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In this paper we provide a unifying energy-based approach to the modeling,analysis and control of power systems and markets, which is based on theport-Hamiltonian framework. Using a primal-dual gradient method applied to thesocial welfare problem, a distributed dynamic pricing algorithm inport-Hamiltonian form is obtained. By interconnection with the physical model aclosed-loop port-Hamiltonian system is obtained, whose properties are exploitedto prove asymptotic stability to the optimal points. This result is extendedsuch that also general nodal power constraints are included into the socialwelfare problem. Additionally, the cases of line congestion and powertransmission cost in (a)cyclic networks considering (non)linear power flowmodels are covered as well. Finally, we provide port-Hamiltonian descriptionsand analysis of the well studied distributed averaging proportional integral(DAPI) and certain internal-model-based controllers, which solve an optimalfrequency regulation problem.

A unifying energy-based approach to optimal frequency and market regulation in power grids