An advanced interface between the Lightning Induced ... - EMTP

An advanced interface between the Lightning Induced Overvoltage Code (LIOV) and EMTP-RV M. PAOLONE and F. RACHIDI ÉCOLE POLYTECHNIQUE FÉDÉRALE DE LAUSANNE – EPFL SWITZERLAND A. BORGHETTI, F. NAPOLITANO and C.A. NUCCI, UNIVERSITY OF BOLOGNA ITALY

EMTP-RV European User Group Meeting April 3, 2012– Paris, La Défense, France

The problem

z'

H

IMMAGINE

dz'i(z',t)

R

R'

r

x

yZ

L

zz'

P(x,y,z)

Zo

Eh

E

r

zE

EEx

P(x,y,z)

φ

IMAGE

v

i(z’,t): lightning current; H: lightning channel height; v: lightning wave front speed.

Computation of overvoltages induced by electromagnetic fields produced by lightning return strokes nearby overhead lines.

Outline

¨  Introduction ¨  2nd order FDTD for the solution of the Agrawal et

al. coupling model ¨  Boundary conditions

¤ Numerical treatment ¤ Structure of the interface

¨  Advantages of the proposed interface ¨  Comparison between experimental recordings and

simulation results ¨  Conclusions

Introduction

The evaluation of the lightning performance of overhead distribution lines has been the object of several studies e.g. : ¨  IEEE Std. Guide 1410; ¨  Joint Cigré-Cired WG C4.4.02;

The inherent complexity of distribution systems, namely: ¨  number of lines (main feeder with laterals) ¨  presence of power components (transformers, surge arresters, groundings, etc.) is well far from the straight line configuration generally adopted in these type of studies.

Introduction

Example: Influence of network topology on the indirect-lightning performance of distribution networks

0.0001

0.0010

0.0100

0.1000

1.0000

50 100 150 200 250Voltage [kV]

Ann

ual n

umbe

r of e

vent

s ex

ceed

ing

the

valu

e in

ab

scis

sa

straight lineH-shaped network (type 1)H-shaped network (type 2)T-shaped network

A. Borghetti, M. Paolone, C.A. Nucci, “Indirect-Lightning Performance of Overhead Distribution Networks With Complex Topology”, IEEE Trans. on PWRD, vol. 24-4, Oct. 2009, pp. 2206-2213.

Introduction

The contribution presents an improvement of the already developed LIOV-EMTP interface by introducing: ¨  improved boundary condition treatment of LEMP-illuminated lines (à time delays issues are fixed) ¨  integration of the LIOV code with the augmented nodal analysis technique implemented in the EMTP-RV.

Interface structure n-port (EMTP-RV)

LIOV-lines

Outline






2nd order FDTD for the solution of the Agrawal et al. coupling model

Agrawal et al. field-to-transmission line coupling model for a lossless single conductor overhead line

),,(),('),( thxEttxiL

xtxv e

x

s

=∂

∂+∂

∂

0),('),( =∂

∂+∂

∂ttxvC

xtxi s

∫−=+=ih

ez

si

ei

sii dztzxEtxvtxvtxvtxv

0

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

2nd order FDTD for the solution of the Agrawal et al. coupling model

⎟⎟⎠

⎞⎜⎜⎝

⎛Δ

−+−Δ−Δ−⎟⎟⎠

⎞⎜⎜⎝

⎛Δ−Δ−= −+−+−++

21111

2111 2

2''22' xvvv

xEhEh

CLt

xii

Ctvv

nk

nk

nk

nk

nk

nk

nkn

knk

⎟⎟⎠

⎞⎜⎜⎝

⎛Δ−+

Δ−+Δ+⎟⎟⎠

⎞⎜⎜⎝

⎛−

Δ−Δ−=

−+−+−++

tEhEhC

xiii

CLtEh

xvv

Ltii

nk

nk

nk

nk

nkn

k

nk

nkn

knk 2

'2''22'

11

211

2111

n n i v 0 0 , n k

n k i v max max ,

n k

n k i v ,

R 0

∫ h

e z dz t E

0 ) , 0 , 0 ( ∫

h e z dz t L E

0 ) , 0 , (

R L

) t , h , x ( E e x

n+1

n

n - 1

k k+1 k - 1 spatial discretization

time discretization

Outline





simulation results ¨  Application example: lightning-to-fault correlation ¨  Conclusions

Boundary conditions Numerical treatment

( ) ∫+Γ−=h

ez

n dztEiv0

000 ),0,0(

( ) ∫+Γ=h

ezkk

nk dztLEiv

0max ),0,(

maxmax

Problem: since the numerical solution of the internal FDTD nodes (k = 1,…, kmax-1) provided by the LIOV code is split from the one of the boundary conditions provided by EMTP-RV, explicit in a closed form the boundary conditions linking the voltages and currents at the terminal FDTD nodes is a non trivial task.

