Distributed energy resources challenge the situational awareness of power flows. Many distribution grid (DG) operators have not yet implemented state estimation (SE) due to the expense or privacy constraints of measurements that lead to an unobservable system, as well as inaccurate grid parameters. A key concern with the latter is the presence of medium- and low-voltage transformers with off-load tap changers, whose tap positions critically influence voltage levels across the network. Identifying transformers where the registered position is likely incorrect — and, when on-site verification is impractical, estimating a plausible tap setting — constitutes a valuable contribution to improving network observability and operational accuracy. Although operators could manually inspect each transformer, this is impractical — there are, for instance, up to 20,000 transformers in the Southern Netherlands.

To address these challenges, this thesis proposes a novel topology-aware framework for estimating state and transformer tap positions in unobservable DGs. The framework comprises two key components. First, a generative adversarial network (GAN) is used to train a generative model conditioned on the network topology and synthetic power flow data, generating realistic measurements. Second, an integrated model, referred to as the TapSEGNN model, is proposed for estimating state and transformer tap positions.

Both of these components employ a core model architecture which combines graph and simplicial complex neural networks to capture spatial dependencies between nodes, edges, and higher-order structures. To train these components, an industrial-grade data-processing pipeline was developed using a real DG topology and simulating the exact available measurement locations. The results show that balanced adversarial training of GAN accurately imputes the missing active power injection measurements, but produces high variance in imputations for voltage magnitude and active power flow measurements. The performance of the TapSEGNN model demonstrates at least tenfold higher accuracy for SE compared to conventional methods, and it predicts transformer tap positions with 100% accuracy in a computationally efficient manner. TapSEGNN also shows promising scalability for larger networks; however, it struggles with generalisability across similar real networks. Finally, the suboptimal performance of both components in certain aspects warrants further investigation, which is recommended as future work.