  This paper 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 network. The approach involves a novel data-driven
``basis-dictionary free" lifting of the system dynamics into a higher
dimensional linear space over which an MPC (model predictive control) is
exercised, making it both scalable and rapid for practical real-time
implementation. A Koopman-inspired deep neural network (KDNN) encoder-decoder
architecture for the linear embedding of the underlying dynamics under
distributed controls 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 ad-hoc
selection of the nonlinear basis functions (e.g., polynomial or radial) used in
conventional approaches for lifting to higher dimensional linear space. We
validate the efficacy and robustness of the approach via application to the
standard IEEE 39-bus system.