Scattered voltages


Solution of the problem replace the spatial numerical discretization at the two line terminations (x=0 and x=L) by means of two Bergeron lines suitably extended to take into account the presence of the exciting LEMP: illuminated Bergeron Lines

utx =

ΔΔ

à Additional contraint to be applied to space (Δx) and time (Δt) integration steps which are correlated by means of the Courant stability condition:

Being u the propagation speed


Bergeron equations (without external exciting LEMP) at the two terminations of a lossless line:

),(),(),0(),0( tttuZitttuvtZitv Δ−Δ−Δ−Δ=−

),(),(),(),( tttuLZitttuLvtLZitLv Δ−Δ−+Δ−Δ−=+

Where: ¨  v(0,t), i(0,t) and v(L,t), i(L,t) are the voltages and currents at the

beginning and at the end (L) of the LIOV line respectively;

¨  Z is the surge impedance of the line (assumed to be frequency independent).


Bergeron equations in presence of external exciting LEMP at the two ideal line terminations:

∫Δ

−Δ−Δ−Δ−Δ=−tuex

ss dxthxEtttuZitttuvtZitv0

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

∫Δ−

+Δ−Δ−+Δ−Δ−=+L

tuL

ex

ss dxthxEtttuLZitttuLvtLZitLv ),,(),(),(),(),(

In the discretized form:

v0n+1 − Zi0

n+1 = v1n − Zi1

n − Δx2

Eh0n+1 + Eh1

n( )

vkmaxn+1 + Zikmax

n+1 = vkmax−1n + Zikmax−1

n + Δx2

Ehkmaxn+1 + Ehkmax−1

n( )

Boundary conditions Structure of the interface

( )00 iΓ

( )nn EhEhx1

102

+Δ +

( )hEzn ⋅+10

( )nk

nk EhEhx

11

maxmax2 −+ +Δ

( )hEz nk ⋅+1max

11

11 ,

++ nn iv 12

12 ,

++ nn iv 12

12 maxmax, +

−+

−nk

nk iv 1

111 maxmax, +

−+

−nk

nk iv

…… 1

01

0 ,++ nn iv 11

maxmax, ++ nk

nk iv

( )maxmax kk iΓ

Z Z Z Z

EMTP-RV EMTP-RV LIOV line

0G maxkG0'G max'kG

( )nnnnnn EhEhxZivZiv 11

0111

01

0 2+Δ−−=− +++

( )nk

nk

nk

nk

nk

nk EhEhxZivZiv 1

111

11maxmaxmaxmaxmaxmax 2 −

+−−

++ +Δ++=+

Boundary conditions Structure of the interface

The main system of equations in EMTP-RV is given by:

⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡

v

n

V

n

dr

cn

vi

iv

VVVY

¨  Yn is the nodal admittance matrix; ¨  submatrices Vc, Vr and Vd are used to include non-nodal

type equations, such as branch relations (called voltage-defined equations), but can also use current coefficients;

¨  vn, iV unknown quantities (nodal voltages and branch currents);

¨  In current injections and vv voltage-defined equations.

DLL interface

DLL interface

Outline






Advantages of the proposed interface

Comparison between the previous LIOV-EMTP96 and LIOV-EMTP-RV interfaces

1000 m

10 m

1 cm

Zc Zc

50 m

Stroke Location

Side view

Top view

500 m

Observation point

Observation point

Lightning current (subs) ¨  12 kA amplitude

¨  40 kA/μs of max time derivative

¨  r.s. speed:1.3·∙108 m/s

¨  r.s. time-space distribution represented with the MTLE model


Comparison with Δx = 5 m, Δt = 1.66·∙10-8 s, Δx = 10 m, Δt = 3.33·∙10-8 s, Δx = 20 m, Δt = 6.66·∙10-8 s Line represented as a single straight line (1 section)

