ALMA MATER STUDIORUM – UNIVERSITA’ DI BOLOGNA

IEEE St 1410

Revision

Lightning Induced Voltages

A. Borghetti C.A. Nucci M. Paolone

2009 IEEE JTCMeetingAtlanta, GA

Lightning Performance of Distribution Lines

To get the ___ we need:

1. Statistical distribution of lightning current parameters (peak, rise time, …)

2. Incidence model

3. Induced-voltage model

4. Statistical approach

1.00 10.00 100.00 1000.00

0.050.10

0.501.002.00

5.00

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20.0030.004 0.0050.0060.0070.0080.00

90.00

95.00

98.0099.0099.50

99.9099.95

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1. Statistical Distribution of Lightning Current Amplitude

6.2*

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31/1

1)(

P

PPI

IIP

[kA]

IEEE:

Ip 20kAIp = 61.1 kAln Ip = 1.33

Ip > 20 kAIp = 33.3 kAln Ip = 0.605

Cigré:

For our purposesthe two approaches are equivalent

Lightning Performance of Distribution Lines

To get the ___ we need:

1. Statistical distribution of lightning current parameters (peak, rise time, …)

2. Incidence model

3. Induced-voltage model

4. Statistical approach

Lightning Performance of Distribution Lines

To get the ___ we need:

1. Statistical distribution of lightning current parameters (peak, rise time, …)

2. Incidence model

3. Induced-voltage model

4. Statistical approach

0.65s I10r sg rr 0,9

2g2

sl hrrd

IEEE WG lateral attractive distance

2. Incidence model

It is just worth mentioning that other expressions exist: - Eriksson- Rizk- Dellera and Garbagnati (LPM)

rs

rg

Nearby stroke

hdl

Direct stroke

Lightning Performance of Distribution Lines

To get the ___ we need:

1. Statistical distribution of lightning current parameters (peak, rise time, …)

2. Incidence model

3. Induced-voltage model

4. Statistical approach

2

00

21

1

12

11

cvc

vyhIZ

Umax

2

00

21

1

12

11

cvc

vyhIZ

Umax

Rusck simplified formula

30/4/1 00 oZ

Assumptions: a. single-conductor b. infinitely long lines above ac. perfectly cond. groundd. step current waveshape

v return stroke velocity

3. Induced voltage calculation model (present)

'1

2sw sw c

sw g

h ZU

U h Z R

'1

2sw sw c

sw g

h ZU

U h Z R

h=0,75h=0,75

Too simple: not adequate in many cases!

Return stroke model: Modified Transmission Line Exponential Decay (MTLE) or any other typeLEMP: Uman and McLain and Cooray-RubinsteinCoupling model: Agrawal extended to the case of lossy ground

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dztzxEtxv e

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3. Induced voltage calculation model (revised)

Note: the shield wire is simply one of the conductors of the n-conductor system

Lightning Performance of Distribution Lines

To get the ___ we need:

1. Statistical distribution of lightning current parameters (peak, rise time, …)

2. Incidence model

3. Induced-voltage model

4. Statistical approach

4. Statistical approach (present)a) The assumed range of peak values of lightning current Ip at the

channel base, from 1 kA to 200 kA, is divided in 200 intervals of 1 kA.

b) For each interval i, the probability pi of current peak value Ii to be within interval i is found as the difference between the p for current to be than the lower limit and the p for current to reach or exceed the higher limit. These ps are obtained by using the formula seen before

c) For each interval i, also two distances form the line (in m) are calculated: 1) the minimum distance ymin,i (using the IEEE incidence

model) for which lightning of peak current Ii (in kA) will not divert to

the line, and 2) the maximum distance ymax,i at which lightning may

produce an insulation flashover (using the Rusck formula), i.e. an induced voltage equal to the line critical flashover voltage CFO (in kV), multiplied by a factor equal to 1.5 (to take into account the turn-up in the insulation volt-time curve for short front-time surges).

d)

200

max min1

0,2 i ip g i

i

F y y N p

4. Statistical approach (present)a) The assumed range of peak values of lightning current Ip at the

channel base, from 1 kA to 200 kA, is divided in 200 intervals of 1 kA.

