Chapter 4: 19P (page 226)
Re-work Problem 4.18 if the phase spacing between adjacent conductors is (a) increased by to
or (b) decreased by
to
. Compare the results with those Of Problem 4.18.
Problem 4.18
A, three-phase completely transposed overhead line has one ACSR
conductor per phase and flat horizontal phase spacing, With
between adjacent conductors. Determine the inductance in
and the inductive reactance in
.
Short Answer
(a) The inductance and inductive reactance of completely transposed overhead line are
and
respectively. The inductance is increased by
and inductive reactance is increased by
when the spacing is increased by
.
(b) The inductance and inductive reactance of completely transposed overhead line are and respectively. The inductance is decreased by
and inductive reactance is decreased by
when the spacing is decreased by
.
Step by step solution
Write the given data from the question.
The voltage of the line.
The frequency of the system.
Spacing between the conductorsis.
Theincreased spacing between the conductorsis
.
Thedecreased spacing between the conductorsis
.
Refer to table A4, the geometric mean radius of the overhead conductor for ,
The inductance calculated in problem 4.18 is and inductive reactance is
.
Determine the equation to calculate the inductance and inductive reactance.
The equation to calculate the inductance transposed overhead line inductance is given as follows.
…… (1)
Here, is the distance between conductor
and
,
is the distance between conductor
and
,
is distance between
and
.
The equation to calculate inductive reactance of transposed overhead line is given as follows,
…… (2)
The equation to calculate the change in the inductance is given as follows.
…… (3)
Hereis the inductance after increasing or decreasing the spacing and
is the inductance calculated in problem 4.18.
The equation to calculate the change in the inductive reactance is given as follows.
…… (4)
Hereis the inductive reactance after increasing or decreasing the spacing and
is the inductive reactance calculated in problem 4.18.
Conversion from foot to metres.
Calculate the inductance and inductive reactance of the transposed overhead line when the spacing between the conductor is .
Consider the completely transposed overhead line schematic diagram as follows.
Calculate the inductance of the transposed overhead conductors.
Substitute for
,
for
and
for
,
for
into equation (1).
Calculate the change in the inductance.
Substitute for
and
for
into equation (3)
Calculate the inductive reactance of the transposed overhead conductors.
Substitute for
and
for
into equation (2).
Calculate the change in the inductive reactance.
Substitute for
and
for
into equation (4).
Hence the inductance and inductive reactance of completely transposed overhead line are and
respectively. The inductance is increased by
and inductive reactance is increased by
when the spacing is increased by
.
Calculate the inductance and inductive reactance of the transposed overhead line when the spacing between the conductor is .
(b)
Calculate the inductance of the transposed overhead conductors.
Substitute for
,
for
and
for
,
for
into equation (1).
Calculate the change in the inductance.
Substitute for
and
for
into equation (3)
Calculate the inductive reactance of the transposed overhead conductors.
Substitute for
and
for
into equation (2).
Calculate the change in the inductive reactance.
Substitute for
and
for
into equation (4).
Hence the inductance and inductive reactance of completely transposed overhead line are and
respectively. The inductance is decreased by
and inductive reactance is decreased by
when the spacing is decreased by
.
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