# Using Average Monthly Temperature to Model Home Energy Use

Discuss how monthly electric and gas billing data can be combined with average monthly temperature data to model a building's energy use, quantify energy conservation opportunities and verify performance improvements.

The following steps are used determine to determine the characteristic curve for a particular building:

Step One - Normalize electricity and/or gas usage in terms of Watts/Ft2 (or Watts/m2).

Electricity, W/Ft2 = ([Monthly kWh] x 1000 Watts/kW) / ([Days/Bill] x 24 Hr/Day x [Bldg. Area])

Natural Gas,

W/Ft2 =               ([Monthly Therms] x 100,000 BTU/Therm)

(3.413 BTU/Watt x [Days/Bill] x 24 Hr/Day x [Bldg. Area])

Step Two - Determine average monthly temperature for each billing period.

Step Three - Plot each month's normalized energy use verses that month's average monthly temperature.

After performing this anlysis on many buildings, we have discovered consistent trends.  A typical all-electric home with electric resistance heat will use about 3.5 Watts/Ft2 at 20F and approximately 0.75 Watt/Ft2 around 60F, rising to about 1 Watt/Ft2 at 70F.  An all-electric home with an air-source heat pump will be similar except the home will use about 2.5 Watts/Ft2 at 20F instead of 3.5 for the electric resistance home.

The slope of the line between 20F and 50F corresponds to the heat loss coefficient of the building due to conduction, infiltration and ventilation.  Reducing the slope by a prescribed amount will predict the energy savings that will occur by replacing windows, adding insulation, reducing infiltration or reducing ventilation air.

The intersection of this line with the X axis, typically 70F, indicates the average temperature maintained inside the home.  (Although, as Michael Blasnik correctly states in his comments below, the intersection of the UA line can be significantly influenced by solar gains or non-electric loads within the home.) Shifting the line to the left will predict the savings that occur by setting the thermostat back to a lower temperature.

I prefer to use watts per square foot (or watts per square meter) instead of using British Thermal Units (BTU's), kilowatt hours (kWh's) or Joules to normalize a building’s monthly or annual energy use for the following reasons:

1. A watt is one of the few metric measurements that is commonly used and understood by most Americans. (75 watt light bulb, 1,500 watt heater, etc.) Because lighting and heating loads are often stated in terms of watts, it is relatively easy to quantify their contribution to a building’s normalized overall energy when it is also represented in terms of average watts per unit area.

2. Even though a watt is a measurement of power, not energy, I find that energy represented in terms of average watts to be more intuitive than BTU’s, kWh or Joules.

3. Switching between metric and non-metric values is relatively easy. The rule of the thumb conversion between square meters and square feet is a simple factor of ten (1 meter by 1 meter = 10.75 square feet). One watt per square foot is 10.76 watt per square meter.

4. Direct solar gain at the surface of the earth at noon on a clear day near the equator is roughly 1,000 watts per square meter, or approximately 100 watts per square foot. These rule-of-thumb values make it easier to relate solar heat gains to other heat gains within a home.

The graph below shows the metered AC electrical energy generated by a 6.5 kW solar PV array that has been normalized in terms of watts per unit area of a 2,000 sq. ft. all-electric house.  Although the energy generated each month by the solar array is not perfectly correlated with average monthly temperature, it shows just how far this house on the east side of the Cascades in the Pacific Northwest has to go to reach net zero energy.

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### Replies to This Discussion

It's always fun to look at usage data, but of course I've got a few questions/comments:

1) I'm curious why you don't use degree days rather than monthly average temperature -- an 80F day at the end of May doesn't offset the heating needed during the 45F day at the beginning of May. With degree days, linear fits tend to work pretty well (especially with linear heating systems -- not quite as well with heat pumps).

2) I'm wondering about your statement that the x intercept is an estimate of average indoor temperature -- that doesn't quite add up since the temperature float between indoor temperature and heating requirements is a function of all gains (solar, occupant, plug, other baseload, adjusted for utilization) and not just the gains for the fuel analyzed.

