复杂系统的韧性盆地：以产消者对电网的影响为例
Resilience basins of complex systems: an application to prosumer impacts on power grids
AI总结：
该研究提出一种量化复杂系统韧性的“韧性盆地”框架，并应用于低压直流电网中产消者随机出现的影响评估，发现线路升级可提供无限韧性，而家庭电池韧性有限，并有助于优化预算分配策略。
摘要：
与传统系统动力学中的稳定性概念类似，韧性通常通过评估系统响应质量的方式来衡量，例如恢复速度。我们提出了一种广泛适用的补充性测量框架，该框架类似于盆地稳定性，通过估计“韧性盆地”来量化韧性，该盆地反映了系统能够充分恢复的不利影响的范围。与盆地稳定性不同，这里考虑的不利影响不一定是状态空间中的位移，而是对系统的任意复杂影响，通过适当的参数进行量化。作为概念验证，我们展示了两个应用：（i）经过充分研究的单节点电力系统作为一个易于理解的示例，以及（ii）一个低压直流电网的随机模型，该电网正在经历一场无监管的能源转型，表现为产消者的随机出现。这些产消者作为光伏发电的分散供应者，在电网拓扑结构不变的情况下改变了潮流模式。该韧性测量框架被应用于评估两种响应方案的效果和效率：（i）升级现有电力线路的容量，以及（ii）在产消者家庭中安装电池。该框架表明，线路升级可以提供针对能源分散化的潜在无限韧性，而家庭电池则固有地受限（实现不超过线路升级韧性的70%）。此外，该框架通过指向阈值预算值以及依赖于预算的线路升级分配和电池充电算法的理想策略，有助于优化预算效率。
英文摘要：
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.
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