I looked at the parts catalog on the Cub Cadet site. The diagram with the charging system did not show a regulator. But the parts list for that diagram listed a regulator at the bottom of the list with no reference number. The part number is BS-794360. Searching the web for it shows a square part with what appears to be an aluminum housing and 2 wires attached. One is red and the other yellow. It appears to be held on by a single screw through the middle. Going to PartsTree, the diagrams for your engine show that regulator as one of the configurations that engine could have. Searching that number, there seem to be plenty available with prices from about $60 to twice that. The same search will show you plenty of pictures of it. Look around on your motor for a square piece of aluminum.