transmission line electromagnetic transients with special...

Transmission Line Electromagnetic Transients with

special Reference to the Lightning Performance of

Transmission and Distribution Lines

Short course – Part II

by

Carlo Alberto Nucci

University of Bologna – Faculty of Engineering – Department of Electrical Engineering

University of Sevilla

June 27 and 28, 2011

The material contained in this lectures is based on the results obtained within the framework of a joint research collaboration among the

University of Bologna, the Swiss Federal Institute of Technolgy – Lausanne, the University of Rome ‘La Sapienza’, and the University of Florida.

© Carlo Alberto Nucci

Summary of main points of first day

course

1. Transient Perturbations in Power Networks: a General Overview

- we noticed that when a line is illuminated by an external field we need

more complex equations than the classical TL equations

2. ‘Generalized’ Transmission Line Equations (with Illumination of

an External Electromagnetic Field)

- Total EM field = Incident field + scattered field

- Using the TL approximation we can integrate Maxwell’s equations and

obtain TL ‘coupling’ equations in terms of lumped parameters (p.u.l.) and

of external sources (p.u.l.); the latter depend on the incident EM field

- When the source terms are set = 0 we obtain the classical TL eqs

- There are different equivalent formulations: the most popular is the

Agrawal et al., which is in terms of scattered and incident fields

- With respect to the ideal case, the presence of ground losses result in a

modification of the line parameters (Zg) and of the source term depending

on the horizontal electric field


Course Outline 1/3 1. Transient Perturbations in Power Networks: a General Overview

2. ‘Generalized’ Transmission Line Equations (with Illumination of

an External Electromagnetic Field)

2.1. Preface and Main Assumptions

2.2. Single Conductor Line above a Perfectly Conducting Ground

- Agrawal, Price, and Gurbaxani model

- Taylor, Satterwhite, and Harrison model

- Rachidi model

- Contribution of the different components of the electromagnetic field in the

coupling mechanism

- Other models

- Classical Transmission Line Equations (no External Field Illumination)

2.3. Single Conductor Line above a Lossy Ground

- Agrawal, Price, and Gurbaxani model extended to a lossy ground

- Classical Transmission Line equations (no External Field Illumination)


Course Outline 2/3 2.4. Coupling Equations for a Multi-Conductor Line

2.5. Line Parameters for Multi Conductor Line above a Perfectly

Conducting Ground

2.6. Line Parameters for Multi Conductor Line above a Lossy Ground

3. The Lightning Discharge as a Source of EM Transients 3.1. Phenomenology

3.2 Lightning current statistics

3.3 Lightning Attachment (direct strokes)

3.4 Return Stroke Models for LEMP calculations (indirect strokes)

3.5 Horizontal component of the Electric field

4. LIV: Mechanism of Induction and Effect of Losses 3.1. Mechanism of induction of LIV

3.2 Effect of ground resistivity

3.3 Effect of corona


Course Outline 3/3

5. The LIOV-EMTP code 5.1 The LIOV code

5.2 Interface with EMTP

5.3 Experimental validation

5.4 Some cases of interest: presence of surge arresters, effect of

shield wire.

6. Lightning performance of distribution lines 6.1 Preface

6.2 Evaluating the Lightning Performance of a Distribution Line -

IEEE 1410 and CIGRE proposed methodology, based on the

LIOV code and LIOV-EMTP

6.3 Experimental activity run in Italy


Part 3

The Lightning Discharge as a

Source of EM Transients


First Return

Stroke *

t = 0 1.00 ms 1.10 ms 1.20 ms

19.00 ms 20.00 ms 20.10 ms 20.20 ms

40.00 ms 60.00 ms 61.00 ms 62.05 ms

A drawing illustrating various

processes comprising a negative

cloud-to-ground lightning flash.

Adapted from Uman (1987, 2001).

** Second Return

Stroke

3.1 Lightning Phenomenology

10 – 100 C

^

^^


z

Leader and Return Stroke – Simple Modeling



z




v

z




z




z

http://www.youtube.com/watch?gl=IT&v=A0XkNfTyR9A




z

http://www.youtube.com/watch?gl=IT&v=A0XkNfTyR9A




Slow_Motion_Lightning Negative_2.mp4

17

Classification – according to Berger

Downward

negative

Upward

positive

Downward

positive

Upward

negative



Typical ‘normalized’

lightning current

waveshapes (Adapted

from Berger et al.,

[1975]) (*)

First return stroke

Subsequent return stroke

(*) from direct tower measurements



95% 50% 5%

Stroke First Subs First Subs First Subs

Ipeak [kA] 14 4.6 30 12 80 30

Time to

crest [ms] 1.8 0.2 5.5 1.1 18 4.5

(di/dt)max

[kA/ms] 5.5 12 12 40 32 120


(Adapted from Berger et al., [1975])


20

Ip 20kA

Ip = 61.1 kA

ln Ip = 1.33

Ip > 20 kA

Ip = 33.3 kA

ln Ip = 0.605

tf = 3.83 ms

ln tf = 0.553

1 0 0 0 . 0 0 1 0 0 0 0 . 0 0 1 0 0 0 0 0 . 0 0 1 0 0 0 0 0 0 . 0 0

I P i n A

0 . 0 1 0 . 0 1

0 . 0 5 0 . 1 0

0 . 5 0 1 .

