skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Uncovering Droop Control Laws Embedded Within the Nonlinear Dynamics of Van der Pol Oscillators

Abstract

This paper examines the dynamics of power-electronic inverters in islanded microgrids that are controlled to emulate the dynamics of Van der Pol oscillators. The general strategy of controlling inverters to emulate the behavior of nonlinear oscillators presents a compelling time-domain alternative to ubiquitous droop control methods which presume the existence of a quasistationary sinusoidal steady state and operate on phasor quantities. We present two main results in this paper. First, by leveraging the method of periodic averaging, we demonstrate that droop laws are intrinsically embedded within a slower time scale in the nonlinear dynamics of Van der Pol oscillators. Second, we establish the global convergence of amplitude and phase dynamics in a resistive network interconnecting inverters controlled as Van der Pol oscillators. Furthermore, under a set of nonrestrictive decoupling approximations, we derive sufficient conditions for local exponential stability of desirable equilibria of the linearized amplitude and phase dynamics.

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:
1364161
Report Number(s):
NREL/JA-5D00-63335
Journal ID: ISSN 2325-5870
DOE Contract Number:  
AC36-08GO28308
Resource Type:
Journal Article
Journal Name:
IEEE Transactions on Control of Network Systems
Additional Journal Information:
Journal Volume: 4; Journal Issue: 2; Journal ID: ISSN 2325-5870
Country of Publication:
United States
Language:
English
Subject:
24 POWER TRANSMISSION AND DISTRIBUTION; averaging; droop control; nonlinear oscillator circuits; synchronization; Van der Pol oscillators

Citation Formats

Sinha, Mohit, Dorfler, Florian, Johnson, Brian B., and Dhople, Sairaj V. Uncovering Droop Control Laws Embedded Within the Nonlinear Dynamics of Van der Pol Oscillators. United States: N. p., 2015. Web. doi:10.1109/TCNS.2015.2503558.
Sinha, Mohit, Dorfler, Florian, Johnson, Brian B., & Dhople, Sairaj V. Uncovering Droop Control Laws Embedded Within the Nonlinear Dynamics of Van der Pol Oscillators. United States. doi:10.1109/TCNS.2015.2503558.
Sinha, Mohit, Dorfler, Florian, Johnson, Brian B., and Dhople, Sairaj V. Tue . "Uncovering Droop Control Laws Embedded Within the Nonlinear Dynamics of Van der Pol Oscillators". United States. doi:10.1109/TCNS.2015.2503558.
@article{osti_1364161,
title = {Uncovering Droop Control Laws Embedded Within the Nonlinear Dynamics of Van der Pol Oscillators},
author = {Sinha, Mohit and Dorfler, Florian and Johnson, Brian B. and Dhople, Sairaj V.},
abstractNote = {This paper examines the dynamics of power-electronic inverters in islanded microgrids that are controlled to emulate the dynamics of Van der Pol oscillators. The general strategy of controlling inverters to emulate the behavior of nonlinear oscillators presents a compelling time-domain alternative to ubiquitous droop control methods which presume the existence of a quasistationary sinusoidal steady state and operate on phasor quantities. We present two main results in this paper. First, by leveraging the method of periodic averaging, we demonstrate that droop laws are intrinsically embedded within a slower time scale in the nonlinear dynamics of Van der Pol oscillators. Second, we establish the global convergence of amplitude and phase dynamics in a resistive network interconnecting inverters controlled as Van der Pol oscillators. Furthermore, under a set of nonrestrictive decoupling approximations, we derive sufficient conditions for local exponential stability of desirable equilibria of the linearized amplitude and phase dynamics.},
doi = {10.1109/TCNS.2015.2503558},
journal = {IEEE Transactions on Control of Network Systems},
issn = {2325-5870},
number = 2,
volume = 4,
place = {United States},
year = {2015},
month = {11}
}