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Re: OT Interesting power requirements... MORE

Subject: Re: OT Interesting power requirements... MORE
From: Johnny B Good
Date: Sun, 9 Nov 2008 06:33:17 GMT
Newsgroups: uk.comp.homebuilt
The message <[email protected]>
from Rob Morley <[email protected]> contains these words:

> On Sat, 8 Nov 2008 13:30:49 GMT
> Johnny B Good <[email protected]> wrote:

> >  Or, borrow a real (analogue) wattmeter and get some proper readings.
> > 
> I did wonder about power factor.

 It's not a PF issue other than that a low PF will aggravate the real
issue of insufficient digital resolution, both in the magnitude and time
domain parameters.

 The cheap digital meters will show true (FSVO 'truth') power in the
presence of non unity PF loadings in the hundreds of watts and above
readings range. It's their limited resolution which causes errors at low
powers (typically becoming a significant problem for loads less than 50
watts).

 The 'PF Problem' in switched mode psus is more to do with narrow
conduction angles in the rectifier pack, the so called PF correction
inductors now being fitted into modern ATX PSU boxes are simply to
extend the rectifier conduction angle and reduce the peak current demand
at the voltage crest of the cycle.

 SMPSUs don't produce low PF loadings in the sense that there is a
lagging or leading current creating imaginary out of phase power flows
as is the case for inductively ballasted discharge lamps, or purely AC
only motors. The current flow remains in the same phase as the voltage,
it simply only flows for a small fraction of each half cycle period.

 When a switchmode PSU is only lightly loaded, the conduction angle
still remains relatively narrow (PF inductor, not withstanding) and the
resulting low power demand current is further depressed by the fact that
the voltage is close to the peak.

 A reasonable estimate of conduction angle, in this case, might be 45
deg which represents a 1:4 duty cycle. The average voltage would be
somewhere around the 300 to 320 volt mark. Assuming an average power
demand of 6 watts from 300 volts at a 1:1 duty cycle, this gives a
current of just 20mA. Multiplying by four to account for a 1:4 duty
cycle, we end up with one hundred 80mA pulses per second.

 For a digital wattmeter to achieve a 1% accuracy in this case, it would
have to be sampling better than 800 samples a second, however, this
assumes a sample reading error within 0.5% of an 80mA reading as well[1]
requiring a resolution of current flow samples to be 0.4mA or better.
Since these meters are designed for a UK mains current to at least 13A
rms (a peak of 18.382A) this gives us an FSD count value of 45956 (times
2 to cover both negative, as well as positive values). This requires a
17 bit representation. I rather suspect that this is where the cheap 'n'
cheerful digital wattmeter falls down.

 The voltage samples don't really require as great a resolution since
the mains supply voltage is pretty well defined to be no greater than
265 v rms or 374.71 peak. Measuring to the nearest volt should suffice.
In fact, an 8 bit signed integer (2s complement) would probably suffice
here.

 It's the current resolution that's most critical regarding accuracy for
a (well defined) mains voltage wattmeter. I don't think the cheap meters
use ADCs with better than 10 bit accuracy to feed the multiplier and I
suspect their sampling rate falls short of the 800 calculations[2] a
second requirement.

[1] That 0.5% accuracy relates to only one parameter that's going to be
multiplied by yet another parameter, so you need an error percentage
figure of half the final power reading error percentage. The errors
multiply up and, it seems to me, this is the problem with the cheap
digital wattmeter.

[2] The calculations also involve summation of the multiplier results,
preferably over several cycles and a 'sliding window' of the average of
all the sums of the instantaneous power calculations. A purely reactive
load of 100 VA should result in a zero watts reading given sufficient
sampling accuracy.

-- 
Regards, John.

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