# Load calculations vs. actual fuel use

I’ve done my own fairly in-depth heating load calculation, tweaking and re-thinking certain aspects over time as I’ve learned more, and my result is 10,800 BTU/hr.

Today I decided to analyze my electric bills to reconcile theory vs. reality. What I found is that, despite a lot of attention to accuracy, I think I still over-sized by a lot. My heating load appears to only be about 5,800 BTU/hr.

Some details up front: I’m in zone 4c. The house is about 900sqft, built in 1950, single story, heated with a Mitsubishi FE18NA. During the period I analyzed, the basement had no heat of its own. (We just very recently put another mini split down there.) The attic is air sealed with R-50 of cellulose, and the walls are 2×4 construction with dense packed cellulose. The basement is uninsulated, but reasonably well air sealed at this point.

Here was my process:

- Looking through my electricity usage history, I found a very mild summer week where we used almost no heating or cooling. During this week we used 12.57 to 17.31 kWh/day. Based on this, I roughly guessed my baseline load (i.e. a day with zero heating/cooling) to be about 12 kWh/day.
- I found the harshest day in winter. During this day we used 58.52 kWh. It was Christmas Eve and heavy cooking clearly padded this number, but not by a huge amount.
- I subtracted 12 from 58.52 to find out roughly how much energy was spent solely on heating on that day.
- I found the Heating Degree Days for that day.
- I divided the kWh-used-for-heating by the HDD to find out how many kWh were spent on heat per HDD on the worst day.
- I multiplied that last number by the HDD expected on a design day (i.e. at 25F) to see what my kWh would be on a design day.
- I converted that to BTU and then divided by 24 to find the BTU/hr I need on a design day.

Is that a reasonable way to calculate what I’m looking for? 5,800 BTU/hr still might be a little too high, given that we did so much cooking on that worst day. But it seems surprisingly low. And now that my basement is heated, this upstairs unit will have even less load than that. So my upstairs heat pump is probably 3x or even 4x oversized. How embarrassing!

Martin: If you’re looking for article ideas, a guide to performing this kind of calculation could be a great companion to your heat loss calculation series.

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## Replies

I forgot that the heat pump's input is different from its output. So the input is 5,800BTU/hr but the output is that multiplied by the COP. So, assuming a COP of 3, that's 17,400. So maybe I am right-sized after all -- or at worst, just slightly oversized.

Nick,

With your correction for COP, I think your calculation method is correct.

As you point out, there are a few assumptions built into this method -- the most important being the uncertainty concerning your baseload number.

You can simplify this method by eliminating all references to heating-degree days. Thus:

1. On the coldest day of the year you used 58.5 kWh, of which 12 kWh was baseline usage. So, with these assumptions, your heating fuel use was 46.5 kWh per day.

2. Let's assume that the coldest day of the year corresponds to your design heating load. On that day, you used 158,704 BTU, equivalent (if we divide by 24) to 6,613 BTU/h.

3. Assuming a COP of 3.0 -- note that you might want to assume a higher or lower COP, depending on your climate zone, but 3.0 might make sense -- your design heating load is 19,839 BTU/h.

Lots of assumptions here, but this is a good back-of-the-envelope way to see if a Manual J passes the smell test. You may be left wondering whether Christmas Eve 2017 (or whenever) was really as cold as your design temperature warrants -- and I'm aware that my simplification eliminates your HDD calculations that was intended to clarify this very point -- but you can always look up the meteorological data to find out the low temperature on that date, and see if it seems to be, in fact, a "really cold day" for your region.

If your oven was used for 8 hours on Christmas Eve to bake pies and roast a turkey, and your oven is electric, then some of your heat on Christmas Eve was produced at a COP of 1.0. If you did a lot of baking on Christmas Eve, and your oven is fueled with natural gas, then the design heating load calculation method described here underestimates your actual load. As I said, this is a crude method.

