How to convert a device pluggable to a car lighter, changing to a regular home socket
Get yourself a cheap power supply with a built in 13.8 VDC port. I have an old one from Radio Shack that I bought 20 years ago, and still use for exactly this purpose.

Your cigarette lighter plug will socket directly into the supply - into the round hole just above the terminals.



Another option is to get a supply like this: 
iSaddle, 12 VDC, 10 A. It's more restrictive, but great price.