :
from __future__ import division
import math

#Variable declaration:
d = 200                   #cm

#Calculation:
L = 10**-7*(0.5+2*math.log(d/r))*10**3             #Inductance/phase/km

#Result:
print "The inductance per km of a 3-ph transmission line is",round(L*10**3,1),"mH"

The inductance per km of a 3-ph transmission line is 1.2 mH


### Example 9.4, Page Number: 214¶

In :
from __future__ import division
import math

#Variable declaration:
D12 = 2                   #m
D23 = 2.5                 #m
D13 = 4.5                  #m
r = 0.62                  #m

#Calculation:
Deq = (D12*D23*D13)**(1/3)*100         #Equivalent equilateral spacing(cm)
L = 10**-7*(0.5+2*math.log(Deq/r))*10**3

#Result:
print "The inductance per km of the line is",round(L*1000,3),"mH"

The inductance per km of the line is 1.274 mH


### Example 9.5, Page Number: 214¶

In :
from __future__ import division
import math

#Variable declaration:
r = 1.25                     #cm
D12 = 2                       #m
D23 = 2                       #m
D13 = 4                       #m

#Calculation:
Deq = (D12*D23*D13)**(1/3)*100         #Equivalent equilateral spacing(m)
L = 10**-7*(0.5+2*math.log(Deq/r))*10**3

#Result:
print "The inductance per km of the line is",round(L*1000,2),"mH"

The inductance per km of the line is 1.11 mH


### Example 9.6, Page Number: 214¶

In :
from __future__ import division
import math

#Variable declaration:
r = 0.5                          #radius of conductor(m)
Dab = 25                          #cm
Daa1 = 100                        #cm
Dbb1 = 100                        #cm
Dab1 = 103                        #cm
Da1b = 103                        #cm
Da1b1 = 25                        #cm

#Calculation:
GMR = 0.7788*r                    #G.M.R. of conductor(cm)
Ds = (GMR*Daa1)**(1/2)               #Self G.M.D. of aa1 combination(cm)
Dm = (Dab*Dab1*Da1b*Da1b1)**(1/4)   #Mutual G.M.D. between a and b(cm)
L1 = 2*10**-7*math.log(Dm/Ds)       #Loop inductance per conductor per m(H)
L = 2*L1*1000

#Result:
print "The inductance per km of the line is",round(L*1000,2),"mH"

The inductance per km of the line is 0.84 mH


### Example 9.7, Page Number: 216¶

In :
from __future__ import division
import math

#Variable declaration:
Dab = 3                            #m
Dab1  = 6.7                        #m
Da1b = 6.7                         #m
Da1b1 = 3                          #m
Daa1 = 8.48                        #m
Da1a = 8.48                        #m
Dbb1 = 6                           #m
Db1b = 6                           #m
Dca = 6                            #m
Dc1a = 6                           #m
Dca1 = 6                           #m
Dc1a1 = 6                          #m

#Calculation:
GMR = 1.3*0.7788/100                   #m
Daa = GMR
Da1a1 = GMR
Dbb = GMR
Db1b1 = GMR
Ds1 = (Daa*Daa1*Da1a1*Da1a)**(1/4)             #m
Ds2 = (Dbb*Dbb1*Db1b1*Db1b)**(1/4)             #m
Ds = (Ds1*Ds2*Ds1)**(1/3)                       #m
DAB = (Dab*Dab1*Da1b*Da1b1)**(1/4)             #m
DBC = DAB
DCA = (Dca*Dc1a*Dca1*Dc1a1)**(1/4)             #m
Dm = (DAB*DBC*DCA)**(1/3)            #Equivalent mutual G.M.D(m)

L1 = 2*10**-7*math.log(Dm/Ds)       #Loop inductance per conductor per m(H)
L = L1*1000

#Result:
print "The inductance per km of the line is",round(L*1000,2),"mH"

The inductance per km of the line is 0.58 mH


### Example 9.8, Page Number: 217¶

In :
from __future__ import division
import math

#Variable Declaration:
Db1b = 5.5                       #m
Dca = 6                         #m
Dca1 = 4                         #m
Dc1a = 4                          #m
Dc1a1 = 6                        #m

#Calculation:
GMR = 0.7788*r                     #m
Dab = (3**2+0.75**2)**0.5         #m
Dab1 = (3**2+4.75**2)**0.5         #m
Daa1 = (6**2+4**2)**0.5            #m
Daa = GMR/100                      #m
Da1a1 = Daa                       #m
Da1a = Daa1                      #m
Dbb = GMR/100                      #m
Dbb1 = 5.5                       #m
Db1b1 = Dbb                      #m

Ds1 = (Daa*Daa1*Da1a1*Da1a)**(1/4)          #m
Ds2 = (Dbb*Dbb1*Db1b1*Db1b)**(1/4)          #m
Ds3 = Ds1
Ds = (Ds1*Ds2*Ds3)**(1/3)       #Equivalent self G.M.D. of one phase(m)
DAB = (Dab*Dab1*Da1b*Da1b1)**(1/4)   #m
DCA = (Dca*Dca1*Dc1a*Dc1a1)**(1/4)    #m
DBC = DAB                             #m
Dm = (DAB*DBC*DCA)**(1/3)             #Equivalent mutual G.M.D.(m)

L1 = 2*10**-7*math.log(Dm/Ds)       #Loop inductance per conductor per m(H)
L = L1*1000

#Result:
print "The inductance per km of the line is",round(L*1000,3),"mH"

