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A steadily increasing fraction of renewable energy sources for electricity production requires a better understanding of how stochastic power generation affects the stability of electricity grids. Here, we assess the resilience of an IEEE test grid against single transmission line overloads under wind power injection based on the dc power flow equations and a quasi-static grid response to wind fluctuations. Thereby we focus on the mutual influence of wind power generation at different nodes. We find that overload probabilities vary strongly between different pairs of nodes and become highly affected by spatial correlations of wind fluctuations. An unexpected behaviour is uncovered: for a large number of node pairs, increasing wind power injection at one node can increase the power threshold at the other node with respect to line overloads in the grid. We find that this seemingly paradoxical behaviour is related to the topological distance of the overloaded line from the shortest path connecting the wind nodes. In the considered test grid, it occurs for all node pairs, where the overloaded line belongs to the shortest path.

Resilience of electricity grids against transmission line overloads under wind power injection at different nodes