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.
An integrated probabilistic forecasting framework with three linked stages: extreme-weather load identification, TimeGAN-based sample augmentation, and conformal quantile forecasting, which improves forecasting accuracy under extreme-weather conditions.
Hao Zhang, Xi-Yang Liu, Ruotian Gao et al.· International journal of pat...· 0 citations
This paper proposes DCR-PatchTST-CQ, a unified multi-task probabilistic forecasting framework that combines condition-aware dynamic routing combined with stratified conformal calibration to jointly improve quantile ordering, interval sharpness, and coverage reliability.
Water distribution systems face persistent challenges from leakage, with approximately 20% of distributed water lost in the UK. This study presents a unified framework for 24h water-demand forecasting and early-leakage warning, integrating classification, regression and uncertainty quantification within a temporal fusion transformer (TFT) architecture.
The framework evaluates three TFT variants: a recent-TFT (R-TFT) using one week of preceding flow, a lagged-TFT (L-TFT) using flow from two weeks prior and a combined-TFT (C-TFT) fusing both through Bayesian Markov chain Monte Carlo (MCMC) sensor fusion. It is trained and validated on approximately 18,600 flow groupings from ∼2,000 district metred areas in the UK, benchmarked against a vanilla long short-term memory (LSTM), the Informer transformer and the minimum night flow (MNF) industry standard, under both balanced and imbalanced class distributions. An operational decision framework translates the outputs into structured early warning protocols.
The C-TFT achieves the strongest overall performance, with the highest central-prediction accuracy (median index of agreement 0.901) and tightest uncertainty bounds (median prediction interval normalised average width 0.696). The classification head achieves an area under the receiver operating characteristic curve (ROC-AUC) of 0.906, with recall stable above 80% under imbalanced conditions, substantially outperforming the minimum night flow baseline (AUC 0.738). TFT interpretability through variable selection and attention mechanisms aligns with physical consumption dynamics.
No existing framework unifies flow forecasting, leakage classification, uncertainty quantification and interpretability within a single architecture. This work addresses that gap and demonstrates consistent performance across balanced and imbalanced evaluations, supporting deployment in operational environments where leakage events are rare.
Martin Rapp, J. Fayaz· Smart and Sustainable Built...· 0 citations
Electricity price forecasting has traditionally relied on point predictions, which provide a single expected value for each future delivery period. However, the high volatility, spikes, heavy tails, negative prices and regime changes observed in modern electricity markets make point forecasts insufficient for many trading, bidding, storage, scheduling and risk-management decisions. This review focuses on probabilistic electricity price forecasting (PEPF), which represents uncertainty through quantiles, prediction intervals, predictive densities and multivariate scenarios. It systematizes recent developments in post-processing methods, Quantile Regression Averaging, conformal prediction, Bayesian and heteroscedastic models, distributional neural networks, copula-based approaches, normalizing flows, generative models and scenario generation. Particular attention is paid to probabilistic forecast evaluation, including proper scoring rules, calibration diagnostics and statistical testing. The review highlights the transition from marginal uncertainty quantification toward coherent multivariate and decision-oriented forecasting, and identifies open challenges related to calibration, dependence modeling, benchmark design, economic value assessment and reproducibility.
Grzegorz Dudek, Paweł Piotrowski, M. Kopyt et al.· Energies· 1 citation
Forecast accuracy alone is an incomplete proxy for operational value when load distributions change. This paper presents ARLOS, an auditable forecast–uncertainty–decision framework that combines static and adaptive XGBoost forecasts, rolling performance monitoring, residual-bootstrap uncertainty, and explicit fixed-margin, quantile, and risk-target operating rules. The evaluation uses 2021 for ex ante training and capacity-proxy definition and 2022–2023 for strictly sequential testing on two Ecuadorian distribution substations under a measured baseline, smooth growth, and intraday structural shift. Under the four shifted station–scenario cases, adaptive fixed-margin operation reduced the weighted operational objective by 24.8–46.0% relative to the static fixed-margin baseline; baseline-regime changes ranged from −2.5 to 11.2%, showing that adaptation is valuable primarily when mismatch is present rather than universally. A 2×2 ablation further shows that adaptation and uncertainty are distinct, non-additive sources of operational value: aggregate normalized cost changes from 0.987 for static/fixed operation to 0.650 for adaptive/fixed, 0.515 for static/quantile, and 0.546 for adaptive/quantile. Realized one-sided exceedance, computed from observed load rather than from the bootstrap sample itself, remains within 0.0039–0.0111 of the target across the controlled cases, while nominal 10–90% interval coverage ranges from 78.0% to 78.6%. A nine-substation deployment check corroborates the calibration and identifies a measured drift episode in which adaptation limits, but does not eliminate, forecast degradation. The results support ARLOS as a transparent framework for studying how adaptation and uncertainty propagate into operational consequences under distribution shift.These contributions align with Sustainable Development Goal 7 (Affordable and Clean Energy) and Sustainable Development Goal 9 (Industry, Innovation and Infrastructure) by supporting more reliable, efficient, and intelligent operation of electricity distribution infrastructure.
J. C. Castillo, Alba Miranda, Jessica N. Castillo et al.· Energies· 0 citations
A practical contribution is provided in the form of a forecasting method that is not only accurate but also statistically reliable in estimating operational risk, thereby bridging the gap between industry demands for robust systems and the constraints imposed by real-world data quality.
Lasmedi Afuan, Agus Darmawan, Raden Demas Amirul Plawirakusumah et al.· Engineering, Technology &...· 0 citations
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