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.

本研究介绍了一种数据学习的线性 Koopman 嵌入非线性网络动态的方法，并将其用于实现电网中的实时模型预测紧急电压控制。该方法包括一种新颖的 “基字典自由” 的数据驱动系统动态升维方式、基于 Koopman 的深度神经网络编码器解码器架构用于分布式控制下潜在动力学的线性嵌入以及使用真实系统轨迹数据一次性学习三个连续变换的端到端成分。通过在标准 IEEE 39 总线系统上进行应用程序验证了该方法的效力和鲁棒性。