As a lot of people on this forum are on-the-job trained electrians as opposed to engineers, I went ahead and drafted up a few phasor diagrams, hopefully they won't be too hard to understand!
These are Phasor Diagrams drawn in polar coordinates. (A phasor is basically a voltage represented as a vector.) Vectors represent voltage; angle represents the sine wave and phase shift.
1 full rotation represents 1 cycle, or about 1/60th of a second. If this were viewed in real time, you would see the vectors rotating counter-clockwise 60 times a second. The distance between the vectors is 1/3 of a cycle, or 120 degrees and represents the phase shift between each of the 3-phases.
This is what a normal Wye (star) looks like as a phasor diagram. Each leg is 120V long, and each is rotated 120 degrees apart.
Delta is derived by going line-to-line. The phasor diagram makes it easy to see the relationship between the wye and delta voltages. Mathematically, this is how the difference in voltages is derived.
In this diagram, the vectors we drew in the above diagram have been shifted on the graph so they're all measured relative to 0V. You can see that the delta voltages are rotated 30 degrees ahead of the wye voltages- this is what's referred to when people say delta is leading wye by 30 degrees or vice versa. The square root of 3 (1.73x) difference is easily visible here, too.
In this diagram, the blue represents the delta primary on a delta/wye transformer. The green phasors represent the wye created on the wye secondary. As the wye secondary is wrapped around the same coils as the delta primary, it essentially is taking the new wye and forcing it onto the delta. And since that delta was leading the old wye by 30 degrees...
Well, it's hard to explain this in a way that doesn't come off as incomprehensible gibberish, but hopefully staring at the pictures long enough will make sense
[This message has been edited by SteveFehr (edited 10-28-2006).]