Data-Driven Linear Koopman Embedding for Networked Systems: Model-Predictive Grid Control

Abstract

This article presents a data-learned linear Koopman embedding of nonlinear networked dynamics and uses it to enable real-time model predictive emergency voltage control in a power grid. The approach involves a novel data-driven “basis-dictionary free” lifting of the system dynamics into a higher dimensional linear space over which a model predictive control is exercised, making it both scalable and rapid for practical real-time implementation. A <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Koopman-inspired deep neural network</i> (KDNN) encoder–decoder architecture for the linear embedding of the underlying networked dynamics under distributive control is presented, in which the end-to-end components of the KDNN, comprising of a triple of transforms is learned from the system trajectory data in one go: a neural network (NN)-based lifting to a higher dimension, a linear dynamics within that higher dimension, and an NN-based projection to the original space. This data-learned approach relieves the burden of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ad hoc</i> selection of the nonlinear basis functions (e.g., radial or polynomial) used in conventional approaches for lifting to a higher dimensional linear space. We validate the efficacy and robustness of the approach via application to the standard IEEE 39-bus system.