lightning parameters

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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

AbstractThe paper presents the statistical data of the signi-cant parameters of lightning ash, collected by many researchers

over many years around the world. The signicant parameters of alightning ash are: peak current, waveshape and velocity of the re-turn stroke, the totalash charge and . Negative rststrokeshave traditionally been considered to produce the worst stress onthe system insulation. The subsequent negative strokes have sig-nicantly lower peak current but shorter wavefronts. This maystress the system insulation more. The positive strokes have aboutthe same median current value as the negative rst 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 signicantly higher

charge and

. The relationship between the return-stroke ve-locity and the current peak is a signicant parameter in estimatinglightning-induced voltages and also in estimating the peak currentfrom the radiated electromagnetic elds 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 coefcient between variouslightning parameters is another important parameter which willaffect the analysissignicantly. Lightningcharacteristics should beclassied according to geographical regions and seasons instead of assuming these characteristics to be globally uniform.

Index Terms Lightning parameters, lightning statistics.

I. INTRODUCTION

A N accurate knowledge of the parameters of lightningstrokes is essential for the prediction of the severity of the transient voltages generated across power apparatus eitherby a direct stroke to the power line/apparatus, or by a nearbylightning stroke (indirect stroke). However, no two lightningstrokes are the same. Therefore, the statistical variations of the lightning-stroke parameters must be taken into account inassessing the severity of lightning strokes on the specic designof a power line or apparatus.

The lightning return-stroke current and the charge deliveredby 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. Thereturn-stroke current is specied by its peak value and its wave-shape. The waveshape, in turn, is specied 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 Identier 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 beingseveral orders of magnitude longer than the front time, its statis-tical variation is of lesser importance in the computation of thegenerated voltage. The generated voltage is a function of thepeak current for both the direct and indirect strokes. For back-ashes in direct strokes and for indirect strokes the generatedvoltage is higher the shorter the front time of the return-strokecurrent [1]. The front time (and the tail time, to a lesser extent),inuence the withstand capability (volt-time characteristics) of the power apparatus. The charge in a stroke signies the energytransferred 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 eld of the lightning stroke [ 1]. Field tests have shownthat the parameters of the rst 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 eld.The objective of this report is to present the statistical data of the signicant parameters collected by many researchers overmany years around the world.

II. DATA ACQUISITION TECHNIQUESCompilation of lightning parameters is best accomplished by

direct measurements on actual lightning. Data gathering can beaccelerated by triggered lightning, whereby a rocket trailing athin conducting wire is shot toward a charged cloud. The rocketis struck by lightning as it approaches the charged cloud andthe trailing thin wire is evaporated by the heavy current ow,thus simulating the lightning channel. The rst stroke cannot besimulatedby triggered lightning. It does simulate thesubsequentstroke.

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 intoa recording device. The magnitude of the return-stroke currenthas 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 andtransmission-line tower legs. The currents owing through theseparts magnetize the magnetic links, and the peak current can beestimated 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 beenestimated by measuring the radiated magnetic eld of the light-ning stroke. The relationship between the peak current, ,

0885-8977/$20.00 2005 IEEE


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

and the radiated electric eld, , 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 thestroke from the antenna, =velocity of the return-stroke, and

=peak magnetic induction.

III. S TATISTICAL DISTRIBUTION OF LIGHTNINGSTROKE PARAMETERS

From eld data on lightning strokes to masts, chimneys, etc.,the statistical variation of the lightning stroke parameters canbe approximated by a log-normal distribution, where the statis-tical variation of the logarithm of a random variable, x, followsthe 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 valueof x. Putting, , the cumulativeprobability, , that the parameter will exceed x, is given byintegrating (2) between u and , giving:

(3)

As an example, if the critical current of ashover of an over-head power line is 20 kA, then from Table I,and .

; or .That is, the probability of a negative rst-stroke current greaterthan 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 cient of correlation.If x and y are independently distributed, then , and

. The cumulative probability thatand :

(5)

where , and. Similarly, if , the joint cumulative

probability is given by:

(6)

The conditional probability density function of y for a givencan be found by change of variables [ 5], [ 6]:

(7a)

(7b)

where

and

(8a)

This new log-normal distribution of y has then a medianvalue, , 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 parametershave been found and are shown later (Table XI). For cumulativeprobability of y from to :

By putting and ,

(9)


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

TABLE IISTATISTICAL PARAMETERS OF LIGHTNING STROKES IN JAPAN [13]

Note : ;

TABLE IIISTATISTICAL DISTRIBUTION OF MULTISTROKE NEGATIVE

LIGHTNING FLASHES [10]

2.5-m long rods on the top of the towers. The amplitude of thepeak current was found to be dependent neither on tower heightnor on altitude. The statistical data are shown in Table II.

