Toward Model Reduction for Power System Transients With Physics-Informed PDE

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 PDEbased modeling will initialize a physics-informed machine learning approach for real-time modeling, n − 1 feasibility assessment and transient stability analysis of power systems.

A Comprehensive Analysis of PINNs for Power System Transient Stability

“…Further implementation in systems of varying scales is essential to fully ascertain and validate their effectiveness. Moreover, recent studies have investigated model reduction techniques for power system transient stability at the transmission level using partial differential equations (PDEs) [30]. This approach provides a more detailed representation of system dynamics compared to ODEs and offers a promising direction for future research, potentially serving as an alternative for investigating transient stability in power systems.…”

The stochastic nature of power-grid frequency in South Africa

“…the time scale at which a non-Markovian process can safely be modelled in a Markovian setting [28]. For an inhomogeneous spatially extended parabolic partial differential equation of coupled swing equations, see [55]. Secondly, we can already suspect that our Gaussian description of the distribution of the frequencies (5) might not be sufficient.…”

Data-driven modeling of power system dynamics: Challenges, state of the art, and future work

“…In Ref. [115], system model parameters are identified in real time using the least squares method based on linear expansion of the system operating points. The disadvantage is that the approximation error of linearization.…”