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660IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 50, NO. 3, AUGUST 2008

Responses of Airport Runway Lighting System to

Direct Lightning Strikes: Comparisons of TLM

Predictions With Experimental Data

Nelson Theethayi, Member, IEEE, Vladimir A. Rakov, Fellow, IEEE, and Rajeev Thottappillil, Senior Member, IEEE

Abstract—A test airport runway lighting system, including a

buried cable protected by a counterpoise and vertical ground rods,

was subjected to direct lightning strikes, and currents and voltages

measured in different parts of the system were reported earlier

by Bejleri et al. In this paper, we attempt to model the lightning

interaction with this system using the transmission line theory.

Lumped devices along the cable such as current regulator and

transformers are ignored; possible nonlinear phenomena (arcing)

in the system are neglected; the soil is assumed to be homogeneous.

Themodel-predictedcurrentsinthecounterpoise,groundrod,and

the cable are compared with the measurements, and a reasonable

agreement was found for the currents along the counterpoise. It is

found that current in the counterpoise is not much influenced by

the presence of the cable. Further, vertical ground rods connected

to the counterpoise do not have significant influence on the current

distribution along the counterpoise. It appears that the model is

unable to predict cable currents and voltages in the test system,

presumably due to neglecting nonlinear phenomena in the soil

and in cable’s insulation and electromagnetic coupling with the

lightning channel.

Index Terms—Buried cables, counterpoise, lightning, lighting

system, transient analysis, transmission line modeling (TLM).

I. INTRODUCTION

L

anism of lightning interaction with such systems and to access

the efficacy of their lightning protection employed by the U.S.

Federal Aviation Administration, Bejleri et al. [1] conducted an

experimentalstudyofthetestairportrunwaysystem.Intheirex-

periments conducted at Camp Blanding, Florida, lightning was

triggered using the rocket-and-wire technique. This study is an

attempt to simulate the experiments of Bejleri et al. [1] using a

model based on the transmission line theory [3]–[7]. Sensitivity

analysisisperformedtoidentifythefactorsthatinfluencemodel

predictions.

IGHTNING strikes can cause damage to airport runway

lighting systems. In order to better understand the mech-

Manuscript received November 8, 2007; revised March 3, 2008. This work

was supported in part by the Swedish Research Council under VR Grant 621-

2005-5939, in part by B. John F. and Svea Andersson donation fund, and in part

by the National Science Foundation under Grant ATM-0346164.

N. Theethayi and R. Thottappillil are with the Division for Electricity,

Department of Engineering Sciences, Uppsala University, S-75121 Upp-

sala, Sweden (e-mail: nelson.theethayi@angstrom.uu.se; rajeev.thottappillil@

angstrom.uu.se).

V. A. Rakov is with the Department of Electrical and Computer Engineering,

University of Florida, Gainesville, FL 32611-6130 USA, and also with the In-

ternational Center for Lightning Research and Testing, Starke, FL 32091 USA

(e-mail: rakov@ece.ufl.edu).

Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TEMC.2008.926907

Under direct lightning strike conditions, insulation break-

down and/or soil ionization can occur in the buried lighting

system (involving both insulated and bare conductors). Weather

conditions and ground inhomogeneities introduce uncertainties

in values of ground conductivity and ground permittivity. Fur-

ther, there are some lumped elements, including a current reg-

ulator, transformers, can- and stake-mounted lights, etc., whose

characteristics required for lightning interaction modeling are

not available. Finally, there are limitations and uncertainties

associated with the measurements. All these factors are disre-

garded in our initial modeling attempt presented in this paper.

II. RUNWAY LIGHTING SYSTEM TESTED BY BEJLERI ET AL.

The test airport runway system tested by Bejleri et al. was

similar to those found in many small airports. The schematic

representation of this test runway and its lighting system, which

still exists at the International Center for Lightning Research

and Testing (ICLRT) at Camp Blanding, Florida, can be found

in [1] and [2]. Different configurations were tested. Only one

configuration (configuration 4) is considered here.

