Synchronization of LienardType Oscillators in Uniform Electrical Networks
Abstract
This paper presents a condition for global asymptotic synchronization of Lienardtype nonlinear oscillators in uniform LTI electrical networks with series RL circuits modeling interconnections. By uniform electrical networks, we mean that the perunitlength impedances are identical for the interconnecting lines. We derive conditions for global asymptotic synchronization for a particular feedback architecture where the derivative of the oscillator output current supplements the innate current feedback induced by simply interconnecting the oscillator to the network. Our proof leverages a coordinate transformation to a set of differential coordinates that emphasizes signal differences and the particular form of feedback permits the formulation of a quadratic Lyapunov function for this class of networks. This approach is particularly interesting since synchronization conditions are difficult to obtain by means of quadratic Lyapunov functions when only current feedback is used and for networks composed of series RL circuits. Our synchronization condition depends on the algebraic connectivity of the underlying network, and reiterates the conventional wisdom from Lyapunov and passivitybased arguments that strong coupling is required to ensure synchronization.
 Authors:
 Publication Date:
 Research Org.:
 National Renewable Energy Lab. (NREL), Golden, CO (United States)
 Sponsoring Org.:
 NREL Laboratory Directed Research and Development (LDRD)
 OSTI Identifier:
 1320376
 Report Number(s):
 NREL/CP5D0065194
 DOE Contract Number:
 AC3608GO28308
 Resource Type:
 Conference
 Resource Relation:
 Conference: Presented at the 2016 American Control Conference (ACC), 68 July 2016, Boston, Massachusetts
 Country of Publication:
 United States
 Language:
 English
 Subject:
 24 POWER TRANSMISSION AND DISTRIBUTION; oscillators; synchronization; integrated circuit interconnections; integrated circuit modeling; Lyapunov methods; limitcycles; mathematical model
Citation Formats
Sinha, Mohit, Dorfler, Florian, Johnson, Brian B., and Dhople, Sairaj V.. Synchronization of LienardType Oscillators in Uniform Electrical Networks. United States: N. p., 2016.
Web. doi:10.1109/ACC.2016.7525600.
Sinha, Mohit, Dorfler, Florian, Johnson, Brian B., & Dhople, Sairaj V.. Synchronization of LienardType Oscillators in Uniform Electrical Networks. United States. doi:10.1109/ACC.2016.7525600.
Sinha, Mohit, Dorfler, Florian, Johnson, Brian B., and Dhople, Sairaj V.. Mon .
"Synchronization of LienardType Oscillators in Uniform Electrical Networks". United States.
doi:10.1109/ACC.2016.7525600.
@article{osti_1320376,
title = {Synchronization of LienardType Oscillators in Uniform Electrical Networks},
author = {Sinha, Mohit and Dorfler, Florian and Johnson, Brian B. and Dhople, Sairaj V.},
abstractNote = {This paper presents a condition for global asymptotic synchronization of Lienardtype nonlinear oscillators in uniform LTI electrical networks with series RL circuits modeling interconnections. By uniform electrical networks, we mean that the perunitlength impedances are identical for the interconnecting lines. We derive conditions for global asymptotic synchronization for a particular feedback architecture where the derivative of the oscillator output current supplements the innate current feedback induced by simply interconnecting the oscillator to the network. Our proof leverages a coordinate transformation to a set of differential coordinates that emphasizes signal differences and the particular form of feedback permits the formulation of a quadratic Lyapunov function for this class of networks. This approach is particularly interesting since synchronization conditions are difficult to obtain by means of quadratic Lyapunov functions when only current feedback is used and for networks composed of series RL circuits. Our synchronization condition depends on the algebraic connectivity of the underlying network, and reiterates the conventional wisdom from Lyapunov and passivitybased arguments that strong coupling is required to ensure synchronization.},
doi = {10.1109/ACC.2016.7525600},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Mon Aug 01 00:00:00 EDT 2016},
month = {Mon Aug 01 00:00:00 EDT 2016}
}

We study the Deserter Hubs Model: a Kuramotolike model of coupled identical phase oscillators on a network, where attractive and repulsive couplings are balanced dynamically due to nonlinearity of interactions. Under weak force, an oscillator tends to follow the phase of its neighbors, but if an oscillator is compelled to follow its peers by a sufficient large number of cohesive neighbors, then it actually starts to act in the opposite manner, i.e., in antiphase with the majority. Analytic results yield that if the repulsion parameter is small enough in comparison with the degree of the maximum hub, then the fullmore »

New type of synchronization of oscillators with hard excitation
It is shown that stable limiting cycles corresponding to nonlinear beats with complete energy exchange between oscillators can exist in a system of two weakly coupled active oscillators (generators). The oscillatory regime of this type, which implements a new type of synchronization in an active system, is an alternative to the wellstudied synchronization in a regime close to a nonlinear normal mode. In this case, the ranges of dissipative parameters corresponding to different types of synchronization do not intersect. The analytic description of attractors revealed in analysis is based on the concept of limiting phase trajectories, which was developed earliermore » 
Time Synchronization in Hierarchical TESLA Wireless Sensor Networks
Time synchronization and event time correlation are important in wireless sensor networks. In particular, time is used to create a sequence events or time line to answer questions of cause and effect. Time is also used as a basis for determining the freshness of received packets and the validity of cryptographic certificates. This paper presents secure method of time synchronization and event time correlation for TESLAbased hierarchical wireless sensor networks. The method demonstrates that events in a TESLA network can be accurately timestamped by adding only a few pieces of data to the existing protocol. 
Synchronization Algorithms for CoSimulation of Power Grid and Communication Networks
The ongoing modernization of power grids consists of integrating them with communication networks in order to achieve robust and resilient control of grid operations. To understand the operation of the new smart grid, one approach is to use simulation software. Unfortunately, current power grid simulators at best utilize inadequate approximations to simulate communication networks, if at all. Cooperative simulation of specialized power grid and communication network simulators promises to more accurately reproduce the interactions of real smart grid deployments. However, cosimulation is a challenging problem. A cosimulation must manage the exchange of informa tion, including the synchronization of simulator clocks,more »