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In view of highly decentralized and diversified power generation concepts, inparticular with renewable energies such as wind and solar power, the analysisand control of the stability and the synchronization of power networks is animportant topic that requires different levels of modeling detail for differenttasks. A frequently used qualitative approach relies on simplified nonlinearnetwork models like the Kuramoto model. Although based on basic physicalprinciples, the usual formulation in form of a system of coupled ordinarydifferential equations is not always adequate. We present a new energy-basedformulation of the Kuramoto model as port-Hamiltonian system ofdifferential-algebraic equations. This leads to a very robust representation ofthe system with respect to disturbances, it encodes the underlying physics,such as the dissipation inequality or the deviation from synchronicity,directly in the structure of the equations, it explicitly displays all possibleconstraints and allows for robust simulation methods. Due to its systematicenergy based formulation the model class allows easy extension, when furthereffects have to be considered, higher fidelity is needed for qualitativeanalysis, or the system needs to be coupled in a robust way to other networks.We demonstrate the advantages of the modified modeling approach with analyticresults and numerical experiments.

Qualitative Stability and Synchronicity Analysis of Power Network Models in Port-Hamiltonian Form