Schematic representation of the system for configuration 4

is shown in Fig. 1. The runway pavement is about 92 m ×

23 m. The lighting system includes a generator, current regula-

tor,bothplacedintheelectricalvault,andaburiedserieslighting

cable (outer radius of about 5 mm and central conductor radius

being 1.6 mm) feeding, via insulating transformers, five equally

spaced stake-mounted lights (cable directly buried in the soil

and note that in the experiments corresponding to configuration

4 by Bejleri et al. [1], one of the stake-mounted lights was re-

moved as shown in Fig. 1) and five equally spaced can-mounted

lights[cableplacedinaburiedpolyvinylchloride(PVC)pipeof

2.5 cm radius and about 4-mm thick] on either side of the run-

way, and two signs at the corners (northeast and southwest) of

the runway. The insulated single-conductor unshielded cable is

buriedatadepthof0.4and3mawayfromthepavementedge.A

counterpoise, a bare copper wire of diameter 4.11 mm, is placed

about 10 cm directly above the cable. When the lightning cur-

rent enters the ground, the counterpoise is expected to intercept

the current thereby protecting the cable from direct current in-

jection. The counterpoise is connected to three vertical ground

rods, as shown in Fig. 1, which have a length of 2.4 m and

1.56 cm diameter, as well as to all the stakes and cans. The later

connections are not shown in Fig. 1. As shown in Fig. 1, cur-

rents along the cable and the counterpoise and in the ground

rods were measured (a total of 11 current measurements),

when the lightning current was injected into the counterpoise.

0018-9375/$25.00 © 2008 IEEE

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THEETHAYI et al.: RESPONSES OF AIRPORT RUNWAY LIGHTING SYSTEM TO DIRECT LIGHTNING STRIKES 661

Fig.1.

4 [1], [2].

Measurementpointsalongthecableandcounterpoiseforconfiguration

Voltages have also been measured at five points, as shown in

Fig. 1. We will compare predictions of the model presented in

this paper with the experimental results for the configuration

shown in Fig. 1.

III. TRANSMISSION LINE MODEL OF THE SYSTEM

In case of direct current injection into the counterpoise, cur-

rent waves propagate along the counterpoise and, depending

upon the conductivity of the soil, some current leaks into the

ground. There will also be induced currents in the cable due

to the electromagnetic coupling between the cable and coun-

terpoise. We shall describe the propagation of current pulses in

the test system based on the multiconductor transmission line

(MTL) theory.

The coupled transmission line equations for the counterpoise

and the cable are given in the frequency domain by the voltage

(1) and current (2) wave equations, for an arbitrary propaga-

tion direction, say, x. Note that the counterpoise and the cable

each form a buried horizontal loop (discussed later), with the

counterpoise loop being above the cable loop.

In (1) and (2), Vcnt(x,jω) and Icnt(x,jω) are the voltage

and current at point x along the counterpoise, respectively, and

Vcab(x,jω) and Icab(x,jω) are the voltage and current at point

x along the cable, respectively. In (1), [Z] is the per unit length

series impedance matrix whose elements are self-impedances

of the counterpoise and cable and the mutual impedance be-

tween them. In (2), [Y ] is the per unit length shunt admittance

matrix whose elements are self-admittances of the counterpoise

and cable and the mutual admittance between them. For a given

source, the magnitude and shape of the voltage or current pulses

dVcab(x,jω)

dx

dVcnt(x,jω)

dx

dIcab(x,jω)

dx

dIcnt(x,jω)

dx

+ [Z]

?Icab(x,jω)

Icnt(x,jω)

?

=

?0

0

?

(1)

+ [Y ]

?Vcab(x,jω)

Vcnt(x,jω)

?

=

?0

0

?

.

(2)

propagating along the cable and counterpoise are largely deter-

mined by the impedance and admittance values. Those values

aredependentonthegeometry(wireradii,conductorseparation,

andburialdepths)groundconductivity,groundpermittivity,and

properties of insulation material. We use here the transmission

line model (TLM) for buried conductors described in [3], [6],

and [7]. Elements of 2 × 2 symmetric impedance matrix Z in

(1) are given by

√jωµ1σ1

2πσ1R1

I1

?

Z12= Z21=jωµ0

2πγgD

where γg=?jωµ0(σg+ jωεg). In the previous equations,

cable, the radius of the counterpoise, depth of counterpoise,

depthofcable,andverticalseparationbetweenthecableandthe

counterpoise, respectively. I0(·) and I1(·) are Bessel’s functions

offirstkindwithorderzeroandone,respectively.In(3b),RX =

R2the outer radius of the cable for the cable section in direct

contactwiththesoil,andRX = Rp(theouterradiusofthePVC

pipe) for the section that is placed in buried PVC pipe. In (3),

µ0is the free-space permeability and σgand εgare the ground

conductivity and permittivity, respectively. Also, in (3), µ1and

σ1 are the permeability and conductivity of the counterpoise

material and µ2and σ2are the permeability and conductivity of

the cable conductor material.

