Unbalanced Systems

By all means I didn't originate this question; but it's something that I had wondered about.

Let's keep it simple for now; You have a house pot 120/240 service. 30 amps on one leg 20 amps on the other, so you end up with 10 amps on the neutral. I get that.

Awhile back another another guy I work with both questioned how about 3 phase on a feeder; how many amps on the neutral.

Here was the question that originated somewhere:

Need to know how unbalanced my system is. Have 173 amps an A phase, 132 amps on B phase and only 76 amps on C phase. Assuming normal 120 degree phase shifting between phases, how much current is on the neutral?

I went and thought about it and this was an answer that I came up with;

I'm wanting to say 102 amps but I'm unsure of this. Took the average number of all 3 phases and then took the sum of all the differences from the average.

So to check myself I went to the top and got an answer from an engineer. The answer is 84 amps.

This involves some formulas to put together. Fortunately I was given an excel spreadsheet calculator to input the data and get the correct answer. I don't expect very many people to be able to get this scientific unless your an engineer.

Attached you'll find the calculator and a document as to how he arrived with the answers.

Now I can't get any further in this; but this is specific for the system that I work in that from what I'm told is a ABC clockwise rotation; in other areas of our system there is a ACB rotation from what I was told and I stop there.

If any of ya'll care to enlighten me in layman terms I'm game.