Running the Numbers on a Heat Pump

post by jefftk (jkaufman) · 2024-02-09T03:00:04.920Z · LW · GW · 12 comments



I recently looked into installing a heat pump mini-split system to heat and cool our house. While it's expensive to install, I had thought a combination of it being nicer than what we currently have and cheaper to operate would make it worth it. Unfortunately, after running the numbers on our utility costs it turns out it would be substantially more expensive to power than our current gas system.

I got excited about a potential heat pump system after learning that over the past few years their cold-weather performance has improved dramatically and then that MA would provide a $20k subsidy ($10k for each of two units) for us to switch over. I liked that it would allow us to adjust the level of heating we had in each room, provide heat to one room that currently is only heated passively through the walls, replace the small amount of resistive heat we use in another room, and provide cooling (where we currently use a whole-house fan, plus window units during the hottest part of the summer). Friends who had installed them were happy, and then I found someone putting together a buying collective to negotiate pricing. I got a MassSave energy audit, to qualify for the $20k rebate, talked to the contractor (great experience!) and got a quote. Since it was a lot of money I wanted to run the numbers first, and then that's when my excitement drained.

The quote was for Mitsubishi MXZ-SM42NAMHZ mini-split condensers, which are pretty efficient, and have a Region IV [1] HSPF2 rating of 10.55 (10,550 BTU/kWh) [2] . This means that averaging over the heating season, to produce 100k BTU of heat we'd need 9.48 kWh of electricity. Burning one therm of natural gas also gives you 100k BTU, but our condensing boiler is rated 96% efficient so we'd need 1.04 therms for that 100k BTU.

Massachusetts has some of the highest energy costs in the country, and our marginal costs are $1.999/therm [3] for gas and $0.316/kWh for electric. That means heating our house by 100k BTU would cost $2.08 with gas vs $3.00 for electric (44% more). What's the scale of this?

In 2023 we burned 1,199 therms of natural gas. During the summer when the heat was off we burned ~16 therms a month, for hot water, so I'll estimate we used 1,007 therms for heating and 192 for hot water.

Doing the same calculation for more years, it sounds like 1,000 therms is typical:

Year Therms Heating Therms
2023 1,199 1,007
2022 1,146 954
2021 1,182 990

This means we'd be paying another $900/year in operating costs, let alone the cost of the installation. I'd also predict the maintenance costs would be higher, since there are a lot more moving parts to break.

Now, one thing some people will recommend is to run the heat pump most of the time, and fall back to gas for the coldest part of the year. The heat pump uses electricity roughly in proportion to how much colder it is outside than inside:

This shows the Coefficient of Performance (COP): how many kWh of heat do you get out for each kWh of electricity you put in. At our current electricity and gas prices, we'd break even at a COP of 4.45. Interpolating between the minimum-output performance at 47F and 17F, since in warm weather we wouldn't full system capacity, break-even is at temperatures of 43F and above. So we could run gas when it's colder than that, and the heat pump when it's warmer. But (a) running the system only when it was 43F+, but that's only a small portion of the heating season, and (b) to get the $20k rebate you need to permanently disable your existing heating system [4].

I was pretty surprised (and disappointed) when I went through this. Polling housemates around the dinner table the guesses I got for the operating cost were around a 25% to 50% decrease. I'd thought that this was more like solar panels or electric cars: more money up front, but savings over time.

One thing to keep in mind, though, is that even though the electricity here is mostly produced by burning gas you do actually burn less gas by turning it into electricity and then using it to run a heat pump than just burning it for heat. Even if the marginal electricity here were 100% gas, the plants are about 60% efficient and the COP averaged over the season is 3.09 [2], so when we combine these we get 53% as much gas when using the heat pump. Still, if the system were free (which it's definitely not!) this would come to $900/y to save ~3.2T CO2e, or $281 a ton. This is above the social cost of carbon, and even above what direct air capture would cost. If I wanted to spend money to reduce carbon emissions this wouldn't be the place to start.

If this is so expensive, who does it make sense for around here? If you have oil heat, and especially if you have an older less-efficient boiler, then it could save you quite a bit. A gallon of heating oil is 138.5k BTU, and around here costs $4.05, so if your boiler is 80% efficient you're paying $3.66 per 100k BTU, 22% more than I estimated for a heat pump above. And it's even worse for propane, with a similar cost per gallon but only 2/3 the energy density. People who need to heat varying portions of their house but don't have matching heating zones would also benefit from a mini-split system like we were considering. And the tradeoffs are also different in other parts of the country: if it's warmer or your electricity is cheaper relative to your gas it can be a good deal. Additionally you might expect the cost of gas to rise relative to electricity during the life of the system.

