A new error measure for forecasts of household-level, high resolution electrical energy consumption

As low carbon technologies become more pervasive, distribution network operators are looking to support the expected changes in the demands on the low voltage networks through the smarter control of storage devices. Accurate forecasts of demand at the individual household-level, or of small aggregations of households, can improve the peak demand reduction brought about through such devices by helping to plan the most appropriate charging and discharging cycles. However, before such methods can be developed, validation measures which can assess the accuracy and usefulness of forecasts of the volatile and noisy household-level demand are required. In this paper we introduce a new forecast verification error measure that reduces the so-called “double penalty” effect, incurred by forecasts whose features are displaced in space or time, compared to traditional point-wise metrics, such as the Mean Absolute Error, and p-norms in general. The measure that we propose is based on finding a restricted permutation of the original forecast that minimises the point-wise error, according to a given metric. We illustrate the advantages of our error measure using half-hourly domestic household electrical energy usage data recorded by smart meters, and discuss the effect of the permutation restriction.