B-TGPRF: A Bayesian Temporal Graph Probabilistic Model for Calibrated Overload-Risk Forecasting in Power Transmission Grids

Modern power transmission grids are increasingly operated under volatile load, variable generation, and near-limit line-flow conditions. In such environments, deterministic line-flow forecasting is insufficient for operational decision support because operators require calibrated risk probabilities, uncertainty intervals, and reliable early warning signals. This article proposes B-TGPRF, a Bayesian Temporal Graph Probabilistic Risk Forecaster for calibrated overload-risk forecasting in power transmission grids. The proposed framework is positioned as a hybrid probabilistic graph-temporal forecasting system rather than as a new end-to-end graph neural network; its novelty lies in the leakage-controlled sequential combination of temporal forecasting, electrical graph descriptors, calibrated Bayesian risk estimation, residual correction, and compact interval uncertainty assessment. The model integrates temporal line-flow, load, and generation features with graph-topological descriptors, operating-regime indicators, residual correction, conformal interval estimation, probability calibration, and a Bayesian risk layer. A leakage-controlled data preparation pipeline was built using an open large-scale benchmark for machine learning applications in transmission grids. The final modeling dataset contains more than 3.48 million observations, 100 selected critical lines, train-only risk thresholds, and chronological train, validation, test, and external-like scenario splits. B-TGPRF was compared with persistence baselines, linear models, Bayesian baselines, tree ensembles, boosting models, neural temporal models, and compact state-of-the-art-style temporal and graph-temporal architectures. On the strict external-like test, B-TGPRF achieved MAE = 0.3650, RMSE = 0.5478, R2 = 0.9962, Brier Score = 0.0147, and ECE = 0.0064. The results show that the proposed model provides a strong overall balance between line-flow forecasting accuracy, calibrated risk estimation, compact interval prediction, and low false-positive risk-signaling, while boosting models remain highly competitive for pure risk-class detection.