0 0 2 . 0 0

5 . 0 0

1 0 . 0 0

2 0 . 0 0

3 0 . 0 0 4 0 . 0 0 5 0 . 0 0 6 0 . 0 0 7 0 . 0 0

8 0 . 0 0

9 0 . 0 0

9 5 . 0 0

9 8 . 0 0 9 9 . 0 0 9 9 . 5 0

9 9 . 9 0 9 9 . 9 5

9 9 . 9 9

1.00E-7 1.00E-6 1.00E-5 1.00E-4

Tempo alla cresta tf in s

0.010.01

0.050.10

0.501.002.00

5.00

10.00

20.00

30.0040.0050.0060.0070.00

80.00

90.00

95.00

98.0099.0099.50

99.9099.95

99.99

Pro

ba

bili

tà

Current amplitude [A] Time to crest [s]

First return stroke



21 1 . 0 0 1 0 . 0 0 1 0 0 . 0 0 1 0 0 0 . 0 0

0 . 0 5 0 . 1 0

0 . 5 0 1 . 0 0 2 . 0 0

5 . 0 0

1 0 . 0 0

2 0 . 0 0

3 0 . 0 0 4 0 . 0 0 5 0 . 0 0 6 0 . 0 0 7 0 . 0 0

8 0 . 0 0

9 0 . 0 0

9 5 . 0 0

9 8 . 0 0 9 9 . 0 0 9 9 . 5 0

9 9 . 9 0 9 9 . 9 5

9 9 . 9 9 [kA]

IEEE:

I 20kA

mI = 61.1 kA

sI = 1.33

I > 20 kA

mI = 33.3 kA

sI = 0.605

Cigré:

Comparison between

CIGRE and IEEE

cumulative statistical

distributions

(peak value, neg. first r.s.)

P(If ≥I) = 1+(I / 31)2.6

1



3.3. Lightning Attachment (direct strokes)

Lightning leader approaching ground: downward motion unperturbed

unless critical field conditions develop juncture with the nearby tower,

called final jump.

Assuming leader channel perpendicular to the ground plane the flash

will stroke the tower if its prospective ground termination point, lies within

the attractive radius r.

r depends on several factors, such as

charge of the leader,

its distance from the structure,

type of structure (vertical mast or horizontal conductor),

structure height,

nature of the terrain (flat or hilly)

ambient ground field due to cloud charges.

Several expressions have been proposed to evaluate such a radius.

Some of them are based on the so-called electrogeometric model.


psr I g sr k r

2

2 for s g gr r r h h r for s gr r h r

r s

r g

nearby stroke

direct stroke

h r

r s = r

r g

nearby stroke direct stroke

h

Where rs and rg are the so called ‘striking distances’ to the structure

and to ground respectively.



Electrogeometrical

Attractive radius

expression

k

Armstrong and

Whitehead 6.7 0.80 0.9

IEEE 10 0.65 0.55

psr I g sr k r



25

Modeling: charge simulation method [Singer, Steinbigler

and Weiss,1973]

fictitious line charges as particular solutions of

Laplace and Poisson’s equations to calculate the

leader electric field at any point, satisfying

boundary conditions.

Using Maxwell theory, Poisson’s equation

solves the surface potential distribution for

a volume of charge density ρv and

permittivity ε.

Leader progression models more phisically plausible models than

EGM, which have been developed from knowledge of discharge physics

on long air gaps under switching surge conditions. Hp: good similarity between propagation and inception of downward

and upward leaders at laboratory tests and lightning phenomena in

spite of the 10x difference in scale.



26

c A b

Eriksson 0 0.84 h 0.6 0.7 h 0.02

Rizk 0 4.27 h 0.41 0.55

Dellera-

Garbagnati 3 h0.6 0.028 h 1

b

l IAcd

Simple expressions of the following type have been inferred by using

the LPM, relating the lateral distance dl and the lightning current peak I:

direct stroke

h dl

indirect stroke



3.4. Return Stroke Models for LEMP

calculations (indirect strokes)

Definition Mathematical specification of the spatial-temporal

distribution of the lightning current i(z,t) along the discharge

channel (or the channel line charge density).

