him76er,
We won't be able to give you a simplified answer, but I think we could break it down into simpler steps. You will need to ask questions/research the steps that you don't understand.
1) You start with 'Kirchhoff's current law' which basically says that any current flowing into a point needs to be balanced by current flowing out of that point. Think of a set of loads connected 'wye' to a neutral...all of the current flowing into the center point of the 'wye' needs to flow out somewhere. We know the currents on the legs of the wye, so we sum those three up to figure out how much current must flow through the neutral to balance this.
http://en.wikipedia.org/wiki/Kirchhoff's_circuit_laws
2) Now you have the problem that you are adding up AC currents which are constantly changing. The trick here is that sinusoidal AC current may be represented by a 'vector'. A vector is simply a way of describing a line segment that has both magnitude (length) and direction (angle). So for each of your three phases, you represent the current flowing by a vector, where the length of that vector is the RMS current, and the angle of that vector is the phase angle of the current flow. There are a bunch of different ways to add vectors; the easiest to understand is graphically; you just stick the vectors head to tail and draw a new vector from the tail of the first to the head of the second.
http://hyperphysics.phy-astr.gsu.edu/hbase/vect.html#vec7
3) The next step is to figure out the phase angles of the currents. For a 'unity power factor' load, the currents are in phase with the applied voltages. The three phase voltages are 120 degrees out of phase, so if you have three unity power factor loads you get three currents that are 120 degrees out of phase. In your example your loads have different power factor, so you need to figure out the 'current angle' from the power factor.
http://en.wikipedia.org/wiki/Power_factor#Definition_and_calculation Power factor is the cosine of the angle between the voltage and current,so if you know the power factor you can use the inverse cosine to get the phase angle difference. You have to add this phase angle difference to the phase of the applied voltage (since each phase has a different voltage phase angle) to get the current phase angle.
So once you know the current in each phase, represented in both magnitude _and_ phase angle, you simply add up all three currents, and this will give you the net current flowing on the neutral.
Consider balanced loading, where the current on each phase is exactly the same, and the power factor is the same. You represent this with three vectors, all of the same length, but with three different angles, all 120 degrees apart. If you draw this out, and add all three vectors 'head to tail', you will get an equilateral triangle; the head of the last vector touches the tail of the first, so the sum of these three vectors has length zero. Thus with balanced loading you have zero neutral current.
As I said, there are a number of different ways to add up vectors, including methods that are purely calculation based (no graphics at all). The formula that we've been discussing is one such method, though it assumes specific phase angles. Once you understand the basics of what is going on (the use of vector representation and vector addition) you can figure out the formula, but if you don't have these 'background' concepts, then the formula will be meaningless.
Heh, a GE book from 1911 has this spelled out quite nicely:
http://books.google.com/books?id=QB...mR9Ll43yV&dq=AC+current+vector+representation
-Jon
