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39
Synchronization and transient stability in power networks and nonuniform Kuramoto oscillators,”
 IEEE Transactions on Automatic Control,
, 2010
"... AbstractMotivated by recent interest for multiagent systems and smart grid architectures, we discuss the synchronization problem for the networkreduced model of a power system with nontrivial transfer conductances. Our key insight is to exploit the relationship between the power network model a ..."
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Cited by 72 (12 self)
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AbstractMotivated by recent interest for multiagent systems and smart grid architectures, we discuss the synchronization problem for the networkreduced model of a power system with nontrivial transfer conductances. Our key insight is to exploit the relationship between the power network model and a firstorder model of coupled oscillators. Assuming overdamped generators (possibly due to local excitation controllers), a singular perturbation analysis shows the equivalence between the classic swing equations and a nonuniform Kuramoto model characterized by multiple time constants, nonhomogeneous coupling, and nonuniform phase shifts. By extending methods from synchronization theory and consensus protocols, we establish sufficient conditions for synchronization of nonuniform Kuramoto oscillators. These conditions reduce to and improve upon previouslyavailable tests for the classic Kuramoto model. By combining our singular perturbation and Kuramoto analyses, we derive concise and purely algebraic conditions that relate synchronization and transient stability of a power network to the underlying network parameters and initial conditions.
Synchronization and Power Sharing for DroopControlled Inverters in Islanded Microgrids
, 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 powerfrequency droop controllers can be cast as a Kuramoto model of phasecoupled oscillators ..."
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Cited by 30 (9 self)
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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 powerfrequency droop controllers can be cast as a Kuramoto model of phasecoupled 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 timevarying load. Remarkably, this distributedaveraging integral controller has the additional property that it preserves the power sharing properties of the primary droop controller. Our results hold without assumptions on identical line characteristics or voltage magnitudes.
Attack detection and identification in cyberphysical systems
 IEEE Trans. Automat. Contr
"... Cyberphysical systems are ubiquitous in power systems, transportation networks, industrial process control 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 fo ..."
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Cited by 30 (4 self)
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Cyberphysical systems are ubiquitous in power systems, transportation networks, industrial process control 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 characterize fundamental monitoring limitations from systemtheoretic and graphtheoretic perspectives; and (iii) we design centralized and distributed attack detection and identification monitors. Finally, we validate our findings through compelling examples. I.
Algorithms for leader selection in large dynamical networks: Noisefree leaders
 in Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference
, 2011
"... Abstract — We examine the leader selection problem in multiagent dynamical networks where leaders, in addition to relative information from their neighbors, also have access to their own states. We are interested in selecting an a priori specified number of agents as leaders in order to minimize th ..."
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Cited by 22 (8 self)
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Abstract — We examine the leader selection problem in multiagent dynamical networks where leaders, in addition to relative information from their neighbors, also have access to their own states. We are interested in selecting an a priori specified number of agents as leaders in order to minimize the total variance of the stochastically forced network. Combinatorial nature of this optimal control problem makes computation of the global minimum difficult. We propose a convex relaxation to obtain a lower bound on the global optimal value, and use simple but efficient greedy algorithms to obtain an upper bound. Furthermore, we employ the alternating direction method of multipliers to search for a local minimum. Two examples are provided to illustrate the effectiveness of the developed methods. Index Terms — Alternating direction method of multipliers, consensus, convex optimization/relaxation, greedy algorithm, leader selection, performance bounds, variance amplification. I.
Cyberphysical attacks in power networks: Models, fundamental limitations and monitor design
, 2011
"... Future power networks will be characterized by safe and reliable functionality against physical and cyber attacks. This paper proposes a unified framework and advanced monitoring procedures to detect and identify network components malfunction or measurements corruption caused by an omniscient adve ..."
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Cited by 17 (4 self)
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Future power networks will be characterized by safe and reliable functionality against physical and cyber attacks. This paper proposes a unified framework and advanced monitoring procedures to detect and identify network components malfunction or measurements corruption caused by an omniscient adversary. We model a power system under cyberphysical attack as a linear timeinvariant descriptor system with unknown inputs. Our attack model generalizes the prototypical stealth, (dynamic) falsedata injection and replay attacks. We characterize the fundamental limitations of both static and dynamic procedures for attack detection and identification. Additionally, we design provablycorrect (dynamic) detection and identification procedures based on tools from geometric control theory. Finally, we illustrate the effectiveness of our method through a comparison with existing (static) detection algorithms, and through a numerical study.
Synchronization in Complex Networks of Phase Oscillators: A Survey
, 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 realworl ..."
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Cited by 13 (1 self)
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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 realworld synchronization phenomena, that generalize the celebrated Kuramoto model, and that feature a rich phenomenology. We review the history and the countless applications of this model throughout science and engineering. We justify the importance of the widespread coupled oscillator model as a locally canonical model and describe some selected applications relevant to control scientists, including vehicle coordination, electric power networks, and clock synchronization. We introduce the reader to several synchronization notions and performance estimates. We propose analysis approaches to phase and frequency synchronization, phase balancing, pattern formation, and partial synchronization. We present the sharpest known results about synchronization in networks of homogeneous and heterogeneous oscillators, with complete or sparse interconnection topologies, and in finitedimensional and infinitedimensional settings. We conclude by summarizing the limitations of existing analysis methods and by highlighting some directions for future research.
