Differential Geometric Methods for Power Electronics

Power electronics is the key technology for many existing and emerging applications such as renewable energy systems, electric vehicles, energy storage systems, LED lighting, telecommunication systems, AI and data centres, etc. Power electronics technology primarily includes power electronic circuitry and control systems. Although power circuits perform the required power conversions, the control system is what controls the conversion. Thus, the control system is an integral part of this technology, which directly determines the system's performance.

The main focus of this book is to present new differential geometric control techniques tailored for power electronics technology. Differential geometry is the foundation of nonlinear control theory, and thus it can be used to effectively capture nonlinear behavior of power electronic converters. The proposed framework provides advanced tools to derive nonlinear models and design control techniques for power electronic converters on manifolds, where their nonlinear behavior can be fully characterized, accurate stability margins can be investigated, and optimal performance can be achieved.

In this book, the authors develop differential geometric techniques for power electronic converters. We first introduce a new mathematical framework based on differential geometry for modeling power electronics. Then, the differential geometric models are used to develop the Lie group theory for designing controllers for power electronic converters. Thus, the book is divided into two main sections: The first section describes the basics of differential geometry and respective tools. It also includes the appropriate differential geometric framework for modeling and control of power converters. The second section focuses on designing differential geometric control for various applications in power electronics.