Florian Dörfler

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Cyber-physical systems are ubiquitous in power systems, transportation networks, industrial control processes, and critical infrastructures. These systems need to operate reliably in the face of unforeseen failures and external malicious attacks. In this paper (i) we propose a mathematical framework for cyberphysical systems, attacks, and monitors; (ii) we(More)
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(More)
Motivated by recent interest for multi-agent systems and smart power grid architectures, we discuss the synchronization problem for the network-reduced model of a power system with non-trivial transfer conductances. Our key insight is to exploit the relationship between the power network model and a first-order model of coupled oscillators. Assuming(More)
The emergence of synchronization in a network of coupled oscillators is a fascinating topic in various scientific disciplines. A widely adopted model of a coupled oscillator network is characterized by a population of heterogeneous phase oscillators, a graph describing the interaction among them, and diffusive and sinusoidal coupling. It is known that a(More)
Consider a weighted undirected graph and its corresponding Laplacian matrix, possibly augmented with additional diagonal elements corresponding to self-loops. The Kron reduction of this graph is again a graph whose Laplacian matrix is obtained by the Schur complement of the original Laplacian matrix with respect to a specified subset of nodes. The Kron(More)
The emergence of synchronization in a network of coupled oscillators is a fascinating subject of multidisciplinary research. This survey reviews the vast literature on the theory and the applications of complex oscillator networks. We focus on phase oscillator models that are widespread in real-world synchronization phenomena, that generalize the celebrated(More)
Modeled after the hierarchical control architecture of power transmission systems, a layering of primary, secondary, and tertiary control has become the standard operation paradigm for islanded microgrids. Despite this superficial similarity, the control objectives in microgrids across these three layers are varied and ambitious, and they must be achieved(More)
Motivated by the growing interest in energy technology and smart grid architectures, we consider the problem of voltage stability and reactive power balancing in low-voltage electrical networks equipped with DC/AC inverters (“microgrids”). It is generally believed that high-voltage equilibria of such networks are stable, but the locations of these(More)
In this work we present new distributed controllers for secondary frequency and voltage control in islanded microgrids. Inspired by techniques from cooperative control, the proposed controllers use localized information and nearest-neighbor communication to collectively perform secondary control actions. The frequency controller rapidly regulates the(More)