Synchronization of Lienard-Type Oscillators in Heterogenous Electrical Networks

DOI 10.1109/INDIANCC.2018.8307985

Publicly accessible License

Motivated by potential applications for power-electronic converters in microgrids, we study the problem of global asymptotic synchronization of Lienard-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 Lienard oscillators in homogeneous electrical networks. Numerical simulations are provided to validate the results.

Citation Formats

TY  - DATA
AB  - Motivated by potential applications for power-electronic converters in microgrids, we study the problem of global asymptotic synchronization of Lienard-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 Lienard oscillators in homogeneous electrical networks. Numerical simulations are provided to validate the results.
AU  - Johnson, Brian
A2  - Sinha, Mohit
A3  - Dorfler, Florian
A4  - Dhople, Sairaj
DB  - C-MIX - Community Microgrid Information Exchange
DP  - Open EI | National Laboratory of the Rockies
DO  - 10.1109/INDIANCC.2018.8307985
KW  - Power electronics and inverters
KW  - Power electronics
KW  - Inverters
KW  - Battery energy storage
KW  - Solar
KW  - Photovoltaics
KW  - PV
KW  - Diesel generators
KW  - Other liquid-fuel generators
KW  - Case studies
KW  - Performance
KW  - Planning and design
KW  - Planning
KW  - Design
KW  - Maintenance and operations
KW  - Operations
KW  - Maintenance
KW  - Commissioning
LA  - English
DA  - 2018/01/01
PY  - 2018
PB  - University of Minnesota
T1  - Synchronization of Lienard-Type Oscillators in Heterogenous Electrical Networks
UR  - https://doi.org/10.1109/INDIANCC.2018.8307985
ER  -

Export Citation to RIS

Johnson, Brian, et al. Synchronization of Lienard-Type Oscillators in Heterogenous Electrical Networks. University of Minnesota, 1 January, 2018, C-MIX - Community Microgrid Information Exchange. https://doi.org/10.1109/INDIANCC.2018.8307985.

Johnson, B., Sinha, M., Dorfler, F., & Dhople, S. (2018). Synchronization of Lienard-Type Oscillators in Heterogenous Electrical Networks. [Data set]. C-MIX - Community Microgrid Information Exchange. University of Minnesota. https://doi.org/10.1109/INDIANCC.2018.8307985

Johnson, Brian, Mohit Sinha, Florian Dorfler, and Sairaj Dhople. Synchronization of Lienard-Type Oscillators in Heterogenous Electrical Networks. University of Minnesota, January, 1, 2018.  Distributed by C-MIX - Community Microgrid Information Exchange. https://doi.org/10.1109/INDIANCC.2018.8307985

@misc{CMIX_Dataset_112,
title = {Synchronization of Lienard-Type Oscillators in Heterogenous Electrical Networks},
author = {Johnson, Brian and Sinha, Mohit and Dorfler, Florian and Dhople, Sairaj},
abstractNote = {Motivated by potential applications for power-electronic converters in microgrids, we study the problem of global asymptotic synchronization of Lienard-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 Lienard oscillators in homogeneous electrical networks. Numerical simulations are provided to validate the results.},
url = {https://cmix.openei.org/submissions/112},
year = {2018},
howpublished = {C-MIX - Community Microgrid Information Exchange, University of Minnesota, https://doi.org/10.1109/INDIANCC.2018.8307985},
note = {Accessed: 2026-10-13},
doi = {10.1109/INDIANCC.2018.8307985}
}

https://dx.doi.org/10.1109/INDIANCC.2018.8307985

Details

Data from Jan 1, 2018

Last updated Mar 30, 2026

Submitted Jun 2, 2026

Organization

University of Minnesota

Contact

Brian Johnson

Authors

Brian Johnson

University of Minnesota

Mohit Sinha

ETH Zurich

Florian Dorfler

NLR

Sairaj Dhople

University of Minnesota

Keywords

Power electronics and inverters, Power electronics, Inverters, Battery energy storage, Solar, Photovoltaics, PV, Diesel generators, Other liquid-fuel generators, Case studies, Performance, Planning and design, Planning, Design, Maintenance and operations, Operations, Maintenance, Commissioning