3) I find that normalizing by floor area tends to make smaller homes seem less efficient than large homes since it's the building shell that loses (or gains) heat and not the floor area.
Hello Michael,
Here's my response to your questions:

Michael Blasnik said:
It's always fun to look at usage data, but of course I've got a few questions/comments:

1) I'm curious why you don't use degree days rather than monthly average temperature -- an 80F day at the end of May doesn't offset the heating needed during the 45F day at the beginning of May. With degree days, linear fits tend to work pretty well (especially with linear heating systems -- not quite as well with heat pumps).
JW's Response: In my opinion, dealing with heating and cooling degree days (HDD and CDD) makes things more complicated than necessary. It all depends on what method you are used to dealing with. I have found that most homes I deal with do not have a balance point of 65F that is commonly used for calculating HDD. Also, if the temperatures do not rise above the 65F balance point, the results for average monthly temperature and HDD are mathmatically the same. Simply plotting average loads verses average monthly temperatures gives me a characteristic plot that quickly illuminates many characteristics of a home's energy use; such as level of internal gains, overall air conditioning loads, and the extent of electric heat. Another interesting aspect of the average temperature vs. average load plot, is that the peak loads for the home can also be calculated by extrapolating the heating line out to the design temperature in question.
I wrote a paper with Howard Reichmuth in 1996 that discuss the relationship between heating degree days and average monthly temperatures. The paper goes into much greater detail regarding the slope of the "UA" (heat loss coefficient x building area) line, how cooling, solar gain, reheat, setback and many other factors can be viewed when looking at a building using average monthly temperature and and average loads in terms of Watts/Unit area.

2) I'm wondering about your statement that the x intercept is an estimate of average indoor temperature -- that doesn't quite add up since the temperature float between indoor temperature and heating requirements is a function of all gains (solar, occupant, plug, other baseload, adjusted for utilization) and not just the gains for the fuel analyzed.
JW's Response: Solar gains and exterior loads will shift the X intercept in a prescribed way, but internal plug and base loads do not tend to shift the position of the x-intercept. The paper I mentioned above goes into greater detail if you want to see how I dealt with these factors using the average temperature model.

3) I find that normalizing by floor area tends to make smaller homes seem less efficient than large homes since it's the building shell that loses (or gains) heat and not the floor area.
JW's response: I agree, houses below 1,000 square feet tend to have higher relative heat loss values and higher internal gains on a per square foot basis.
I don't see how using degree days makes things more complicated -- they are just as easy to use and provide a better representation of space conditioning use in terms of engineering and statistics. There isn't a huge difference in the ultimate estimates of heating or cooling loads -- although you need to be more careful in how you analyze the temperature data. But there's no real advantage to using average monthly temperature.

Also, when I mentioned degree days I didn't actually say using base 65. You can choose a lower base temperature or you can statistically fit the best base temperature for the degree days -- which is what the PRISM model does (and you can also replicate on your own).

I think you also over-state what you can discern from such a plot -- how does it identify a cooling load from a dehumidifier load from fans from a pool pump? How does it tell you about internal gains? Also, the extrapolation to peak loads requires some considerable assumptions and could be done at least as well using a degree day method.

Your response about the indoor temperature estimate also isn't convincing -- the X intercept is NOT an estimate of the average indoor temperature and I think it's misleading to make this claim. You would be better off using a variable base degree day fit and adding in an estimated temperature float based on estimated useful gains than you would be using the X intercept of a single fuel monthly energy use.

I'm glad to see that at least we agree that energy use per square foot isn't a great way to "normalize".
Hello Michael,
Clearly you are more comfortable using degree days. I don't see the advantage of using heating degree days if you are going to change the building balance point from 65F. I have found that average temperature plots typically do show baseline energy use that occurs during the shoulder months (April/May or Sept/Oct for our area). Increases that occur during the summer are "typically" due to air conditioning loads. I'm not sure what you mean by "dehumidifier load from fans from a pool pump", but obviously summer loads would be influenced by pool heaters, pool pumps, irrigation pumps, large yard lights or other exterior loads on a home.

I am curious to know why you disagree with the assertion that the X-axis intercept is at the average indoor space temperature. I make this statement based on over 350 homes and business that we have plotted, many DOE2 simulations on commercial buildings, combined with the fact that it makes intuitive sense. There are definite exceptions, such as large solar gains, exterior plug loads, heating occasionally with wood, owners leaving on vacation, etc.

The following plot can be generated automatically from monthly electric utility billing data and inputting the building's total conditioned square footage.

