You
should be able to keep the goats in with only one strand, at nose height, if the goats are trained to respect electric
fence. If they aren't , you will hardly be able to keep them in no matter how many wires you use. To train them, run the wire first along the inside of the physically fenced paddock, so that the goats will encounter the hot wire before hitting the physical
fence. After a few good shocks, you should see them avoid the perimeter completely, rather than rubbing against the fence or trying to poke their noses through like they would an undefended physical fence. To be extra sure, and train them extra quickly, you can bait the wire. Put little tags of aluminum foil every ten feet or so along the electric wire. Daub peanut butter or jam or something else yummy on the tags. The critters will lick these and get a really good shock. Best be sure the ground is moist and the fencer well grounded for this
project. It sounds cruel but it works! Incidentally the same technique will get
deer to respect a single wire boundary for months, also....