I just saw that you wrote the word inductively, though clever, you probably won't get enough stable current to power up your circuit. In addition, it would require that current always be flowing i.e. a few kW of constant usage in the house.
I assume you will also be measuring the current inductively to calculate usage?
Have you considered solar power to keep the logic going?
Make sure you stay clear of those bare un-fused rails, they are certain death if you touch them.