Synchronization of Liénard-type oscillators in heterogenous electrical networks

Mohit Sinha, Florian Dorfler, Brian B. Johnson, Sairaj V. Dhople

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

5 Scopus citations


Motivated by potential applications for power-electronic converters in microgrids, we study the problem of global asymptotic synchronization of Liénard-type nonlinear oscillators in heterogenous LTI electrical networks with series R-L circuits modeling interconnections. By heterogeneous, we mean that the resistance-to-inductance ratios of the lines are not all the same. Building on our previous work, we derive sufficient conditions for global asymptotic synchronization by using a first-order filter on the outputs of the oscillators. Our approach leverages a coordinate transformation to a system that emphasizes signal differences and the use of passivity based arguments to establish synchronization of the network of oscillators asymptotically. The analysis subsumes and generalizes previous conditions that have been derived for Liénard oscillators in homogeneous electrical networks. Numerical simulations are provided to validate the results.

Original languageEnglish (US)
Title of host publication2018 Indian Control Conference, ICC 2018 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9781538629048
StatePublished - Mar 7 2018
Event4th Indian Control Conference, ICC 2018 - Kanpur, India
Duration: Jan 4 2018Jan 6 2018

Publication series

Name2018 Indian Control Conference, ICC 2018 - Proceedings


Other4th Indian Control Conference, ICC 2018

Bibliographical note

Funding Information:
M. Sinha and S. V. Dhople are with the Department of Electrical and Computer Engineering at the University of Minnesota, Minneapolis, MN (email: sinha052, sdhople@UMN.EDU). Their work was supported in part by the National Science Foundation under the CAREER award, ECCS-1453921 and grant ECCS-1509277. F. Dörfler is with the Automatic Control Laboratory at ETH Zürich, Zürich, Switzerland (email: dorfler@ETHZ.CH). His research is supported by ETH Zürich funds and the SNF Assistant Professor Energy Grant #160573. B. B. Johnson is with the Power Systems Engineering Center at the National Renewable Energy Laboratory (NREL), Golden, CO (email: brian.johnson@NREL.GOV). His work was supported by the U.S. Department of Energy (DOE) Solar Energy Technologies Office under Contract No. DE-EE0000-1583 and by the DOE under Contract No. DE-AC36-08-GO28308 with NREL.

Publisher Copyright:
© 2018 IEEE.

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