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IEEE PES Winter Meeting Singapore, January 25, 2000

Mini-Tutorial: Advanced Computational Methods

in Lightning Performance

The Lightning Induced Over-Voltage

(LIOV) Code

C.A. Nucci

Dept. of Electrical Engineering

University of Bologna - 40136 Bologna, Italy

[email protected]

The presentation is based on work carried out as part of a collaborative project betweenthe University of Bologna (C.A. Nucci), the University of Lausanne EPFL (M.Ianoz,

F. Rachidi) and and the University of Roma-La Sapienza (C. Mazzetti)

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Outline of the tutorial

1. Introduction

2. Theoretical basis of the LIOV codeReturn-Stroke Current Model

LEMP model

Coupling Model

3. Application of LIOVSensitivity analysisStatistical studies

4. Interface with EMTP

5. Conclusions

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1. Introduction


LEMP model

Coupling Model



5. Conclusions

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Introduction

Which are the main factors that may affect waveshapeand intensity of lightning-induced voltages?

Waveshape of lightning current (Ipeak, dI/dt)

Position of stroke location

Ground (soil) resistivity Line construction

Shielding wire (pole grounding)

Presence of surge arresters

Learder-induction effects

Channel tortuosity and inclination

Corona

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Introduction Cont.

7.68 m

1.07 m 1.07 m

Top View

4.3 km 5.6 km

Short C. Open C.

Observation Point

b)

a)

Eriksson and Meal experimentTrans. of IEE, 1982

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Introduction Cont.

2 3 4 5 6 7 89 2 3 4 5 610000 100000

10.00

20.00

30.00

40.00

50.00

60.00

70.00

80.00

90.00

95.00

98.00

99.0099.50

99.9099.95

99.99

confidence limits 95%from 281 events

Eriksson and Meal

Voltage [V]

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Introduction Cont.

From: IEEE Guide for Improving the LightningPerformance of Electric Power Overhead

Distribution Lines, 1997.

dhIZU maxmax 0=

Using the Rusck simplifiedformula

== 30/4/1 00 oZ

where

which applies to infinitely longlines above perfectly

conducting ground

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Introduction Cont.

Note that even the simple case of an infinitely long lineabove a perfectly conducting ground has been theobject of several discussions on which models are the

most adequate for the calculation of the inducedvoltages (see Nucci et al., 1995a, 1995b for a survey).

See also at http://www.pti-us.com/pti/

Lightning induced overvoltages, slide presentationby C.A. Nucci and F. Rachidi given at the Panel SessionDistribution Lightning Protection, IEEE T&D, NewOrleans, 1999.

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Introduction Cont.

The availability of a computer code for the

calculation of lightning-induced disturbances onmore relistic configurations of transmission lines

is of interest for solving problems of

Power quality

Electromagnetic compatibility (EMC)

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Introduction Cont.

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Introduction Cont.

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Introduction Cont.

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Introduction Cont.

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Introduction Cont.

Distribution line

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Introduction Cont.

Three research groups of three different Universities

Bologna (Faculty of Engineering, Dept. of ElectricalEngineering)

Lausanne (Swiss Federal Institute of Technology, PowerNetwork Laboratory)

Rome (Faculty of Engineering, Dept. of ElectricalEngineering)

Started some years ago a program aimed at developing acomputer code for the calculation of lightning-induced

voltages on realistic line configurations using the mostadequate models. the LIOV code.

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Introduction Cont.

Based on previous studies on the subject (see References) andexperimental data obtained by several researchers in the world

Brasil (University of Sao Paulo) Colombia (National University of Colombia)

France (St. Privat dAllier) Japan (Criepi, University of Tokyo) Mexico (IEE)

Norway (University of Trondheim) South Africa (Escom, NEERI) Sweden (Royal Institute of Technology, University of

Uppsala)

United States (University of Florida)

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Adapted from Barker et al. IEEE Trans. on PWDR, Vol. 11, pp. 980-995, 1996.

Introduction Cont.

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Introduction Cont.

The Camp Blanding lightning triggeringfacility in Florida.Courtes of M.A. Uman .

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Introduction Cont.

Figure1:Experimental station"Ilyapa"

D.L.M.T.

D.L.M.T.

