Linear Response Theory for Renewable Fluctuations in Power Grids with Transmission Losses

TL;DR

This paper develops a linear response theory to analyze how renewable power fluctuations spread through electrical grids with transmission losses, revealing vulnerability patterns linked to network eigenmodes and flow directions.

Contribution

It introduces a network-adapted linear response framework that explains fluctuation amplification and vulnerability patterns in both idealized and realistic power grid models.

Findings

Fluctuations are amplified opposite to power flow in tree-like networks.

Vulnerability patterns are connected to the left Laplacian eigenvectors.

The theory explains observed patterns in the IEEE RTS-1996 test system.

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 micro-grids. While exact mathematical derivations are only possible for tree like networks with 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.