Today, the inherent stability of a network of synchronous generators coupled with various types of loads and power sources (such as inverters) is an area of high interest and intense research. This is partly due to the proliferation of power sources that are not synchronous generators, which threatens the stability of the power grid. In this talk I will consider one basic ingredient of this system, one synchronous generator, and investigate its stability when it is connected to a much more powerful grid, so that this one generator has practically no influence on the grid. Thus, the grid is modeled as an infinite bus. I will address the following question: will the synchronous generator, driven by a prime mover with constant torque, having a constant field current and starting from an arbitrary initial state, converge to a state of synchronous rotation with a constant difference between the grid and the rotor angles? The importance of this problem has been recognized for a long time. However, as far as we know, all the available studies are based on some sort of simplification/reduction of the problem, reducing it to a second order possibly non-linear swing equation, or linearizing the original higher order system. In contrast we consider the original nonlinear fourth order system and examine its stability rigorously. I will present conditions for the system parameters, under which the answer to the aforementioned question is positive. A motivation for studying this problem comes from the recent development of synchronverters, which are inverters that mimic synchronous generators. The results in this talk are useful for choosing the parameters of the synchronverter.
Vivek Natarajan received the B.Tech. degree in mechanical engineering from the Indian Institute of Technology Madras, Chennai, India, in 2004, the M.S. degree in mechanical engineering from The Ohio State University, Columbus, OH, USA, in 2006, and M.S. degree in mathematics in 2009 and Ph.D. degree in mechanical engineering in 2012, both from the University of Illinois at Urbana-Champaign, Urbana, IL, USA. Since 2012 he has been a Postdoctoral Researcher in the School of Electrical Engineering, Tel Aviv University, Ramat Aviv, Israel. His current research interests include distributed parameter systems, nonlinear analysis, and adaptive control.