D.L.M.T: Direct Lightning Measurement TowerI.M.: Induced Voltage Measurement pointsT: Transformer

Layout of the experimental station Ilyapa in Colombia(courtesy of H. Torres)

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1. Introduction


LEMP model

Coupling Model



5. Conclusions

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2. Theoretical basis of the LIOV code

i (0,t)

Return-Stroke Current

RSC i (z,t)

Lightning ElectroMagnetic Pulse

i (z,t) LEMP E, B

ElectroMagnetic Coupling

E, B EMC V, I

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Return Stroke Current Model

Transmission Line [Uman and McLain, 1969]

v

z

i z t i t z v( , ) ( , / )= 0

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Return Stroke Current Model Cont.


z

i z t i t z v( , ) ( , / )= 0

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z

i z t i t z v( , ) ( , / )= 0

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z

i z t i t z v( , ) ( , / )= 0

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z

i z t i t z v( , ) ( , / )= 0

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Travelling Current Source [Heidler, 1985]

i z t i t z c( , ) ( , / )= +0z

Modified TL [Nucci, Mazzetti, Rachidi, Ianoz, 1988]

i z t i t z v ez

k m

( , ) ( , / ) ( / )=

=

0

1 3

DU [Diendorfer and Uman, 1990]

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A review of the various return-stroke models has beenrecently made by Rakov and Uman onIEEE EMC Transactions, Special Issue on Lightning,1998 where they have discussed, among others, thefollowing engineering models

Bruce-Golde (BG)

Transmission Line (TL) Uman, McLain, Krider

Traveling Current Source (TCS) Heidler

Modified Transm. Line - Linear (MTLL) Rakov and Dulzon

Modified Transm. Line - Exponential (MTLE) Nucci et al. Diendorfer-Uman (DU)

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Experimental validation

Given a channel-base current ==>the RSC model must reproduce thecorresponding Electromagnetic field

For Natural lightning:

PROBLEM: practically no existing data sets ofsimultaneously measured current and fields

Data of this kind have been collected usingthe Triggered lightning technique

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TRIGGERED LIGHTNING:TRIGGERED LIGHTNING:

LightningLightning isis artificiallyartificiallyinitiatedinitiated firingfiring smallsmall rocketsrockets

trailingtrailing groundedgrounded wireswires

upwardupward a fewa few hundredhundredmetersmeters underunder

thunderstormsthunderstorms..

Validation by means of triggered lightning

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Validation by means of triggered lightning Contd

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Return-stroke current model Cont.

Camp Blanding experiments, 1999.Courtesy of M.A. Uman

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TCS

microseconds microseconds

V/m TCS MTL

Validation by means of triggered lightning ContdAdapted by Thottappillil and Uman, 1993.

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Summary of statistics on the absolute error of the model peak fields on the basisof triggerd ligthning simultaneously measured currents, velocities and fields

(subsequent return strokes)adapted from Thottappillil and Uman[1993].

Abs. Error=

(Ecal

- Emeas

) /Emeas

TL MTL TCS DU MDU

Mean 0.17 0.16 0.43 0.23 0.21

St.Dev. 0.12 0.11 0.22 020 0.19Min. 0.00 0.00 0.14 0.00 0.02

Max. 0.51 0.45 0.84 0.63 0.60

Validation by means of triggered lightning Contd

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LEMP Model

z'

H

Immagine

dz' i(z',t)R Punto di osservazione

Piano conduttore

R'

r

v

E r

Ez

Pya

ar

ax

az

a

E

Image

Conducting plane

Observation point

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Vertical Electric Field:

Transverse Magnetic field:

can be calculated

LEMP Model Cont.

assuming the ground as

perfectly conducting

M.A. Uman, D.K. McLain, E.P. Krider"The electromagnetic radiation from a finite antenna",Am. J. of Physics, Vol. 43, pp. 33-38, 1975.

LEMP M d l

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LEMP Model Cont.

Vertical Electric Field

[

]t

cRtzi

Rc

rcRtzi

cR

rzz

cRziR

rzzzdtzrE

t

o

z

)/,()/,(

)(2

d)/,()(2

4),,,(d

32

2

4

220

5

22

+

+

=

Transverse Magnetic field

[]

t

cRtzi

cR

r

cRtziR

rz

tzrB

o

r

)/,(

)/,(4

d

),,,(d

2

3

=

LEMP M d l

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LEMP Model Cont.

[

]t

cRtzi

Rc

zzr

cRtzi

cR

zzr

cRzi

R

zzrzdtzrE

t

o

r

)/,()(

)/,()(3

d)/,()(3

4

),,,(d

32

4

0

5

+

+

+

+

=

o permittivity of the free spacec speed of light

Horizontal electric field however

LEMP M d l C

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LEMP Model Cont.

ground resistivity has to be taken into account =>

=> more complex approaches are needed

ogrg

o

prprj

c

jrHjzrEjzrE

+= ),0,(),,(),,(

rg,

rg relative permittivity and permeability of ground),0,( jrH p Fourier-transforms of E(r,z,t) and of H(r,0,t)

both calculated assuming a perfectly

conducting ground

),,( jzrErp

Cooray-Rubinstein expression - Correction by Wait

LEMP M d l C

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LEMP Model Cont.