Jim-

I think the advantage of degree days is pretty clear -- they are based on the concept that you don't have negative heating use when it's hot outside. When you use monthly temperatures, you are implicitly making this obviously erroneous assumption. If May starts out at 40F for a few days and then turns warm and ends in a heat wave at 90F then degree days recognizes that there was heating going on in the month while average monthly temperature does not.

My listing of other summer end uses like dehumidifiers was in response to your comment about being able to clearly see cooling loads in the data.

My reason for saying the X intercept isn't the average indoor temperature is based on a basic physics model of the building. It may be intuitive to you but it isn't consistent with building science. Heating energy use is proportional to the difference between outdoor temperature and the indoor temperature minus the temperature float provided by heating from other sources -- solar, occupants, other fuels' baseloads. The temperature float can be estimated as I/UA where I is the sum of these other gains (Btu/hr) and UA is the slope of that heating use line (Btu/hr/F) -- the resulting units are in degrees F.

In your analysis of 350 buildings -- are you saying that you monitored the average indoor temperatures in all these buildings and compared them to your usage analysis estimates? If not, how do you know that your indoor temperature estimates are accurate?

I have found that average temperature plots typically do show baseline energy use that occurs during the shoulder months (April/May or Sept/Oct for our area). Increases that occur during the summer are "typically" due to air conditioning loads. I'm not sure what you mean by "dehumidifier load from fans from a pool pump", but obviously summer loads would be influenced by pool heaters, pool pumps, irrigation pumps, large yard lights or other exterior loads on a home.

I am curious to know why you disagree with the assertion that the X-axis intercept is at the average indoor space temperature. I make this statement based on over 350 homes and business that we have plotted, many DOE2 simulations on commercial buildings, combined with the fact that it makes intuitive sense. There are definite exceptions, such as large solar gains, exterior plug loads, heating occasionally with wood, owners leaving on vacation, etc.

The following plot can be generated automatically from monthly electric utility billing data and inputting the building's total conditioned square footage.

Woops -- I accidentally left a chunk of your comment at the end of my last reply. To be clear, my last paragraph was:

In your analysis of 350 buildings -- are you saying that you monitored the average indoor temperatures in all these buildings and compared them to your usage analysis estimates? If not, how do you know that your indoor temperature estimates are accurate?
Here is a graph which shows how to construct an average temperature plot of a building's electrical energy usage. This characteristic "Ski jump" is typical of an all-electric home that we see here in the Pacific NW. If this home were located in a warmer climate, there would be no data points for the colder temperatures, and the data points would be extrapolated out to the right if the average temperatures exceed 80F, but the points would all lie along the same curve.

As Michael B. correctly stated, a straight line drawn through the heating month data points does not always intersect the interior space temperature. There are logical and predictable reasons why this is true, but changes in interior electric loads is not one of them. Later on I will discuss other charcteristics than can be drawn from this plot.

The plot below shows how the average temperature plot for a home defines the extent of where energy is being used within the home. We use this monthly billing analysis to predict energy savings when customers want to know how much energy they will save if they replace their windows or add insulation.

For example, the total heat loss through the windows in terms of Watts/Ft2/F is equal to:

Window W/Ft2/F = Sum([Window U-Value, BTU/Hr/Ft2/F] x [Window Area, Ft2])

([Total Building Ft2] x 3.413 BTU/Watt-Hr)

and

Air Infiltration W/Ft2/F =        [Air Change/Hr] x [Volume of Home]

([Total Building Ft2] x 3.413 BTU/Watt Hr x 55.6)

You said:
...a straight line drawn through the heating month data points does not always intersect the interior space temperature. There are logical and predictable reasons why this is true, but changes in interior electric loads is not one of them.
-----
I'm glad we're starting to agree -- somewhat. I do agree that there are logical reasons why it isn't true (that I already mentioned) but I would have to disagree on those reasons being predictable. I think it's not that easy to predict the gains with sufficient accuracy to allow a good estimate of indoor temperature. I also disagree that electric gains have nothing to do with it -- that would only be true if 100% of the electric loads were converted into usable heat within the conditioned space -- which implies not electric uses outside the heated space (like outdoor lights) and no electric water heating (where heat leaves the building down the drain), etc.

