parameters of lightning strokes a review

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346 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 20, NO. 1, JANUARY 2005

Parameters of Lightning Strokes: A ReviewLightning and Insulator Subcommittee of the T&D Committee

Abstract—The paper presents the statistical data of the signifi-cant parameters of lightning flash, collected by many researchers

over many years around the world. The significant parameters of alightning flash are: peak current, waveshape and velocity of the re-turn stroke, the totalflash charge and

. Negative first strokeshave traditionally been considered to produce the worst stress onthe system insulation. The subsequent negative strokes have sig-nificantly lower peak current but shorter wavefronts. This maystress the system insulation more. The positive strokes have aboutthe same median current value as the negative first strokes andlonger fronts, thus producing less stress. However, their durationis longer than that of the negative strokes. Therefore, the systeminsulation may be damaged because of the lower volt-time char-acteristic for long-duration waves. The positive strokes may alsocause more thermal damage because of their significantly higher

charge and

. The relationship between the return-stroke ve-locity and the current peak is a significant parameter in estimatinglightning-induced voltages and also in estimating the peak currentfrom the radiated electromagnetic fields of the lightning channel.For better accuracy, the current and the velocity should be mea-sured simultaneously. Better methods to measure the stroke cur-rent need to be developed. Correlation coefficient between variouslightning parameters is another important parameter which willaffect the analysis significantly. Lightningcharacteristics should beclassified according to geographical regions and seasons instead of assuming these characteristics to be globally uniform.

Index Terms—Lightning parameters, lightning statistics.

I. INTRODUCTION

AN accurate knowledge of the parameters of lightning

strokes is essential for the prediction of the severity of

the transient voltages generated across power apparatus either

by a direct stroke to the power line/apparatus, or by a nearby

lightning stroke (indirect stroke). However, no two lightning

strokes are the same. Therefore, the statistical variations of

the lightning-stroke parameters must be taken into account in

assessing the severity of lightning strokes on the specific design

of a power line or apparatus.

The lightning return-stroke current and the charge delivered

by the stroke are the most important parameters to assess the

severity of lightning strokes to power lines and apparatus. Thereturn-stroke current is characterized by a rapid rise to the peak,

, within a few microseconds and then a relatively slow decay,

reaching half of the peak value in tens of microseconds. The

return-stroke current is specified by its peak value and its wave-

shape. The waveshape, in turn, is specified by the time from zero

Manuscript received March 28, 2003. Paper no. TPWRD-00144-2003.P. Chowdhuri, J. G. Anderson, W. A. Chisholm, T. E. Field, M. Ishii,

J. A. Martinez, M. B. Marz, J. McDaniel, T. R. McDermott, A. M. Mousa,T. Narita, D. K. Nichols, and T. A. Short are members of the Task Force 15.09on Parameters of Lightning Strokes.

Digital Object Identifier 10.1109/TPWRD.2004.835039

to the peak value ( , front time) and by the time to its subse-quent decay to its half value ( , tail time). The tail time being

several orders of magnitude longer than the front time, its statis-

tical variation is of lesser importance in the computation of the

generated voltage. The generated voltage is a function of the

peak current for both the direct and indirect strokes. For back-

flashes in direct strokes and for indirect strokes the generated

voltage is higher the shorter the front time of the return-stroke

current [1]. The front time (and the tail time, to a lesser extent),

influence the withstand capability (volt-time characteristics) of

the power apparatus. The charge in a stroke signifies the energy

transferred to the struck object. The ancillary equipment (e.g.,

surge protectors) connected near the struck point will be dam-

aged if the charge content of the stroke exceeds the withstandcapability of the equipment. The return-stroke velocity will af-

fect the component of the voltage which is generated by the in-

duction field of the lightning stroke [1]. Field tests have shown

that the parameters of the first stroke are different from that of

the subsequent strokes.

Lightning being random in nature, its parameters must be ex-

pressed in probabilistic terms from data measured in the field.

The objective of this report is to present the statistical data of

the significant parameters collected by many researchers over

many years around the world.

II. DATA ACQUISITION TECHNIQUES

Compilation of lightning parameters is best accomplished by

direct measurements on actual lightning. Data gathering can be

accelerated by triggered lightning, whereby a rocket trailing a

thin conducting wire is shot toward a charged cloud. The rocket

is struck by lightning as it approaches the charged cloud and

the trailing thin wire is evaporated by the heavy current flow,

thus simulating the lightning channel. The first stroke cannot be

simulated by triggered lightning. It does simulate the subsequent

stroke.

