An energy-based analysis of reduced-order models of (networked) synchronous machines

Abstract: Stability of power networks is an increasingly important topic because of the high penetration of renewable distributed generation units. This requires the development of advanced (typically model-based) techniques for the analysis and controller design of power networks. Although there are widely accepted reduced-order models to describe the dynamic behavior of power networks, they are commonly presented without details about the reduction procedure, hampering the understanding of the physical phenomena behind them. The present paper aims to provide a modular model derivation of multi-machine power networks. Starting from first-principle fundamental physics, we present detailed dynamical models of synchronous machines and clearly state the underlying assumptions which lead to some of the standard reduced-order multi-machine models, including the classical second-order swing equations. In addition, the energy functions for the reduced-order multi-machine models are derived, which allows to represent the multi-machine systems as port-Hamiltonian systems. Moreover, the systems are proven to be passive with respect to its steady states, which permits for a power-preserving interconnection with other passive components, including passive controllers. As a result, the corresponding energy function or Hamiltonian can be used to provide a rigorous stability analysis of advanced models for the power network without having to linearize the system.