If you have an area as large as 2 acres, there are some options. One is a simple 1 or 2 wire fence. Robert P who posts on BYC now and then is an advocate of a simple 1 wire system for enclosing large areas, claiming it works to keep the birds in and predators out. I tried it and moved on up to a 2 wire system, and while that may have been effective on the birds and most varmints, I found our little house dog was able to defeat it by jumping over it. If he could, I figured a fox or coyote could just as easily, so I upped that to a 4 wire system and since doing that, have not seen anyone go past it. Fowl or varmint. Top wire is still no more than 18 inches or so off the deck and I simply step over it. No gates needed.
You would not think a low wire system would work on birds, but it does. They don't like getting shocked anymore than anything else does and once they realize it is there, and recognize it as a barrier not to go near, they avoid it. My birds didn't fly over it, then stepped on it. With one foot on the wire and one on the ground, their foot got it and they would launch in the air, and still be cackling 30 seconds later. So there is a learning curve associated with it. Like everything else, the birds have to experience it, then learn to avoid it by not going near it. I can't tell if they all have to experience it or once one does, word gets around. Do chickens communicate like that? I'm firmly convinced some birds can and do.
If one does get on the outside and wants back in, they either punch through or simply hop over it. So its no physical barrier at all, but that is the nature of most electric fences. They are not a physical barrier. They are a mental one. The exception to this being the plastic netting hot fences, which are both physical and electrical. What they do is shorten the learning curve. They are also more effective for close quarters. They are also more expensive and require a lot more maintenance.
As others have noted, you help the fence by not putting your birds next to it. You put the shade and cover and green stuff in the middle away from the fences. This also helps with predators, as if the birds are in the middle away from the fences, approaching predators may still be in the sneaking closer mode when they encounter the fence. Too close and they may be moving fast and rushing the birds when they encounter the fence, and may not get shocked or if they do, not notice it in the frenzy of their attack.