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

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

doi:10.1109/tac.2017.2671026

Cited by 32 publications

(33 citation statements)

References 30 publications

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“…All other parameters are kept constant. Furthermore, we define the error coordinates x in (3.2) with respect to the unstable equilibrium point, i.e., satisfying |θ Moreover, in line with the observations made in [30,31], Figure 2a shows that the required damping increases with the machine loading and the excitation magnitude. This is consistent with the well-known power-angle characteristic that can be employed for reduced-order SG models and states that the likelihood of an SG to undergo instability after a change in load increases with the SG being operated closer to its generation limit [1,35].…”

Section: Numerical Examplementioning

confidence: 88%

“…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,Section D].…”

Section: (B) Existing Literature and Contributionsmentioning

confidence: 99%

“…The SMIB system is introduced in this section based on [30,31,35]. We employ a generator reference direction, i.e, current flowing out of the SG terminals is counted positively.…”

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). Assumption 1.…”

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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Section: Numerical Examplementioning

confidence: 88%

Section: (B) Existing Literature and Contributionsmentioning

confidence: 99%

“…The SMIB system is introduced in this section based on [30,31,35]. We employ a generator reference direction, i.e, current flowing out of the SG terminals is counted positively.…”

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

confidence: 99%

Section: (A) Error Coordinatesmentioning

confidence: 99%

See 2 more Smart Citations

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.

Self Cite

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“…We anticipate that the proposed multivariable cell structure approach may prove useful in a variety of scenarios and applications. For instance, the original cell structure approach has recently been combined in [7] with LaSalle's invariance principle and in [43] with the ISS result of [18] to establish global properties of a synchronous machine infinite bus system. The extensions of this analysis to the multi-machine case [41] and to the Kuramoto model by using the methods derived in the present paper are under current investigation.…”

Section: Introductionmentioning

confidence: 99%

On Boundedness of Solutions of State Periodic Systems: A Multivariable Cell Structure Approach

Efimov

Schiffer

2019

IEEE Trans. Automat. Contr.

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Many dynamical systems are periodic with respect to several state variables. This periodicity typically leads to the coexistence of multiple invariant solutions (equilibria or limit cycles). As a consequence, while there are many classical techniques for analysis of boundedness and stability of such systems, most of these only permit to establish local properties. Motivated by this, a new sufficient criterion for global boundedness of solutions of such a class of nonlinear systems is presented. The proposed method is inspired by the cell structure approach developed by Leonov and Noldus and characterized by two main advances. First, the conventional cell structure framework is extended to the case of dynamics, which are periodic with respect to multiple states. Second, by introducing the notion of a Leonov function the usual definiteness requirements of standard Lyapunov functions are relaxed to sign-indefinite functions. Furthermore, it is shown that under (mild) additional conditions the existence of a Leonov function also ensures input-to-state stability (ISS), i.e., robustness with respect to exogenous perturbations. The performance of the proposed approach is demonstrated via the global analysis of boundedness of trajectories for a nonlinear system. The preliminary formulations of the main results of this paper are given in [17] without proofs.

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

Cited by 32 publications

References 30 publications

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

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

On Boundedness of Solutions of State Periodic Systems: A Multivariable Cell Structure Approach

Almost global asymptotic stability of a grid-connected synchronous generator

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