It may include

- return stroke wavefront velocity,

- charge distribution along the channel, and

- a number of adjustable parameter related, in general, to the

discharge phenomenon and which should be inferred by

means of model comparison with experimental results.


i(z', t) i(0, t)

i (0,t)

i (z,t)

‘engineering models’:




Transmission Line [Uman, McLain and Krider, 1975]

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

v

z




Travelling Current Source [Heidler, 1985]

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

MTL(E) [Nucci, Mazzetti, Rachidi, Ianoz, 1988]

i z t i t z v e z

km

( , ) ( , / ) ( / )

0

1 3

‘engineering models’




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

Conducting plane

Observation point

Image

z




Vertical Electric Field

t

cRtzi

Rc

rcRtzi

cR

rzz

cRziR

rzzzdtzrE

t

oz

)/,()/,(

)(2

d)/,()(2

4),,,(d

32

2

4

22

0

5

22

Transverse

Magnetic field

t

cRtzi

cR

r

cRtziR

rztzrB o

r

m

)/,(

)/,(4

d),,,(d

2

3




t

cRtzi

Rc

zzr

cRtzicR

zzr

cRziR

zzrzdtzrE

t

or

)/,()(

)/,()(3

d)/,()(3

4),,,(d

32

4

0

5

o permittivity of the free space

c speed of light

Horizontal electric field … for this case

3.4. Horizontal component of the Electric field


rg, mrg relative permittivity and permeability of ground

),0,( jrH pFourier-transforms of E(r,z,t) and of H(r,0,t)

both calculated assuming a perfectly

conducting ground

The above is the Cooray-Rubinstein eq. - Correction by Wait

… ground resistivity has to be taken into account

more complex approaches are needed

ogrg

oprpr

j

cjrHjzrEjzrE

s

m

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

),,( jzrErp



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

-100

-50

0

50

100

150

200

Cooray-Rubinstein

Perfect ground

Zeddam and Degauque [1990]



r = 1500 m

Cooray-Rubinstein

Perfect ground Zeddam and Degauque [1990]

0 5 10 15 20 25 30

Time in µs

-10

-8

-6

-4

-2

0

2

4



-20

-15

-10

-5

0

5

10

15

0 1 2 3 4 5 6 7

Time in ms

Hori

zonta

l E

fie

ld*r

*r in M

V*m

50m

250m

500m

1000m-250

-200

-150

-100

-50

0

50

100

150

200

0 1 2 3 4 5

Time in ms

Hori

zonta

l E

fie

ld in V

/m

infinite

0.1 S/m

0.01 S/m

0.001 S/m

-70

-60

-50

-40

-30

-20

-10

0

10

0 1 2 3 4 5

Time in ms

Hori

zonta

l E

fie

ld in V

/m

infinite

0.1 S/m

0.01 S/m

0.001 S/m

Horizontal electric field 8 m above ground

(Cooray-Rubinstein formula). Return-stroke

current typical of subsequent return-strokes (12 kA

peak amplitude, 40 kA/µs maximum time-

derivative); return-stroke velocity: 1.9 m/s. a: Field

at four distances r from the stroke location (for

illustrative purpose, the values are multiplied by

the square of the distance from the stroke

location) calculated assuming a ground

conductivity of 0.01 S/m. b: Field at 250 m from

the stroke location, for three different values of

ground conductivity: 0.1; 0.01; 0.001 S/m. c: as in

b but at 1 km from the stroke location

0.01 S/m

1 km

250 m


Part 4

LIV: Mechanism of Induction and

Effect of Losses


D D

E 1

i

R 2

1 2 3 4

R 1

E 2

i E

3

i

E 4

i

D x x x D x

Stroke Location

1

= D x

2 c

2 =

D x

2 c

3 3

= D x

2 c

5 4

= D x

2 c

7

R 0

R L u L

E i x 1

D x E i x 2 D x E i x 3 D x E i x 4

D x

u 2 u 0

3.1. Mechanism of induction of LIV


1 R /c

1

2 R /c

2

2 x D x E 2

D x

1 x E 2

4

4 x

D x E 2

3

3 x D x E 2

u 0

D D

E 1

i

R 2

1 2 3 4

R 1

E 2

i E

3

i

E 4

i

D x x x D x

Stroke Location

1

= D x

2 c

2 =

D x

2 c

3 3

= D x

2 c

5 4

= D x

2 c

7

u 0

Horiz E field contribution



D D

E 1

i

R 2

1 2 3 4

R 1

E 2

i E

3

i

E 4

i

D x x x D x

Stroke Location

1

= D x

2 c

2 =

D x

2 c

3 =

3D x

2 c

4 =

5D x

2 c

u 1

2 x D x E 2

1 R /c 4

1

2 R /c

3

3

4 x

D x E 2

x D x E 2

2

u 1

t




D D

E 1

i

R 2

1 2 3 4

R 1

E 2

i E

3

i

E 4

i

D x x x D x

Stroke Location

1

= 3D x

2 c

2 =

D x

2 c

3 =

D x

2 c

4 =

3D x

2 c

u 2


t

1 R /c

R /c

1

2

3

u 2

1 x

D x E 2 4

x D x E 2

2 x

D x E 2 3

x D x E 2



0 1 2 3 4 5 6 7 8

Time in us

-60

-40

-20

0

20

40

60

80

Total VoltageIncident VoltageEx contributionRisers contribution

a)

Observation point

Stroke location


0 1 2 3 4 5 6 7 8

Time in us

-40

-20

0

20

40

60

80

Total VoltageIncident VoltageEx contributionRiser contribution

b)

Observation point

Stroke location


0 1 2 3 4 5 6 7 8

Time in us

-300

-200

-100

0

100

200

300

Total VoltageIncident VoltageEx contributionRisers contribution

c)

Observation point

Stroke location


We now have the means to understand the effect of both ground and

corona losses.

