Learning to Learn Topology and Parameters of Distribution Grid With Matrix Completion Under Partial Observability

The incomplete and inaccurate information on topology parameters resulting from limited measurement availability affects state monitoring, control, and monitoring of active distribution networks. These challenges have been addressed by formulating a Graph Convolutional Networks with Topological Enhancements (TE-GCN) for topology and parameters estimation. The interpretability of GCN is enhanced by incorporating physical connections between nodes and embedding the power flow (PF) equations as node features. It allows GCNs to learn the interdependence of nodes from data, enabling accurate estimations while maintaining physics of the system. In cases where nodes without voltage measurements are considered hidden nodes, a neural network is employed to recover the voltage matrix completion model, augmented with PF constraints. The PF equations are then estimated using GCN while ensuring physics consistency. To learn the topological structure from the acquired node measurements, a mapping is proposed that learns from node data to the structure. This method initially unrolls an iterative Primal-Dual Splitting (PDS) algorithm into a neural network structure. Subsequently, it replaces the topology proximal projection with a Variational Auto Encoder (VAE), thereby enhancing the estimated network topology with improved topological properties. The effectiveness of the proposed model is demonstrated on four IEEE bus systems with actual household demands.