Question about calculating power factor...

[Default User]

Hi,

Let's say I start with 120VAC and 2A, both RMS. If I generate samples for
one cycle @ 60hz, I will have voltage samples raning from -169.7V to 169.7V,
and current samples from -2.83A to 2.83A. Let's say I then make the current
lag behind the voltage by 45 degrees, and I multiply the V sample by the A
sample to get a VA sample, I get these three graphs from Excel:

http://home.earthlink.net/~alank2/pf.gif

The top one is voltage, the middle one is amps, and the bottom one is V*A
(watts).

If I average all the samples in the V*A chart, I believe I will get True
Power (watts) from this measurement.

My question is, without the V or A samples, just the V*A samples, can you
calculate the Apparent and Reactive Power?

It seems to me that looking at the graph (bottom one) that there should be a
way, but I can't figure out how to do it.

I was able to calculate the RMS value of the V samples, and the RMS value of
the A samples, and then multiple that together and call it Apparent Power.

Can this be done by looking at the V*A samples alone? If so, how? If not,
why not?

Thanks,

Alan

 

[Eeyore]

Hi,

Let's say I start with 120VAC and 2A, both RMS. If I generate samples for
one cycle @ 60hz, I will have voltage samples raning from -169.7V to 169.7V,
and current samples from -2.83A to 2.83A. Let's say I then make the current
lag behind the voltage by 45 degrees, and I multiply the V sample by the A
sample to get a VA sample, I get these three graphs from Excel:

http://home.earthlink.net/~alank2/pf.gif

The top one is voltage, the middle one is amps, and the bottom one is V*A
(watts).

If I average all the samples in the V*A chart, I believe I will get True
Power (watts) from this measurement.

My question is, without the V or A samples, just the V*A samples, can you
calculate the Apparent and Reactive Power?

It seems to me that looking at the graph (bottom one) that there should be a
way, but I can't figure out how to do it.

I was able to calculate the RMS value of the V samples, and the RMS value of
the A samples, and then multiple that together and call it Apparent Power.

Can this be done by looking at the V*A samples alone? If so, how? If not,
why not?

Get a copy of Mathcad / Matlab etc.

Graham

 

[Default User]

Hi John,

Yes again.

Thanks for confirming this.

The instantaneous product of V*I has a DC (averaged) component, the
true power, and a 120 Hz AC component, the 2F thing in your third
graph; see the trig identity for the product of two sines. I think
there's enough info in them to derive the power factor, at least for
pure sine waves. I don't care to do the math this particular
afternoon, but it looks fairly simple.

I want to make the 3 calculations on any set of samples, sinusoidal or not.
Do you think it can be done on just the V*I samples in this case? I just
see that clean graph showing clearly where power is being taken and power is
being returned and if it is possible calculate the 3 values (true, apparent,
and reactive) based on it.

Thanks,

Alan

 

[Default User]

Hi John,

Dunno. Too hard to think about for free.
But if you have the E and I samples, why not use them?

I probably will, I just like to figure out stuff so I know why something
works or doesn't work.

My theory is that when you multiply v*i to end up with power that you lose
something in that process which makes it impossible to calculate the other
two values (apparent and reactive). Like 4x6=24 and 2x12=24, but once you
have the 24, you don't know whether it was 4x6 or 2x12. It just seemed like
the power graph had enough info to calculate it, but I've tried many ways
without success.

Thanks for the help!

Alan

 

[Phil Allison]

"Default User"

Let's say I start with 120VAC and 2A, both RMS. If I generate samples for
one cycle @ 60hz, I will have voltage samples raning from -169.7V to
169.7V, and current samples from -2.83A to 2.83A. Let's say I then make
the current lag behind the voltage by 45 degrees, and I multiply the V
sample by the A sample to get a VA sample, I get these three graphs from
Excel:

http://home.earthlink.net/~alank2/pf.gif

The top one is voltage, the middle one is amps, and the bottom one is V*A
(watts).

