The towers of a transmission line are 36 m tall and spaced 300 m apart. They are

Question

The towers of a transmission line are 36 m tall and spaced 300 m apart. They are joined at their tops by a ground wire whose surge impedance is 540 Ohm. The tower footing resistance is 25 Ohm. One tower is struck by lightning. The lightning current rises linearly to a peak of 60 mu s before commencing to decline. Compute the tower top potential and the tower base potential for the first microsecond after the stroke makes contact. The tower surge impedance is 140 Ohm; that of the lightning channel can be neglected. Assume all waves travel at 2.98 times 10 m/s.

Explanation / Answer

Given data :

Height of tower = 36 m

spacing between tower = 300 m

Surge impedance ( Zg ) = 540 ohm

tower footing resistance = 25 ohm

lightning current = 60 kA in 2 microseconds or 30 kA in 1 microseconds

Tower surge impedance ( ZT ) = 140 ohm

speed of waves = 2.98 * 108 m/s

First we have to find terminating impedance

Z = ZT / ( 1 + 2ZT/ Zg )

by putting value and solving we get

Z = 140 / ( 1+ 2* 140 /540 )

Z = 92.19 ohm

Formula for tower top potential = VT = Io *Z / ( 1 + Z/ ZT )

so solving we get

VT = 30 * 92.19 / ( 1 +92.19/140 )

VT = 1640 kV

Tower base potential

VB = Io * Z / ( 1 + ZT/Z )

VB = 30 * 92.19 / ( 1 + 140/92.19 )

We get VB = 1099 kV

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