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

Abstract

Comparable to the traditional notion of stability in system dynamics, resilience is currently predominantly measured in a way that quantifies 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 represents the extent of adverse influences that the system can recover from in a sufficient manner.As a proof of concept, the resilience measurement framework is applied to a stochastic low-voltage DC power grid model which faces the unregulated rise of decentralized energy supply by solar-powered prosumers. Two response options are examined regarding their resilience effect and efficiency: Upgrading the load capacity of existing power lines and installing batteries in the prosumer households.The framework is able to show that line upgrades, while being more laborious to execute, can provide potentially unlimited resilience against energy decentralization. Household batteries, on the other hand, are simpler to realize but also inherently limited in terms of their resilience benefit (achieving only 70% of the resilience of line upgrades in our scenario). This is explained by considering that they can only reduce fluctuations in the power flows, but not the mean flow magnitude. Further, the framework can aid in optimizing budget efficiency by pointing towards threshold budget values as well as ideal strategies for the allocation of the line upgrades and for the battery charging algorithm, respectively, which both happen to depend on the budget size.

A modeler’s guide to studying the resilience of social-technical-environmental systems

“…in a way similar to basin volume-based metrics proposed by Menck et al (2013), Mitra et al (2015), Hellmann et al (2016), Kan et al (2016)or the quantifiers following Hodgson et al (2015). One example of this is the work of Bien et al (2021) in the context of power grids. A more sophisticated type of novel resilience metric might be a real-valued function f that maps a combination of four indicators-one for the current state x of the system, one for the acceptable threshold θ of the sustainant, one for the strength σ of potential adverse influences, and one for the allowable recovery time T-to the probability p = f(x, θ, σ, T) that the system will return to acceptable levels of the sustainant within the allowable time after suffering in the specified state an adverse influence of the given strength.…”