Re: UPS VA ratings (was: Re: [PLUG] equipment give-away on Wed evening)

[Jeff Abrahamson <jeff@purple.com>]

Dividing by the square root of two is more than a good approximation:

   <http://whatis.techtarget.com/definition/0,,sid9_gci213722,00.html>

To compute the root mean square of a sinusoidal wave form, we want to
compute the square root of the mean value of the square of the
wave. In other words, square the sin, add it up (integrate), and
divide by the length of what we integrated before taking a square
root.

It suffices to find the root of the mean from 0 to pi, since sin
squared is periodic with period pi:

    sqrt ( integral(0,pi)[sin^2 x dx] / pi )

In other words, compute the area under the curve of sin squared from 0
to pi, divide by the length to get the mean, and then take the square
root.

The integral of sin^2 x is 1/2 x - 1/2 sin x cos x + C. The second
term is zero at both zero and pi, and the first term is zero at
zero. Since the constant cancels out, the integral from 0 to pi is
pi/2. Divide by pi and we get 1/2. Take the square root.

-Jeff


On Tue, Jan 07, 2003 at 08:18:06PM -0500, Tom wrote:
> The model numbers on APC products usually correspond to the Volt-Amp rating of 
> the UPS.  Volt-Amps = Volts (i.e. 120 VAC) * Amps (i.e. current draw). On AC 
> sources you have to multiply by the power factor because of the fact that 
> it's an AC sine wave source.  Voltage and current aren't always in sync in an 
> AC load.  That's why multiplying VA by square root of 2 (0.707) is a good 
> approximation of how much power you can draw from an UPS.
> 
> HTH,
> Tom
>  
> On Tuesday 07 January 2003 17:50, Fred K Ollinger wrote:
> > > On Tue, Jan 07, 2003 at 03:54:07PM -0500, Jeff Abrahamson wrote:
> > > > I have two UPS'es (uninterruptible power supplies). They are 420 and
> > > > 450 VA respectively. Remembering freshman calculus and root mean
> > > > squares, this means they are rated 300 and 320 W respectively.
> > >
> > > Care to elaborate on that? I'm glad to admit my complete lack of
> > > knowledge; I'd presumed those were model numbers. (I've got a pair
> > > of 1100s, and it sounds like it was a good idea to go that large,
> > > being as I've got a 450 W power supply in my IA32 machine...)
> >
> > Actually, IMHO, the model numbers (at least for apc products) are the
> > voltages.
> >
> > Fred

Attachment: pgpU6kSgrsUNz.pgp
Description: PGP signature