  Efficiently solving unbalanced three-phase power flow in distribution grids
is pivotal for grid analysis and simulation. There is a pressing need for
scalable algorithms capable of handling large-scale unbalanced power grids that
can provide accurate and fast solutions. To address this, deep learning
techniques, especially Graph Neural Networks (GNNs), have emerged. However,
existing literature primarily focuses on balanced networks, leaving a critical
gap in supporting unbalanced three-phase power grids. This letter introduces
PowerFlowMultiNet, a novel multigraph GNN framework explicitly designed for
unbalanced three-phase power grids. The proposed approach models each phase
separately in a multigraph representation, effectively capturing the inherent
asymmetry in unbalanced grids. A graph embedding mechanism utilizing message
passing is introduced to capture spatial dependencies within the power system
network. PowerFlowMultiNet outperforms traditional methods and other deep
learning approaches in terms of accuracy and computational speed. Rigorous
testing reveals significantly lower error rates and a notable hundredfold
increase in computational speed for large power networks compared to
model-based methods.
