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L43

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Jorge Cáceres

Academic year: 2022

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Lightning Example

Consider a transmission line with towers that are 40m tall and spaced 280m apart. Assume that there is a single shield wire with a characteristic impedance of 520 ohm and assume that the tower ground strap has a characteristic impedance of 135 ohm and the tower has a footing resistance of 30 ohm. Assume a propagation velocity of the speed of light for the ground wires and 0.85 times the speed of light for the tower ground strap. Assume that the phase conductors are 75% of the way up the tower and that the ground wire is segmented and open at the top of each of the adjacent towers.

Consider the case of a lightning strike where the current rises to 40kA in 2 s and falls to 20kA after 40 s.

Define parameters: Rfoot  30ohm Zc_gw 520ohm

Htower  40m Zc_tower  135ohm

Hconductor  0.75 H tower Hconductor  30 m Dspan 280m

Define speed of light: μo 4 π 10 7H

 m εo 8.854 10 12 F

 m

c 1

μoεo

 c 3105 km

sec

νgw  c

νtower  0.85 c νtower 2.5483105 km

sec

μsec 106sec

(2)

(a) Find the peak voltage at the tower top, the bottom of the tower and at the conductor height if the lightning strike the top of the tower.

30 ohm TOWER CROSSA

RFOOT

TOWER TTOP

CROSSA I STROKE

Grnd Wire

VFARL Grnd Wire

VFARR

ATPDraw Schematic

(3)

ATP Data File

BEGIN NEW DATA CASE

C --- C Generated by ATPDRAW April, Wednesday 25, 2012

C A Bonneville Power Administration program

C by H. K. Høidalen at SEfAS/NTNU - NORWAY 1994-2009 C --- C dT >< Tmax >< Xopt >< Copt ><Epsiln>

2.5E-9 5.E-5

500 1 0 0 0 0 0 1 0

C 1 2 3 4 5 6 7 8

C 345678901234567890123456789012345678901234567890123456789012345678901234567890 /BRANCH C < n1 >< n2 ><ref1><ref2>< R >< L >< C > C < n1 >< n2 ><ref1><ref2>< R >< A >< B ><Leng><><>0 RFOOT 30. 2

-1CROSSARFOOT 135.2.55E8 30. 1 0 0

-1TTOP CROSSA 135.2.55E8 10. 1 0 0

-1VFARL TTOP 520. 3.E8 280. 1 0 0

-1TTOP VFARR 520. 3.E8 280. 1 0 0

/SWITCH C < n 1>< n 2>< Tclose ><Top/Tde >< Ie ><Vf/CLOP >< type > STROKETTOP MEASURING 1

/SOURCE C < n 1><>< Ampl. >< Freq. ><Phase/T0>< A1 >< T1 >< TSTART >< TSTOP > 13STROKE-1 4.E4 2.E-6 2.E4 4.2E-5 1.

/OUTPUT

TTOP CROSSA BLANK BRANCH

Plot of lightning current:

(f ile prob2a.pl4; x-v ar t) c:STROKE-TTOP

0 10 20 30 40 *10-6 50

0 5 10 15 20 25 30 35 40

*103

(4)

Voltages at tower top, cross arm and footing resistance.

(f ile prob2a.pl4; x-v ar t) v :TTOP v :CROSSA v :RFOOT -

0 10 20 30 40 *10-6 50

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

*106

Zoom in on peak of voltage waveform:

(f ile prob2a.pl4; x-v ar t) v :TTOP v :CROSSA v :RFOOT -

0 2 4 6 8 10 12 14 *10-6 16

0.6 0.8 1.0 1.2 1.4 1.6

*106

As one would expect, the top shows the biggest peaks in voltage.

Note also the time delay in the voltage at the footing resistor.

Vpeak_top 1.5609 10 3kV at ttop 2.5075μsec Vpeak_crossarm 1.4876 10 3kV at tcross  2.5400μsec

Note that this is actually the second relative

peak in this waveform Vpeak_foot  1.3294 10 3kV at tfoot 4.3275μsec

(5)

(b) Repeat of the lightning strike occurs 100m away from the tower top (in either direction).

Grnd Wire VFARR

30 ohm Grnd Wire

VFARL Gnd Wire

STRIKE I STROKE

TOWER CROSSA

RFOOT

TOWER TTOP

ATP Draw Circuit Diagram

Voltages at tower top, cross arm and footing resistance.