As tall structures are struck more frequently by lightning,

the return-stroke current has traditionally been measured by in-

stalling current transducers either at the top or the bottom of tall towers. The output of the current transducer is then fed into

a recording device. The magnitude of the return-stroke current

has also been measured by magnetic links, which are small bun-

dles of high retentivity steel laminations about three centime-

ters long, placed at various locations on the shield wires and

transmission-line tower legs. The currents flowing through these

parts magnetize the magnetic links, and the peak current can be

estimated from the magnetization of the magnetic links. How-

ever, such measurements have long been discarded because of

unreliability. The peak of the return-stroke current has also been

estimated by measuring the radiated magnetic field of the light-

ning stroke. The relationship between the peak current, ,

0885-8977/$20.00 © 2005 IEEE



CHOWDHURI et al.: PARAMETERS OF LIGHTNING STROKES: A REVIEW 347

and the radiated electric field, , was derived from the trans-

mission-line model of the lightning stroke for a lossless earth

[2]:

and (1)

where c=velocity of light in free space, D=distance of the

stroke from the antenna, =velocity of the return-stroke, and

=peak magnetic induction.

III. STATISTICAL DISTRIBUTION OF LIGHTNING

STROKE PARAMETERS

From field data on lightning strokes to masts, chimneys, etc.,

the statistical variation of the lightning stroke parameters can

be approximated by a log-normal distribution, where the statis-

tical variation of the logarithm of a random variable, x, follows

the normal (Gaussian) distribution. In that case, the probability

density function, p(x), of x is given by [1], [3], [4]:

(2)

where =standard deviation of , and =median value

of x. Putting, , the cumulative

probability, , that the parameter will exceed x, is given by

integrating (2) between u and , giving:

(3)

As an example, if the critical current of flashover of an over-

head power line is 20 kA, then from Table I,

and .

; or .

That is, the probability of a negative first-stroke current greater

than 20 kA is 82.11%.

The joint probability density function of two stroke parame-

ters, x and y, can be expressed as:

(4)

where

and =coef ficient of correlation.

If x and y are independently distributed, then , and

. The cumulative probability that

and :

(5)

where , and

. Similarly, if , the joint cumulative

probability is given by:

(6)

The conditional probability density function of y for a given

can be found by change of variables [5], [6]:

(7a)

(7b)

where

and

(8a)

This new log-normal distribution of y has then a median

value, , which is the antilog of b and a standard deviation,

. b can be written in an alternate form:

(8b)

or (8c)

where

(8d)

and

(8e)

Such relationships, i.e., (8c), among lightning parameters

have been found and are shown later (Table XI). For cumulative

probability of y from to :

By putting and ,

(9)




If, however, the conditional is for x within a range, e.g., to

, then (7a) needs to be integrated:

(10)

Two examples of the conditional probability are shown below.

In the first example, the limiting current is 20 kA, i.e.,

for a given front time of current, . Assuming

median current from Table I, , , me-

dian front time, and , and applying

(9), the cumulative probability is shown below for three values

of the correlation coef ficient, , between and .

Such analysis is applicable for estimating outage rates for

strokes to nearby ground and also for back flash outages. Without

the conditional of front time, the cumulative probability of cur-

rent exceeding 20 kA, by applying

(3).

The second example pertains to gapless MOV surge protec-

tors for the case of a lightning stroke hitting a phase conductor

of a shielded line [7]. For a perfectly shielded line, the shieldingcurrent will be equal to the critical current, and no insulator

flashover will occur. However, currents lower than the shielding

current may hit the phase conductors; the charge in the light-

ning flash will then be absorbed by the surge protector. If this

chargeexceeds the limit of the protector, then the surge protector

will be damaged. Assuming the shielding current, ,

and the limiting charge of the surge protector, (i.e.,

), what is the probability for

, given ? The statistical parameters of the

positive-polarity lightning flash are as follows: ,

, , and . From

(10), putting and , taking the lower limit of tobe very small, e.g., :

and

From (10), the probabilities for three values of the correlation

coef ficient, , are shown below:

TABLE ISTATISTICAL PARAMETERS OF FIRST NEGATIVE RETURN-STROKE

CURRENT [4], [9]–[11]

Note 1: References [4], [9]–[11] suggest that the measured

distribution of the first negative stroke is better approximated

by two straight lines intersecting at 20 kA when plotted on a

probability paper. Then, for ,

and ; for , , and

. However, the log-normal approximation of the

entire distribution can be represented by: , and

.

Note 2: is time interval between the 10% and 90%

of the current peak on the current wavefront,

.

; ;

; ; =max. current rate

of rise on wavefront.

Note 3: .

Without the conditional of ,

and .

