Download 98 - Protection Against Direct Lightning Strokes by Charge

Protection AgaindDirect Lightning Strokes by Charge
Transfer System
Roy B. Carpenter Jr.
Mark M. Drabkin
Lightning Eliminators & Consultants,Inc.
6687 ArapahoeRd
Boulder, Colorado,USA
Lightning Eliminators & Consultants,Inc.
6687 ArapahoeRd
Boulder, Colorado, USA
Abstract: Implementation of the Charge Transfer System
(CTS) offers a wide range of protection against direct
lightning strokes; from the enhancement of the strike
collection ability to the total prevention of strokes into the
protected premise. Design of such a system requires
engineering specifics about the site to be protected and the
data related to the lightning activity and weather conditions in
that particular location. The engineeringdata for the premise
to be protected is usually readily available, but lightning data,
statistical and probabilistic by nature, varies from region to
region. Some times this data is only partially available, and
that createssome complexity for the design process of CTS.
The paper discusses the major steps of the engineering
approachto the designof CTS.
Introduction
Protecting a premise against direct lightning strokes by
preventing lightning stroke is not exactly a new idea. It was
Franklin’s original idea that he could dissipate the
thundercloud electricity by installing the pointed iron rod,
which would quietly conduct the electricity away. However,.
he changed his mind after his lightning rods were hit by
lightning insteadof preventing the strokes.He then postulated
that it would be better to provide a preferablepath to earth for
lightning by erecting the elevated groundedrods. During the
past 250 years the Franklin rod successfUlly protected
structures from the lightning-caused damage.And that was
the & requirementto the lightning protection against direct
hits till last 40 - 50 years.
In the recent 4 decades,due to the explosive progress in
computers/electronicstechnology, the secondaryeffect of the
lightning stroke became the major concern in many cases.
Generated by lightning current, the strong magnetic field
around the downward conductor connectingthe lightning rod
to the grounding system causedthe induced voltagesof such a
magnitudethat it permanentlydamagedor causedmalfunction
of sensitive electronic equipment located nearby. The
prevention of the direct lightning strokes into the premise is
one of the ways to eliminate the damaging consequencesof
the secondaryeffect.
0-7803-5015-4/98/$10.000 1998IEEE
Mechanism of preventing the lightning stroke
The idea of preventing the lightning stroke is based on the
so-called point discharge phenomenon.Sharp edged objects
such as leaves of trees , bushes and grass as well as pointed
electrodessuch as lightning rods), when exposedto the strong
electric field, start to emit current into the surrounding air.
This current is a result of an ionization process in the air
surroundingthe sharpenedpoints. The strength of the electric
field, called the critical initiating field is required to initiate
such an ionization process.The magnitude of critical field can
vary widely depending on factors like an availability of free
electrons in that area, barometric pressure, temperature,etc.
As an example,note the following empirical formula (1) used
frequently in power transmission and distribution engineering
to determine the critical value of the electric field strength
which will start a corona from the line conductors:
EC,=
23.36(1+ $$&),
0
where 6 is the relative air density factor depending on
temperatureand pressure,and ro is the radius of the conductor.
For quick estimation of the critical field strength the Peek’s
empirical formula, Ecr = 316 (kV/cm), can be used.
In calculations of the electric fields due to the lightning, the
thunderstormcloud is often representedby a simplified model
(see Figure 1) of point charges located on one vertical line.
The main positive charge is at the top of the cloud, the
negative charge at the bottom of the cloud, and an additional
local positive charge at some distance below the negative
charge [I]. The electric field at the ground level can then be
calculatedby the following equation (2):
where: Qposand Qnegare the positive and negative chargesof
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a thundercloudcell,
qpDs
is a local positive chargebelow the thundercloud
cell,
Hpos,Hnegand hposare the heights of the
correspondingchargesabovethe ground level, and
D is the horizontal distanceof the point at the Earth’s
surfacefrom the thundercloudcell charges.
strengthof the electric field, wind velocity past the points, and
barometric pressure. Appearance of an additional charge
locatedrelatively close to the ground changesthe total electric
field E. [4]. Inserting a new componentof total electric field
causedby the presenceof the spacecharge qSc,into Equation
(2), we introduce Equation (3), which can be used to calculate
the new value of the electric field strength with consideration
of an additional positive chargeq,, at the height h,, above the
ground.