Let us start with ground losses. We have already seen that they

affect both line parameters and incident field.

Line parameters surge is attenuated in amplitude

Incident field it may result in voltage amplitude

enhancement, depending on stroke location

and observation point

This means that, overall, the ground resistivity may result in an

amplitude enhancement of the induced voltages, depending on

stroke location and observation point.

This is shown in the following couple of slides.

3.2 Effect of ground losses


0.5 km 0.5 km

0 200 400 600 800 1,000

Obs. point along the line in m

30

50

70

90

110

s infinite

s =0.01 S/m

From: Guerrieri S., Nucci C.A., Rachidi F., “Influence of the ground resistivity on the polarity and intensity of lightning induced

voltages”, Proc. of the 10th International Symposium on High Voltage Engineering, Montréal, Canada, 25-29, 1997.

Stroke location



1 km

0 200 400 600 800 1000

Obs. point along the line in m

-40

-20

0

20

40

s infinite

s = 0.01 S/m

From: Guerrieri et al, 1997]



Let us now explain this somewhat unexpected behavior.

The explanation is based – as earlier mentioned – on what we have

seen earlier concerning the formation of the induced voltages.

We need to take into account the contributions to the total voltages of

the various components of the Agrawal model:

- Incident voltage

- Scattered voltage

The scattered voltage itself has two components, due the

horizontal electric field and another due to

the so called ‘risers’, the two voltage sources at the line termination.



50 m 500 m

1000 m

TOP VIEW

U A

50 m 500 m

1000 m

TOP VIEW

U A

-20000

-10000

0

10000

20000

30000

40000

50000

60000

70000

0,00 1,00 2,00 3,00 4,00 5,00 6,00 7,00

Time (ms)

UA

(V

olt)

UA Total (sg infinite)



50 m 500 m

1000 m

TOP VIEW

U A

-20000

-10000

0

10000

20000

30000

40000

50000

60000

70000

0,00 1,00 2,00 3,00 4,00 5,00 6,00 7,00

Time (ms)

UA

(V

olt)


Ex

contr. Ui

Riser

contr.



50 m 500 m

1000 m

TOP VIEW

U A

-20000

-10000

0

10000

20000

30000

40000

50000

60000

70000

0,00 1,00 2,00 3,00 4,00 5,00 6,00 7,00

Time (ms)

UA

(V

olt)

UA Total (sg=0.01S/m)


Ex

contr. Ui

Riser

contr.



50 m 500 m

1000 m

TOP VIEW

U A

-20000

-10000

0

10000

20000

30000

40000

50000

60000

70000

0,00 1,00 2,00 3,00 4,00 5,00 6,00 7,00

Time (ms)

UA

(V

olt) UA Total (sg=0.01S/m)


Ex

contr.Ui

Riser

contr.



50 m 500 m

1000 m

TOP VIEW

U B

-20000

0

20000

40000

60000

80000

100000

120000

140000

0,00 1,00 2,00 3,00 4,00 5,00 6,00 7,00

Time (ms)

UB

(V

olt)

UB Total (sg=0.01S/m)

UB Total (sg infinite)



-2,50E+05

-1,50E+05

-5,00E+04

5,00E+04

1,50E+05

2,50E+05

0,00 1,00 2,00 3,00 4,00 5,00 6,00 7,00

Time (ms)

UB

(V

olt)

UB Total (sg=0.01S/m)

UB Total

(sg infinite) Ex contr.

Ui

Riser

contr.

50 m 500 m

1000 m

TOP VIEW

U B



50 m

500 m

1000 m

TOP VIEW

U A

50 m

-20000

0

20000

40000

60000

0,00 1,00 2,00 3,00 4,00 5,00 6,00 7,00

Time (ms)

UA

(V

olt)

UA Total (sg=0.01S/m)




50 m

500 m

1000 m

TOP VIEW

U A

50 m

-1,00E+05

-5,00E+04

0,00E+00

5,00E+04

1,00E+05

1,50E+05

2,00E+05

0,00 1,00 2,00 3,00 4,00 5,00 6,00 7,00

Time (ms)

UA

(V

olt) UA Total (sg=0.01S/m)


Riser

contr.

Ui

Ex contr.



