# 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 seems that we are getting closer to agreement on issue #2. In your initial post you said "The intersection of this line with the X axis, typically 70F, indicates the average temperature maintained inside the home." I disagreed with that claim. In your latest post you say "the x-intercept, when corrected for solar gain, is directly related to interior space temperature". This is a very different claim. I never said that the X intercept isn't related to or affected by the interior temperature. I just said that it wasn't equal to the interior temperature. Now that you have changed your claim, we are pretty much in agreement on this point.

Average monthly temperatures will not represent usage patterns as well as degree day methods. It seems like your main argument against degree days is that they are harder to use. I don't find it to be a problem -- it can be readily automated in whatever analysis tool you use. If you don't want to bother that's up to you -- the temperature plots and fits are useful, just not as good.

Your claims about assessing savings based on one or two months of data are not bolstered by showing one building,. I didn't say that 1 or 2 months of data isn't potentially useful for assessing savings, just that it can be misleading and has considerably larger uncertainty than using more data -- this year they went away for Christmas break and last year they hosted extended family....wow look at all the savings from changing a light bulb...;) I think it boils down to what sorts of claims can and should be made about what billing data can and can't tell us about an individual home. I think you overstate the level of detail and certainty while I exercise a little more caution.

Here is a plot that shows the electricity generated by a 6.5 kW solar PV array compared to the energy consumed by an all-electric 2,000 square foot home that is heated by an air source heat pump.  The energy generated by the solar PV array is based on actual monthly kWh production meter reads and has been normalized in terms of the home's square footage.

Typical electricity billing information is shown in yellow below.The information highlighted in yellow above is shown in the bar graph below. The bar chart below does not account for different billing days in each month or for weather differences that occur each month.

The above chart can be normalized for weather variations and different number of billing days in each month by plotting the average kW for each month versus each month's average temperature.

Average kW is equal to: kW = [kWh/Month] / ([Days/Month] x 24 Hr/Day).

The above chart can now be analyzed in terms of heating, cooling and baseload energy consumption.

The above chart can be used to calculate the savings of installing a ductless heat pump or other heat related or air conditioning based conservation measure, such as a ductless heat pump.

The "Generic Billing Analysis" spreadsheet that I uploaded came up as a .zip file instead of an Excel spreadsheet.  The spreadsheet below is another attempt to upload the Excel spreadsheet that can be used to conduct a billing analysis of gas and electric bills.

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