Synchronization of Nonlinear Oscillators in an LTI Electrical Power Network

Johnson, Brian; Dhople, Sairaj V.; Hamadeh, Abdullah; Krein, P.T.

doi:10.1109/tcsi.2013.2284180

Cited by 105 publications

(102 citation statements)

References 29 publications

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“…This is particularly important for certain complex networks from both Nature and Technology. For example, in certain applications arising from power networks [24] one would like to synchronize all the network nodes onto a desired periodic orbit and deviations from such a synchronous solution would result in electrical losses. In this context, following Theorem 2, one may want to mitigate the diffusion of noise through the network in order to avoid deviations from the desired synchronous solution.…”

Section: Discussionmentioning

confidence: 99%

Stabilizing Quorum-Sensing Networks via Noise

Rotoli

Russo

Bernardo

2018

IEEE Trans. Circuits Syst. II

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Abstract-We investigate how a single node injecting noise in a quorum-sensing network can dramatically affect its convergence towards synchronization. We show that adding some white noise of sufficiently high intensity on a single node can stabilize the collective behavior of all nodes in the network towards the origin. A sketch of the proof of the convergence result is given, together with the outcome of some numerical experiments on the challenging problem of stabilizing a network of bistable systems onto a common unstable equilibrium point.

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Section: Discussionmentioning

confidence: 99%

Stabilizing Quorum-Sensing Networks via Noise

Rotoli

Russo

Bernardo

2018

IEEE Trans. Circuits Syst. II

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“…In this work we focus on dynamics associated with the reactive power flow equation (1b), and refer the reader to [6]- [8], [34] and the references therein for analyses of microgrid active power/frequency dynamics. We will work under the standard decoupling approximation, where |θ i − θ j | ≈ 0 and hence cos(θ i − θ j ) ≈ 1 for each {i, j} ∈ E; see [12], [35].…”

Section: Preliminaries and Notationmentioning

confidence: 99%

“…In this low-gain limit, B (43) becomes very large and for any fixed Q L the second term in the linearization (34) dominates, leading to large voltage deviations. This violates the premise under which the linearization was derived, and may lead to the loss of the closed-loop system's equilibrium point or to violation of the decoupling assumption.…”

Section: Proof Of Theorem 42mentioning

confidence: 99%

Voltage Stabilization in Microgrids via Quadratic Droop Control

Simpson-Porco

Dörfler

Bullo

2017

IEEE Trans. Automat. Contr.

149

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Abstract-We consider the problem of voltage stability and reactive power balancing in islanded small-scale electrical networks outfitted with DC/AC inverters ("microgrids"). A drooplike voltage feedback controller is proposed which is quadratic in the local voltage magnitude, allowing for the application of circuit-theoretic analysis techniques to the closed-loop system. The operating points of the closed-loop microgrid are in exact correspondence with the solutions of a reduced power flow equation, and we provide explicit solutions and small-signal stability analyses under several static and dynamic load models. Controller optimality is characterized as follows: we show a oneto-one correspondence between the high-voltage equilibrium of the microgrid under quadratic droop control, and the solution of an optimization problem which minimizes a trade-off between reactive power dissipation and voltage deviations. Power sharing performance of the controller is characterized as a function of the controller gains, network topology, and parameters. Perhaps surprisingly, proportional sharing of the total load between inverters is achieved in the low-gain limit, independent of the circuit topology or reactances. All results hold for arbitrary grid topologies, with arbitrary numbers of inverters and loads. Numerical results confirm the robustness of the controller to unmodeled dynamics.Index Terms-Inverter control, microgrids, voltage control, Kron reduction, nonlinear circuits I . I N T R O D U C T I O NThe wide-spread integration of low-voltage small-scale renewable energy sources requires that the present centralized electric power transmission paradigm to evolve towards a more distributed future. As a flexible bridge between distributed generators and larger distribution grids, microgrids continue to attract attention [1]- [3]. Microgrids are low-voltage electrical distribution networks, heterogeneously composed of distributed generation, storage, load, and managed autonomously from the larger primary grid. While often connected to the larger grid through a "point of common coupling", microgrids are also able to "island" themselves and operate independently [2], [4]. This independent self-sufficiency is crucial for reliable power delivery in remote communities, in military outposts, in developing nations lacking large-scale infrastructure, and in backup systems for critical loads such as hospitals and campuses. Energy generation within a microgrid can be quite heterogeneous, including photovoltaic, wind, micro-turbines, etc. Many of these sources generate either variable frequency AC power or DC power, and are interfaced with a synchronous AC grid via power electronic DC/AC inverters. In islanded operation, at least some of these inverters must operate as gridforming devices. That is, control actions must be taken through them to ensure synchronization, voltage stability, and load sharing in the network A. Literature ReviewThe so-called droop controllers (and their many derivatives) have been used with some success t...

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“…Using (8) and (11), (12) one obtains the state-space description of the inverter's dynamics (see (13)) while the measurement equation of the inverter's model is…”

Section: Dynamics Of the Invertermentioning

confidence: 99%

Decentralised control of parallel inverters connected to microgrid using the derivative‐free non‐linear Kalman filter

Rigatos

Siano

Zervos

et al. 2015

IET Power Electronics

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Decentralised control for parallel inverters connected to the power grid is developed using differential flatness theory and the derivative-free nonlinear Kalman filter. It is proven that the model of the inverters, is a differentially flat one. This means that all its state variables and the control inputs can be written as differential functions of a single algebraic variable which is the flat output. By exploiting differential flatness properties it is shown that the multiple inverters model can be transformed into a set of local inverter models which are decoupled and linearized. For each local inverter the design of a state feedback controller becomes possible. Such a controller processes measurements not only coming from the individual inverter but also coming from other inverters which are connected to the grid. Moreover, to estimate the non-measurable state variables of each local inverter, the derivative-free nonlinear Kalman filter is used. Furthermore, by redesigning the aforementioned filter as a disturbance observer it becomes also possible to estimate and compensate for disturbance terms that affect each local inverter.

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Synchronization of Nonlinear Oscillators in an LTI Electrical Power Network

Cited by 105 publications

References 29 publications

Stabilizing Quorum-Sensing Networks via Noise

Stabilizing Quorum-Sensing Networks via Noise

Voltage Stabilization in Microgrids via Quadratic Droop Control

Decentralised control of parallel inverters connected to microgrid using the derivative‐free non‐linear Kalman filter

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