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

Abstract

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’.

Global synchronization analysis of droop-controlled microgrids—A multivariable cell structure approach

“…For the present case of a system with periodic dynamics, Leonov [41,42] and Noldus [43] proposed the cell structure approach, which signicantly relaxes the positive deniteness and smoothness requirements of the standard Lyapunov function approach, while allowing to assess Lagrange stability of the system. These properties have recently been exploited to provide global stability analyses for power systems with conventional synchronous generators [44,45]. Yet, these analyses are restricted to the single-machine-innite-bus scenario, because the cell structure approach of Leonov and Noldus is only applicable to systems, whose dynamics are periodic with respect to a scalar state variable.…”

“…To show that the set X is almost globally asymptotically stable, we note that Lemma 7 implies that the Jacobian of the dynamics (22) evaluated at any unstable equilibrium point has at least one eigenvalue with positive real part. Thus, following the analyses in [44,45,52], we invoke [61,Proposition 11] to conclude that the region of attraction of any unstable equilibrium point has zero Lebesgue measure. Hence, for all initial conditions, except a set of measure zero, the solutions of the system (22) asymptotically converge to an isolated point in the set X , completing the proof.…”

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

“…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.…”

Energy management: flexibility, risk and optimization

“…In particular, there are two 'framework' contributions that cover important general applications of stochastic and probabilistic modelling, namely smart grid and low-carbon power system planning [1], and system stability analysis [13]. Then, a number of papers deal with more specific and technical topics such as optimal location of advanced measurement devices in transmission networks [14], distribution network voltage control through multi-agent systems [15] and identification of analytical conditions for synchronous generators' stability [16].…”

“…Schiffer et al [16] deal with another classical power system application of mathematical concepts, namely, stability analysis of synchronous generators (see also [13]). Specifically, analytical conditions for almost global stability of an operating point of a synchronous generator connected to a strong network are derived under certain conditions.…”