RESUMEN
Research on cascading failures in power-transmission networks requires detailed data on the capacity of individual transmission lines. However, these data are often unavailable to researchers. Consequently, line limits are often modeled by assuming that they are proportional to some average load. However, there is scarce research to support this assumption as being realistic. In this paper, we analyze the proportional loading (PL) approach and compare it to two linear models that use voltage and initial power flow as variables and are trained on the line limits of a real power network that we have access to. We compare these artificial line-limit methods using four tests: the ability to model true line limits, the damage done during an attack, the order in which edges are lost, and accuracy ranking the relative performance of different attack strategies. We find that the linear models are the top-performing method or are close to the top in all the tests we perform. In comparison, the tolerance value that produces the best PL limits changes depending on the test. The PL approach was a particularly poor fit when the line tolerance was less than two, which is the most commonly used value range in cascading failure research. We also find indications that the accuracy of modeling line limits does not indicate how well a model will represent grid collapse. The findings of this paper provide an understanding of the weaknesses of the PL approach and offer an alternative method of line-limit modeling.
RESUMEN
We argue that theories and methods drawn from complexity science are urgently needed to guide the development and use of digital twins for cities. The theoretical framework from complexity science takes into account both the short-term and the long-term dynamics of cities and their interactions. This is the foundation for a new approach that treats cities not as large machines or logistic systems but as mutually interwoven self-organizing phenomena, which evolve, to an extent, like living systems.