I'm also still waiting for your reply about whether you have monitored indoor temperatures for those 350 buildings you mentioned.
Hello Michael,
We have found that the average temperature plots vs Watts per square foot provides a simple and easy to use tool for analyzing customers' electric bills. Within two minutes of a customer calling with a high bill complaint I can determine what kind of heating system they have, if their usage is consistently higher than normal, if that increase is due to high base loads, higher than normal heating loads, air conditioning loads, or something out of the ordinary. I can also identify if there has been a change in the customer's energy use patterns and pinpoint when that change occurred. It has also been very useful in determining a customer's energy conservation potential, and being able to verify actual energy savings that occur after receiving only one or two months of post-retrofit billing data.

I maintain tha the slope of the UA line is a function of two variables; heat loss and solar heat gain. Higher heat losses will predictably and logically increase the slope of the UA line relative to the balance point of the building. Solar heat gain will also predictably and logically increase the slope of the UA line, but instead of pivoting at the balance point of the building, solar heat gain will pivot around the average temperature where there is negligible solar heat gain. For simplicity, I have chosen that point to be about 0F. Increasing the solar heat gain and rotating the UA line of a home will shift the x-intercept of the UA line below the interior space temperature. Decreasing or increasing the interior space temperatures will not change the slope of the UA line, but will predictably shift the UA line to the left or right respectively. Reducing interior lighting or plug loads does not change the slope of the UA line or shift it sideways for a home heated with electric resistance heat because any reduction from these sources simply causes the heater to run longer. A home heated with heat pumps will see a reduction of winter energy usage when interior loads are reduced. Reducing the interior lighting or plug loads will obviously reduce the energy used during the summer and shoulder months.

Regarding your rhetorical question about indoor temperatures, it was not necessary to monitor the indoor temperatures for all 350+ buildings that we have analyzed because a majority of the x-intercepts on their graphs consistently land in 60 to 70F range. My experience with other building simulations, formal education and observations leads me to believe that the 5 to 10F shift below 70F is primarily due to solar heat gains. I'm not saying that's the only reason. There may be other explanations and I'm open to hearing them.

I will be the first to admit that this average temperature model is not the "end-all / be-all" solution. There are definite limitations, but for those looking for a simple, low-cost and intuitive approach, I believe this methodology has value as a useful tool for predicting energy savings potential, verifying actual energy savings and characterizing a building's overall energy use. Sitting down and discussing all these issues together over a couple of beers, I am sure we would find that we agree more than we disagree on the technical points and limitations of this model.

Cheers,
Jim
some post holiday replies:

You said:"We have found that the average temperature plots vs Watts per square foot provides a simple and easy to use tool for analyzing customers' electric bills. Within two minutes of a customer calling with a high bill complaint I can determine what kind of heating system they have, if their usage is consistently higher than normal, if that increase is due to high base loads, higher than normal heating loads, air conditioning loads, or something out of the ordinary. I can also identify if there has been a change in the customer's energy use patterns and pinpoint when that change occurred. It has also been very useful in determining a customer's energy conservation potential, and being able to verify actual energy savings that occur after receiving only one or two months of post-retrofit billing data. "

Any graph of usage against temperature or even just a time series plot will show many of the things you mention. Large winter or summer usage spikes are obvious using any approach. Your claim that you can verify energy savings with one or two months of post-retrofit billing data is a stretch at best. The variance of an individual monthly bill can be fairly large given occupancy effects and non-temperature weather effects. I published a paper on short-term billing analysis approaches back in 1988 (ACEEE Summer Study). The short-term data can give some decent indications but is subject to greater variance and potential bias.

I also disagree with your claims in the next paragraph about UA and solar gain (there is 0 solar gain when it's 0F outside -- really??). Although the house UA will dominate the slope of the graph (if you use degree days, or if you only look at real winter data) other factors can also affect the slope and the intercept-- many loads including hot water, lighting and refrigeration vary seasonally, infiltration is not linear, internal gains vary over time, etc. Things are also a lot more complicated if you aren't working with an all electric home with resistance heat but are analyzing gas bills or electric bills of gas heated homes.

