This paper explores whether graph embedding methods can be used as a tool for analysing the robustness of power-grids within the framework of network science. The paper focuses on the strain elevation tension spring embedding (SETSe) algorithm and compares it to node2vec and Deep Graph Infomax, and the measures mean edge capacity and line load. These five methods are tested on how well they can predict the collapse point of the giant component of a network under random attack. The analysis uses seven power-grid networks, ranging from 14 to 2000 nodes. In total, 3456 load profiles are created for each network by loading the edges of the network to have a range of tolerances and concentrating network capacity into fewer edges. One hundred random attack sequences are generated for each load profile, and the mean number of attacks required for the giant component to collapse for each profile is recorded. The relationship between the embedding values for each load profile and the mean collapse point is then compared across all five methods. It is found that only SETSe 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 conditions line load performs exceptionally well ($R=0.99$). However, the SETSe algorithm provides valuable qualitative insight into the state of the power-grid by leveraging its method local smoothing and global weighting of node features to provide an interpretable geographical embedding. This paper shows that graph representation algorithms can be used to analyse network properties such as robustness to cascading failure attacks, even when the network is embedded at node level.
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