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Abstract

We study the spreading of renewable power fluctuations through grids with Ohmic losses on the lines. By formulating a network-adapted linear response theory, we find that vulnerability patterns are linked to the left Laplacian eigenvectors of the overdamped eigenmodes. We show that for tree-like networks, fluctuations are amplified in the opposite direction of the power flow. This novel mechanism explains vulnerability patterns that were observed in previous numerical simulations of renewable microgrids. While exact mathematical derivations are only possible for tree-like networks with a homogeneous response, we show that the mechanisms discovered also explain vulnerability patterns in realistic heterogeneous meshed grids by studying the IEEE RTS-1996 test system. Recently, many studies have analyzed the spreading of short-term renewable power fluctuations through power grids. In most of these studies, it was assumed that the power transmission on the lines is lossless. For lossless flow networks, the flows at the emitting and receiving end of a line are equal. Hence, any flow change will be symmetric on both ends of the line. In contrast, for networks with transmission losses, the flow at the receiving end is always smaller than on the emitting end and changes in the flow at both ends are not symmetric anymore. The spreading of fluctuations through the network will, therefore, depend on the flow direction at each link. Consequently, the nodes that are particularly vulnerable to power fluctuations are not necessarily those that have the strongest excitation for power fluctuations at other nodes. In fact, for renewable fluctuations, we find that all nodes are almost equally excited, while the most vulnerable nodes are located in the high consumption regions in the network, i.e., at the sinks of the power flow.