Lightning Damage to Electric Vehicle Charging systems
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1 Lightning Damage to Electric Vehicle Charging systems 05 Copyright of A. Martin
2 Abstract This is a living document and represents the current thinking of EEE PES SPDC W.6. on Electric Vehicle Supply Equipment. Based on the SPDC s experience of lightning events affecting electrical and electronic systems, a series of scenarios are discussed. At present these are done on a mainly theoretical basis, as there are not enough field reports of damage ntroduction There are ways lightning could cause damage to the DC charging circuit: By nduction from a nearby strike (see clause.) Through the effects of C (ground current rise see clause.) Via flashover due to P (ground potential rise) and follow current (see clause.) By a direct strike (see clause ) A direct lightning strike is the worst case, but unlikely to happen. So designing protection to meet this threat may not be economic. So let s consider the indirect effects in order.. Potential damage from indirect effects. nduction from a nearby strike n this case we want to calculate the amount of current induced in the loop which represents the DC fastcharging circuit in Figure caused by a lightning flash, represented by the long straight wire in Figure Figure epresentation of a lightning flash coupled to a loop To do that we need to first calculate the mutual inductance between the wire and the loop. To calculate the mutual inductance M, we first need to know the magnetic flux through the rectangular loop. The magnetic 05 Copyright of A. Martin
3 9 0 field at a distance r away from the straight wire is B = μ 0 / πr, using Ampere s law. The total magnetic flux Φ B through the loop can be obtained by summing over contributions from all differential area elements da =l dr: Thus the mutual inductance is: 5 B 0l S W M ln S Let () at bt t e e i V V () peak di at bt t M M ae be s W peak () dt s peak b a s as b M s () s s s V V (5) Z L c W n equation 5, assume that Z is the lowest it can be, which is the impedance of the DC feed. Then in equation 5, L W is the inductance of the wire, s = jω, and c = W /L W. Substitution equation () in equation (5) we have: b as s a s b s c M peak ( s L (6) W W ) The LaPlace transform of which is: t M L peak W at bt ae be a c c b ct cb ae a c c b W (7) To get an estimate of the size of W (t), let s put some numbers in equation 7. Let the height of the loop l be the spacing between the DC feed wire and the ground return, and assume 0. m (the calculation is 05 Copyright of A. Martin
4 insensitive to this value see equation ). The worst-case cable length W is assumed to be 0 m, and assume the lightning flash is S = 0 m away. Then from equation (), where μ 0 = π x 0-7 H/m M = 5.75x0-9 H Now assume that the feed cable is a 0 m length of #6 AW wire, for which W = 0.00 ohms and L W = 5.5 μh. Let the lightning surge be the median surge from CE TD 59 Table.5: 0 ka 5.5/75 [5.5 microseconds rise time /75 microseconds to half-peak]. Then a = x0, b = 8.x0 5, and c = 8. Putting these numbers into equation (7) we can make the plot shown in Figure Figure Current induced in a charging cable due to a typical 5.5/75 0 ka first flash Since the induced current depends on di/dt, it is of interest to see what the induced current is for a./ ka median second flash, which has a much faster rise time than the first flash. n this case a =.x0 and b =.78x0 6. Using these numbers for a and b, and otherwise the same assumptions as used for the median first surge, we can use equation (7) to make the plot shown in Figure. Here we can see that the faster rise time of the subsequent flash partially compensates for its lower peak current, relative to the first flash. But the first flash is still the worst case. 05 Copyright of A. Martin
5 Figure Current induced in a charging cable due to a typical./ ka subsequent flash Figure predicts that on the average a current of 0 0 A could flow on a charging cable due to induction. An extreme lightning flash can have several times the peak current of a median flash, but it is usually accompanied by a much slower rise time, so the net effect might not be a much greater induced current. The actual induced current depends on many things, but it will likely be a few tens of amps. The induced current will add to (or subtract from) the current due to ground potential rise (P), which we will consider next Copyright of A. Martin
6 round potential rise (P) and ground current rise (C) n the case of a uniform ground, the current density from a lightning flash spreads out from the point of contact of the flash. The voltage created by the spreading flash current density decreases as the distance from the flash increases, as illustrated in Figure. The result is that the ground potential at a point closer to the flash, e.g. point A in Figure, is greater than the ground potential at a more remote point B, hence there is a difference in potential due to a P between points B and A Figure Spread of P from the source. Here V > V >V 6 Now referring to Figure, suppose a car is located at point A, and a charging system is located at point B. When the car battery is being charged, point A and point B are connected by a wire having an impedance Z Copyright of A. Martin
7 An equivalent circuit for this arrangement is shown in Figure 5. Here is the resistance of the earth between the flash striking point and point A, is the resistance of the earth between the flash striking point and point B, is the earth resistance between point A and a remote ground, and is the earth resistance between point B and a remote ground. F is the current due to the lightning flash. F V V 5 V Z V V Figure 5 Equivalent circuit for a car at point A and a charging system at point B Analyzing the equivalent circuit, the current in the charging circuit, 5 due to a P can be expressed as: 90 5 F (8) T Z 9 Where T = Copyright of A. Martin
