When can power be converted?
You lose the rest. Conversions are performed only on your turn. According to the rulebook (p. 13):


  Anytime during your turn, on top of your Action, you may do any number of Conversions.


and from p. 9:


  Once all Power tokens are in Bowl III, you cannot gain further Power.


Therefore, if you are close to the limit of your Power, and expect to gain more before your next turn, you may want to consider Converting some of it to a useful resource.