A probabilistic framework for forecasting household energy demand profiles

Recent work introduced a novel time-permuting error measure for forecasts of half-hourly, household-level energy demand, designed to reward forecasts which predict extremes (spikes) in demand at approximately the right times, albeit perhaps slightly early or late. In many applications such as smart storage control, such forecasts are preferable to those that predict no spikes at all. Building on that idea, we make three contributions. First we introduce a probabilistic framework to estimate error distributions for actuals about forecasts, using the time-permuting error measure. The framework includes a variable discount for older, possibly less relevant data. Second we employ this framework to derive conditions to be satisfied by the optimal forecast under the time-permuting error measure. In turn this requires a mixture of discrete (non derivative) optimisation and calculus to condition forecasts on available historical observations. Finally we demonstrate the usefulness of our framework by using it to forecast the daily energy demand profiles for a large number of domestic energy customers. In particular we illustrate how such customers might be classified according to the relative forecastability of their behaviour and the corresponding need for different amounts of history to achieve such forecasts.