Uncovering Droop Control Laws Embedded Within the Nonlinear Dynamics of Van der Pol Oscillators
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.
- Research Organization:
- National Renewable Energy Laboratory (NREL), Golden, CO (United States)
- Sponsoring Organization:
- NREL Laboratory Directed Research and Development (LDRD)
- DOE Contract Number:
- AC36-08GO28308
- OSTI ID:
- 1364161
- Report Number(s):
- NREL/JA--5D00-63335
- Journal Information:
- IEEE Transactions on Control of Network Systems, Journal Name: IEEE Transactions on Control of Network Systems Journal Issue: 2 Vol. 4; ISSN 2325-5870
- Country of Publication:
- United States
- Language:
- English
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