LIOV-EMTP96 LIOV-EMTP-RV

-10

0

10

20

30

40

50

60

70

0 2 4 6 8 10

Indu

ced

volta

ge (k

V)

Time (µs)

Δx = 5 m, Δt = 1.666E-8 s

Δx = 10 m, Δt = 3.333E-8 s

Δx = 20 m, Δt = 6.666E-8 s

-10

0

10

20

30

40

50

60

70

0 2 4 6 8 10

Indu

ced

volta

ge (k

V)

Time (µs)

Δx = 5 m, Δt = 1.666E-8 s

Δx = 10 m, Δt = 3.333E-8 s

Δx = 20 m, Δt = 6.666E-8 s

-10

0

10

20

30

40

50

60

70

0 2 4 6 8 10

Indu

ced

volta

ge (k

V)

Time (µs)

Δx = 5 m, Δt = 1.666E-8 s

Δx = 10 m, Δt = 3.333E-8 s

Δx = 20 m, Δt = 6.666E-8 s


LIOV-EMTP96 LIOV-EMTP-RV

Comparison with Δx = 5 m, Δt = 1.66·∙10-8 s, Δx = 10 m, Δt = 3.33·∙10-8 s, Δx = 20 m, Δt = 6.66·∙10-8 s Line segmented into 5 straight sections

-10

0

10

20

30

40

50

60

70

0 2 4 6 8 10

Indu

ced

volta

ge (k

V)

Time (µs)

Δx = 5 m, Δt = 1.666E-8 s

Δx = 10 m, Δt = 3.333E-8 s

Δx = 20 m, Δt = 6.666E-8 s

Outline






Comparison between experimental recordings and simulation results

Reduced scale model experiment Experimental data obtained by Piantini and Janischewskyj

A. Piantini, J.M. Janiszewski, “An experimental study of lightning induced voltages by means of a scale model”, Proc. of the 21st International Conference On Lightning Protection, Berlin, Germany, September, 1992.

1400 m

10 m

2 cm

Zc Zc

70 m

Stroke Location

Side view

Top view

700 m

Measurement point

Lightning current ¨ 27.5 kA amplitude

¨ Time to peak: 3.5 µs

¨ r.s. speed:0.33·∙108 m/s

¨ r.s. time-space distribution represented with the TL model

Ideal ground


Reduced scale model experiment

-20

0

20

40

60

80

100

120

140

0 5 10 15 20

Indu

ced

volta

ge (k

V)

Time (µs)

MeasuredSimulated


!

Full-scale experiment Experimental campaign carried out in 2003 at the (ICLRT [12-14]) operated by the University of Florida.

The facility consists of an experimental un-energized overhead multi-conductor power distribution line, illuminated by electromagnetic fields produced by artificially triggered lightning. The line is 0.75-km long, consisting of 4 conductors (3–phase conductors plus neutral, periodically grounded) and equipped with surge arresters.


Full scale model experiment: models

Grounding has been modeled adopting a lumped-parameter approach by using the Rundeberg model and by segmenting the RLC network into 50 segments

R. Rudenberg, Electrical Shock Waves in Power Systems. Cambridge, MA: Harvard Univ. Press, 1968.


Comparison between experimental and simulation results for the 6th return stroke of the lightning flash triggered 02 august 2003; induced-current flowing through the arrester located at pole 6 phase B

-50

0

50

100

150

200

250

0.E+00 2.E-06 4.E-06 6.E-06 8.E-06 1.E-05Time [s]

Indu

ced

Cur

rent

[A]

IBN6 SimulatedIBN6 Measured

M. Paolone, F. Rachidi, A. Borghetti, C.A. Nucci, M. Rubinstein, V.A. Rakov, M. Uman, “Lightning Electromagnetic Field Coupling to Overhead Lines: Theory, Numerical Simulations, and Experimental Validation”, IEEE Trans. on EMC, vol. 51-3, part 1, Aug. 2009, pp. 532-547.


