Probabilistic load forecasting considering temporal correlation: Online models for the prediction of households' electrical load

Highlights: • Methods suitable for online applications. • Modelling temporal correlation structures improve probabilistic forecasting models. • Correlations modelled by the multivariate predictive covariance of AR models. • Implementation example using data from an inhabited house and weather forecast. Home Energy Management Systems (HEMSs) are expected to become an inevitable part of the future smart grid technologies. To work effectively, HEMSs require reliable and accurate load forecasts. In this paper, two new modelling methods are presented. They are both suited for producing multivariate probabilistic forecasts, which consider the temporal correlation between forecast horizons. The first method employs point forecasts generated with Recursive Least Squares (RLS) models and subsequently analyses the forecasts' residuals to estimate the marginal distributions and temporal correlation. The second method is based on quantile regression to estimate marginal distributions, and a Gaussian copula for linking them together. Furthermore, the application of two modelling approaches for the temporal correlation estimation are investigated for each of the two modelling methods. As a case study, a numerical experiment is designed to emulate an online HEMS operation using data from an inhabited home located in Denmark. Simulation results show a robust performance for the proposed models, with the quantile–copula ensemble outperforming the RLS-based models in predicting the marginal distributions and capturing the temporal correlation.