Protection AgaindDirect Lightning Strokes by Charge Transfer System

Roy B. Carpenter Jr. Lightning Eliminators & Consultants, Inc.

6687 Arapahoe Rd 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 engineering data 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 creates some complexity for the design process of CTS. The paper discusses the major steps of the engineering approach to the design of 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 instead of preventing the strokes. He then postulated that it would be better to provide a preferable path to earth for lightning by erecting the elevated grounded rods. During the past 250 years the Franklin rod successfUlly protected structures from the lightning-caused damage. And that was the & requirement to the lightning protection against direct hits till last 40 - 50 years.

In the recent 4 decades, due to the explosive progress in computers/electronics technology, the secondary effect of the lightning stroke became the major concern in many cases. Generated by lightning current, the strong magnetic field around the downward conductor connecting the lightning rod to the grounding system caused the induced voltages of such a magnitude that it permanently damaged or caused malfunction 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 consequences of the secondary effect.

Mark M. Drabkin Lightning Eliminators & Consultants, Inc.

6687 Arapahoe Rd Boulder, Colorado, USA

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 electrodes such as lightning rods), when exposed to the strong electric field, start to emit current into the surrounding air. This current is a result of an ionization process in the air surrounding the sharpened points. 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 temperature and 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 thunderstorm cloud is often represented by 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 calculated by the following equation (2):

where: Qpos and Qneg are the positive and negative charges of a thundercloud cell, qpDs is a local positive charge below the thundercloud cell, Hpos, Hneg and hpos are the heights of the corresponding charges above the ground level, and

0-7803-5015-4/98/$10.00 0 1998 IEEE 1094

D is the horizontal distance of the point at the Earth’s surface from the thundercloud cell charges.

H P*s

.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. These values are not in any disagreement with E,, because the electric field, E,, at sharpened points and edges is much stronger than Eo. The field enhancement factor, which is defmed as b = Ep/Eo , depends on the shape, dimensions, and height of the sharpened point. It is difficult to calculate exact value of k, because the analytical solution for most shapes is yet to be developed. However, for the simple forms, like vertical or horizontal conductors, reasonable approximations can be made using the equations developed for a conducting prolate semi-ellipsoid [3]. Calculations of the enhancement coefficient, k, based on this approximation show that k, can be as great as 100 - 600 depending on the electrode height 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 increasing electric field, E,, the ionization of the air surrounding the sharpened points is intensified, leading to development of the positive space charge around the sharpened points. The size of such a space charge depends on many factors, the most important being the

strength of the electric field, wind velocity past the points, and barometric pressure. Appearance of an additional charge located relatively close to the ground changes the total electric field E. [4]. Inserting a new component of total electric field caused by the presence of the space charge 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 charge q,, at the height h,, above the ground.

*o =- 2Qp.Pp + 2QnegHneg 4m+(Ig,, +Tlp3’* 4xq)(H&+Dy 29po&oo + %&c

- 4nq,(h;os+d)3’2 4xq&c+lI+)3’*

It can be shown that a relatively small space charge, qSo above the sharpened points, (a small fraction of the charge of the stepped leader) causes a significant reduction of the total electric field strength at the points. This is because the electric field is proportional to the size of the charge but inversly proportional to the square of the height of this charge.

The more current that is flowing from the sharpened points into the air, and the longer duration of that current flow, the larger the space charge will be. An increasing space charge will weaken the 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 phase of the lightning development process, the situation exists where the space charge above the sharpened points 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 sometimes fails 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 space charge is driven away from the points by the forces of electric fields and wind. Traveling far enough from the space charge will not shield the points anymore. The field strength at the points will increase again, and new ionization process will take place. But during each ensuing period, the field strengthens much more rapidly and becomes stronger with each step of the lightning leader as it descends from a thundercloud , approaching closer and closer to the sharpened points. In such conditions the new space charge generated may be not sufficient to influence the electric field and will not have enough time to move from the points to provide adequate shielding. The streamer formed in such circumstances will eventually result in establishing the conducting path between the descending stepped leader and moving upward streamer from the sharpened points. The direct lightning stroke will occur. And this is a desirable event for the lightning rods or other devices designed to collect lightning strokes. In the case when the space charge is still large enough and able to reduce the electric field at the points,

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even within a very short time given by the stepped leader’s pauses before 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 parameters influencing the choice of the attachment point for the descending stepped leader at its final steps are:

. charge lowered by the stepped leader, l distance between tip of the stepped leader and the

points, . speed of the stepped leader propagation and the time

interval available for formation of the space charge of the required size,

e magnitude of point discharge current 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 average charge lowered by the stepped leader is the average charge 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 stepped leader. 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) or AQ., = ps~*(Hneg - v*fh (4)

where psi is the stepped leader charge density (assumed being constant),

Hr is the height of the stepped leader tip at time t, and v is the average speed of the stepped leader.