(f ile prob2b.pl4; x-v ar t) v :TTOP v :CROSSA v :RFOOT -

0 10 20 30 40 *10-6 50

0.0 0.5 1.0 1.5 2.0 2.5

*106

Note that the peak voltages are higher in this case.

(6)

Zoom in on peak of voltage waveform:

(f ile prob2b.pl4; x-v ar t) v :TTOP v :CROSSA v :RFOOT -

0 3 6 9 12 *10-6 15

0.2 0.6 1.0 1.4 1.8 2.2

*106

Again,the top shows the biggest peaks in voltage. Note also the time delay in the voltage at the footing resistor.

Vpeak_top 2.0707 10 3kV at ttop 2.8275μsec

Note that the time to the peak is delayed, due to travel time along the ground wire.

Vpeak_crossarm 1.9251 10 3kV at tcross  2.8650μsec

Vpeak_foot  1.6244 10 3kV at tfoot 4.0525μsec

Note that this is actually the second relative peak in this waveform, but it is earlier than the last case.

(c) Repeat part (a) if the adjacent towers are each grounded, with the same ground strap characteristics and the same footing resistances.

For this case, we will just model the adjactent towers in detail, since we aren't concerned

with waiting for further reflections to come back.

We do model both ground wires at the top of each though.

(7)

TOWER CROSSA

RFOOT 30 ohm Grnd Wire Grnd Wire VLFT

VFARL

TOWER TTOP I STROKE

TOWER

30 ohm

TOWER

TOWER

30 ohm

TOWER Grnd Wire

VRGHT

Grnd Wire VFARR

(f ile prob2c.pl4; x-v ar t) v :TTOP v :CROSSA v :RFOOT -

0 10 20 30 40 *10-6 50

0.0 0.3 0.6 0.9 1.2 1.5

*106

(f ile prob2c.pl4; x-v ar t) v :TTOP v :CROSSA v :RFOOT -

0 2 4 6 8 10 *10-6 12

0.0 0.3 0.6 0.9 1.2 1.5

*106

(8)

(f ile prob2c.pl4; x-v ar t) v :VFARR v :VFARL

0 10 20 30 40 *10-6 50

0 50 100 150 200 250 300 350

*103

(9)

(a) Find the peak voltage at the tower top, the bottom of the tower and at the conductor height if the lightning strike the top of the tower.

PSCAD Schematic from file Lightning1.psc

Surge

Simple Lightning Surge:

I = 40kA/T1 * t - C1(t-T1) TIME

Tower1

Tow er1 T

Tower1Tower2

Tow er2 T

Tower2 CrossA

30[ohm]

VFOOTVtop GWL

GWL T

GWL

10e10 [ohm]

GWR

GWR T

GWR

10e10 [ohm]

Vtop

CrossA

Vfoot

Ia

Notes:

Note the transmission line models used for the ground

straps and static wires

PSCAD requires a terminating impedance at the end

of a line, it can't be open circuited. A very large resistance has been placed at the end of the line

(10)

Current surge source dialog box:

Plot of lightning current:

Main : Graphs

0.000 0.010m 0.020m 0.030m 0.040m 0.050m

0.0 5.0k 10.0k 15.0k 20.0k 25.0k 30.0k 35.0k 40.0k

y (kA)

Surge

Voltages at tower top, cross arm and footing resistance.

Main : Graphs

0.000 0.010m 0.020m 0.030m 0.040m 0.050m

0.0 0.2M 0.4M 0.6M 0.8M 1.0M 1.2M 1.4M 1.6M

y (kV)

Vtop CrossA Vfoot

(11)

Zoom in on peak of voltage waveform:

Main : Graphs

0.000 0.002m 0.004m 0.006m 0.008m 0.010m 0.012m 0.014m 0.016m 0.018m 0.0

0.2M 0.4M 0.6M 0.8M 1.0M 1.2M 1.4M 1.6M

y (kV)

Vtop CrossA Vfoot

As one would expect, the top shows the biggest peaks in voltage.

Note also the time delay in the voltage at the footing resistor.

Vpeak_top 1.5609 10 3kV at ttop 2.5075μsec Vpeak_crossarm 1.4876 10 3kV at tcross  2.5400μsec

Note that this is actually the second relative

peak in this waveform Vpeak_foot  1.3294 10 3kV at tfoot 4.3275μsec

(12)

(b) Repeat of the lightning strike occurs 100m away from the tower top (in either direction).

