Power System Dynamics: Foundations
In this chapter, we briefly review basic material about nonlinear ordinary differential equations that is important background for later chapters. After a preliminary discussion of the basic properties of differential equations including the existence and uniqueness of solutions, we turn to a short discussion of stability in the sense of Lyapunov. In addition to stating the most important theorems on stability and instability, we provide a number of illustrative examples. As part of this discussion, we introduce Lagrangian systems—a topic to be treated at great length later. This chapter is concerned exclusively with dynamical systems with smooth systems. It is presumed that the material discussed is not new to the reader, and we provide only a short summary of those elements considered immediately relevant. For a more complete discussion, many excellent textbooks are available. We reference a number of them in the sequel.