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This paper explores whether graph embedding methods can be used as a tool foranalysing the robustness of power-grids within the framework of networkscience. The paper focuses on the strain elevation tension spring embedding(SETSe) algorithm and compares it to node2vec and Deep Graph Infomax, and themeasures mean edge capacity and line load. These five methods are tested on howwell they can predict the collapse point of the giant component of a networkunder random attack. The analysis uses seven power-grid networks, ranging from14 to 2000 nodes. In total, 3456 load profiles are created for each network byloading the edges of the network to have a range of tolerances andconcentrating network capacity into fewer edges. One hundred random attacksequences are generated for each load profile, and the mean number of attacksrequired for the giant component to collapse for each profile is recorded. Therelationship between the embedding values for each load profile and the meancollapse point is then compared across all five methods. It is found that onlySETSe and line load perform well as proxies for robustness with $R^2 = 0.89$for both measures. When tested on a time series normal operating conditionsline load performs exceptionally well ($R=0.99$). However, the SETSe algorithmprovides valuable qualitative insight into the state of the power-grid byleveraging its method local smoothing and global weighting of node features toprovide an interpretable geographical embedding. This paper shows that graphrepresentation algorithms can be used to analyse network properties such asrobustness to cascading failure attacks, even when the network is embedded atnode level.

High Tension Lines: Predicting robustness of high-voltage power-grids to cascading failure using network embedding