Calculating break-even point when mini-split costs same as running boiler

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I have original steam boiler that is maybe 75% efficient (it is converted to gas 10-year old boiler). Recently, because we wanted AC, we installed air-source heat pumps (Mitsubishi MXZ-2B20NA with MSZ-GE06NA and MSZ-GE09NA head units). Basically one heat pump has one 6K and one 9K heads.

I am located in Boston. COP of Mitsu I calculated at 2.6 since HSPF is 8.9.

So what I am struggling to figure out is at which outdoor temperature it makes sense to switch from boiler, that costs \$1.5 per therm at current New England prices, to mini-splits at current \$0.243 per KWh.
It was suggested to me that it is somewhere around 40F outside, but my gut is temperature number might be lower.

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Replies

1. GBA Editor
| | #1

Apollo,
To get 100,000 BTU output from a 75% efficient boiler, you need to input 133,333 BTU of gas. That's 1.33 therms of gas, which costs you exactly \$2.00.

To get 100,000 BTU (29.3 kWh) output from a ductless minisplit with a COP of 2.6, you need to input 11.27 kWh of electricity, which costs you \$2.74.

So the minisplit won't be cheaper until the COP of the minsplit rises to 3.56.

If you can find a graph that shows you the outdoor temperature at which the COP of the minisplit rises to 3.56, you'll know how warm it has to be outdoors for the minisplit to save you any money.

2. Expert Member
| | #2

There is no single graph of COP vs. temperature, nor can there be. The oversizing factor & modulation level has a large effect on it's operating efficiency. A 2.6 COP would be on the extreme low side if it's operating at half of it's maximum capacity.

It probably delivers a COP better @ 40F even if it's running both the compressor and the heads at max speed, but the heat load of the house at 40F may only be half it's max output, so it'll be doing something like 3.5-4. Without modeling the heat load of your house relative to the outdoor temps it's impossible to say where it will be in it's modulation range.

Take a look at the submittal sheets:

Note that at +17F if you're only operating it at 12,500BTU/hr of output its only pulling 1350watts. At 3.412 BTU/watt-hour that's 4606 BTU of input, for 12500 BTU of output, a COP of about 2.7, even at that low temp. But your heat load is probably over 12,500 BTU/hr @ +17F, if your house is old enough to have a steam boiler.

At 47F the GE06 + GE09 combination can deliver the full 25,500 BTU/hr, but it takes about 1650 watts to get there, which is 5630 BTU/.hr of input, for a COP of 4.5, and that's a max speed (!). But since your heat load at 47F is only about 10-15K, it'll be doing better than that, maybe bumping on 5.

If you look at page 3, at +17F GE06 + GE09 combination can deliver a max of (7400 + 11,000= )18,400 BTU/hr. But to deliver that it's using 2250watts, or 7677 BTU/hr of power to get there, which is a COP of only 2.4.

To estimate the crossover point you first need to know the heat load across temp (which is roughly linear), from which you can estimate the modulation level of the multi-split. Using the few points on the curve provided in the submittal sheets you can interpolate to come up with the approximate COP at different temps at the anticipated modulation level.

3. | | #3

Martin and Dana,

Part of the house that is served by steam and mini-splits was built in '38 and gut-remodeled in '55.

I am usually running only 9K head on one minisplit and 6K head on another. Amazingly enough they seem to be able to get rooms up to temperature fairly quickly and without going into max mode. The other two heads are in less used rooms, so they aren't on most of the time, since those rooms sit at 55F. I also don't heat the house to 70F as most design days are done, 68F is only for 4 hours in the day, rest of the day I keep the house at 62F when away and 64F at night.

Manual J wasn't done that well, but contractor calculated that portion of the house we could heat with minisplits at needing about 20818 Btuh. Code level insulation in the attic and new windows, but empty walls.
I think that is for 1400sq ft, if I am reading manual J right. I am probably heating half that with steam or minisplits. Other side of the house is forced air with 97%AFUE furnace, so not part of this conundrum.

Architect we are interviewing to work on our energy retrofits and remodel was the one who really doubted my 40F break even rough calculation.

4. Expert Member
| | #4

Using deep setbacks with modulating heat pumps generally uses more power than if you kept it at a constant temperature or with minimal setbacks. This is because it operates at substantially lower efficiency during the recovery ramp (even if it's not at max-speed) than if you just let it modulate at part load all the time.

