ect168

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n 168lightning andHV electrical

installations

E/CT 168 first issued june 1994

Benot de Metz-Noblat

Following graduation from the ESEengineering school, worked forSaint-Gobain first as a researchengineer, then in maintenance andnew projects on a production site.Joined Merlin Gerin in 1986 and iscurrently in the Network Research

Section where he directs a groupinvestigating overvoltages,harmonics and the dynamic stabilityof networks.

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Cahier Technique Merlin Gerin n 168 / p.2

glossary

BIL: (Basic Impulse Level): the impulsevoltage that the insulation of a device isdesigned to withstand.

Gas-insulated metal-enclosedsubstation: a substation which is made

up of only gas-insulated (generallySF6) metal-enclosed switchgear, oftenreferred to in as GIS (Gas-InsulatedSwitchgear) in EHV applications.

Must not be confused with metal-cladswitchgear which is placed in separatecompartments with metal partitions(see IEC 298).

MCOV: (Maximum ContinuousOperating Voltage): the maximumcontinuous voltage that a lightningarrester is designed to withstand.

pace voltage: voltage that may appear

between the feet of someone walking.

Note

Voltage levels have been classed in various manners, defined by national andinternational standards as well as by specifications issued by certain electricitydistribution utilities. The following are definitions for alternating voltages greater than1,000 V:

s the French regulation dated 14 november 1988 defines two voltage levels:

HTA (High Voltage A) = 1 kV < U 50 kV,HTB (High Voltage B) = U > 50 kV.

s CENELEC (European Electrotechnical Standardisation Committee) defined twolevels in a document issued on 27 july 1992:

MV = 1 kV < U 35 kV,HV = U > 35 kV.

s IEC 71 defines a range of maximum voltages for equipment:

range A= 1 kV < U < 52 kV,

range B = 52 kV U < 300 kV,range C = U 300 kV.A revision is planned and will result in only two ranges:

range I = 1 kV < U 245 kV,range II = U > 245 kV.

s the French electrical authority (EDF) presently uses the definition laid out in theFrench regulation mentioned above.

Note: The acronyms EHV and UHV, though occasionally used, have never beenofficially defined by a standard. In this document, EHV is used for voltages greater

than 300 kV.

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lightning and HV electrical installations

summary

1. Introduction p. 4

2. Lightning General p. 5

Main characteristics p. 5

Lightning forecasting p. 6

Impact mechanism andelectro-geometrical model p. 7

3. Lightning and electrical Lightning strikes on a line p. 8

Wave propagation p. 9

Effects of lightning p. 10

4. Protection General p. 10

Protection level 1 p. 11



Protection distance p. 13

Network operation andnon-availability p. 16

Standards p. 175. Example of a lightning study General p. 19

Calculation methods p. 19

Substation modelling p. 19

Deterministic simulations p. 20

Statistical calculation of lightningfrequencies and the associatedrisks p. 20

Interpretation of calculations p. 22

6. Conclusion p. 23

Appendix: bibliography p. 24

The goal of this Cahier Techniquepublication is to:s present an overview of lightningphenomena and their effects on

electrical installations,s present currently available means toprotect installations and limitdetrimental effects,s discuss problems concerningcontinuity of service,s indicate the main steps in lightningstudies on the basis of an exampleinvolving an EHV installation developedby the Network Research Departmentat Merlin Gerin.

This document deals in particular withthe transmission and distribution ofelectricity over medium and high-voltage networks. When designingthese networks, the effects of lightningmust be taken into account forinsulation coordination. Low-voltageaspects are also mentioned, but in nogreat detail.

A short bibliography is included in theappendix.

installations

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1. introduction

Lightning is a major source of distur-bances for all electrical installations andcan affect them in several manners:s all power and voltage levels areconcerned, ranging from EHVtransmission systems to integratedcircuits and including LV powersupplies and data transmission circuits,s it can cause transient disturbances tothe continuity of service, therebyreducing the quality of the power supplysystem,s it can damage equipment and resultin long interruptions in installationoperation,s it can be dangerous for life (pacevoltage, increased potential of exposedconductive parts and earthing circuits).

Lightning has always been a source ofdisturbances for users of electricity, yetthe fairly recent and growing demandfor quality electrical systems (reliability,

availability, continuity of service, etc.)must be taken into account, as well asthe permanent necessity to minimisethe costs of the production and the useof electrical power. It may be said thatin the efforts to improve the abovefactors, lightning has come toconstitute an obstacle. That explainswhy it is now one of the majorpreoccupations of everyone in thesector, whether they are distributors(EDF, private companies),

manufacturers (Merlin Gerin, etc.),designers (design offices, engineeringfirms) or installers.

A study on the effects of lightningcomprises two steps, but first requiresin-depth knowledge of thephenomenon. Starting in the 1970's,major international research programswere initiated, notably by EDF inFrance, and today, sufficient

knowledge on lightning mechanisms isavailable.The two steps are:s anticipate what can happen in a giveninstallation and recommendimprovements. This is possible usingdedicated software, validated byexperience, that simulates installationbehaviour.s carry out an engineering and coststudy on insulation coordination, takinginto account the cost of installations,

maintenance and disruptions inoperation.

Note: insulation coordination consists indefining, on the basis of the voltageand overvoltage levels likely to occur inan installation, one or several levels ofprotection against overvoltages, then inselecting installation equipment andprotection devices. This subject iscovered in the Cahier Techniquen 151.

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2. lightning

Following a few general indications onatmospheric electrical phenomena, thissection presents:s the main characteristics of lightning,considered from an engineering point ofview,s information on forecasting,s the impact mechanism using theelectro-geometrical model.

general

The earth and the electrosphere(conductive zone of the atmosphere,ranging in thickness from roughly 50to 100 km) constitute a natural,spherical capacitor which charges byionisation, producing an electrical field,some several hundred V/m (Volt/meter) in strength, directed toward theearth.In that air being a poor conductor,there is a permanent conductioncurrent associated with the electricalfield, of approximately 1,500 A for theentire earth. Electrical equilibrium is

maintained by discharges via points,rain and lightning strikes.The formation of storm clouds, in effectmasses of water in the form ofaerosols, is accompanied byelectrostatic phenomena in whichdifferently charged particles separate.The light, positively charged particlesare drawn upward by ascending aircurrents and the heavy, negativelycharged particles fall under their ownweight. There may also be clusters ofpositive charges at the bottom ofclouds where there is intense rainfall.

