Improving Spatial Allocation for Energy System Coupling with Graph Neural Networks

Xuanhao Mu; Jakob Geiges; Nan Liu; Thorsten Schlachter; Veit Hagenmeyer

cs.LGFeb 24, 2026

Improving Spatial Allocation for Energy System Coupling with Graph Neural Networks

Authors: Xuanhao Mu, Jakob Geiges, Nan Liu, Thorsten Schlachter, Veit Hagenmeyer

Organizations: Institute for Automation and Applied Informatics (IAI), Karlsruhe Institute of Technology, 76344 Eggenstein-Leopoldshafen, Germany

Abstract

In energy system analysis, coupling models with mismatched spatial resolutions is a significant challenge. A common solution is assigning weights to high-resolution geographic units for aggregation, but traditional models are limited by using only a single geospatial attribute. This paper presents an innovative method employing a self-supervised Heterogeneous Graph Neural Network to address this issue. This method models high-resolution geographic units as graph nodes, integrating various geographical features to generate physically meaningful weights for each grid point. These weights enhance the conventional Voronoi-based allocation method, allowing it to go beyond simply geographic proximity by incorporating essential geographic information.In addition, the self-supervised learning paradigm overcomes the lack of accurate ground-truth data. Experimental results demonstrate that applying weights generated by this method to cluster-based Voronoi Diagrams significantly enhances scalability, accuracy, and physical plausibility, while increasing precision compared to traditional methods.

Figures & tables

Panel of Figure 1 — Figure 1: Flowchart of the GNN-based spatial allocation method. The main pipeline (blue) generates weights, while the self-supervised loop (red) computes the loss for training by reconstructing macro-indicators.

Training Set
Region	VD	VD-GPM	VD-GNN-GPM	CIVD	CIVD-GPM	CIVD-GNN-GPM
London	21.085	16.234	17.013 ( -4.80% )	19.933	16.220	15.998 (+1.37%)
TLH2	8.805	6.735	6.656 (+1.17%)	7.647	5.816	5.778 (+0.65%)
TLH3	9.269	7.265	7.064 (+2.77%)	9.069	6.727	6.535 (+2.85%)
TLJ1	15.831	9.981	9.979 (+0.02%)	13.676	8.917	8.493 (+4.76%)
TLF1	11.966	8.591	8.129 (+5.38%)	10.840	7.627	7.072 (+7.28%)

Table 1: Comparison of Root Mean Squared Error (RMSE) Performance Across Various Geographic Regions

Figure 2: Land Use Distribution with Substation in Region TLD4

Figure 3: Land Use Distribution and Weights Heat Map for region London (top) and TLC1 (bottom)

Geospatial Representation Learning

Geospatial representation learning builds reusable embeddings of places, imagery, maps, mobility, and Earth data for spatial prediction and reasoning.

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Assessing the Generalization of Graph Neural Networks for Fault Location Across Increasing Distributed Energy Resource Penetration Levels

Burak Karabulut, Olayiwola Arowolo, Carlo Manna, Chris Develder+1

Dept. of Information Technology, IDLab Ghent University – imec, Ghent, Belgium · Water and Energy Transition Unit VITO, Mol, Belgium · Dept. Electrical Sustainable Energy TU Delft, Delft, Netherlands

OOD Generalization Fault Localization Spatiotemporal GNNs Fault Diagnosis Power Systems

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Accurate fault location is critical for distribution network reliability. However, increasing distributed energy resource (DER) penetration complicates fault location due to intermittent generation and bidirectional power flows that reshape fault signatures. Spatio-Temporal Graph Neural Networks (STGNNs) have shown promise by jointly modeling spatial and temporal dependencies, but their behavior under increasing DER penetration has not been studied rigorously. In this paper, we (i) systematically benchmark spatio-temporal graph attention network (STGATv2) against purely temporal (gated recurrent unit, GRU), purely spatial (GATv2) and traditional machine learning baselines, and (ii) evaluate how well models generalize across increasing DER penetration levels (10%, 25%, 50%) on a reconfigured IEEE 123-bus feeder with multiple DER injection points and moderate-to-high impedance faults. Results show that STGATv2 consistently outperforms neural baselines, achieving 92-94% macro F1 in-distribution. Notably, generalization across penetration levels is asymmetric: training at 50% penetration retains near in-distribution F1 score at lower levels, whereas training at 10% degrades considerably at 50% - with STGATv2 retaining 81-84% F1 under these drastic shifts, substantially higher than GATv2 and GRU which drop to 69-74% F1 and 73-75% F1 respectively. Under realistic measurement noise, STGATv2 maintains > 85% F1, while GRU drops as low as 33.5% F1, highlighting the critical role of topological awareness for robust fault location in active distribution networks.

Abstract

Geospatial Representation Learning

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