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An Optimal Control Approach to Identify the Worst-Case Cascading Failures in Power Systems

Cascading failures in power systems normally occur as a result of initial disturbances or faults on electrical elements, closely followed by situational awareness errors of human operators. It remains a great challenge to systematically trace the source of cascading failures in power systems. In this paper, we develop a mathematical model to describe the cascading outages of transmission lines in power networks. In particular, the direct current power-flow equation is employed to calculate the power flow on the branches. By regarding the disturbances on branches as the control inputs, the problem of identifying the initial disruptive disturbances is formulated with optimal control theory, which provides a systematic approach to explore the most disruptive disturbances that give rise to changes of branch admittance in addition to direct branch outages. Moreover, an iterative search algorithm is proposed to look for the optimal solution leading to the worst-case cascading failures. Theoretical analysis guarantees the asymptotic convergence of the iterative search algorithm. Finally, numerical simulations are carried out on the IEEE test systems to validate the proposed approach.