If you want to set up your own OpenID provider, I can suggest two available options that you might like to look at. They're both PHP solutions.
The first is the easiest to implement, phpMyID, has been deprecated by its owner but it has risen again on GitHub. I quickly tested this yesterday using PHP 5.6.8. It's just two PHP files.
The second one is called SimpleID and is what I am currently using. I've used it to log on to a number of sites including this one.
Neither are OpenID Connect, however. I am looking for a solution to that so that I can upgrade (this search drew me to your question). The best candidate that I have found so far is called Gluu but it appears to be a behemoth and I haven't yet tried it.
SimpleID has a Trac ticket and a development branch to support OpenID Connect but it would appear to be dormant.
Another interesting thing I found while searching is web sign in and IndieAuth. Not OpenID, but interesting nonetheless.
