Exercise Lightning 2 [PDF]

Zitiervorschau

LATIHAN: LIGHTNING

1. Prove the reflection coefficient, α and the transmission coefficient, β for an incident lightning surge on the transmission line as follows:

i.

α=

Z 2 − Z1 Z 2 + Z1

ii.

β=

2Z 2 Z 2 + Z1

2. The towers of a transmission line are 38 m tall. They are spaced 280 m apart and are joined at their tops by a single ground wire of surge impedance 520 Ω. The surge impedance of the towers themselves is 135 Ω. Lightning strikes the ground wire 100 m from a tower. The stroke current rises to a peak of 50 kA in 1.5 µs. determine the voltage of the closest tower top 0.75 µs after the lightning contacts the ground wire. Assume the impedance of the lightning channel is 1500 Ω and the footing resistance is 25 Ω. Waves on the tower travel at 90 % of the speed of light. 3. The towers of a transmission line are 25 m tall and spaced 300 m apart. They are joined at their tops by a ground wire whose surge impedance is 450 Ω. The tower footing resistance is 30 Ω. One tower is struck by lightning. The lightning current rises linearly to a peak of 50 kA in 2 µs before commencing to decline. Compute the tower top potential for the first microsecond after the stroke makes contact. The tower surge impedance is 80 Ω and surge impedance for lightning channel can be neglected. Assume all waves travel at 2.98 x 108 m/s. 4. A lightning stroke which reaches a peak current of 35 kA in 1 us strikes a 20 m tower on a 345 kV transmission line. The line has a ground wire joining the tops of the towers; its surge impedance is 520Ω. The tower surge impedance is 90Ω and the ground footing resistance is 40Ω. Compute the tower top potential for the first microsecond after the

stroke makes contact. The surge impedance for lightning channel can be neglected. Assume all waves travel at 2.98 x 108 m/s. 5. A 300m length of overhead earth conductor which is laid between two towers is struck by lightning. The lightning struck to a point of a distance of one third of the length from one of the tower. The earth conductor and tower surge impedances are 300 Ohm and 100 Ohm respectively. The lightning strike carries peak current of 25 kA within 1.5µs and the surge impedance is 1500 Ohm. Determine the surge voltage at the tower top after the strike.

8. A lightning surge with the waveshape of Figure 1 below strikes a tower which has a single ground wire in both directions. The characteristics are as follows: Surge impedance of lightning channel Surge impedance of tower Surge impedance of ground wire Velocity of wave propagation on lines Velocity of wave propagation on tower Coupling factor of phase conductors Height of tower Effective tower footing resistance

= = = = = = = =

infinity 150 Ω 340 Ω 298m/µs 240 m / µs 0.25 30 m 40Ω

Determine the maximum tower top potential, after 0.4 µs the tower has been struck by lightning. Please show clearly all the calculations involving coefficients of reflection and refraction. Show the surge progressions in the form of Bewley Lattice diagram. a) What will happen if the tower footing resistance increases in value? b) Provide a reason for the tower footing resistance to increase c) Why the speed of surge is higher in the conductor than in the tower structure?

25 kA

20 µs

1 µs Figure 1

9. A lightning stroke which reaches a peak current of 30kA in 1µS strikes a 25 m tower on a 275kV transmission line. The line has a ground wire joining the tops of the towers; its surge impedance is 500Ω. The tower surge impedance is 120Ω and the ground footing resistance is 60Ω. Determine whether the line insulators will flashover as a consequence of the surge, assuming that their impulse flashover strength is 1050 kV. A coupling factor 0.3 with the phase conductor can be assumed; the impedance of the stroke channel can be ignored; a wave velocity on the tower of 2.98 x 10^8 m/s can be assumed. Show the surge progressions in the form of Bewley lattice diagram.