Synchronization of nonlinear circuits in dynamic electrical networks

Florian Dorfler, Sairaj Dhople, Brian B. Johnson, Abdullah Hamadeh

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations


Synchronization of coupled oscillators is a pervasive theme of multi-disciplinary research. Focused on circuit-theoretic applications, in this paper, we derive sufficient conditions for global asymptotic synchronization in a system of identical nonlinear circuits coupled through linear time-invariant (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.

Original languageEnglish (US)
Title of host publication2014 European Control Conference, ECC 2014
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9783952426913
StatePublished - Jan 1 2014
Event13th European Control Conference, ECC 2014 - Strasbourg, France
Duration: Jun 24 2014Jun 27 2014


Other13th European Control Conference, ECC 2014


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