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My other idea is using insulated tanks of distilled water buried in the ground for residential peak shaving. Overnight, the water is heated to 90°C using cheap excess capacity. During the morning peak, the heat pump uses it as a source of readily available heat for central heating. You can even have a fully mechanical heat pump "trickle-heating" the water during the night from a small wind turbine, since you just need to run the compressor and move the liquids around. There should be enough wind to heat up a tank of water even with a small backyard turbine.

I'm a complete dilettante in this, so I'm probably missing 99 reasons why this would be a lot more difficult.
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@monsieuricon This is a thing, except not usually buried. Search for "non-pressurized hot water storage tank". I have a friend who has one in conjunction with his geothermal system. It has something like 4" thick styrofoam walls.

Sometimes there's a heat exchanger in the tank, and sometimes the heat exchanger is outside the tank. My friend's geothermal system uses the external geothermal heat exchanger for this purpose, so the tank is really just a styrofoam box. His is a rectangular prism; some are cylindrical.

Just keep it completely separate from your plumbing system; these energy storage system hot water tanks can get some fairly nasty bacteria growing in them that stay alive at unreasonable temperatures.

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