> For a buffer to work, it necessarily needs to be hotter than supply temperature, which means more losses and more work for the heat pump.

The buffer is there so the heat pump doesn't have to cycle or throttle but can work with maximum efficiency as long as possible. That is all. It is not there to heat your house for next few hours. I think newer ones that have throttling can just work with hydraulic clutch.

But the biggest difference is that heat pumps really want that more flow with lower temperature situation (as of course efficiency drops with the temperature), so you really want to have either higher area heaters or floor heating.

> Since heat pump can easily adjust the supply temperature, the most efficient system will be the one where the energy delivered to underfloor heating or radiators is just balanced out by heat loss of the building.

That's independent from heat source really. Also if you're using heat pump you need to define efficiency in "how much you pay for power".

If, say you have cheap power at night, it might very well make more financial sense to pump more heat into the system (i.e. heating house a degree or two more) in the night rather than waiting for morning where tariff will make you pay more to do that. Similar if you have solar system.

> If one really needs 25kW heat source, one really needs a 25kW heat source. There is no clever way around it. The real question is whether one really needs 25kW heat source (which can be answered definitively by either measuring the delivered==required power, looking at the peak continuous fuel consumption (let's say the coldest day or week), or by having accurate heat loss model of the building. In a heating season, the buffer cannot realistically be large enough to significantly reduce the power requirement. For example, 1m3 of hot water when used as a buffer can store roughly 30kWh (when heated 25 degC above supply temperature). My house needed 240kWh of energy in the coldest day, so the buffer would only cover 10% of the needed heat.

240kWh is 10kW energy continous. So you wouldn't need 25kW heat pump, you'd need 10kW one working all the time, maybe 12kW if you couldn't tolerate temperature dropping at night by a degree or two. Of course, that's gonna suck if you lower temperature (say going on holiday) then get it back to usual (compared to twice as powerful gas heating) but you can work around that with programming.

The buffer is there mostly to avoid pump from cycling, electric engines like to spin at constant speed instead of being started and stopped every 10 minutes. Also your entire house is a heat buffer too.

Gas boilers are also very often oversized, especially in older homes where someone might've put some isolation in but not tweaked the boiler size for it. Or if you have dual-purpose one that is extra powerful for heating. Less of a problem now as a lot of them can modulate heat output but still.

And actually the condensing gas boilers also like low water temperature on return because the condensation is more efficient.

energy-wise the best solution would probably be gas-engine heat pump (basically heat pump gas engine instead of electric one + piping to also recover heat from that gas motor), but last time I've checked that's pricy for home scale and more maintenance compared to just electric powered one. But you get significantly over 100% efficiency compared to just burning that gas.

Other interesting thing I saw is so-called "co-generators" where you just have electric generator powering your house (and selling excess to the network) + use the waste heat for heating but that looks like a bit hard to balance between too much power and too little heat.