Synchronization of Open Systems: Application to the Lossy Power Grid

The transient stability assessment of multi-machine power systems has been a deeply explored research area in the power system community. The nonlinear nature of the evolving dynamics warrants distinctive control approaches, of which, the time domain simulations and Lyapunov based methods have been majorly applied for assessment and estimating the regions of attraction. However, these methods find limitations when applied to the lossy power grid and demand different modeling procedures. Treating the lossy grid as an open system aids in addressing the challenging problems of assessing their stability and achieving control. In this context, this paper explores the synchronization of open systems through the first order non-uniform Kuramoto model, which renders equivalence between rotor angle stability and phase synchronization of coupled oscillators. This paper investigates the distributed and decentralized control architectures for lossy networks and highlights the contexts under which they are applicable. The mean field Kuramoto model is central to the application of distributed control, whereas a generic framework for developing potential functions using notions of passivity to exercise decentralized control is also discussed.