+ 2QnegHneg
*o=- 2Qp.Pp
4m+(Ig,, +Tlp3’*
H P*s
29po&oo
- 4nq,(h;os+d)3’2
.pos
Figure 1. Simplified model of a
thundercloud cell
Chalmers [2] noted that the electric field of 600 to 1000 V/m
at ground level is sufficient to initiate the ionization process
from the points at the top of trees. Thesevalues are not in any
disagreement with E,, because the electric field, E,, at
sharpenedpoints and edges is much stronger than Eo. The
field enhancementfactor, which is defmed as b = Ep/Eo ,
dependson the shape,dimensions,and height of the sharpened
point. It is difficult to calculate exact value of k, becausethe
analytical solution for most shapesis yet to be developed.
However, for the simple forms, like vertical or horizontal
conductors,reasonableapproximationscan be made using the
equations developed for a conducting prolate semi-ellipsoid
[3]. Calculations of the enhancementcoefficient, k, basedon
this approximation show that k, can be as great as 100 - 600
dependingon the electrodeheight and radius of curvature.
When a stepped leader starts its downward movement, it
lowers the main negative charge located at the bottom of the
thundercloud cell and may or may not neutralize the local
positive charge. The electric fields, Eo, and correspondingly,
Ep, have intensified rapidly, approximately in accordance
with the vertical component of the average speed of the
stepped leader and the charge distribution along the leader
channel.
Under influence of the rapidly increasingelectric field, E,,
the ionization of the air surrounding the sharpenedpoints is
intensified, leading to development of the positive space
charge around the sharpenedpoints. The size of such a space
chargedependson many factors, the most important being the
+
4xq)(H&+Dy
%&c
4xq&c+lI+)3’*
It can be shown that a relatively small space charge, qSo
above the sharpenedpoints, (a small fraction of the charge of
the steppedleader) causesa significant reduction of the total
electric field strengthat the points. This is becausethe electric
field is proportional to the size of the charge but inversly
proportionalto the squareof the height of this charge.
The more current that is flowing from the sharpenedpoints
into the air, and the longer duration of that current flow, the
larger the space charge will be. An increasing space charge
will weakenthe electric field at the points, The point discharge
current will continue to flow until the electric field strength
drops below the level where the further ionization will cease
to exist. At this particular phaseof the lightning development
process,the situation exists where the space chargeabove the
sharpenedpoints acts as a shield, making a direct lightning
stroke into the points impossible. This well known
phenomenon leads to a better understanding as why a
lightning rod sometimesfails to attract lightning.
Unfortunately, a favorable situation for lightning protection
situation with regard to lightning charges and space charge
does not remain static during the process of lightning
progressing.Qnce developed,the spacecharge is driven away
from the points by the forces of electric fields and wind.
Traveling far enoughfrom the spacechargewill not shield the
points anymore.The field strength at the points will increase
again, and new ionization processwill take place. But during
each ensuingperiod, the field strengthensmuch more rapidly
and becomesstrongerwith each step of the lightning leaderas
it descendsfrom a thundercloud , approaching closer and
closer to the sharpenedpoints. In such conditions the new
spacechargegeneratedmay be not sufficient to influence the
electric field and will not have enoughtime to move from the
points to provide adequateshielding. The streamerformed in
such circumstanceswill eventually result in establishingthe
conducting path between the descendingstepped leader and
moving upward streamer from the sharpened points. The
direct lightning stroke will occur. And this is a desirableevent
for the lightning rods or other devices designed to collect
lightning strokes. In the case when the space charge is still
large enoughand able to reducethe electric field at the points,
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even within a very short time given by the stepped leader’s
pausesbefore the fmal jump, the direct stroke will be avoided.
And that is desirable performance for the lightning strokes
prevention system.
