# Measuring power factor with microcontroller

Discussion in 'Electronic Design' started by [email protected], Oct 28, 2007.

1. ### Guest

I'm using a microcontroller and its built in A/D to measure energy
usage, watts, and PF on 120VAC 60Hz. I'm sampling the voltage and
current with the A/D. I have a circuit working as a level shifter so
that 1/2 of the A/D's full scale is 0, allowing it to measure negative
voltage and current. That's all well and good.

The problem is with measuring PF. I'm measuring watts by multiplying
each voltage sample by the corresponding current sample, and summing
them over a period of time. This seems to work well. (never mind
for right now that the current and voltage sampling are not occurring
at the exact same time; I've accounted for this) I thought that the
apparent power could be calculated by taking the absolute value of
each voltage/current product, but this doesn't seem to work. My PF
measurements are way off for some known loads. However, it does
indicate 99 or 100% for purely resistive loads.

So, what am I doing wrong? How do you calculate apparent power with
discrete V and I samples?

2. ### Guest

You're not taking into account the non-linear effects of many loads.
http://en.wikipedia.org/wiki/Power_factor
You're in for a lot more math than just multiplying.
Why not just buy a PF meter?

3. ### Guest

I actually read the Wikipedia article and was lost as to how to deal
with the non-linearities. This is just a power-meter I'm building and
really doesn't need to measure PF, so it may be easier to leave it out.

4. ### John LarkinGuest

One trick is to just add a little phase lag into the voltage signal
conditioning path, enough to correct for the sampling lag between
voltage and current. Another is to alternate voltage:current samples
with current:voltage samples.
No, that's not right. The apparent power calculation must be
independent of the E:I phase angle.
What I usually do is square individual voltage samples, lowpass filter
them, then square root the filter output to get true RMS volts. Then
do the same for current. Now multiply those results to get apparent
power, VA's.

PF = real power / apparent power.

You can simplify the math by lowpass filtering the absolute values of
E and I, rather than doing the true RMS stuff. You'll get the same
result for sine waves, just as an averaging AC voltmeter is as good as
a TRMS meter for sine waves. You can also do block averages instead of
lowpass filtering.

This technique gives a pretty good number, but loses the
on algorithms to do it better. But they turn out to be fairly
compute-intensive, Hilberts or dsp pll stuff, or FFTs maybe, so we'll
probably do that math in an FPGA.

What's your sample rate? That's a very interesting issue here.

There are lots of situations where the meaning of PF is debatable.

John

5. ### Phil AllisonGuest

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** The definition of VA = rms voltage x rms current.

You will at lest need to compute the " true rms " value of the current wave
over one cycle and multiply this number by the similar voltage one.

The voltage wave could be assumed to be sine to a reasonable approximation
for the purpose - then you only need to scale the peak value.

........ Phil

6. ### Tim WescottGuest

This is what I would recommend.
This would start working into what the customer expects, too -- do they
just care about leading/lagging and harmonic content, or do they want a
detailed spectrum (with phases!) of the various harmonics?
It can make a huge difference. I've scratched the surface here:
http://www.wescottdesign.com/articles/Sampling/sampling.html.
Or perhaps one should say "where one must define the meaning carefully".

The meanings in common use have certainly expanded since I was in school.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" gives you just what it says.
See details at http://www.wescottdesign.com/actfes/actfes.html

7. ### John LarkinGuest

I sold roughly 12,000 16-channel power survey meters that were used
for a lot of end-use load surveys, by utilities and research
institutes. They sampled each channel at 26.9947 Hz.

My newer stuff, with more compute power, samples at 263.032 Hz.

One survey did a bunch of fast-food restaurants. The deep-fat friers
used burst-mode zero-crossing temperature controllers for the heaters;
you know, maybe 5 cycles on, 11 cycles off or whatever. There were
heated (pun!) debates about what the pf might be in that situation.

John

8. ### defaultGuest

Technique we used in the 70's to get PF - and in those days circuits
were always inductive, but the basic idea will work for either leading
or lagging:

Phase angle can be derived from a few op amps rather simply. Current
and Voltage are put directly into two op amps with no feedback so you
are using the full open loop gain of the amps (200K or more - but
protecting the input with some diodes and resistors so the input
doesn't exceed the supply voltages). (can also be done with logic
IC's like CMOS inverters, since you just need a lot of gain to make
square waves from sine waves)

Current is sensed with a current transformer on the power line to the
device under test - voltage with a step down transformer or directly
with dropping resistors.

You get a square wave out of both amps - the zero crossing on each is
used to make a charge pump. One amp sends voltage through a resistor
to an integrating cap the other terminates the charging until the next
cycle. (basically an AND gate) The voltage on the cap reflects the
power factor - at unity there is no charging of the cap at 90 degrees
there's maximum charging.

We used a buffer amp to drive a meter to read PF in degrees directly.

9. ### Phil AllisonGuest

"default"

** Shame how it does not work for a non-linear load.

Where there simply is no phase angle.

( snip drivel)

** Bollocks - PF is a number, less than or equal to one.

Even Wiki is way up on you.

http://en.wikipedia.org/wiki/Power_factor

........ Phil

10. ### Guest

My sample rate is a little over 13ksps; that's including separate
voltage and current samples. I may raise it, but this might be
unnecessary.

11. ### John LarkinGuest

Good grief, I've done AC power meters at 27 Hz! But if you've got the
CPU horsepower, why not?

John