50 m

500 m

1000 m

TOP VIEW

U C

50 m

-40000

-20000

0

20000

0,00 1,00 2,00 3,00 4,00 5,00 6,00 7,00

Time (ms)

UC

(V

olt)

UC Total (sg=0.01S/m)

UC Total (sg infinite)



50 m

500 m

1000 m

TOP VIEW

U C

50 m

-80000

-60000

-40000

-20000

0

20000

40000

60000

80000

0,00 1,00 2,00 3,00 4,00 5,00 6,00 7,00

Time (µs)

UC

(V

olt

)

UC Total (sg=0.01S/m)

Ex

Ui

Riser

UC Total (sg infinite)



64

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

Conducting plane

Observation

point

Image

The ‘responsible’ is the Horizontal E field © Carlo Alberto Nucci

rg, mrg relative permittivity and permeability of ground

),0,( jrH p Fourier-transf. of E(r,z,t) and H(r,0,t)

calculated assuming a perfectly

conducting ground

Cooray-Rubinstein expression

ogrg

oprpr

j

cjrHjzrEjzrE

s

m

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

),,( jzrErp


0.01 S/m

E hor above ground (Cooray-Rubinstein formula). Return-stroke current : 12 kA peak, 40

kA/µs max di/dt; return-stroke velocity: 1.9 m/s. Field at four distances r from the stroke

location (for illustrative purpose, the values are multiplied by the square of the distance

from the stroke location) calculated assuming a ground conductivity of 0.01 S/m.

h=8m

-20

-15

-10

-5

0

5

10

15

0 1 2 3 4 5 6 7

Time in m s

Horizonta

l E

fie

ld*r

*r in M

V*m

50m 250m 500m 1000m


250 m

Field at 250 m from the stroke location, for three different values of ground conductivity:

0.1; 0.01; 0.001 S/m.

h=8m

-250

-200

-150

-100

-50

0

50

100

150

200

0 1 2 3 4 5

Time in m s

Horizonta

l E

fie

ld in V

/m

infinite 0.1 S/m 0.01 S/m 0.001 S/m


1 km

As in previous figure but at 1 km from the stroke location

-70

-60

-50

-40

-30

-20

-10

0

10

0 1 2 3 4 5

Time in m s

Horizonta

l E

fie

ld in V

/m

infinite

0.1 S/m

0.01 S/m

0.001 S/m

h=8m


The two effects (Zg

and Ex) can be

assessed

separately by

means of

computer codes

0 4 8 12 16 20Time [µs]

-200

-150

-100

-50

0

50

100

Ind

uce

d o

verv

olta

ge

s [k

V]

lossy line

ideal line

0 m

500 m

2500 m

5000 m

A

O' 50 m 5 km



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

Experimental

evidence



This Section on corona losses contains results that are part of a joint

research collaboration with Prof. Teresa Correia de Barros and with

Prof. Gleb Dragan.

C.A. Nucci, S. Guerrieri, M.T. Correia de Barros, F. Rachidi, “Influence of Corona on the Voltages Induced by

Nearby Lightning on Overhead Distribution Lines”, IEEE Trans. On Power Delivery, Vol 15, No. 4, pp. 1265-

1273, October 2000.

G. Dragan, G. Florea, C.A. Nucci, M. Paolone, “On the influence of corona on lightning-induced overvoltages”,

Proc. 30° ICLP, 2010, Cagliari.

3.3 Effect of corona


Corona model (dynamic expression)

Total voltage, defined by the Agrawal model:

1. v(x,t)<vth then C’dyn(x,t)=C’ and can be calculated, for the case

of single conductor line, by means of the known expression.

2. v(x,t)>vth

dztzxEtxvtxvtxvtxv

h

e

z

sis

0

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

thdyn

th

B

th

dyn

vtxvCtxC

vtxvv

txvCBtxC

,for ','

,for ,

','

1

0,for 24.3121.1

0,for 263.2153.0

txvrB

txvrB

Model proposed

by G. Dragan

1 cm of diameter


Corona model (dynamic expression)

0

1

2

3

0 50 100 150 200 250

Ch

arg

e [μ

C/m

]

Voltage [kV]

Corona Q-V curve that resulting from the Dragan expressions


Results

Adopted line configuration and stroke locations

1000 m

10 m

1.06 cm

Zc (stroke location A) Open (stroke location B)

Zc

50 m

Stroke Location A

Side view

Top view

500 m

Observation point #3(500 m)

Observation point #1 (0m)

50 m

50 m

Stroke Location B

1000 m

Observation point #2 (250 m)


Results

Adopted current waveshapes

-10

0

10

20

30

40

50

0

5

10

15

20

25

30

35

40

0 2 4 6 8 10

Lig

htn

ing

cu

rre

nt tim

e d

eri

va

tive

[kA

/μs]

Lig

htn

ing

cu

rre

nt [k

A]

Time [μs]

Current

Time derivative

-10

0

10

20

30

40

50

60

70

0

10

20

30

40

50

60

0 2 4 6 8 10

Lig

htn

ing

cu

rre

nt tim

e d

eri

va

tive

[kA

/μs]

