6

Characteristics of Lightning Strokes

Francisco De la Rosa

Electric Power Systems

6.1    Introduction

6.2    Lightning Generation Mechanism

First Strokes • Subsequent Strokes

6.3    Parameters of Importance for Electric Power Engineering

Ground Flash Density • Current Peak Value • Correlation between Current and Other Parameters of Lightning

6.4    Incidence of Lightning to Power Lines

6.5    Conclusions

References

6.1    Introduction

Lightning, one of the most spectacular events of Mother Nature, started to appear significantly demystified after Franklin showed its electric nature with his famous electrical kite experiment in 1752. Although a great deal of research on lightning followed Franklin’s observation, lightning continues to be a topic of considerable interest for investigation (Uman, 1969, 1987). This is particularly true for the improved design of electric power systems, since lightning-caused interruptions and equipment damage during thunderstorms stand as the leading causes of failures in the electric utility industry. It is prudent to state that in spite of the impressive amount of lightning research conducted mostly during the last 50 years, the physics of the phenomenon is not yet fully understood. The development of powerful digital recorders with enough bandwidth to capture the microstructure of lightning waveforms and the advent of digital computers and fiber optic communication along with sophisticated direction finding sensors during this period facilitated the extraordinary evolution of lightning monitoring and detection techniques. This allowed for a more accurate description of lightning and the characterization of lightning parameters that are relevant for power system protection.

On a worldwide scale, most lightning currents (over 90%) are of negative polarity. However, it has to be acknowledged that in some parts of the world, mostly over the Northern Hemisphere, the fraction of positive lightning currents can be substantial. A formal assessment of the effects of positive lightning on electric power systems will require using the corresponding parameters, since they may show large deviations from negative flashes in peak current, charge, front duration, and flash duration as it will be described.

6.2    Lightning Generation Mechanism

6.2.1 First Strokes

The wind updrafts and downdrafts that take place in the atmosphere create a charging mechanism that separates electric charges, leaving negative charge at the bottom and positive charge at the top of the cloud. As charge at the bottom of the cloud keeps growing, the potential difference between cloud and ground, which is positively charged, grows as well. This process will continue until air breakdown occurs. See Figure 6.1.

The way in which a cloud-to-ground flash develops involves a stepped leader that starts traveling downward following a preliminary breakdown at the bottom of the cloud. This involves a positive pocket of charge, as illustrated in Figure 6.1. The stepped leader travels downward in steps several tens of meters in length and pulse currents of at least 1 kA in amplitude (Uman, 1969). When this leader is near ground, the potential to ground can reach values as large as 100 MV before the attachment process with one of the upward streamers is completed. Figure 6.2 illustrates the final step when the upward streamer developing from a transmission line tower intercepts the downward leader.

The connection point-to-ground is not decided until the downward leader is some tens of meters above the ground plane. The downward leader will be attached to one of the growing upward streamers developing from elevated objects such as trees, chimneys, power lines, telecommunication towers, etc. It is actually under this principle that lightning protection rods work, that is, they have to be strategically located so that they can trigger upward streamers that can develop into attachment points to downward leaders approaching the protected area. For this to happen, upward streamers developing from protected objects within the shielded area have to compete unfavorably with those developing from the tip of the lightning rods, which are positioned at a higher elevation.

FIGURE 6.1  Separation of electric charge within a thundercloud.

FIGURE 6.2  Attachment between downward and upward leaders in a cloud-to-ground flash.

TABLE 6.1 Lightning Current Parameters for Negative Flashes

Parameters	Units	Sample Size	Value Exceeding in 50% of the Cases
Peak current (minimum 2 kA)	kA
First strokes		101	30
Subsequent strokes		135	12
Charge (total charge)	C
First strokes		93	5.2
Subsequent strokes		122	1.4
Complete flash		94	7.5
Impulse charge (excluding continuing current)	C
First strokes		90	4.5
Subsequent strokes		117	0.95
Front duration (2 kA to peak)	μs
First strokes		89	5.5
Subsequent strokes		118	1.1
Maximum di/dt	kA/μs
First strokes		92	12
Subsequent strokes		122	40
Stroke duration (2 kA to half peak value on the tail)	μs
First strokes		90	75
Subsequent strokes		115	32
Action integral (∫ i2dt)	A2
First strokes	s	91	5.5 × 104
Subsequent strokes		88	6.0 × 103
Time interval between strokes	ms	133	33
Flash duration	ms
All flashes		94	13
Excluding single-stroke flashes		39	180

Source: Adapted from Berger, K. et al., Electra, 41, 23, 1975.

