Your numbers are actually correct. A nonrefundable credit means that you don't just get money back that YOU DID NOT pay in. It is different thana refundable credit like the Additional Child Tax Credit or the Earned Income Credit, where you get back money even if you didn't pay anything in.
When a nonrefundable credit lowers your tax liability, it DOES allow you to get a refund of the amount YOU PAID IN. So, the $37,888 that you had either withheld or paid in, you over paid once the solar credit was added into the mix. Before the credit, you still owed the government $1,173 because you underpaid your liability. Now you are getting back the $18,516 that you overpaid to the IRS because your tax liability was reduced by $19,689 because of the solar credit.
The nonrefundable credits can give you a refund of YOUR money that was yours to start with, but it will NOT give you a refund of the GOVERNMENTS money.
A Refundable credit will give you a refund of GOVERNMENT money that was never yours and that you never paid in.
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