Dog Friendly Goat/Sheep Fence

I've got a decent (to me at least) amount of land and 2 dogs that love having free run of it. It's 5 1/2 acres and I have all but the front near the road electric fenced (the kind with the collars not the zappy-ouchy kind). I want to put in some fence and get some goats or sheep, but I don't want to block off all of the land from the dogs. Does anyone have any suggestions for away to contain the goats but allow the dogs to come and go? I've never had sheep/goats so I'm not entirely sure what they are capable of. I was thinking maybe I could put a dog door in the fence, but I'm guessing goats would figure that out pretty quick. Maybe put a culvert under the fence? My dogs would figure that out quick, but can goats crawl? If anyone has already implemented a solution to this problem I'd love to hear about it!

Are you positive that your dogs won't try to chase or harass the goats/sheep, and need to be kept separated anyway?

I don't know much about sheep or goats, but dog-wise, there are dog doors that are activated by a sensor on the dog's collar. You could build a gate in a fence with one of those doors, and it would only open for your dogs, and close several seconds later. You'd have to check how well they would hold up to the elements, and you'd need a source of electricity.

I agree about separating the goats/sheep from the dogs.

Are your dogs trained to herd animals or LGD?

Once you have the dogs acclimated to the goats/sheep then your plan might work.

If you do decide to make the fence accessible to the dogs, Greg Judy of Regenerative agriculture has a neat idea for a fence for dog.  He has small areas of his fields for his LGD living with his sheep flocks full time.  It is a fence the dogs can lay down and scoot under to get to their feed without the other animals being able to follow.  

I don't own sheep and goats, so never seen one go under a fence, but he claims it works well to give his guard dogs a space to eat without harassment.  

Totally agree, dogs must be trained to not harass your own animals. Dogs love to play and won't understand they they can't chase an rough house your goats.

Portable electric netting fence may work. We use it. We also spent time training our goats and dogs to electric fence. We raise LSD too.

Any dog breed with a high prey instinct is going to be very challenging if not impossible to keep on a farm.