On the overall macroscopic scale, adipole exists.When the limiting gradient of thebreakdown voltage is reached, adischarge takes place in the cloud,between clouds or between the cloudand the earth. The latter case is calledlightning.

The cloud-to-earth electrical field mayreach up to -15 to -20 kV/meter on flatterrain. However, the presence ofobstacles locally increases anddeforms the electrical field by a factorof 10 to 100, or even 1,000, dependingon the form of the irregularities(sometimes referred to as the pointeffect). The air ionisation threshold(approximately 30 kV/cm) is thenreached and discharges due to thecorona effect take place. For relatively

large objects (skyscrapers,smokestacks, towers), thesedischarges may result in lightningstrikes or orient them.

Classification of lightning strikes

A lightning strike between a cloud andthe earth comprises two phases, firstthe development of a predischarge orleader (an ionised channel), whichprovokes the lightning strike itself, adischarge of a visible, high-current arc.

Two main criteria distinguish lightningstrikes, their direction and their polarity:s descending lightning strikes, in whichthe leader runs from the cloud to theearth (relatively flat terrain),

s ascending lightning strikes, in whichthe leader runs from the earth to thecloud (mountainous terrain),s negative lightning strikes when thenegatively charged part of the clouddischarges (80 % of lightning strikesunder temperate climates),s positive lightning strikes when thepositively charged part of the clouddischarges.

main characteristicsWave formLightning, as a physical phenomenon,corresponds to an impulse currentsource, that is a series of discharges ofa quantity of electricity over a shortperiod of time.

The actual wave form is quite variableand comprises a steep front to themaximum amplitude (ranging from afew to 20 microseconds), followed by along decreasing tail of several tens ofmicroseconds (see fig. 1).

The associated spectral field covers aband ranging from 10 kHz to severalMHz.

fig. 1: oscillogram of a lightning impulse current.

0 25 50 75 100 125 150

0

- 20

- 45

time

in s

Iin kA

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Amplitude of lightning strikesThe experimental statistical distributionof lightning strikes as a function of theiramplitude follows a normal distribution

as illustrated in figure 2.

Wave front

The distribution of lightning strikes as afunction of front steepness is illustratedin figure 3.

For lightning studies, the followingvalues are generally used:s amplitudes of 100 kA or 200 kA, withrespective probabilities of 5 % and 1 %that the level will be exceeded,s triangular wave form with a 2 s frontduration and a 50 s time to half value,i.e. a 50 or 100 kA /s front.

Note: this front duration is not that ofthe standardised wave (1.2 s) definedfor laboratory testing (see IEC 60).

Charge of lightning strikes

On average, the charge is a few tens ofcoulombs, but may exceed 300 C.

lightning forecastingIn France, the Mtorage lightningobservation network was set upin 1986.

This network comprises detection

stations spread over the entire countryand linked to the operational computingcentre in Paris.The stations, positioned 200 to 300 kmfrom one another, measure theelectromagnetic waves created bystorm discharges up to 800 km away.Storms can be characterised on thebasis of the following measured data:s location,s date and time (to the millisecond),s wave polarity (> 0, < 0),s wave amplitude (0 to severalhundred kA),s number of arcs.

Mtorage offers a number of usefulservices for a wide range ofapplications, in particular thetransmission and distribution ofelectrical power. Among the servicesoffered are warnings, indications,observations, monitoring, assessments,qualification, consulting and statistics.

The following two forecasting elementsare used in lightning studies.

Keraunic level Nk

This corresponds to the number of daysper year when thunder is heard at a

fig. 3: experimental statistical distribution of positive and negative lightning currents as a

function of front steepness (IEEE).

di

d t(kA / s)

fig. 2: experimental statistical distribution of positive and negative lightning strikes as a function

of their amplitude (IEEE).

0.1

0.51

510

20

30

40506070

80

90

99

1 2 5 10 20 50 100 200 1,000

positive

lightning

strikes

99.9 %

negative

lightning

strikes

amplitude (kA)

IEEE

average

probability

0.1

0.9

1

5

10

2030

40506070

80

90

99

0.1 0.5 50 100

positive

lightning

strikes

99.9 %

negative

lightning

strikes

1 2 5 10 20

3

969798

99.5

probability

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given location. Though at first glance,this may seem a highly approximatenotion, it is nonetheless a useful value.In France, the average Nk level is 20,

with extremes ranging from 10 in theChannel coast regions to over 30 inmountainous regions.In other parts of the world, Nk levelsmay be much higher, for example over180 in tropical Africa and Indonesia, forexample.

Lightning density NThis is defined as the number oflightning strikes hitting the earth persquare kilometer and per year,whatever the amplitude.In France, density N ranges, dependingon the region, from 2 to 6 strikesper km2 and per year.The general ratio between the twoabove values may be defined, on thebasis of average values, as N = Nk / 7.

impact mechanism andelectro-geometrical modelThe lightning impact mechanism maybe broken down as follows:s a leader originating in a cloudapproaches the ground at low speed.As soon as the electrical field is strong

enough, conduction takes placesuddenly, producing the discharge oflightning.s experimental data has been used toderive the relationship between thedistance separating the beginning (arc)and the end (discharge) of a lightningchannel (i.e. the striking distance), onthe one hand, and the amplitude of thelightning strike, on the other:

d = 9.4 I2/3 or d = 6.7 I0.8

depending on the authors, where:d is the striking distance in meters,

Iis the lightning current in kA.

s an electro-geometrical model canthen be established, similar to the onefor a vertical rod in the example below(see fig. 4).

Consider a vertical rod with a height hand its summit at H. The zones definedin the surrounding space are thefollowing:s zone I, situated between the groundand parabola p. The latter defines thepoints equidistant from H and theground. At the moment of the strike, aleader located in this zone will hit theground because it is closer than H.szone II, situated above the parabola.At the moment of the strike, a leaderlocated in this zone will be captured by

H if the distance to H is less than thestriking distance d.It follows that for a given current I, i.e.for the resultant striking distance d, the

distance x to the rod, called the capturerange, is:

if d > h x = 2 d h h2

if d < h x = d

The capture range of the rodincreases with the amplitude of thelightning strike. For very lowamplitudes, the capture range drops toless than the height of the rod whichcan then capture strikes along itslength. This has been verifiedexperimentally.

fig. 4 : protection zones surrounding a vertical rod.

parabola py

x

H

h/2

h

d

d

h

zone I

ground strikes

zone II

rod capture zone

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3. lightning and electrical installations

This section deals with lightning strikeson a line, wave propagation and theeffects of lightning.

lightning strikes on a lineOn the basis of the electro-geometricalmodel, the frequency of lightning strikescan be calculated using the capturerange of the considered object.

