PhysGTT: A Physics-Guided Self-Supervised Graph Temporal Transformer for Forecasting Electricity Inconsistencies in Mini-Grids

Electricity inconsistencies in mini-grids, stemming from meter drift, telemetry faults, topology misconfiguration, non-technical losses, phase imbalance or data manipulation, often emerge as weak, spatially distributed deviations that are difficult to anticipate, yet timely warning is important for future monitoring frameworks in rural electrification and island mini-grids. Existing approaches either apply post hoc threshold-based alarms to individual channels or employ deep learning models that treat metering points independently, ignoring the spatial coupling imposed by the electrical topology and lacking mechanisms to enforce physical feasibility under scarce labeled data. This paper introduces PhysGTT, a Physics-Guided Self-Supervised Graph Temporal Transformer that models the mini-grid as a topology-aware graph and combines a residual Graph Convolutional Network encoder with a temporal Transformer. PhysGTT employs self-supervised pretraining via masked multi-sensor reconstruction and contrastive regime alignment to exploit unlabeled operational data and incorporates gradient-coupled physics regularization through power-balance, voltage-bound and ramp-rate penalties applied to a learned reconstruction head, while producing constraint-level attributions that identify the dominant physical violation pattern for each forecast. PhysGTT is evaluated on a proxy benchmark derived from the UCI Individual Household Electric Power Consumption dataset and on the IEEE 13-node test feeder simulated in OpenDSS and it is compared under identical experimental protocols with eight baselines spanning recurrent, graph-temporal and unsupervised architectures. On the proxy benchmark, PhysGTT achieves an AUC-ROC of 0.8959, an F1-score of 0.8307 and a False Alarm Rate of 0.41%, improving the F1-score by 2.2% relative to the strongest recurrent baseline (GRU) and by up to 15.2% relative to the LSTM baseline, while reducing the False Alarm Rate by approximately 52% relative to the LSTM baseline. On the IEEE 13-node feeder, PhysGTT attains an AUC-ROC of 0.9016 and an F1-score of 0.8361. These results indicate that integrating topology-aware encoding, self-supervised pretraining and physics-guided learning provides a promising and interpretable framework for proactive inconsistency forecasting under synthetic and feeder-simulation benchmarks, although field validation on naturally occurring faults remains necessary.