It becomes obvious from the general discussion of this the
lightning stroke preventative mechanism, that the major
parametersinfluencing the choice of the attachmentpoint for
the descendingsteppedleader at its final stepsare:
. charge lowered by the steppedleader,
l
distance betweentip of the steppedleader and the
points,
. speedof the steppedleader propagationand the time
interval available for formation of the spacecharge
of the required size,
e magnitude of point dischargecurrent
All these parameters are mutually interdependent on each
other.
The charge deposited on the stepped leader channel varies
from a few Coulombs to 10 to 20 C with 5 C being an average
value. Another method of an estimation of the averagecharge
lowered by the steppedleader is the averagecharge density of
1mC per 1 meter of the channel length.
Calculation of the electric field strength at the ground level
according to Equation (3) is not valid in the case of the
initiation of a steppedleader. Equation (3) has to be modified,
taking into consideration that a part of the main negative
charge, Qneg,is moving downwards. That part, AQneg,can be
defmed at any given time fiom the moment of the stepped
leader initiation assuming linear charge density distribution is
as follows (Equation (4)):
AQ,, = PslYHnep-
HT)
AQ.,
or
=
ps~*(Hneg
- v*fh
(4)
where psiis the steppedleader charge density (assumedbeing
constant),
Hr is the height of the steppedleadertip at time t, and
v is the average speedof the steppedleader.
After substitution of these changes into Equation (3) we will
produce Equation (5) for the calculation of E0and E,:
4nso(D2+h;,,)3’2
2Pd
1
4’=0 [ (D2+H;)“*
-
4mo(D2+h;c)3’2
(D2+&q)1’2
+
1
The distance between the tip of the stepped leader and the
sharpened points of the CTS is extremely important at the
fmal steps of the leader propagation, where a so-called
discrimination process will start when ground objects
influence the further path of the leader. If that distance will
reach the length of the striking distance (a distance before the
fmal jump occurs), the lightning stroke will or will not occur.
It will depend on the size of the space charge above the
Charge Transfer System.
Several methods for calculating the striking distance as a
function of the magnitude of the lightning current of the return
stroke have been developed [5]. These methods have quite
large (up to almost 400%) variation of the striking distance for
the same given value of lightning current. The following
analytical expression is used widely by power transmission
lines engineers:
d = 10i”*65,
(6)
where d is the striking distance in [ml, and
I is the amplitude of the lightning current in [kA]
The striking distance together with the height of the
sharpenedpoints determines the final length of the stepped
leader and the size of the charge of the leader channel (without
consideration of charge in multiple branches of the leader).
This data can be used for an estimation of the space charge
that might be generatedby the points during the last steps of
the lightning leader.
The space charge, qse, is a product of the point-discharge
current and duration of that current flowing. Both magnitude
and duration of the point-discharge current depend on the
electric field strength, which is, in turn, a function of the
height and charge of the steppedleader.
Investigations of the point-discharge current in laboratory
conditions resulted in development of the empirical equations
as follows:
I = klV2
or I = k2V(V - Vo),
(7)
where k, and kZ are constants,V is voltage applied across the
gap in a laboratory test setup, and V. is the minimal voltage
caused initiating the ionization process. Studies of the pointdischarge currents in natural weather conditions led to
development of the expression similar to (6) but with
considerationof the speedof the wind past the point:
I = a(V - V0)(W2 + c2V2)ln,
63)
where a, V. and c are constants,V is the potential difference
between the points and their surroundings (this voltage is a
function of the local electric field, height of the points and
their geometry), and W is the speed of the wind past the
points.
When many points are used for the development of the space
charge (like in the CTS), the question is how to estimate the
total current flowing from such a system into the air. There are
two extremesto answer this question. One of the extremes is
that the total current from such a multitude of the points is
equal or even less than the single point-discharge current. The
other extreme is that the total current output fi-om such a
system is equal to a single point-discharge current multiplied
by the number of points in the system. There are some
theoretical and laboratory studies supporting these extremes.
