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A heat pump gets more heat from a given amount of electricity than if the electricity is use for resistive heating. So the ideal design is solar cell + sodium battery + heat pump.

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Also when the temperature differential is lower, so ideal might be solar -> battery (to time shift to warmest outdoor temperature) -> heat pump -> thermal battery (to time shift to when you need heat).

Does seem like a lot of added complexity (and likely machinery cost) though.

The question is would it cost less over the long term than any other solution. My intuition is it would, at least for a lot of use cases, but it would need to be put into practice and studied to see if this is actually true.

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