This chapter provides an overview of some mathematical concepts not always covered in electrical engineering curricula. Our main goal is to give the readers an overview of nonlinear system dynamics, a perspective that will prove useful when we embark on a more detailed analysis of complex power system voltage stability problems. In our exposition we assume some prior knowledge of linear algebra and linear systems theory. Readers who are already familiar with the theory of nonlinear systems may choose to skip this chapter. Those interested in a detailed mathematical analysis of nonlinear dynamics are urged to consult specialized textbooks, such as [HK92, GH83, Wig90, Sey88].
KeywordsEquilibrium Point Unstable Manifold Stable Manifold Center Manifold Mathematical Background
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