Short-term hierarchical photovoltaic forecasting with cross-sectional reconciliation in Belgium

Accurate forecasting of photovoltaic (PV) power generation is critical for grid stability, energy trading, and capacity planning due to the strong temporal variability and spatial diversity of solar resources. This study analyzes short-term PV forecasting across a threelevel spatial hierarchy in Belgium, comprising national, regional, and provincial data from January 2020 to March 2025. A diverse set of statistical, machine learning, foundation, and hybrid deep learning models was evaluated for short-term (24-hour horizon) PV forecasting, incorporating meteorological, calendar, and periodic features as exogenous inputs. Six cross-sectional reconciliation methods were assessed: Bottom-Up, Ordinary Least Squares, Weighted Least Squares, Structural Scaling, Covariance-based, and Shrinkage-based. The LightGBM model achieved the lowest NRMSE (1.26) with the Bottom-Up approach, followed by TBATS (1.53) and TimeGPT (1.56) using the covariance estimator. Hybrid deep learning models such as NHITS and NBEATSx obtained the largest error reductions, ranging from 17% to 42%. These findings can support grid operators in real-time scheduling and policy planning for renewable integration.