> If you just use di/dt for calculating voltage drops on lightning
> conductors you can get some very misleading answers. Sure if you have a
> known rise time and inductance you can calculate a voltage, but that
> doesn't convey much information. It isn't even the fast edges on the
> lightning pulses that cause the most damage. Those can punch holes in
> you coax jacket, but they won't melt the coax (unless it happens to be
> in the center of an arc). The huge voltages cause big arcs, but most of
> the damage is done by the energy contained within the wider pulses.
> Those wider pulses may be up to 10 ms wide or more, at hundreds to tens
> of thousands of amps.
Hmmm.. are we talking direct hits? The lightning literature is fairly
full of the electrical properties of lightning strokes, and the current
pulse typical stroke is substantially less than 1 ms long (classic model
is 2 us rise (10%-90%), 50 us fall to half max magnitude). There are
some super strokes with longer durations and/or large "continuing
currents" but they constitute substantially less than 1% of the overall
strikes at a given location.
The longer pulses with high currents show up as fault currents in power
systems. A lightning stroke causes a flashover of the line to something
else, and the continuing arc burns until something interrupts it (an
upstream circuit breaker, for instance). A 1000 Amp surge with many
millisecond duration wouldn't be unusual (I can't recall what the
"standard" surge is off hand). However, this would be very unlikely for
a tower scenario (while actually being more likely for a power line
There's some experimental data collected in, I believe, Canada, where
they did a lot of statistics on actual surges. It was done in the last
20 years or so to inform updates on testing standards and methods, which
were based on 50-100 year old measurements of fairly large uncertainty.
> So if you are trying to calculate voltages and currents on things you
> need a tool that considers the whole waveform. Also you need to decide
> what the source waveform should be. It will vary a lot at different
> points on the tower and it will vary a lot between different types of
> lightning strikes. Many times you will see references to a standard
> lightning waveform, but that is for a specific purpose, usually cables
> on a power pole or in a conduit or something like that, with different
> levels for different conditions. A tower will be completely different.
> It's out there in the open being hit directly so it is subject to the
> entire wide variety of lightning waveforms that mother nature can
> generate, and they are not nearly all the same. Even the max current
> pulse that should be used is questionable. Current pulses up to 340,000
> amps have been recorded. Those are apparently rare (recording is also
> rare), but what number should you use a design criteria? I would think
> it should be something more than a typical value. A tower will also
> ring like a bell when hit with a strike. Not only do you get the
> initial pulses but you get some sort of distorted damped sinusoid
> following that.
In fact, folks have modeled this sort of thing with NEC. A 300kA stroke
would be very unusual. One might design for "fail safe" in that case.
Typical guidelines design for things like 30kA or 50kA.
> To complicate the problem even more, you have to calculate the induced
> currents. In a lightning strike these are NOT negligible. Just ask
> anyone who has some long cables near a strike, or has a house
> wired-intercom and lightning happens to hit near the house. Near the
> tower, induced currents can be huge.
probably, actually, a bigger problem than direct hits. Lots more
"nearby strikes" than direct hits, in any given area. And much tougher
to model. However, the magnitude is, almost certainly, less (the
induced current has to be less than the stroke current, because the
magnetic coupling has to be something <1)
> Once you analyze all this you can start to get a feeling of what is
> really happening. It's not a trivial analysis. When you see cable
> lightning currents calculated by very simple formulas, you can bet the
> answers are completely worthless.
Not at all. You can use a simple formula to give yourself some bounds,
or to estimate general magnitude. If one uses a simple formula and
finds that the estimate is, say, 10 Volts, and your "danger threshold"
is 1000 Volts, you can walk away and be done with it. Likewise, if the
simple formula returns 100kV and your threshold is 1000 Volts, you stop
your analysis right there. It's when you're trying to compare the
estimate of 500Volts against the threshold of 1000 Volts wherein the
danger of simple approximation lurks.
> A couple of other points:
> 1. Obvious but worth stating: For the high frequency edges on lightning
> strikes, inductance always dominates the calculations for conducted
> currents. However, as stated above those aren't the currents that cause
> the most damage. Also induced currents have to be added and those may
> not take the same paths.
> 2. You can reduce conducted currents on a cable by coiling the cable to
> make a choke, but it is a two edged sword. Reducing the currents
> increases the voltage drop across the choke and it may increase
> susceptibility to induced currents.
The latter from what mechanism? Because the choke is a coil
intercepting the changing field? A quick and dirty fix would be to wind
the choke with two windings, in different directions, side by side (i.e.
the coils are coplanar, so they don't have much mutual coupling). or to
form the coils in a toroidal form.
Obviously, one can't get away from issues about high voltage across the
choke. In the long run, putting the cable underground or in a conduit
or cable tray is probably a better solution than flailing away with chokes.
> It is obvious that this gets very complicated when you try to calculate
> anything. It would be really nice if everyone was able to optimize his
> tower system by calculating the expected currents on things, but it just
> isn't going to happen for the average guy, at least not with any
> dependable accuracy. I'm afraid we are limited to the (hopefully)
> overdesign by rules method.
> Jerry, K4SAV
TowerTalk mailing list