3 phase - Unbalanced loads from line to line
I find it easy to use complex numbers for something like this.

In your first example:

- Red:   20*cos(120)  +j20*sin(120) =  -10+j17,32
- Green:                            =   15+j0
- Blue:   5*cos(-120) +j5*sin(-120) = -2.5-j4.33


That gives a result of:

(-10+15-2.5)+j(17.32+0-4.33) = 2.5+j12.99


Total current through neutral wire:

sqrt(2.5^2+12.99^2) = sqrt(175) = 13.23


Angle:

arctan(12.99/2.5) = 79.1 degrees




In your second example, the red current does not influence the neutral current, so the red current is essentially 0:

- Red:                              =    0+j0
- Green:                            =   15+j0
- Blue:   5*cos(-120) +j5*sin(-120) = -2.5-j4.33


That gives a result of:

(0+15-2.5)+j(0+0-4.33) = 12.5-j4.33


Total current through neutral wire:

sqrt(12.5^2+(-4.33^2)) = sqrt(175) = 13.23


Angle:

arctan(-4.33/12.5) = -19.1 degrees


Hope this helps.




I think in America they use the z=a+bi notation instead of z=a+jb? Not sure.
I should really figure out how to post real formulas, sorry