A Hierarchical Spatio-Temporal Refinement Network with residual temporal convolutional networks and closed-form calibration for national-scale short-term load forecasting

Accurate national-scale short-term load forecasting is essential for reliable dispatch, reserve allocation, and cost-efficient operation under weather-driven demand variability. Most existing models either rely mainly on load and calendar inputs or fuse high-dimensional weather grids through simple concatenation, which underuses spatial structure and can increase error at the national scale. This work addresses this gap with the Hierarchical Spatio-Temporal Refinement Network (HST-RefNet), which learns directly from nationwide meteorological fields and historical load without decomposition. The model uses a Spatio-Temporal Representation Temporal Convolutional Network (STR-TCN) to learn dominant spatio-temporal patterns, a Residual-Focused Refinement Temporal Convolutional Network (RFR-TCN) to correct hard regimes, and a lightweight random-feature calibrator with closed-form training to refine remaining nonlinear errors. Iterative training is concentrated in the two TCN stages, while the final calibrator adds low computational overhead through closed-form estimation. The comparative study includes both generic sequence baselines and dedicated spatio-temporal baselines for structured high-dimensional meteorological inputs. On the Pakistan National Transmission and Despatch Company (NTDC) load and National Aeronautics and Space Administration (NASA) Prediction Of Worldwide Energy Resources (POWER) benchmark, HST-RefNet achieves an average Normalized Root Mean Squared Error (NRMSE) of 5.00% and a Coefficient of Determination ( 𝑅 2 ) of 0.91 over the first 6 forecast horizons, while reducing NRMSE by 7.09% relative to the strongest spatio-temporal baseline.