Designing for Robustness in Electric Grids via a General Effective Resistance Measure

TL;DR

This paper introduces a mathematical framework to enhance the robustness of electric grids by optimizing transmission line susceptance values to minimize system vulnerability to perturbations, aiding integration of renewables.

Contribution

The paper develops a tractable semidefinite programming approach to optimize edge weights in electric grid networks for improved robustness against perturbations.

Findings

Framework effectively reduces vulnerability measures in electric grid models.

Optimized susceptance values improve frequency synchronization stability.

Method supports better integration of renewable energy sources.

Abstract

We propose a mathematical framework for designing robust networks of coupled phase-oscillators by leveraging a vulnerability measure proposed by Tyloo et. al that quantifies how much a small perturbation to a phase-oscillator's natural frequency impacts the system's global synchronized frequencies. Given a fixed complex network topology with specific governing dynamics, the proposed framework finds an optimal allocation of edge weights that minimizes such vulnerability measure(s) at the node(s) for which we expect perturbations to occur by solving a tractable semidefinite programming problem. We specify the mathematical model to high voltage electric grids where each node corresponds to a voltage phase angle associated with a bus and edges correspond to transmission lines. Edge weights are determined by the susceptance values along the transmission lines. In this application, frequency synchronization is increasingly challenged by the integration of renewable energy, yet is imperative to the grid's health and functionality. Our framework helps to alleviate this challenge by optimizing the placement of renewable generation and the susceptance values along the transmission lines.