Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: clever nonlinear meters

At 06:25 AM 3/21/01 -0600, Kossom wrote:
Could you be more specific as to how the electric meter works.

How does one go about calibrating one?

See
http://www.avointl.com/products/watthour/xtra/notes/kwatmeter/kwhmetr.html

The general description on that page is OK, although some of the details of
the physics are muddled or skipped altogether.

Here's how I explain it:

The instrument contains a voltage coil (consisting of many fine wires) and
a current coil (a smallish number of fat wires). The instrument is
inserted into the circuit as follows:

V0 I0->
generator ----------------current--------------
| coil |
| I1-> |
-------------- |
| |
voltage customer
coil load
| |
| |
ground ----------------------------------------


Physically, the poles of the coils are arranged symmetrically around the
axis of the rotor disk like this:

vN v for voltage
iS iN i for current
vS N/S for North/South

That is, a positive current in the current coil creates a North pole in the
3:00 position. A sustained positive voltage on the voltage coil eventually
creates a North pole at the 12:00 position. Note that I said "sustained
... eventually" because the magnetic field in the voltage coil is not
proportional to the instantaneous voltage. The coil is an inductor. The
current I1 in the voltage coil goes like
I1 = integral (V0) dt
and the magnetic field in the voltage coil depends on I1, not I0. That
means that if V0 is a cosine wave, I1 is a sine wave, i.e. its phase is
delayed 90 degrees.

It is important that the voltage coil be a good inductor. If you made it
out of cheap wire with a lot of resistance, the meter wouldn't work right.

If the rotor were a permanently magnetized bar magnet, it would rotate at
60 revolutions per second: 3600 rpm. But of course the rotor is not
permanently magnetized. So the picture is:

Step 1: Put a positive current through the current coil and hold it for a
while. Eddy currents in the disk start to die out due to resistivity in
the disk. This allows the magnetic field to penetrate the disk.

Step 2: Let the current I0 decrease to zero. For a while, flux will
remain trapped in the disk, as eddy currents oppose the change. The
downward zero crossing in I0 corresponds to a maximum in I1. The trapped
flux at the 3:00 position will be attracted to the pole at 12:00, and the
trapped flux at 9:00 will be attracted to the pole at
6:00. Result: counterclockwise torque.

Step 3: Meanwhile, the voltage coil is pushing some flux into the disk at
12:00 and 6:00.

Step 4: The current in the voltage coil goes to zero. At this time the
current in the current coil is reaching its negative extremum. The trapped
flux at 12:00 is attracted to 9:00, and the trapped flux at 6:00 is
attracted to 3:00.

Et cetera. You get the idea.

Note that the instrument won't work if the disk is too resistive, and it
also won't work if the disk is a perfect conductor (zero resistivity).

========

Now consider the case where the load is highly reactive, i.e. there is a
horrible power factor. (For example, fluorescent lighting is a notoriously
reactive load: the ballast is a huge inductor.) That means that I0 could
be nearly 90 degrees out of phase with V0 (ahead or behind). That would
make I0 nearly in phase with I1. The disk almost wouldn't know whether to
rotate clockwise or counterclockwise. It would correctly register that the
average power is much smaller than the product of RMS voltage times RMS
current.

If your load has a really bad power factor, the power company might get
mad. They might show up with an additional meter (of a different type) and
start charging you for integral(I^2) not just integral(I*V).

=========

The physics is simplest if the disk is rotating relatively slowly -- much
slower than 3600 RPM. Also we need to know how the motion is related to
the torque. Therefore... they have a "retarding magnet" which just applies
a DC magnetic field to the rotor somewhere. This gives a retarding force
(and torque) proportional to the velocity.

You can recalibrate the meter by changing the strength of the magnetic
coupling between the retarding magnet and the disk.

===========

In the absence of friction, the foregoing would work pretty well. The next
refinement allows them to correct for friction. Stray friction is most
noticeable when the disk is moving very slowly. We assume the voltage V0
is relatively constant, but the current I0 might be sometimes rather
small. To overcome friction, they use a "shaded pole" on the voltage
coil. That is, they put a loop of copper on the downstream side of each
pole of the voltage coil, roughly at the 11:00 and 5:00 positions on the
diagram above. (Remember, the disk is rotating counterclockwise.) This
means that even when the current is zero, the thing works like a shaded
pole induction motor, providing enough torque to counteract *almost* all
the friction.

This improves the accuracy under normal conditions. However...
-- They need to be careful not to get carried away with this, because if
the correction term is too big, the meter will run even when the load is
totally disconnected. The customers tend to notice this, and get really vexed.
-- The shaded pole trick ruins the symmetry of the instrument. If you
were trying to sell small amounts of power back to the power company, the
meter would be doubly-inaccurate at the low end of the scale: you would be
fighting friction *and* the shaded pole.

Finally, do you know how the new electronic meters work?

I've never seen one, but the obvious hypothesis is that they measure the
voltage using a standard digital voltmeter circuit, and measure the current
with a precision 4-terminal milliohm series resistor and another voltmeter.