Synchronization of Open Systems

The study of complex systems involves interactions between its sub-systems resulting in the emergence of collective behaviour, attempts of perceiving which have been the driving force for developments in science and engineering. Such systems exhibit unique spatio-temporal characteristics, which have rendered them as highly attractive targets of exploration. Of greater importance is the existence of the idea of stability of the attained equilibrium state of the system, in the sense of Lyapunov. A special class of systems for which formulation of a Lyapunov function becomes formidable are open systems, e.g., the three body problem of celestial mechanics, as these systems are "nearly integrable¿. Inspired by these notions, this book proposes to perceive multi machine power system with transfer conductances (lossy) as an open system. The main objective of the book is to highlight the limitations in the traditional procedures for evaluating stability of the lossy grid. With supporting rationale from macroscopic theories, this work provides tools to assess stability of the lossy power grid.