Figure 5 indicates, for a density N = 4(4 lightning strikes per km2 and per

year and a corresponding kerauniclevel of approximately 30), thefrequency of lightning strikes (numberof strikes per year) for a vertical rodwith a height h and for a horizontalconductor with a length of 100 km anda height h.

The general empirical formula forcalculating lightning strikes (totalnumber per year) on a line (towers,phase and earth wires) is the following:

NL = NkN1

30+ l

70

L100

where:Nk = keraunic level,NL = strikes on a line,N1 = strikes on the highest horizontalconductor (see fig. 5),L = lenght of the line in kilometers,l = width of the line in meters (distancebetween outside conductors), = influence coefficient taking intoaccount the influence of towers andearth wires (see fig. 6).

This formula takes into account:s lightning trikes on a conductor (N1),

s presence of outside conductors (l),s distribution between the tower andthe line depending on the structure ofthe line (),s length of the line (L) :s for insulation coordinationcalculations, L 1.5 km is generallyselected because over greaterdistances, the effect of the lightningstrike becomes negligible,s for continuity of service calculations,the important factor is the total length ofthe line exposed to strikes, therefore tointerruptions in service.

Direct lightning strikes(on phase conductors)

When lightning hits a phase conductor

of a line, the total current i(t) at thepoint of impact is split in two and the

two halves are propagated along the

conductor in opposite directions.

The wave impedance Z of the

conductor is 300 to 500 (see fig. 7).The result is an associated voltage

wave:

u(t) = Z i(t)2

At the towers, the voltage increasesand propagates:s as a full impulse, reaching itsmaximum value

Umax = Z I max2

when

ZI max

2 < Ua

where Ua = impulse flashover voltageof the insulators string or of any

protective spark-gap devices that maybe present. This voltage is roughly

fig. 6: distribution of strikes between towers and wires.

fig. 5: lightning frequency for a density N = 4 lightning strikes per km2and per year:

s curve 1: vertical rod with a height h (with N1 x 10-3),

scurve 2: horizontal conductor, 100 km long, at height h (with N1).

number of earth

wires 0 1 2 3

lightning strike on tower (%) 55 35 20 10

on wires 45 65 80 90(earth orphase)

influence coefficient 1.65 1.40 1.20 1.05

2 3 4 5 6 8 10 20 30 4050 70 100 200 500 1,000

10

20

30

N1

0

strikes/year

h in

meters

(2)

(1)

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i

t

U

i/2

i/2

i

proportional to the distance through air( 550 kV / m) and must take intoaccount a delay in flashover for verysteep frontss as a chopped impulse, with a voltagelimited by flashover, when

ZI max

2 Ua

The lightning current above whichflashover, i.e. interruption in service,

occurs is called the critical current Ic:Ic = 2 Ua / Z.

The magnitude of Ic is in the region of5.5 kA for 225 kV lines, 8.5 kA for400 kV lines and 19 kA for 750 kVlines. The corresponding frequencies of

occurrence are respectively 95 %, 90 %and 60 % (see fig. 2). Note that for20 kV lines, the Ic value is practically 0and flashover always occurs.

Indirect lightning strikes (on earthwires or towers)(see fig. 8)The flow of the lightning current to earthcauses an increase in the potential ofthe metal structures.The top of the tower reaches a potentialthat depends on its inductance L andthe resistance of the earth R to theimpulse.

u(t) = R i(t) + L di(t)dt

This voltage may reach the impulseflashover voltage of the insulators, inwhich case back-flashover occurs. Apart of the current is propagated alongthe affected phase conductor(s) towardusers. This current is in general greaterthan that of a direct lightning strike.

On extra high-voltage transmissionsystems, back-flashover is unlikelydue to the insulation level of theinsulators. Earth wires are therefore a

solution in that they limit the number ofinterruptions in service. However,below 90 kV, back-flashover and theresulting interruption in service occureven when earth resistance values arelow (< 15 ), thus reducing theusefulness of earth wires.

wave propagationPropagation of lightning impulse wavesis a concept with which electro-technicians are rarely confronted in dayto day work.

What actually takes place ?Any modification in the electrical stateof a conductor at a given point travelsat high speed, ranging from 150,000 to

300,000 km/s depending on theinsulator surrounding the conductor. Ata power frequency of 50 Hz, thedistance covered in one period is 3,000to 6,000 km.In the industrial sector, this distance isfar greater than the length of theconcerned conductors, except in veryparticular situations. It is thereforepossible to simplify by considering thatthe transmission of the wave isinstantaneous throughout theinstallation.Lightning produces high-frequency

phenomena ranging from several tensof kHz to several MHz, levels far

greater than the low 50 Hz or 60 Hzpower frequencies.

Characteristics of high-frequencyphenomenaIn this range of frequencies, theelectrical laws commonly used are nolonger sufficient for our purposes:s first, the system cannot beconsidered to be under standing (state)conditions, with instantaneoustransmission of the wave throughoutthe installation. The transmission timeis no longer negligible with respect tothe period of the consideredphenomena (at 1 MHz, the period is1 s which corresponds to 300 m).s secondly, stray capacitance from thevarious elements, skin effect,

electromagnetic coupling, etc. becomeimportant, even dominant, factors.

fig. 8: lightning strike on an earth wire.

fig. 7: lightning strike on a phase conductor.

U = k R i + Ldi

dt

U = Zi

2

L

R

U

(1/2 - k) ik i

i/2i/2

i

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and the practical consequencesfor lightning studiesIt follows that to quantitatively determinethe effects of lightning (see the example

in section five), it is necessary to:s first, take into account the lawsgoverning wave propagation. Given thedistances involved, ranging from a fewmeters to several kilometers, propa-gation does not stabilise instanta-neously, either in space or in time.s then, take into account the lawsgoverning reflection, refraction at pointsof discontinuity and superposition ofwaves at each point in time and at eachpoint along the line.s finally, adapt the model describing thephysical operation of the various

elements to take into account thedominant high-frequencyphenomena.

Example: under high-frequencyconditions, a transformer subjected to atransient no longer behaves like aseries-connected inductance with atransformation ratio, but as a capacitivedivider (HV/earth, LV/earth,HV/LV capacitances), in which case theHV/LV transformation ratio may be quitedifferent from its value at powerfrequencies.

