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Conditions for Existence of Equilibria of Systems with Constant Power Loads

Santiago Sanchez 1 R. Ortega 2 R. Grino 3 Gilbert Bergna Diaz 4 M. Molinas 1
1 NTNU - Norwegian University of Science and Technology [Trondheim]
2 L2S - Laboratoire des signaux et systèmes
3 UPC - Universitat Politècnica de Catalunya [Barcelona]
4 E3S - Supélec Sciences des Systèmes [Gif-sur-Yvette]
Abstract : In this paper we investigate the sine qua non condition of existence of equilibria for electrical systems with external sources furnishing constant power to the loads, which is a scenario encountered in modern applications. Two general cases are considered, when the system is (i) linear time-invariant or (ii) nonlinear, with dynamic behavior described by a port-Hamiltonian model with constant dissipation and switching interconnection matrix. The latter class includes the practically important case of power converters. For both cases necessary and sufficient conditions for existence of equilibria are given, which impose that the power dissipated in steady-state should exceed the extracted constant power. The equilibrium is ensured if and only if the inequality is satisfied.
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Conference papers
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https://hal-supelec.archives-ouvertes.fr/hal-00926131
Contributor : Stéphanie Douesnard <>
Submitted on : Thursday, January 9, 2014 - 10:32:37 AM
Last modification on : Wednesday, October 14, 2020 - 3:56:48 AM

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Santiago Sanchez, R. Ortega, R. Grino, Gilbert Bergna Diaz, M. Molinas. Conditions for Existence of Equilibria of Systems with Constant Power Loads. 52nd IEEE Conference on Decision and Control, Dec 2013, Florence, Italy. 6p., ⟨10.1109/CDC.2013.6760443⟩. ⟨hal-00926131⟩

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