Theory-guided lightweight decomposition for efficient and robust day-ahead electrical load forecasting

Accurate electrical load forecasting is important for operational planning and dispatch in modern power systems, yet existing models often face a trade-off among predictive accuracy, computational efficiency, and robustness to imperfect exogenous inputs. To address this challenge, we propose a Theory-guided Lightweight Efficient Decomposition (TgLED) framework with a Structured Temporal–Exogenous Mixer (STEM) for day-ahead electrical load forecasting. TgLED transforms raw load data into a normalized load-ratio series and decomposes it into a transferable dimensionless trend and a local fluctuation component. The trend captures stable structural patterns through domain knowledge, whereas the fluctuation is learned by STEM, a lightweight dual-path architecture that separately models temporal inertia and exogenous drivers using efficient feedforward operations. Four-fold cross-validation on hourly load and weather data from 12 districts in Beijing shows that TgLED achieves an average MSE of 0.056, reducing the error by 9.8% compared with the previous theory-guided baseline TgDLF. Compared with recently proposed lightweight time-series forecasting baselines, TgLED achieves evident superiority in forecasting performance. On the same RTX 4090 platform, TgLED reduces the training time from 768.66 s to 6.85 s and the inference time from 19.25 s to 1.91 s, indicating its practical value for frequent retraining and multi-district day-ahead forecasting. Additional noise-injection experiments on weather inputs show slower performance degradation, indicating stronger robustness to exogenous-input uncertainty and weather forecast errors. These results demonstrate that TgLED provides an efficient and interpretable approach to electrical load forecasting under limited computational budgets and imperfect exogenous information.