When I compare heat pumps, I tend to first look at the COP-factor (how much energy you get out in relation to how much energy you need to put in), and then translate that to the COP curve (so it can be used together with the knowledge of the temperatures at your location).
It can be argued this is the most important factor, since if the effect is way too low, you will have no possibility to create the heat needed, independent of what COP you have. This is true.
But the reason for me to state it in this order is that the differences of size within a series of heat pumps from the same vendor tend to make very small improvements to your investment, since the bigger sizes tend to have worse COP and higher prices, whereas finding vendors with higher COPs make a huge difference in saved energy.
Different locations have different temperatures. Since the heat pump COP curve is different at different temperatures, you can only valuate what the effects of the curve mean for you by comparing it to the temperatures at your location.
Thus you need to have access also to temperature data. These are available in different ways, and it should be possible to find data for a location reasonably close to yours.
To simplify this kind of comparison, I have provided a simple form, doing basic calculations, and a form using daily temperature data to compare heat pump paybacks.
A house demands energy to be kept warm. How much energy is needed is not easy to calculate. In general, it can be said that the need increases rather lineary with the temperature, so a normal statement is to say "x Watts per degree Celcius". For my house, used in the calculations below, I have an approximate curve calculated for the energy needed.
If the house has originally been desgned for another heating system, and thus need water with higher temperatures than coming from the heat pump, the heat pump might not be able to heat the house, even if it delivers enough power. In that case, you need to make changes also to the radiators.
Calculations on heat cost can be done in different ways. For example based on yearly COP figures at location from a vendor or test institute, or based on quarterly or monthly figures, or ...
There is a compromise to make. If calculations are to rough, they will miss a lot of factors. If they are too compliceted, it will be hard both to find the data and to make them. The best compromise I have found is calculating based on day to day values.
The starting point in my case is a house with an existing electric heater and an existing air to water heat pump. Both of these devices are old, so there is better equipment on the market. But it turns out that exchanging them in a profitable way is hard as long as they are working.
The newer equipment is a lot better. But the cost associated with the investment to exchange them should be weighed against the additional savings that are done. Also, the cost for going to the best alternative should not be weighed only to the current situation, but also to the second best alternative. It turns out that the additional saving in each extra improvement step often has a decrease in gain and an additional associated cost compared to the previous step making it a lot less profitable.
As an example I will compare three alternative heat pumps from NIBE (the Fighter 2020 series). In this case, most important calculations are done as comparisons to the alternatives themselves, instead of as comparisons to the existing situation. This gives other results than I would have expected from a quick thought:
- The smallest and cheapest heat pump in the series (2020 8) is a good alternative when my current heat pump breaks, but is not strong and good enough to take away much more of the electric heater than today (the heat pump is weaker than my current, but with a better COP factor and producing heat down to -20 instead of down to -10). Thus, the small heat pump, although saving some money, has a very long payoff time (above 30 years) as long as my existing pump works.
- The larger heat pump (2020 10) is stronger, and thus makes the electric heater needed a lot less. Since the electric heater has no COP factor, this is what I would have expected to be the most economic solution. And it does save more heating cost than the smaller heat pump. But the difference in saved yearly energy is very small. The reason being that the COP-factor is not as good for that heat pump as the smaller one at a little higher temperatures (those temperatures are very common where I live). Thus, on average, the profit from needing the electric furnace less, is almost lost due to the decreased COP during a great part of the year. If there is a very small price increase for the bigger pump, then it might be a good choice, but some locations and some decades will see temperatures that makes it a very long payoff time.
- The largest heat pump is giving the same results, that is, taking away even more of the electric furnace (almost all), but still not improving the yearly cost to any high degree. Since the cost for the pump itself is even higher, the business case for buying that pump is worse, possibly not even profitable at all.
Considering the price of the pumps, the safest alternative turns out to be the smallest one. Intentionally dimensioning the heat pump so that the electric heater will work a lot during cold winter days, but relying on those days are fewer than the days where the COP for that pump is having the advantage. And even then, the investment is not worth doing until the old heat pump breaks down.
The tap water that is to be heated in the house is both similar and different to the water used for the heating. In some cases the heating water might need some more heating than can be provided by a heat pump. However for the tap water, it is more than likely tha this will be the case (yoy might want the water heated fast, and you might want it warmer than the heat pump can achieve). A rough business case calculation based on current tap water heating energy needs reveals a possible good business case.