IV. FIRST NEGATIVE RETURN-STROKE CURRENT

The log-normal characteristics of the negative-polarity first

stroke are shown in Table I where is the standard deviation of

the log (base e) of the variate.

Most of the data were taken by Berger [8], which were later

analyzed and updated [4], [9]–[11]. Fig. 1 shows the waveshape

of the typical return-stroke current as recorded by Berger.

The cumulative probability distribution, , of the re-

turn-stroke current, , can be estimated from (3) by replacing x

with and with (median value). The values of andare given in Table I. A much simpler form for , approx-

imating the log-normal distribution for the return-stroke current

in (3), was given by Anderson [12]:

(11)

Reference [13] provides data from field tests during

1994–1997 in Japan. Sixty 500-kV double-circuit trans-

mission towers with overhead shield wires were instrumented.

The towers included 1000-kV design, but operating at 500 kV.

The tower height ranged from 40 m to 140 m, and the altitude of

the observed sites varied from 150 m to 1500 m. The lightningstroke currents were measured by Rogowski coils, attached to




Fig. 1. Waveshape of typical return-stroke current [4].

TABLE IISTATISTICAL PARAMETERS OF LIGHTNING STROKES IN JAPAN [13]

Note: ;

TABLE III

STATISTICAL DISTRIBUTION OF MULTISTROKE NEGATIVE

LIGHTNING FLASHES [10]

2.5-m long rods on the top of the towers. The amplitude of the

peak current was found to be dependent neither on tower height

nor on altitude. The statistical data are shown in Table II.

V. SUBSEQUENT NEGATIVE RETURN-STROKE CURRENTS

A ground flash very frequently consists of multiple strokes.

Based on a survey of almost 6000 flash records from different

regions of the world, Anderson and Eriksson estimated the fol-

lowing percentages (Table III) of multiple strokes in a ground

flash [10].

In general, there is no correlation between the first and the

subsequent stroke peak amplitudes. The median value of the

subsequent stroke is significantly lower than that of the first

stroke. Assuming log-normal distribution, the median value and

the standard deviation of the subsequent stroke have been pro-

posed by Eriksson as [9]:

and (12)

The cumulative probability that a subsequent-stroke current

will exceed a given level, , can be estimated, similar to (3),

with the statistical parameters of (12). A simplified equation,

similar to (11) has also been proposed [14]:

(13)

Although the median value of the subsequent stroke current

is lower than that of the first stroke, the individual value of a

subsequent-stroke current can be higher than the preceding first-

stroke current; factors as high as 200% have been recorded [11].

The physical phenomena associated with artificially triggered

lightning are believed to be similar to that of the subsequent

stroke of natural lightning. However, there may be potential

disparities between triggered lightning and the subsequent

stroke of natural lightning [15]: (i) the triggered discharge

occurs under cloud conditions where a discharge may not have

occurred under natural conditions, (ii) the lower portion of the triggered lightning channel may be contaminated by metal

vapor. However, in spite of the possible differences between

triggered lightning and subsequent strokes of natural lightning,

it will be interesting to compare the field-test results. Fisher

et al. [15] have reported extensive test results of triggered

lightning, and have compared the various parameters obtained

from their tests and those of Berger [8] on subsequent strokes

from natural lightning, as reported by Anderson and Eriksson

[10]. These comparisons are shown in Table IV.

It should be mentioned that in their triggered lightning field

tests, Fisher et al. found very little or no correlation between

peak current and and time to half value on the current tail.

There were, however, strong correlations between the peak cur-rent and (correlation coef ficient, ) and

.

VI. POSITIVE STROKES

Less than 10% of the ground flashes are of positive polarity.

However, the incidence of positive ground flashes varies season-

ally, being more frequent in the winter. It also varies globally.

Also, very tall structures produce upward positive strokes, in

contrast to the usual downward strokes. Reference [8] states that

the analysis was made only on the downward flashes. However,

Berger suggested later that these strokes were upward negative

leaders followed by downward flash from positively-charged

cloud [16]. The parameters of the positive stroke/ flash are given

in Table V.

The median value (35 kA) of the positive-stroke current in

Table V is somewhat higher than that of the first negative-stroke

current. However, this could be misleading because the max-

imum value of the positive-stroke currents are significantly

higher than that of the first negative-stroke current. According

to [8], 5% of the positive strokes exceed 250 kA, the corre-

sponding magnitude of the first negative strokes being only 80

kA.