Voltages across an area of a network
 IEEE Transactions on Power Systems
"... Abstract—We define the voltage across an area of a resistive network by suitably combining voltages at buses (nodes) on the border of the area. The new voltage across the area satisfies circuit laws. The same concept works to define the voltage angle difference across an area of a DC load flow netw ..."
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Cited by 10 (4 self)
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Abstract—We define the voltage across an area of a resistive network by suitably combining voltages at buses (nodes) on the border of the area. The new voltage across the area satisfies circuit laws. The same concept works to define the voltage angle difference across an area of a DC load flow network and the complex voltage difference across an area of an AC load flow network. We first define the voltage across a cutset of lines, and then derive and explain the voltages across areas, including generalizations to several voltages across an area and multiple areas. The new voltages across areas seem promising for both power system monitoring and network reduction, and we describe their application to monitoring area stress. Index Terms—Circuit analysis, network theory, phasor measurement units, power grids, power system modeling, smart grids. I.
Multiresolution graph signal processing via circulant structures
 IN IEEE DSP/SPE WORSKHOP 2013. IEEE
, 2013
"... We offer a new paradigm for multiresolution analysis and processing of graph signals using circulant structures. Among the essential features of circulant graphs is that they accommodate fundamental signal processing operations, such as linear shiftinvariant filtering, downsampling, upsampling, an ..."
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Cited by 7 (2 self)
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We offer a new paradigm for multiresolution analysis and processing of graph signals using circulant structures. Among the essential features of circulant graphs is that they accommodate fundamental signal processing operations, such as linear shiftinvariant filtering, downsampling, upsampling, and reconstruction—features that we take to substantial advantage. We design twochannel, criticallysampled, perfectreconstruction, orthogonal latticefilter structures to process signals on circulant graphs. To extend our reach to more general graphs, we present a method to decompose a connected, undirected graph into a linear combination of circulant graphs. Our circulant decomposition is analogous to designing linear timevarying lattice filters by suitably adapting the coefficients of a linear timeinvariant filter. To evaluate the systems and methods that we have propounded, we offer examples of synthetic and realworld graph datasets and their multiscale decompositions.
Voltage stabilization in microgrids using quadratic droop control
 in IEEE Conf. on Decision and Control
, 2013
"... Abstract — Motivated by the recent and growing interest in energy technology, we study the operation of DC/AC inverters in an inductive microgrid. We consider the problem of voltage stability and reactive power balancing, and propose a novel quadratic drooplike controller. The natural structure of ..."
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Cited by 6 (4 self)
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Abstract — Motivated by the recent and growing interest in energy technology, we study the operation of DC/AC inverters in an inductive microgrid. We consider the problem of voltage stability and reactive power balancing, and propose a novel quadratic drooplike controller. The natural structure of the quadratic droop controller allows us to exactly characterize the behavior of the network of inverters and loads. Specifically, we find that the equilibrium points of the droopcontrolled network are in exact correspondence with the solutions of a reduced power flow equation. For the common case of a parallel microgrid, we provide a necessary and sufficient condition for the existence of an exponentially stable highvoltage fixed point. The simplicity of these results comes from exploiting the inherent quadratic structure of the controller and power flow equations, and allows a nonlinear analysis of the network via a Kronlike reduction to an equivalent reduced network. We compare and contrast our design with the conventional voltagedroop controller, and investigate the relationship between them. I.
Distributed Detection of CyberPhysical Attacks in Power Networks: A Waveform Relaxation Approach
"... Abstract — Future power grids will be required to operate safely and reliably against cyberphysical attacks. The large dimensionality and the difficulty in calibrating dynamical network models precludes the use of centralized attack detection algorithms. This paper proposes a unified modeling frame ..."
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Cited by 5 (3 self)
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Abstract — Future power grids will be required to operate safely and reliably against cyberphysical attacks. The large dimensionality and the difficulty in calibrating dynamical network models precludes the use of centralized attack detection algorithms. This paper proposes a unified modeling framework and an advanced detection procedure whose implementation requires only local network knowledge. We model a power network as a linear timeinvariant descriptor system and cyberphysical attacks as unknown inputs. This modeling framework captures, for instance, network components malfunction and measurements corruption. In our detection method the power network is partitioned among geographically deployed control centers, possibly located at transmission substations. Each control center has knowledge of only its respective subarea dynamics, is able to acquire information from neighboring areas, and is capable of performing basic computations. Under these minimal technological requirements and a reasonable observability assumption, we design an entirely distributed detection filter which requires only local network knowledge and yet achieves guaranteed global performance. Our detection filter is based on a sparse residual filter in descriptor form, which can be stabilized via decentralized output injection and implemented distributively via waveform relaxation. I.