8 Let r 0 be the radius of the area where the lightning flash strikes, let r be the distance of the car ground from the lightning flash striking point, and let x be the distance of the charging system ground from the car (points A and B respectively, in Figure ). Then is the resistance of the green area in Figure 6 between r 0 and r ; and is the resistance of the yellow area between r and remote earth Figure 6 Areas corresponding to resistances and Similarly is the resistance of the gray area in Figure 7 between r 0 and r + x; and is the resistance of the blue area between r + x and remote earth Copyright of A. Martin
9 05 Copyright of A. Martin 9 Figure 7 Areas corresponding to resistances and 0 Let ρ be the resistivity of the ground. Then using the guidance of EEE Std.: r r (9) 05 0 x r r (0) 06 r () 07 x r () 08 T T r 0 () 09 Substituting equations (9) () into equation (8) we get equation () 0 5 ) ( Z T F () The voltage ΔV = (V V ) is also of interest. t is simply Z V 5 (5) Let Z = S + sl S, where S is the sum of all resistances between the two ground points (circuit resistance, resistance of the ground at A, and the resistance of the ground at B), and L S is the sum of all inductances. 5
10 6 7 8 eferring to Figure 8, assume that the ground is ionized over the patterned area on the green, and that the man s feet are a foot apart. With these assumptions r 0 is estimated to be. m (the calculation is not very sensitive to this number). Fitting some typical numbers to equations () and (5), Figure 8 Used for estimating r 0, assuming the man s feet are foot apart (courtesy CTEL) r is a variable for Figure 9, otherwise it is 0 m x = 0 m ρ = 00 ohm-m S = is a variable for Figure 0, otherwise it is 7 ohms (estimated total ground connection resistance, calculated according to EEE Std.:99) L S = 5.5 μh (roughly the inductance of a #6 wire over a ground plane) Let the waveform be the median first stroke 0 ka 5.5/75, for which pk = 0, a =.0x0, and b = 8.x0 5 For the waveform assumed, the maximum value of sl S is 0.8 ohms at 8.9 khz, very much less than S. So sl S can be neglected, and Z = S Copyright of A. Martin
11 5 6 7 For this set of variables, Figure 9 has two plots. The first shows the surge current that could flow in the charging wire due to a C as the distance of the lightning strike from the car is varied up to 00 amps in this case for a total ground resistance of 7 ohms (calculated according to EEE Std.:99). The second plot shows the P voltage that can be developed across the sum of the ground resistances and the resistance of the charging circuit. The voltage across S can reach 0 kv, if the lightning flash is close to the charging circuit Figure 9 Variation in peak wire current, and voltage across s for s = 7 ohms and ground spacing = 0 m 05 Copyright of A. Martin
12 5 Figure 0 is a plot of equation () as s is varied, with r = 0 m and ground spacing = 0 m.. n this case for a reasonable value of s the current in the charging circuit could reach 00 A. The voltage across s doesn t vary much with as s is varied. For example in the present case the voltage across s goes from 500 V to 6000 V as s goes from 0 ohms to infinity Figure 0. Variation in peak wire current with total ground resistance s, for r = 0 m and ground spacing = 0 m. The peak currents in Figure 9 and Figure 0 were calculated for a median lightning flash, and could be more or less than that shown, depending (among other things) on the peak current of the lightning flash and the distance of the lightning strike from the car Lightning direct strike Although it would be a rare event, it s interesting to see what would happen to the DC feed wire if it was hit by a direct strike. From [B] for copper wire A t 0.0d (6) Where d = diameter of the copper wire in mils. For a double exponential lightning surge of time-to-half peak = τ, 05 Copyright of A. Martin
13 59 A (7) 0.7 peak d (8) peak From Wikipedia d AW log (9) 5 Knowing peak and τ, the largest diameter of a wire that would fuse is given by equation (8), and the corresponding AW by equation (9). Thus any AW with a number higher than that calculated from eauation (9) would fuse by the chosen lightning flash. For example for a median 0 ka 5.5/75 flash, any AW with a number equal to or higher than 9 would fuse. Simerly a 00kA 0/50 would fuse any wire with an AW equal to or higher than 7. The feed wire will likely have a low enough AW that it would survive a direct lightning flash, but the system would need to be protected against it Damage potential Both the induced current and the C current due to P depend on many things, including the waveshape of the flash, the distance of the flash from the charging cable, and the resistances of the grounds. As an estimate, the combined peak induction current and peak C current could be in the range A. There is a possibility that this current adds to, or subtracts from the normal battery charging current. f it subtracts from the normal charging current, and if it is greater than the charging current, then reverse current can flow through the battery, which will damage it. This case is most probable if the charging cable is connected to the car, but not running charging current (for example, if the battery is fully charged; or the charger is not turned on). Another possibility is that the voltage due to a P causes insulation breakdown, which if it happened in the charging circuit could allow power follow current to flow. n this case damage would most certainly occur. A high voltage could also cause damage to any electronics associated with the charging circuit. Without sufficient field reports of damage for guidance, it is hard to determine the most prominent cause of damage due to lightning. The EEE PES SPDC W.6. is developing a uide to cover this subject. For example, this warning from a lithium battery manufacturer: Do not reverse the positive (+) and negative (-) terminals when charging. Otherwise, the battery pack will be reverse-charged, abnormal chemical reactions will occur, and the excessively high current will cause damage, overheating, smoke emission, bursting, and/or fire. 05 Copyright of A. Martin
14 Annex A (informative) Bibliography [B] Kenneth C. Chen, Larry K. Warne, Yau T. Lin, obert L. Kinzel, Johnathon D. Hu, Michael B. McLean, Mark W. Jenkins, and Brian M. utherford, CONDUCTO FUSN AND APPN FO BOND WES, Progress n Electromagnetics esearch M, Vol., 99-, 0 05 Copyright of A. Martin
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