Forecast of Electric Power Consumed by Public Buildings: Univariate and Multivariate Approaches Based on Quantile Regression Models

Load forecasting has become a key tool, especially for distribution system operators, to ensure optimal grid management and control. In recent years, attention has shifted toward probabilistic load forecasting (PLF), as it can model forecast uncertainty. Because electricity demand is strongly influenced by time-dependent factors such as seasonal patterns and daily habits, non-parametric PLF methods are particularly suitable because they make no assumptions about the distribution of variables. This study focuses on quantile regression (QR), a widely studied non-parametric PLF technique that models forecast uncertainty by only assuming a linear dependency among variables. It is applied every hour to forecast the daily consumption of three large public buildings—an elderly healthcare center, a biomedical research facility, and a polyclinic—with different demand variability profiles. Forecasts are carried out using real-world consumption data and evaluated considering both univariate and multivariate approaches. The performance of both QR approaches is rigorously evaluated against that of two persistence-based methods through standard evaluation metrics. For the univariate case, two aggregation levels are considered: single buildings and aggregation of buildings. The results confirm the effectiveness of both uQR and mQR, which consistently outperform persistence-based benchmarks. In terms of the pinball loss (PL) function, the QR approaches exhibit values ranging from 1% to 1.8% across all case studies. Both approaches demonstrate reliable and sharp prediction intervals (PIs); for example, for the PI(10–90) using the uQR, the PI coverage probability (PICP) ranges from 0.78 to 0.89 and the PI normalized average width (PINAW) from 0.09 to 0.26. Overall, uQR achieves lower PL, whereas mQR yields slightly better PICP and PINAW results for the building characterized by an irregular and unpredictable consumption profile.