How to model and predict electricity usage for a heat pump
The obvious question when considering a heat pump is how much electricity it will use and whether it will save money compared to other heating options. With a heat pump this is a more complicated question than with a combustion heating source. With combustion, a BTU is basically a BTU, you can calculate a house’s BTU per heating degree day and multiply it by the degree-days for that climate and get a pretty good idea of how much energy it’s going to use.
With a heat pump, the BTUs produced per unit of electricity depends upon the outside temperature as well as the heating load relative to the capacity of the heat pump. Most heat pumps are more efficient at part load than at full load. So projecting the energy usage of a heat pump depends upon the building, the climate, and the heat pump.
I’m going to present a methodology for estimating energy usage. As an example, I’ve prepared a spreadsheet where I implement this methodology for an imaginary house in Boston, MA.
The spreadsheet is at:
https://docs.google.com/spreadsheets/d/1Ypd-CbwBXfya-9S8t9qCKdnMm-6cvj5VDhXJO80sgLc/edit?usp=sharing
Step 1: gather information about your house
You need to know the heating load for your house. If it’s an existing house and you have a fuel use history from heating it in the past, you can use the method in this article: https://www.greenbuildingadvisor.com/article/replacing-a-furnace-or-boiler
If it’s new construction or extensively renovated, you’ll have to estimate the heating load using Manual J or another estimating technique.
Since in this example I’m using an imaginary house, I’m just assuming that the heating load is 30,000 BTU/hr. In my spreadsheet, in the “Assumptions” section of the “Summary” tab that goes into cell B4.
Step 2: Gather information about your heat pump
The best place to get information is the online database maintained by NEEP.org at https://ashp.neep.org/#!/product_list/ . They have performance information on over a hundred thousand heat pumps. Each unit has a product page, and on the product page there is a section labeled Performance Specs which has minimum and maximum output, and COP at each point, for several temperatures.
For my example, I’m using a Mitsubishi M-Series, 3 ton nominal. The NEEP page is at: https://ashp.neep.org/#!/product/34584/7/25000/95/7500/0///0
Information about it goes into the tab “Heat Pump Performance Curve.” In cells K2 to Q13 I pasted the performance specs copied from the NEEP website. Cells A2 to H6 are organized to reformat the pasted data in a more usable layout.
Step 3: gather information about your climate
If you are in the US, NEEP will provide this for you. On the heat pump product page there is a link labeled “Advanced Data – System Sizing.” If you click on that link you get a form where to put in your zip code and it will let you pick a weather station from a dropdown list of nearby ones. Then put in the heat load that you calculated in Step 1, and click on “Run System Sizing.”
This will produce a chart showing system performance at various temperatures. In the upper right corner of the chart there is a button with three horizontal lines. Click on that and select “Download CSV” from the menu that pops up.
The downloaded data is a table of performance at temperature, with each row representing a degree F. Column J is heating load at that temperature, and column K is annual load at that temperature. Dividing column K by column J gives annual hours at that temperature, which is what you’ll need.
In the tab “Data from NEEP.org” I pasted in the downloaded information. The Neep data goes down to -67F, but since the average annual low for Boston is -6F, I only copied cells for that temperature and above.
For reasons that aren’t clear to me NEEP has two rows for the design temperature, in this case 13F. So after pasting you have to delete one of the rows.
NEEP will also tell you the design temperature. That goes into the “Assumptions” area of the “Summary” tab in cell B3.
Step 4: At every temperature of your heating season, calculate the heating load
You have the heating load and design temperature from Step 1, this is a simple straight-line extrapolation based on the difference between indoor and outdoor temperatures.
In the “Summary” tab the calculated load is in column C and repeated in the tab “Heat Pump Performance Curve” in column F.
Step 5: At every temperature of your heating season, calculate the minimum and maximum output of your heat pump, and the COP at those outputs.
Again, this is a straight-line approximation. The heat pump performance data gave minimum and maximum outputs for several temperatures. For temperatures between those points, just do a straight-line interpolation between the two closest temperatures. Do the same for COP.
In the tab “Heat Pump Performance Curve” this is in columns B through E.
Step 6: At every temperature of your heating season, calculate the COP at the heating load calculated in step 4, and calculate the electricity used using that COP
For each temperature, if the calculated heating load from step 4 is between the minimum and maximum output calculated in Step 5, do a straight-line approximation between them to get the estimated COP. If the load is below the minimum output use the minimum output COP, and if the load is greater than the maximum output use the maximum output COP.
In the tab “Heat Pump Performance Curve” the calculated COP at load is in column G.
In the tab “Summary” the calculated heat pump output is in column G and electricity usage is in column J.
Step 7: Adjust for undersizing
If the load is greater than the maximum output at that temperature, supplemental heat will be needed. I assume that the supplemental heat is resistance heat with a COP of 1.0.
In the tab “Summary” the supplemental heat needed is in column K.
Step 8: Adjust for short-cycling
If the load is less than the minimum output, the heat pump will cycle on and off. This will cause some efficiency loss. I’ve tried to quantify that, but I’ve been unable to come up with any method of doing so. My best guess is that every time the unit turns on there are two minutes of runtime before it starts producing, and the shortest part of any cycle will be ten minutes.
If the duty cycle is more than 50% the off-time will be ten minutes and the on-time will be whatever gives the needed duty cycle. For example, if the duty cycle is 75% the off time will be ten minutes and the on time will be 30 minutes. There will always be two minutes of lost output, so the efficiency hit will be two minutes divided by the on time; in this case, 2/30 or 6.7%.