Just after the attachment process takes place, the charge that is lowered from the cloud base through the leader channel is conducted to ground as a breakdown current pulse, known as the return stroke, travels upward along the channel. The return stroke velocity is around one-third the speed of light. The median peak current value associated to the return stroke is reported to be on the order of 30 kA, with rise time and time to half values around 5 and 75 μs, respectively. See Table 6.1 adapted from Berger et al. (1975).

Associated to this charge-transfer mechanism (an estimated 5 C total charge is lowered to ground through the stepped leader) are the electric and magnetic field changes that can last several milliseconds. These fields can be registered at remote distances from the channel and it is under this principle that lightning sensors work to produce the information necessary to monitor cloud-to-ground lightning.

6.2.2    Subsequent Strokes

After the negative charge from the cloud base has been transferred to ground, additional charge can be made available on the top of the channel when discharges known as J and K processes take place within the cloud (Uman, 1969). This can lead to a number of subsequent strokes of lightning following the first stroke. A so-called dart leader develops from the top of the channel lowering charges, typically of 1 C, until recently believed to follow the same channel of the first stroke. Studies conducted in the past few years, however, suggest that around half of all lightning discharges to earth, both single- and multiple-stroke flashes, may strike ground at more than one point, with separation between channel terminations on ground varying from 0.3 to 7.3 km and a geometric mean of 1.3 km (Thottappillil et al., 1992).

Generally, dart leaders develop no branching and travel downward at velocities of around 3 × 10⁶ m/s. Subsequent return strokes have peak currents usually smaller than first strokes but faster zero-to-peak rise times. The mean interstroke interval is about 60 ms, although intervals as large as a few tenths of a second can be involved when a so-called continuing current flows between strokes (this happens in 25%–50% of all cloud-to-ground flashes). This current, which is on the order of 100 A, is associated to charges of around 10 C and constitutes a direct transfer of charge from cloud to ground (Uman, 1969).

The percentage of single-stroke flashes presently suggested by CIGRE of 45% (Anderson and Eriksson, 1980) are considerably higher than the following figures recently obtained from experimental results: 17% in Florida (Rakov et al., 1994), 14% in New Mexico (Rakov et al., 1994), 21% in Sri Lanka (Cooray and Jayaratne, 1994), and 18% in Sweden (Cooray and Perez, 1994).

6.3    Parameters of Importance for Electric Power Engineering

6.3.1    Ground Flash Density

Ground flash density, frequently referred to as GFD or N_g, is defined as the number of lightning flashes striking ground per unit area and per year. Usually it is a long-term average value and ideally it should take into account the yearly variations that take place within a solar cycle—believed to be the period within which all climatic variations that produce different GFD levels occur.

A 10-year average GFD map of the continental United States (IEEE Guide, 2005) obtained by and reproduced here with permission from Vaisala, Inc. of Tucson, Arizona, is presented in Figure 6.3. Note the considerable large GFD levels affecting remarkably the state of Florida, as well as all the southern states along the Gulf of Mexico (Alabama, Mississippi, Louisiana, and Texas). High GFD levels are also observed in the southeastern states of Georgia and South Carolina. To the west side, Arizona is the only state with GFD levels as high as 8 flashes/km²/year. The lowest GFD levels (<0.5 flashes/km²/year) are observed in the western states, notably in California, Oregon, and Washington on the Pacific Ocean, in a spot area of Colorado and in the northeastern state of Maine on the Atlantic Ocean.

FIGURE 6.3  Ten-year average GFD map of the United States. (Reproduced from Vaisala, Inc. of Tucson, AZ., Standards Information Network, How to protect your house and its contents from lightning, IEEE Guide for Surge Protection of Equipment Connected to AC Power and Communication Circuits, IEEE Press, New York, 2005. With permission.)

It is interesting to mention that a previous (a 5-year average) version of this map showed levels of around 6 flashes/km²/year also in some areas of Illinois, Iowa, Missouri, and Indiana, not seen in the present version. This is often the result of short-term observations that do not reflect all climatic variations that take place in a longer time frame.

