The solar tax credit is a non-refundable credit, which means it will reduce your tax liability, but not below zero. Based on your numbers, your tax liability is around $8,700 ($13,000 - 4,300); therefore, if you are eligible for a $9,000 solar tax credit, you can only claim $8,700. This will reduce your tax liability to $0, and you will receive the entire $13,000 that you paid in as a refund. Tax credits do not reduce your refund, but rather increase it.
Also, as a side note, your home's basis must be reduced by the amount of solar tax credit that you claim.
