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Wattmeter measurements (Output Voltage vs. Firing Rate)


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From:  Antonio Carlos M. de Queiroz [SMTP:acmq-at-compuland-dot-com.br]
Sent:  Sunday, August 16, 1998 12:30 AM
To:  Tesla List
Subject:  Wattmeter measurements (Output Voltage vs. Firing Rate)

John Freau wrote:

> I hadn't realized about the rms problem.  This wattmeter says it's
> accurate to 1/4 of 1 % up to 125 Hz.  I wonder how severe the errors
> might be?  Has anyone compared such wattmeters with true (electronic)
> reading wattmeters in TC circuits to get a ball park figure of possible
> errors?

When I first replied to your post mentioning a wattmeter I hadn't
realized that if the voltage is a 60 Hz sinusoid the measurement with
a moving-coil wattmeter is not so flawed. The inductance of the current
coil causes attenuation of higher current harmonics, but they do not
contribute to the average power, because the average product of two
sinusoidal signals of different frequencies is always zero.

(A moving-coil wattmeter measures the attractive force between two coils,
one with a current proportional to the voltage (v) over the load, and another 
with a current proportional to the current (i) on the load. This force is 
proportional to the average value of the vi product, exactly as the average
power.)

And if there is severe distortion on the 60 Hz voltage waveform due to the 
loading of the coil system on the power line? This distortion is mainly due
to linear elements (wire resistance, transformer leakage inductance), that
cannot transfer power from 60 Hz to other frequencies. The wattmeter will 
still measure correctly the average power, because there is no average power 
coming from harmonics above 60 Hz. (A possible problem here is the wattmeter
changing the phase relationship between the voltage and current at high
harmonics, causing wrong measurements.)

> I wonder if we're talking 10%, 30%, or 200% error.  Someone once
> suggested they thought the errors might be around 10% using a
> wattmeter.  Does this seem reasonable?

There is a possible test: Filter the current and voltage signals with
precise 60 Hz band-pass filters (that do not add delay) and feed the
signals to the wattmeter. If it measures the same power, it can be used
directly. A more accurate test would be to sample the current and
voltage waveforms with a storage oscilloscope and compute the power
from the average vi product.
If too distorted waveforms may cause saturation on the wattmeter,
the solution is to feed it with attenuated samples of the signals,
and measure a fraction of the average power.
 
> Also any clue as to how inaccurate the rms technique might be
> (ignoring power factor issues for now)?

An extreme case: The current is a 180 Hz sinusoid. The voltage is a 
60 Hz sinusoid. The product Vrms*Irms is not zero, but the wattmeter
measures (correctly) zero. 

Antonio Carlos M. de Queiroz