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.
Bibliographical noteFunding Information:
This work was supported in part by the National Science Foundation under the CAREER award ECCS-CAR-1453921 and Grant ECCS- 1509277, in part by the Office of Naval Research under Grant N000141410639, in part by ETH Z?rich funds and the SNF Assistant Professor Energy Grant #160573, and in part by the Laboratory Directed Research and Development Program at NREL and the U.S. Department of Energy under Contract No. DE-AC36-08-GO28308 with NREL.
© 2014 IEEE.
- Van der Pol oscillators
- droop control
- nonlinear oscillator circuits