Chapter 4: 21P (page 226)
Rework Problem 4.20 if the bundled line has (a) three ACSR, 1351 kcmil conductors per phase or (b) three ACSR, 900 kcmil conductors per phase, without changing the bundle spacing or the phase spacings between bundle centers. Compare the results with those of Problem 4.20.
Short Answer
(a) The inductive reactance of completely transposed overhead line is and it is decreased by
.
(b) The inductive reactance of completely transposed overhead line isand it is increased by
.
Step by step solution
Write the given data from the question.
The voltage of the line,
The frequency of the system,
The bundle spacing,
The horizontal spacing between the conductor are and
.
The inductive reactance calculated in problem 4.20 is.
Determine the equation to calculate the inductance and inductive reactance.
The equation to calculate the geometric mean distance of completely transposed overhead line 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 the bundle geometric mean radius of completely transposed overhead line is given as follows.
…… (2)
The equation to calculate the inductance transposed overhead line inductance is given as follows.
…… (3)
The equation to calculate inductive reactance of transposed overhead line is given as follows,
…… (4)
The equation to calculate the change in the inductive reactance is given as follows.
…… (5)
Here is the inductive reactance and
is the inductive reactance calculated in problem 4.20.
Conversion from foot to metres.
Calculate the inductive reactance of the transposed overhead line for .
(a)
Refer to table A4, the geometric mean radius of the overhead conductor for ,
.
Calculate the geometric mean distance.
Substitute for
,
for
and
for
into equation (1).
Calculate the bundle GMR.
Substitute for
and
for
into equation (2).
Calculate the inductance of the transposed overhead conductors.
Substitute for
,
for
into equation (3).
Calculate the inductive reactance of the transposed overhead conductors.
Substitute for
and
for
into equation (4).
Calculate the change in the inductive reactance.
Substitute for
and
for
into equation (5).
Hence the inductive reactance of completely transposed overhead line isand it is decreased by
.
Calculate the inductive reactance of the transposed overhead linefor .
(b) Refer to table A4, the geometric mean radius of the overhead conductor for ,
Calculate the geometric mean distance.
Substitute for
,
for
and
for
into equation (1).
Calculate the bundle GMR
Substitute for
and
for
into equation (2).
Calculate the inductance of the transposed overhead conductors.
Substitute for
,
for
into equation (3).
Calculate the inductive reactance of the transposed overhead conductors.
Substitute for
and
for
into equation (4).
Calculate the change in the inductive reactance.
Substitute for
and
for
into equation (5).
Hence the inductive reactance of completely transposed overhead line isand it is increased by
.
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