# An Introduction to Building Models

Degree Day Primer

How do the characteristics of a building affect its energy usage? We can develop intuition for an answer with simple mathematical models, instead of waiting to measure changes from new insulation or different boilers. One such model of monthly utility usage is depicted below; it has six adjustable variables which represent physical characteristics. This model expands on the simpler—and more widely used— three-variable PRISM model (see notes below).

The interactive primer below replaces the equation parameters with sliders you can adjust. The various graphs illustrate the monthly   electric cooling ▾   gas heating ▾   usage of a building due to changing average daily temperatures. One month is highlighted (inset and colored dot) to help follow the changing energy consumption.

At WegoWise, we use these industry-standard models to infer heating and cooling usage, detect anomalies in seasonal usage, and measure the success of building upgrades.

The simplest slider is the baseload, the portion of usage not dependent on the weather, such as .

On top of the baseload, weather-dependent usage is directly proportional to the number of degree days per month. Degree days indicate the number of degrees the system's balance point, per day. The thermostat setpoint adjusts the indoor temperature at which the system turns on, while the balance point is the corresponding outdoor temperature. The system will generally start up at a lower balance point, because internal gains like sunlight or appliances will provide additional heat. Note how changing the internal gains slider affects the balance point.

As illustrated in the highlighted month's daily temperature inset, the number of degree days (unit blocks) decreases as the balance point but cannot be negative.

The amount of energy required per degree day is represented by the slope of the line in the lower right graph; a lower slope indicates a more efficient building. The system efficiency slider directly influences this slope. The building envelope leakage affects the slope, since it determines how much of the energy escapes, and it also affects the degree days by determining how much of the internal gains contribute to a lowered balance point. For similar reasons, the ventilation flow impacts both the slope and balance point: a higher flow means more outside air must be each day.

Basic models like the one demonstrated here can extract a remarkable amount of information from monthly utility bills. Moreover, they show how a building is like a tunable engine, which can be optimized to sip energy instead of guzzle it.

• The widely used PRISM model (Fels, 1986) uses only three parameters: the baseload, the balance point, and the slope of the degree day vs. usage line.
• The more physically-motivated extension can be found in the appendix of the paper above. The model augments the PRISM equation to include the six adjustable sliders above, which can be combined and reduced into the original three.
• The daily temperatures were measured in Boston in 2013 and 2014, and range from 8 to 89 degrees Fahrenheit. Thermostat setpoints range between 50 and 80 degrees Fahrenheit.