I've heard of a trigger that allows some protoss buildings to be powered without a pylon, such as a cannon. Is this possible? I've heard that it only works on smaller maps... Thanks if you take up this task to help me.

I think you have to create and remove the pylon rapidly?

If you use the Enable Doodad State action on them they become powered, this is the same for all protoss buildings, but whenever a new unit is created, either by triggers or by building, and some other factors also do this I think, the cannon will become disabled again until you enable it once more.

Created or killed, I think.

You can also force them to be active by preserving the trigger for enabling their state plus hyper triggers...
You'll still see times in which the cannon spas's out... but it works for the most part.

Just for completeness.
It is sad but once the building which is upgrading something got disabled, the upgrade won't continue after enabling.
As far as I remember training men works fine though.

I still don't know how to do it, I used center locations on units then enable doodad state as well as doing an overall doodad enable trigger. The cannons don't work, but the gateways do... Sort of.

You can only enable one at a time, but if you give it away then it gets disabled once again, so in order to make it work you must place burrowed units under each cannon, and center on each burrowed unit, enable the cannon there, then give the burrowed unit away and center on the next one.