How to restore Java Minecraft server after power outage
Solution 1:
Did you run the server on your local network, on your own system or on a public server?
If you ran the server yourself the server files should be in the directory you ran your server from.
If you ran the server from your client it should be in your minecraft client folder (see below)
Windows computers
Press Win+R, then type %appdata%\.minecraft, then press Ok.
OS X
In the Finder, from the Go menu, select 'Go to Folder', then type: ~/Library/Application Support/minecraft, and click Go.
Detailed description
If you ran your server on a public server there should be some periodic server back-ups you could access in a way. There is a boat-load of different scenario's for this depending on how this server was set-up and who managed the server. More information would be needed to answer this scenario further.
If you managed to locate your server files I would probably copy the files to another folder on your system and run the server once. This shall generate the server files it needs again with a blank world. After this is done, shut down the server and place your copied files back (overwrite Yes). This should be the last state your server was saved in. This is ofcourse excluding that your server files were damaged beyond repair due to your power outage. Let us know how it goes!