V. SUBSEQUENT NEGATIVE RETURN -STROKE CURRENTS

A ground ash very frequently consists of multiple strokes.Based on a survey of almost 6000 ash records from differentregions of the world, Anderson and Eriksson estimated the fol-lowing percentages (Table III) of multiple strokes in a groundash [10].

In general, there is no correlation between the rst and thesubsequent stroke peak amplitudes. The median value of thesubsequent stroke is signi cantly lower than that of the rststroke. Assuming log-normal distribution, the median value andthe standard deviation of the subsequent stroke have been pro-posed by Eriksson as [ 9]:

and (12)

The cumulative probability that a subsequent-stroke currentwill exceed a given level, , can be estimated, similar to (3),with the statistical parameters of (12). A simpli ed equation,similar to (11) has also been proposed [ 14]:

(13)

Although the median value of the subsequent stroke currentis lower than that of the rst stroke, the individual value of asubsequent-stroke current can be higher than the preceding rst-stroke current; factors as high as 200% have been recorded [ 11 ].

The physical phenomena associated with arti cially triggeredlightning are believed to be similar to that of the subsequentstroke of natural lightning. However, there may be potentialdisparities between triggered lightning and the subsequentstroke of natural lightning [ 15]: (i) the triggered dischargeoccurs 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 metalvapor. However, in spite of the possible differences betweentriggered lightning and subsequent strokes of natural lightning,it will be interesting to compare the eld-test results. Fisheret al. [15] have reported extensive test results of triggeredlightning, and have compared the various parameters obtainedfrom their tests and those of Berger [ 8] on subsequent strokesfrom 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 eldtests, Fisher et al. found very little or no correlation betweenpeak current and and time to half value on the current tail.There were, however, strong correlations between the peak cur-rent and (correlation coef cient, ) and

.

VI. P OSITIVE STROKES

Less than 10% of the ground ashes are of positive polarity.However, the incidence of positive ground ashes varies season-ally, being more frequent in the winter. It also varies globally.Also, very tall structures produce upward positive strokes, incontrast to the usual downward strokes. Reference [ 8] states thatthe analysis was made only on the downward ashes. However,Berger suggested later that these strokes were upward negativeleaders followed by downward ash from positively-chargedcloud [ 16]. The parameters of the positive stroke/ ash are givenin Table V.

The median value (35 kA) of the positive-stroke current inTable V is somewhat higher than that of the rst negative-strokecurrent. However, this could be misleading because the max-imum value of the positive-stroke currents are signi cantlyhigher than that of the rst negative-stroke current. Accordingto [8], 5% of the positive strokes exceed 250 kA, the corre-sponding magnitude of the rst negative strokes being only 80kA.

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


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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 pointon front and the rst peak.

(stroke duration) is the time interval between 2-kA pointon front and the 50% of peak current on tail.

;.

Note 2 : Numbers in parenthesis are for negative rst strokes.Note 3 : .

TABLE VISTATISTICAL PARAMETERS OF POSITIVE STROKES IN W INTER [17]

Note : ; is the time interval between the startof 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 winterpositive lightning strokes are given in Table VI. No statisticaldifference was found between the cumulative statistical distri-butions of the peak values of the positive- and negative-polaritycurrents. All these incidents were upward strokes.

Two types of lightning were reported in Fukui [ 17]: one typewith high peak currents and strong luminosity of the lightningchannel (type-A), and the other type with small current peaksand weak lightning-channel luminosity (type-B).

Comparing Tables IV VI, it should be noticed that the fronttime and duration of the positive strokes are signi cantly longerand 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. T YPICAL 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 nothave enough common features to produce an acceptable meanwaveshape. This could also be partly due to the small numberof positive strokes recorded.

The waveshape of the mean negative rst stroke current isshown in Fig. 1. Most of the data came from Berger s work onMount 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 beinghigher in magnitude. The front time is based on the rst peak,and the peak amplitude on the second peak.

