Methodology
The billing model uses the daily model with small configuration changes and billing (monthly or bimonthly) interval data.
Model Theory🔗
Converting from billing data to daily data🔗
The billing model intakes billing data and calculates the average energy usage for each given period. For example if a bill covers 31 days and uses 93 therms total, then each day would be given 3 therms of usage. A billing period is assumed to start on the datetime in which it has a value and to end 1 day prior to the next datetime with a value with 1 final empty datetime signifying the end of the year resulting in 13 total datetimes for monthly billing data and 7 for bimonthly billing data. Pulling the temperature from EEweather ensures that each day’s mean temperature is correct.
From here, the data is treated as daily interval data and uses the daily model internally.
Model Shape and Balance Points🔗
The daily model, at its core, utilizes a piecewise linear regression model that predicts energy usage relative to temperature. The model determines temperature balance points at which energy usage starts changing relative to temperature.
Key Concepts🔗
- Balance Points: Outdoor temperature thresholds beyond which heating and cooling effects are observed.
- Heating and Cooling Coefficients: Rate of increase of energy use per change in temperature beyond the balance points.
- Temperature Independent Load: The regression intercept (height of the flat line in the diagram).
- Billing Data: Because the billing data is converted to daily data, plots will show lines of data points where the usage is the same over a range of temperatures seen during that period.
Model Archetypes🔗
Based on the site behavior, there are four different model types that may be generated:
- Heating and Cooling Loads
- Heating Only Load
- Cooling Only Load
- Temperature Independent Load
Smooth Transitions🔗
The billing model disables this feature of the daily model.
Robust, Adaptive Outlier Downweighting🔗
The billing model disables this feature of the daily model.
Model Fit🔗
When the model is fit, each site will receive its own unique model fit and coefficients. The general model fitting process is as follows:
- Balance points are estimated with a global optimization algorithm.
- Sum of Squares Error (SSE) is minimized with Lasso regression inspired penalization.
- The best model type is determined (ex. cooling load only model) using the penalized SSE.
The Lasso inspired penalization means that increased model complexity must be justified by decreased SSE and balanced against these general rules:
- Slopes are pushed to 0
- Intercept is pushed to 0
- Balance points are pushed together
- Balance points are pushed towards the nearest edge (most extreme temperature)
At this point the billing model is now fit and can be used for prediction.
Model Splits🔗
The billing model disables this feature of the daily model.
Real Data Example🔗
Here are 6 examples of how the billing model performs on real data.
