Towards Model Reduction for Power System Transients with Physics-Informed PDE

TL;DR

This paper proposes a novel PDE-based model reduction technique for power system transients, translating discrete swing equations into a continuous PDE form to improve efficiency and fidelity in transient dynamics simulation.

Contribution

It introduces a physics-informed PDE approach to accurately and efficiently model power system transients, bridging discrete swing equations and continuous PDE models.

Findings

PDE model reproduces swing dynamics faithfully.

Proper coarse-graining yields efficient simulations.

Method applicable to large-scale power grids.

Abstract

This manuscript reports the first step towards building a robust and efficient model reduction methodology to capture transient dynamics in a transmission level electric power system. Such dynamics is normally modeled on seconds-to-tens-of-seconds time scales by the so-called swing equations, which are ordinary differential equations defined on a spatially discrete model of the power grid. Following Seymlyen (1974) and Thorpe, Seyler, and Phadke (1999), we suggest to map the swing equations onto a linear, inhomogeneous Partial Differential Equation (PDE) of parabolic type in two space and one time dimensions with time-independent coefficients and properly defined boundary conditions. We illustrate our method on the synchronous transmission grid of continental Europe. We show that, when properly coarse-grained, i.e., with the PDE coefficients and source terms extracted from a spatial convolution procedure of the respective discrete coefficients in the swing equations, the resulting PDE reproduces faithfully and efficiently the original swing dynamics. We finally discuss future extensions of this work, where the presented PDE-based modeling will initialize a physics-informed machine learning approach for real-time modeling, $n-1$ feasibility assessment and transient stability analysis of power systems.