The low incidence of lightning does not necessarily mean an absence of lightning-related problems. Power lines, for example, are prone to failures even if GFD levels are low when they pass through high-resistivity soils like deserts or when lines span across hills or mountains, where ground wire or lightning arrester earthing becomes difficult. An exception to this may be a procedure being tested by some utilities to protect high GFD (frequently stricken) transmission line structures on elevated spots in mountainous areas by installing surge arresters directly across the insulator strings (Munukutla et al., 2010). This may prove to be a cost-effective method to deal with lightning-related outages in transmission lines where achieving low footing resistance values may become prohibitive.

The GFD level is an important parameter to consider for the design of electric power and telecommunication facilities. This is due to the fact that power line performance and damage to power and telecommunication equipment are considerably affected by lightning. Worldwide, lightning accounts for most of the power supply interruptions in distribution lines and it is a leading cause of failures in transmission systems. In the United States alone, an estimated 30% of all power outages are lightning related on annual average, with total costs approaching $1 billion (Kithil, 1998).

In De la Rosa et al. (1998), it is discussed how to determine GFD as a function of TD (thunder days or keraunic level) or TH (thunder hours). This is important where GFD data from lightning location systems are not available. Basically, any of these parameters can be used to get a rough approximation of GFD. Using the expressions described in Anderson et al. (1984) and MacGorman et al. (1984), respectively,

$N_{\text{g}}=0.04{\text{TD}}^{1.25}{\text{flashes/km}}^{\text{2}}/\text{year}$

(6.1)

$N_{\text{g}}=0.054{\text{TH}}^{1.1}{\text{flashes/km}}^{\text{2}}\text{/year}$

(6.2)

6.3.2    Current Peak Value

Regarding current peak values, first strokes are associated with peak currents around two to three times larger than subsequent strokes. According to De la Rosa et al. (1998), electric field records, however, suggest that subsequent strokes with higher electric field peak values may be present in one out of three cloud-to-ground flashes. These may be associated with current peak values greater than the first stroke peak.

Tables 6.1 and 6.2 are summarized and adapted from Berger et al. (1975) for negative and positive flashes, respectively. They present statistical data for 127 cloud-to-ground flashes, 26 of them positive, measured in Switzerland. These are the types of lightning flashes known to hit flat terrain and structures of moderate height. This summary, for simplicity, shows only the 50% or statistical value, based on the log-normal approximations to the respective statistical distributions. These data are amply used as primary reference in the literature on both lightning protection and lightning research.

The action integral is an interesting concept, that is, the energy that would be dissipated in a 1 Ω resistor if the lightning current were to flow through it. This is a parameter that can provide some insight into the understanding of forest fires and on damage to power equipment, including surge arresters, in power line installations. All the parameters presented in Tables 6.1 and 6.2 are estimated from current oscillograms with the shortest measurable time being 0.5 μs (Berger and Garbagnati, 1984). It is thought that the distribution of front duration might be biased toward larger values and the distribution of di/dt toward smaller values (De la Rosa et al., 1998).

The action integral is an interesting concept, that is, the energy that would be dissipated in a 1 Ω resistor if the lightning current were to flow through it. This is a parameter that can provide some insight into the understanding of forest fires and on damage to power equipment, including surge arresters, in power line installations. All the parameters presented in Tables 6.1 and 6.2 are estimated from current oscillograms with the shortest measurable time being 0.5 μs (Berger and Garbagnati, 1984). It is thought that the distribution of front duration might be biased toward larger values and the distribution of di/dt toward smaller values (De la Rosa et al., 1998).

TABLE 6.2 Lightning Current Parameters for Positive Flashes

Parameters	Units	Sample Size	Value Exceeding in 50% of the Cases
Peak current (minimum 2 kA)	kA	26	35
Charge (total charge)	C	26	80
Impulse charge (excluding continuing current)	C	25	16
Front duration (2 kA to peak)	μs	19	22
Maximum di/dt	kA/μs	21	2.4
Stroke duration (2 kA to half peak value on the tail)	μs	16	230
Action integral (∫ i2dt)	A2s	26	6.5 × 105
Flash duration	ms	24	85

Source: Adapted from Berger, K. et al., Electra, 41, 23, 1975.

