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This work considers the task of finding an ac-feasible operating point of a severely damaged transmission network while ensuring that a maximal amount of active power loads can be delivered. This AC maximal load delivery (AC-MLD) task is a nonconvex nonlinear optimization problem that is incredibly challenging to solve on large-scale transmission system data sets. This work demonstrates that convex relaxations of the AC-MLD problem provide a reliable and scalable method for finding high-quality bounds on the amount of active power that can be delivered in the AC-MLD problem. To demonstrate their effectiveness, the solution methods proposed in this work are rigorously evaluated on 1000 $N$ - $k$ scenarios on seven power networks ranging in size from 70 to 6000 buses. The most effective relaxation of the AC-MLD problem converges in less than 20 seconds on commodity computing hardware for all 7000 of the scenarios considered. [ABSTRACT FROM AUTHOR]

This paper introduces a statistical classifier that quickly locates line outages in a power system utilizing only time series phasor measurement data sampled during the system's transient response to the outage. The presented classifier is a linear multinomial regression model that is trained by solving a maximum likelihood optimization problem using synthetic data. The synthetic data is produced through dynamic simulations which are initialized by random samples of a forecast load/generation distribution. Real time computation of the proposed classifier is minimal and therefore the classifier is capable of locating a line outage before steady state is reached, allowing for quick corrective action in response to an outage. In addition, the output of the classifier fits into a statistical framework that is easily accessible. Specific line outages are identified as being difficult to localize and future improvements to the classifier are proposed. [ABSTRACT FROM PUBLISHER]