# [Beowulf] UPS & power supply instability

Robert G. Brown rgb at phy.duke.edu
Wed Sep 28 16:03:38 PDT 2005

Jim Lux writes:

> But, what you're really concerned about is harmonic content in the load
> current, not the phase, per se.  If you hooked a big inductive load up, the
> current would lag the voltage but still be sinusoidal, and you might not
> have any problems.
>
> Just as an example.. if the third harmonic current were equal to the
> fundamental (i.e. equal power in the harmonic and the fundamental), the PF
> would be .707.  (and, in a three phase system, the neutral current would be
> 3*.71 * leg current)

If you have a hard time understanding what Jim is talking about with his
third harmonic stuff, visit the mirus international link and look at the
pictures.  It just means that a switching power supply typically draws
most of its current in the middle third of each half phase, or (for

V(t) = V_0 sin(120\pi t)  (\omega = 2 \pi f with f = 60 Hz)

the current is drawn only when \omega t \in [\pi/3,2\pi/3] or
[4\pi/3,5\pi/3].  The current is thus IN PHASE with the voltage -- it is
drawn in 60 Hz pulses in phase with V(t) -- but current is drawn
basically only when the voltage crosses a fixed threshold.

Now it is a True Fact that

I_0 sin(\omega t) + I_0 sin(\omega t + 2\pi/3) + I_0 sin (\omega t +
4\pi/3) = 0

This is the expected cancellation on a shared neutral wire for three

It is also a True Fact that the shared neutral current on three lines
that only draw in the middle third of the half cycle DO NOT OVERLAP --
the period is broken up into sixths and in each sixth cycle one and only
one line is drawing and dumping current.  Furthermore, it is drawing a
peak current that is LARGER than you'd expect from the rms power
consumption.  So instead of cancelling, you have a line current on the
neutral that is something like I_0 sin(3\omega t), or the third harmonic
of the base frequency \omega.  As Jim noted, EACH cycle of this current
would carry as much as any single line, so your rms current (think
"average" for the purpose of determining e.g. line heating, voltage drop
on the neutral, and so on) is 3x as great.

Line heating is given by I^2 R, so 3x the current is 9x the joule
heating of the neutral line and will ALSO produce overheating in your
primary three phase transformer, reducing its lifetime if nothing worse.
Carrying 60 amps (give or take) on a line that's safe at 20 amps is a
Bad Idea.  You can often tell you've got a shared neutral switching
power supply by grabbing the shared neutral (by the insulation, of
course:-).  If you go "ouch" and let go -- well, a normal 12/2 line
carrying 20 amps should be no more than just barely warm, so it won't
e.g. set your house on fire inside the walls even if it is wrapped in
wall insulation that partially traps the heat, on a hot day.

On our cluster, the circuit breakers were quite hot indeed until we had
it rewired, and we couldn't run any circuit at much more than 50% of
theoretical load without popping the line breaker.

rgb
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