The 6F swing from 62F to 68F during the day is probably using more power than keeping it 66-68F all day. During the day the outdoor temperatures are higher (= higher efficiency at any given speed) and the heat load lower (= lower modulation level which means higher efficiency). You'd be "saving" at best 6% for those hours by letting the indoor temperature drop, lowering the rate of heat loss, but the difference in efficiency during the recovery ramp is going to eat those saving up and then some.

The guy in this study who was basically setting back 10F whenever he was away ended up using 57% more power than folks who kept it in a range. See Figures 27 & 28 and Figure 40, and the text discussing how the mini-splits were used for Lot 23.

Letting the thing modulate, and only stepping it up or down to deal with offsets between the setpoint and the actual room temp related to load (a common issue when the mini-split is sensing only the incoming air temp at the head, not the average room air) is (almost) always going to use less power than stepping it up & down multiple times per day.

At current IRC 2012 code min most 1400' houses would have a heat load at +12F (Boston's 99% temperature bin: http://www.energystar.gov/ia/partners/bldrs_lenders_raters/downloads/Outdoor_Design_Conditions_508.pdf ) well under 20,000 BTU/hr for the whole house, let alone just one zone. With no insulation in the walls but with recent U0.34 windows and R30+ in the attic you're probably looking at something like 25-30K for the whole house, half that for just half the house. If you let the mini-splits modulate they'll be basically idling along at low-speed/high-efficiency deep into the 20s F. If a COP of 3.5 is the magic financial crossover point, that probably happens somewhere in the low-30s given your oversizing factor, but without a lot more information than is appropriate for a web-forum analysis this is little more than a WAG.

A 75% steady-state efficiency of a steam boiler does not translate into it's as-used AFUE. If you're heating mostly with the ductless units it's duty cycle is much lower, and heat-up & standby losses much higher. The net result is a higher heat loss out of the boiler room (due to higher boiler room temps) and higher distribution losses, more heat being "abandoned" in the boiler. At the very low duty cycle your real AFUE is probably more like 60%, 65% tops, assuming a steady state combustion efficiency of 75%. If the ductless keeps up with the heat load it's probably better to just moth-ball the steam system, or set the thermostat to 5F below the ductless setpoint(s) as the Hail Mary backup for those 5 days per decade when the outdoor temps drop below 0F, (assuming the ductless won't keep up then,)

This winter's high electricity price is a fluke, with the generating companies recouping their losses from mis-managing the natural gas grid capacity constraints a year ago. It would be surprising if the rates were more than 20cents next winter, given the increased regional liquified natural gas (LNG) capacity, and the wiser management thereof by the generators and gas utilities after last winter's financial disaster (that we're paying for in this winter's rates.) Under MA regulations they are only allowed to adjust the rates 2x per year- expect a big discount starting late this spring. But since they didn't set back on their heels by the severe constraints that had them scrambling to fire up #2 oil peakers just to keep the lights on last year,it's unlikely that they would get the same rate increases approved for next winter. The price of both #2 oil & LNG is substantially down compared to last year, and even during the cold snaps they didn't hit the gas-grid limits, despite even cooler weather than last year. Unless something drastic happend, you should probably pencil out the crossover point using \$1.25-1.40 natural gas at 60% efficiency and \$0.18-0.20 electricity at a COP of 2.8-3, if looking at next year.

5. | | #5

Dana,
This is very helpful and a lot to digest.

Those deep setbacks I came to exclusively for steam. I did several months of experimentation and together with stepped recovery in temps. I start heating at 5PM in stages, I let thermostats catch up to radiators heating space, and by 7PM, when we get home, two boiler cycles make up the difference. This setup cut about 10% compared to 4F setback during the day and 2F during the night. Comparison was done by manually recording the meter reading every day. Granted, my steam system is not piped right and radiators are undersized in one area and oversized in another.

Heat-pumps I have used maybe for a week at different times. I know it costs me \$18 per day to heat the house. Going to experiment in the coming month by letting minisplits work in 20F+ weather and boiler for below that.

I am really really looking into PV. Have a lot of East and West roof space unshaded. And my wife is not a fan of steam with our very active toddler running around. Those rads get hot.

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