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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 the port-Hamiltonian framework. Using a primal-dual gradient method applied to the social... more
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 the port-Hamiltonian framework. Using a primal-dual gradient method applied to the social welfare problem, a distributed dynamic pricing algorithm in port-Hamiltonian form is obtained. By interconnection with the physical model a closed-loop port-Hamiltonian system is obtained, whose properties are exploited to prove asymptotic stability to the optimal points. This result is extended such that also general nodal power constraints are included into the social welfare problem. Additionally, the cases of line congestion and power transmission cost in (a)cyclic networks considering (non)linear power flow models are covered as well. Finally, we provide port-Hamiltonian descriptions and analysis of the well studied distributed averaging proportional integral (DAPI) and certain internal-model-based controllers, which solve an optimal frequency regulation problem.
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Het modelleren van fysische verschijnselen door middel van differentiaalvergelijkingen heeft een rijke geschiedenis die zeker drie eeuwen omspant. Aan dit klassieke en levendige vakgebied zijn in de vorige eeuw vele nieuwe aspecten... more
Het modelleren van fysische verschijnselen door middel van differentiaalvergelijkingen heeft een rijke geschiedenis die zeker drie eeuwen omspant. Aan dit klassieke en levendige vakgebied zijn in de vorige eeuw vele nieuwe aspecten toegevoegd. Uit de behoefte om deze fysische processen zichzelf te laten besturen is de systeemtheorie voortgekomen. Hierbij kan men denken aan electrische circuits, robots, de automatische piloot in een vliegtuig of de thermostaat van een verwarming. De ontwikkeling van een vakgebied zoals bijvoorbeeld de ruimtevaart is zonder de systeemtheorie ondenkbaar. Arjan van der Schaft, samen met H. Nijmeijer auteur van het op dit gebied veel gebruikte boek ‘Nonlinear Dynamical Control Systems’ en hoogleraar deterministische systeem- en besturingstheorie aan de Faculteit der Toegepaste Wiskunde van de Universiteit Twente, geeft in zijn inaugurele rede een overzicht van dit vakgebied.
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This article provides a concise summary of the basic ideas and concepts in port-Hamiltonian systems theory and its use in analysis and control of complex multiphysics systems. It gives special attention to new and unexplored research... more
This article provides a concise summary of the basic ideas and concepts in port-Hamiltonian systems theory and its use in analysis and control of complex multiphysics systems. It gives special attention to new and unexplored research directions and relations with other mathematical frameworks. Emergent control paradigms and open problems are indicated, including the relation with thermodynamics and the question of uniting the energy-processing view of control, as emphasized by port-Hamiltonian systems theory, with a complementary information-processing viewpoint.