Michael Lindner

Christian Nauck, Michael Lindner, Konstantin Schürholt et al.

To mitigate climate change, the share of renewable energies in power production needs to be increased. Renewables introduce new challenges to power grids regarding the dynamic stability due to decentralization, reduced inertia, and volatility in production. Since dynamic stability simulations are intractable and exceedingly expensive for large grids, graph neural networks (GNNs) are a promising method to reduce the computational effort of analyzing the dynamic stability of power grids. As a testbed for GNN models, we generate new, large datasets of dynamic stability of synthetic power grids, and provide them as an open-source resource to the research community. We find that GNNs are surprisingly effective at predicting the highly non-linear targets from topological information only. For the first time, performance that is suitable for practical use cases is achieved. Furthermore, we demonstrate the ability of these models to accurately identify particular vulnerable nodes in power grids, so-called troublemakers. Last, we find that GNNs trained on small grids generate accurate predictions on a large synthetic model of the Texan power grid, which illustrates the potential for real-world applications.

Christian Nauck, Michael Lindner, Konstantin Schürholt et al.

To mitigate climate change, the share of renewable needs to be increased. Renewable energies introduce new challenges to power grids due to decentralization, reduced inertia and volatility in production. The operation of sustainable power grids with a high penetration of renewable energies requires new methods to analyze the dynamic stability. We provide new datasets of dynamic stability of synthetic power grids and find that graph neural networks (GNNs) are surprisingly effective at predicting the highly non-linear target from topological information only. To illustrate the potential to scale to real-sized power grids, we demonstrate the successful prediction on a Texan power grid model.

Christian Nauck, Rohan Gorantla, Michael Lindner et al.

The geometry of a graph is encoded in dynamical processes on the graph. Many graph neural network (GNN) architectures are inspired by such dynamical systems, typically based on the graph Laplacian. Here, we introduce Dirac--Bianconi GNNs (DBGNNs), which are based on the topological Dirac equation recently proposed by Bianconi. Based on the graph Laplacian, we demonstrate that DBGNNs explore the geometry of the graph in a fundamentally different way than conventional message passing neural networks (MPNNs). While regular MPNNs propagate features diffusively, analogous to the heat equation, DBGNNs allow for coherent long-range propagation. Experimental results showcase the superior performance of DBGNNs over existing conventional MPNNs for long-range predictions of power grid stability and peptide properties. This study highlights the effectiveness of DBGNNs in capturing intricate graph dynamics, providing notable advancements in GNN architectures.

Christian Nauck, Junyou Zhu, Michael Lindner et al.

The robustness of synchronization is typically characterized by scalar, per-node stability indices whose dependence on topology is studied via network science or graph neural networks (GNNs). We propose a novel upstream task, learning stability landscapes, which provide deeper insights into synchronization behavior and from which many such scalar indices can be derived. Crucially, we pioneer a graph-to-image prediction paradigm: learning image-like landscapes as per-node targets directly from graph topology, a formulation we are not aware of having been established elsewhere in the literature. To support this task, we release two datasets of 10,000 graphs each at 20 and 100 nodes with per-node landscape labels, based on a conceptual oscillator model, capturing power grid synchronization behavior. A GNN encodes topology and a CNN decoder renders per-node images, learned end-to-end with good in-distribution accuracy, generalizing across graph sizes and to realistic power grid topologies. This demonstrates that stability landscapes, while beyond the reach of conventional network science, are learnable from topology and open new avenues for moving beyond scalar stability indices in biology, neuroscience, and power grids.

Julian Geis, Michael Lindner, Tom Brown

A rapid expansion of system flexibility is essential to integrate increasing shares of renewable energy into future energy systems. However, flexibility needs and technology-specific contributions to flexibility remain poorly quantified in energy system modelling. Existing methods are not widely applied, leaving key questions unanswered: which flexibility technologies are critical for climate neutrality, and what are the cost implications of alternative deployment strategies? To address this gap, we apply a correlation-based flexibility metric to a high-resolution, sector-coupled model of the German energy system, covering its transformation towards climate neutrality. For our default scenario, we find that daily flexibility needs increase by a factor of 3.7 between 2025 and 2045, driven primarily by the expansion of solar PV. By 2045, stationary batteries provide 38% of daily flexibility, while flexible electric vehicle charging contributes 30%. Systems with constrained flexibility increase system costs by 6.9%, electricity prices by 14 EUR/MWh and trigger 47% higher hydrogen and e-fuel imports compared to an unconstrained system in 2045. In contrast, scenarios with high shares of flexible electric vehicle charging, vehicle-to-grid, and industrial demand-side management achieve system cost reductions of 3.3%, while also reducing import dependence. Higher flexibility also reduces electricity price ranges, decreases average electricity prices by 3 EUR/MWh, and reduces backup capacity by 22% (22 GW). Overall, our results highlight the decisive role of specific flexibility technologies in achieving cost-efficient and energy-secure climate-neutral energy systems, providing quantitative guidance for policy and investment decisions.

Christian Nauck, Michael Lindner, Nora Molkenthin et al.

A central question of network science is how functional properties of systems arise from their structure. For networked dynamical systems, structure is typically quantified with network measures. A functional property that is of theoretical and practical interest for oscillatory systems is the stability of synchrony to localized perturbations. Recently, Graph Neural Networks (GNNs) have been shown to predict this stability successfully; at the same time, network measures have struggled to paint a clear picture. Here we collect 46 relevant network measures and find that no small subset can reliably predict stability. The performance of GNNs can only be matched by combining all network measures and nodewise machine learning. However, unlike GNNs, this approach fails to extrapolate from network ensembles to several real power grid topologies. This suggests that correlations of network measures and function may be misleading, and that GNNs capture the causal relationship between structure and stability substantially better.

Christian Nauck, Anna Büttner, Sebastian Liemann et al.

Due to the increasing share of renewables, the analysis of the dynamical behavior of power grids gains importance. Effective risk assessments necessitate the analysis of large number of fault scenarios. The computational costs inherent in dynamic simulations impose constraints on the number of configurations that can be analyzed. Machine Learning (ML) has proven to efficiently predict complex power grid properties. Hence, we analyze the potential of ML for predicting dynamic stability of future power grids with large shares of inverters. For this purpose, we generate a new dataset consisting of synthetic power grid models and perform dynamical simulations. As targets for the ML training, we calculate the fault-ride-through probability, which we define as the probability of staying within a ride-through curve after a fault at a bus has been cleared. Importantly, we demonstrate that ML models accurately predict the fault-ride-through probability of synthetic power grids. Finally, we also show that the ML models generalize to an IEEE-96 Test System, which emphasizes the potential of deploying ML methods to study probabilistic stability of power grids.

Christian Nauck, Michael Lindner, Konstantin Schürholt et al.

The prediction of dynamical stability of power grids becomes more important and challenging with increasing shares of renewable energy sources due to their decentralized structure, reduced inertia and volatility. We investigate the feasibility of applying graph neural networks (GNN) to predict dynamic stability of synchronisation in complex power grids using the single-node basin stability (SNBS) as a measure. To do so, we generate two synthetic datasets for grids with 20 and 100 nodes respectively and estimate SNBS using Monte-Carlo sampling. Those datasets are used to train and evaluate the performance of eight different GNN-models. All models use the full graph without simplifications as input and predict SNBS in a nodal-regression-setup. We show that SNBS can be predicted in general and the performance significantly changes using different GNN-models. Furthermore, we observe interesting transfer capabilities of our approach: GNN-models trained on smaller grids can directly be applied on larger grids without the need of retraining.