Linear response theory for renewable fluctuations in power grids with transmission losses

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.