The incidence of positive strokes significantly increasesduring the winter months. Winter lightning data were collected




TABLE IVCOMPARISON BETWEEN TWO STUDIES ON NEGATIVE SUBSEQUENT-STROKE CURRENT PARAMETERS [10], [15]

Note: ; ; ;

TABLE VSTATISTICAL PARAMETERS OF POSITIVE STROKES [8]

Note 1: (front time) is the time interval between 2-kA point

on front and the first peak.

(stroke duration) is the time interval between 2-kA point

on front and the 50% of peak current on tail.

;

.

Note 2: Numbers in parenthesis are for negative first strokes.

Note 3: .

TABLE VISTATISTICAL PARAMETERS OF POSITIVE STROKES IN WINTER [17]

Note: ; is the time interval between the start

of the wave and the 50% of peak current on tail.

at Fukui (at sea level) in Japan [17]. The height of the mea-surement tower was 200 m. The statistical data on the winter

positive lightning strokes are given in Table VI. No statistical

difference was found between the cumulative statistical distri-

butions of the peak values of the positive- and negative-polarity

currents. All these incidents were upward strokes.

Two types of lightning were reported in Fukui [17]: one type

with high peak currents and strong luminosity of the lightning

channel (type-A), and the other type with small current peaks

and weak lightning-channel luminosity (type-B).

Comparing Tables IV–VI, it should be noticed that the front

time and duration of the positive strokes are significantly longer

and the front steepness is lower than that of the negative strokes.

The same is true for the winter positive strokes compared to thatof the summer positive strokes.

VII. TYPICAL LIGHTNING CURRENT WAVESHAPES

More than 90 percent of the cloud-to-ground strokes are of

negative polarity, except for seasonal and regional variations.

According to [8], the positive-polarity stroke currents do not

have enough common features to produce an acceptable mean

waveshape. This could also be partly due to the small number

of positive strokes recorded.

The waveshape of the mean negative first stroke current is

shown in Fig. 1. Most of the data came from Berger’s work on

Mount San Salvatore in the southern part of Switzerland, col-

lected by a 60-m mast. This waveshape has distinctly a con-

cave wavefront with the greatest rate of change near the peak.

Many of the current waves have two peaks, the second one being

higher in magnitude. The front time is based on the first peak,

and the peak amplitude on the second peak.

The negative subsequent stroke current has, in general,

shorter wavefront than that of the negative first stroke current.

The negative subsequent stroke currents do not show the pro-nounced concavity of the wavefront of the first stroke current.

This is shown in Fig. 2 [4].

The concavity of the negative first stroke current, i.e., the ini-

tial slow rise followed by fast rise, may be attributed to the up-

ward streamer from the object to be struck reaching out to the

downward streamer from the cloud [4]. The slow-rising upward

streamer carries comparatively small current. However, when

the upward streamer meets the downward leader, the current

rises fast. As the subsequent strokes are not preceded by up-

ward streamers, the wavefront of these strokes do not show the

concavity.

Several empirical equations have been proposed for the wave-shape of the negative first stroke current [9], [11], [18], of which

the equation proposed in [18] has been widely used. This is

given by:

(14)

where =peak current, =correction factor of the peak cur-

rent, , , =time constants determining current rise-

and decay-time, respectively, and n=current steepness factor. It

was stated in [18] that the usual double-exponential function to

represent a transient waveshape has a discontinuity of its first

derivative at ; therefore, it is not convenient for the LEMPcalculations. This dif ficulty does not arise with (14).




Fig. 2. Examples of negative-polarity return-stroke currents [4]. Uppermost

curve: first stroke; middle curve: second stroke; bottom curve: third stroke.

VIII. STROKE CHARGE

Most of the charge delivered by lightning flashes does not

occur during the current pulses with the high current peaks. In-

stead, it is contained in the slow continuing low-magnitude cur-

rents between or after the high current peaks. To some extent,

a flash behaves like an arc welder as far as surface ablation and

arc ignition is concerned. Reference [8] provides observational

results for a large number of flashes. However, for delivered

charge, statistics of the highest magnitudes of charge are of most

concern, and only a few observations always exist at the end of

any probability curve. Hence, for the data of most interest, the

probable error is the highest.

Following [8] and assuming log-normal probability distri-

bution, the parameters for the statistical distribution of the

stroke/ flash charge were developed and given in Table VII. The

numbers in parenthesis in Table VII are from [15].

The following approximate cumulative probability equations

for delivered charge were developed from data in [8], where

is the probability that the charge Q (in coulombs) will be

exceeded in a single flash.Total charge delivered by a negative flash:

(15)

Total charge delivered by a positive flash:

(16)

Charge delivered by a negative first stroke:

(17)

TABLE VIISTATISTICAL PARAMETERS OF STROKE /FLASH CHARGE [8], [15]

TABLE VIIISTATISTICAL PARAMETERS OF FLASH

[8], [15]

Charge delivered by a negative subsequent stroke:

(18)

Charge delivered by a positive stroke:

(19)

The charge delivered by positive and negative strokes is only

within the first two milliseconds. Charge beyond that time is

classified as in a continuing current.