Lig

htn

ing

cu

rre

nt [k

A]

Time [μs]

Current

Time derivative

Stroke location A

Stroke location B


Results

0

20

40

60

80

100

120

140

160

0 1 2 3 4 5 6

Ove

rvo

lta

ge

[kV

]

Time [μs]

with corona

without corona

Obs.point #3

Obs.point #2

Obs.point #1

50 m

Stroke Location A

500 m

50 m

50 m

Stroke Location B

1000 m

Ideal ground


Results

50 m

Stroke Location A

500 m

50 m

50 m

Stroke Location B

1000 m

0

20

40

60

80

100

120

140

160

180

0 1 2 3 4 5 6

Ove

rvo

lta

ge

[kV

]

Time [μs]

with corona

without corona

Obs.point #1

Obs.point #2

Obs.point #3

Ideal ground


Results

50 m

Stroke Location A

500 m

50 m

50 m

Stroke Location B

1000 m

Lossy ground (0.001 S/m)

-50

0

50

100

150

200

250

300

0 1 2 3 4 5 6 7 8 9 10

Ove

rvo

lta

ge

[kV

]

Time [μs]

with corona

without corona

Obs.point #3

Obs.point #2

Obs.point #1


Results

50 m

Stroke Location A

500 m

50 m

50 m

Stroke Location B

1000 m

Lossy ground (0.001 S/m)

-200

-100

0

100

200

300

400

500

600

0 1 2 3 4 5 6 7 8 9 10

Ove

rvo

lta

ge

[kV

]

Time [μs]

with corona

without coronaObs.point #3

Obs.point #2

Obs.point #1


-20

0

20

40

60

80

0 2 4 6 8

Time (µs)

E contribution

E contribution

Total

X

Z

Explanation


D D

E 1

i

R 2

1 2 3 4

R 1

E 2

i E

3

i

E 4

i

D x x x D x

Stroke Location

1

= D x

2 c

2 =

D x

2 c

3 3

= D x

2 c

5 4

= D x

2 c

7

R 0

R L u L

E i x 1

D x E i x 2 D x E i x 3 D x E i x 4

D x

u 0

Explanation


1 R /c

1

2 R /c

2

2 x D x E 2

D x

1 x E 2

4

4 x

D x E 2

3

3 x D x E 2

u 0

D D

E 1

i

R 2

1 2 3 4

R 1

E 2

i E

3

i

E 4

i

D x x x D x

Stroke Location

1

= D x

2 c

2 =

D x

2 c

3 3

= D x

2 c

5 4

= D x

2 c

7

u 0

Explanation


0 1 2 3 4 5

Time [us]

-50

0

50

100

150Risers contribution

Incident Voltage

Ex contribution

Total Voltage

Stroke location: A

Observation point at 0 m

Explanation


Explanation

Stroke location: A

Observation point at 0 m

1 R /c 1

2 R /c

2

2 x D x E 2

D x

1 x E

2

4

4 x

D x E 2

3

3 x D x E 2

u 0


R

0 U

7 km 2 km

R

2 km 2 km 7 km

1 U

2 U

3 U

0 5 10 15 20 25 30 35 40

Time [us]

0

100

200

300

400

500

600

700

800U0

U1U2

U3

a)

Time in us

Ip = 4 kA

Verification (numerical)

Direct stroke


R

0 U

7 km 2 km

R

2 km 2 km 7 km

1 U

2 U

3 U

0 5 10 15 20 25 30 35 40

Time [us]

0

50

100

150

200

250

300

350

400

450

U0U1

U2U3

b)

Ip = 4 kA

Direct stroke

Time in us

Verification (numerical)


Part 5

The LIOV-EMTP code


LIOV i (0,t)

U(x,t)

I (x,t)

5.1. The LIOV code


http://www.epfl.ch/

LIOV Return stroke Current Model

RSC i (z,t)

Lightning ElectroMagnetic Pulse Model

i (z,t) LEMP E, B

ElectroMagnetic Coupling Model

E, B EMC

i (0,t)

U(x,t)

I (x,t)

5.1. The LIOV code


In the LIOV code [Nucci and Rachidi, 2003] the Agrawal et al. model has

been implemented for dealing with the case of multi-conductor lines

closed on resistive terminations. In principle, the LIOV code could be

suitably modified, case by case, in order to take into account the

presence of the specific type of termination, line-discontinuities (e.g.

surge arresters across the line, see next slide) and of complex system

topologies.

This procedure requires that the boundary conditions for the

transmission-line coupling equations be properly re-written case by case,

as discussed in [Nucci et al., 1994]. Nucci C.A., F. Rachidi, Interaction of electromagnetic fields with electrical networks generated by lightning,

Chapter 8 of "The Lightning Flash: Physical and Engineering Aspects", IEE Power and Energy Series, 2003, ISBN

0 85296 780 2.

