State estimation (SE) plays a critical role as a prerequisite for grid control and operation. However, the increasing penetration of distributed energy resources (DERs) and integrated energy systems (IES) introduces new challenges—such as unreliable pseudo-measurements and time-varying slack bus conditions—which make traditional methods like weighted least squares (WLS) increasingly difficult to apply. Moreover, DER integration leads to more frequent topological changes due to safety requirements and economic considerations. Yet, most existing machine learning methods for SE do not explicitly consider the topological changes. Therefore, this study evaluates three GNN-based models—GCN, GAT, and EvolveGCN—for state estimation in power grids under topological changes.

First, in the scenario without topological changes, where only the phase angle of the slack bus is fixed and noisy measurements are used, WLS performs worse than the three GNNs, indicating its susceptibility to interference under non-ideal conditions. Second, among the static GNNs, GAT performs best when topological changes are visible during training, but it cannot fully predict the voltage drops of unseen topological changes. GCN, on the other hand, demonstrates better generalization to unseen topologies and effectively suppress overfitting caused by noise. Third, although EvolveGCN is less accurate overall, it shows greater stability on nodes near PV buses, highlighting its potential to use historical information to enhance the time dimension when dealing with problems such as weak spatial correlation or local information loss.

These results suggest that GCN and GAT are potentially more suitable than WLS for SE in distribution grids with high DER penetration or IES. However, PV buses pose unique modeling challenges: they are physically but not numerically correlated with neighboring nodes, which make static GNNs hard to model their value change. Accurate estimation at PV buses is crucial, as they inject power into the system; in this context, EvolveGCN shows promise due to its stable predictions at these nodes.