The bottom line for us is that we'll stick with our forced hot water natural gas heat for now, and revisit if costs change dramatically. But I will get someone out to tweak the current system so that we're not overheating any of the rooms.

[1] Unfortunately what I really want is the Region V rating, since Boston is in Region V:

On the other hand, Somerville is a heat island, so it's probably not that bad to be using the Region IV rating.

[2] This is a bit silly units-wise: Wh and BTU are both measures of energy (1 BTU = 0.293 Wh) so I think we could just say the average coeficient of performance is 3.09 (10.55 BTU converted to Wh). But let's ignore this.

[3]] This is suspiciously round, though it divides as:

Charge Per-therm
Generation Service Charge $0.768
Distribution Charge $0.6674
Revenue Decoupling Charge $0.0603
Distribution Adjustment Charge $0.5033

[4] This is new for 2024, but it's not as strict as it sounds: per the guidelines (pdf) it counts if "pre-existing thermostat(s) have been disconnected from both the system board and walls," and there's nothing stopping you from putting them back again later.

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comment by Foyle (robert-lynn) · 2024-02-09T07:01:16.749Z · LW(p) · GW(p)

[disclaimer: I am a heat pump technology developer, however the following is just low-effort notes and mental calcs of low reliability, they may be of interest to some. YMMV]

It may be better to invest in improved insulation.

As rough rule of thumb COP is = eff * Theat/(Theat-Tcold), with Temperatures measured in absolute degrees (Kelvin or Rankine), eff for most domestic heat pumps is in range 0.35 to 0.45, high quality european units are often best for COP due to long history of higher power costs - but they are very expensive, frequently $10-20k

Looking at the COP for the unit you quoted the eff is only about 0.25 at rated conditions, not good, unless you get a much larger unit and run it at a less powerful more efficient load point.

That's a pretty huge electricity price, about 4.5x gas price (which is distorted-market nuts, 3x is more usual globally).  Given that differential it might be better to look at an absorption heat pump like that gives up to 1.7x gas heat - though they look to be on the order of $10k. 

Here's an annoying fact; If you ran that $2/therm gas (~$0.07/kWh) through a reasonably efficient (~40%) natural gas genset it would produce electricity cheaper than what you currently pay for power, and you would have 2/3rds of the gas energy left over as heat.  A genset in your neighbourhood could provide a few 10's of houses with cheaper electricity and low cost waste heat, though no doubt prevented by regulatory issues.   There are a few small combined heat and power (CHP) domestic units on the market, but they tend to be very expensive, more tech-curios than economically sensible.  

Replies from: jkaufman, nim
comment by jefftk (jkaufman) · 2024-02-09T18:43:01.873Z · LW(p) · GW(p)

If you ran that $2/therm gas (~$0.07/kWh) through a reasonably efficient (~40%) natural gas genset it would produce electricity cheaper than what you currently pay for power, and you would have 2/3rds of the gas energy left over as heat.

I was curious about this, and here are the numbers I got. I looked around and even a 23% efficient Generac 7171 comes out ahead. It's rated for 9kW at full output on natural gas. They say it uses 127 ft3/hr which is 1.37 or 39kWh. This is $0.304/kWh.

Of course this ignores the cost of the generator, maintenance, lower efficiency when run below full capacity, etc. but it's still pretty weird!

Replies from: AnthonyC
comment by AnthonyC · 2024-02-12T13:54:28.078Z · LW(p) · GW(p)

Yeah, I came to say the same. You're basically running into the problem that electricity in MA is expensive relative to natural gas, which is very much a contingent fact of policy/history/infrastructure. If you were living elsewhere, or living off-grid, the numbers would look very different.

You may (or may not) find the MA policy mix and cost structure changing in the future, so if nothing else, be ready to revise your numbers over time. Especially if your current gas system breaks and you have to replace it with something no matter what, that can change the economics a lot too. 

comment by nim · 2024-02-09T16:30:21.987Z · LW(p) · GW(p)

Seconding the importance of insulation, especially for disaster preparedness and weathering utility outages.

