Long and Short term forecasting of daily and quarter-hourly electrical load and price data: a torus-based approach

The thesis addresses two types of forecasting problems arising in the electricity market: the long- and short-time prediction of electrical demand at country level and the prediction of spot prices of electric commodities. The former problem, in spite of an extensive literature ranging from classical time-series methods to the most recent computational intelligence techniques, is still an active research topic. Our analysis of several years of load data coming from Italy, Belgium and Ireland, highlights an interesting feature: once the loads are log-transformed and detrended, their multi-seasonal pattern (yearly, weekly and daily), also known as \potential", is remarkably stable across the years. This nding is the starting point for the development of modular long- and short-term forecasters that rely on a novel representation of the potential, modeled as a continuous function dened over a torus (for daily prediction) or hypertorus (for intraday predictions). The 2011- 2014 time series of the three countries are used to validate the proposed forecasters and also to compare their performances with some established methods. The performances of the new long-term forecaster, dubbed TOR4- S are remarkably good: in all the 12 years (4 years for each of the three countries) used for testing, the daily MAPE (Maximum Average Percentage Error) is always less than 4%, while the short-forecaster, TOR4-S yields a MAPE below 2.2%. TOR4-S denitely improves not only on classical ARMA, SARIMA and Holt-Winters predictors, but also on two forecasters currently used by the Italian Transmission System Operator. Likewise, intra-day quarter-hourly predictors (both long- and short-term) is successfully addressed: the long -term forecaster achieves a MAPE always below 9%, while the MAPE of the short-time one is always below 6%. Concerning the second issue, that is the prediction of spot prices, attention is focused on the calibration of stochastic dierential equation models. As an alternative to techniques relying on standard likelihood maximization, the adoption of a fully Bayesian paradigm is explored, that relies on Markov Chain Monte Carlo (MCMC) stochastic simulation in order to estimate the posterior distributions of the model parameters. The proposed method is tested on oneand two-factor stochastic dierential models, using both simulated and real data. The results demonstrate good agreement between the ML and MCMC point estimates, although the latter approach provides a more complete characterization of the model uncertainty, an information that could be exploited in also to obtain a more realistic assessment of the forecasting error.