the lightning induced over-voltage (liov) code - unibo.it...c.a. nucci dept. of electrical...

IEEE PES Winter Meeting – Singapore, January 25, 2000Mini-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 between the 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)

Outline of the tutorial

1. Introduction

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

3. Application of LIOVSensitivity analysisStatistical studies

4. Interface with EMTP

5. Conclusions

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• …

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

Introduction Cont.

2 3 4 5 6 7 8 9 2 3 4 5 610000 100000

10.00

20.0030.0040.0050.0060.0070.0080.00

90.00

95.00

98.0099.0099.50

99.9099.95

99.99

confidence limits 95%from 281 events

Eriksson and Meal

Voltage [V]

Introduction Cont.

From: “IEEE Guide for Improving the Lightning Performance of Electric Power Overhead

Distribution Lines”, 1997.

dhIZU max

max 0=

Using the Rusck simplified formula

Ω== 30/4/1 00 oZ εµπwhere

which applies to infinitely long lines above perfectly conducting ground

Introduction Cont.

Note that even the “simple” case of an infinitely long line above a perfectly conducting ground has been the object of several discussions on which models are the most adequate for the calculation of the induced voltages (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 Session“Distribution Lightning Protection”, IEEE T&D, New Orleans, 1999.

Introduction Cont.

The availability of a computer code for the calculation of lightning-induced disturbances on more relistic configurations of transmission lines

is of interest for solving problems of

• Power quality

• Electromagnetic compatibility (EMC)

Introduction Cont.

Introduction Cont.

Distribution line

Introduction Cont.

Three research groups of three different Universities

• Bologna (Faculty of Engineering, Dept. of ElectricalEngineering)

• Lausanne (Swiss Federal Institute of Technology, Power Network Laboratory)

• Rome (Faculty of Engineering, Dept. of Electrical Engineering)

Started some years ago a program aimed at developing a computer code for the calculation of lightning-induced voltages on realistic line configurations using the mostadequate models. the LIOV code.

Introduction Cont.

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

• Brasil (University of Sao Paulo)• Colombia (National University of Colombia)• France (St. Privat d’Allier)• 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)

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

Introduction Cont.

Introduction Cont.

The Camp Blanding lightning triggering facility in Florida. (Courtesy of M.A. Uman).

Introduction Cont.

Figure 1 :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)

Outline of the tutorial

1. Introduction

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

3. Application of LIOVSensitivity analysisStatistical studies

4. Interface with EMTP

5. Conclusions

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

Return Stroke Current Model

Transmission Line [Uman and McLain, 1969]

v

z

i z t i t z v( , ) ( , / )= −0

Return Stroke Current Model Cont.

Transmission Line [Uman and McLain, 1969]

z

i z t i t z v( , ) ( , / )= −0


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 e z

km

( , ) ( , / ) ( / )= − −

= −

01 3

λ

λ

DU [Diendorfer and Uman, 1990]


A review of the various return-stroke models has been recently made by Rakov and Uman on IEEE EMC Transactions, Special Issue on Lightning, 1998 where they have discussed, among others, the following ‘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)


Experimental validationGiven a channel-base current ==>the RSC model must reproduce the corresponding Electromagnetic field

For Natural lightning:

PROBLEM: practically no existing data sets of simultaneously measured current and fields

Data of this kind have been collected usingthe Triggered lightning technique


TRIGGERED LIGHTNING: TRIGGERED LIGHTNING: LightningLightning isis artificiallyartificiallyinitiatedinitiated firingfiring smallsmall rocketsrocketstrailingtrailing groundedgrounded wireswiresupwardupward a few a few hundredhundredmetersmeters under under thunderstormsthunderstorms..

Validation by means of triggered lightning


Validation by means of triggered lightning Cont’d

Return-stroke current model Cont.

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


TCS

microseconds microseconds

V/m TCS MTL

Validation by means of triggered lightning Cont’dAdapted by Thottappillil and Uman, 1993.


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 0.21St.Dev. 0.12 0.11 0.22 020 0.19

Min. 0.00 0.00 0.14 0.00 0.02Max. 0.51 0.45 0.84 0.63 0.60

Validation by means of triggered lightning Cont’d

LEMP Model

z'

H

Immagine

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

Piano conduttore

R'

r

v

E r

Ez

Pyaar

ax

az

φ

aφ

E

Image

Conducting plane

Observation point

Vertical Electric Field:

Transverse Magnetic field:

can be calculated

LEMP Model Cont.

assuming the ground asperfectly 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 Model Cont.

Vertical Electric Field

[

]t

cRtziRc

rcRtzicR

rzz

cRziR

rzzzdtzrEt

oz

∂∂

ττπε

φ

)/,()/,()(2

d)/,()(24

),,,(d

32

2

4

220

5

22

−′−−′−′−

+

+−′−′−′= ∫

Transverse Magnetic field

[

]t

cRtzicR

r

cRtziRrztzrB o

r

∂∂π

µφ

)/,(

)/,(4d),,,(d

2

3

−′

−′′

=

LEMP Model Cont.

