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- Fabio Pasqualetti, Florian Dörfler, Francesco Bullo
- IEEE Trans. Automat. Contr.
- 2013

—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 cyber-physical systems, attacks, and monitors; (ii)… (More)

- Florian Dörfler, Francesco Bullo
- IEEE Trans. on Circuits and Systems
- 2013

—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)

- Florian Dörfler, Francesco Bullo
- SIAM J. Control and Optimization
- 2012

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)

- Florian Dörfler, Michael Chertkov, Francesco Bullo
- Proceedings of the National Academy of Sciences…
- 2013

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)

- John W. Simpson-Porco, Florian Dörfler, Francesco Bullo
- Automatica
- 2013

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)

- Florian Dörfler, Francesco Bullo
- Automatica
- 2014

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)

— Inter-area oscillations in power networks are typically poorly controllable by means of local decentralized control. Recent research efforts have been aimed at developing wide-area control strategies that involve communication of remote signals. In conventional wide-area control strategies the control structure is fixed a priori typically based on modal… (More)

- Florian Dörfler, Bruce A. Francis
- IEEE Trans. Automat. Contr.
- 2010

- Florian Dörfler, John W. Simpson-Porco, Francesco Bullo
- IEEE Transactions on Control of Network Systems
- 2016

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)

- John W. Simpson-Porco, Florian Dörfler, Francesco Bullo
- IEEE Trans. Automat. Contr.
- 2013

— 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 (" micro-grids "). It is generally believed that high-voltage equilibria of such networks are stable, but the locations of these… (More)