PSCAD Circuit Diagram from file Lightning2.psc

Surge

Simple Lightning Surge:

I = 40kA/T1 * t - C1(t-T1) TIME

Tower1

Tow er1 T

Tower1Tower2

Tow er2 T

Tower2 CrossA

30[ohm]

VFOOT

Vtop

GWL

GWL T

GWL

10e10 [ohm]

GWR

GWR T

GWR

10e10 [ohm]

Vtop CrossA

Vfoot

Ia

GWL2

GWL2 T

GWL2

(13)

Voltages at tower top, cross arm and footing resistance.

Main : Graphs

0.000 0.010m 0.020m 0.030m 0.040m 0.050m

0.0 0.3M 0.5M 0.8M 1.0M 1.3M 1.5M 1.8M 2.0M 2.3M

y (kV)

Vtop CrossA Vfoot

Note that the peak voltages are higher in this case.

Main : Graphs

0.000 0.002m 0.004m 0.006m 0.008m 0.010m 0.012m 0.014m 0.016m 0.0

0.3M 0.5M 0.8M 1.0M 1.3M 1.5M 1.8M 2.0M 2.3M

y (kV)

Vtop CrossA Vfoot

Zoom in on peak of voltage waveform:

Again,the top shows the biggest peaks in voltage. Note also the time delay in the voltage at the footing resistor.

Vpeak_top 2.0707 10 3kV at ttop 2.8275μsec

Note that the time to the peak is delayed, due to travel time along the ground wire.

Vpeak_crossarm 1.9251 10 3kV at tcross  2.8650μsec

Vpeak_foot  1.6244 10 3kV at tfoot 4.0525μsec

Note that this is actually the second relative

peak in this waveform, but it is earlier than the last case.

(14)

(c) Repeat part (a) if the adjacent towers are each grounded, with the same ground strap characteristics and the same footing resistances.

For this case, we will just model the adjacent towers in detail, since we aren't concerned

with waiting for further reflections to come back.

We do model both ground wires at the top of each though.

The model includes the static wires beyond the next tower as well, terminated with a very

large resistance

From file Lightning3.psc

Surge

Simple Lightning Surge:

I = 40kA/T1 * t - C1(t-T1) TIME

Tower1

Tow er1 T

Tower1Tower2

Tow er2 T

Tower2 CrossA

30[ohm]

VFOOT Vtop GWL

GWL T

GWL

10e10 [ohm]

GWR GWR

T

GWR

10e10 [ohm]

Vtop CrossA

Vfoot

Ia

GWR2 GWR2

T

GWR2

Tow er3 T

Tower3

Tower3 30[ohm]

Tower4

Tow er4 T

Tower4 30[ohm]

GWL2 GWL2

T

GWL2

(15)

Main : Graphs

0.000 0.010m 0.020m 0.030m 0.040m 0.050m

0.0 0.2M 0.4M 0.6M 0.8M 1.0M 1.2M 1.4M

y (kV)

Vtop CrossA Vfoot

Voltages at tower top, cross arm and footing resistance.

Main : Graphs

0.000 0.002m 0.004m 0.006m 0.008m 0.010m 0.012m 0.014m 0.016m 0.0

0.2M 0.4M 0.6M 0.8M 1.0M 1.2M 1.4M

y (kV)

Vtop CrossA Vfoot

Zoomed voltages at

tower top, cross arm and footing resistance.

Note that the peak

voltage is significantly lower than the other cases

Main : Graphs

0.000 0.005m 0.010m 0.015m 0.020m 0.025m 0.030m 0.035m 0.00

50.00k 100.00k 150.00k 200.00k 250.00k 300.00k 350.00k

y (kV)

VTopL VTopR

Voltages at tops of the next towers to the left and right

(16)

