Phase Stabilizer Arrays is an upgrade to the Vasari Orkulus Star Base allowing it to operate as a Phase Stabilizer. Useful if you manage to set one up in neutral space or even on top of the enemies, as it allows you to send reinforcements from anywhere in the system. It can also be used to retreat, avoiding any potential ambushes as your fleet safely arrives at your homeworlds.
The Phase Stabilizer is often an important target to invaders, so it may be a better idea for Vasari players to put their Phase Stabilizers on their Starbases. This gives them a lot more hitpoints and armor plus any offensive upgrades they have installed. That should give your fleet enough time to align and jump that they might not have had if the Vasari player had only built a Phase Stabilizer.
In team games, this can be an awesome way to help your allies. And all you need at first is a cheap Jarun Migrator that you send to one of their planets. Not only will they have another starbase for defense, but should they be in real trouble your fleet can be there in no time to help them. Watch the face of the enemy when his certain victory evaporates as your main fleet unexpectedly jumps in...
Do not forget however to have a Phase Stabilizer somewhere back home.... not that it is your fleet being lightyears away from your empire when an invasion force is pounding your helpless worlds.
The power of this ability should not be underestimated... more often than not your allies are defeated because you are to far away and not because you do not have the military power to help them.