Measurement-Based Probabilistic Power Flow Using a Basis Constrained Graph Convolutional Network with Few-Shot Node Adaptation

Probabilistic power flow quantifies voltage and phase angle uncertainty under variable photovoltaic generation, but repeated AC Monte Carlo simulation is costly. A local topology change also modifies the electrical operator and state dimension when only a small target data set is available. We propose a Basis Constrained Graph Convolutional Network (BCGCN) for few-shot adaptation after local bus additions in small-scale grids. BCGCN predicts nonlinear residuals around a first-order solution using graph Laplacian and Proper Orthogonal Decomposition modes. It transfers source coordinates; adapts only the new bus rows, rotation, readouts, and correction gate; and freezes the backbone. The experimental results indicate that BCGCN leads all four reported errors on the IEEE 14 and IEEE 57 expansions. IEEE 118 and Polish 2746 establish the scale boundary. BCGCN wins only 9 of 64 IEEE 118 error cells and none on Polish 2746, while retaining compact updates. The paired IEEE 118 PV study shows that target pilots reduce zero-shot error and residual correction removes most high variability linearization error. BCGCN is therefore effective for local few-shot adaptation in small grids but not an accuracy-preserving adapter for large networks.