Data-Driven Linear Koopman Embedding for Model-Predictive Power System Control

This paper presents a linear Koopman embedding for model predictive emergency voltage regulation in power systems, by way of a data-driven lifting of the system dynamics into a higher dimensional linear space over which the MPC (model predictive control) is exercised, thereby scaling as well as expediting the MPC computation for its real-time implementation for practical systems. We develop a {\em Koopman-inspired deep neural network} (KDNN) architecture for the linear embedding of the voltage dynamics subjected to reactive controls. The training of the KDNN for the purposes of linear embedding is done using the simulated voltage trajectories under a variety of applied control inputs and load conditions. The proposed framework learns the underlying system dynamics from the input/output data in the form of a triple of transforms: A Neural Network (NN)-based lifting to a higher dimension, a linear dynamics within that higher dynamics, and an NN-based projection to original space. This approach alleviates the burden of an ad-hoc selection of the basis functions for the purposes of lifting to higher dimensional linear space. The MPC is computed over the linear dynamics, making the control computation scalable and also real-time.