The first step in most HVAC design projects is to calculate heating and cooling loads. These calculations become the basis for sizing equipment and, when required, projecting energy use. While energy-use projections can be data- and calculation-intensive, even the most sophisticated procedures consist of little more than calculating the heating or cooling load at each outdoor temperature of interest, multiplying by the number of hours of each outdoor-temperature occurrence in a year, and summing. Engineers might not realize they can apply the process in reverse: use historical energy-use and weather data to infer building heating or cooling loads and understand how a building uses energy.

A historical-energy-use analysis consists of gathering two or three years of utility bills and corresponding weather data, plotting energy use against degree days, and analyzing the results. A small office building near Hartford, Conn., offers an example of this process.

### Heating Energy

Table 1 presents one year of gas-use data for the office building.

The billing-period and gas-use data came from the customer’s utility bills. “Ccf” stands for 100 cu ft, which is equal to 1 therm or 105 Btu at a nominal higher heating value of 1,000 Btu per cubic foot, typical for utility-supplied natural gas.

Heating degree days came from local weather data. A degree day is calculated by subtracting the mean of the high and low temperature for a day from a base temperature (for heating, usually 65°F).

For example, in Boston on Jan. 25, 2013, the high temperature was 24°F, and the low temperature was 10°F. The mean temperature, then, was 17°F, resulting in 48 heating degree days (HDD) (65 − 17). The number of degree days in any period, such as a month, is the sum of the number of degree days for each day in the period.

Figure 1 is a plot of gas use against HDD. The solid line is the least mean squares linear regression line. The graph and the regression line lead to the following observations and analysis:

• For this building, like many others, all of the data points are fairly close to the regression line. The factor R2 quantifies how well the line fits the data. R2 ranges from 0, meaning no relationship between the dependent variable (in this case, gas use) and the independent variable (in this case, outdoor temperature as measured by degree days), to 1, meaning perfect correlation.

A lot of scatter in the data (low R2 correlation coefficient) means outdoor temperature is not the main determinant of building energy use. That might be because domestic water heating or other process loads use more energy than space heating does. It also might be because the building uses a lot of energy for reheat or controls do not maintain steady indoor temperature.

It is not unusual for buildings with well-controlled heating systems to have correlation coefficients of 0.96 or 0.98. Buildings with erratic control might show a correlation coefficient of less than 0.80, while buildings with fuel use dominated by domestic water heating or process loads that do not vary with outdoor temperature might show a correlation coefficient of 0.40 or less.

• The equation for the line takes the form of:

y = mx + b

where:

y is gas use in hundreds of cubic feet per month

m is the slope of the line in hundreds of cubic feet per HDD

x is HDD per month

b is the intercept in hundreds of cubic feet per month

The slope, m, provides a measure of actual heating load. By adjusting the units, slope can be expressed in traditional heating-load units of British thermal units per hour per degree Fahrenheit. In this example, the slope of 5.218 ccf per HDD converts to an inferred heating load of 21.74 MBH per degree Fahrenheit of temperature difference, as follows:

5.218 ccf per HDD × 105 Btu per ccf × 1 day ÷ 24 hr = 21.74 MBH per °F

Both heat-loss theory (Q = U × A × ∆T) and fuel-use analysis show fuel use/heat loss is linear with outdoor temperature (as measured by HDD). Therefore, the inferred heating load of 21.74 MBH per degree Fahrenheit can be applied to any indoor/outdoor temperature of interest. For design temperatures of 70°F indoors/0°F outdoors, the inferred design heating load becomes 1,522 MBH.

The intercept, b, represents the amount of gas the building requires at 0 degree days (when outdoor temperature equals the degree-day base temperature: 65°F in most cases). In this building, the intercept is −159.01 ccf per month. With 730 hr in a month, the intercept equates to −22 MBH.

The negative intercept means internally generated heat plus free solar heat gain is more than the heat loss at 65°F (the degree-day base) outdoors. Many well-insulated commercial buildings have a negative intercept.

Buildings with substantial weather-independent loads, or base use, will have a positive intercept, which is the average fuel load to support the base use.

• Comparing the intercept of −22 MBH with the heat-loss rate of 21.74 MBH per degree Fahrenheit (1,522 MBH peak/70°F temperature difference) shows that internally generated heat in the building overcomes 1°F (22 MBH/21.74 MBH per degree Fahrenheit) of indoor-outdoor temperature difference. Expressed another way, the balance point where the building needs neither heating nor cooling is 65°F (degree-day base) minus 1°F, or 64°F. It is not unusual for modern, well-insulated commercial buildings to have an occupied-hours balance point of 35°F to 40°F.

Because it is an accurate measure of actual building heating load, a fuel-use analysis with a high correlation coefficient can be used to size a replacement boiler. While fuel-use analysis is not a substitute for heat-loss calculations, it is a decidedly better measure than British-thermal-units-per-hour-per-square-foot or British-thermal-units-per-hour-per-cubic-foot rules of thumb.

It might be tempting to convert the slope of the fuel-use-analysis regression line to British thermal units per hour. However, that almost certainly would result in an undersized boiler. The reason is that the slope/peak heating load determined from the degree-day analysis is an average over the course of a day. It includes the effects of “free” heat, such as solar gain, and internal heat gains from lights, people, and equipment. A heating system has to be able to heat an empty building at the coldest nighttime hour of the year. Letting the indoor temperature drop several degrees during the coldest hours on the premise the building can catch up later in the day, when the outdoor temperature is higher, might not be acceptable. Experience has shown that increasing the heating load determined from a degree-day slope by 20 percent results in realistic boiler sizing.