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.
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.
<p>The risk of triggering multiple climate tipping points if global warming levels were to exceed 1.5&#176;C has been heavily discussed in recent literature. Current climate policies are projected to result in 2.7&#176;C warming above pre-industrial levels by the end of this century and will thereby at least temporarily overshoot the Paris Agreement temperature goal.</p> <p>Here, we assess the risk of triggering climate tipping points under overshoot pathways derived from emission pathways and their uncertainties from the PROVIDE ensemble using PyCascades, a stylised network model of four interacting tipping elements including the Greenland Ice Sheet, the West Antarctic Ice Sheet, the Atlantic Meridional Overturning Circulation, and the Amazon Rainforest.</p> <p>We show that up until 2300, when overshoots are limited to 2&#176;C, the upper range of the Paris Agreement goal, the median risk of triggering at least one element would be less than 5%, although some critical thresholds may have been crossed temporarily. However, the risk of triggering at least one tipping element increases significantly for scenarios that peak above the Paris Agreement temperature range. For instance, we find a median tipping risk in 2300 of 46% for an emission scenario following current policies. Even if temperatures would stabilize at 1.5&#176;C after having peaked at temperatures projected under current policies, the long-term median tipping risks would approach three-quarters.</p> <p>To limit tipping risks beyond centennial scales, we find that it is crucial to constrain any temperature overshoot to 2&#176;C of global warming and to stabilize global temperatures at 1.0&#176;C or below in the long-term.</p>
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