Trust-region approximation of extreme trajectories in power system dynamics

TL;DR

This paper introduces a trust-region optimization method utilizing second-order sensitivities to accurately compute extreme trajectories in power system dynamics under uncertainty, improving over previous sensitivity-based approaches.

Contribution

It presents a novel, efficient technique combining trust-region algorithms and second-order sensitivities for trajectory bounds in uncertain power systems, addressing nonlinearity limitations.

Findings

Method achieves high accuracy in trajectory bounds.

Demonstrates scalability on large power system models.

Outperforms sampling-based techniques in efficiency.

Abstract

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.