Resilience basins of complex systems: an application to prosumer impacts on power grids

TL;DR

This paper introduces a new framework for measuring system resilience called the 'resilience basin,' applied to power grids with prosumer impacts, demonstrating how infrastructure upgrades can enhance resilience efficiently.

Contribution

The paper presents a novel resilience measurement framework that accounts for complex impacts, extending basin stability concepts to power grid applications with prosumers.

Findings

Line upgrades can provide near-unlimited resilience against decentralization.

Household batteries offer limited resilience, up to 70% of line upgrades.

The framework helps optimize budget and response strategies for power grid resilience.

Abstract

Comparable to the traditional notion of stability in system dynamics, resilience is typically measured in a way that assesses the quality of a system's response, for example the speed of its recovery. We present a broadly applicable complementary measurement framework that quantifies resilience similarly to basin stability by estimating a "resilience basin" which reflects the extent of adverse influences that the system can recover from in a sufficient manner. In contrast to basin stability, the adverse influences considered here are not necessarily displacements in state space, but arbitrarily complex impacts to the system, quantified by adequate parameters. As a proof of concept, we present two applications: (i) the well-studied single-node power system as an easy-to-follow example and (ii) a stochastic model of a low-voltage DC power grid undergoing an unregulated energy transition consisting in the random appearance of prosumers. These act as decentral suppliers of photovoltaic power and alter the flow patterns while the grid topology remains unchanged. The resilience measurement framework is applied to evaluate the effect and efficiency of two response options: (i) upgrading the capacity of existing power lines and (ii) installing batteries in the prosumer households. The framework demonstrates that line upgrades can provide potentially unlimited resilience against energy decentralization, while household batteries are inherently limited (achieving <=70% of the resilience of line upgrades). Further, the framework aids in optimizing budget efficiency by pointing toward threshold budget values as well as budget-dependent ideal strategies for the allocation of line upgrades and for the battery charging algorithm.