That assumes sinusoidal voltages and currents. No true anymore, in these days of nonlinear loads.
You need to sample voltage and current, multiply individual samples, then integrate.
PF=cos(phi) is only true for pure sine waves.
For current samping, look at LEM, Honeywell, and Tamura products.
Watch out for COTS transformers used at their spec voltage rating. Many are designed to run close to saturation, to save iron. They distort quite a bit.
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"For a successful technology, reality must take precedence
over public relations, for nature cannot be fooled."
(Richard Feynman)
If you create an artificial ground using 2 Y capacitors (like the ones used in every mains adapter) for your circuit you can use 2 safety rated resistors and a differential amplifier to sense the voltage. In most cases the seconday circuit is either floating or somehow connected to ground (earth). Some means of overvoltage protection will probably be required to protect the resistors (common mode filter + MOV).
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Failure does not prove something is impossible, failure simply
indicates you are not using the right tools...
nico@nctdevpuntnl (punt=.)
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I used to design multichannel survey meters that were used by academics and utilities for end-use load studies. We sold several thousand, 16 channels each. There were raging debates about the meaning of PF.
One fun one was around deep-fat friers in a restaurant chain. The load is resistive, but it's controlled by a burst-cycle triac thing that doles out full line cycles into the heater. The on/off time scale can be sub-second up to minutes (which is basically thermostat mode) depending on the controller.
Some utility people said that the PF is 1, because the load is resistive. Certainly PF correction capacitors wouldn't help. Some said that the PF is lower, based on the peak/average power ratio. The PF sort of depends on the observation period.
How about a resistive heater that's on for an hour at a time and off for an hour, 12 on/off cycles per day? What's the PF? Would a utility charge for below-unity power factor?
It's that correlation, of I(t) and V(t), that is the power factor. If one has only simple real sinewave functions, the arccosine of that correlation is an angle, which can be identified with a phase shift betwixt F1 and F2.
So, mathematically, one can define all this stuff, AS LONG AS YOU AGREE ON A TIME INTERVAL to do integration. If your signals are non periodic, there's no natural reason to agree (and mathematicians will complain bitterly about the scientists' habit of choosing a time interval as 'sufficiently long').
Yup. (I've also used integer cycle switching to "PWM" neon transformers.) ...Jim Thompson
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