Elements of 2 × 2 symmetric admittance matrix Y in (2) are

given by

Y11= yg22+yg12(yg11+ jωCeff)

jωCeff+ yg11+ yg12

jωCeff(yg11+ yg12)

jωCeff+ yg11+ yg12

Z11=

√jωµ2σ2

2πσ2Rc

I0

I1

?

?Rc√jωµ2σ2

?1 + γgRX

?

?Rc√jωµ2σ2

ln

γgR2

? +jωµ0

+2e−2d2|γg|

4 + R2

2π

ln

?RX

Rc

?

?

+jωµ0

2π

?

Xγ2

g

(3a)

Z22=

I0

?R1√jωµ1σ1

?1 + γgR1

?1 + γgD

?

?

+2e−(d1+d2)|γg|

4 + D2γ2

?R1√jωµ1σ1

ln

γgR1

?

+jωµ0

2π

+2e−2d1|γg|

4 + R2

1γ2

g

?

?

(3b)

?

ln

?

g

(3c)

Rc,R1,d1,d2, and D are the inner (conductor) radius of the

(4a)

Y22=

(4b)

Y12= −

jωCeffyg12

jωCeff+ yg11+ yg12

(4c)

where

?yg11

?Yg11

yg12

yg21

yg22

?

?

=

?Yg11+ Yg12

?Zg11

−Yg12

Yg22+ Yg12

?−1

−Yg12

?

(5)

Yg12

Yg21

Yg22

≈ γ2

g

Zg12

Zg21

Zg22

.

(6)

In(6),thematrixZgisthematrixofgroundimpedancewhose

elements are given by (3) with terms involving γg only. Note

that in (4), Ceff is the effective capacitance depending upon

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662IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 50, NO. 3, AUGUST 2008

Fig. 2.

containing buried counterpoise (solid line) and cable (dashed line).

Schematic representation of the modeled distributed-circuit system

whether the section of cable is in contact with the soil or placed

in a buried pipe. If the cable is in contact with the soil, then

Ceff= 2πε1[ln(R2/Rc)]−1, where ε1is the permittivity of the

cable insulation. For the cable section in the PVC pipe, Ceff is

CP as given by

?1

?

?

?

and is the series combination of the capacitance due to cable

insulation, that due to the air insulation between cable and the

inner surface of the PVC pipe and that due to the PVC pipe

wall. In (7), ε0 and ε2 is the free-space permittivity and the

permittivity of the PVC pipe, respectively, and tw is the PVC

pipe wall thickness.

CP =

Ci

+

1

Ca

+

1

Cw

??−1

?−1

(7a)

Ci= 2πε1

ln

?R2

?Rp− tw

?

Rc

(7b)

Ca= 2πε0

ln

R2

??−1

??−1

(7c)

Cw= 2πε2

ln

Rp

Rp− tw

(7d)

IV. APPLICATION OF THE MODEL TO CONFIGURATION

SHOWN IN FIG. 1

A schematic representation of the system under study is

shown in Fig. 2. Lightning strike is represented by a lumped

current source. There should be electromagnetic coupling be-

tween the lightning channel located above the injection point

and buried conductors, but it is not included in the sim-

ulations presented here. As stated in Section I, nonlinear

processes such as breakdown between cable and counter-

poise and soil ionization around the counterpoise, if any, are

neglected.

For the simulations, we use the measured return stroke cur-

rent IL1 corresponding to stroke 1 of Flash U9841 presented

by Bejleri et al. [1], [2] whose waveform we approximated by

IL1(t) = 16 × 103(e−8.5×103t− e−2.0×106t)(seeFig.3),where

IL1 is in amperes and t is in seconds. The total length of

Fig. 3.Measured and approximated total lightning currents.

Fig.4.

andthemeasurementpointsforcurrentsonthecounterpoise(solidlineandwith

current subscripts “ctp”) and the cable (dashed line and with current subscripts

“c”), as well as for voltages between the cable and counterpoise. Distances

are not to scale. Also shown is the section of cable inside the pipe. Dotted

lines connecting the line ends to their terminations represent short circuits. Line

terminations are at the electric vault.

