problem 80
DESCRIPTION
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Wildi Industrial Problem 80 (practical level)
Inductance of a single-phase transmission line
As you know, a single-phase transmission line (Fig. 80-1) possesses a certain resistance that depends upon the size of the conductor and the material of which it is made. The resistance produces an IR voltage drop in the line whenever it carries a current.
However, the transmssion line also possesses a certain inductance L which gives rise to a reactance XL given by XL = 2πfL. As a result, the line experiences an inductive reactance voltage drop IXL in addition to the IR drop.
If the line consists of two conductors that have a diameter d and are spaced apart by a distance D (Fig. 80-2), it can be shown that its inductance is given by the formula:
L = 0.92 × l × log10 2.6 D/d
in which
L = inductance [μH]
l = length [m]
D = distance between the centers of the two conductors [m]
d = diameter of the conductors [m]
0.92 = numerical constant to take care of units
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For example, referring to Fig. 80-2, the inductance of a 40 km transmission line composed of two cables having a diameter d of 8 mm and spaced at a distance apart D of 0.6 m is
L = 0.92 × l × log10 2.6 D/d
= 0.92 × 40 000 × log10 (2.6 × 0.6/0.008)
= 36 800 × log10 (195)
= 36 800 × 2.29
= 84 272 μH = 84.3 mH = 0.0843 H.
The following Industrial Problem illustrates that the inductance of a transmission line changes only very moderately, even for large changes in D and d.
Technical data and relevant questions
Using the example given in the introduction above, you are asked to determine the inductance of the following transmission lines:
a) The inductance of the transmission line in Fig 80-1 if the diameter of the conductors is 4 mm instead of 8 mm [mH]
b) The inductance of the transmission line in Fig. 80-1 if the distance between the conductors is 6 m instead of 0.6 m [mH]
c) The inductance of the transmission line in Fig. 80-1 if the distance between the conductors is 60 m instead of 0.6 m [mH]
d) The inductance of the transmission line in Fig. 80-1 if the distance between the conductors is 600 m instead of 0.6 m [mH]
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e) The inductance of the transmission line in Fig. 80-1 if the distance between the conductors is 3 m instead of 0.6 m and the diameter of the conductors is 40 mm instead of 8 mm [mH]
f) Assuming a frequency of 50 Hz, calculate the value of the inductive reactance of the transmission line in item (e) above [Ω]
References
Electrical Machines, Drives, and Power Systems, 6th Edition by Theodore Wildi
Sections 2.15, 25.21, 25.23, 25.26
Answers
a) 95.3 mH b) 121 mH c) 158 mH d) 195 mH e) 84.3 mH f) 26.5 Ω
Solution to Industrial Problem 80
don't peek until you've done your best to answer the questions by yourself
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