If any of your friends have a fancy thermal camera, see if you can borrow it. If not, there are some cheap options for building your own or pre-built ones on ebay. The cheap ones don't have great screens or refresh rates, but they do the job of visualizing which things are warmer and which are cooler.

Using a thermal imager, I managed to figure out the importance of closing the window blinds to keep the house warm. Having modern high-efficiency windows lulls me into a false sense of security about their insulative value, which I'm still un-learning.

comment by Steven Byrnes (steve2152) · 2024-02-09T13:09:04.389Z · LW(p) · GW(p)

I also live in Massachusetts and tried to figure this out a year or two ago, you can compare your results with mine that I wrote up at Electric heat pumps (Mini-Splits) vs Natural gas boilers [LW · GW]. Like you, I found that gas was much cheaper.

comment by nim · 2024-02-09T16:24:46.463Z · LW(p) · GW(p)

One thing to keep in mind, though, is that even though the electricity here is mostly produced by burning gas you do actually burn less gas by turning it into electricity and then using it to run a heat pump than just burning it for heat.

Fascinating! I guess it'd fall into the "more moving parts to break" bucket, but it gets me wondering about switching from my current propane HVAC to propane generator + electric heat pump. 

Searching the web for models that do both in a single unit, I find a lot of heat pumps using propane as their refrigerant, but no immediate hits using it as their fuel.

Replies from: AnthonyC
comment by AnthonyC · 2024-02-12T14:07:20.036Z · LW(p) · GW(p)

My question about this is, are there generator systems that allow you to safely dump the waste heat from combustion inside the way a forced-air furnace system does?

Getting more speculative/forward looking: if we can get the up front costs down enough to consider swapping the generator in your model for a methane fuel cell, would it be cheaper to heat and power your house with natural gas than to run off the grid? (Not that any MA town I've lived in would be likely to approve a building permit for such a thing, but still, interesting question).

FWIW there are RVs with electric heat pumps (though less efficient than residential ones, usually) as well as on-board (propane, gas, or diesel) generators. In this context there are definitely cases where it's cheaper to run the generator and heat pump than to run the propane furnace. These kinds of systems also benefit from the presence of batteries (which, set up properly, can stabilize power draw and from the generator, and minimize generator run time and start/stop cycles, as the heat pump turns on and off). Last summer I dry camped in Wyoming for about a month, and my 10kWh battery + 3kW inverter let me cut my generator fuel use (for AC, not heat, but similar idea) in half (would have been even better but I was limited by max converter charging rate and battery thermal management) compared to if I didn't have that.

comment by Bucky · 2024-02-09T14:11:49.120Z · LW(p) · GW(p)

One extra thing to consider financially is if you have a smart meter then you can get all of your hot water and a chunk of your heating done at off peak rates. Our off peak electricity rates are about equal per kWh to gas rates.

Without this I think our system would be roughly the same cost per year as gas or slightly more, with it we save £200 per year or so I think. (This would be a very long payback time but there was a fully funded scheme we used).

If it helps anyone we are in Scotland and get average COP=2.9

Replies from: AnthonyC
comment by AnthonyC · 2024-02-12T14:10:52.302Z · LW(p) · GW(p)

I recently had a coworker in the UK tell me they can get better off-peak rates if they install a home battery system and let the utility control it. I think in general the peak/off-peak rate difference could make a significant difference to these kinds of questions, but it's very dependent on local and regional policy choices shaping energy markets.

comment by Gerald Monroe (gerald-monroe) · 2024-02-09T03:15:00.751Z · LW(p) · GW(p)

So you need roughly 50 percent more efficiency for a heat pump to be just as efficient.

Does the market sell these? Yes:!/product/134030/7/25000/95/7500/0///0

The "min max" setup is several splits of the tier above, combined with a 96 percent gas furnace that is ducted.

Replies from: jkaufman
comment by jefftk (jkaufman) · 2024-02-09T03:32:24.300Z · LW(p) · GW(p)

Interesting: comparing the DLCPRBH18AAK you linked to the MXZ-SM42NAMHZ2 I was quoted for, yours has maximum efficiency at a relatively high output level while mine has maximum efficiency at it's lowest output level. And yours even is even labeled as able to put out more heat at 5F than 17F, without losing COP, which is pretty weird?

Replies from: gerald-monroe
comment by Gerald Monroe (gerald-monroe) · 2024-02-09T03:58:36.578Z · LW(p) · GW(p)

Yes that's weird and probably wrong. Real question is what would the crossover temperature be if you had both gas and these.