A Structure-Preserving Model and Sufficient Condition for Frequency Synchronization of Lossless Droop Inverter-Based AC Networks

Ainsworth, Nathan; Grijalva, Santiago

doi:10.1109/tpwrs.2013.2257887

Cited by 62 publications

(61 citation statements)

References 21 publications

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“…Notice that, with the exception of the inertial terms M iθi and the possibly non-unit coefficients D i , the power network dynamics (8)-(10) are a perfect electrical analog of the coupled oscillator model (1) with ω i ∈ {−P l,i , P m,i , P d,i }. Thus, it is not surprising that scientists from different disciplines recently advocated coupled oscillator approaches to analyze synchronization in power networks (Tanaka et al, 1997;Subbarao et al, 2001;Hill and Chen, 2006;Filatrella et al, 2008;Buzna et al, 2009;Fioriti et al, 2009;Simpson-Porco et al, 2013;Dörfler and Bullo, 2012b;Rohden et al, 2012;Dörfler et al, 2013;Mangesius et al, 2012;Motter et al, 2013;Ainsworth and Grijalva, 2013). The theoretical tools presented in this article establish how frequency synchronization in power networks depend on the nodal parameters (P l,i , P m,i , P d,i ) as well as the interconnecting electrical network with weights a ij .…”

Section: Electric Power Network With Synchronous Generators and Dc/amentioning

confidence: 87%

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Synchronization in complex networks of phase oscillators: A survey

2014

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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 real-world 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 finite-dimensional and infinite-dimensional settings. We conclude by summarizing the limitations of existing analysis methods and by highlighting some directions for future research.

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Section: Electric Power Network With Synchronous Generators and Dc/amentioning

confidence: 87%

“…, n}, see , Lemma 3) for a formal proof. Along the same lines, condition (27) can also be extended from a single node to a cutset in the graph (Ainsworth and Grijalva, 2013, Theorem 1).…”

Section: Lemma 42 (Necessary Sync Condition)mentioning

confidence: 94%

Synchronization in complex networks of phase oscillators: A survey

2014

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“…In order to preserve the identity of all grid components, including DICs, loads, and lines, and provide more physical interpretations among them, we will use the network-preserving models to depict dynamical interactions among various components in micro-grids [34], [35]. Network-preserving models are usually described by differential and algebraic equations (DAE).…”

Section: A Model Descriptionsmentioning

confidence: 99%

Consensus-Based Secondary Frequency and Voltage Droop Control of Virtual Synchronous Generators for Isolated AC Micro-Grids

Chu

2015

IEEE J. Emerg. Sel. Topics Circuits Syst.

174

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As the penetration of renewable energy sources is increasing in the AC micro-grid, the stability of the closed-loop system has raised a major concern since conventional distributed interface converters (DICs) used in the AC micro-grid do not have a rotating mass, and hence low inertia. High penetration of DIC-based micro-grid may result in poor frequency and voltage response during large disturbance. In order to overcome this difficulty, the virtual synchronous generator (VSGs) was proposed recently in which the DIC mimics conventional synchronous generators (SGs) by designing proper parameters of the SG into each local droop control mechanism of the DIC. Meanwhile, due to the recent advances of distributed control, the concept of consensus-based control can be applied to study this droop control problem of VSGs. One important feature of this consensus-based control is that it can be implemented on each local DIC with communications among their neighboring DICs. In contrast to most existing secondary control schemes, no central controller is required. Under this framework, if DICs are redesigned as VSGs, the frequency and voltage of each DIC can be restored to their pre-specified values obtained from the steady-state analysis. In addition, the proper real and reactive power sharing still can be achieved according to the nominal rating of each DIC. The stability of the closed-loop system is ensured by the transient energy function under certain mild conditions. Numerical experiments of a 14-bus/6-DIC micro-grid system on real-time simulators are performed to validate the effectiveness of the proposed control mechanism. Index Terms-Consensus algorithm, distributed interface converters (DICs), droop control, micro-grid (MG), transient energy function (TEF), virtual synchronous generator (VSG). 2156-3357

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“…The model is essentially a weighted graph where each node represents a commonvoltage point of power injection, and branches represent microgrid node-interconnecting lines [16], [1].…”

Section: Decentralised Droop Control Modelmentioning

confidence: 99%

Ultimate boundedness of droop controlled microgrids with secondary loops

Heidari

Serón

Braslavsky

2014

2014 4th Australian Control Conference (AUCC)

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In this paper we study theoretical properties of inverter-based microgrids controlled via primary and secondary loops. Stability of these microgrids has been the subject of a number of recent studies. Conventional approaches based on standard hierarchical control rely on time-scale separation between primary and secondary control loops to show local stability of equilibria. In this paper we show that (i) frequency regulation can be ensured without assuming time-scale separation and, (ii) ultimate boundedness of the trajectories starting inside a region of the state space can be guaranteed under a condition on the inverters power injection errors. The trajectory ultimate bound can be computed by simple iterations of a nonlinear mapping and provides a certificate of the overall performance of the controlled microgrid.

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A Structure-Preserving Model and Sufficient Condition for Frequency Synchronization of Lossless Droop Inverter-Based AC Networks

Cited by 62 publications

References 21 publications

Synchronization in complex networks of phase oscillators: A survey

Synchronization in complex networks of phase oscillators: A survey

Consensus-Based Secondary Frequency and Voltage Droop Control of Virtual Synchronous Generators for Isolated AC Micro-Grids

Ultimate boundedness of droop controlled microgrids with secondary loops

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