208 three phase

[Carultch]

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?

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|)

 

[Joethemechanic]

Whisky doesn’t mix with arithmetic.

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

 

[Joethemechanic]

Kinda like Neil degrasse tyson describing 3 different types of truth.

He stole that from Karl Popper

 

[Tyler C]

Since the other method includes phase angle, just for giggles, how does power factor in percent convert to phase angle displacement in degrees?

inverse cosine - so for example, a pf of 0.95:
arccos(0.95) = 18.195 deg

 

[ramsy]

don't know how you can be baked 24/7 and solve equations in her head faster than I can type them in

Have you seen that person lately?
THC concentration in modern weed is no fun anymore, with paranoid delusions, clinically known as Cannabis-Induced Psychosis.

 

[jim dungar]

power factor in percent

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.

 

[winnie]

Technically Power Factor is not in percent.
PF is a dimensionless number that goes from -1 to +1.

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]

Why can't a dimensionless number be expressed as a percentage?

Upon further review, you would not be wrong, as PF is the ratio of kVA and kW.

By the way percent is also dimensionless.