Another way to assess the thermal severity of a lightning flash

is to estimate the integral of of the flash. Table VIII shows

the data from [8]. is the median value of . The num-

bers in parenthesis are from [15].

It should be borne in mind that is a measure of thermal

severity if the current flows into a constant resistance. For most

lightning strikes the current flows into either a cathode spot

whose voltage drop is quasiconstant or into an impedance that

reduces dramatically as current increases making much less

heating.

IX. RETURN-STROKE VELOCITIES

The field data from four papers [19]–[22] were investigated.

In [19], both the straight-line velocity and the track (two-dimen-

sional) velocity were tabulated for 36 strokes each. Of the 36points, only 7 were for the first stroke. In [20], 16 more mea-

surement points were given. However, they were not given in

tabular form, and the velocities were plotted without differen-

tiating between the first and the subsequent strokes. Therefore,

the data from [20] could not be used. Of the 14 data points in

[21], only 4 were from the first stroke. In [22], of the 63 data

points, 17 were for the first strokes. Hence, of the 113 measured

velocities, 28 were for the first stroke and 85 were from the sub-

sequent strokes. Table IX compares the mean and the standard

deviation of the return-stroke velocity for both the first and the

subsequent strokes.

It has been observed that the return-stroke velocity, for both

the first and the subsequent strokes, decreases as the stroke pro-gresses upwards toward the cloud [22]. Therefore, the average




TABLE IXCOMPOSITE FIELD DATA ON VELOCITY OF RETURN STROKES NEAR GROUND [19], [21], [ 22]

TABLE XCOMPOSITE FIELD DATA ON RETURN-STROKE VELOCITY [19], [21], [22]

DATA FROM REF. [22] FOR CHANNEL LENGTH OF AT LEAST 0.7 km

velocity measured over a longer channel length will be lower

than that for a shorter channel length. In [22], two sets of data

were given; one set for observations at ground levels, and the

other set for channel lengths of at least 0.7 km. These data, to-

gether with the data from [19] and [21] are shown in Table X.

There is significant disparity in results among the three

studies. These differences may be attributed to: i) region; ii)

sample size; iii) channel length; iv) experimental error. The

tests in [19] were performed in South Africa; the tests in [21]

were performed in Albany, NY; and the tests in [22] were at theKennedy Space Center in Florida and at the Langmuir Labora-

tory near Socorro, NM. The mean first return-stroke velocities

in Florida and New Mexico were 66 and 150 ,

respectively; similarly, for the subsequent strokes 110

and 130 , respectively. The measurement error in [21]

was estimated to vary between 30 to 60%, and the maximum

error in [22] was estimated to be 35% or less. The estimated

error in [19] is not known. In [21], some measurements were

taken within 300 m of the ground, and some within 1 km of the

ground. In [22], some measurements were taken near ground

(1.3 km or less), and some were taken over a minimum of 0.7

km of channel measured from the ground. For [19], the channel

length and height are not exactly known, but is estimated to belonger [22].

As the return-stroke currents were not measured concurrently,

the cumulative distribution of velocity was calculated first from

the field data, and then this distribution was matched with the

CIGRE cumulative distribution of current [2], [9]. The perti-

nent log-normal parameters of the currents have been shown in

Table I.

Two empirical equations relating the velocity to the current of

the first stroke are widely used. One equation was proposed by

Lundholm [23] and Rusck [24], and the other by Wagner [25].

These equations are plotted in Fig. 3. The disparity is caused

mainly because the old AIEE current distribution was assumed

in the derivation of these equations.

A relationship between the return-stroke current and its ve-

locity is proposed:

(20)

The velocity is plotted as a function of the return-stroke current,

, in Fig. 4.

X. CORRELATIONS BETWEEN LIGHTNING PARAMETERS

As shown in Section III, correlation between lightning pa-

rameters significantly influences the estimation of the cumula-tive probability. Once the correlation coef ficient, , between




Fig. 3. Velocity vs. first-stroke current from composite field data.

,

. (a) Lundholm-Rusck equation; (b) Wagnerequation.

