Parameters determination of time-delayed embedding with application to Koopman operator-based model predictive frequency control

Abstract

Power systems around the world have been registering a degenerating inertial response in view of the growth of inverter-based resources along with the withdrawal of conventional coal units. Therefore, there is a need for swift frequency support and its control, preferably by means of power electronic-interfaced storage devices, owing to their beneficial capabilities. Despite being particularly efficient, pragmatically, the traditional model-based non-linear control techniques are not highly popular in power system control design, primarily due to the complications faced in obtaining accurately suitable models for certain power system components. Lately, the modelfree Koopman operator-based model predictive control (KMPC) has proven to be highly conducive for data-driven non-linear control design. The principle behind KMPC is to change the coordinates in a manner to get an approximately linear model, which can then be controlled using a linear model predictive control. In this study, we employed time-delayed embedding of measurements to reconstruct a new set of preferable coordinates, thereby suggesting an approach for finding the optimal number of time lags and the embedding dimensions which are the key parameters of this algorithm. The efficacy of this KMPC framework is established by adopting a decentralized frequency control problem through a decoupled synchronous machine system, which we proposed for both the Kundur two-area system as well as the IEEE 39-bus test system.