Comparison between experimental and simulation results for the 6th return stroke of the lightning flash triggered 02 august 2003; induced-current flowing through the grounding of pole 6

-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-05Time [s]

Indu

ced

Cur

rent

[A]

IG6 SimulatedIG6 Measured



Comparison between experimental and simulation results for the 6th return stroke of the lightning flash triggered 02 august 2003; induced-current flowing through the grounding of pole 2

-500

0

500

1000

1500

2000

0.E+00 2.E-06 4.E-06 6.E-06 8.E-06 1.E-05Time [s]

Indu

ced

Cur

rent

[A]

IG2 SimulatedIG2 Measured



Comparison between experimental and simulation results for the 6th return stroke of the lightning flash triggered 02 august 2003; induced-current flowing through the phase B at pole 6

-250

-200

-150

-100

-50

0

50

100

150

0.E+00 2.E-06 4.E-06 6.E-06 8.E-06 1.E-05Time [s]

Indu

ced

Cur

rent

[A]

IB6 Simulated

IB6 Measured


Coordinate Gauss-Boaga x [km]

Coo

rdin

ate

Gau

ss-B

oaga

y [k

m]

5080

5082

5084

5086

5088

5090

5092

2345 2347 2349 2351 2353 2355 2357

Coo

rdin

ate

Gau

ss-B

oaga

y [k

m]



Real network measurements


LLS data summary: §  period: March 2007–August 2008; §  flashes: 569 flashes; §  strokes: 851 strokes (778 negative and 73

positive); §  425 flashes (75% of the total) are

composed by only 1 stroke; §  82 flashes (14%) are composed by 2

strokes; §  remaining 62 flashes (11%) are

composed by 3 or more strokes; §  area: rectangular surrounding the

distribution feeder having a maximum distance of 2 km from the feeder extremities (in total:144 km2).

5080

5082

5084

5086

5088

5090

5092

2344.5 2346.5 2348.5 2350.5 2352.5 2354.5 2356.5


Coo

rdin

ate

Gau

ss-B

oaga

y [k

m]

Return strokes Distribution network

Overvoltage measurement system data summary: §  transients: more than 1700; §  faults: 2 self-extinguishing and 4 causing circuit breaker opening.

2345 2346 2347 2348 2349 2350 2351 2352 2353 2354 2355 23565081

5082

5083

5084

5085

5086

5087

5088

5089

5090

5091

5092

Unit 3

Unit 2

Unit 1

substation

1

2 34

km

km

-5

-4

-3

-2

-1

0

1

2

3

4

0 10 20 30 40 50

Volta

ge (k

V)

Time (µs)

calcolate

10 Per. Media Mobile (misurate)

calculationsmeasurements

-4

-2

0

2

4

6

8

10

0 10 20 30 40 50

Volta

ge (k

V)

Time (µs)

calcolate

10 Per. Media Mobile (misurate)

calculationsmeasurements

Unit 1

LLS event nr: 30260-3 Current peak: -20.9 kA

Unit 3


F. Napolitano, A. Borghetti, M. Paolone, M. Bernardi, “Voltage transient measurements in a distribution network correlated with data from lightning location system and from sequence of events recorders “, Electric Power Systems Research, vol. 81, Issue 2, Feb. 2011, pp: 237-253.

Outline






Conclusions

¨  A new interface between the LIOV code and the EMTP-RV has been developed in order to properly simulate the response of realistic distribution networks against external electromagnetic fields produced by nearby lightning.

¨  Compared to the already presented interface between the LIOV code and the EMTP96, the proposed one avoids the small time shift introduced between each illuminated LIOV-line and the boundary solution provided by the EMTP-RV.

Conclusions

¨  The proposed interface has been tested versus several experimental data sets, obtained by means of reduced scale models and triggered lightning à as expected, good agreement has been obtained.

¨  The proposed interface represent a powerful tool for the analysis of the distribution networks response against nearby lightning, insulation coordination studies, lightning-to-fault correlation, design and optimal placement of protection devices.

An advanced interface between the Lightning Induced Overvoltage Code (LIOV) and EMTP-RV M. PAOLONE and F. RACHIDI ÉCOLE POLYTECHNIQUE FÉDÉRALE DE LAUSANNE – EPFL SWITZERLAND A. BORGHETTI, F. NAPOLITANO and C.A. NUCCI, UNIVERSITY OF BOLOGNA ITALY

EMTP-RV European User Group Meeting April 3, 2012– Paris, La Défense, France

An advanced interface between the Lightning Induced ... - EMTP

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