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.

Majid Pahlevani is an Associate Professor in the Department of Electrical and Computer Engineering at Queen’s University. Prior to joining Queen’s University, he served as an Assistant Professor at the University of Calgary from 2016 to 2019. He received his Ph.D. in electrical engineering from Queen’s University in 2012.

From 2011 to 2016, Dr. Pahlevani held several senior technology leadership roles at SPARQ Systems Inc., including Chief R&D Engineer, Vice President of Technology, and Chief Technology Officer. During his tenure at SPARQ, he developed several innovative power-circuitry and digital-control techniques for the company’s product platforms. He also introduced advanced differential geometric control methods for photovoltaic microinverters, which became key technological differentiators for SPARQ’s products in a competitive market.

Earlier in his career, from 2008 to 2011, Dr. Pahlevani collaborated with Freescale Semiconductor Inc., where he led a research team focused on the design and implementation of power converters for a pure electric vehicle.

Dr. Pahlevani’s research and industrial contributions span renewable energy systems, energy storage systems, electric vehicles, and LED lighting. He has led or contributed to more than 20 industry-driven projects and has authored or co-authored more than 250 journal and conference papers. He is also the holder of 150 issued or pending patents.

He is a Fellow of the IEEE, a member of the IEEE Power Electronics Society, and an Associate Editor of the IEEE Journal of Emerging and Selected Topics in Power Electronics. His achievements have been recognized through numerous distinctions, including the Early Research Excellence Award from the Province of Alberta, the Research Achievement Award and multiple Teaching Achievement Awards from the University of Calgary and Queen’s University, the Engineering and Applied Sciences Outstanding Thesis Award from Queen’s University, the Research Excellence Award from IEEE Canada, and the Distinguished Research Award from the University of Calgary.