You can have powers during the day, you have 90 Power Points to spend however you like. All I'm saying is that your concept / background have got to be within the scope of what is more in line with our real world during the day. Take our world, push the boundaries a little but don't break them.
In our real world magic doesn't exist but in this setting it can exist but it would either be low scale magic to avoid public scrutiny or you're perhaps part of a secret cult of mages or something like that. This way, you can have powers without breaking the boundaries. If you've seen anime then there are lots of shows that demonstrate relatively normal worlds like our own where the characters are still capable of doing things that a normal person in our world wouldn't be able to and that's the sort of thing I'm aiming for during the day.
Hopefully that makes sense.