The converter should have a wire to connect a battery. You may have to search for a manual to find the wire color, or post the make and model and someone here might know. I would recommend 10ga wire to connect the battery to the converter with an inline fuse close to the battery. Connect the battery ground to the trailer frame 10ga as well.
In your other thread you you mentioned your tow harness is a four-pin. There is no connection from the battery to the tow vehicle with a 4-pin. The 4-pin harness powers only the brake/turn/running lights.