Chris,
Thanks a lot for your detail discussion.
I think people had the concept of power factor long long time ago,
concentrating on the efficiency of power delivery in fundamental frequency. The
concept of harmonics, however, occured recently for the power emissions
distributed into harminic frequencies.
I got an impression from your kind input that the power factor correction box
works to solve harmonics problem because it changes the wave shape by wasting
some power in the attached box. That is a quick solution although not ideal.
Barry Ma
--------------
On Fri, 03 November 2000, "Maxwell, Chris" wrote:
>
> Barry,
>
> Vitaly Gordesky asked me the same question. (off line, just like you)
>
> In trying to explain the difference, It caused me to re-think some of the
> definitions. I like explaining this because it reinforces my understanding.
>
> Verbally, I think that in the most basic sense, we use Power Factor as a
> measure of how much rms current you need to put into a system in order to
> get the desired Real Power delivered to the system.
>
> Although I've never seen it written this way, I think that a good, basic,
> universal definition would be:
>
> PF = ARP/(Vrms*Irms)
>
> where PF = power factor
> ARP = average real power delivered over one fundamental period.
> Vrms= the root mean square of the input voltage over that same period.
> Irms = the root mean square of the input current over that same period.
>
>
> With that "verbal" definition in mind, we can then look at the math. Note
> that this definition assumes that the voltage and current are periodic with
> the same fundamental frequency.
>
> Mathematically
>
> 1. We can start by breaking the Current and Voltage waveforms down into
> their Fourier series.
>
> 2. Irms then equals the root mean square of the entire Fourier series for
> the Current (take each term, find its rms (Vpeak/2 for cosines), square it,
> add them all up, and take the square root.
>
> 3. Vrms equals the root mean square of the entire voltage Fourier series
> (same process as above).
>
> 4. Average Real Power ("ARP") then equals the integral of the product of the
> Voltage Fourier series and the Current Fourier series. This would be really
> messy because you would have to take each term of the Voltage's Fourier
> series (which could be infinite), multiply it by each term of the Current's
> Fourier series (which also could be infinite), integrate this product over
> one fundamental time period and divide by the period to "normalize" the
> result.
>
> This is where reality sets in (we realize we can't multiply and integrate an
> infinite number of terms with an infinite number of terms in our lifetime).
> At this point, some math wizard used mathematical identities and some
> assumptions to keep our sanity.
>
> The first mathematical identity is that the integral of cos(n*2*pi*f) with
> cos(m*2*pi*f) over one period of f is zero. (assuming that n and m are
> integers and are not equal). This means that we throw out all of the terms
> where the current and voltage frequency aren't equal.
>
> The second mathematical identity is that the integral of cos(n*2*pi*f) with
> cos(n*2*pi*f) over one period has a value of 1/2.
>
> Great, now we are left with ARP being equal to Vdc*Idc + the infinite
> summation of (1/2*Vn*In*cos(p(n))
> where:
>
> Vdc = the DC component of the voltage.
> Idc = the DC component of the current
> Vn = the nth Fourier coefficient of the Voltage
> In= the nth Fourier coefficient of the Current
> p(n) = the phase difference between the nth current and voltage harmonic.
>
> OK, we're almost there.
>
> If we then assume that the voltage has no harmonics (it's a pure sinewave at
> the fundamental frequency). And if we assume that the voltage has no DC
> offset.
>
> Then,
>
> This whole mess reduces to
>
> PF = cos(Po)* (Io/Irms)
>
> where:
> Po = the phase difference between the fundamental of the voltage and the
> current.
> Io = the current's fourier coefficient at the fundamental frequency
> Irms= defined above.
>
> The "cos(Po)" term is the familiar "displacement Power Factor" that arises
> from the phase shift between the voltage and current. The "Io/Irms" term is
> called the "distortion Power Factor" that arises from the current waveform
> being distorted and having harmonic components. High levels of harmonics
> hurt the "distortion Power Factor".
>
> Now, you may ask how "Power Factor Correction" works. It works by adding a
> module to the front of the power supply which draws enough fundamental
> current (and minimal harmonic currents) to feed the supply all of the
> fundamental and harmonic current that it would normally take. At the input
> to the power factor corrector, the value of Io/Irms becomes closer to 1.
> The power factor corrector draws more fundamental current which means that
> the product will need to be rated for a higher input power. Higher input
> power ratings mean that less products can be connected to the same mains
> circuit. Less products connected to the mains circuit equals a lower ratio
> of harmonic currents drawn from the mains circuit. The penalty is that, if
> you look at the power input to the power factor corrector module and compare
> it to the output power of the power supply, the system takes a big
> efficiency penalty.
>
> Thanks for asking. It's fun to look at this stuff sometimes.
>
> Chris Maxwell, Design Engineer
> GN Nettest Optical Division
> 6 Rhoads Drive, Building 4
> Utica, NY 13502
> PH: 315-797-4449
> FAX: 315-797-8024
> EMAIL: [email protected]
>
>
>
>
>
>
>
>
> > -----Original Message-----
> > From: Barry Ma [SMTP:[email protected]]
> > Sent: Friday, November 03, 2000 1:21 PM
> > To: [email protected]
> > Subject: Power Factor and Harmonics
> >
> > Hi Chris,
> >
> > When I read your email below I suddenly had a question: What's the
> > difference between Power factor and Harmonics? I could not remember
> > clearly the concept of power factor I learnt long time ago. They both
> > should come from the similar source: non-pure resistance load of AC mains.
> > But they should not be identical. What do you think?
> >
> > Barry Ma
> > ------------
> > From: Maxwell, Chris, Date: 31-Oct-00
> >
> > Vicor makes power factor correction modules that can be put in-line with a
> > power supply's input. My understanding is that they are not a
> > "stand-alone" product. You would still need to put the module inside your
> > enclosure. However, if you have room in your enclosure for the module, it
> > may prevent the power supply redesign that you're dreading. I don't know
> > all of the specifics of your application, so I'm not sure if this is a
> > good fit. Checkout www.vicr.com, you'll probably find enough information
> > there to tell you whether or not to pursue this solution.
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