The inductance per km of the line is 0.627 mH


### Example 9.9, Page Number: 218¶

In :
from __future__ import division
import math

#Variable Declaration:

#Calculation:
GMR = 0.7788*r                          #m
DAA = GMR                                #m
DAA1 = 24                                #m
DA1A1 = DAA                              #m
DA1A = 24                                #m

DBB = GMR                                #m
DBB1 = 24                                #m
DB1B1 = DBB                              #m
DB1B = 24                                #m
Ds1 = (DAA*DAA1*DA1A1*DA1A)**(1/4)        #m
Ds2 = (DBB*DBB1*DB1B1*DB1B)**(1/4)        #m
#Similarly:
Ds3 = 0.995                              #m
Ds = (Ds1*Ds2*Ds3)**(1/3)   #Equivalent self-G.M.D. of one phase(m)
#DAB = (DAB × DAB′ × DA′Β × DA′B′)**1/4
DAB = (8*32*16*8)**(1/4)                 #m
DBC = DAB                               #m
#DCA = (DCA × DCA′ × DC′A ×DC′A′)1/4    #m
DCA = (16*8*40*16)**(1/4)                 #m

Dm = (DAB*DBC*DCA)**(1/3)                   #m

L = 2*10**-7*math.log(Dm/Ds)       #Loop inductance per conductor per m(H)

#Result:
print "The inductance per m of the line is",round(L*10**7,2),"* 10**-7  H/m"

The inductance per m of the line is 5.36 * 10**-7  H/m


### Example 9.10, Page Number: 219¶

In :
from __future__ import division
import math

#Variable Declaration:

#Calculation:
#Mutual G.M.D., Dm = (Dab*Dab'*Da'b*Da'b')**(1/4)
Dm = (120*140*100*120)**(1/4)          #m

#Self G.M.D., Ds = (Daa*Daa'*Da'a'*Da'a)**(1/4)
#Daa = Da'a' = 0.7788 cm; Daa' = Da'a = 20 cm
Ds = (0.7788*20*0.7788*20)**(1/4)         #cm
L = 4*10**-4*math.log(Dm/Ds)              #H/km

#Result:
print "The total inductance of the line per km is",round(L*1000,2),"mH/km"

The total inductance of the line per km is 1.36 mH/km


### Example 9.11, Page Number: 224¶

In :
from __future__ import division
import math

#Variable declaration:
d = 300                       #conductor spacing(cm)
e = 8.854*10**-12             #permitivity of free space(F/m)

#Calculation:
C = math.pi*e/math.log(d/r)         #F/m

#Result:
print "Capacitance of the line per km is",round(C*10**11,4),"* 10**-2  uF/km"

Capacitance of the line per km is 0.4877 * 10**-2  uF/km


### Example 9.12, Page Number: 225¶

In :
from __future__ import division
import math

#Variable declaration:
d = 200                       #conductor spacing(cm)
e = 8.854*10**-12             #permitivity of free space(F/m)

#Calculation:
C = 2*math.pi*e/math.log(d/r)         #F/m

#Result:
print "Capacitance of the line per km is",round(C*10**9,4),"  uF/km"

Capacitance of the line per km is 0.0096   uF/km


### Example 9.13, Page Number: 225¶

In :
from __future__ import division
import math

#Variable Declaration:
d1 = 2                       #m
d2 = 2.5                     #m
d3 = 4.5                     #m
r = 0.625                    #conductor raius(cm)
l = 100                      #line length(km)
Vl = 66000                  #line voltage(V)
f = 50                       #frequency of current(Hz)
e = 8.854*10**-12             #permitivity of free space(F/m)

#Calculation:
d = (d1*d2*d3)**(1/3)*100          #cm

#(i)Line to neutral capacitance,
C1 = 2*math.pi*e/math.log(d/r)*10**9     #uF/km
C11 = C1*100                           #uF

#(ii)Charging current per phase,
Ic = Vl*2*math.pi*f*C11*10**-6/(3**0.5)      #A

#Result:
print "Capacitance per phase is",round(C11,2),"uF"
print "Charging current per phase is",round(Ic,1),"A"

Capacitance per phase is 0.91 uF
Charging current per phase is 10.9 A


### Example 9.14, Page Number: 225¶

In :
from __future__ import division
import math

#Variable declaration:
d = 250                      #equilateral conductor spacing(cm)
e = 8.854*10**-12             #permitivity of free space(F/m)

#Calculation:
C = 2*math.pi*e/math.log(d/r)*10**9         #uF/km
C1 = C*100                       #F

#Result:
print "Capacitance of the line per km is",round(C1,4),"uF/phase"

Capacitance of the line per km is 1.0075 uF/phase


### Example 9.15, Page Number: 226¶

In :
from __future__ import division
import math

#Variable Declaration:
d1 = 4                        #m
d2 = 4                        #m
d3 = 8                        #m
r = 1                         #conductor raius(cm)
l = 100                       #line length(km)
Vl = 132000                    #line voltage(V)
f = 50                        #frequency of current(Hz)
e = 8.854*10**-12             #permitivity of free space(F/m)

#Calculation:
Deq = (d1*d2*d3)**(1/3)*100          #cm
C = 2*math.pi*e/math.log(Deq/r)*10**9     #uF/km
C1 = C*100                           #uF
Ic = Vl*2*math.pi*f*C1*10**-6/(3**0.5)      #A

#Result:
print "Charging current per phase is",round(Ic,2),"A"

Charging current per phase is 21.41 A