Stochastic Uncertainty Propagation in Power System Dynamics using Measure-valued Proximal Recursions

TL;DR

This paper introduces a scalable, nonparametric proximal algorithm that propagates stochastic uncertainties in power system dynamics by operating on probability measures, avoiding high-dimensional gridding and leveraging system nonlinearities.

Contribution

The paper presents a novel measure-valued proximal recursion method for uncertainty propagation in power systems, exploiting nonlinear dynamics without the need for state space discretization.

Findings

Algorithm effectively propagates uncertainties in high-dimensional power system models.

Method leverages system nonlinearities for improved accuracy.

Numerical examples demonstrate scalability and effectiveness.

Abstract

We present a proximal algorithm that performs a variational recursion on the space of joint probability measures to propagate the stochastic uncertainties in power system dynamics over high dimensional state space. The proposed algorithm takes advantage of the exact nonlinearity structures in the trajectory-level dynamics of the networked power systems, and is nonparametric. Lifting the dynamics to the space of probability measures allows us to design a scalable algorithm that obviates gridding the underlying high dimensional state space which is computationally prohibitive. The proximal recursion implements a generalized infinite dimensional gradient flow, and evolves probability-weighted scattered point clouds. We clarify the theoretical nuances and algorithmic details specific to the power system nonlinearities, and provide illustrative numerical examples.