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
carloalberto.nucci@mail.ing.unibo.it

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 code
Return-Stroke Current Model LEMP model Coupling Model

3. Application of LIOV
Sensitivity analysis Statistical studies

4. Interface with EMTP 5. Conclusions

Outline of the tutorial

1. Introduction 2. Theoretical basis of the LIOV code
Return-Stroke Current Model LEMP model Coupling Model

3. Application of LIOV
Sensitivity analysis Statistical studies

4. Interface with EMTP 5. Conclusions

Introduction
Which are the main factors that may affect waveshape and 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
1.07 m 1.07 m

Cont.

4.3 km

5.6 km

7.68 m

Short C.

Open C.

Observation Point

b) a)

Top View

Eriksson and Meal experiment Trans. of IEE, 1982

Introduction
10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 95.00 98.00 99.00 99.50 99.90 99.95 99.99 10000 2 3 4 5 6 7 89 100000 2 Voltage [V] 3 4 5 6

Cont.
confidence limits 95% from 281 events

Eriksson and Meal

Introduction
Using the Rusck simplified formula

Cont.

Umax
where

Imax h = Z0 d

Z0 = 1/ 4 0 / o = 30
which applies to infinitely long lines above perfectly conducting ground

From: IEEE Guide for Improving the Lightning Performance of Electric Power Overhead Distribution Lines, 1997.

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 presentation by 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.

Introduction

Cont.

Introduction

Cont.

Introduction

Cont.

Distribution line

Introduction

Cont.

Three research groups of three different Universities Bologna (Faculty of Engineering, Dept. of Electrical Engineering) 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 most adequate 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 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)

Introduction

Cont.

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

Introduction

Cont.

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

Introduction

Cont.

D.L.M.T. D.L.M.T.

"Ilyapa"Experimental station :1Figure

D.L.M.T: Direct Lightning Measurement Tower I.M.: Induced Voltage Measurement points T: 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 code
Return-Stroke Current Model LEMP model Coupling Model

3. Application of LIOV
Sensitivity analysis Statistical studies

4. Interface with EMTP 5. Conclusions

2. Theoretical basis of the LIOV code

Return-Stroke Current i (0,t) 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]

z

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

Return Stroke Current Model

Cont.

Transmission Line [Uman and McLain, 1969]

z

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

Return Stroke Current Model

Cont.

Transmission Line [Uman and McLain, 1969]

z

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

Return Stroke Current Model

Cont.

Transmission Line [Uman and McLain, 1969]

z

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

Return Stroke Current Model

Cont.

Transmission Line [Uman and McLain, 1969]

z

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

Return Stroke Current Model

Cont.

Travelling Current Source [Heidler, 1985]

z

i( z , t ) = i( 0, t + z / c )
Modified TL
[Nucci, Mazzetti, Rachidi, Ianoz, 1988]

i( z , t ) = i( 0 , t z / v )e
= 1 3 km

( z/ )

DU [Diendorfer and Uman, 1990]

Return Stroke Current Model

Cont.

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)

Return Stroke Current Model

Experimental validation Given a channel-base current ==> the RSC model must reproduce the corresponding Electromagnetic field For Natural lightning:

Cont.

PROBLEM: practically no existing data sets of simultaneously measured current and fields Data of this kind have been collected using the Triggered lightning technique

Return Stroke Current Model

Cont.

TRIGGERED LIGHTNING: Lightning is artificially initiated firing small rockets trailing grounded wires upward a few hundred meters under thunderstorms.

Validation by means of triggered lightning

Return Stroke Current Model

Cont.

Validation by means of triggered lightning

Contd

Return-stroke current model

Cont.

Camp Blanding experiments, 1999.

Courtesy of M.A. Uman

Return Stroke Current Model

TCS TCS
V/m

Cont.

MTL

microseconds Adapted by Thottappillil and Uman, 1993.

microseconds

Validation by means of triggered lightning

Contd

Return Stroke Current Model

Cont.

Summary of statistics on the absolute error of the model peak fields on the basis of triggerd ligthning simultaneously measured currents, velocities and fields (subsequent return strokes) adapted from Thottappillil and Uman [1993].
Abs. Error =(Ecal TL Mean St.Dev. Min. Max. 0.17 0.12 0.00 0.51 MTL 0.16 0.11 0.00 0.45 - Emeas) / Emeas TCS 0.43 0.22 0.14 0.84 DU 0.23 020 0.00 0.63 MDU 0.21 0.19 0.02 0.60

Validation by means of triggered lightning

Contd

LEMP Model

H z'

dz' i(z',t) r

Observation point Punto di osservazione

Er Ez
E

Piano conduttoreplane Conducting

R'

Image Immagine

az

ay P ar a ax

LEMP Model

Cont.

can be calculated assuming the ground as Transverse Magnetic field: perfectly conducting Vertical Electric Field:

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
dz dE z ( r , , z , t ) = 4 o

Cont.

2( z z ) 2 r 2 5 i( z , R / c)d + R 0
t

2( z z ) 2 r 2 r 2 i ( z , t R / c ) i ( z , t R / c ) 2 3 + 4 cR c R t

Vertical Electric Field

o dz r [ R 3 i (z,t R / c ) dBr (r , , z,t ) = 4 r i (z,t R / c ) ] 2 cR t Transverse Magnetic field

LEMP Model
dz dE r ( r , , z , t ) = 4 o

Cont.

