3 circuit multi-branch theory question

Status
Not open for further replies.
M

muellerp

Member
Greetings;

I'm looking for confirmation of my understanding of the "theory" having to do with the differential current supported by the neutral in a 3 phase multi-branch circuit configuration - I'm trying to visualize what is actually taking place. Suppose for this question I have: a 6A load on ph1, 8A on ph2 and 11A on ph3. The neutral will by design, safely support the differential current of 5A... but will it actually only be carrying that current (5A) for 20 of the 60 cycles? So, actually, during each second the neutral will see (equally spaced) 5A/2A/3A? Have I got this right? Apologies if answered in past, I couldn't find it if so.
 
180926-2105 EDT

muellerp:

Assume sine waves. The sum of two sine waves of identical frequency and phase related is simply a sine wave of the indentical frequency, and some phase angle. See any rerfernce on trigonometric functions.

After doing this once, then take that result, add the third sine wave, and the result is still another sine wave.

.
 
Also, the three sine wave amplitudes of a three phase wye circuit add as vectors with a 120 degree rotation from one to the other.
You cannot calculate the neutral current by simply subtracting 6 from 11.
To get a quick approximation you can indeed subtract 6 from each of the three amplitudes, since those three currents will cancel out on the neutral, which leaves 2A on L2 and 5A on L3.
The sum of those two sine waves at a 120 degree angle is about 6A.
***PS: major brain fog visualization there. Approximate vector sum is closer to 4A***

Sent from my XT1585 using Tapatalk
 
Last edited:
A more accurate method is to take 6x6 + 8x8 + 11x11 - 6x8 - 6x11 - 8x11, which equals 19, and then take the square root of that. Result is just under 4.4 amps.
 
180927-1945 EDT

muellerp:

Your statement
but will it actually only be carrying that current (5A) for 20 of the 60 cycles? So, actually, during each second the neutral will see (equally spaced) 5A/2A/3A? Have I got this right?
Click to expand...
seems to imply that you are not visualizing 3 sine waves added together on an instantaneous basis.

To better visualize this take a squared piece of paper (graph paper), and draw three sine waves overlapping each other. All are drawn on top of each other on the same X axis. The three are displaced along the X axis spaced 120 degrees apart.

At whatever small increment along the X axis add the three values at that point and plot the value. Repeat this for a full cycle. After these new points are created plot a smooth curve thru the points.

First, do this for equal amplitude waveforms. What is the result?

Next, do this for the waveform values you proposed. What is this result? Note that your plot peak values will be sq-root of 2 (1.414) times the RMS values you suggested.

What did you mean by
for 20 of the 60 cycles?
Click to expand...

.
 
Status
Not open for further replies.
Top