Re: power-grid physics

["John S. Denker" <jsd@AV8N.COM>]

On 08/30/2003 05:11 PM, Bernard Cleyet wrote:
> Our discussion on line frequency prompted my horologist friend to
> measure it with his MicroSet:
>
> http://www.bmumford.com/clocks/60cycle/

Thanks for the data.

I don't want to sound ungrateful -- any data
is better than no data -- but there is room
for improvement in the design of that experiment.

In particular, it would be much more useful to
record the *phase* rather than the frequency.
Given phase data, I can always differentiate
it to get the instantaneous frequency.  In
contrast, if I try to integrate the frequency
to get the phase, I am at the mercy of cumulative
roundoff errors.  (I suppose the errors could
perhaps be minimized by recording frequency data
with tremendous precision, but that would be quite
a clumsy way to proceed.)

The power companies claim that the long-term
phase error is bounded (implying that the long-term
frequency error converges to zero).  It would be
amusing to check this claim.

=====================

If somebody wants to do the experiment, here's
a hint, i.e. an outline of how I would attack
it:

1) Grab a linux box.  Phase lock its clock to
the Naval Observatory using xntpd
  http://www.eecis.udel.edu/~ntp/
(I do this on all my computers routinely.  It
has saved my bacon on a number of occasions
when hunting Wide-Area Network bugs.)

2) Grab a doorbell transformer and put a
voltage divider on the output to produce
a 1Vac signal at powerline frequency.  Use
a low-pass RC filter if you want to
minimize the hassles from high-frequency
hash (which is rather common on power lines).

3) Feed the signal into the left channel of
the sound-card on the computer.

4) Get the computer to put out a phase
reference signal, which you can hairpin back
into the right channel of the sound card.
I would use a 1Hz square wave, such that
the rising edge was synchronized with the
beginning of each second.

I would probably just hack the timekeeping
code in the kernel, adding a couple of lines
to write directly to the parallel port,
assuming that's available for use.

5) Record the stereo signal into a file.

6) Be sure to note the start time of the file.
This doesn't need to be super exact, just
good enough that you can tell which second
is which in the right-channel sync signal.
Synchronizing a file to the nearest second
is easy;  synchronizing it to the nearest
millisecond is not so easy, which is why
we need the right-channel sync signal.

7) Analyzing the data should be easy.  For
each second's worth of data, take the FFT of
the left channel and look at the phase in
the slot corresponding to powerline frequency
(60Hz in North America).  Watch the phase as
a function of time.