Propagation attenuation due to the

corona effectLightning surges travelling alongconductors are distorted by the corona

effect (losses due to ionisation of theair surrounding the conductor, whichcan be sizeable when U > 1 MV). Theresult is an attenuation in amplitude

and in front steepness. It is generallyconsidered that over distances greaterthan 1.5 km, lightning surges nolonger represent a danger forsubstations.

effects of lightningThis section discusses the main effects,both direct and indirect, of thepropagation of lightning currents. Notethat even if the current is transmitted bythe high-voltage lines, it can affect allelectrical circuits (conducted and

radiated disturbances) at all voltagelevels. The effects can be:s thermal (welding of parts, fire,explosions).s mechanical, due to theelectrodynamic forces exerted onnearby parallel conductors.s dielectric shock, following increasesin potential during wave propagationthrough the impedance of theconductors.s insulation breakdown followingflashover of a phase insulator,resulting in a follow-on current flowing

to earth at power frequency.s increase in earth potential. Potentialscommonly reach several hundred kV at

the earthing electrodes of theconcerned HV equipment. Therelationship describing the potential asa function of the distance to the

earthing connector is approximatelyhyperbolic, resulting in very highpotentials and associated gradientsnear the earthing electrode and evenat distances of several tens of meters.s high-frequency electromagneticinterference (very wide spectrum),including radiated interference,induction and circuit coupling.s electrochemical, acoustic andphysiological.

All the above phenomena can cause:s damage to equipment, either violent,

for example dielectric breakdowns dueto overvoltages, or in the form ofpremature ageing due to non-destructive, but repeated stresses,s malfunctions in installations due inparticular to interference in control/monitoring and communicationequipment connected to low-currentcircuits,s reduced continuity of service due tointerruptions that may be long (damageto equipment) or short (malfunctions innetwork automatic control systems),s dangerous situations for people or

animals, in particular due to pacevoltages which may result in electricalshock or even electrocution.

4. protection

Following a few general remarks on

protection, this section discusses ingreater detail the means to ensureprotection, both primary (directdischarge) and secondary (limitation ofthe transmitted disturbances).

generalThe best protection, in particular ofhuman life, is provided by directing amaximum of the disturbance to earth atthe closest possible point to the sourceof the disturbance.

Effective protection therefore requires

the lowest possible earth impedances.This can be ensured by creatingearthing networks and interconnectionsbetween earthing electrodes whereverpossible. On high voltage B systems,an earth impedance of less than 1 atpower frequency is commonlyspecified for substations, whereas fortowers, an impedance of 10 to 15 isstrived for.There are several levels of protectionagainst lightning currents and theresulting increases in potential.

These are based on energy levels:s

level 1, consisting of diversion of themajor part of the impact to earth andinitial clipping. This level appliesprimarily to objects likely to be struck bylightning (lines and substations).s level 2, consisting of limitation of theresidual voltage by further clipping. Thislevel is intended to protect substationequipment and/or installations againstconducted overvoltages. Several pro-tection devices distributed throughoutthe installation may be required todissipate the clipped energy.

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s level 3, consisting of additional

devices such as series-connectedfilters and/or overvoltage limiters, which

may be required in LV systems for

sensitive equipment (computersystems, automatic control systems,

telecommunications, LV networks,

etc.).

Note: All the above protection systems

should be considered right from thedesign phase of installations and

systems because subsequentmodifications are difficult to implement

and costly.

protection level 1

The purpose of level 1 protection is tolimit the effects of direct impacts onelectrical installations by diverting thelightning current to the desiredlocations.Controlled diversion of lightningcurrent to precise points is possibleusing:s lightning rods implementing thestriking distance principle. These thinrods are placed at the top of thestructure requiring protection andconnected to earth by the most directpath (via conductors descending

around the protected structure andconnected to the earthing network).Observations have shown that a goodprotection against direct lightningstrikes is provided in a cone with itssummit at the top of the lightning rodand extending downward at 45 angleswith respect to the vertical.s Faraday cages or shields whichconsist of closed grids of horizontaland vertical conductors connected toan earthing network. The mesh sizemust be less than 15 m and verticalrods are placed at the nodes on the

top part. Coverage of the zonerequiring protection is equivalent tothat provided by a multitude oflightning rods.

In either case, lightning rods or cages,the electro-geometrical modeldetermines the protected zone usingthe fictive sphere method.The point of impact of the lightningstrike is determined by the first objecton the ground falling within the strikingdistance d of the leader.

It is as if the leader were at the centre

of a fictive sphere with a radius d. To

ensure proper protection, the fictive

sphere, as it moves along the ground

with the leader, must encounter a

protection device without touching the

objects requiring protection (see fig. 9).

For protection against a very low

lightning current, approximately 2 kA

(cumulative probability 100 %), thecritical striking distance is 15 m. If a

97 % probability is acceptable, the

corresponding lightning current is 5 kA

and the critical distance is 27 m.

s screens

This category comprises earth wireswhich are conductors running parallelto and above the phase conductors.

Earth wires are connected to the earthvia the towers and constitute effectiveprotection against lightning strikes onoverhead lines in that they capturestrikes with amplitudes greater than thecritical current Ic.

The concepts discussed in thepreceding section can be used todetermine the optimum position of earthwires.

fig. 9: determining the protected zone using the fictive sphere method.

lightning rod

leader

fictive

sphereprotected

zone

(cone)

45

d = critical

striking distance

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The different striking zones for anoverhead line are shown in figure 10:s zone I: earth strikes,s zone II: strike on a phase conductor

without insulator flashover (I < Ic),s zone III: strike on the earth wire.

Protection of the phase conductors bythe earth wire is determined by theoptimum protection angle opt.When opt, screen faults mayoccur, i.e. lightning strikes with currentsexceeding the critical current mayreach the phase conductors andprovoke faults. The number of screenfaults depends on .

protection level 2

This type of protection applies to HVsystems.It must ensure that the BIL (BasicImpulse Level) of the various substationelements is not exceeded (coordinationof insulation).It creates an earthing circuit enablingdiversion of the lightning current bysparkover or conduction. Two types ofdevices are used to limit lightningsurges, spark gaps, based on arelatively old technique, and lightningarresters, which today are used toreplace the former in a wide range of

applications.s spark gaps, which implementsparkover, have a number of majorhandicaps:s fairly high dispersion of the sparkovervoltage (up to 40 %),s a sparkover delay that is a function ofthe overvoltage,s the sparkover phenomenon issensitive to external influences, forexample atmospheric conditions,s the spark gap creates a very steepchopped wave front that can destroy thewindings of nearby machines,s it also creates a 50 Hz follow current.

