In order to detect unexpected excess energy use against a background of natural week-by-week* fluctuations, you need an accurate estimate of expected consumption for each monitored stream of consumption. Knowing the expected consumptions enables exception reporting, diagnosis of energy waste, verification of savings and rigorous budgeting.

You get expected consumptions from formulae relating consumption to one or more relevant driving factors (degree days, hours of darkness, product throughputs and the like) and the most common form of expected-consumption formula (ECF) is a straight-line relationship which separates consumption into fixed and variable parts, with the expected consumption E in a given week expressed as a formula

E = c + m.D

D is the measured value of the driving factor and c and m are constants, c being the intercept on the vertical axis (fixed or base-load weekly consumption) and m being the gradient of the line (kWh per degree day, or per tonne of output, or whatever). In practice c and m are usually derived from historical weekly data using a statistical technique called regression analysis, and the formula is sometimes known as a â€˜regression modelâ€™. Once determined, the values of c and m are baked into the ECF until there is a justifiable reason to review it.

Straight-line models are not the only possibility. You may see curved or discontinuous relationships, but if you see those there has to be a physical explanation for the non-linear behaviour. In the absence of a physical explanation it is more likely to signify a problem.

Another common type of ECF is one in which there are multiple driving factors: for example where an air conditioning load (driving factor: cooling degree days) is mixed with a major external lighting installation (driver: hours of darkness) on the same meter. Multi-factor models are often appropriate in manufacturing contexts, particularly energy-intensive industries with multiple product lines.

Although the term ‘regression model’ is widely used as a synonym for the expected-consumption formula, it’s a bit misleading because there are non-statistical ways to derive the ECF, notably by working from theoretical first principles. I’ll conclude by saying that where ECFs are derived by statistical analysis of past performance, the analysis should be moderated by the use of cusum techniques to enable unrepresentative performance to be disregarded.

**Footnote: for simplicity I refer to weekly analysis. Other intervals may be used*