Free energy or universal basic income: which requires more economic restructuring?

There has been a fair amount of discussion around UBI and the implications it would have on society/ how it would work. Most of that conversation seems to surround autonomous systems replacing human jobs. But another potential in the future is free and abundant energy. Our systems and economies are heavily influenced by utilities and power distribution. If free and abundant energy became a reality, would that be a cause for UBI and, either way, how would the economic restructuring work to account for it?