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Many countries are looking to phase out fossil fuels for domestic heat and hot water within this decade (see related question).

Which alternative energy sources will primarily replace fossil fuels? Options include on-site sources (e.g. pellets, or solar panels with heat pump/geothermal) and off-site sources (e.g. pellets with district heat, or grid electricity with heat pump/geothermal). Are there indications which of these will become the dominant energy sources?

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There's an interesting summary of the situation in the UK here.

In short, the most widespread option is likely to be heat pumps, despite some significant disadvantages, such as cost, and that fact that they don't always work well with existing heating infrastructure.

It may be that hydrogen, generated by renewable power, will also play a significant role - either with pure hydrogen boilers, or hybrid gas/hydrogen. It's supporters claim that it will be able to use the current gas distribution infrastructure, which if true would be a major advantage.

Wood-based heating has fallen out of favour recently, largely due to the fact that it produces dangerous pollutants, and the inability to grow enough wood to meet any large expansion.

Whilst district heating may be viable for densely populated urban areas or apartment blocks, there has been very little progress on this front in the UK.

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In terms of efficiently using sun's energy. Let's not forget passive solar. With no mechanical parts to break, a sufficiently heavy or phase change thermal mass can go a long way when the house is properly insulated. 4 m2 of windows (40 sq ft) is close toe 4 kW. (circa 12 000 BTU )

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The greatest trend in energy is electrification. I suspect this trend will dominate heat production, so heat would be produced using heat pumps. Their source can be industrial waste heat, datacenter heat, geothermal heat or even seawater heat.

Alternatives would be small nuclear reactors that produce only heat at low pressure and not steam at high pressure for electricity generation, and deep binary geothermal systems that don't require any heat pumps because 7 km below the ground the temperature is quite high.

Now, electrification is only part of the story. The big question is how the electricity is being produced.

In my country, Finland, the largest clean energy installations will be Olkiluoto-3 and Hanhikivi-1 nuclear power plants. Olkiluoto-3 has about a decade of extra delay and it seems the bill will be mainly paid by the supplier of the plant and not by the future owner of the plant. Hanhikivi-1 comes from Russia and the supplier of the plant has priced in all risks so Hanhikivi-1 will be far more expensive to the future owners than Olkiluoto-3 will be.

I suspect the high price of Hanhikivi-1 means it will be the last nuclear reactor constructed in Finland.

Already today the cheapest energy source in Finland is not nuclear power but wind power. There is plenty of land area in Finland for wind. So wind power installation is happening at a very rapid pace, in fact at a faster pace than construction of the new nuclear power plants as measured by actual produced average megawatts per year.

The problem of wind is that if the amount of wind power is sized to produce on average the needed electricity, with capacity factor of only 30% you get 3.33 times as much energy as you need during windy hours. So something will need to be done with the excess energy.

There are two ways the excess energy can be used:

Firstly, you can produce hydrogen with electrolysis, store it pressurized under ground and later turn it back to electricity with combined cycle power plants. Fuel cells can't really compete with combined cycle power plants as a fuel cell needs an inverter but a combined cycle power plant does not, fuel cell lifetimes are short and stationary fuel cells are more expensive than combined cycle power plants. Plus, even the theoretical best efficiencies of fuel cells are at about the same level as combined cycle plants.

Secondly, you can produce heat with heat pumps from various sources and store the hot nearly boiling water in some storage areas, to be used later to provide heat. Such storage areas can be underground caves (the rock is already a good enough insulator if the cave is big enough to have any meaningful storage capacity), or insulated floating storage sites constructed in the sea. Of course this storage only makes sense in district heating networks. Small individual homes having their own heat production means can't necessarily store much heat.

Also, because solar power production doesn't have a full correlation with wind power production, I suspect the future energy system will also have some proportion of solar photovoltaics installations and not just wind power.

Also it is worth mentioning that the existing installed hydropower capacity can also be used to adjust for variations in wind power production, but the trouble is there's not enough hydropower so other storage means are necessary too.

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