# Optimal Topology Design for Disturbance Minimization in Power Grids

## TL;DR

This paper presents a unified framework using the $H_2$ norm to analyze and optimize power grid topologies for improved robustness against disturbances, applicable to both radial and meshed grids.

## Contribution

It introduces a novel $H_2$ norm-based approach for topology design in power grids, including a combinatorial solution for radial grids and a greedy algorithm for loopy grids.

## Key findings

- Optimal topology design improves disturbance robustness.
- Radial grid problem reduces to a known graph theory problem.
- Performance validated on various test grid configurations.

## Abstract

The transient response of power grids to external disturbances influences their stable operation. This paper studies the effect of topology in linear time-invariant dynamics of different power grids. For a variety of objective functions, a unified framework based on $H_2$ norm is presented to analyze the robustness to ambient fluctuations. Such objectives include loss reduction, weighted consensus of phase angle deviations, oscillations in nodal frequency, and other graphical metrics. The framework is then used to study the problem of optimal topology design for robust control goals of different grids. For radial grids, the problem is shown as equivalent to the hard "optimum communication spanning tree" problem in graph theory and a combinatorial topology construction is presented with bounded approximation gap. Extended to loopy (meshed) grids, a greedy topology design algorithm is discussed. The performance of the topology design algorithms under multiple control objectives are presented on both loopy and radial test grids. Overall, this paper analyzes topology design algorithms on a broad class of control problems in power grid by exploring their combinatorial and graphical properties.