Uncovering droop control laws embedded within the nonlinear dynamics of van der pol oscillators

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

Research output: Contribution to journalArticlepeer-review

126 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)347-358
Number of pages12
JournalIEEE Transactions on Control of Network Systems
Issue number2
StatePublished - 2017

Bibliographical note

Publisher Copyright:
© 2014 IEEE.


  • Averaging
  • Van der Pol oscillators
  • droop control
  • nonlinear oscillator circuits
  • synchronization


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