# What is the relationship between air source heat pump and indoor heat pump water heater?

I am sure this has been analyzed here before, but I want to check my reasoning. A criticism of heat pump water heaters is that they cannibalize the home heat source and so during the heating season perform exactly as electric water heater efficiency. However if the heat is provided at COP 3 from an external air source mini split, then am I correct that the heat that is being “borrowed” by the heat pump water heater is also COP 3 and so year round the heat pump water heater functions at COP 3 or better?

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## Replies

You have the right general idea but the analysis is more complex. In an idealized analysis, suppose the COP of the water heater was 2 and the space heating system had COP = 3. For two joule of heat energy in the water, the water heater would pull one joule out of the air, and one from the electric supply. The joule that came out of the air would need to be replaced by the space heating system, which would require 1/3 of a joule from the electric supply. The total electricity use would be 1.33 joules, to supply 2 joules of water heating, so the net overall effective COP would be 1.5.

In practice, some of that heat might come out of the ground if the water heater is in the basement, and to some extent it results in the basement being a little cooler which might decrease heat loss from the basement to the outdoors. So the net effective COP is at least 1.5.

In the summer, you could similarly credit the extra cooling and dehumidification provided by the water heater, and come up with an effective COP greater than the actual water heater COP. So just assuming that the effective annual average COP is equal to the rated water heater COP is not likely to be very far off, unless you are in an extreme climate.

Charlie, I was thinking of Stiebel Eltron Accelera 300 hot water heat pump which has a COP of 4 at 68 degrees F. So it is pulling 3 kwh of energy out the air for every 1 kwh it is providing electrically. Those 3 kwh have been provided by 1 kwh of electricity from the air source heat pump so we get 2 free kwh for the hot water pump so it ends up being cop 3 in actuality, I think. (This question should be on an IQ test!)

Ven, using your numbers, of the 4 Kw heat into the water, 1 Kw is electricity to the HPWH, 1 kW is electricity to the space heating ASHP, and 2 kW comes from ambient air (what you call free). Since there is 2 kW of electricity to produce 4 kW of water heat, the COP is 4/2 = 2.0.

Reid, I think you passed the IQ test. That sounds right to me.

Ven,

Here is recent analysis done by the NRDC comparing the efficiencies of ER/Hybrid/Split System DHWH's by state - https://www.nrdc.org/experts/pierre-delforge/very-cool-heat-pump-water-heaters-save-energy-and-money. While I don't think it addresses your cannibalization issue, it does address performance based on location climate - i.e. split system (Sanden) more efficient in FL vs NJ because of the warmer outdoor temps, hybrid (discontinued GE) worse in NJ vs FL because of need for backup electric resistance. So for NJ the COP's are 3.14 for a split/2.47 hybrid/.95 for ER. Since NJ is a heating dominated climate, that would mean the hybrid is a something less than 2.47 if cannibalization not factored in. If you look at FL, split and hybrid are 3.47 and 2.86, respectively. Again, assuming cannibalization not factored in, the hybrid number would be better in FL than shown.

I think this analysis supports the general belief that hybrids and split systems perform better in warm climates than in cold climates and split systems perform better than hybrids in cold climates - even in Alaska.

Jonathan,

Thanks for that. It certainly make sense that all heat pumps perform better in warm climates than cold. The question really is, how well do hot water heat pumps perform year round in cold climates when used in conjunction with a high efficiency mini split. And I think the answer is that, the year round efficiency (based on Stiebel eltron accelera 300) is 7 months at cop 4 and 5 months at cop 2. In percentage 75% reduction 7 months and 50% reduction 5 months for a total reduction over electric heater of 65% year round. With that info one can decide if they are economically worth it over their lifespan, or perhaps that they are ecologically worth it, but only break even economically.

Ven,

It is definitely better ecologically. I looked at the DOE annual kWh estimates for the Rheem 80 gallon ER and the Stiebel 80 gallon. They estimated annual usage of 4622 for the Rheem and 1289 for the Stiebel, which does not factor in the cannibalization. As for economically, I took a look at what my payback might be assuming I decided to go with the Stiebel for my upcoming new build and came up with the following:

* Incremental cost of Steibel: $2500 - $600 = $1900 (let's assume install costs are the same and I do it in 2017 so no rebate)

* Annual energy savings: 4622-1289 = 3,333, but let's use 3,000 to factor in something for cannibalization

* My annual energy savings at $.165/kW: 3000*$.165=$495

* My payback: $1900/$495=3.83 years - not bad assuming my numbers are correct

Next I checked the cost to go net zero with the Stiebel. Len Moskowitz recently posted that he was able to install a 9600 kWh nominally rated PV system for $17640 after tax credit in NJ, so let's assume I can do it for the same cost as Len since he is located not far from me and I would be the builder too. Based on the PVWatts calculator, the system would generate 12,000 kwh.

* My cost/kWh after tax credit would be: $17640/12000=$1.47.

* My cost to offset 1,622 kWh annually would be: 1622*$1.47=$2384 (includes 333 kWh for cannibal fudge factor)

* My total incremental cost for the Stiebel plus offset panels: $2384+$2500=$4884

* My payback would be: $4,884/(4622*$.165) = 6.41 years.

So worst case scenario is that at least 97% of scientists are wrong about global warming, not to mention health issues associated with pollution from fossil fuels, and the cost of carbon is actually zero, then I would still be better of going net zero than just go ER without solar. Assuming there is a cost to carbon, then payback is less than 6.4 years.

I don't know enough about solar thermal beyond the fact that is dead, really, really dead, but I wonder how the numbers would work out with that.