Journal
AUTOMATICA
Volume 49, Issue 9, Pages 2603-2611Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.automatica.2013.05.018
Keywords
Inverters; Power-system control; Smart power applications; Synchronization; Coupled oscillators; Kuramoto model; Distributed control
Funding
- National Science Foundation NSF [CNS-1135819]
- National Science and Engineering Research Council of Canada
- Direct For Computer & Info Scie & Enginr [1135819] Funding Source: National Science Foundation
- Division Of Computer and Network Systems [1135819] Funding Source: National Science Foundation
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Motivated by the recent and growing interest in smart grid technology, we study the operation of DC/AC inverters in an inductive microgrid. We show that a network of loads and DC/AC inverters equipped with power-frequency droop controllers can be cast as a Kuramoto model of phase-coupled oscillators. This novel description, together with results from the theory of coupled oscillators, allows us to characterize the behavior of the network of inverters and loads. Specifically, we provide a necessary and sufficient condition for the existence of a synchronized solution that is unique and locally exponentially stable. We present a selection of controller gains leading to a desirable sharing of power among the inverters, and specify the set of loads which can be serviced without violating given actuation constraints. Moreover, we propose a distributed integral controller based on averaging algorithms, which dynamically regulates the system frequency in the presence of a time-varying load. Remarkably, this distributed-averaging integral controller has the additional property that it preserves the power sharing properties of the primary droop controller. Our results hold for any acyclic network topology, and hold without assumptions on identical line admittances or voltage magnitudes. (C) 2013 Elsevier Ltd. All rights reserved.
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