What’s the cheapest way to heat and cool a house?

I’m currently in research mode looking into the next step towards energy independence. For the next investment (actually reinvestment, of savings from previous investments, particularly the electric car), I’m weighing up Battery Storage or a Heat Pump. Each have their merits. Battery storage provides a way to store excess Solar PV in summer, and to store cheap night rate electricity (€0.05 / kWh) in winter to remove daytime electricity costs (€0.19 / kWh) – like PV, prices are falling rapidly, though it is still probably on the expensive side. A heat pump would allow us to heat the house fully with electricity, meaning we can generate it ourselves at a fixed price per kWh no matter what gas / oil markets do, remove our gas connection and it’s costs completely, and obviously remove our gas bills.

I’ve done some maths, and the picture looks like this:

The Numbers

The research got me thinking about how to calculate the long term cost of every type of heating system, including both the capital investment, and the yearly running costs (e.g. the fuel costs). Using average gas, electricity and oil costs from the here, and using my own house’s heating load for 2016, here are some back of the envelope cost comparisons:
 
For the year of 2016, our house required 19,898kWh of heating. The various yearly costs across different heating sources for this would be:

• Gas: 19,898 kWh * €0.0652 = €1,297.35
• Oil: 19,898 kWh * €0.0710 = €1,412.76
• Heat Pump with Night Rate electricity (with 300% efficiency, with night rate electricity @ €0.05 / kWh): 19,898 kWh / 300% efficiency = 6,632.6667 kWh  * €0.05 = €331.63
• Heat Pump with Solar PV, including PV installation cost (with 300% efficiency, half with excess PV @ €0.00 / kWh and half with night rate electricity @ €0.05 / kWh): €248.73

 
In the Heat Pump + PV scenario around, calculating the split between excess PV and night rate is tricky – most excess PV will be in summer when there is little heating requirement, so this figure will fall somewhere between €165.82 and €331.63, so I take the average of the two €165.82 + €331.63 = €497.45 / 2 = €248.73

Assuming installation costs of: Gas (€2000), Oil (€3500), Heat Pump (€4000) and Heat Pump plus PV (€7000), coupled with their yearly running costs above for 15 years gives the chart above.

Heat pumps certainly come out cheapest. A heat pump will be cheapest of all if you already Solar PV installed, as some of the heating can be done with excess PV generation. If you don’t already have PV installed, then it wouldn’t make sense to install PV just to run a heat pump, it would be cheaper to bring in all of your heating needs with a heat pump during cheaper night rate electricity.

The installation costs are rough estimates – I haven’t installed these before so I’m not sure. But you could re-do the chart above yourself based on your own installation costs and heating requirements to figure out what is cheapest over the 15 years. Oil and gas prices taken from here. Day / Night rate prices taken from what I’m currently paying.

How is a Heat Pump More than 100% Efficient?

Wait, in the figures above, the heat pump is 300% efficient. How can that be? A rather amazing thing about a heat pump is that they are often more than 100% efficient. For every 1 watt of electrical energy used to run them, they can pull in 3 or 4 watts of heat energy into your house. No, they do not violate the laws of thermodynamics. They do not “create” energy, they “move” energy. They move it from one medium (heatpumps use air, brine, water) with “low” temperature to an other medium (or the same) with “higher” temperature. This is pretty compelling, particularly when you can quite easily generate your own electricity with Solar PV – they provide a path to generating all of your own heating and electricity at very low costs. Dig more into heat pumps here. The Heat Pump in the figures above is 300% efficient, so it takes 19,898kWh of heat energy demand / 3 = 6,632 kWh of electricity to pump in 19,898kWh to the house.
Here’s a useful overview of how heat pumps work:

How Heat Pumps works

If you live in a hot country that requires cooling in summer, you’re in luck also: Reversible Heat Pumps work in either direction to provide heating or cooling to the internal space. A reversible heat pump works like this:

How Reversible Heat Pumps provides both heat and cooling

Here’s what a Heat Pump actually looks like:

An Air Source Heat Pump hooked up to a house