Conformalized graph neural networks for distribution system state estimation with finite-sample-valid uncertainty quantification

Abstract

Distribution system state estimation provides the network-wide voltage awareness required to operate active feeders, yet scarce real-time metering forces reliance on uncertain pseudo-measurements. This paper studies how to attach empirically auditable, finite-sample prediction intervals to learned network-wide voltage estimates. A graph attention network (GAT) maps measurement-derived node features to point estimates and conditional quantiles, and conformalized quantile regression is calibrated separately for every fixed bus and output coordinate across held-out snapshots. At 20% measurement density on the IEEE 33-bus and 69-bus feeders, voltage-magnitude coverage is 0.901 and 0.903 against nominal 0.90, with angle coverage 0.896 and 0.904. The revision broadens the benchmark to matched quantile GBT, quantile MLP, MC-dropout Bayesian, and two-stage MFBNN-style baselines; architecture, calibration-size, temporal-split, simultaneous-coverage, meter-placement, topology-transfer, physics-consistency, missing-meter, and contamination-mismatch tests; and robust WLS. These tests materially narrow the claim: GBT and MLP are stronger fixed-topology backbones, learned attention is diffuse and seed-sensitive, and marginal intervals do not imply simultaneous network coverage. Random mask training limits the 40% dropout coverage loss to 0.887 (33 buses) and 0.796 (69 buses), while matched recalibration reaches 0.899 and 0.846. Max-score conformal calibration raises simultaneous voltage-magnitude coverage from 0.258/0.075 to 0.901/0.902 at a width cost. The contribution is therefore a DSSE-specific integration and failure-boundary benchmark for model-agnostic, fixed-bus conformal calibration, rather than a claim that attention is universally preferable or that nominal validity survives arbitrary shift.