Almost global attractivity of a synchronous generator connected to an infinite bus

Barabanov, Nikita; Schiffer, Johannes; Ortega, Roméo; Efimov, Denis

doi:10.1109/cdc.2016.7798895

Cited by 11 publications

(15 citation statements)

References 21 publications

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“…The present work extends our previous results in [25] in several regards. Namely, we provide physical interpretations of part of our conditions; the proofs of the main theoretical contributions are presented in more detail; we provide extensive numerical experiments illustrating the usefulness of our approach.…”

Section: Contributionssupporting

confidence: 91%

Conditions for Almost Global Attractivity of a Synchronous Generator Connected to an Infinite Bus

Barabanov

Schiffer

Ortega

et al. 2017

IEEE Trans. Automat. Contr.

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Section: Contributionssupporting

confidence: 91%

Conditions for Almost Global Attractivity of a Synchronous Generator Connected to an Infinite Bus

Barabanov

Schiffer

Ortega

et al. 2017

IEEE Trans. Automat. Contr.

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“…we show that for all initial conditions, except a set of measure zero, the solutions of the SMIB system asymptotically converge to an asymptotically stable equilibrium point. Differently from our previous related work [30,31], in which LaSalle's invariance principle is employed, the present ISS-based approach has the advantage of providing additional robustness guarantees with respect to exogeneous inputs. Both properties-stability and robustness-are highly desirable from a practical point of view to characterize the performance of power systems under persistent disturbances, such as load variations [32, §D].…”

Section: (B) Existing Literature and Contributionsmentioning

confidence: 98%

“…The SMIB system is introduced in this section based on [30,31,35]. We employ a generator reference direction, i.e.…”

Section: Model Of a Synchronous Generator Connected To An Infinite Busmentioning

confidence: 99%

“…current flowing out of the SG terminals is counted positively. Following [30,31], we make some standard assumptions on the SG [15,35], which are also used in [12,18,19]: the rotor is round; the machine has one pole pair per phase; there are no damper windings and no saturation effects; there are no Eddy currents; the rotor current i f is a real constant. The latter can be achieved by choosing the excitation voltage such that i f is kept constant [12].…”

Section: Model Of a Synchronous Generator Connected To An Infinite Busmentioning

confidence: 99%

“…The existence of isolated equilibria is a natural prerequisite for any stability analysis. Therefore, we make the following natural assumption that by [30,Proposition 1] implies the existence of two unique steady-state solutions (modulo 2π ) of the system (2.11). With assumption 3.2, we denote one of the two equilibrium points of the system (2.11) by (θ s 1 , ω s , i s d,1 , i s q,1 ) and introduce the error states…”

Section: (A) Error Coordinatesmentioning

confidence: 99%

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An input-to-state stability approach to verify almost global stability of a synchronous-machine-infinite-bus system

Schiffer

Efimov

Ortega

et al. 2017

Phil. Trans. R. Soc. A.

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Conditions for almost global stability of an operating point of a realistic model of a synchronous generator with constant field current connected to an infinite bus are derived. The analysis is conducted by employing the recently proposed concept of input-to-state stability (ISS)–Leonov functions, which is an extension of the powerful cell structure principle developed by Leonov and Noldus to the ISS framework. Compared with the original ideas of Leonov and Noldus, the ISS–Leonov approach has the advantage of providing additional robustness guarantees. The efficiency of the derived sufficient conditions is illustrated via numerical experiments. This article is part of the themed issue ‘Energy management: flexibility, risk and optimization’.

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Almost global asymptotic stability of a grid-connected synchronous generator

Natarajan

2018

Math. Control Signals Syst.

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We study the global asymptotic behavior of a grid-connected constant field current synchronous generator (SG). The grid is regarded as an "infinite bus", i.e. a three-phase AC voltage source. The generator does not include any controller other than the frequency droop loop. This means that the mechanical torque applied to this generator is an affine function of its angular velocity. The negative slope of this function is the frequency droop constant. We derive sufficient conditions on the SG parameters under which there exist exactly two periodic state trajectories for the SG, one stable and another unstable, and for almost all initial states, the state trajectory of the SG converges to the stable periodic trajectory (all the angles are measured modulo 2π). Along both periodic state trajectories, the angular velocity of the SG is equal to the grid frequency. Our sufficient conditions are easy to check computationally. An important tool in our analysis is an integro-differential equation called the exact swing equation, which resembles a forced pendulum equation and is equivalent to our fourth order model of the grid-connected SG. Apart from our objective of providing an analytical proof for a global asymptotic behavior observed in a classical dynamical system, a key motivation for this work is the development of synchronverters which are inverters that mimic the behavior of SGs. Understanding the global dynamics of SGs can guide the choice of synchronverter parameters and operation. As an application we find a set of stable nominal parameters for a 500kW synchronverter.

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Almost global attractivity of a synchronous generator connected to an infinite bus

Cited by 11 publications

References 21 publications

Conditions for Almost Global Attractivity of a Synchronous Generator Connected to an Infinite Bus

Conditions for Almost Global Attractivity of a Synchronous Generator Connected to an Infinite Bus

An input-to-state stability approach to verify almost global stability of a synchronous-machine-infinite-bus system

Almost global asymptotic stability of a grid-connected synchronous generator

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