The negative subsequent stroke current has, in general,shorter wavefront than that of the negative rst stroke current.The negative subsequent stroke currents do not show the pro-nounced concavity of the wavefront of the rst stroke current.This is shown in Fig. 2 [ 4].

The concavity of the negative rst 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 thedownward streamer from the cloud [ 4]. The slow-rising upwardstreamer carries comparatively small current. However, whenthe upward streamer meets the downward leader, the currentrises fast. As the subsequent strokes are not preceded by up-ward streamers, the wavefront of these strokes do not show theconcavity.

Several empirical equations have been proposed for the wave-shape of the negative rst stroke current [ 9], [11 ], [18], of whichthe equation proposed in [ 18] has been widely used. This isgiven 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. Itwas stated in [ 18] that the usual double-exponential function torepresent a transient waveshape has a discontinuity of its rstderivative at ; therefore, it is not convenient for the LEMPcalculations. This dif culty does not arise with (14).


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Fig. 2. Examples of negative-polarity return-stroke currents [ 4]. Uppermostcurve: rst stroke; middle curve: second stroke; bottom curve: third stroke.

VIII. S TROKE CHARGE

Most of the charge delivered by lightning ashes does notoccur 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 ash behaves like an arc welder as far as surface ablation andarc ignition is concerned. Reference [ 8] provides observationalresults for a large number of ashes. However, for deliveredcharge, statistics of the highest magnitudes of chargeare of mostconcern, and only a few observations always exist at the end of any probability curve. Hence, for the data of most interest, theprobable error is the highest.

Following [ 8] and assuming log-normal probability distri-bution, the parameters for the statistical distribution of thestroke/ ash charge were developed and given in Table VII. Thenumbers in parenthesis in Table VII are from [ 15].

The following approximate cumulative probability equationsfor delivered charge were developed from data in [ 8], where

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

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

(15)

Total charge delivered by a positive ash:

(16)

Charge delivered by a negative rst 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 onlywithin the rst two milliseconds. Charge beyond that time isclassi ed as in a continuing current.

Another way to assess the thermal severity of a lightning ashis to estimate the integral of of the ash. Table VIII showsthe 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 thermalseverity if the current ows into a constant resistance. For mostlightning strikes the current ows into either a cathode spotwhose voltage drop is quasiconstant or into an impedance thatreduces dramatically as current increases making much lessheating.

IX. R ETURN -STROKE VELOCITIES

The eld 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 rst stroke. In [ 20], 16 more mea-surement points were given. However, they were not given intabular form, and the velocities were plotted without differen-tiating between the rst 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 rst stroke. In [ 22], of the 63 datapoints, 17 were for the rst strokes. Hence, of the 113 measuredvelocities, 28 were for the rst stroke and 85 were from the sub-sequent strokes. Table IX compares the mean and the standarddeviation of the return-stroke velocity for both the rst and thesubsequent strokes.

It has been observed that the return-stroke velocity, for boththe rst and the subsequent strokes, decreases as the stroke pro-gresses upwards toward the cloud [ 22]. Therefore, the average


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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 lowerthan that for a shorter channel length. In [ 22], two sets of datawere given; one set for observations at ground levels, and theother 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 signi cant disparity in results among the threestudies. These differences may be attributed to: i) region; ii)sample size; iii) channel length; iv) experimental error. Thetests 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 rst return-stroke velocitiesin Florida and New Mexico were 66 and 150 ,respectively; similarly, for the subsequent strokes 110and 130 , respectively. The measurement error in [ 21]was estimated to vary between 30 to 60%, and the maximumerror in [ 22] was estimated to be 35% or less. The estimatederror in [ 19] is not known. In [ 21], some measurements weretaken within 300 m of the ground, and some within 1 km of theground. In [ 22], some measurements were taken near ground(1.3 km or less), and some were taken over a minimum of 0.7km of channel measured from the ground. For [ 19], the channellength 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 rst fromthe eld data, and then this distribution was matched with theCIGRE cumulative distribution of current [ 2], [9]. The perti-nent log-normal parameters of the currents have been shown inTable I.

