  In this work we present a novel technique, based on a trust-region
optimization algorithm and second-order trajectory sensitivities, to compute
the extreme trajectories of power system dynamic simulations given a bounded
set that represents parametric uncertainty. We show how this method, while
remaining computationally efficient compared with sampling-based techniques,
overcomes the limitations of previous sensitivity-based techniques to
approximate the bounds of the trajectories, when the local approximation loses
validity because of the nonlinearity. In addition, we show how this method can
be adapted to account for those cases in which the initial conditions depend on
the uncertain parameter. To conclude, we present several numerical experiments
that showcase the accuracy and scalability of the technique, including a
demonstration on the IEEE New England test system.