Fig. 4. Proposed velocity vs. first-stroke current relationship. , .

the current and another parameter, y, is known, then the effec-

tive median value of the variate can be found from (8a), andthe probability density function can be estimated from (7b). It

should be borne in mind that certain uncertainties exist in the es-

timation of . Table XI shows , a and d of (8c), and

of (8a). was taken from [4] and [8]; a and d were computed

from (8d) and (8e), respectively; was computed from

(8a) where was taken from Tables I and V for the negative

first strokes and the positive strokes. The values of for the

negative subsequent strokes were computed from the 95% and

5% cumulative probabilities given in Table I of [8].

XI. REGIONAL VARIATION OF RETURN-STROKE CURRENT

The regional variation of the return-stroke current is illus-trated in Tables XII and XIII. The data was taken from the Na-

tional Lightning detection network (NLDN) by Global Atmo-

spherics, Inc. The recent improvements of NLDN has been de-

scribed in [33], [34]. The data shown in Tables XII and XIII

are from the central, northwest and southeast regions of U.S.A.

for four lightning seasons, represented in two 2-year periods

(1997–1998 and 1999–2000). These three regions were selected

to represent the most extreme differences in the characteristics.The areas of the three regions are rectangular, designated with

the southwest and northeast corners by the latitudes and longi-

tudes of these corner points. The log-normal plots of the cumu-

lative probabilities are shown in Figs. 5–7.

The absolute uncertainty in peak current is 20–30% which

is due mainly to modeling errors. The random error between

regions is small due to the large number (typically 6–7) of sen-

sors that are used to estimate the peak current for each individual

flash.

The median current and the standard deviation were

computed from the raw data provided by Global Atmospherics,

Inc. As there is no significant regional variation in the instru-

mentation, the differences in the lightning parameters are pre-dominantly due to the difference in the climates in the three re-

gions. It should be noted that the cumulative probability pro-

files do not entirely fit the log-normal distribution. They seem

to have different slopes in the entire range of current, similar

to the two-slope characteristic of the Berger data [4]. It should

also be noticed that the median value of the positive strokes does

not always exceed that of the negative strokes, e.g., southeast

region of the USA. The small percentage of positive flashes is

probably biased by the misclassification of some small positive

cloud to-cloud discharges as cloud-to-ground flashes [33].

XII. DISCUSSION

Most of the measurements reported here were taken on tall

towers with current transducers either located at the top or the

bottom of the structure. There are several sources of error as-

sociated with such measurements. First, the measured median

current will be different from that to flat ground [26]. Second, re-

flections at both ends of the tower of the traveling current waves

along the tower will distort the recorded current wave.

In recent years, from the National Lightning Detection Net-

work (NLDN), the return-stroke current is estimated from the

radiated magnetic field of the lightning stroke by (1), assuming

the transmission-line model of stroke channel. Several errors areencountered in this method of measurement: i) the return-stroke

velocity is a function of the peak current; therefore, the assump-

tion of a constant velocity is incorrect; ii) several models of the

return stroke have been proposed; none has been accepted as

superior to the others; iii) for nearby strokes, the assumption of

the radiation field is not acceptable; iv) even when the stroke is

distant, the radiated field is attenuated when it reaches the an-

tenna, the degree of attenuation being a function of the ground

resistivity.

The NLDN system was calibrated with peak currents from trig-

gered lightning return strokes lowering negative charge mea-

sured at the NASA Kennedy Space Center, Florida. The radiated

field of the triggered lightning was measured by six sensors,one in Georgia and five in Florida, ranging from 117.9 km to




TABLE XICORRELATION COEFFICIENTS AND DERIVED FUNCTIONS

CONDITIONAL MEDIAN,

TABLE XIIREGIONAL VARIATION OF NEGATIVE RETURN-STROKE CURRENT IN THE USA.

TABLE XIIIREGIONAL VARIATION OF POSITIVE RETURN-STROKE CURRENT IN THE USA.

426.8 km from the trigger site [36]. The tests were later repeated

with about three fold larger data set [37]. A relationship between

the peak current and the magnetic signal strength was proposed

[2]:

(21)

where SS is the signal strength of the magnetic field in arbitraryunits and . This assumed a return-stroke velocity to

be . However, a triggered lightning does not rep-

resent a natural lightning. Moreover, the return-stroke velocity

in a natural lightning is related to the peak current. Using this

relationship from data on negative triggered lightning to pos-

itive strokes is highly unjustified. The attenuation of the radi-

ated field will depend upon the soil resistivity as well as the fre-

quency (waveshape) of the radiated signal. Therefore, applica-

tion of (21) to other natural lightning and to other regions wouldresult in significant error.




Fig. 5. Cumulative probability distribution of lightning strokes in the central region of U.S.A. (a) Negative strokes; (b) positive strokes.