The practical solution of this problem is that the total current
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from the multiple points is a function of spacing between the
Equation (4). Having the engineeringdata
adjacentpoints. The greater this distanceis, the closer the total
of a structureto be protected (height.,size, specific
current is to the product of a single point-discharge current
architecturalor other requirementsor considerations)and
and a number of the points.
the assumedgeometry of the sharpenedpoints of the
The point-discharge current has a pulsed nature. In each
strike prevention system, calculate field enhancement
pulse the current startsto flow from the point into surrounding
coefficient, &, and electric field at the points.
air at the moment when the electric field at the point will reach 5. Compute the minimal spacecharge,qsmrequired to have
the critical value E,,. This current moving away from the point
local electric field reduced to the minimal value Eomin.
createsthe space charge, which reduces the field close to the
This calculations can be performed using the Equation (4)
point. But, because the current depends on the field at the
or (5), where E,h/k, should be used as a value for Eomin,
point, the weakened field will result in decreasingthe current. 6. Computethe multi-point dischargecurrent, IcTS,required
At a certain point, there will be a situation of balance when
to develop the spacecharge qsc.This can be done using
there will be just enough current to create the spacecharge of
the following approximate expression:qse= I,--& where
such a size to produce the field at the point that supplies the
t is the duration of the point-discharge current flow,
which may be estimatedusing lightning data (leader
current. But even that balanced situation will not last for any
stepsaveragelength and speedof propagation, leader
significant period, becauseof the local field change and space
pausesduration, etc.).
charge migration is influenced by the variables of wind and
electric field. At the moment when the electric field reaches 7. Define the number of points required using the total
systemcurrent, Ices, a single point-discharge current, Isp,
the value E,,,h the current will cease.So the total duration of
calculatedaccording to the Equation (7) or (S), and a
the single pulse of the point-discharge current will be the
system efficiency coefficient which value dependson
interval between the moment of initiation and the ceasing of
the point spacing and geometry and is usually obtained as
the current. This time is strongly dependenton the location of
result of laboratory testing.
the lightning charges relative to the point and speed of the
steppedleader propagation.
Conclusion
Engineering approach to design of the CTS
The performance of a system preventing the occurrence of the
The key point to a successful performance of a system direct lightning stroke into the structure protected by such a
designedto prevent direct lightning strokes into a structure is system is described. The major engineering steps to design
the computation of the number of points and their geometry to such a systemare proposed.
produce a space charge which will shield the protected
structure. The following design procedure can be offered to References
define the major parametersof such a system:
[l] Uman M. A. The lightning Discharge, Academic Press,
1. Determine of the worst-case situation. In most casesit
Inc., Orlando, Florida, 1987
might be a situation where the lightning steppedleader is
[2] ChalmersJ.A. Atmospheric Electricity, PergamonPress
within the zone of two - three stepsbefore the “final
Ltd., Oxford, 1967
jump”. In another situations the caseof the positive
[3] Smythe,W. R., Static and Dynamic Electricity,Mc
Grawlightning stroke with the main positive charge located at
Hill, New York, 1950
the bottom of the thunderstorm cell. It might be a situation
[4] Carpenter,R. B., Drabkin M. M., Improvement of
where a thundercloud cell located in close proximity to
Lightning Protection Again.qtDirect Lightning Strokes,
the structure to be protected. In such a situation, a direct
IEEE 1997 International Symposium qn Electromagnetic
lightning stroke takes place betweenthe thundercloud cell
Compatibility
and a streamermoving upwards from the structure (in
[5] Golde, R. H. (ed) Lightning Protection, Vol. 2, Academic
most casesa tall building or an broadcastingtower) to be
Press,New York, 1977
protected.
2. For a chosenworst casesituation, defme the data required
for computation of the local electric field strength
according to Equation (3). This data should include
(if available) local data of lightning activity such as the
frequency of occurrenceof lightning flashesto ground,
probabilistic distribution of lightning currents in return
strokes, chargesaccumulatedin thundercloudsand their
distribution, etc. For example, parametersshown on
Figure 1 of the simplified model of a thundercloudcell,
may vary from location to location, from one country to
another.
3. Compute the local electric field strength accordingto the
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