How the calculation works
The calculator fits a straight line through the baseline data by least squares:
The intercept a is the fixed energy used in each period regardless of output. The slope b is the energy used per extra unit produced. For each reporting period, the model predicts what the plant would have used under baseline performance. The difference between expected and actual energy is the saving, normalised for production.
R² = 1 − SSresidual ÷ SStotal
CV(RMSE) = √(SSresidual ÷ (n − 2)) ÷ mean energy
Worked example
The sample data loaded above is a year of monthly production and electricity use for a plant, followed by three reporting months after an energy improvement project.
- Baseline model: energy = 144,432 + 165.4 × production. The plant uses about 144,000 kWh a month whatever it produces, plus 165 kWh per tonne.
- R² is 0.982 and CV(RMSE) 0.9%, so production explains energy use very well.
- For the three reporting months, the model expects 952,700 kWh. The plant actually used 919,000 kWh.
- Normalised saving: 33,700 kWh, or 3.5%. A plain kWh comparison with last year would not show this, because production also changed.
Using this for ISO 50001
- ISO 50001 asks for energy baselines and energy performance indicators (EnPIs) that are normalised for relevant variables. A regression model like this one is a common way to do that; ISO 50006 gives guidance.
- A common rule of thumb is to accept a model with R² of 0.75 or more. For monthly data, ASHRAE Guideline 14 calibration criteria (CV(RMSE) of 15% or less) are often used as a further check.
- Use at least 12 monthly periods so the baseline covers a full seasonal cycle, and document any static factors, such as product mix or shift pattern, that must stay the same for the model to remain valid.
- If energy depends strongly on weather, production alone is not enough. A model with degree days as a second variable is needed.
Questions
What is an EnPI?
An energy performance indicator: a measure used to track energy performance, from a simple ratio such as kWh per tonne to a regression model that accounts for several variables.
Why use regression instead of kWh per tonne?
Because most plants have a fixed energy load. Regression separates the fixed part from the part that varies with output, so savings are not hidden or inflated by changes in production.
How much data do I need for a baseline?
Twelve monthly periods is a common minimum, as it covers a full year of seasonal variation. Weekly or daily data can give a stronger model if the meter data is reliable.