An expected-consumption formula is a mathematical model. You put in information about weather, activity levels or other driving factors for a given week (or other interval) and the model tells you what energy consumption you should expect under those conditions. The most common form of model is a straight-line relationship with a single driving factor, usually derived from regression analysis of past observations. Consumption that depends on two or more driving factors can be similarly modelled using multiple regression analysis.
You can think of these regression models as being a rather simple form of ‘digital twin’, a term that has become familiar in the context of sophisticated simulation models. Indeed in principle there is no reason why a fully-fledged digital twin should not be used as a way to estimate expected energy consumption. It should be very good for the purpose, with the added advantage that it can be used in situations where there are no historical data to feed into a regression analysis.
However, if a full digital twin is not feasible, you might be able to build a model using calculations from first principles. I did this once for a distillation process where the liquid product was dissolved in a blend of two solvents that had to be boiled off. With the benefit of real-time measurement of temperatures, flow rates and incoming blend proportions, it was possible to work out in theory how much sensible and latent heat must have been absorbed by the process in a given interval; we did the sums at 20-minute intervals, aggregating up to weekly totals for reporting and diagnostic purposes.
Many processes which rely on forced evaporation—drying in paper manufacture, for example—can be modelled using loss of weight as the driving factor, with the great advantage that the physical properties of the material (in this case the latent heat of evaporation of water) can be used to build the model, or at least to sense-check a model derived statistically.
Finally I want to mention ‘state-based’ models, which I have seen used in continuous industrial processes where energy is mainly used in handling and manipulating the materials but is not embedded in the product to any significant degree. Here it may be possible to define a range of states that the process can be in (running, standing by, or stopped for instance) and to assign a typical power level in kilowatts for each state. Then by logging how many hours the process spent in each state over the course of a week you can calculate how many kilowatt hours that implied.