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DSSP: Asymptotic stability of a grid-connected synchronous generator

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Location: F110, School of Engineering

'Asymptotic stability of a grid-connected synchronous generator'

George Weiss, School of Electrical Engineering, Tel Aviv University

Abstract

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 standard frequency droop loop. We present newly derived sufficient conditions on the SG parameters under which there exist exactly two periodic state trajectories, 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 $2\pi$). Along both periodic state trajectories, the angular velocity of the generator 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 {\em exact swing equation} (ESE), 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. Synchronverters could become the backbone of the future grid, especially with the large penetration of HVDC lines under way now, because they enable a seamless transition from generators to inverters as the main source of power in the grid. Understanding the global dynamics of SGs can guide the choice of synchronverter parameters and operation. Already, this research has enabled us to significantly improve the structure and transient behaviour of a synchronverter that we have built in collaboration with industry. We shall give a very brief insight into this development work. The full paper is available upon request.

 

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