Power Lines
The power transmission line is one of the major
components of an electric power system. Its major
function is to transport electric energy, with minimal
losses, from the power sources to the load centers,
usually separated by long distances. The design of a
transmission line depends on four electrical parameters:
1. Series resistance
2. Series inductance
3. Shunt capacitance
4. Shunt conductance
Parameters of Power Lines
Resistance:
L
R= r
A
Where :
R is series resistance
The resistance increases along the
temperature, as the temperature is
bound to increase with the increase
of currant carried by the line.
Rt = R0 (1+0)
Where:
 is a resistivity of material used
Rt is Resistance at temperature t
L is length of the line
R0 is resistance at 00 C
A is a x-sectional area of the line.
0 is temperature coefficient
And for uniform cable this is defined in per unit
length: R = /A
Power Line Parameters..
Inductance

A current-carrying conductor produces concentric
magnetic flux lines around the conductor. If the current
varies with the time, the magnetic flux changes and a
voltage is induced. Therefore, an inductance is
present, defined as the ratio of the magnetic flux
linkage and the current. The magnetic flux produced
by the current in transmission line conductors
produces a total inductance whose magnitude
depends on the line configuration. To determine the
inductance of the line, it is necessary to calculate, as
in any magnetic circuit with permeability , the
following factor :



1.Magnetic field intensity H
2.Magnetic field density B
3. Flux linkage 
Power Line Parameters
Inductance:
The value of inductances varies due to type of
transmission lines;


Outer Flux
Two parallel lines or
Coaxial line
Inner Flux
Internal Inductance Due to
Internal Magnetic Flux
To obtain the internal inductance, a magnetic field with
radius x inside the conductor of length l is chosen, as
2
shown in:
px
Ix =I 2 (A)
pr
Ampere’s law
determines the
magnetic field intensity
Hx, constant at any
point along the circle
contour as:
Ix
I
Hx =
=
x ( AT )
2p x 2p r
Ix
Hx
r
dx
L Length
Inductance due to Internal Flux
The magnetic flux density Bx is obtained:
Ix
Bx = mH x = m
(T )
2
2p r
For nonmagnetic material =0 = 4x10-7
r
-7
-7
I
4p .10 .I 10
l int = ò dl = m0 =
=
.I (wb)
8p
8p
2
0
l int m0 4p .10- 7 10- 7
Lint = = =
=
(H )
I 8p
8p
2
External Inductance
The external inductance is
evaluated assuming that the total
current I is concentrated at the
conductor surface (maximum
skin effect). At any point on an
external magnetic field circle of
radius y (Fig.),the magnetic
field intensity Hy and the
magnetic field density By, per unit
length, are:
y
r
D1
D2
dy
I
Hy =
2p y
(AT )
m I
By = mH y =
(T )
2p y
Two Wire System
The system have two
wires carrying current
in reverse direction.
External flux of each
is interacting with
other internal of the
other cable. The
effective Flux and
therefore inductance
is super positioned of
both.
D
Total Flux & Inductance
D2
D2
m0
dy m0
D1
4p .10- 7
D1
l 1® 2 = ò dl =
Iò
=
I ln( ) =
.I Ln(
(Wb )
2p D1 y 2p
D2
2p
D2
D1
D1
= 2.10 .I Ln( )
D2
- 7
(Wb )
m 1
D
I
[
+
Ln
(
)]
int
2p 4
r
l + l ext
m 1
D
Ltot = int
=
[ + Ln(
)] (H / m )
I
2p 4
GMR
4p .10- 7 1
D
1
D
=
[ + Ln(
)] = 2.10- 7 [ + Ln(
)] (H / m )
2p
4
GMR
4
GMR
D
= 10- 7 [0.5 + 2.Ln ] (H / m )
r1
l
+ l
ext =
Where GMR is geometric Mean Radius
Example No 1
Find the loop inductance per km of a single
phase overhead lie consisting of two
conductors, each 1.213 cm diameter. The
spacing between conductors is 1.25 m and
frequency is 50 Hz.
Solution No 1
r= 1.213/2 = 0.6065 cm
r ’= 0.7788 x0.6065= 0.4723 cm
L= 4x10-7Ln (125/0.4723)
= 22.31x10-7 H/m or 22.31x 10-4 H/km
X= 2..f.L= 2..50.22.31x10-4 Ohms/km
= 0.7 /km
Types of Line Conductors

There are two types of transmission line conductors:
overhead and underground. Overhead conductors, made
of naked metal and suspended on insulators, are
preferred over underground conductors because of the
lower cost and easy maintenance. Also, overhead
transmission lines use aluminum conductors, because of
the lower cost and lighter weight compared to copper
conductors, although more cross-section area is needed
to conduct the same amount of current. There are
different types of commercially available aluminum
conductors: aluminum-conductor-steel-reinforced
(ACSR), aluminum-conductor-alloy-reinforced (ACAR),
all-aluminum-conductor (AAC), and all-aluminum-alloyconductor (AAAC
Multiple Strand LINE
ACSR is one of the most
used conductors in
transmission lines. It
consists of alternate layers
of stranded conductors,
spiraled in opposite
directions to hold the
strands together,
surrounding a core of steel
strands. Figure shows an
example of aluminum and
steel strands combination.
Types of Line Conductors
The purpose of introducing a steel core inside the
stranded aluminum conductors is to obtain a high
strength-to-weight ratio. A stranded conductor
offers more flexibility and easier to manufacture
than a solid large conductor. However, the total
resistance is increased because the outside
strands are larger than the inside strands on
account of the spiraling [8]. The resistance of
each wound conductor at any layer, per unit
length, is based on its total length as follows