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.

Abstract. The incorporation of vapor transport has become a key demand for snowpack modeling in which accompanied phase changes give rise to a new, nonlinear coupling in the heat and mass equations. This coupling has an impact on choosing efficient numerical schemes for 1D snowpack models which are naturally not designed to cope with mathematical particularities of arbitrary, nonlinear partial differential equations (PDEs). To explore this coupling we have implemented a stand-alone finite element solution of the coupled heat and mass equations in snow using the computing platform FEniCS. We focus on the nonlinear feedback of the ice phase exchanging mass with a diffusing vapor phase with concurrent heat transport in the absence of settling. We demonstrate that existing continuum-mechanical models derived through homogenization or mixture theory yield similar results for homogeneous snowpacks of constant density. When snow density varies significantly with depth, we show that phase changes in the presence of temperature gradients give rise to nonlinear advection of the ice phase amplifying existing density variations. Eventually, this advection triggers a wave instability in the continuity equations. This is traced back to the density dependence of the effective transport coefficients as revealed by a linear stability analysis of the nonlinear PDE system. The instability is an inherent feature of existing continuum models and predicts, as a side product, the formation of a low-density (mechanical) weak layer on the sublimating side of an ice crust. The wave instability constitutes a key challenge for a faithful treatment of solid–vapor mass conservation between layers, which is discussed in view of the underlying homogenization schemes and their numerical solutions.