Fig. 6. Cumulative probability distribution of lightning distribution in the northwest region of the USA. (a) Negative strokes; (b) positive strokes.

Additionally, this method estimates only the current peak; it

cannot estimate the waveshape of the current. Reference [27]provides a comprehensive discussion on the limitations in the

measurement of lightning parameters.

The amplitude of the return-stroke current being the most im-

portant parameter of lightning in estimating the severity of the

overvoltage across insulators, an urgent need exists to develop

new techniques to measure lightning return-stroke current. One

possibility is to measure the intensity of luminosity of the light-

ning channel and relate it to the current amplitude [17]. Sev-

eral attempts have been made to measure the return-stroke lu-

minosity [17], [28]–[30]. The profiles of the channel luminosity

against time showed striking resemblance to the double-expo-

nential impulse current wave. The cumulative probability dis-

tribution of the channel luminosity distribution also showed re-semblance to the cumulative probability distribution of the cur-

rent [30]. However, the analysis of [30] showed the relation-

ship between the luminosity and current is neither linear norquadratic. Although a definite correlation was found in [17], no

mathematical formulation was given. However, as was pointed

out in [17], atmospheric conditions, such as rain and fog, will

distort the luminosity and will pose a problem in the calibration.

Another possibility is the spectroscopic study of the lightning

channel to determine its electrical characteristics.

The front time of the return-stroke current is another impor-

tant parameter which is often overlooked. Shorter front time will

produce higher voltages across insulators for both direct and in-

direct strokes [1]. Therefore, this parameter needs to be mea-

sured accurately, and an analytical expression which closely fol-

lows the field data should be specified.

The present standards specify a double-exponential mathe-matical expression to represent the lightning return-stroke




Fig. 7. Cumulative probability distribution of lightning distribution in the southeast region of the USA. (a) Negative strokes; (b) positive strokes.

currents. However, questions have been raised about the

adequacy of this double-exponential waveshape since the

publication of Berger’s data showing concave wavefront of

the negative-polarity first stroke. Of the several analytical ex-

pressions suggested for the concave current wavefront, the one

proposed by Heidler [18] and shown in (14) has been widely

used. Three examples of waveshape plotted by using (14) are

shown in Fig. 8.

None of the three examples in Fig. 8 resembles Fig. 1. The

following questions need to be addressed for considering a con-

cave wavefront to be a standard:a) Is the concavity caused by the upward streamer from the

struck tower? If the upward streamer is responsible for

the concavity, then the concave wavefront should not be

standardized. Many, perhaps most, wavefronts of the re-

turn stroke do not show the concave characteristic.

b) How will the concave wavefront be specified? The front

time may be specified as . In addition, the

maximum steepness ( in should be specified

along with its location on the wavefront.

The severity of insulator voltage stress caused by direct

strokes is not a function of the return-stroke velocity. However,

the induced voltage is a function of return-stroke velocity forindirect lightning strokes [1]. Moreover, it has been postulated

that the return-stroke velocity is a function of the return-stroke

current, increasing with increase of the current peak [23]–[25].

Therefore, the relationship between the current and the velocity

of the return stroke needs to be known to estimate the voltage

induced by the indirect stroke.

Simultaneous measurement of the return-stroke velocity and

the current has not been done in the previous studies; velocity

and current were matched on the basis of equal probability of

occurrence, e.g., the median value of the velocity was matched

with the median value of the current [23]–[25]. Simultaneous

measurement of velocity and current is highly desirable.

All field data show that the first stroke peak current is signif-icantly higher than the subsequent stroke currents for the nega-

tive strokes; however, the steepness of the first negative stroke

is less than that of the subsequent negative strokes. Therefore, it

is possible for an insulator to survive the first stroke but to flash

over during the subsequent stroke. The volt-time characteristics

of the insulator under voltages of different front times will also

play a decisive role in its survival.

The median value of the peak positive stroke current is some-

what higher than that of the negative stroke(Table V). The steep-

ness of the positive stroke current is significantly lower and its

duration is longer than that of the negative stroke. Therefore, the

voltage across an insulator will be lower under a positive stroke.However, it may spark over because of the longer front time and

time to half value of the applied voltage. Therefore, research

on the volt-time characteristics of insulators under nonstandard

lightning voltages for both polarities of voltage should have pri-

ority.

Because of the significantly longer duration of the positive

stroke, its charge and are higher than that of the negative

stroke. This may increase ablation damage at its terminal point.

Worse still, a positive stroke may exceed the thermal capability

of a surge protector because of larger charge (Table VII).

