Just stumbled across this while looking at Lithium Iron Phosphate batteries. Qychex appears to have a energy system they expect to be selling for home power that seems to claim it puts out more power than it consumes. It uses "two distinguishable energy sources to coexist with each other, and therefore produce a by-product electrical chemical reaction, greater than the sum of the two independent power sources."
They claim to have prototypes installed in homes and some business that are working and available in 5kw, 10kw and 20kw units. They say the plan to sell starting 2017 but it appears they are not yet selling them now in 2019 although it may be possible to obtain a unit via their contact. They mention an ongoing Patent Pending Certification and Underwriters Laboratory testing.....
Take a look here: https://www.qychex.org/qychex-power-generator.html (https://www.qychex.org/qychex-power-generator.html)