What question did this study set out to answer?

The aim is to forecast electric power consumption in public buildings using quantile regression models.

March 1, 2026Open Access

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

Key Points

The aim is to forecast electric power consumption in public buildings using quantile regression models.
Utilized real-world consumption data from three public buildings
Implemented univariate and multivariate approaches for predictions
Applied quantile regression to model forecast uncertainty
Compared performance against persistence-based benchmarks
Quantile regression approaches consistently outperformed persistence-based methods
Pinball loss values ranged from 1% to 1.8% across case studies
Prediction intervals showed coverage probabilities between 0.78 and 0.89
Univariate QR achieved lower pinball loss while multivariate QR provided better PICP and PINAW for irregular consumption profiles

Abstract

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.

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