> We can have a heat pump with a COP of 3.5 or so. Let's say we put in 1kW of electricity, and take out 3.5kW of heat energy.
A heat pump COP of 3.5 or higher or happens only at relatively low delta-T between the source and destination temps of the heat pump [1] - like the delta-T typical for space or water heating. The COP degrades exponentially with increasing delta T as it has to work ever harder to pump heat against an ever higher temperature/pressure (assuming thermal storage with a fixed volume with few losses).
The refrigeration cycle can't raise temperatures even hundreds (much less thousands) of degrees C - otherwise we'd already have heat pump stoves and ovens.
This is coincidentally also one reason why all else equal, heat pump clothes dryers (which are great) take a bit longer than conventional technologies to dry clothes: they only reach about 50C (vs 70C-75C for standard gas or electric resistance dryers).
> Push that back into the heat pump and, violà, 1kW of free heat left over!
Because the COP degrades with the delta-T, it bottoms out at 1 (an electrical resistance heater), and in your scenario, you end up with 1kWH in, and 400Wh out, so a theoretically 40% efficient battery.
Minus the electrical generation, and at much lower temperatures, your scenario with a heat pump + thermal storage does however describe how the new domestic thermal heat batteries can work with heat pumps [2].
A heat pump COP of 3.5 or higher or happens only at relatively low delta-T between the source and destination temps of the heat pump [1] - like the delta-T typical for space or water heating. The COP degrades exponentially with increasing delta T as it has to work ever harder to pump heat against an ever higher temperature/pressure (assuming thermal storage with a fixed volume with few losses).
The refrigeration cycle can't raise temperatures even hundreds (much less thousands) of degrees C - otherwise we'd already have heat pump stoves and ovens.
This is coincidentally also one reason why all else equal, heat pump clothes dryers (which are great) take a bit longer than conventional technologies to dry clothes: they only reach about 50C (vs 70C-75C for standard gas or electric resistance dryers).
> Push that back into the heat pump and, violà, 1kW of free heat left over!
Because the COP degrades with the delta-T, it bottoms out at 1 (an electrical resistance heater), and in your scenario, you end up with 1kWH in, and 400Wh out, so a theoretically 40% efficient battery.
Minus the electrical generation, and at much lower temperatures, your scenario with a heat pump + thermal storage does however describe how the new domestic thermal heat batteries can work with heat pumps [2].
1. https://www.engineeringtoolbox.com/heat-pump-efficiency-rati...
2. https://sunamp.com/