) t 3r ( z z 5 i( z , R / c)d + R 0

3r ( z z ) i ( z , t R / c ) + + 4 cR r ( z z ) i ( z , t R / c ) + c2R3 t
o permittivity of the free space
c speed of light

Horizontal electric field however

LEMP Model

Cont.

ground resistivity has to be taken into account => => more complex approaches are needed
E r (r , z, j ) = E rp (r , z, j ) H p (r ,0, j ) c o

rg + g j o

rg, rg

relative permittivity and permeability of ground

E rp (r , z, j )

H p (r ,0, j ) Fourier-transforms of E(r,z,t) and of H(r,0,t)

both calculated assuming a perfectly conducting ground

Cooray-Rubinstein expression - Correction by Wait

LEMP Model

Cont.

200 150 100 50 0 -50 -100 0 5 10 15 20 25 30 Adapted by Rachidi et al,

Cooray-Rubinstein Wavetilt Perfect ground Zeddam and Degauque [1990]

Time in s

r = 200m

LEMP Model
4 2 0 -2 -4 -6 -8 -10 0 5 10 15 20 25 30
Cooray-Rubinstein Wavetilt Perfect ground Zeddam and Degauque [1990]

Cont.

Time in s
Adapted by Rachidi et al,

r = 1500 m

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 general external field excitation However, for a lightning channel perpendicular to the ground plane ===> Rusck = Agrawal

Coupling Model

Cont.

Incident field

TOTAL FIELD Scattered field

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

Coupling Model

Cont.

u s ( x,t ) i ( x,t ) i Ex ( x, h,t ) + L' = x t

i ( x,t ) u s ( x,t ) + C' =0 x t

u s ( x,t ) + u i ( x,t ) = u( x,t )
Transmission line Coupling equations by Agrawal et al. (single-wire, perfectly conducting ground)

Coupling Model

Cont.

i(x)
+ -

L'dx

E ix dx
+

i(x+dx)
+

-u i (0) R0 0 x

u (x)

C'dx

u s (x+dx)

-u i (L)
-

RL u (x)
i

x+dx

Agrawal et al.

Coupling Model CONTROLLO RETICOLO

Cont.
u s ( x,t ) i ( x,t ) i + L = E x ( x, h,t ) x t i ( x,t ) u s ( x,t ) + C =0 x t
i u (0,t ) = Ro i (0,t ) u (0,t ) = Ro i (0,t ) + Ez (0, z,t )dz s i 0 i u s (L,t ) = RL i (L,t ) u i (L,t ) = RL i (L,t ) + Ez (L, z,t )dz 0 h h

Equations
x

Boundary conditions

Point-Centered Finite-Difference Method

u1 u2 i2 ukmax-1 ukmax ikmax-2 ikmax-1 ikmax

i0
h

i0 i1

Ez,0
z y x 0

R0

R L

Ez,L ikmax

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

Coupling Model CONTROLLO RETICOLO

Cont.
n n n n n n uk +1 uk i k i k 1 usk + usk 1 +L = 2 x t
n n 1 n n i k 1 i k 1 uk uk 1 +C =0 x t

n uk = u s {(k 1)x, nt }
n i k = i {(k 0.5 )x, (n + 0.5 )t }

n i usk = E x {(k 0.5 )x, (n + 0.5 )t }

k and n denote space and time increments

X
k+1 xu

X xik i n-1 k un-1 k un k i k-1

n-1

uk+1 i n-1 k in k un k

xik
k xu

k xu

x k+1 i

a)

n t n-1 t u i

t in

t n-1 i

tn u

tn i

Coupling Model
Internal nodes:
n n 1 i k 1 i k 1 n 1 u = A1 A2uk x n n n n usk + usk 1 uk +1 uk n n + A4i k 1 i k = A3 x 2 n k

Cont.
1 C' C' A1 = A2 = t t 1 L' L' A3 = A4 = t t

with

Boundary nodes:
n n 3 i1 i 2 i = 2 n 0

u = hE
n 1

n i z 0

n n Ro i 0
n n + RL iKmax

n Kmax

n n 3iKmax 1 iKmax 2

n Kmax

= hE

n i z K max

Initial conditions (t=0):

0 i k = 0k = 0,1,..., kmax 0 uk = 0k = 0,1,..., kmax

Coupling Model

Cont.

Reduced scale model at the University Of So Paulo - Brazil

Coupling Model
140 120 100 80 60 40 20 0 0 2 4 6 8 10 12 130 m 40 m CALCULATED MEASURED

Cont.

OBSERVATION POINT

70 m 100 m

Time in s

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

Coupling Model

Cont.

Using NEMP simulators (SEMIRAMIS, EPFL, Lausanne)

Coupling Model

Cont.

Using NEMP simulators

Adapted by Guerrieri et al., 19

Coupling Model
160 140 120 100 80 60 40 20 0 -20 -40 -60 0 0.5 1 1.5 2 2.5 3 3.5 4
Calculated dV/dt Measured dV/dt Measured dV/dt (filtered)

Cont.

Time in us

Using reduced-scale line model

Experimental data: by A. Piantini, Univ. Of So Paulo