This was the subject of a graduate level course that I took during my masters degree program. I might give you a notion of what the terms mean, but I can?t teach you how to use them, or at least not without getting a serious case of carpal tunnel syndrome.
To start with, we tend to presume that all loads are balanced among the three phases. That allows us to use simple methods of adding loads. If the loads are not balanced, the math becomes very tricky. If you look at a non-balanced fault (e.g., single line to ground, line to line, or double line to ground, anything other than a bolted three phase fault), the math is also very tricky.
But some brilliant guy (who, by the way, I understand was awarded a PhD on the basis of about 20 pages of hand-written text), came up with a simple way to model unbalanced loads (including unbalanced faults). He created a model that uses three sets of data. One set of data (meaning current and voltage data) would be balanced within itself, and would have the same phase sequence (A-B-C) as the original (unbalanced) load. The second set of data (again meaning current and voltage data) would also be balanced within itself, but it would have the opposite phase sequence (A-C-B). Those two sets of data are called the positive sequence and the negative sequence. The third set of data is also balanced within itself, but there is no phase sequence. All three of its voltages are in phase with each other, as are all three of its currents.
What you are left with are three simple problems, instead of one complex one. You begin the analysis by converting the unbalanced problem into three balanced problems. Then you do the three problems separately. Finally, you combine them back by converting to a single set of data. The mathematical tool used to perform these manipulations is matrix algebra.
There. That?s about all my wrists can handle for now. Did this help?
