Maybe it will work out with deep drilling and a brine-water heat pump! Since the temperature of the heat source is relatively constant throughout the year, there is probably hardly any need for electric supplementary heating.
Back to the topic of photovoltaic + heat pump:
Here is an example chart from my logs at the end of October. I have already separated the household consumption into household electricity (below the fine line with dashed markers "corrected consumption") and heat pump electricity (dark blue when drawing from the grid, otherwise green or turquoise above the fine line) using the heat pump data. The accumulated figures in the box next to the legend are not quite accurate yet because some value is still missing somewhere. The correction in the consumption line includes, besides the separation of consumers, also a correction of the household consumption recorded by the smart meter, which can be seen with large shares of photovoltaic surplus (yellow) where the direct consumption drops below the black line. Sometimes this is 200+ W. Since this has both a relatively constant portion and a percentage dependent on the fed-in power (conversion losses?), I can correct it mathematically very well, which I was able to validate during vacation times with constant household consumption.
With appropriate battery settings, I can also prevent the heat pump electricity (which costs me 20 ct/kWh) from being drawn from the battery, as can be seen, for example, between 08:10 and 9 o’clock.
Due to the not too high heating demand, I have not yet used the heat pump's heating element configurable between 0.5 and 6.5 kW. However, mathematically it is even better to generate heat with the compressor using heat pump electricity at 20 ct with a COP of 3-5 than to "burn" photovoltaic surplus for that, since then for the same heat output with COP 1 I would need at least three times the electricity (in addition to the already running compressor), for which I would incur costs of more than 3*8 = 24 ct + self-consumption taxes due to lost feed-in. Arguments in favor of the heating element would be: avoidance of heating with the compressor at significantly lower outside temperatures at night (for air-water heat pumps), storing heat in the screed in order to cover house electricity from the battery only overnight, and lower wear of the compressor.
