%0 Journal Article %A Zhang, Yingrui %A Yagan, Osman %D 2016 %T Optimizing the robustness of electrical power systems against cascading failures %U https://kilthub.cmu.edu/articles/journal_contribution/Optimizing_the_robustness_of_electrical_power_systems_against_cascading_failures/5558140 %R 10.1184/R1/5558140.v1 %2 https://ndownloader.figshare.com/files/9642199 %K complex networks %K electrical and electronic engineering %X Electrical power systems are one of the most important infrastructures that support our society. However, their vulnerabilities have raised great concern recently due to several large-scale blackouts around the world. In this paper, we investigate the robustness of power systems against cascading failures initiated by a random attack. This is done under a simple yet useful model based on global and equal redistribution of load upon failures. We provide a comprehensive understanding of system robustness under this model by (i) deriving an expression for the final system size as a function of the size of initial attacks; (ii) deriving the critical attack size after which system breaks down completely; (iii) showing that complete system breakdown takes place through a first-order (i.e., discontinuous) transition in terms of the attack size; and (iv) establishing the optimal load-capacity distribution that maximizes robustness. In particular, we show that robustness is maximized when the difference between the capacity and initial load is the same for all lines; i.e., when all lines have the same redundant space regardless of their initial load. This is in contrast with the intuitive and commonly used setting where capacity of a line is a fixed factor of its initial load. %I Carnegie Mellon University