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.
Adding Residential Solar PV Systems
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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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.
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]