Question 2 (W3.10)
In a three-core cable, the capacitance between the three cores short-circuited
together and the sheath is 0.87 F/km, and that between two cores connected
together to with the sheath and the third core is 0.84 F/km. Determine the
kVA required to keep 16 km of this cable charged when the supply is 33
kV, three phase, 50 Hz.
Question 2 (W3.10)
kVA for charging 16 km of cable with 33 kV supply
Three-core cable:
2)
1)
1) Capacitance between the three cores short-circuited together and the sheath is 0.87
n
F/km:
C A  0.87
μF
1
μF
 3
 C1  C1  C A  0.29
km parallel
3
km
C1
C1
C1
CA
2) Between two cores connected together with the sheath and the third core is 0.84 F/km:
μF
C B  0.84
 2  C 2  C1
km
1
1
μF
μF
 C 2  C B  C1   0.84  0.29 
 0.275
2
2
km
km
n
C1
C2
C2
CB
Question 2 (W3.10)
kVA for charging 16 km of cable with 33 kV supply
We can make a delta-star transformation for easier solution:
U
2
Q  3UI  sin



3
U


3
U
Y

Z

 1( cap.)
Q  3
2
U  1
2


I  sin



3


U
Y

3  1(cap.)
 3  Z
U
 Y  3Y
power
equilibrium

Q
Question 2 (W3.10)
kVA for charging 16 km of cable with 33 kV supply
C1  0.29
μF
km
C 2  0.275
μF
km
Something to go after…
From the sheats/neutrals perspective:
“n”
Cap. per phase :
μF
μF
 1.115
km
km
μF
For a 16 - km cable : C  1.115
 16km  17.84μF
km
C  C1  3C 2  0.29  3  0.275
For a three-phase system the apparent power is:
2


U  1
2

S  3
 YU 2  CU 2  2fCU 2  2  50  17.84  10 6  33  10 3 VA
 3 Z
 6.1 MVA
Question 3 (G4.3)
An AAC is composed of 37 strands, each having a
diameter of 0.333 cm. Compute the dc resistance
in ohms per kilometer at 75C. Assume that the
increase in resistance due to spiraling is 2%.
Use
resistivity for aluminum:
0.0283 Ωmm^2/m at 20°C
temperature dependence:
0.00403 /°C
Question 3 (G4.3)
dc resistance
An AAC is composed of 37 strands, each having a
diameter of 0.333 cm. Compute the dc resistance in
ohms per kilometer at 75C. Assume that the increase in
resistance due to spiraling is 2%.
AAC is an all-aluminum conductor
Resistivity 
  2.83  10 8 m at 20C
and
 = 0.00403 per C
Diameter of a strand is d = 0.333 cm = 0.00333 m
Total area of the conductor A  37 
R20  
l
A

R20  2.83  10 8 m
 
 1000
l
A 3.222  10  4 m 2

 0.0878
km

4
0.003332  3.222 10 4 m 2
Question 3 (G4.3)
dc resistance
An AAC is composed of 37 strands, each having a
diameter of 0.333 cm. Compute the dc resistance in
ohms per kilometer at 75C. Assume that the increase in
resistance due to spiraling is 2%.
R20

 0.0878
l
km
Spiraling effect :
R' 20
R
Ω
Ω
 1.02  20  1.02  0.0878
 0.0896
l
l
km
km
Zero at DC
R75 R' 20
1   75  20

l
l
 0.0896  1  0.00403  75  20   0.109

km
Question 4 (G5.6)
A three-phase 60-Hz line has flat horizontal spacing. The
conductors have an outside diameter of 3.28 cm with 12 m
between conductors. Determine the capacitive reactance
to neutral in ohm-meters and the capacitive reactance
of the line in ohms if its length is 200 km.
Question 4 (G5.6)
d  3.28cm  0.0328m
A three-phase 60-Hz line has flat horizontal spacing. The
conductors have an outside diameter of 3.28 cm with 12 m
between conductors. Determine the capacitive reactance to
neutral in ohm-meters and the capacitive reactance of the line
in ohms if its length is 200 km.
 r  0.0164m
D  12m
l  200km
D
D
Deq  3 Dab  Dbc  Dac  3 12  12  24 m  15.12m
The line-to-neutral capacitance per meter and capacitive reactance in ohm-meters =
F
C  
m
 XC
2 0
 Deq
ln
 r




10 9
F

 8.138 10 12
m
 15.12 
18  ln

 0.0164 
 Deq 

ln
r 
 Deq
1

7


 4.77  10  ln
9
10
C 2  60  2 
 r
36
10 9  F 
12 F
0 

8
.
842

10
36  m 
m

  3.256  108   m


Question 4 (G5.6)
d  3.28cm  0.0328m
A three-phase 60-Hz line has flat horizontal spacing. The
conductors have an outside diameter of 3.28 cm with 12 m
between conductors. Determine the capacitive reactance to
neutral in ohm-meters and the capacitive reactance of the line
in ohms if its length is 200 km.
 r  0.0164m
D  12m
l  200km
Line capacitance and reactance for the 200 km line:
C  8.138 10 12
 XC 
F 1000 m

 200km  1.63 μF
m
km
1
1

 1627
6
C 2  60  1.63  10