Mathcad - L43ece.uidaho.edu/ee/power/ECE524/Lectures/L43/L43.pdfGWL2 GWL2 T GWL2. ECE 524 Transients in Power Systems Session 43; Page 13/22 Spring 2018 Voltages at tower top, cross

ECE 524Transients in Power Systems

Session 43; Page 1/22 Spring 2018

Lightning Example

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

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

Define parameters: Rfoot 30ohm Zc_gw 520ohm

Htower 40m Zc_tower 135ohm

Hconductor 0.75 Htower Hconductor 30m

Dspan 280m

Define speed of light: μo 4 π 107

H

m εo 8.854 10

12F

m

c1

μo εo c 3 10

5km

sec

νgw c

νtower 0.85 c νtower 2.5483 105

km

sec

μsec 106

sec



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

30 ohm

TOWER

CROSSA

RFOOT

TOWER

TTOP

CROSSA

I STROKE

Grnd WireVFARL

Grnd Wire

VFARR

ATPDraw Schematic



ATP Data File

BEGIN NEW DATA CASEC --------------------------------------------------------C Generated by ATPDRAW April, Wednesday 25, 2012C A Bonneville Power Administration programC by H. K. Høidalen at SEfAS/NTNU - NORWAY 1994-2009C --------------------------------------------------------C dT >< Tmax >< Xopt >< Copt ><Epsiln> 2.5E-9 5.E-5 500 1 0 0 0 0 0 1 0C 1 2 3 4 5 6 7 8C 345678901234567890123456789012345678901234567890123456789012345678901234567890/BRANCHC < 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/SWITCHC < n 1>< n 2>< Tclose ><Top/Tde >< Ie ><Vf/CLOP >< type > STROKETTOP MEASURING 1/SOURCEC < 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 CROSSABLANK BRANCH

Plot of lightning current:

(f ile prob2a.pl4; x-v ar t) c:STROKE-TTOP 0 10 20 30 40 50*10-6

0

5

10

15

20

25

30

35

40

*103



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 50*10-6

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 16*10-6

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 103kV at ttop 2.5075μsec

Vpeak_crossarm 1.4876 103 kV at tcross 2.5400μsec

Note that this is actually thesecond relativepeak in this waveform

Vpeak_foot 1.3294 103kV at tfoot 4.3275μsec



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

Grnd Wire

VFARR

30 ohm

Grnd WireVFARL

Gnd Wire

STRIKE

I STROKE

TOWER

CROSSA

RFOOT

TOWER

TTOP

ATP Draw Circuit Diagram


(f ile prob2b.pl4; x-v ar t) v :TTOP v :CROSSA v :RFOOT - 0 10 20 30 40 50*10-6

0.0

0.5

1.0

1.5

2.0

2.5

*106

Note that the peak voltages are higher in this case.




(f ile prob2b.pl4; x-v ar t) v :TTOP v :CROSSA v :RFOOT - 0 3 6 9 12 15*10-6

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 timedelay in the voltage at the footing resistor.

Vpeak_top 2.0707 103 kV at ttop 2.8275μsec

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



Note that this is actually the second relativepeak in this waveform, but it is earlier than the lastcase.

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

For this case, we will just model the adjactent towers in detail, since we aren't concernedwith waiting for further reflections to come back.We do model both ground wires at the top of each though.



TOWER

CROSSA

RFOOT

30 ohm

Grnd WireVLFT

Grnd WireVFARL

TOWER

TTOP

I STROKE

TOWER

30 ohm

TOWER

TOWER

30 ohm

TOWER

Grnd WireVRGHT

Grnd WireVFARR

(f ile prob2c.pl4; x-v ar t) v :TTOP v :CROSSA v :RFOOT - 0 10 20 30 40 50*10-6

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 12*10-6

0.0

0.3

0.6

0.9

1.2

1.5

*106



(f ile prob2c.pl4; x-v ar t) v :VFARR v :VFARL 0 10 20 30 40 50*10-6

0

50

100

150

200

250

300

350

*103



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

PSCAD Schematic from file Lightning1.psc

Surge

Simple Lightning Surge:

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

TIME

To

we

r1

Tow er1T

To

we

r1T

ow

er2

Tow er2T

To

we

r2

Cro

ssA

30

[oh

m]

VF

OO

T

Vto

p

GWL

GWLT

GWL

10

e1

0 [o

hm

]

GWR

GWRT

GWR

10

e1

0 [o

hm

]

Vtop

CrossA

Vfoot

Ia

Notes:Note the transmission line models used for the groundstraps and static wiresPSCAD requires a terminating impedance at the endof a line, it can't be open circuited. A very largeresistance has been placed at the end of the line



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 (k

A)

Surge


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 (k

V)

Vtop CrossA Vfoot




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 (k

V)

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.