If the duty cycle is less than 50% the on time will be ten minutes and the off time will be something greater. The efficiency loss will always be 20%. I don’t know how accurate this estimate is. I include it because if you don’t, you’ll come to the conclusion that bigger is always more efficient, which suggests gross oversizing.
In the tab “Summary” the calculated short-cycling penalty is in column H in percent and column I in kWh.
Step 9: Total it all up.
The final step is to add up the electricity usage for each row, and then add them all up to get total annual projected usage. If you divide that by total annual heating load you get weighted average COP.
In the tab “Summary” the total electricity usage for each row is in column L. The weighted average COP is in cell F12. In this case it’s 3.3.
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Replies
From weighted-average COP there are a couple of analyses you can do. If you know the price of electricity and competing fuels in your area you can compare the cost of a heat pump compared to a combustion appliance. You can also model strategies like using another fuel to supplement the heat pump.
In the tab “Analysis” I do some comparisons, using an assumed cost of electricity of $0.27/kWh and heating oil at $3.50/gallon with an 80% burner efficiency.
Switching from oil to a heat pump saves $545.71 on an annual heating bill of $2,263.78 with oil.
One strategy that is sometime suggested is to use an oil burner for the supplemental heat instead of resistance electric. That would save $ 3.11 per year.
Another strategy, more commonly suggested, is to switch to oil when the temperature crosses the point where oil is cheaper, in this case 20F. That would save $ 51.47 per year over using the heat pump alone.
Even more common is the recommendation that the heat pump should be shut off below some arbitrary number, usually around 30F. In this case, switching at 30F would cost more than using the heat pump alone, to the tune of $ -6.53.
Having done a few of these analyses I've come to believe that dual fuel systems just aren't a good idea. Even in the best scenario a "backup" oil burner wouldn't justify the cost of an annual cleaning in fuel savings, and the oft-cited "30 degree rule" actually costs more money than just using the heat pump by itself.
In most cases, if someone is pushing for dual fuel it really means they just don't believe in heat pumps.
That is really good stuff DC. Thanks for putting it together!
Another takeaway is that if you are in a place where you can install PV, even in a heat pump is more expensive to run from the grid, the PV can offset a lot of the operating cost.
Thanks.
Yeah, the one case I could see dual fuel making sense is if you had a cheap source of electricity but it was somehow limited. For example, if you have solar, once it's installed it's essentially free until you've used all that you produce.
Just one nitpick: At ambient temperatures just above freezing you will see more defrost and therefor a hit in capacity and COP. Depends on the climate - if "winters" are generally wet at like 32-40°F - then this will make a difference. I would not use a linear interpolation in that area but use the meanufacturers docu in a more precise curve.
The coil is going to be about 20F below ambient so maximum defrost is going to be around 50F, the air contains so much more moisture at warmer temperatures.
I have no clue how to model it though.
Mitsubishi does publish a correction factor for defrost for their units. Worst seems to happen around freezing where capacity drops to 88%. I would guess that 12% time is spent defrosting, so not insignificant amount of energy. This assumes the unit is running full tilt at that temperature which would only be the case for units in milder climates.
Interesting part is not all units defrost much. I have some ducted Midea units and they barley produce any ice in the winter but under the Gree AWHP it is a skating rink. Both units run a couple of blocks away so pretty much the same climate.
I think oversized units will tend to frost up less, so if you are in an area where local climate means operating near freezing, might want to upsize a bit.
Great work!
Thanks.
Really interesting. Thanks DC!
I've been thinking more about the issue of when dual fuel is appropriate. The Analysis tab is set up so that you* can put in different costs of fuel and it update automatically.
Somewhat counter-intuitively, the maximum benefit from combining fuels comes when the two fuels are closest in cost. If electricity is much cheaper than oil, there's no temperature at which oil is cheaper, and if electricity is much more expensive there's no temperature at which electricity is cheaper. In my model, with oil at $3.50 per gallon, at any electricity price below 18.3 c/kWh electric is cheaper through the entire temperature range. And at any electricity price above 45.5 c/kWh oil is cheaper though the entire temperature range.
The maximum savings comes with electricity at 35.5 c/kWh. At this price all-electric and all-oil are exactly the same price, $2263 per year. Switching from electric to oil at the break-even temperature, 29F, saves $243 per year over either electric or oil alone.
That's 10.8%. So that's not nothing. But as the cost of electricity moves away from the equilibrium point the savings quickly diminish. Here's a list of savings in nickel increments:
25c 1.6%
30c 5.5%
40c 5.0%
45c 0.4%
*(Well I can, you can't, because I've shared it as read-only. But you can make your own copy to play with.)
I think dual fuel has use. But not for saving substantial money.
I can think of a few cases off the top of my head, I'm sure there are others:
* Electricity is cheaper, but it's an existing house and the ductwork is too small for a heat pump and increasing capacity wouldn't be cost effective.
* Similarly if the electrical capacity isn't enough for a full heat pump implementation.
* You live in a place with unreliable power and want to be able to run heat on emergency power.
* Electricity is cheaper, but where you live gets colder than a heat pump can work.
But I see a lot of cases where installers specify dual fuel without even thinking about it, they just assume it's necessary. The most egregious cases are with air-to-water heat pumps, where installers go to great length to integrate a boiler without ever questioning whether in fact it is necessary.