Functional clustering and linear regression for peak load forecasting

In this paper we consider the problem of short-term peak load forecasting using past heating demand data in a district-heating system. Our data-set consists of four separate periods, with 198 days in each period and 24 hourly observations in each day. We can detect both an intra-daily seasonality and a seasonality effect within each period. We take advantage of the functional nature of the data-set and propose a forecasting methodology based on functional statistics. In particular, we use a functional clustering procedure to classify the daily load curves. Then, on the basis of the groups obtained, we define a family of functional linear regression models. To make forecasts we assign new load curves to clusters, applying a functional discriminant analysis. Finally, we evaluate the performance of the proposed approach in comparison with some classical models.