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Synchronization of nonlinear circuits in dynamic electrical networks


F. Dörfler, S. Dhople, B. Johnson, A. Hamadeh

European Control Conference (ECC), Strasbourg, France

Synchronization of coupled oscillators is a pervasive theme of multi-disciplinary research. Focused on circuittheoretic applications, in this paper, we derive sufficient conditions for global asymptotic synchronization in a system of identical nonlinear circuits coupled through linear timeinvariant (LTI) electrical networks. The nonlinear circuits are composed of a parallel combination of passive LTI circuit elements and a nonlinear voltage-dependent current source with finite gain. The terminals of the nonlinear circuits are coupled through LTI networks characterized by either identical per-unit-length impedances or identical effective impedances between any two terminals. This setup is motivated by a recently proposed control strategy for inverters in microgrids. We analyze synchronization by means of an input-output analysis of a coordinate-transformed system that emphasizes signal differences. To apply the synchronization analysis to a broad class of networks, we leverage recent results on Kron reduction—a circuit reduction and transformation procedure that reveals the interactions of the nonlinear circuits. We illustrate our results with simulations in networks of coupled Chua’s circuits.


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% Autogenerated BibTeX entry
@InProceedings { D_rEtal:2014:IFA_4902,
    author={F. D{\"o}rfler and S. Dhople and B. Johnson and A. Hamadeh},
    title={{Synchronization of nonlinear circuits in dynamic electrical
    booktitle={European Control Conference (ECC)},
    address={Strasbourg, France},
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