The diverted current is detected by theearth-fault protection device whichactuates upstream breaking of theconcerned line.

s a lightning arrester (or more generallya surge arrester) is a semi-conductorwith non-linear resistance ranging froma few to several M. It is generallymade of zinc oxide (ZnO), a materialwhose characteristics are wellunderstood.

It is connected between the phasesand the earth.s operation is similar to that of thespark gap, but it offers better control of

the voltage:- low dispersion of its residual voltageU = f (I),- virtually no delay in conduction,- natural return to its initial state(insulator), thus avoiding follow current.s the main sizing criteria for a lightningarrester are:- maximum continuous operatingvoltage (MCOV), which must be greaterthan the maximum network operatingvoltage with a safety margin of 5 %;- rated voltage, which must be1.25 x MCOV;- protection level;

- capacity to withstand the energy oftransient overvoltages, determined byan amplitude vs. duration curve.

s lightning arresters or spark gapsprovide effective protection only whencertain installation conditions are

respected, in particular the distancesseparating them from the equipmentto be protected and from the earth.

That explains the importance of theprotection distance of the lightning

arrester, which will be discussed

below.

protection level 3Applied in LV systems and for sensitive

equipment, this level of protection

against lightning and its effects is not

discussed in length in this

Cahier Technique publication. Forfurther information, consult the

documents listed in the bibliography.

fig.10: different cases for lightning strikes on an overhead line. Note that protection

angle=opt.

earth cable

phase 1

phase 2

phase 3

p

d

d

limiting striking distance on phase

wires when I = Ic

h

line determining the position of the

earth wire for = opt

zone II

zone I

zone III

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Note that this type of protection isbased on the following:s electromagnetic-compatibility (EMC)studies,

s earthing-network design(interconnections, sizing, etc.),s coordination of overvoltage limiterswith overload, short-circuit anddifferential protection devices,s parallel-connected protection to limitimpulse voltage using surge arresters:gas spark gaps, varistors (SiC, ZnO),avalanche diodes, RC filters,s series-connected protection to limitthe power transmitted using waveabsorbers (or HF filters), shieldedisolating transformers, networkconditioners or UPS systems.

protection distanceThe concept of protection distance isillustrated in the example below, whichhas been voluntarily simplified.

ExampleConsider an overvoltage impulse wavetravelling down a line and arriving at asubstation comprising a transformerprotected by a lightning arrester (seefig. 11).

The various elements are defined asfollows:

s line:s surge impedance: Zc,s wave propagation velocity: v,s distance between arrester andtransformer: D,s propagation time between A and B:

= D / v,s lightning arrester with perfectcharacteristics, i.e. for all voltagesgreater than Vp, conduction isinstantaneous and the voltage is limitedto precisely Vp,s earthing electrode with an impedanceequal to zero,s arrester/equipment and arrester/earthconnections zero in length,s transformer with an input impedance,at the considered frequencies, muchhigher than Zc. An arriving voltagewave is almost totally reflected (voltagedoubles at point of reflection),s incident overvoltage wave with aconstant-slope (r = dV / dt) front and aconstant tail voltage where T = Vp / r isthe front duration up to Vp (see fig. 12).

There are three possible cases whichare summarised in figure 13.

The diagrams in figures 14, 15 and 16illustrate the phenomena for cases 1

and 2 (see pages 14, 15 and 16).ExampleIf the maximum permissible impulsevoltage for the transformer is set at1.3 x Vp, then

1.3 x Vp Vp + 2r D

v

It follows that the arrester/transformer

distance must not exceed:

D 0.15Vp v

r = 0.15 T v

Using the applicable figures:

Vp = 1,200 kV,v = 300 m / s,r = 2,000 kV /s, D 27 m.Note:In reality, the following elements must betaken into account:s lightning arrester connections toequipment and to the earth,s actual lightning arrestercharacteristics,s network configuration with impedancebreaks and the different propagationvelocities,s

capacitive elements, including thetransformers. fig. 12: overvoltage wave diagram.

fig. 11: circuit diagram (line and transformer

substation) for study of lightning overvoltage

wave propagation.

fig. 13: maximum overvoltages on the transformer, a practical example.

case criteria maximum overvoltage comments

on transformer

1 2 Vp steep front slope r, long distance D.

Arrester distance has no effect on the

maximum voltage on transformer, the

arrester limits the voltage to 2 Vp.

2 steep front slope r, long distance D.

Arrester presence limits, by the distance

i.e.: T > 2 overruneffect, the maximum voltage on the

transformer. Overrun of thresholdVp is proportional to D and to r, hence

the protection distance concept.

3 limit case between 1 and 2.

i.e.: T = 2

i.e.: T < 2

Vp + 2r D

v

= 2r D

v

Vp + 2r D

v = Vp (1 +

2

T)

= Vp 2T

D = v Vp

2 r

D < v Vp

2 r

D > v Vp

2 r

Vp + 2r D

v

= Vp + Vp = 2Vp

A

B

Zc

Zc

transformer

lightning arrester

line

D, v,

A and B: measurement points

V

T

Vp

t

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Vp

Vp

Vp

Vp

Vp

A B

Vp

-Vp

Vp

-Vp

Vp

wave arrives at A

wave arrives at B

2 Vp

Vp

Vmaxi

wave from the

arrester arrives

at B

arrester produces a

second wave to

maintain at A a

constant voltage

equal to Vp

second wave from

the arrester arrives

at B

second wave from

the arrester reflected

at B

wave reflection at B,

reflection reaches A

arrester produces awave to maintain at

A a constant voltage

equal to Vp

wave from the

arrester reflected at

B reaches A

Vp

-Vp

Vpwave from the

arrester reflectedat B

reflection reaches A

arrester produces awave to maintain at

A a constant voltage

equal to Vp

wave arrives at A

wave arrives at B

wave reflection at B

Vp

Vp

2 Vp

Vp

wave from the

arrester arrives at B

2 Vp

Vp

Vp

-Vp

wave from the

arrester reflected at B

A B

-Vp

Vp wave from the


reaches A

-Vp

Vp arrester produces a

second wave to

maintain at A a

constant voltage

equal to Vp

Vp second wave from the

arrester arrives at B

-Vp

Vp second wave from the


-Vp

case n2case n1

Vp

Vp

t = 0

t = T +

t = 3

t = T + 2

t = 4

t = T + 3

t = 5

t = T + 4

t = 3

t = T/2 + 2

t = 4

t = T/2 + 3

t = 5

t = T/2 + 4

t = 6

t =

t = T

t = 2

t = 0

t =

t = 2

t = T/2 +

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fig. 14 (opposite page): diagrams illustrating lightning wave propagation for cases 1 (steep front slope) and 2 (low front slope) described in

figure 13. Positions A and B are shown in figure 11.

fig. 15: voltages on the line protected by the lightning arrester as a function of time, for cases 1 (steep front slope) and 2 (low front slope)

described in figure 13.