6.3.3    Correlation between Current and Other Parameters of Lightning

Lightning parameters are sometimes standardized for the purpose of the assessment of lightning performance of specific power line designs (IEEE Std 1410-1997, 1997). Although this can be adequately used to determine effectiveness of different lightning protection methods in a comparative basis, it is important to understand the limitations that this approach may encompass: Lightning parameters may show considerable deviations often caused by spatial and temporal variations (Torres, 1998). On the other hand, gathering data on lightning parameters other than current makes it an impossible task. Among the parameters which can be associated with lightning damage are lightning peak current (i_p), rate of rise (T_front and peak di/dt), charge transfer (Q_imp and Q_flash), and energy (action integral), as described in De la Rosa et al. (2000). Unfortunately, contemporary lightning detection systems (LDS) are not able to provide accurate estimates of many of these parameters, including the current, since they are designed only to sense and record radiated electric and magnetic fields within hundreds of kilometers from the source. Nevertheless, it seems tangible to envision that even with the limited accuracy of lightning current derived from LDS, it will be possible to infer other lightning parameters directly linked to lightning damage. This will allow us to continue assessing the efficacy of lightning mitigation methods based on records of lightning current and other parameters obtained from LDSs.

Table 6.3 shows an interesting correlation study conducted by Dellera (1997) where he found moderate-to-high correlation coefficients between lightning peak current with other parameters measured in a number of research experiments that involved lightning strikes to instrumented towers. This work presented a way to obtain estimates of the total probability of a specific range of simultaneous values (e.g., i > I_o and Q > Q_o), thereby refining the probability estimates for the conditions under which a lightning-related failure may occur. Table 6.3 comprises relevant findings for positive flashes, negative first strokes, and negative subsequent strokes. The table entries for parameters in negative discharges provide more accurate results, due to broader bandwidth (higher frequency) recording instruments. Table entries that are not filled in (—) were not analyzed by Dellera.

To illustrate the interpretation of the table, we observe that a moderate-to-high correlation is found between lightning current and all but peak rate of rise in positive flashes. Therefore, extreme heating should be expected in arcing or transient currents conducted through protective devices following insulation flashover produced by positive lightning flashes. Note that lightning parameters associated with heat are charge and action integral and that rate-of-change of lightning current is connected with inductive effects, which do not show strong from the correlation table.

Similarly, overvoltages from negative lightning strokes should be associated with peak current producing large inductive overvoltages especially due to subsequent strokes because of their larger di/dt (by a factor of 3 or more) relative to first strokes. Heating effects, however, are loosely correlated with peak current, since correlation coefficient for the total charge (Q_flash) is poor. It is possible that consideration of all stroke peak currents and interstroke intervals in negative flashes, which are available in some modern LDS, will prove a more deterministic means to infer heating due to negative flashes.

TABLE 6.3 Correlation between Lightning Parameters

Lightning Parameter	Correlation (Correlation Coefficient)	Data Source
Positive flashes
Front time (Tfront)	Low (0.18)	Berger and Garbagnati (1984)
Peak rate of rise (di/dt)	Moderate (0.55)	Berger and Garbagnati (1984)
Impulse charge (Qimp)	High (0.77)	Berger and Garbagnati (1984)
Flash charge (Qflash)	Moderate (0.59)	Berger and Garbagnati (1984)
Impulse action integral (Wimp)	—
Flash action integral (Wflash)	High (0.76)	Berger and Garbagnati (1984)
Negative first strokes
Front time (Tfront)	Low (—)	Weidman and Krider (1984)a
Peak rate of rise (di/dt)	Moderate/high (—)	Weidman and Krider (1984)a
Impulse charge (Qimp)	High (0.75)	Berger and Garbagnati (1984)
Flash charge (Qfllsh)	Low (0.29)	Berger and Garbagnati (1984)
Impulse action integral (Wimp)	High (0.86)	Berger and Garbagnati (1984)
Flash action integral (Wflash)	—
Negative subsequent strokes
Front time (Tfront)	Low (0.13)	Fisher et al. (1993)
Peak rate of rise (di/dt)	High (0.7–0.8)	Fisher et al. (1993) and Leteinturier et al. (1990)b
Impulse charge (Qimp)	—
Impulse action integral (Wimp)	—

Source: Adapted from Dellera, L., Lightning parameters for protection: And updated approach, CIGRE 97 SC33, WG33.01, 17 IWD, August 1997.

^a Inferred from measurements of electric fields propagated over salt water.

