Hierarchical reconciliation and per-bus adaptive conformal calibration for distribution-level residential load forecasting: a critical assessment of topology priors

Distribution-level load forecasts must be coherent across aggregation levels and calibrated at individual buses. This paper evaluates two widely proposed post-processing steps for that purpose: hierarchical reconciliation and topology-aware conformal calibration. A multi-level benchmark maps 114 de-identified apartment smart-meter profiles onto standard IEEE distribution feeders by mean-load rank. This preserves temporal shapes but alters magnitudes, coincident peaks and spatial correlation, so absolute values do not transfer. Minimum-trace shrinkage reconciliation enforces exact coherence, reducing incoherence from \(4.26\,%\) of aggregate load to machine precision. It improves aggregate accuracy by \(0.28\) percentage points over bottom-up aggregation, at a cluster-level cost of \(0.11\) percentage points concentrated on the most volatile buses. Under a matched-null test, a conformal layer weighting conformity scores by electrical distance yields improvements indistinguishable from those obtained under random permutation of the profile-to-bus assignment. Electrical distance is uncorrelated with score similarity (Spearman \(ρ = +0.02\) ), and on a measured 906-bus feeder the kernel is \(36\,%\) – \(70\,%\) worse than using no topology. Per-bus adaptive conformal inference, by contrast, reduces the across-bus standard deviation of coverage by \(67\,%\) – \(92\,%\) across four architecture families, raising the share of buses within two percentage points of nominal from \(52\,%\) – \(67\,%\) to \(97\,%\) – \(100\,%\) at almost unchanged width, without an exchangeability assumption. In a network-constrained battery-dispatch study, calibrated intervals cut dispatch regret by \(14\,%\) – \(29\,%\) . Electrical-topology priors are not identifiable at this aggregation scale; a matched-null protocol for testing them is provided.