# Hypothetical daily cost comparison (minisplits vs. electric resistance)

| Posted in Mechanicals on

I’m trying to help steer a colleague towards heat pumps since his old equipment is in need of replacement, and am trying to determine some hypothetical comparison numbers. No heat loss calculation has been done, but that is besides the point for this comparison since it would be a fixed number specific to his house, and not the heating equipment. Heat loss could be 20,000 or 100,000btu, but i am using 30,000 for this example. He currently heats with wood and electric resistance backup…(but that is not the point below)

Assumptions:
-Does not factor in solar heat gain, internal heat gain, of daily fluctuation in ambient temperature (assume fixed for the full day), duct losses, etc. Just very high level comparison
-15,000btu/hr average day load for a typical winter/cold fall day
-Delivered electricity rate of \$0.26/kw/hr including taxes (average, not including time of use factors)
-Example 1: 10KW electric central furnace (34,121btu)
-Example 2: 3x 12KBTU cold climate ductless minis (36,000btu, and input max wattage of 1000W each- using the Fujitsu numbers) 3KW total

Example #1A: Electric Resistance during design conditions
For 1hr of heat, the furnace will run at 10KW for 87.9% of the time (30,000/34,121 x 10), consuming 8.79kw/hr, @ \$0.26/kw/hr x 24 = \$54.86/day.

Example #1B: Electrical Resistance during average winter condition
For 1hr of heat, the furnace will run at 10KW for 43.9% of the time (15,000/34,121 x 10), consuming 4.39kw/hr, @\$0.26/kw/hr x 24 = \$27.43/day

Example #2A: Three ductless minisplits for design conditions
For 1Hr of heat, the minis will modulate to 83% full capacity (30,000/36,000 x 3), consuming 2.5kw/hr, @ \$0.26/kw/hr x 24 = \$15.60/day [COP=3.5]

Example #2B: Three ductless minisplits for average winter condition
For 1Hr of heat, the minis will modulate to 41.7% of full capacity (15,000/36,000 x 3) consuming 1.25kw/hr, @\$0.26kw/hr x 24= \$7.80/day [COP=3.5]

Is this an appropriate comparison? To vaguely determine dollars saved per day. I’m trying to simplify the comparison as much as possible for him.
Thanks,

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### Replies

1. GBA Editor
| | #1

Ryan,
I haven't yet verified your math, but I don't know why I should. If you don't know the actual design heat loss of the house, and you don't have actual utility bills or fuel use records, you are flying blind.

Here's what you can say: An air-source heat pump with an average COP of 3 will use 1/3 as much electricity as electric resistance heat. How's that for simple math?

2. | | #2

Thanks Martin, for some reason i can't convince him on the 1/3 approach, and am trying make vague assumptions and prorate it over a 4-5 month heating season, but in hindsight, the relationship between electric resistance and minis is fairly linear when considering a seasonal/average cop. If he went all electric with no wood it would cost him X/year, if he went minis it would cost 0.33X/year. Maybe just delete this thread since there really isn't anything constructive here.

3. Expert Member
| | #3

There seems to be some conflating of energy and power in the math that makes it a pain to read. Kw are not kwh hours, and there is no conversion from kw to BTU.

At what outside design temperature is the load presumed to be 30,000 BTU/hr?

What is presumed to be the average mid-winter outdoor temperature?

Assumptions about efficiency can be pretty far astray too, since they are highly dependent on outdoor temperature, not just the modulation rate. Even during fairly mild weather a mini-split running at 83% of it's maximum capacity would be very unlikely to see a COP of 3.5, but it might be 2.5 or even 3, at say +10C, even at 83% modulation. If you let it modulate with load it'll hit 4 during low load moderate temperature periods.

But at -25C at 83% modulation it's COP will be a bit under 2, and that does not include the capacity & energy hit from defrost cycles or the pan heater.

Over an entire season in a location with an outside design temp of -13C if you right-size the ductless for the load you will probably break an SEASONAL average COP of 2.5 or even 3, but it's highly unlikely the seasonal average would ever hit 3.5 in a climate that cool, and it's also unlikely that the seasonal average would be less than 2.

With both accurate wood use and electricity use numbers it's possible to make reasonable load calculations based on fuel use, but it'squishy- the error bars are large on both the efficiency of his wood-burner and the BTU content of the wood.

Ductless mini-splits "play nice" with wood burners when they have a high turn down ratio and aren't ridiculously oversized, since they modulate up smoothly as the wood-burner cools off, at higher efficiency than if they were carrying the entire load (without the wood burner.) But the difference in efficiency between minimum modulation and maximum modulation isn't huge when it's -15C or cooler, nowhere near as large as when it's -5C or warmer. See Table 5 (in the appendix) and Figure 5 (in the text) of this document, which would be pretty similar to the behavior of a Fujitsu 12RLS3H, just scaled somewhat differently

4. | | #4

Hi Dana,
For the electric furnace, i randomly picked a 10KW off google rated at 34,120btu.
For the minis, i used the fujitsu technical data sheet which said an input wattage of 1.01KW...but after looking at the tables you provided above, it would seem that the 12rls3 will pull north of 2KW when it gets ramped up.

It would seem you looked up the design conditions for the Ottawa area. -25C i believe is the 99%, and -13C sounds about right for design temp. It's about 4000HDD (C) and 7200HDD (F). His house is 30 years old, 2x6 w/fiberglass and dual panes, 1600-1800 sqft single level with finished basement. He says R40 attic, R12 in the basement walls, and no slab insulation. Likely leaky too. And yes, i have recommended an energy audit.

He's never monitored his electric use, but i might be able to convince him to monitor it over the remainder of this heating season. He burns 6 cord/season in a central wood furnace (no stove/fireplace). He will be travelling during the winter months more and more, so the wood furnace will likely sit idle in the coming years when it would be most welcomed.

