I bought a couple current transformers and TI's BQ25504 energy harvesting kit. I was able to charge a 1.5F supercap with a space heater. It took quite a while (tens of minutes) because the current transformers were actually rated for 20 kilohertz, and didn't seem very efficient at 60 Hz. I plan to remove the ballast resistor from a split core transformer like the one pictured and I will try to harvest the higher voltage available from that circuit.