0 5 10 15 20 25 30Time in s r = 200m

-100

-50

0

50

100

150

200

Cooray-Rubinstein

WavetiltPerfect groundZeddam and Degauque [1990]

Adapted by Rachidi et al,

LEMP Model C t

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LEMP Model Cont.

r = 1500 m

Cooray-Rubinstein

WavetiltPerfect ground

Zeddam and Degauque [1990]

0 5 10 15 20 25 30

Time in s

-10

-8

-6

-4

-2

0

2

4

Adapted by Rachidi et al,

Coupling Model C t

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Coupling Model Cont.

Three coupling models have been used so far:

Rusck [1958]

Chowdhuri-Gross [1969]

Agrawal et al. [1980]

Of the three models, the Agrawal one is

considered the most adequate for a generalexternal field excitation

However, for a lightning channel perpendicular tothe ground plane ===> Rusck = Agrawal

Coupling Model Cont

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Incident field

Scattered field

TOTAL FIELD

Transverse dimensions of the line < 10 x wavelength Line response: quasi TEM

Coupling Model Cont

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=

+

t

txiLx

txus

),('),( ),,( thxEix

0),('),( =

+

t

txuCx

txis

),(),(),( txutxutxu is =+

Transmission line Coupling equations by Agrawal et al.(single-wire, perfectly conducting ground)

Coupling Model Cont

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0

+

--u i (0)

R 0

+

-

L

-u i (L)

R L

u (x)

i(x) L'dx

x x+dx

+-

i(x+dx)

us (x+dx)

u i(x)

iEx

dx

sC'dx

Agrawal et al.

Coupling Model CONTROLLO RETICOLO

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Point-Centered Finite-Difference Method

),,(

),(

),(thxE

t

txiL

x

txu ix

s

=+

0

),(),( =+ ttxuC

xtxi

s

+==h

izo

io

s dztzEtiRtutiRtu0

),,0(),0(),0(),0(),0(

+==

hi

zL

i

L

s

dztzLEtLiRtLutLiRtLu0

),,(),(),(),(),(

x: spatial-integration stept: time-integration step


Cont.

x

y

z

0 L

R R0 LEz,0

0i

Ez,L

kmaxi

kmaxii i i i i

u u u u1

0 1

2

2 kmax-2 kmax-1

kmax-1 kmax

x

h

Equations Boundary conditions


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2

111

+ +=

+

nkn

k

n

k

n

k

n

k

n

k usus

t

iiL

x

uu

0

11

1

1

=

+

tuuC

xii

n

k

n

k

n

k

n

k

( ){ }tnxkuu snk = ,1

( ) ( ){ }tnxkiink += 5.0,5.0

( ) ( ){ }tnxkEus ixnk += 5.0,5.0

kand ndenote space and time increments


Cont.

X

T

xik

xuk

xik+1

ukn-1

ikn-1

ukn

i k-1n-1

tn-1i

tnu t

ni

X

T

xuk+1

xik

xuk

uk+1n

ikn-1

ikn

uk

n

tn-1i tnu t

nia

Coupling Model Cont

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Internal nodes:

=

x

iiuAAu

nk

nkn

knk

11

11

21

+

+= +

1

41

1

32

nk

nk

nk

nk

nkn

k iAx

uuususAi

=

=

=

=

t

LA

t

LA

t

CA

t

CA

''

''

4

1

3

2

1

1

with

Boundary nodes:

2

3 210

nnn iii

=

2

3 21 maxmaxmax

nK

nKn

K

ii

i

=

nno

niz

n iREhu 00

1 =

n

K

n

L

n

K

i

z

n

K iREhu maxmaxmax+=

Initial conditions (t=0):

max

0

,...,1,00 kkik ==max

0 ,...,1,00 kkuk ==

Coupling Model Cont

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Reduced scale model at the University Of So Paulo - Brazil

Coupling Model Cont

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0 2 4 6 8 10 12

Time in s

0

20

40

60

80

100

120

140

CALCULATED

MEASURED

70 m

130 m 40 m 100 m

OBSERVATION POINT

Example of validation of the Agrawal coupling modelExperimental data: courtesy of Dr. A. Piantini, Univ. Of So Paulo

Coupling Model Cont

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Using NEMP simulators (SEMIRAMIS, EPFL, Lausanne)


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Using NEMP simulators

Adapted by Guerrieri et al., 19


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0 0.5 1 1.5 2 2.5 3 3.5 4Time in us

-60-40

-20

0

2040

60

80

100

120

140

160Calculated dV/dt

Measured dV/dt

Measured dV/dt (filtered)

Using reduced-scale line modelExperimental data: by A. Piantini, Univ. Of So Paulo

Documents

LIOV_1