After substitution of these changes into Equation (3) we will produce Equation (5) for the calculation of E0 and E,:

4nso(D2+h;,,)3’2 - 4mo(D2+h;c)3’2 +

2Pd [

1 - 4’=0 (D2+H;)“* (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 sharpened points 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 generated by 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 stepped leader.

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 point- discharge currents in natural weather conditions led to development of the expression similar to (6) but with consideration of the speed of 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 extremes to 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 adjacent points. The greater this distance is, the closer the total current is to the product of a single point-discharge current and a number of the points.

The point-discharge current has a pulsed nature. In each pulse the current starts to flow from the point into surrounding air at the moment when the electric field at the point will reach the critical value E,,. This current moving away from the point creates the space charge, which reduces the field close to the point. But, because the current depends on the field at the point, the weakened field will result in decreasing the current. At a certain point, there will be a situation of balance when there will be just enough current to create the space charge of such a size to produce the field at the point that supplies the current. But even that balanced situation will not last for any significant period, because of the local field change and space charge migration is influenced by the variables of wind and electric field. At the moment when the electric field reaches the value E,,,h the current will cease. So the total duration of the single pulse of the point-discharge current will be the interval between the moment of initiation and the ceasing of the current. This time is strongly dependent on the location of the lightning charges relative to the point and speed of the stepped leader propagation.

Engineering approach to design of the CTS

The key point to a successful performance of a system designed to prevent direct lightning strokes into a structure is the computation of the number of points and their geometry to produce a space charge which will shield the protected structure. The following design procedure can be offered to define the major parameters of such a system: 1. Determine of the worst-case situation. In most cases it

might be a situation where the lightning stepped leader is within the zone of two - three steps before the “final jump”. In another situations the case of the positive lightning stroke with the main positive charge located at the bottom of the thunderstorm cell. It might be a situation where a thundercloud cell located in close proximity to the structure to be protected. In such a situation, a direct lightning stroke takes place between the thundercloud cell and a streamer moving upwards from the structure (in most cases a tall building or an broadcasting tower) to be protected.

2. For a chosen worst case situation, 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 occurrence of lightning flashes to ground, probabilistic distribution of lightning currents in return strokes, charges accumulated in thunderclouds and their distribution, etc. For example, parameters shown on Figure 1 of the simplified model of a thundercloud cell, may vary from location to location, from one country to another.

3. Compute the local electric field strength according to the

Equation (4). Having the engineering data of a structure to be protected (height., size, specific architectural or other requirements or considerations) and the assumed geometry of the sharpened points of the strike prevention system, calculate field enhancement coefficient, &, and electric field at the points.

5. Compute the minimal space charge, qsm required to have local electric field reduced to the minimal value Eomin. This calculations can be performed using the Equation (4) or (5), where E,h/k, should be used as a value for Eomin,

6. Compute the multi-point discharge current, IcTS, required to develop the space charge qsc. This can be done using the following approximate expression: qse = I,--& where t is the duration of the point-discharge current flow, which may be estimated using lightning data (leader steps average length and speed of propagation, leader pauses duration, etc.).

7. Define the number of points required using the total system current, Ices, a single point-discharge current, Isp, calculated according to the Equation (7) or (S), and a system efficiency coefficient which value depends on the point spacing and geometry and is usually obtained as result of laboratory testing.

Conclusion

The performance of a system preventing the occurrence of the direct lightning stroke into the structure protected by such a system is described. The major engineering steps to design such a system are proposed.

References

[l] Uman M. A. The lightning Discharge, Academic Press, Inc., Orlando, Florida, 1987

[2] Chalmers J.A. Atmospheric Electricity, Pergamon Press Ltd., Oxford, 1967

[3] Smythe, W. R., Static and Dynamic Electricity,Mc Graw- Hill, New York, 1950

[4] Carpenter, R. B., Drabkin M. M., Improvement of Lightning Protection Again.qt Direct Lightning Strokes, IEEE 1997 International Symposium qn Electromagnetic Compatibility

[5] Golde, R. H. (ed) Lightning Protection, Vol. 2, Academic Press, New York, 1977

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