If I average all the samples in the V*A chart, I believe I will get True
Power (watts) from this measurement.

My question is, without the V or A samples, just the V*A samples, can you
calculate the Apparent and Reactive Power?

It seems to me that looking at the graph (bottom one) that there should be
a way, but I can't figure out how to do it.

I was able to calculate the RMS value of the V samples, and the RMS value
of the A samples, and then multiple that together and call it Apparent
Power.

Can this be done by looking at the V*A samples alone? If so, how? If
not, why not?

** The phase angle is given by the fraction (F) of each period when the
"V*A" samples have negative sign.

phi = F x 360

Apparent power is then = Watts / cos( phi)

Assuming all sine waves.


........ Phil

 

[Phil Allison]

"John Larkin"
"Phil Allison"

If the voltage and current are 180 degrees apart,

** Max phase angle is 90 degrees for pure L or C loads.

If they're 90 apart, F=0.5, and F*360 = 180.

Is the correct expression phi = F * 180?

** Yes.

Since the " V*I " curve has half the period of the originals.




....... Phil

 

[Default User]

Hi,

Ok, so from the V samples, A samples, and VA samples, I am calculating

True Power
Apparent Power
Reactive Power --> SQR(Apparent^2-True^2)
Power Factor --> True/Apparent
Phase Angle --> ACOS(Power Factor)

Given that I have the samples for V, A, and of course VA, is there a way to
find or technique out if the current is leading or lagging that does not
rely on the waveform being sinusoidal?

Thanks,

Alan

 

[Phil Allison]

"Default User"

Given that I have the samples for V, A, and of course VA, is there a way
to find or technique out if the current is leading or lagging that does
not rely on the waveform being sinusoidal?

** No precise one.

In any case, PF is not related to phase angle UNLESS the waves are sine.

The basic formula is

PF = watts/VA

See, no phase angle involved.



....... Phil

 

[Don Klipstein]

Hi,

Ok, so from the V samples, A samples, and VA samples, I am calculating

True Power
Apparent Power
Reactive Power --> SQR(Apparent^2-True^2)
Power Factor --> True/Apparent
Phase Angle --> ACOS(Power Factor)

Given that I have the samples for V, A, and of course VA, is there a way to
find or technique out if the current is leading or lagging that does not
rely on the waveform being sinusoidal?

A common issue nowadays is where voltage waveform is sinusoidal and
current waveform is not.

Power factor in that situation requires determining RMS amps (and RMS
supply voltage - easier) and load watts. RMS amps is usually not 1.111
(pi/sqr[8]) times average amps when the current waveform is not
sinusoidal. When the current waveform is spikier than a sinusoid, RMS
amps will generally be more than 1.111 times average amps.

Power factor is ratio of watts to product of RMS volts and RMS amps.

Leading and lagging are not so much the issue here as current waveform
having harmonics.

==============================

If you have time for mathematical exercising, this can also be done in
"frequency domain".

(Assuming sinusoidal voltage)

Determine amps in each frequency component - fundamental and all
harmonics.

Total harmonic current is square root of the sum of the squares of RMS
current for every frequency.
If you calculate separately sine and cosine components, total RMS amps
is still the square root of the sum of the squares of RMS value of each.

VA is that result times RMS voltage.

Watts is RMS voltage times RMS current for the fundamental frequency
component part that is in phase with the voltage (sine subpart if you have
voltage being sine, cosine subpart if you have voltage being cosine, or
volts times amps times cosine of phase difference from voltage if you
determine fundamental frequency component of current in total and its
phase relationship to the voltage.).

Power factor is ratio of watts to VA.

- Don Klipstein ([email protected])

 

[Default User]

Hi Phil,

** No precise one.
In any case, PF is not related to phase angle UNLESS the waves are sine.
See, no phase angle involved.

Good point!!

Thanks for the help everyone,

Alan