Using a single day's power use is fraught with potential error from other uses of electricity to solar gain(bringing in extra BTUs through the windows), and hot water use (where most of the BTUs went down the drain), etc.

It's more accurate to do it over a winter period of at least 30 days (a full electric billing period), more than 50 days is even better.

Another error that's harder to estimate is the as-used COP of an FE18 when it is clearly oversized for your actual loads. The minimum output of that minisplit is 7500 BTU/hr @ 47F, and at 25F it's minimum output is still over half the load at 25F. Even though the steady state COP at minimum modulation at 25F outdoors is likely to be over 3, the cycling losses and defrost cycles take at bite out of that. AHRI capacity of the FE18 is 21,600 BTU/hr @ +17F, so it's about a 2x oversize factor for your actual heating load, and probably 2x oversized for your cooling load too.

The FE12 (13,600 BTU/hr @ +17F with a minimum output of 3000 BTU/hr @ 47F) would probably have been a better fit and run slightly more efficiently, but the capacity margin would be a bit slim unless you already had a better handle on the heating & cooling loads ahead of time.

http://meus1.mylinkdrive.com/files/MSZ-FE18NA_MUZ-FE18NA_Submittal.pdf

https://nonul.mylinkdrive.com/files/MSZ-FE12NA-MUZ-FE12NA_Submittal.pdf

(I have a relative in WA (zone 4C) with a comparably sized house and heat load heating with the FE18 too, but that was before she installed better windows to get the heat load down that low.)

Though that horse has long left the barn, insulating the basement walls with the second mini-split money might have made more sense. (If the basement was already finished living space, maybe not, due to the higher expense of demolition & re-build.)

Even better is to put an energy meter on the heat pump and then plot HDD vs kwh for each day of a month.

The limited data suggests that your heat pump is about right sized, not 2x or 3x over-sized for your actual load.

Also see here for the advantages of some over-sizing:

https://www1.eere.energy.gov/buildings/publications/pdfs/building_america/variable-capacity-heatpumps-indoor-ductwork.pdf

Jon R: It's definitely not 3x oversized, but could easily be close to or more than 2x oversized. Since it wasn't sub-metered some of that power use was for things other than space heating.

The calculated load was 10,800 BTU/hr @ 25F twice that is 21,600 BTU/hr, which less than the maximum (not rated) 25,800 BTU/hr output of the FE18 at +17F, which is 8F cooler than Nick's 99th percentile temperature bin. The minimum capacity of the FE18 at +17F is 4300 BTU/hr (according to NEEP data) and would be substantially higher than that at Nick's 25F design temp, probably on the order of half or more his 25F design load.

Assuming the calculation is at least sort-of-close, the load increase by about 240 BTU/hr for every degree F temperature difference between indoors & outdoors. So at +47F (23F cooler than 70F) the load is about 5500 BTU/hr, , 2000 BTU/hr less than the minimum output of the FE18. So it'll be cycling rather than modulating whenever the outdoor temp is north of about 42-43F, which is MOST of the time, even in January in locations like Charlotte (99% design temp +23F):

https://weatherspark.com/m/18893/1/Average-Weather-in-January-in-Charlotte-North-Carolina-United-States#Sections-Temperature

With the FE12 and it's 3000 BTU/hr minimum @ +47 it'll be modulating even at temps north of +50F, yet at full speed it can still deliver ~15K @ +17F (when the load would be about 12,700 BTU/hr.) It'll still have a bit more than a 1.5x oversize factor for the calculated 99% heat load of ~11K @ 25F and much closer to the oversizing sweet spot than the FE18. The savings in the power bill going to the 1-tonner would be small (but real), and comfort-wise it would deliver more stable room temps.

The FE09 could even cover his design heat load and would be modulating even at ~60F. But at +17F it would be marginal, with a max output matching the load almost exactly at that temperature.

The other variable is body heat. At 100 W each, 2.4 kwh/day/person is significant if you had company on christmas eve.