The power grid is a critical component of city infrastructure. If it is damaged by an earthquake, there can be a huge impact on the safety and well-being of society and individuals. Identifying nodes in the grid that are highly vulnerable to earthquake damage is significant for effective pre-earthquake damage prevention, emergency response, and post-earthquake relief. Three indicators, the probability of node disconnection, the node hierarchical level, and the node critical threshold, were chosen, and their combined ability to represent node vulnerability to damage from an earthquake event was analyzed. A variable fuzzy clustering model was used to classify and order the nodes in the grid. The 20-node power grid of a city was used as an example to show how highly vulnerable nodes were identified, and how the reasons for the high vulnerability of these nodes were drawn out of the analysis. Countermeasures were given to reduce network vulnerability. The variable fuzzy clustering method used in this paper offers a new perspective on network vulnerability, and it quantifies the vulnerability of grid nodes more comprehensively than existing methods of assessing grid vulnerability. This research is significant as a baseline reference for future studies of grid vulnerability.
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