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Stability of power networks is an increasingly important topic because of thehigh penetration of renewable distributed generation units. This requires thedevelopment of advanced (typically model-based) techniques for the analysis andcontroller design of power networks. Although there are widely acceptedreduced-order models to describe the dynamic behavior of power networks, theyare commonly presented without details about the reduction procedure, hamperingthe understanding of the physical phenomena behind them. The present paper aimsto provide a modular model derivation of multi-machine power networks. Startingfrom first-principle fundamental physics, we present detailed dynamical modelsof synchronous machines and clearly state the underlying assumptions which leadto some of the standard reduced-order multi-machine models, including theclassical second-order swing equations. In addition, the energy functions forthe reduced-order multi-machine models are derived, which allows to representthe multi-machine systems as port-Hamiltonian systems. Moreover, the systemsare proven to be passive with respect to its steady states, which permits for apower-preserving interconnection with other passive components, includingpassive controllers. As a result, the corresponding energy function orHamiltonian can be used to provide a rigorous stability analysis of advancedmodels for the power network without having to linearize the system.

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