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When creating a baseline M&V model for a linear regression approach, one of the first questions an M&V professional will face is “What variables will significantly affect energy consumption for this project?”
Variables are required in a linear regression model and must be noted in the M&V plan. The most common variables are weather, occupancy, and production, but you may need to include more if your project is more complex or if you are isolating savings for a single piece of equipment. Each variable will have its own coefficient, meaning X amount of kWh/kW/gas/water consumption will increase or decrease with that variable.
Weather is the most common independent variable in a linear regression model, as most building equipment operates differently as temperatures increase or decrease. M&V professionals can use actual weather data or a normalized weather dataset. Actual meteorological year (AMY) datasets reflect the site’s true, recorded data. This data is typically used in forecast models to predict what consumption would have been without the ECM, using weather conditions from that reporting year. Typical meteorological year (TMY) datasets provide normalized weather data. To normalize weather data, TMY datasets use averages (temperature, humidity, dry bulb temp, etc.) over long periods of time to indicate “what is the weather usually like for this zip code”. Normalizing your weather data lets you project savings and can support the end useful life (EUL) of energy savings. AMY and TMY weather datasets come from many free sources, making this an easy variable to source.
Building occupancy is another common variable an M&V professional can use, but sourcing this data can be challenging. However, occupancy typically plays a huge role in energy consumption. For example, a school will use much more energy at 12 pm on a Tuesday than at 12 am on a Sunday. A Time-of-Week and Temperature (TOWT) model is a great way to source occupancy trends, allowing you to create an occupancy coefficient without having to source the data from the building owner. Developed by Lawrence Berkeley National Laboratory (LBNL), these models learn patterns in occupancy based on consumption and use an indicator variable to specify if it is a time period that either increases or decreases energy consumption. However, this modeling approach only works with hourly interval data.
Production is a great variable to use for industrial customers. Luckily, most industrial customers have this data readily available. Some industrial projects can use a simple “X amount of units produced per hour/day” as a variable. However, industrial facilities typically have intricate datasets, which can become complex when determining which variables are significant. The M&V professional must be careful to not overfit the model with too many variables (more on this below).
Beyond the big three (weather, occupancy, and production), you can include many other variables in a linear regression model. Solar projects typically include solar irradiance, precipitation, and snowfall to understand day-to-day generation fluctuations. Equipment-level linear regression models can source a ton of variables from the BMS. For example, HVAC and VFD equipment can use airflow, tonnage, fan speed, water flow, etc. in the regression models.
The significance of the variables in your model can be confirmed by the R2 and P-value. R2 represents the overall model, while each variable has its own P-value. Per the IPMVP, the model must produce an R2 of 0.75 or higher to indicate that all variables used are statistically significant. P-values are less stringent within the IPMVP protocol and are more a best-practice suggestion than a strict requirement. Typically, you want your P-value to be less than 0.31 for a standard model (68% confidence level).
M&V professionals should be careful to avoid overfitting the linear regression model. Overfitting means that you have used too many variables relative to your sample size. Just because you have variable data does not mean you need to use it in your model. Negative coefficients, high p-values, or significant changes in R2 can indicate that a variable you used is not significant for the model.