[

]t

cRtziRc

zzr

cRtzicR

zzr

cRziR

zzrzdtzrEt

or

∂∂

ττπε

φ

)/,()(

)/,()(3

d)/,()(34

),,,(d

32

4

05

−′′−+

+−′′−

+

+−′′−′

= ∫

εo permittivity of the free spacec speed of light

Horizontal electric field … however

LEMP Model Cont.

… ground resistivity has to be taken into account =>=> more complex approaches are needed

ogrg

oprpr j

cjrHjzrEjzrEεωσε

µωωω φ+

−= ),0,(),,(),,(

εrg, µrg relative permittivity and permeability of ground

),0,( ωφ jrH p Fourier-transforms of E(r,z,t) and of H(r,0,t) both calculated assuming a perfectlyconducting ground

),,( ωjzrE rp

Cooray-Rubinstein expression - Correction by Wait

LEMP Model Cont.

0 5 10 15 20 25 30Time in µs r = 200m

-100

-50

0

50

100

150

200

Cooray-RubinsteinWavetiltPerfect groundZeddam and Degauque [1990]

Adapted by Rachidi et al,

LEMP Model Cont.

r = 1500 m

Cooray-RubinsteinWavetiltPerfect groundZeddam and Degauque [1990]

0 5 10 15 20 25 30

Time in µs

-10

-8

-6

-4

-2

0

2

4

Adapted by Rachidi et al,

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 isconsidered the most adequate for a generalexternal field excitationHowever, for a lightning channel perpendicular tothe ground plane ===> Rusck = Agrawal


Incident field

Scattered field

TOTAL FIELD

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


=∂

∂+

∂∂

ttxiL

xtxus ),('),( ),,( thxEi

x

0),('),(=

∂∂

+∂

∂t

txuCx

txi s

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

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


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)

iE x dx

s C'dx

Agrawal et al.

Point-Centered Finite-Difference Method

),,(

),(

),( thxEt

txiLx

txu ix

s

=′+∂

∂∂

∂

0

),(

),( =′+

ttxuC

xtxi s

∂∂

∂∂

∫+−=−−=h

izo

io

s dztzEtiRtutiRtu0

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

∫+=−=h

izL

iL

s dztzLEtLiRtLutLiRtLu0

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

∆x: spatial-integration step∆t: time-integration step

Coupling Model CONTROLLO RETICOLO 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

2

111

−−+ +

=∆−

+∆− n

knk

nk

nk

nk

nk usus

tiiL

xuu

011

11

=∆−

+∆− −−

−−

tuuC

xii n

knk

nk

nk

( ) tnxkuu snk ∆∆−= ,1

( ) ( ) tnxkii nk ∆+∆−= 5.0,5.0

( ) ( ) tnxkEus ix

nk ∆+∆−= 5.0,5.0

k and n denote space and time increments

Coupling Model CONTROLLO RETICOLO Cont.

X

T

xik

xuk

xik+1

ukn-1

i kn-1

ukn

i k-1n-1

tn-1i tnu tn

ib)

X

T

xuk+1

xik

xuk

uk+1n

ikn-1

ikn

ukn

tn-1i tn

u t nia)


Internal nodes:

⎭⎬⎫

⎩⎨⎧

∆−

−=−−

−−

xiiuAAu

nk

nkn

knk

11

11

21

⎭⎬⎫

⎩⎨⎧

+∆−

−+

= −+−

14

11

3 2nk

nk

nk

nk

nkn

k iAx

uuususAi ⎪⎪

⎭

⎪⎪

⎬

⎫

⎟⎠⎞

⎜⎝⎛∆

=⎟⎠⎞

⎜⎝⎛∆

=

⎟⎠⎞

⎜⎝⎛∆

=⎟⎠⎞

⎜⎝⎛∆

=

−

−

tLA

tLA

tCA

tCA

''

''

4

1

3

2

1

1

with

Boundary nodes:

23 21

0

nnn iii −=

23 21 maxmax

max

nK

nKn

K

iii −− −

=

nno

niz

n iREhu 001 ⋅−⋅=

nK

nL

n

K

iz

nK iREhu

maxmax

max⋅+⋅=

Initial conditions (t=0):

max0 ,...,1,00 kkik ==

max0 ,...,1,00 kkuk ==


Reduced scale model at the University Of São Paulo - Brazil


0 2 4 6 8 10 12

Time in µs

0

20

40

60

80

100

120

140

CALCULATEDMEASURED

70 m

130 m 40 m 100 m

OBSERVATION POINT

Example of validation of the Agrawal coupling model

Experimental data: courtesy of Dr. A. Piantini, Univ. Of São Paulo


Using NEMP simulators (SEMIRAMIS, EPFL, Lausanne)


Using NEMP simulators

Adapted by Guerrieri et al., 19


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

-60

-40

-20

0

20

40

60

80

100

120

140

160Calculated dV/dtMeasured dV/dtMeasured dV/dt (filtered)

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

the lightning induced over-voltage (liov) code - unibo.it...c.a. nucci dept. of electrical...

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