Diagramshowingsectionboundaryconditionsonthetransmissionline

each of the two loop conductors is about 251.5 m and, as per

Fig. 4, if traversed from left to right, the ground rods are lo-

cated at 0 m (termination), 52.5 m (x1), and 196.8 m (x2).

The lightning current injection point is located at 90.5 m (xs).

The cable section inside the pipe begins at 160.5 m (xp). The

sensors measuring currents and voltages are located at approx-

imate distances from the current injection point that are given

in Table I.

The presence of insulating transformers along the cable is

neglected and the source (generator and current regulator) is

replaced by a 2-Ω series resistor (Rs) and a series inductor of

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THEETHAYI et al.: RESPONSES OF AIRPORT RUNWAY LIGHTING SYSTEM TO DIRECT LIGHTNING STRIKES 663

TABLE I

MEASUREMENT POINT LOCATIONS

1mH(Ls).Thevaluesofresistanceandinductanceareexpected

ball-park values. The ground rods are modeled as lumped shunt

resistances at the appropriate locations along the counterpoise.

The resistance of the ground rod is calculated using [4], [5], [8]

?

In (8), lrodis the length of the rod (around 2.4 m) and arodis

the radius of the rod (about 0.78 cm). The shunt resistance rep-

resentation of the ground rod is adopted under the assumptions

that lrod??2/ωµ0σgand lrod? arod, which is valid for the

In general, the solution for voltages and currents in any MTL

system can be obtained by the modal analysis. This involves

decoupling of the transmission line (TL) equations (1) and (2)

and solving for either the modal currents or modal voltages with

appropriate section boundary conditions. The actual currents

and voltages are related to the modal currents and voltages

through the transformation matrix [5]. This procedure for TL

equations used in the present study is as follows. Let us divide

the MTL into five sections, marked in Fig. 4. The solutions for

the voltage and current are given by [5]

V (x) = ZcT?e−γxI+

Rgrod=

1

2πσglrod

ln

?4lrod

arod

?

− 1

?

.

(8)

system under study.

ms+ eγxI−

ms

?.

?

(9a)

I (x) = T?e−γxI+

ms− eγxI−

ms

(9b)

In (9), T is the transformation matrix that depends on the

eigenvalues of the product of impedance and admittance matri-

ces of the transmission line (appropriate product of impedance

and admittance depending on the section of the cable in soil or

in the pipe), the subscript “s” represents section number, and γ

and Zcare given by (10) and (11), respectively

γ =

Zc= ZTγ−1T−1

√

T−1Y ZT

(10)

(11)

?Z?

cT?e−γ?x1I+

−Z?

?Z?

?T?e−γ?xsI+

Similarly, at distance x = xp(see Fig. 4)

?Z??

?T??e−γ??xpI+

At distance x = x2(see Fig. 4)

?Z??

Gs=

m2+ Z?

cT?eγ?x1I−

m1− Z?

m1− T?eγ?x1I−

+(−T?+ Z?

+(T?+ Z?

m2

cT?e−γ?x1I+

T?e−γ?x1I+

cT?eγ?x1I−

m1

?

= 0

(12a)

m1

cT?Gs)e−γ?x1I+

cT?Gs)eγ?x1I−

m2

m2

= 0.

(12b)

Similarly, at distance x = xs(see Fig. 4)

cT?e−γ?xsI+

−Z?

m3+ Z?

cT?eγ?xsI−

m2− Z?

m3− T?eγ?xsI−

−T?e−γ?xsI+

m3

cT?e−γ?xsI+

cT?eγ?xsI−

m2

?

?

= 0

(13a)

m3

m2+ T?eγ?xsI−

m2

= I0. (13b)

cT??e−γ??xpI+

−Z?

m4+ Z??

m3− Z?

m4− T??eγ??xpI−

−T?e−γ?xpI+

cT??eγ??xpI−

cT?eγ?xpI−

m4

cT?e−γ?xpI+

m3

?

?

= 0

(14a)

m4

m3+ T?eγ?xpI−

m3

= 0.

(14b)

cT??e−γ??x2I+

−Z??

+(T??+ Z??

m5+ Z??

cT??eγ??x2I−

m4− Z??

m4− T??eγ??x2I−

+(−T??+ Z??

cT??Gs)eγ??x2I−

m5

cT??e−γ??x2I+

T??e−γ??x2I+

cT??eγ??x2I−

m4

?