Now add the phase conductors to the model. Closest to case 3 above

Note that this is simplified to illustrate how to model

30 ohm TOWER CRSA3

RFOOT3

TOWER TTOP3 I

STROKE

V

ZSRC V

SWS BUS1

LCC F1

40. km

V

F2 VS

F3 BUS2

LCC

10. km

TTOP2

LCC

0.28 km

F1 TTOP1

LCC FS2

0.28 km

ZSRC VR

I

V

30 ohm 30 ohm

30 ohm

V

30 ohm TOWER CRSA2

RFOOT2

TOWER TTOP2

CRSA2

30 ohm TOWER CRSA1

RFOOT1

TOWER TTOP1

CRSA1 ABC

(file ltngcase4.pl4; x-var t) v:TTOP2 v:CRSA2 v:RFOOT2-

0 10 20 30 40 [us] 50

0.0 0.3 0.6 0.9 1.2 1.5 [MV]

(17)

Compare cross arm voltage to case 3:

ltngc as e4.pl4: v:C R S A2 ltngc as e3.pl4: v:C R O S S A

0 2 4 6 8 1 0 [us ] 1 2

0 .0 0 .3 0 .6 0 .9 1 .2 1 .5 [M V ]

Voltages on the footing resistors of the other uprights:

(file ltngcase4.pl4; x-var t) v:G1R - v:G2R - v:G3R -

0 10 20 30 40 [us] 50

-30 -20 -10 0 10 20 30 40 50 [kV]

(18)

Phase conductor voltages (with cross arm level on ground strap)

(file ltn g c a s e 4 .p l4 ; x-va r t) v:F 2 A v:F 2 B v:F 2 C v:C R S A2

0 1 0 2 0 3 0 4 0 [us ] 5 0

-0 .4 -0 .1 0 .2 0 .5 0 .8 1 .1 1 .4 [M V ]

Same voltages without the lightning strike:

( file ltn g c a s e 4 .p l4 ; x-v a r t) v:F 2 A v:F 2 B v:F 2 C v:C R S A 2

0 1 0 2 0 3 0 4 0 [us ] 5 0

-3 0 0 -2 0 0 -1 0 0 0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 [k V ]

(19)

Phase Currents Don't show much effect

( f il e lt n g c a s e 4 . p l 4 ; x - v a r t ) c : F S 2 A - F 2 A c : F S 2 B - F 2 B c : F S 2 C - F 2 C

0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 [ m s ] 0 . 5

- 2 0 0 0 - 1 0 0 0 0 1 0 0 0 2 0 0 0 3 0 0 0 [ A ]

Zoom on one phase:

(file ltngc as e4.pl4; x-var t) c :FS2A -F2A

0.0 0.1 0.2 0.3 0.4 [ms] 0.5

2500 2530 2560 2590 2620 2650

[A ]

(20)

V

FS2 F2

TTOP2

LCC

0.28 km

+ Vf - UI

F1 TTOP1

LCC FS2

0.28 km

30 ohm 30 ohm

V

30 ohm CRSA2

RFOOT2

TTOP2

+ Vf - UI

+ Vf - UI

Now add voltage dependent flashover

switches:

Switch voltages:

(file ltn g c a s e 4 .p l4 ; x -va r t) v :C R S A 2 -F 2 A v :C R S A2 -F 2 B v :C R S A 2 -F 2 C

0 .0 0 0 .0 2 0 .0 4 0 .0 6 0 .0 8 [m s ] 0 .1 0

-1 .0 -0 .5 0 .0 0 .5 1 .0 1 .5 [M V ]

(21)

Phase currents (between towers):

( file ltn g c a s e 4 .p l4 ; x -v a r t) c :F S 2 A -F 2 A c :F S 2 B -F 2 B c :F S 2 C - F 2 C

0 .0 0 0 .0 2 0 .0 4 0 .0 6 0 .0 8 [m s ] 0 .1 0

-5 0 0 0 -3 5 0 0 -2 0 0 0 -5 0 0 1 0 0 0 2 5 0 0 4 0 0 0 [A ]

Phase voltages at Bus 2 (closer bus)

(file ltn g c a s e 4 .p l4 ; x-va r t) v:B U S 2 A v:B U S 2 B v:B U S 2 C

0 .0 0 0 .0 2 0 .0 4 0 .0 6 0 .0 8 [m s ] 0 .1 0

-1 .0 -0 .5 0 .0 0 .5 1 .0 1 .5 [M V ]

(22)

Phase Currents at Bus 2:

(file ltngcase4.pl4; x-var t) c:SWRA -BUS2A c:SWRB -BUS2B c:SWRC -BUS2C

0.00 0.02 0.04 0.06 0.08 [ms] 0.10

-3000 -2000 -1000 0 1000 2000 [A]

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