b) For each interval i, the probability pi of current peak value Ii to be within interval i is found as the difference between the p for current to be than the lower limit and the p for current to reach or exceed the higher limit. These ps are obtained by using the formula seen before

c) For each interval i, also two distances form the line (in m) are calculated: 1) the minimum distance ymin,i (using the IEEE incidence

model) for which lightning of peak current Ii (in kA) will not divert to

the line, and 2) the maximum distance ymax,i at which lightning may

produce an insulation flashover (using the Rusck formula), i.e. an induced voltage equal to the line critical flashover voltage CFO (in kV), multiplied by a factor equal to 1.5 (to take into account the turn-up in the insulation volt-time curve for short front-time surges).

d)

4. Statistical approach (revised)1. Inputs: lightning current parameters, return stroke velocity, line

and ground data2. Random generation of events ( Ip tf x y) (e.g. > 10 000)

3. Selection of indirect lightning events by using a lightning incidence model

4. Induced overvoltage calculation using advanced models (and relevant tools)

5. Counting of the n events generating overvoltages greater than the insulation level (e.g. 1.5·CFO)

6. Plot the graph: No. of flashovers/100 km/year vs CFO where No. of flashovers/100 km/year = (n/ntot)·ng·S·100/L(with ng = annual ground flash density, S = striking area, L=line length)

correlated

4. Statistical approach (revised)1. Inputs: lightning current parameters, return stroke velocity, line

and ground data2. Random generation of events ( Ip tf x y) (e.g. > 10 000)

3. Selection of indirect lightning events by using a lightning incidence model

4. Induced overvoltage calculation using advanced models (and relevant tools)

5. Counting of the n events generating overvoltages greater than the insulation level (e.g. 1.5·CFO)

6. Plot the graph: No. of flashovers/100 km/year vs CFO where No. of flashovers/100 km/year = (n/ntot)·ng·S·100/L(with ng = annual ground flash density, S = striking area, L=line length)

correlated

The revised method and the new Statistical approach

equivalent as far as an ‘infinitely long line’ is concerned

improved in the new version when distribution systems having realistic configurations are analyzed.

4. Statistical approach (revised)

0.001

0.010

0.100

1.000

10.000

100.000

50 100 150 200 250 300

CFO (kV)

Fla

shov

ers/

100k

m/y

r

ideal ground

ground conductivity = 10 mS/m

ground conductivity = 1 mS/m

Fig. 5 of rev. 1410 (Modelling details in Appendix B)

From De La Rosa et al, IEEE Trans. on PWDR, 1988 From Ishii et al. CIGRE Colloquium SC33, Toronto, 1997

Validation – Scale Model, Univ. of Tokyo and Real Lines, IIE, Cuernavaca

0.001

0.010

0.100

1.000

10.000

50 100 150 200 250 300

Fla

shov

ers/

100k

m/y

r

CFO (kV)

(A) IEEE Std. 1410 2004 - Rusck (B.2)

(B) ideal ground

(C) ideal ground, tf =1 μs

Fig. B.3 in Appendix B of rev. 1410 – “Check”

0.001

0.010

0.100

1.000

10.000

50 100 150 200 250

Fla

shov

ers/

100k

m/y

r

CFO (kV)

(A) IEEE Std. 1410 2004 - Rusck (B.2) and (B.3)

(B) tf =1 μs (groundings each 30 m)

(C) tf =1 μs (groundings each 500 m)

Fig. B.4 in Appendix B of rev. 1410 – Effect of shield wire

Fig. B.5 a, b in Appendix B of rev. 1410 – Effect of SA

σg = 1 mS/m

Ideal ground

The LIOV code calculates:• LEMP• Coupling

The EMTP :• calculates the boundary conditions• makes available a large library of power components

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Link between LIOV and EMTP

Data exchange between the LIOV code and the EMTP at the boundary conditions

LIOV-EMTP computer code

LIOVi (0,t)

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The LIOV-EMTP code (http://www.liov.ing.unibo.it)