I agree that the improvements in air source heat pumps over the last couple
decades, with operation down to as low as -25 F (albeit at low COP) has been
a game changer.  For one thing, I think they have made ground source heat
pumps non-competitive due to their much higher cost.  But I am not so sure
they are always the best solution.  

I've looked at this for my house, and this specific case illustrates some of
the variables. I can build a solar thermal system, collectors, pumps,
insulated storage tank and plumbing, with 200 ft^2, collector area for less
than $3k.  This system will provide about 33kWh, 112,600 BTU, of heat to the
storage tank per day (50% efficiency, measured), and about 30kWh into the
house assuming a small amount of loss in the plumbing to the liquid-air heat
exchangers.

Using a cost of around $2.00 per Watt owner-installed, including racks,
inverter, wiring, etc), this $3k would purchase about a 1.5kW PV system
(example prices:
http://www.wholesalesolar.com/gridtie.html#SolarSkySolarWorld).  In my area
that would supply about 7kWh electric per day yearly average, based on 6
years of data on my 5.6kW system. Heat pumps have to be purchased to turn
this into heat into the house.  An 8kW (27,000 BTU) heat pump is around $3k
(for example:
https://www.acwholesalers.com/Fujitsu-Air-Conditioners/AOU24RLXFZ-ASU9RLF-ASU9RLF-ASU9RLF-27000-BTU-18-SEER-Ductless-HeatPump/14513.ac?gclid=CLb7ifC5lsMCFdgHgQod_7UAIg).
 
With COP of 3 this would deliver about 21kWh of heat using the 7kWh of
electric per day, about 30% less than the solar thermal.  But as someone
said, I may use that power year around, but not the heat from the solar
thermal.  In our area we need to heat about 7 months of the year. The 200
ft^2 collector would only supply part of the energy required to heat the
house over most of the winter, so I would use the full output over at least
5 of the 7 months.   

So for 5 months of the year I get 30kWh from solar thermal, and about 20kWh
from PV.  For the other 7 months I get nothing from solar thermal (not
quite, some used for about 2 months) and 7kWh per day, or about $0.84 per
day ($.12/kWh) from solar PV, or about $175.00 per year.  I had to pay an
additional $3k for the solar PV and heat pump system, which would be paid
back in about 17 years at current utility rates.  After that the PV/heat
pump system would save me $175 per year in electric costs at current rates
if I use its full output year round, or the utility pays me retail rate for
surplus electric I supply.  But I am not going to use that full output over
the rest of the year unless I run AC enough during the 7 months to use the
same energy I used from the system for heating during the 5 months of
winter.  I don’t.  I just open the windows at night. In addition, we have
net metering in my state, balanced over a year.  So any surplus I have
supplied at the end of the year is tossed out, I get no payment for it, so I
wouldn’t gain $175 per year to pay back the $3k high cost of the PV/heat
pump system and bank after that.

In this case I pay twice as much for the solar PV/heat pump system and get
less roi from it over a year since I won’t get paid for most of the surplus
electric. In my specific case the solar thermal looks like a better roi.  It
also can be set up to run the pumps off of batteries which are charged by
solar, so independent of the grid.  A consideration where I live since the
power goes out around a half dozen times per year.  With grid tied PV and
heat pump I would not have heat at these times unless I purchase a backup
generator, or a different inverter and battery backup, further increasing
cost.

I think this is a complex calculation with many dependencies, such as
available solar insolation, type of dwelling, type of metering by the
utility, use of AC, installation costs (diy or not), etc, which can vary
greatly with user and location.  It is impossible to give a simple answer
that is accurate for most users in most areas.  Each case needs to be
examined in detail.




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