Two empirical equations relating the velocity to the current of the rst stroke are widely used. One equation was proposed byLundholm [ 23] and Rusck [ 24], and the other by Wagner [ 25].These equations are plotted in Fig. 3. The disparity is causedmainly because the old AIEE current distribution was assumedin 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. C ORRELATIONS BETWEEN LIGHTNING PARAMETERS

As shown in Section III, correlation between lightning pa-rameters signi cantly in uences the estimation of the cumula-tive probability. Once the correlation coef cient, , between


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Fig. 3. Velocity vs. rst-stroke current from composite eld data. , . (a) Lundholm-Rusck equation; (b) Wagner

equation.

Fig. 4. Proposed velocity vs. rst-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). Itshould be borne in mind that certain uncertainties exist in the es-timation of . Table XI shows , a and d of (8c), andof (8a). was taken from [ 4] and [8]; a and d were computedfrom (8d) and (8e), respectively; was computed from(8a) where was taken from Tables I and V for the negativerst strokes and the positive strokes. The values of for thenegative subsequent strokes were computed from the 95% and5% cumulative probabilities given in Table I of [ 8].

XI. R EGIONAL 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 XIIIare 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 withthe 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% whichis due mainly to modeling errors. The random error betweenregions is small due to the large number (typically 6 7) of sen-sors that are used to estimate thepeak current for each individualash.

The median current and the standard deviation werecomputed from the raw data provided by Global Atmospherics,Inc. As there is no signi cant 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-les do not entirely t the log-normal distribution. They seemto have different slopes in the entire range of current, similarto the two-slope characteristic of the Berger data [ 4]. It shouldalso be noticed that the median value of the positive strokes doesnot always exceed that of the negative strokes, e.g., southeastregion of the USA. The small percentage of positive ashes isprobably biased by the misclassi cation of some small positivecloud to-cloud discharges as cloud-to-ground ashes [ 33].

XII. D ISCUSSION

Most of the measurements reported here were taken on talltowers with current transducers either located at the top or thebottom of the structure. There are several sources of error as-sociated with such measurements. First, the measured mediancurrent will be different from that to at ground [ 26]. Second, re-ections at both ends of the tower of the traveling current wavesalong 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 theradiated magnetic eld of the lightning stroke by (1), assuming

the transmission-line model of strokechannel. Several errors areencountered in this method of measurement: i) the return-strokevelocity is a function of the peak current; therefore, the assump-tion of a constant velocity is incorrect; ii) several models of thereturn stroke have been proposed; none has been accepted assuperior to the others; iii) for nearby strokes, the assumption of the radiation eld is not acceptable; iv) even when the stroke isdistant, the radiated eld is attenuated when it reaches the an-tenna, the degree of attenuation being a function of the groundresistivity.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 radiatedeld of the triggered lightning was measured by six sensors,one in Georgia and ve in Florida, ranging from 117.9 km to


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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 repeatedwith about three fold larger data set [ 37]. A relationship betweenthe peak current and the magnetic signal strength was proposed[2]:

(21)

where SS is the signal strength of the magnetic eld 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 velocityin a natural lightning is related to the peak current. Using thisrelationship from data on negative triggered lightning to pos-itive strokes is highly unjusti ed. The attenuation of the radi-ated eld 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 signi cant error.


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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 themeasurement of lightning parameters.

The amplitude of the return-stroke current being the most im-portant parameter of lightning in estimating the severity of theovervoltage across insulators, an urgent need exists to developnew techniques to measure lightning return-stroke current. Onepossibility 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 pro les of the channel luminosityagainst 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 de nite correlation was found in [ 17], nomathematical formulation was given. However, as was pointedout in [ 17], atmospheric conditions, such as rain and fog, willdistort the luminosity and will pose a problem in the calibration.Another possibility is the spectroscopic study of the lightningchannel 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 willproduce 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 eld data should be speci ed.The present standards specify a double-exponential mathe-matical expression to represent the lightning return-stroke


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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 theadequacy of this double-exponential waveshape since thepublication of Berger s data showing concave wavefront of the negative-polarity rst stroke. Of the several analytical ex-pressions suggested for the concave current wavefront, the oneproposed by Heidler [ 18] and shown in (14) has been widelyused. Three examples of waveshape plotted by using (14) areshown in Fig. 8.

None of the three examples in Fig. 8 resembles Fig. 1. Thefollowing 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 forthe concavity, then the concave wavefront should not bestandardized. Many, perhaps most, wavefronts of the re-turn stroke do not show the concave characteristic.

b) How will the concave wavefront be speci ed? The fronttime may be speci ed as . In addition, themaximum steepness ( in should be speci edalong with its location on the wavefront.

