Differential Geometric Methods for Power Electronics: Synthesis Lectures on 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.

Chapter1: Topological Spaces.- Chapter 2 (Smooth).- Chapter 3 Curves, Velocity, and Tangent Bundle.- Chapter 4 Maps between Manifolds and Derivatives of Maps.- Chapter 5 Co-Tangent Space and One-Forms.- Chapter 6 Bilinear Maps.- Chapter 7 Dynamic Equations for Power Electronics.- Chapter 8 Vector Fields and Connections.- Chapter 9 Riemannian Geometry.- Chapter 10 Group Theory.- Chapter 11 Control of Resonant Converters Using Lie Groups.- Chapter 12 Control of Bidirectional DC–DC Converters on Differential Geometry.- Chapter 13 Motor Drive Control Using Lie Groups.- Chapter 14 Grid-Forming PV Microinverters.