208 three phase

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Birken Vogt said:
I have not tried this formula yet. But I got this video from another thread. It basically says polar coordinates with sine and cosine and run it through the Pythagorean theorem. I made an ugly spreadsheet and it works. 8.66 amps. Unfortunately I did not make it that far in math.

Can somebody more mathy than I explain if the SOS/SOP formula above is also correct?

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Let phase A be on the x-axis.
This puts phase B in quadrant III, and phase C in quadrant II, each 30 degrees from the y-axis.

This means each current value in vector form is the following, assuming unity power factor. Multiply each magnitude by the unit vectors at the 3 O'clock position, the 7 O'clock position, and the 11 O'clock position for each phase.
Ɪa = |Ɪa|*<1, 0>
Ɪb = |Ɪb|*<-1/2, -sqrt(3)/2>
Ɪc = |Ɪc|*<-1/2, +sqrt(3)/2>

Add up the x-components, and equate to zero:
Ɪnx + |Ɪa| - 1/2*|Ɪb| - 1/2*|Ɪc| = 0

Repeat for y-components:
Ɪny + |Ɪc|*sqrt(3)/2 - |Ɪb|*sqrt(3)/2 = 0

Solve for Ɪnx and Ɪny:
Ɪnx = 1/2*|Ɪb| + 1/2*|Ɪc| - |Ɪa|
Ɪny = |Ɪb|*sqrt(3)/2 - |Ɪc|*sqrt(3)/2

Combine in Pythagorean theorem:
|Ɪn| = sqrt(Ɪnx^2 + Ɪny^2)
|Ɪn| = sqrt((1/2*|Ɪb| + 1/2*|Ɪc| - |Ɪa|)^2 + (|Ɪb|*sqrt(3)/2 - |Ɪc|*sqrt(3)/2)^2)

Expand:
(1/2*|Ɪb| + 1/2*|Ɪc| - |Ɪa|)^2 = |Ɪa|^2 - |Ɪa|*|Ɪb| - |Ɪa|*|Ɪc| + |Ɪb|^2/4 + (|Ɪb|*|Ɪc|)/2 + |Ɪc|^2/4
(|Ɪb|*sqrt(3)/2 - |Ɪc|*sqrt(3)/2)^2 = (3*|Ɪb|^2)/4 - (3*|Ɪb|*|Ɪc|)/2 + (3*|Ɪc|^2)/4

Gather squares and simplify:
|Ɪa|^2 + |Ɪb|^2/4 + (3*|Ɪb|^2)/4 + |Ɪc|^2/4 + (3*|Ɪc|^2)/4 = |Ɪa|^2 + |Ɪb|^2 + |Ɪc|^2

Gather products and simplify:
- |Ɪa|*|Ɪb| - |Ɪa|*|Ɪc| + (|Ɪb|*|Ɪc|)/2 - (3*|Ɪb|*|Ɪc|)/2 = -|Ɪa|*|Ɪb| - |Ɪb|*|Ɪc| - |Ɪa|*|Ɪc|

Put it all together, and we see the formula is verified:
|Ɪn| = sqrt(|Ɪa|^2 + |Ɪb|^2 + |Ɪc|^2 - |Ɪa|*|Ɪb| - |Ɪb|*|Ɪc| - |Ɪa|*|Ɪc|)
 
ramsy said:
Whisky doesn’t mix with arithmetic.
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I know a pothead chick from around here that's in her early 40's that can do math in her head like a calculator. She is constantly baked. Her old math teacher is one of my friends and she told me she was a math wiz in high school. I don't know how you can be baked 24/7 and solve equations in her head faster than I can type them in
 
jim dungar said:
Technically Power Factor is not in percent.
PF is a dimensionless number that goes from -1 to +1.
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Why can't a dimensionless number be expressed as a percentage?

0.75 = 75% Simply another way of expressing that number. No different than expressing the same value in hexadecimal ( 0x0.C )
 
jim dungar said:
Technically Power Factor is not in percent.
PF is a dimensionless number that goes from -1 to +1.

It is usually not worth mentioning, but as long as this thread is running into the weeds anyway.
Click to expand...

I know it is usually expressed as 0.something but it is also frequently expressed in percent and it was the easiest way to state my request that I could think of at the time.
 
Birken Vogt said:
I know it is usually expressed as 0.something but it is also frequently expressed in percent and it was the easiest way to state my request that I could think of at the time.
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PF is a 'factor', by definition is used in further calculations. Sure, you can move the decimal and call it a percent, but you get to move it right back when you need to apply the factor in calculations.

PF is the inductive/capacitive alignment relative to the voltage waveform. Lead or lag.

Basically it is improper to only say example PF=.7, you must add whether that is capacitive or inductive, lead or lag.

PF is what hangs many ECs, especially when working with motors because PF is a moving target.
 
ramsy said:
Have you seen that person lately?
THC concentration in modern weed is no fun anymore, with paranoid delusions, clinically known as Cannabis-Induced Psychosis.
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Yeah, she was here yesterday made venison and ground pork meatloaf with roasted potatoes, Played with her rock collection, and fell asleep on my futon watching the grapes of wrath movie on her cell phone.

The rock collection is some crazy S, there has to be over a cubic yard of them, maybe 2 yards. Lots of stuff with fools gold imbedded in it, and and stuff with crystals in the middle, but lots of it just looks like round river rock to me. Her math teacher told me she always collected rocks.

paranoid delusions, clinically known as Cannabis-Induced Psychosis.

Yeah I saw some of that stuff on Youtube, not sure what to make of it because I know nothing about whoever made it. Not saying they aren't credible, just saying I don't know.

I got out of high school in 78 so what I knew from my generation could be different now
 
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