The severity of insulator voltage stress caused by directstrokes 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 postulatedthat the return-stroke velocity is a function of the return-strokecurrent, increasing with increase of the current peak [ 23][25].Therefore, the relationship between the current and the velocityof the return stroke needs to be known to estimate the voltageinduced by the indirect stroke.

Simultaneous measurement of the return-stroke velocity andthe current has not been done in the previous studies; velocityand current were matched on the basis of equal probability of occurrence, e.g., the median value of the velocity was matchedwith the median value of the current [ 23][25]. Simultaneousmeasurement of velocity and current is highly desirable.

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

tive strokes; however, the steepness of the rst negative strokeis less than that of the subsequent negative strokes. Therefore, itis possible for an insulator to survive the rst stroke but to ashover during the subsequent stroke. The volt-time characteristicsof the insulator under voltages of different front times will alsoplay 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 signi cantly lower and itsduration 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 andtime to half value of the applied voltage. Therefore, researchon the volt-time characteristics of insulators under nonstandardlightning voltages for both polarities of voltage should have pri-ority.

Because of the signi cantly longer duration of the positivestroke, its charge and are higher than that of the negativestroke. This may increase ablation damage at its terminal point.Worse still, a positive stroke may exceed the thermal capabilityof a surge protector because of larger charge (Table VII).

The NLDN data shown in Tables XII and XIII, and inFigs. 5 7 are widely different from the data for the other partsof the world, shown in the previous Tables. The NLDN mediancurrents of both polarities are signi cantly lower than those of the other parts of the world.

It appears that lightning statistics vary signi cantly from oneregion to another and also from one season to another in thesame region, such as: (i) return-stroke velocities (Tables IX andX) in South Africa [ 19], Albany, NY. [ 21], Florida and NewMexico [ 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 thewest 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-


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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 meteorologicalconditions, the soil resistivity may also be a factor in in uencingthe 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 usedby the various researchers at different times were different. Themeasurement accuracy in most cases is not known. One obviousdifference is in the trigger level. Berger s experiments had atrigger 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 signi cance of correla-tion on conditional probability current front time and charge

current. These were simple computations. Computations canget more involved in the estimation of outage rates. As an ex-ample, the outage rates caused by lightning strikes to nearbyground of a 10-m high line of are given belowfor a ground ash density, [ 35].

Because of this signi cant in uence of the correlation coef -cient, , on the lightning performance of power lines, this pa-rameter needs to be estimated accurately.

XIII. C ONCLUSIONS AND RECOMMENDATIONS

Negative rst strokes have traditionally been considered toproduce the worst stress on transmission-line insulation. Sub-sequent negative strokes have signi cantly lower peak currentbut shorter wavefronts. These subsequent strokes may stressthe 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 rst strokes and longer fronts. However, theextreme current values of positive strokes tend to be higher thanthe negative strokes; hence both positive and negative strokesshould be considered in the lightning simulations of overheadpower lines. Positive strokes may also cause more thermaldamage because of their signi cantly higher delivered chargeand .

Although it has been postulated that the return-stroke ve-locity is related to the return-stroke current, the current andthe velocity have not been measured simultaneously. Since the

return-stroke velocity is a signi cant parameter in estimatingthe lightning-induced voltages and also in estimating the re-turn-stroke currents from measurements of the radiated electro-magnetic eld of the lightning channel, more research is neededto relate the currents and their associated velocities.

Better methods for making remote measurements of strokecurrent magnitudes and waveshapes need to be developed, aswell as formulation of lightning parameters according to geo-graphic region and season instead of assuming that they are aglobally uni ed data set.

In making simulations of lightning performance of overheadpower 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


13/13


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 rst 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 eld-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 assumptionsmade in the analysis can be resolved.

5) The approximation equations [(11) and (13)] and[(15) (19)] be used for cases where local data arenot available. However, it should be recognized that theextreme values at very low and high magnitudes areinadequate.

ACKNOWLEDGMENT

The raw data of the NLDN system was provided by theVaisala-GAI, Inc. The Task Force acknowledges the fruitfulcritique provided by Dr. K. L. Cummins.

REFERENCES

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