= 0

(15a)

m4

cT??Gs)e−γ??x2I+

m5

m5

= 0

(15b)

?00

01/Rgrod

?

.

(16)

We can use the previous equations and appropriate section

boundary conditions to write the following set of linear simul-

taneous equations for each section. For convenience, let us as-

sume that T?, Z?

istic impedance, and propagation constant, respectively, for the

MTL section where the cable is in the soil and T??, Z??

the corresponding terms for the MTL section where the cable

is in the pipe. At distance x = x1(see Fig. 4), the voltage is

continuous and current is discontinuous due to the presence of

ground rod.

At distances x = 0 and x = L, the node equations are (17)

and (18), respectively

c, γ?are the transformation matrix, character-

c, γ??are

Z?

cT?(G11+ G12)I+

−Z??

−T?I+

m1+ Z?

m5− Z??

cT?(G11+ G12)I−

cT??G12eγ??LI−

m1

cT??G12e−γ??LI+

m1+ T?I−

m5

m1

= 0

(17)

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664IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 50, NO. 3, AUGUST 2008

−Z?

cT?G12I+

+Z??

+Z??

m1− Z?

cT?G12I−

m1+ T??e−γ??LI+

m5

cT??(G11+ G12)e−γ??LI+

cT??(G11+ G12)e−γ??LI−

m5

m5− T??e−γ??LI−

m5

= 0

(18)

G11=

?0

?(Rs+ jωL)−1

0

01/(2Rgrod)

?

(19)

G12=

0

01 × 106

?

.

(20)

Solution of the previous linear simultaneous equations gives

us I+

used in (9) to get the current and voltage at any point on the

conductor. Next, we present results of simulations, comparison

with measurements, and sensitivity analysis.

msand I−

mscorresponding to a given section, which can be

V. RESULTS

There is an uncertainty regarding ground conductivity at

Camp Blanding, but it is probably between 1 mS/m (resistivity

1000 Ω m) and 0.25 mS/m (resistivity 4000 Ω m) [1]. For this

reason, we will show simulation results corresponding to two

valuesofgroundconductivity1and0.25mS/m.Thegroundrel-

ative permittivity was assumed to be 10. In each of the figures

showing model predicted waveforms corresponding measured

waveforms are presented as well.

A. Counterpoise and Ground Rod Currents—Single Conductor

With Ground Return Analysis

In this section, we will first examine influence of the cable on

currents in the counterpoise by neglecting the cable and com-

paringmodelpredictionswiththecorrespondingmeasurements.

Further,inordertoevaluatetheefficacyofthethreegroundrods,

we will consider cases with and without ground rods. A model

forasingleburiedbarewireisfoundin[6].Fig.5showscurrents

Ictp1(first window), Ictp2(second window), Ictp3(third win-

dow), and Ictp4(fourth window), and Fig. 6 shows the ground

rod currents Igr2.

It seems that the presence of ground rods does not have any

significant influence on the current distribution along the coun-

terpoise. This observation holds for either of the two ground

conductivity values considered. It is also important to note that

the current distribution along the counterpoise is relatively in-

sensitive to ground conductivity. As expected, close to the cur-

rent injection point, counterpoise currents Ictp1and Ictp2(see

Fig.5,firstandsecondwindows)areleastaffectedbychangesin

ground conductivity. Farther from the injection point, effects of

ground conductivity are more appreciable, particularly in terms

of current rise time (see Fig. 5, third and fourth windows). The

simulated current peaks into the ground rod Igr2(see Fig. 6) are

somewhat larger than the measured current peak, particularly

for the case of 1 mS/m ground conductivity.

The simulations show that Ictp1 is less than Ictp2, but the

measurements show otherwise. Further, measurements show an

unusual waveshape (the tail decaying to zero at about 30 µs) for

Ictp3, while the corresponding simulations predict a very dif-

Fig. 5.

Ictp4, in the absence of the cable with and without ground rods for two values

of ground conductivity, 1 and 0.25 mS/m. Also shown are measured currents.

Model-predicted counterpoise currents, Ictp1,Ictp2,Ictp3, and

Fig. 6.

absence of the cable for two values of ground conductivity, 1 and 0.25 mS/m.

Measured current is also shown.

Model-predicted currents into one of the ground rods, Igr2, in the

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