T/2 + 3

T/2 + 2 T/2 + 3 5 4

T/2 + 4 6

T/2 + 5 2

2 Vp

Vp

0

0 T 2T

6

54

32

1

2 Vp

Vp

0

T +T 3

T + 2 T + 3 5 4

T + 4 6

T + 5 2 0

1

2

3

4

6

5

case 1

case 2

A B

D, v,

transformer

lightning arrester

line

1 2 3 4 5 6

incident wave (T)

first wave produced by the arrester

second wave produced by the arrestervoltage profile

reflected incident wave (T)

first wave produced by the arrester (reflected)

second wave produced by the arrester (reflected)

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fig. 16: maximum overvoltage at transformer input (point B) as a function of T for a given(case 2 in figure 13).

network operation and non-availabilityIn public distribution networks, lightningis one of the causes (50 %) of voltagedips and brief interruptions.

These interruptions in the supply ofpower, provoked by the protectiondevices, are required to clear the fault(end of spark gap discharge or stop ofinsulator flashover).

To improve continuity of service,interruptions are shortened by automaticreclosing of the protection devices(circuit breakers).

Automatic reclosing cycles differ,

depending on the voltage level:

s > 300 kV: high-speed reclosing onsingle-phase systems (< 0.5 s) or slow

on 3 phase systems (1.5 to 5 s),

s 50 kV < U < 300 kV: 3 phasereclosing and the use of shunt circuit

breakers on single-phase systems(0.15 s),

s 1 kV < U 50 kV: high-speed andslow 3 phase reclosing (0.35 s, 15 s).

Interruptions are troublesome forusers and may be alleviated oreliminated by:

s implementing auxiliary sources suchas UPS systems for control/monitoring applications, computersystems, etc.,s designing and implementing correct

discrimination between the protectiondevices on the users network, toensure rapid clearing of faults causedby lightning,s preventing isolating of priorityconsumers during storms. Sensitiveloads can then be supplied by aninternal power supply, while otherloads continue to be supplied by thepublic distribution network.

0 2 3 4 5 6 7 8 9

Vp

2 Vp

T = 3T = 4

T = 2

T = 8 T = 10 T = 12 T = 14 T = 16

A B

transformer

lightning arrester

line

D, v,

line

T = 5 T = 6

T = 7

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standardsInstallation designers can usestandards to assist in determining:s the overvoltage situations that mustbe taken into account when calculatingrepresentative electrical stresses,s the basic impulse levels (BIL) ofequipment,s protection device characteristics.The main applicable standards arelisted in the appendix. A few particularpoints are listed below.

IEC 60-1: high-voltage testtechniques - part 1s section 6: lightning impulse tests.Different wave forms are defined (fulllightning impulse, impulse chopped onthe front or impulse chopped on the tail)

with characteristic durations.Figure 17 shows a standardisedlightning strike.s section 8: current impulse tests. Forthe tests, four standardised currentimpulses of the bi-exponential type,defined by their front duration and thetime to half value, may be used:s 1 s / 2 0 s impulse,s 4 s / 1 0 s impulse,s 8 s / 2 0 s impulse,s 30 s / 8 0 s impulse.IEC 694: common clauses for high-voltage switchgear and controlgear

standards(French standard: NF C 64-010)This standard stipulates that the ratedinsulation levels must be selected fromthe values contained in a series oftables (see fig. 18 for an example).

It also stipulates that lightning impulsevoltage tests must use the standardised1.2 / 50 s wave.IEC 99-1: surge arresters - part 1(French standard: NF C 65-100)Section 6: type tests.This section presents the type testsdefined by the standard:

s external insulation withstandcapacity;s verfication of the residual voltage for8 / 20 s lightning impulses;s withstand capacity for long impulsecurrents;s tests on operation, acceleratedageing, heat dissipation capacities,thermal stability, lightning and operatingovervoltages, etc.

IEC 71-1: insulation coordination -parts 1 and 2

The capacity of insulation to withstandlightning impulses must be determined

taking into account foreseeable over-voltages such that insulationcoordination requirements are satisfiedfor lightning overvoltages. Coordinationmay be based on conventional orstatistical methods.

s using the conventional method, thecoordination criterion is the marginbetween the maximum foreseeablevalue and the withstand voltageindicated by an impulse test. This

margin determines a safety coefficientthat should not be less than the valuederived from practical experience whichis approximately 1.25.

s using the statistical method, whichaccepts that insulation faults mayoccur, the goal is to quantify the risk ofa fault.The coordination criterion to bedetermined is the margin characterisedby a statistical safety coefficient relatingthe statistical impulse withstand voltage(withstand probability of 90 %) to thestatistical overvoltage (2 % probabilityof being exceeded).

rated voltage (kV rms) 7.2 24 72.5 245 420 525

rated insulation levels for 40 95 325 850 1,300 1,425lightning impulses (kV) 60 125 950 1,425 1,550

145 1,050

fig. 18: examples of voltage levels (defined by IEC 694) from which the rated insulation levels

for lightning impulses must be selected.

fig. 17: example of a standardised lightning strike defined by IEC 60. HereT1 = 1.2s,

T2= 50s.

1.0

0.9

0.5

0.3

001

U

B

A

t

T

T1

T'

T1 = 1.67 T

T' = 0.3 T1 = 0.5 T

T2

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Figure 19 is an example showing thecorrelation between the risk of a faultand the statistical safety coefficient.Note that currently, the statistical

method is almost exclusively limited toself-regenerating insulation applicationswhere faults do not result in damage toequipment.

fig. 19 : correlation between the risk of a fault (R) and the statistical safety coefficient ()for

various distributions of lightning overvoltages (g= standard deviation), as defined by IEC 71.

