Forecasting Electricity Demand via Graph Neural Networks and Uncertainty Quantification

Thesis Abstract

Forecasting electricity demand is challenged by nonlinear temporal dynamics and spatial dependencies across a power network, which conventional time-series models inadequately capture. This study addresses the problem by integrating graph neural networks (GNNs) with rigorous uncertainty quantification to improve both point forecasts and predictive intervals for electricity demand across substations and feeders. The aim is to develop a scalable, data-driven framework that leverages network topology and multi-variate drivers (weather, calendar effects, and socio-economic indicators) to enhance forecast accuracy and reliability for operational decision-making. Specific objectives are (i) to design a graph-based forecasting model that encodes the electrical grid as a heterogeneous graph with nodes representing substations and edges reflecting transmission links; (ii) to incorporate exogenous variables (temperature, humidity, wind speed, solar irradiance, holidays, and demand response events) through dynamic feature engineering; (iii) to implement and compare multiple GNN architectures (Graph Attention Networks, Temporal Graph Networks, and Spatial-Temporal Graph Convolutional Networks) for short-term (15–60 minutes) and medium-term (1–24 hours) horizons; (iv) to apply advanced uncertainty quantification techniques, including Monte Carlo dropout, deep ensembles, and conformal prediction, to produce calibrated predictive intervals; (v) to evaluate model robustness under scenario-based perturbations and non-stationarities using backtesting across diverse weather regimes; and (vi) to provide actionable insights for grid operations and planning under uncertainty. The methodology adopts a quantitative, data-driven research design. The population comprises the regional electricity network of a mid-sized national grid, with a dataset of 12 months of historical half-hourly demand records at 250 substations, accompanied by weather (hourly temperature, humidity, wind, solar radiation) and calendar features. A stratified sampling approach ensures coverage of peak and off-peak periods, holidays, and atypical weather events, yielding a training set of 6 months, a validation set of 3 months, and a test set of 3 months. Data collection instruments include SCADA/exported time-series data, publicly available meteorological feeds, and energy market records. Data preprocessing involves anomaly detection, alignment of temporal indices, normalization, and construction of a spatial-temporal graph with node features comprising historical demand and exogenous covariates. Analytical methods combine model development with rigorous evaluation. Baseline models include traditional autoregressive integrated moving average with exogenous inputs (ARIMAX) and gradient boosting machines. The core models are three GNN-based architectures Graph Attention Networks (GAT) to weight neighborhood influence, Temporal Graph Networks (TGN) to model evolving graph connections, and Spatial-Temporal Graph Convolutional Networks (STGCN) to capture joint spatial and temporal dependencies. Uncertainty quantification employs three complementary approaches (i) Monte Carlo dropout to approximate epistemic uncertainty, (ii) deep ensembles to capture predictive variability across model instances, and (iii) conformal prediction to yield valid, distribution-free predictive intervals under non-stationarity. Model evaluation uses both point-forecast metrics (RMSE, MAE, MAPE) and probabilistic metrics (Prediction Interval Coverage Probability, Mean Prediction Interval Width, and Brier scores for calibrated intervals). Hypothesis testing compares the proposed GNN framework against benchmarks using Diebold-Mariano tests for forecast accuracy and reliability diagrams for interval calibration. Anticipated findings indicate that GNN-based models outperform baselines in both accuracy and calibration, with STGCN providing the best balance of short- and medium-term performance. Uncertainty quantification is expected to yield consistently well-calibrated prediction intervals under varying weather conditions and grid stress, enabling more informed operational decisions and risk-aware planning. The study contributes to knowledge by advancing the deployment of graph-based learning for energy demand forecasting with robust uncertainty metrics, enriching the theoretical understanding of spatial-temporal dependencies in power systems, and offering a scalable framework adaptable to different grid topologies and data environments. The main conclusion is that integrating graph-aware architectures with multiple uncertainty quantification strategies substantially improves both forecast accuracy and interval reliability for electricity demand, particularly under non-stationary conditions. Recommendations include implementing the framework within real-time energy management systems, extending experiments to multi-region and cross-border networks, and exploring transfer learning to adapt models to cities or countries with limited historical data.