I've tried to convince him to consider it, but likely won't push it any further. Thanks for all of your 2 cents.

5. | | #5

I would also make sure you look at the numbers. I was scouring Mitsubishi units and found an outdoor compressor that had 5 refrigerant port connections on it for five zones. It was their non NAHZ model, just the NA2. It looked like a great idea, saving nearly \$1100 on the branch box and compressor, until I realized it is only rated at 24k heating at 17 F. That is a huge hit from the 42k at 47 F.

6. Expert Member
| | #6

I did not know the location, and did not look up the design conditions for Ottawa. I was going off the lowest temperature at which the cold climate mini-splits have a specified output. For the RLS3H that's -26C, and you were using 83% modulation of it's max capacity at that temperature, ergo I presumed a design temp of around -25C.

But that is not correct.

The 99th percentile temperature bin at the airport in Ottawa is about -8F/-22C, a temperature at which the cold climate mini-splits have at least a bit more capacity than at -25C.

The binned hourly mean temp in a typical January in Ottawa is about -9C, not -13C, which you can eyeball on the graph on this page:

If the air leakage is tightened up a typical 1800' framed 2x6/R19 house with an insulated basement and R40 fluff in the attic would come in at about 25,000 BTU/hr @ -8C outdoors/+20C indoors, but the error bars are large, depending on the shape. It could be as low as 20,000 BTU/hr or as high as 30,000 BTU/hr. If it's more than 30,000 BTU/hr it implies a LOT of air leakage, or atypically large amount of window area.

Assuming a worst-case source fuel BTU of 25 MMBTU (million BTU) /cord, and an average of 80% combustion efficiency that's a net of 20 MMBTU/cord net heat delivered to the house. So 6 cords delvers 7120 MMBTU/year. Distributed over 4000 HDD-C that's 30,000 BTU/degree-day, or (/24=) 1250 BTU/ degree-hour. At design conditions of -8C out, +20C in that's a delta of 28C, for an implied heat load of 28C x 1250 BTU/ degree-hour= 35,000 BTU/hr, and that's a true upper bound. Realistically the would could be averaging 20 MMBTU//cord which would make the implied load (20/25) x 35,000= 28,000 BTU/hr, and the true combustion efficiency of the wood furnace is likely in the 70s, not 80%. If it's 75% with 20 MMBTU/cord fuel you're looking at an implied load of (75/80) x 28,000= 26,250 BTU/hr, which "feels" about right.

A pair of 15RLS3s would pretty much cover it, even if you assumed the 35K heat load it's pretty much covered at -22C, given that it has a bit more capacity at -22C than at -26C where it can deliver ~15,000 BTU/hr per. Letting the existing baseboard kick when the mini-splits have lost significant ground it would still cut the power use by more than half, given that the average January temp of -9C, and most of the heating season is warmer.

7. | | #7

Project Drawdown mentions Refrigerant Management as the #1 long term solution to global warming/climate change. I know this may not be relevant to the small scale cost factors listed in this post, but it may be a relevant point to readers of GBA and anyone interested in Green Building writ large. One option would then be to look at CO2 heat pumps, such as the Sanden. But this would require a hydronic distribution system.
One major advantage of resistance electric heat is that it can be very easily (and cheaply) zoned. Each room can have a separate controller, so the house can be allowed to get quite cold while bedrooms are kept warm. So depending upon the size of the house, winter heating costs can be significantly reduced by using this zonal capability more effectively.

I, for one, once looked in to replacing my electric baseboards in a small (~800) sf house I owned, and realized I was much better off replacing the windows, insulating the attic, installing a very efficient wood stove, and utilizing the electric resistance zones effectively.

8. Expert Member
| | #8

Ethan,
Most of the houses I have designed or built around here use a wood stove as their primary heat source and baseboard heaters as backup. The combination seems to work well.

I did a house where I used radiant cove heaters instead, but really didn't see any appreciable advantage over baseboards, and considering how much more they cost wouldn't spec them again.

9. | | #9

Malcolm, I am starting to see that a complicated hydronic system may look good on paper, but be overkill if we are hoping to heat with wood a good part of the year.

I think some argue that this isn't sustainable "long-term" because the next owner may not want to be heating with wood, but I think we have to stop designing and building for the "next owner."

Have you found that the occupants of the homes you have built us the wood stoves as a primary heat source regardless of the fact that this cannot be accounted for per code and/or energy modelling?

10. Expert Member
| | #10

Ethan,
Yes they do, but I'm not sure how representative they are of the larger population. I live on Vancouver island in a heavily forested rural area where the largest economic activity is logging. The people who build here are looking for that "West Coast lifestyle". Part of that is wood fires - and the security wood heat provides in our frequent power outages.

The other side of that is the climate is so mild, with no cooling needed, that if they decide to rely on the electric resistant heat, the cost, presently at least, is very reasonable.

11. | | #11

Martin, your simple math may be off if you take into account zoning and smart controls which make sure that unoccupied rooms are not heated... Heating an entire house vs heating 1/3 of it (bedrooms) at night may mess up your simple math...

12. GBA Editor
| | #12

Ethan,
The better insulated a house, and the more airtight a house, the less benefit can be gained by nighttime thermostat setbacks.

In a leaky, poorly insulated house, nighttime setbacks can save quite a bit of money. In a Passivhaus, not so much. (For one thing, a Passivhaus envelope won't lose heat very quickly, so the indoor temperature changes very slowly.)

13. | | #13

Martin, thank you for explaining this. I think it is very hard for those of us who have never actually LIVED in a well sealed, well insulated house to figure out which of our long-held assumptions are invalidated by improved building techniques.

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