0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3

R

1

5

10-1

5

10-2

5

10-3

5

10-4

5

10-5

g = 40 %

g = 60 %

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5. example of a lightning study

This section outlines the procedure fora lightning study, the methods usedand the practical conclusions. It dealsin particular with calculation methods,substation modelling using thecalculation assumptions, deterministicsimulations, statistical aspects and theconclusions.

generalThis study deals with insulation

coordination for an extra high voltageGIS (gas-insulated switchgear)substation. Adequate dielectricbehaviour must be ensured for thevarious elements in the chaincomprising the electrical system. Theelements have different BILs andpractically speaking, the question iswhether lightning arresters are requiredand if so, how to define theircharacteristics (location, ratings).

This type of study is becomingincreasingly common for largesubstations. Customers require that

installers and suppliers of turn-keyinstallations provide numerical datajustifying sizing decisions.This type of study must be carried outby teams of specialised engineers withsufficient experience and know-howand using specific computer software.

Note: The example presented here wasdrawn from a true study concerning thesupply of a 500 kV substation, carriedout by the Network Research Section(a part of the R&D Department), onrequest from the ContractingDepartment of Merlin Gerin in charge of

the project.

calculation methodsA number of successive andcomplementary calculations are made:s first, deterministic calculationsevaluate voltages present in theinstallation depending on a number ofdifferent parameters such as the type of

lightning strike, the intensity and pointof impact, the existence and location oflightning arresters, earth impedance,etc.s secondly, calculations on lightningfrequencies and the correspondingrisks, on the basis of lightning statistics,s finally, calculations on substationwithstand capacities expressed inprobabilistic terms.

Deterministic calculations

s substation modelling

The operation of each network elementand its configuration (physicalinterconnections) in the networktopology are described by equationsbased on the applicable electrical laws.Modelling requires prior analysis of thenetwork to limit the description topertinent aspects.The equations are solved by computersusing dedicated software, for exampleEMTP (Electromagnetic TransientProgram).

s simulation of lightning current wavesand the associated voltages for eachproposed solution. Stepwise equationsolving makes it possible to expressvirtually continuously the evolution ofcurrent/voltage variables at each pointin the network as a function of time.The simulation reproduces actualoperation analogically. Lightning isrepresented by a supply of currentcomprising a triangular or bi-exponential wave with adjustable front/tail durations and peak values.

substation modelling

Modelling in this example is limited to ageneral description that should sufficefor a basic understanding of theprocedure and does not include anumber of details required only byspecialists.

General assumptionsslightning strike on an earth wire, withback-flashover of an insulator on the

second line tower (most unfavourablecase).

s lightning impulse on the earth wire:s peak value: 200 kA,s triangular shape: 2 / 50 s.s length of the struck line taken intoaccount is limited to 1.5 km from thesubstation (see section 2).

s phase subject to flashing:s farthest from the struck earth wire,s with a negligible power voltage.

s substation configuration: GISconfiguration with the maximum lengthof in-service busbars (mostunfavourable case).

s modelling frequency: 1 MHz.

Main technical data

s 500 kV line:s 4 wires per phase, 2 earth wires,s impedance data:

Zdirect 300

Zzero sequence 500

s towers:

s surge impedance: 120 ,s height: 43 m,s earth resistance 25 .s insulators:s chain of 29 elements (cap and pintype),s flashover voltage: 2,600 kV,s discharge delay depends on theshape and the level of the overvoltagedefined by a typical voltage-time curve.

s GIS:s surge impedance: 70 ,s substation earthing electrode

impedance: < 1 .s capacity:s power transformer: 7 nF,s instrument transformer: 4 nF.

s lightning arresters: the U = f(I)characteristic expresses theirnon-linearity.

s all connections (lines excepted):1 H/m linear.

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Studied installation(see fig. 20)

deterministic simulationsThe simulations are carried out for anumber of cases, e.g. with or withoutlightning arresters downstream of thesubstation and at the transformerterminals, and for various arrestercharacteristics.

For each case, the maximumovervoltages occurring at theinstrument transformers, thesubstation and the power transformerare closely observed and comparedto the possible BILs. The results (seefig. 21) show that for a BIL of1,550 kV, at least two lightningarresters are required (for theinstrument and power transformers).

fig. 20: general substation layout and configuration.

The table in figure 21 and the maincurves in figure 22 correspond to thesafest case in which three identicallightning arresters (n 1, 2 and 3) areused.Note the distribution of the 200 kAlightning strike: the lines and towersabsorb the major part of the currentand less than 14 % arrives at thesubstation, where approximately halfis absorbed by the lightning arresters.It is a small fraction of the lightningcurrent (< 5 %) that provokes voltagerises approaching the maximumdielectric withstand capacities of theequipment.

Note: it has been demonstrated thatdirect hits on phase conductors are lessof a problem than back flashover. Theschielding effect of the earth wireslimits the currents resulting from direct

strikes, as calculated using the electro-geometrical model, to approximately12 kA.That is less than the critical current and

the insulators are not subject toflashover. Under these conditions, thecalculated currents in the substationresulting from a direct impact are lessthan those resulting from back flashover.

statistical calculation oflightning frequencies andthe associated risksThe average frequency of lightningstrikes on a line is calculated using theformula presented in section 3:

NL = Nk N130

+ l70

L100

hence NL = 1.03 strikes / year.

3

2

point of

maximum

voltage in

the substation

1energised

de-energised

flashover

lightning arresters:

n1 = incoming line,

n2 = for substation,

n3 = for transformer

instrument

transformer

earth wire

phase conductor

transformer substationnetwork

1 2 transfor-

mer

a)

b)

source n1

1

2

source n2

circuits:

sub-

station

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0

0 2 4 6 8 10 12 14

200

150

100

50

kA

a

b

c

d

a = lightning currentportion of lightning current flowing:b = to earth via the struck tower,c = to earth via the last tower before the substation,d = to the substation via the phase subject to flashover.

0 2 4 6 8 10 12 14

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0

a b c

a = voltage affecting the instrument transformer,b = maximum voltage affecting the substation (see fig. 20),c = voltage affecting the power transformer.

s

10

12

2

4

6

8

00 2 4 6 10 128 14

portion of lightning current flowing:a = to earth via the lightning arrester at the head of the line (1),b = to earth via the lightning arrester for the substation (2),c = to earth via the lightning arrester for the transformer (3),d = to the substation via the phase subject to flashover.

a

b

c

d

a = voltage at the lightning arrester at the head of the line (1),b = voltage at the lightning arrester for the substation (2),c = voltage at the lightning arrester for the transformer (3).

