The main goal of this research project is to develop a comprehensive framework for reduced-order dynamical modeling in energy processing systems. Control-oriented applications of the proposed method are envisioned in power systems (for derivation of load models, for reduction of conventional models in transient stability studies, and for controller design), electric drives (drives with elastic shafts), and motion control systems (multiple drives coupled through the mechanical subsystem). Our hypothesis is that the physical phenomena under investigation often have significantly lower dimensions than the agglomeration of ambient coordinate systems in which component models originate. We propose a methodology that combines features of analytical and physics-based approaches with artificial neural networks (ANNs), and aims to identify continuous-time differential/algebraic (DAE) models of energy processing systems. The proposed research program combines mathematical analysis and practical insight from energy engineering. Our reduced-order models ("dynamic equivalents") are formulated in continuous time, which is consistent with component models derived from physical principles. There exists a number of important differences between standard discrete and continuous dynamical systems. Models based on discrete-time ANNs may predict spurious transients and have attractors that are impossible for continuous-time systems. Our dynamic equivalent comprises differential and algebraic relationships, which is widely accepted as the most accurate representation of energy processing systems. The procedures that will be developed in this program are uniquely suited for identification of systems that exhibit multiple time scales (singularly perturbed systems) which are very common in energy processing. Resulting ANN models are based on measurements, or on (possibly multiple) simulations of detailed models that are to be simplified. We describe initial results along these directions in two examples from power systems and electric machines. This project will develop ANN architectures and training methods that are specific for the modeling tasks in energy processing systems. In particular, new connections and comparisons between standard (physics-based) models and ANN structures will be explored in the domain of "gray-box" models which combine the two classes. New developments will be evaluated within three modeling approaches: (i) time-domain, (ii) standard phasor, and (iii) dynamic phasor framework.
