Re: Ideas for inexpensive True-RMS Metering?

Nope. You can compute power factor for waveforms which aren't even periodic, and thus don't *have* a "phase".

Therein lies the problem with #5, i.e. "phase difference" may not even be a meaningful concept if the waveforms are far enough from sinusoidal.

Actually, #3 suffers from the same problem.

be

But we are talking about AC power, not just random waveform.

No. You can compute true power from the E:I samples, and apparent power from the product of the RMS voltage and current. Then you can divide to get power factor. But the sign of the phase is unknown.

For complex waveforms, "phase" may not even mean much.

John

But "Nobody" is still right. The phase angle and the power factor (as defined as W/VA) are *very* often different animals; if you calculate #4 you may well not have any meaningful answer for #5. ...if #5 has any meaning, or is even measurable.

Harmonics.

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defined

may well

is even

Not really. Take the DFT of a series of samples, find the fundamental. = Compare phase components of V and I. Done. Also, cos(phi) =3D DPF, the = classical (sine wave) power factor that you learn about in Power = Systems.

A complex waveform (mixed frequency, anharmonic, noise, independent V = and I, etc.) may not have much if anything in common, but in that case, = the DPF is pretty weird too, so you get exactly what you should expect.

None of this is meaningless or unmeasurable.

Tim

--=20 Deep Friar: a very philosophical monk. Website:

We were talking about the stuff that you find on real-world mains supplies, not the theoretical concept found in text books.

The voltage waveform may not be *that* far from sinusoidal; if you're metering it, it's probably coming from the grid rather than e.g. a "modified sine" UPS.

While the current waveform probably won't actually be "random" in the mathematical sense, it may well be closer to that than it is to a sine wave.

With a rectifier+capacitor load without PFC, when the rectifier starts to conduct it is actually driving a short (a partially charged C) and the only thing that limits the inrush current is the source impedance of the electric distribution network (mainly source resistance R). This current can be several times the fuse nominal ratings, causing a significant voltage in the source resistance, significantly dropping the voltage at the load from the unloaded sinusoid voltage waveform.

If the RC time constant (network source R, storage capacitance C, with power transformer impedance transfer ratio correction if used) is longer than 1-2 ms, the rectifier will conduct well after the nominal sinus voltage peak, causing voltage drops past the nominal voltage peak.

When the open circuit voltage after the peak drops below the nearly fully charged capacitor, the rectifier finally stops to conduct and no further voltage losses will occur in the source impedance.

If the voltage is measured close to the load, the highest voltage might be measured significantly after the nominal (unloaded) voltage peak, just slightly before the point when the rectifier stops to conduct.

Thus, do not assume that peak voltage measured close to the rectifier load would represent the peak voltage of the source or that the timing of this peak could be used for phase difference measurements.

For voltage phase (reference) measurements, the zero crossing is a better place, but this can also be polluted by harmonics and other high frequency noise.

Compare phase components of V and I. Done. Also, cos(phi) = DPF, the classical (sine wave) power factor that you learn about in Power Systems.

You don't need a full Fourier transform if you just want the fundamental components. Just

S = sum(current_samples * sin(377t))

C = sum(current_samples * cos(377t))

and you can do this over many cycles if you want.

and you can get the phase angles from them. The amount of math is reasonable on a small, busy uP, where a real DFT is likely not. I have assembly code around here somewhere...

But the "power factor" that you get wouldn't be very popular for silly loads.

John

(...)

The biggest current limiters here are capacitive reactance plus the equivalent resistance of the rectifier, yes?

--Winston

be

The wave form may be distorted, but the base frequency (from the power generators) would not change. What's important (for load correction) is the peak voltage and current phase difference, which should not be difficult to measure with a simple micro.

Consider: transformer (optional) -> bridge rectifier -> NO smoothing capacitor -> PWM. The current waveform will look a lot like the PWM waveform, which may not even be at a fixed frequency (e.g. hysteretic buck converter), let alone synchronised to the mains frequency.

If you don't think this is likely, you haven't seen enough cheap Chinese crap (or enough DIY electronics from the kind of person who designed guitar amps in the 1970s). OTOH, if the entire supply is being used for loads like this, it might be more useful to add a built-in smoke detector than phase measurement.