Nucci C.A., Bardazzi V., Iorio R., Mansoldo A., Porrino A., “A code for the calculation of Lightning-Induced

Overvoltages and its interface with the Electromagnetic Transient Program”, Proc. of the 22nd International

Conference on Lightning Protection, Budapest, Hungary, 19-23 Sept. 1994.



The LIOV code calculates:

• LEMP

• Coupling

The EMTP :

• calculates the boundary conditions

• makes available a large library of power

components

0

u (x,t)

i(x,t) L'dx

C'dx

x x+dx

+ - i(x+dx,t)

L

u (x+dx,t)

u i (x,t)

E i x (x,h,t)dx

s s

+

-

G 0

i 0

+

-

G L

u 0 i L u L

-u (L,t) i -u i (0,t)

Node ‘0’

+

-

u0(t), i0(t)

G2

+

- +

-

G0(t)

u1(t), i1(t)

Zc

u0’(t)

i0’(t)

ve(t)

Node ‘1’

LIOV line Bergeron Line EMTP termination

+

- -ve(t)

G1

Zc

u2(t), i2(t)

Node ‘2’ Dx

Link between LIOV and

EMTP

Boundary conditions, data

exchange between the LIOV

code and the EMTP

Structure of a

typical distribution

line

[Nucci C.A. et al., Proc. ICLP; 1994; Paolone M. , PhD Thesis, 2001; Borghetti A-et al, J. Electrostatics, 2004]

G0

LIOV-line

n-port



LIOV-EMTP Experimental validation – Triggered lightning

Courtesy of V.A. Rakov and M.A. Uman



Measurement

campaign Florida,

Camp Blanding,

Aug 2002; 2003.

Universities of:

Bologna, EPFL,

Florida

LIOV-EMTP Experimental validation – Triggered lightning



First event of 02-08-03 6th return stroke

First event of 02-08-03 6th return stroke

Current flowing through the grounding of pole 6

Current flowing through the grounding of pole 2

-400

-200

0

200

400

600

800

1000

1200

1400

0.E+00 2.E-06 4.E-06 6.E-06 8.E-06 1.E-05

Time [s]

Ind

uce

d C

urr

en

t [A

]

IG6 Simulated

IG6 Measured

-500

0

500

1000

1500

2000

0.E+00 2.E-06 4.E-06 6.E-06 8.E-06 1.E-05

Time [s]

Induce

d C

urr

ent

[A]

IG2 Simulated

IG2 Measured

LIOV-EMTP Experimental

validation – Triggered lightning



First event of 02-08-

03 6th return stroke

Current flowing through

the phase conductor of pole 6

LIOV-EMTP Experimental

validation – Triggered lightning



5.4 Some cases of interest: presence of surge

arresters, effect of shield wire


97

Zc

Zc

SA SA

1000 m

Stroke

location

370 m

50

m


98

ZC

SA SA

Zc

SA

500 m

Stroke

location

370 m

50

m


Zc

Zc

500 m

Stroke

location 5

0 m

370 m

SW

gr. point

SW

gr. point

SW

gr. point

Perfectly conducting ground, Rg=0 W © Carlo Alberto Nucci

Part 6

The Lightning Discharge as a Source

of EM Transients


Why we protect distribution systems

again lightning?

1. To prevent line flashover

which improves the PQ of these systems

2. To minimize component failure

6.1. Preface


What type of protection measures do we

generally adopt?

1. surge arresters

2. shield wires

6.1. Preface


105

What is available in the literature or in the

standards?

A number of books and reference literature, besides a large number of

excellent journal/conference papers, exist on the subject of lightning

protection of distribution systems, e.g.:

Books: - R.H. Golde (Edited by), "Lightning", Academic Press, London, 1977;

- A. Hileman, “Insulation coordination for power systems”, CRC Press, 1999.

- V. Cooray (Edited by), “The lightning flash”, IET, 2003.

Standards/Reference literature: - IEEE Std 1410-2004, “Guide for improving the lightning performance of electric power

overhead distribution line”, 2004. NEW EDITION, 2011!

- CIGRE WG C4.401, convener C.A. Nucci “Lightning-induced voltages on overhead lines”,

Electra, part I, No. 161, pp. 74-102, Aug1995; part II, No. 162, pp. 121-145, Oct. 1995; part

III, pp. 27-30, Oct. 2005; part IV in press.

- CIGRE-CIRED Joint Working Group C4.4.02, convener F. Rachidi, “Protection of MV and LV

Networks against Lightning. Part I: Common Topics”, CIGRE Technical Brochure No 287,

December 2005. “Part II: Lightning protection of Medium Voltage Networks”, in press.