The NLDN data shown in Tables XII and XIII, and in

Figs. 5–7 are widely different from the data for the other parts

of the world, shown in the previous Tables. The NLDN median

currents of both polarities are significantly lower than those of

the other parts of the world.

It appears that lightning statistics vary significantly from one

region to another and also from one season to another in the

same region, such as: (i) return-stroke velocities (Tables IX and

X) in South Africa [19], Albany, NY. [21], Florida and New

Mexico [22], (ii) median currents (Tables XII and XIII). Lati-

tudinal variation of lightning characteristics has been suggested

[31]. By analyzing data from New York to Florida and to the

west up to the Mississippi River, Orville suggested that the peak

return-stroke current is higher in the southern latitudes and de-

creases with increase in the latitude [32]. He proposed that thelonger lightning channels in the south, caused by the higher alti-




Fig. 8. Examples of return-stroke current plotted from (14). (a) ;

;

;

; (b)

;

; ; ; (c) ; ;

;

.

tude of the center of the negatively-charged region in the cumu-

lonimbus cloud (at ) may contribute to the higher peak

current in the southern latitudes. Apart from the meteorological

conditions, the soil resistivity may also be a factor in influencing

the lightning stroke characteristics (e.g., front time). Therefore,

it may be appropriate not to have global statistical parametersfor lightning, but regional and seasonal.

It should also be borne in mind that the instrumentation used

by the various researchers at different times were different. The

measurement accuracy in most cases is not known. One obvious

difference is in the trigger level. Berger’s experiments had a

trigger level of 2 kA [8], [10], whereas those in [13] were 9 kA.

Uniform standards for instrumentation should be formulated.

Lastly, correlation among the various lightning parameters isan important parameter which should not be ignored. Two ex-

amples were given in Section III of the significance of correla-

tion on conditional probability—current front time and charge

current. These were simple computations. Computations can

get more involved in the estimation of outage rates. As an ex-

ample, the outage rates caused by lightning strikes to nearby

ground of a 10-m high line of are given below

for a ground flash density, [35].

Because of this significant influence of the correlation coef fi-

cient, , on the lightning performance of power lines, this pa-

rameter needs to be estimated accurately.

XIII. CONCLUSIONS AND RECOMMENDATIONS

Negative first strokes have traditionally been considered to

produce the worst stress on transmission-line insulation. Sub-

sequent negative strokes have significantly lower peak current

but shorter wavefronts. These subsequent strokes may stress

the system insulation more in some cases, particularly for low

footing resistances and tall structures.Positive strokes have about the same median current value

as the negative first strokes and longer fronts. However, the

extreme current values of positive strokes tend to be higher than

the negative strokes; hence both positive and negative strokes

should be considered in the lightning simulations of overhead

power lines. Positive strokes may also cause more thermal

damage because of their significantly higher delivered charge

and .

Although it has been postulated that the return-stroke ve-

locity is related to the return-stroke current, the current and

the velocity have not been measured simultaneously. Since the

return-stroke velocity is a significant parameter in estimatingthe lightning-induced voltages and also in estimating the re-

turn-stroke currents from measurements of the radiated electro-

magnetic field of the lightning channel, more research is needed

to relate the currents and their associated velocities.

Better methods for making remote measurements of stroke

current magnitudes and waveshapes need to be developed, as

well as formulation of lightning parameters according to geo-

graphic region and season instead of assuming that they are a

globally unified data set.

In making simulations of lightning performance of overhead

power lines, conservative values of stroke parameters are ad-

vised in presence of the many uncertainties that presently exist.

Until these uncertainties are resolved, it is prudent to use thosestroke values obtained by direct oscillographic measurements




and to recognize that approximations are inevitable. It is rec-

ommended that until more data are available:

1) The CIGRE waveshape (Fig. 1) be used whenever pos-

sible.

2) Table I be used for negative first strokes, the Anderson-

Eriksson part of Table IV be used for negative subsequent

strokes, and Tables V and VI be used for positive strokes.3) The field-test return-stroke velocity as a function of re-

turn-stroke current in Fig. 4 be tentatively adopted.

4) The NLDN data on stroke magnitudes be viewed with

caution until the validities of the various assumptions

made in the analysis can be resolved.

5) The approximation equations [(11) and (13)] and

[(15)–(19)] be used for cases where local data are

not available. However, it should be recognized that the

extreme values at very low and high magnitudes are

inadequate.

ACKNOWLEDGMENT

The raw data of the NLDN system was provided by the

Vaisala-GAI, Inc. The Task Force acknowledges the fruitful

critique provided by Dr. K. L. Cummins.

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parameters of lightning strokes a review

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