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Journal Articles IEEE Transactions on Circuits and Systems I: Regular Papers Year : 2014

Conditions for Existence of Equilibria of Systems With Constant Power Loads

Sébastien Sanchez
  • Function : Author
Romeo Ortega
Robert Grino
  • Function : Author
Gilbert Bergna
  • Function : Author
M. Molinas-Cabrera
  • Function : Author

Abstract

In this paper we investigate the sine qua non condition of existence of equilibria for electrical systems with external (AC or DC) 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 give an upper bound on the power dissipated in steady-state that should exceed the extracted constant power. The existence of the equilibrium is ensured if and only if the inequality is satisfied.
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Dates and versions

hal-01100800 , version 1 (07-01-2015)

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Sébastien Sanchez, Romeo Ortega, Robert Grino, Gilbert Bergna, M. Molinas-Cabrera. Conditions for Existence of Equilibria of Systems With Constant Power Loads. IEEE Transactions on Circuits and Systems I: Regular Papers, 2014, 61 (7), pp.2204-2211. ⟨10.1109/TCSI.2013.2295953⟩. ⟨hal-01100800⟩
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