6.1. Preface


Introduction

How do we face the problem of

distribution systems protection against

lightning? • We approach the problem in a statistical way we

estimate the so-called ‘lightning performance of a

distribution system’

• Note that the statistical approach if suitably

supported by adequate modeling/computational

tools, allow us to make the best

technical/economical choice concerning the

protection measure (surge arrester, spark gap,

shield wire) and/or the system insulation level

Let us start now with our lecture


We apply a standard 1.2/50 ms impulse voltage to a cap-and-pin insulator

- If the magnitude of the applied voltage is low enough the insulator does not flash

over

- As the magnitide of the impulse is gradually increased there exist a voltage level

where the insulator breakdown occurs the 50% of the tests this is the CFO

- As the voltage magnitude is increased further, the breakdown occurs before the

lightning impulse has reached its prospective peak voltage (steep front impulse)

6.1. Preface


From IEEE Std 1410, 2004

6.1. Preface


Distribution systems

insulation coordination

evaluation of the Nr of

annual flashovers due to

lightning (we focus on indirect)

that a distribution overhead

line may experience,

as a function of

- insulation level

- line construction design

- ground flash density.

LIGHTNING PERFORMANCE

OF A DISTRIBUTION LINE

Nu

mb

er

of

flash

overs

/100 k

m/y

ear

Line CFO

Nu

mb

er

of

ind

uced

vo

ltag

es

wit

h m

ag

nit

ud

e e

xceed

ing

th

e

valu

e i

n a

bscis

sa/1

00km

/yr

Voltage

[kV]

6.1. Preface


Comparison between the line flashover rate curve of IEEE Std. (A) and those obtained by

using LIOV-MC, enforcing tf = 1 μs for each event, for the case of two different shielding

wire grounding spacing, namely 30 m (B), and 500 m (C). (Flashovers are assumed to occur only from the phase conductor to ground)

6.2 Evaluating the Lightning Performance of a Distribution

Line - IEEE 1410 and CIGRE proposed methodology,

based on the LIOV code and LIOV-EMTP





Influence of grounding interval on distribution line flashover rate, using models with fast front time


For purpose of comparison with the IEEE Std. 1410, the results of the previous slide

have been obtained by assuming the flashover occurring only from the phase

conductor to ground, as specified in the figure caption.

In principle, however, the line could experience flashovers between the phase

conductor and the grounded conductor too.

The next slide shows the flashover rates calculated by considering the two different

flashover paths, namely the phase–to-ground path and the phase-to-grounded wire

one.

Note that the results of next slide must be interpreted by keeping in mind that the two

different flashover paths are characterized by different CFOs especially for wooden

poles and crossarms.

If we assume, for instance, a CFO of 200 kV for a phase-to-ground path and a CFO of

130 kV for a phase-to-grounded wire path, we obtain 2.2 flashovers/100 km/yr and 4.8

flashovers/100 km/yr (and not 0.52 flashovers/100 km/yr as it would the case by

improperly assuming the same CFO for the two cases) respectively.





Comparison between phase-to-ground and phase-to-grounded-wire flashover rate

curves calculated for different ground conductivity σg and grounding resistance Rg.

(Shielding wire grounded each 200 m. A linear model is assumed for the grounding impedance of the neutral or shielding wire )

4.8

2.2

0.52





10.8

m

a

b

c

1.3 m

10 m

CFO =125 kV Coordinate Gauss-Boaga x [km]

Co

ord

ina

te G

au

ss-B

oag

a y

[k

m]

5080

5082

5084

5086

5088

5090

5092

2345 2347 2349 2351 2353 2355 2357

Co

ord

ina

te G

au

ss-B

oa

ga

y [k

m]

Coordinate Gauss-Boaga x [km]

6.3. Experimental activity in Italy


Detected stroke locations by the Italian Lightning location system (CESI-SIRF): 582 strokes period: 01 Jan ÷ 31 Dec 2007

5080

5082

5084

5086

5088

5090

5092

2345 2347 2349 2351 2353 2355 2357

Co

ord

ina

te G

au

ss-B

oa

ga

y(k

m)

Coordinate Gauss-Boaga x (km)

Measurementstation 'Maglio'

Measurementstation 'Torrate'

Measurementstation 'Venus'

Primary 132/20 kVsubstation 'Ponterosso'



5080

5082

5084

5086

5088

5090

5092

2345 2347 2349 2351 2353 2355 2357

Co

ord

ina

te G

au

ss-B

oa

ga

y(k

m)






Stroke #2, flash 4373520-08-07 06:32:04.12531

-29.1 kA

Location of the second

stroke of the 3-stroke

flash number 43735

recorded by CESI-SIRF

on Aug. 20, 2007.

Estimated current

amplitude: 29.1 kA,

negative polarity.



-25

-20

-15

-10

-5

0

5

10

15

20

25

0 2 4 6 8 10 12 14

Ligh

tnin

g-in

du

ced

vo

ltag

e [k

V]

Time μs

Simulated

Measured

Phase 1

Phase 2

Phase 3

5080

5082

5084

5086

5088

5090

5092

2345 2347 2349 2351 2353 2355 2357

Co

ord

ina

te G

au

ss-B

oa

ga

y(k

m)






Stroke #2, flash 4373520-08-07 06:32:04.12531

-29.1 kA



transmission line electromagnetic transients with special...

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