Brief Watts Discussion
Date : Tue, 03 Aug 2004 08:06:19 -0600
Subject : 1600 watts magnetizing current?
Original poster: "Steve Conner"
<steve.conner@optosci.com>
>The 1600 watts isnt going to heat, it is magnetizing the core.
The word "watts" should only be used when you're talking about real power.
For reactive power (like the power associated with magnetizing current) use VA.
If you want to be really pedantic, use "VA" for apparent power and VAr for
reactive power.
If we denote real power by "P", reactive power by "Q", apparent power by "S",
and power factor by cos(phi) (phi is the phase shift between voltage and
current) then the following relations hold:
P=Vrms*Irms*cos(phi)
Q=Vrms*Irms*sin(phi)
S=Vrms*Irms
S^2=P^2+Q^2
These assume sine waves. When we start to deal with seriously non-sinusoidal
currents, as in SSTC rectifier/filter power supplies, there are two power
factors- the original "displacement" power factor plus a "harmonic" one.
You probably couldn't care less about this stuff, but at least try to remember
that when you measure line current, and multiply it by 120, the answer you get
is the apparent power S (whereas in most cases you actually want to know P).
Steve C.
******
Date : Wed, 04 Aug 2004 07:29:29 -0600
>How do you
work out power factor when your
>voltage and current are non sinusoidal (we have bad waveform distortion here)?
Well, nowadays you use a "power analyzer" that digitizes the line voltage and
current waveforms, and does the analysis for you. I wrote a program that did
this using voltage and current transformers plugged into the line-in of a PC
soundcard, but I never had the guts to try hooking it to a Tesla coil ;) If
anyone wants the software to play with, they're welcome, but you need to
download the 11MB LabView Run Time Engine to make it go :(
You can also snapshot voltage and current with a 2-channel digital scope, and do
the calculations on a computer.
The basic idea is to do a Fourier analysis of the voltage and current waveforms.
This decomposes them into a combination of sine waves at 60, 120, 180, 240 Hz
etc. 60Hz is the "fundamental" and the rest are the "harmonics".
Then you work out the real and reactive powers for the fundamental and each
harmonic (using the equations I posted, as you are now dealing with sinusoids)
and add them all up (taking care to get the signs right)
If your line voltage is almost sinusoidal, and only the current is distorted, it
gets a bit easier, as you know that only the fundamental of the current waveform
can produce any real power, and all the power associated with harmonic currents
must be reactive.
In this case the math simplifies to:
S=Vrms*Irms
P=Vrms*I(0)*cos(phi) where I(0) is the RMS value of the fundamental current and
phi is the phase shift between Vrms and I(0)
Displacement power factor=cos(phi)
Harmonic power factor=I(0)/Irms
Overall power factor=(displacement PF * harmonic PF)= P/S = I(0)*cos(phi)/Irms
http://www.microconsultants.com/tips/pwrfact/pfarticl.htm Steve C.
Date : Wed, 04 Aug 2004 18:35:59 -0600
Hi Steve,
Another possibility, if the voltage and current waveforms can be captured but a
fourier analysis is either beyond the user, or equipment/sw is not available, is
to discretely sample the waveforms and compute the instantaneous power for each
discrete point over a cycle. The instantaneous power can then be
averaged. Likewise, the sampled waveforms can be used to compute the RMS
current and RMS voltage. Accuracy will depend on how finely the waveforms are
sampled. The power factor will then be:
PF = Average Power/ (Vrms *Irms)
This might be within reach of more people? Gerry R.