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.
"John Larkin" "Phil Allison"
** The OP has the wrong idea about phase angle - he thinks it always exists. ** PF = watts / VA by definition.IF a phase angle exists, it can be quoted.
There is no debate about that.
... Phil
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).
Where?
The regulatory authorities don't.
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?
When "on", the PF is unity, when "off",power is zero, so PF doesn't exist. Same as switching (tungsten) lights on and off.
Average true power over 24 hours = 0.5 Average apparent power over 24 hours = 0.5 Hence power factor =1
Makes no difference whether you integrate over one cycle, or 12*3600*60 cycles. It's unity PF.
Whether a utility would charge for below unity would depend on the ratio of MSEEs to MBAs.
If one declares PF (power factor) to be the cosine of a phase angle, that's true.
The square-sum average of a function of time can be defined
||F|| == integral_time( |F|**2 dT)
and there's an important combination of two functions called the correlation
Corr (F1, F2) == integral_time (cconj(F1(t)) * F2(t) dt) )/sqrt (||F1|| * ||F2||)
which is always in the range {-1, +1}
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
Another opamp and a resistor. Similar mechanism. What's your beef?
?-)
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