^b 30%–90% slope, which corresponds to an “average” di/dt (triggered lightning studies).

6.4    Incidence of Lightning to Power Lines

One of the most accepted expressions to determine the number of direct strikes to an overhead line in an open ground with no nearby trees or buildings is described by Eriksson (1987):

$N=N_{\text{g}}\left(\frac{28h^{0.6}+b}{10}\right)$

(6.3)

where

h is the pole or tower height (m)—negligible for distribution lines

b is the structure width (m)

N_g is the GFD (flashes/km²/year)

N is the number of flashes striking the line/100 km/year

For unshielded distribution lines, this is comparable to the fault index due to direct lightning hits. For transmission lines, this is an indicator of the exposure of the line to direct strikes (the response of the line being a function of overhead ground wire shielding angle on one hand and on conductor-tower surge impedance and footing resistance on the other hand).

Note the dependence of the incidence of strikes to the line with height of the structure. This is important since transmission lines are several times taller than distribution lines, depending on their operating voltage level.

Also important is that in the real world, power lines are to different extents shielded by nearby trees or other objects along their corridors. This will decrease the number of direct strikes estimated by Equation 6.3 to a degree determined by the distance and height of the objects. In IEEE Std. 1410-1997, a shielding factor is proposed to estimate the shielding effect of nearby objects to the line. An important aspect of this reference work is that objects within 40 m from the line, particularly if they are equal or higher than around 20 m, can attract most of the lightning strikes that would otherwise hit the line. Likewise, the same objects would produce insignificant shielding effects if located beyond 100 m from the line. On the other hand, sectors of lines extending over hills or mountain ridges may increase the number of strikes to the line.

The aforementioned effects may in some cases cancel one another so that the estimation obtained form Equation 6.3 can still be valid. However, it is recommended that any assessment of the incidence of lightning strikes to a power line be performed by taking into account natural shielding and orographic conditions (terrain undulations) along the line route. This also applies when identifying troubled sectors of the line for the installation of metal oxide surge arresters to improve its lightning performance. For example, those segments of a distribution feeder crossing over hills with little natural shielding would greatly benefit from surge arrester protection.

Finally, the inducing effects of lightning, also described in Anderson et al. (1984) and De la Rosa et al. (1998), have to be considered to properly estimate distribution line lightning performance or when estimating the outage rate improvement after application of any mitigation action. Lightning strokes terminating on ground close to distribution lines have the potential to develop overvoltages large enough to cause insulation flashover. Under certain conditions, like in circuits without grounded neutral, with low critical flashover voltages, high GFD levels, or located on high-resistivity terrain, the number of outages produced by close lightning can considerably surpass those due to direct strikes to the line.

6.5    Conclusions

Parameters that are important for the assessment of lightning performance of power transmission and distribution lines or for evaluation of different protection methods are lightning current and GFD. The former provides a means to appraise the impact of direct hits on power lines or substations and the latter provides an indication of how often this phenomenon may occur. There are, however, other lightning parameters that can be related to the probability of insulation flashover and heating effects in surge protective devices, which are difficult to obtain from conventional lightning detection equipment. Some correlation coefficients observed between lightning peak current and other relevant parameters obtained from significant experiments in instrumented towers are portrayed in this review.

Aspects like different methods available to calculate shielding failures and back flashovers in transmission lines or the efficacy of remedial measures to improve lightning performance of electrical networks are not covered in this summarizing review. Among these, overhead ground wires, metal oxide surge arresters, increased insulation, or use of wood as an arc-quenching device can only be mentioned. The reader is encouraged to further look at the suggested references or to get experienced advice for a more comprehensive understanding on the subject.

References

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Anderson, R.B., Eriksson, A.J., Kroninger, H., Meal, D.V., and Smith, M.A., Lightning and thunderstorm parameters, IEE Lightning and Power Systems Conference Publication No. 236, London, U.K., pp. 57–61, 1984.

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Berger, K. and Garbagnati, E., Lightning current parameters, results obtained in Switzerland and in Italy, in Proceedings of URSI Conference, Florence, Italy, p. 13, 1984.

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De la Rosa, F., Nucci, C.A., and Rakov, V.A., Lightning and its impact on power systems, in Proceedings of International Conference on Insulation Coordination for Electricity Development in Central European Countries, Zagreb, Croatia, p. 44, 1998.

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