What is the possibility for suing my landlord for overpaid electric?
You need to read your lease very closely but the fact that you don't have a separate meter paying the utility companies directly suggests to me that you don't have a snowball's chance in hell of winning in a courtroom. The landlord may, in such a case, set the rate, I suspect. Once again though, this stuff should be addressed in your lease, WHICH YOU SIGNED.