# Physics-Aware Heterogeneous GNN Architecture for Real-Time BESS Optimization in Unbalanced Distribution Systems

arXiv: https://arxiv.org/abs/2512.09780 · HTML: https://mlsanity.com/paper/2512.09780/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 13 references that are in the map.
- First posted on arXiv 10 Dec 2025.

## Builds on (most cited first, 5 of 5)

- [pandapower - an Open Source Python Tool for Convenient Modeling, Analysis and Optimization of Electric Power Systems](https://mlsanity.com/paper/1709.06743/) (2017)
- [Optimal Power Flow Using Graph Neural Networks](https://mlsanity.com/paper/1910.09658/) (2019)
- [Power Flow Balancing with Decentralized Graph Neural Networks](https://mlsanity.com/paper/2111.02169/) (2021)
- [PowerFlowMultiNet: Multigraph Neural Networks for Unbalanced Three-Phase Distribution Systems](https://mlsanity.com/paper/2403.00892/) (2024)
- [SafePowerGraph-HIL: Real-Time HIL Validation of Heterogeneous GNNs for Bridging Sim-to-Real Gap in Power Grids](https://mlsanity.com/paper/2501.12427/) (2025)

## Abstract (arXiv)

Battery energy storage systems (BESS) have become increasingly vital in three-phase unbalanced distribution grids for maintaining voltage stability and enabling optimal dispatch. However, existing deep learning approaches often lack explicit three-phase representation, making it difficult to accurately model phase-specific dynamics and enforce operational constraints--leading to infeasible dispatch solutions. This paper demonstrates that by embedding detailed three-phase grid information--including phase voltages, unbalanced loads, and BESS states--into heterogeneous graph nodes, diverse GNN architectures (GCN, GAT, GraphSAGE, GPS) can jointly predict network state variables with high accuracy. Moreover, a physics-informed loss function incorporates critical battery constraints--SoC and C-rate limits--via soft penalties during training. Experimental validation on the CIGRE 18-bus distribution system shows that this embedding-loss approach achieves low prediction errors, with bus voltage MSEs of 6.92e-07 (GCN), 1.21e-06 (GAT), 3.29e-05 (GPS), and 9.04e-07 (SAGE). Importantly, the physics-informed method ensures nearly zero SoC and C-rate constraint violations, confirming its effectiveness for reliable, constraint-compliant dispatch.