You said: "Regarding your rhetorical question about indoor temperatures, it was not necessary to monitor the indoor temperatures for all 350+ buildings that we have analyzed because a majority of the x-intercepts on their graphs consistently land in 60 to 70F range. My experience with other building simulations, formal education and observations leads me to believe that the 5 to 10F shift below 70F is primarily due to solar heat gains. I'm not saying that's the only reason. There may be other explanations and I'm open to hearing them. "

Just because it comes up with numbers in the general vicinity of where people might set their thermostats does not mean it actually provides a good estimate of indoor temperature. I could set up a dartboard with numbers ranging from 60-70 and get the same confirmation. If you want to claim that the X intercept is the average interior temperature then you need to have measured the indoor temperatures to claim that the data support what you say. Anything else is just wishful thinking. You say you are open to hearing about other factors that affect the X intercept yet I've already mentioned them (most obviously the internal gains from other fuels, occupants, and solar and also the lack of 100% utilization of the same fuel gains). Building physics indicates that the X intercept is not the average indoor temperature.

Your experience with 350 buildings does not provide evidence for anything since you apparently have no "truth" standard for comparison. I've performed degree day based weather normalization on more than 5 million homes and have developed a keen appreciation for what we can and can't learn from billing data.

I still come back to my original 3 comments: you should use degree days (variable base) instead of average temperatures, the X intercept is not the indoor temperature, and normalizing by floor area is biased against small homes. It seems we agree on just the last one. I'd certainly be willing to have a beer and talk more about 1 and 2 but you'll have a hard time convincing me without some compelling data and physics to support your points.
Hello Michael,
You clearly have vast knowledge, experience and strong preferences for analyzing homes using heating degree days (HDD) and cooling degree days (CDD) that employ "variable base" adjustments. Using HDD and CDD is a useful way to analyze home’s energy use, even though it has many of the same limitations that you make against the average monthly temperature approach that I describe in this forum. For example, internal gains from other fuels impact the expected gas or electric heat balance point of the building, regardless of whether you are using the average temperature approach or HDD. Your statement that, "many loads including hot water, lighting and refrigeration vary seasonally, infiltration is not linear, internal gains vary over time, etc." only reinforces the average temperature approach because they "vary seasonally" and are often correlated with average monthly temperatures. While HDD and CDD with a variable base work best for you, I personally find it unnecessary and prefer to use average monthly temperature vs. average Watts/Ft2 plots because it provides an instant snapshot of a building's historic electric heating, cooling and baseline energy use.

You stated, "Your claim that you can verify energy savings with one or two months of post-retrofit billing data is a stretch at best." I would counter by saying that I have a high degree of confidence that data lying significantly outside of a trend line with an R^2 of 0.98 or greater, drawn through average monthly temperature versus average watts/Ft2, is due to a non-weather changes made within that building. For example, the following graph shows the reduction in heating and cooling that resulted from installing a new heat pump. There is also a single data point that occurred during the month that the heat pump failed. That single data point could be used to accurately predict the annual electricity consumption of continuing to run the home solely on electric resistance heat.

I stand by my assertion that the x-intercept is directly related to the interior space temperature of the building. Solar gains and other non-electric internal loads will shift the intercept, but this is only because those loads are not represented in the building’s monthly electric meter readings. Solar gains can be combined with the building’s overall UA heat loss coefficient for simplicity, and as a way to visually explain the dynamics of what is happening within a home. I chose an average monthly temperature of 0 degrees F as a pivot point for zero solar gain because of my experience living and working in Alaska. For most homes where the average monthly temperature is 0F, the little solar gain that does occur during that month will be insignificant compared to other loads within the building. I also choose peak solar insolation levels peaks in June, even though the highest average temperatures usually occur in July. Extensive plots of DOE2 computer results showing all heat gains and losses versus average monthly temperature provided convincing enough evidence for me that the x-intercept, when corrected for solar gain, is directly related to interior space temperature, but it is understandable if you are not convinced without seeing the data yourself.

At some point, I believe that we both will agree that degree-day and average monthly temperature models are imperfect and cannot be used to adequately determine everything that is happening within a home. For example, these models have a hard time predicting the optimal unoccupied temperature setback for a home with an electric heat pump. Setting the temperature back too far can cause the electric resistance heaters to run longer in the morning, negating any savings that occurred by keeping the house cooler at night. Hourly simulations are not much better at predicting what this optimal unoccupied setpoint should be either, which is why I am encouraged by the analog and object-oriented approach offered by numerical simulation programs such as Matlab’s Simulink.

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