Note that this is actually thesecond relativepeak in this waveform




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

PSCAD Circuit Diagram from file Lightning2.psc

Surge


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

TIME

To

we

r1

Tow er1T

To

we

r1T

ow

er2

Tow er2T

To

we

r2

Cro

ssA

30

[oh

m]

VF

OO

T

Vtop

GWL

GWLT

GWL

10

e1

0 [o

hm

]

GWR

GWRT

GWR

10

e1

0 [o

hm

]

Vtop

CrossA

Vfoot

Ia

GWL2

GWL2T

GWL2




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 (k

V)

Vtop CrossA Vfoot

Note that the peak voltagesare 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 (k

V)

Vtop CrossA Vfoot

Zoom in on peak ofvoltage waveform:

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


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



Note that this is actually the second relativepeak 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 characteristicsand the same footing resistances.

For this case, we will just model the adjacent towers in detail, since we aren't concernedwith 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 verylarge resistanceFrom file Lightning3.psc

Surge


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

TIME

To

we

r1

Tow er1T

To

we

r1T

ow

er2

Tow er2T

To

we

r2

Cro

ssA

30

[oh

m]

VF

OO

T

Vto

p

GWL

GWLT

GWL

10

e1

0 [o

hm

]

GWR

GWRT

GWR

10

e1

0 [o

hm

]

Vtop

CrossA

Vfoot

Ia

GWR2

GWR2T

GWR2

Tow er3T

To

we

r3

To

we

r3

30

[oh

m]

To

we

r4

Tow er4T

To

we

r4

30

[oh

m]

GWL2

GWL2T

GWL2



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 (k

V)

Vtop CrossA Vfoot

Voltages at tower top,cross arm and footingresistance.

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 (k

V)

Vtop CrossA Vfoot

Zoomed voltages attower top, cross armand footing resistance. Note that the peakvoltage is significantlylower than the othercases

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 (k

V)

VTopL VTopR

Voltages at tops of thenext towers to the leftand right



Now add the phase conductors to the model. Closest to case 3 aboveNote that this is simplified to illustrate how to model

30 ohm

TOWER

CRSA3

RFOOT3

TOWER

TTOP3

ISTROKE

VVZSRCSWS BUS1

F1LCC

40. km

V

F2

VS

F3 BUS2

LCC

10. km

TTOP2LCC

0.28 km

F1TTOP1

FS2LCC

0.28 km

ZSRCVRI

V

30 ohm

30 ohm

30 ohm

V

30 ohm

TOWER

CRSA2

RFOOT2

TOWER

TTOP2

CRSA2

30 ohm

TOWER

CRSA1

RFOOT1

TOWERTTOP1

CRSA1

ABC

(file ltngcase4.pl4; x-var t) v:TTOP2 v:CRSA2 v:RFOOT2- 0 10 20 30 40 50[us]

0.0

0.3

0.6

0.9

1.2

1.5

[MV]



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 10 12[us]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 50[us]

-30

-20

-10

0

10

20

30

40

50

[kV]



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

(file ltngc as e4.p l4; x-var t) v:F2A v:F2B v:F2C v:C R S A2 0 10 20 3 0 4 0 5 0[us ]

-0 .4

-0 .1

0 .2

0 .5

0 .8

1 .1

1 .4

[M V ]

Same voltages without the lightning strike:

( file ltngc as e4.p l4 ; x-var t) v:F 2A v:F 2B v:F 2C v:C R S A2 0 1 0 2 0 3 0 4 0 5 0[us ]

-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 ]



Phase Currents Don't show much effect

( f i le l t n 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 .1 0 .2 0 .3 0 .4 0 .5[m s ]

- 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 ltngcase4.pl4; x-var t) c :FS2A -F2A 0.0 0.1 0.2 0.3 0.4 0.5[ms]

2500

2530

2560

2590

2620

2650

[A]



V

FS2 F2

TTOP2LCC

0.28 km

+ Vf -

UI

F1TTOP1

FS2LCC

0.28 km

30 ohm

30 ohm

V

30 ohm

CRSA2

RFOOT2

TTOP2

+ Vf -

UI

+ Vf -

UI

Now add voltage dependent flashoverswitches:

Switch voltages:

(file ltngc as e4.p l4 ; x-var t) v:C R S A2 -F 2A v:C R S A2 -F 2B v:C R S A2 -F 2C 0 .0 0 0 .0 2 0 .0 4 0 .0 6 0 .0 8 0 .1 0[m s ]

-1 .0

-0 .5

0 .0

0 .5

1 .0

1 .5

[M V ]



Phase currents (between towers):

( file ltngc as e4 .p l4 ; x-va r t) c :F S 2A -F 2A c :F S 2B -F 2B c :F S 2C -F 2C 0 .0 0 0 .0 2 0 .0 4 0 .0 6 0 .0 8 0 .1 0[m s ]

-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 ltngc as e4.pl4; x-var t) v:B US 2A v:B US 2B v:B US 2C 0 .00 0 .02 0 .04 0 .06 0 .08 0 .10[m s]

-1 .0

-0 .5

0 .0

0 .5

1 .0

1 .5

[M V ]



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 0.10[ms]

-3000

-2000

-1000

0

1000

2000

[A]

Documents

Mathcad - L43ece.uidaho.edu/ee/power/ECE524/Lectures/L43/L43.pdfGWL2 GWL2 T GWL2. ECE 524 Transients in Power Systems Session 43; Page 13/22 Spring 2018 Voltages at tower top, cross