0 2 4 6 8 10 12 14

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0

a b c

kA

s

s

MV MV

s

fig. 22: curves plotted on the basis of lightning overvoltage simulations.

fig. 21: safety coefficients for each element of the studied equipment. The valid figure for the overall installation is 40.5 %.

location of lightning arresters

near the downstream upstream from

instrument from the the power

transformer substation transformer

yes yes yes

yes no yes

yes yes no

overvoltages (kV) and safety coefficients (%) =BIL Umax

Umax

for each element

instrument transformer substation power transformer

BIL 1,550 kV BIL 1,800 kV BIL 1,550 kV BIL 1,550 kV BIL 1,800 kV

1,096 kV 1,103 kV 1,004 kV

41.4 % 64.2 % 40.5 % 54.2 % 79.3 %

1,263 kV 1,235 kV 1,044 kV

22.7 % 42.5 % 25.5 % 48.5 % 72.4 %

1,096 kV 1,103 kV 1,560 kV

41.4 % 64.2 % 40.5 % - 0.6 % 15.4 %

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The probability of surges caused bylightning strikes 200 kA is indicated bythe curve in figure 2:Probability (P) = 1 %.

The frequency of occurrences istherefore:Fd = NL x

P 0,01 surges / year.The statistical return period Tr betweentwo occurrences isTr = 1 / Fd 100 years.A practical means to express thesefigures is to determine the correspon-ding risk R of such a surge occurringduring the service life t of the substation.

R = 1 e t

Tr .

For a 30-year service lise: R 26 %.

interpretation ofcalculationsThe conclusion of this study may besummed up in a single phrase. There isone chance in four (26 %) that, duringthe service life of the substation(30 years), an overvoltage caused bylightning will reach or exceed 1,103 kV,corresponding to 71 % of the definedBIL (1,550 kV), i.e. a calculated safetycoefficient of 40 %.

This result is of use in definingprotection levels for equipment,depending on standards, technicalpossibilities and cost factors, etc.

Note that all the above calculations arebased on selected values for importantparameters, including a number whichare:s decisive, for example, tower andsubstation earth impedances, lightningstrike amplitudes,s and/or characterised by very widedispersion ranges, for example,breakdown voltages and flashoverdelays of insulators,s and/or poorly understood, forexample, network configurationstatistics or the correlation betweenlightning impulse amplitudes andfronts,s and/or neglected, for example,ageing processes and corona effect.

The values used for these parametersmay lead the reader to suspectinaccurate results. However, practicalexperience, accumulated and analysedprimarily by electrical distributionutilities, confirms their suitability. Themethods outlined in the examplepresented in this section are similar tothose implemented by EDF, the French

electrical authority.

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6. conclusion

This document sums up the mainaspects concerning lightning inelectrical installations, thus constitutinga basic introduction to this oftenobscure, but nonetheless increasinglyimportant subject.

It deals primarily with medium and highvoltage installations. Lightning is amajor constraint on equipment and is adecisive factor in ensuring insulationcoordination.In the low-voltage field, lightning is but

one of many possible electricaldisturbances (see the bibliography).In this Cahier Technique publication,the main practical aspects are

discussed in an effort to provide amaximum of information, bothquantitative and qualitative, includingthe physical aspects of lightning itself,its effects on electrical installations,currently available means of protectionand standards. However, from all theinformation contained in this document,two main points should be remembered:s the concept of the lightning-arresterprotection distance, corresponding towave propagation phenomena at very

high frequencies (MHz);s the example of a lightning study,based on an actual study carried out byMerlin Gerin for a 500 kV installation.

The lightning study, broken down intoits component parts, shows how therisk of damage to equipment bylightning can be calculated.

The electrotechnical community istoday increasingly aware of theproblems caused by lightning and suchstudies are increasingly carried out formajor international projects.The current trend to take lightningphenomena into account starting fromthe initial installation design phase willcontinue to grow in coming years, thuscontributing to further improve thequality of electrical power.

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appendix: bibliography

Standards

s IEC 56: HV AC circuit breakers.

s IEC 60-1: HV test techniques, part 1(French standard: NF C 41-101and 102).s IEC 71: Insulation coordination(French standard: NF C 10-100).

s IEC 76-1: Power transformers, part 1,insulation levels and dielectric tests(French standard: NF C 52-100, part 3).

s

IEC 99-1: Surge arresters, part 1(French standard: NF C 65-100).

s IEC 289: Reactors (French standard:NF C 52-300).

s IEC 298: AC metal-enclosedswitchgear for rated voltages above1 kV and up to and including 52 kV(French standard: NF C 64-400).

s IEC 694: Common clauses for hifh-voltage switchgear and controlgearstandards (French standard:NF C 64-010).

s NF C 17-100: Protection against

lightning - Rules governing installationof lightning arresters.

EDF (French electrical authorityspecifications)

Series HN 65 :s protection against overvoltages in HVapplications,s spark gaps in HV installations,s lightning arresters in HV applications.

HN 112: Insulation coordination on400 kV networks.

HN 115: Design and executionguidelines for earthing systems.

HN 119: Insulation coordination on225 kV networks.

Other publications

s Dielectric properties of air and extrahigh voltages.EDF collection.

s Lightning: understanding the pheno-menon in order to protect against it.Nathan publishing.

s Electricity.Volume 22: high voltage.Ecole polytechnique de Lausanne - EPL

s Electrical and electromagneticdisturbances.CIGRE, Electra Magazine.

s Editions des techniques delingnieur.

s Overvoltage and InsulationCoordinationCIGRE, Committee 33.

Merlin Gerin Cahier Techniquepublications

s Protection of LV wiring againstelectromagnetic interference in the HV/EHV electric substations.Cahier Technique n 137B. CAVALADE.

s Les perturbations lectriques en BT.Cahier Technique n 141R. CALVAS.

s EMC : Electromagnetic compatibility.Cahier Technique n 149F. VAILLANT.

s Surtensions et coordination del'isolement.Cahier Technique n 151D. FULCHIRON.

s Calcul des courants de court-circuit.Cahier Technique n 158B. DE METZ NOBLATG. THOMASSET.

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