*Editorial* **Mathematical Models for the Design of Electrical Machines**

**Frédéric Dubas 1,\* and Kamel Boughrara <sup>2</sup>**


Received: 8 December 2020; Accepted: 9 December 2020; Published: 9 December 2020

Electrical machines are used in many electrical engineering applications, viz, transports (e.g., electric, hybrid, and fuel cell vehicles, railway traction, and aerospace), energy harvesting (e.g., flywheels), renewable energy (e.g., wind power turbines and hydroelectric power plants) and magnetic refrigeration devices, among others. For decades, numerical methods (e.g., finite element, finite difference or boundary-element analysis) were widely used in research and development (R&D) departments for their accuracy as compared to measurements. Nevertheless, mainly in three-dimensional (3-D) applications, these approaches are time-consuming and not suitable for optimization problems. Nowadays, in order to reduce the computation time, R&D engineers must develop full computer-aided design for electrical machines with accurate and fast models in simulations. Hence, the main objective of this special issue is to bring the latest advances and developments in the mathematical modeling and design of electrical machines to different applications. The main models discussed will be based on the following:


The interest topics in the mathematical models include, but are not restricted to the following:


The numerical method, as well as the experimental tests, will be used as comparisons or validations. In this special issue, the authors of selected works contributed to the topics listed above, since contents of their works can be synthesized as follows:

	- - Jabbari [1]. In this research, an analytical model was proposed to calculate the magnetic vector potential in surface-mounted permanent magnet (PM) machines. It was based on the subdomain technique and applied a hyperbolic function. The saturation effect was neglected. A mathematical expression was also derived for optimizing the PM shape to

reduce the cogging torque and electromagnetic torque components. The analytical results were validated through finite element analysis (FEA);


#### • **Electrical, Thermal or Magnetic Equivalent Circuit (EEC, TEC or MEC)**


#### • **Hybrid Models**



At this point, as editors of this book, we would like to express our deep gratitude for the opportunity to publish with MDPI. This acknowledgment is deservedly extensive to the MCA Editorial Office and more particularly to Mr. Everett Zhu, who has permanently supported us in this process.

It was a great pleasure to work in such conditions. We look forward to collaborating with MCA in the future.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


13. Ouamara, D.; Dubas, F. Permanent-Magnet Eddy-Current Losses: A Global Revision of Calculation and Analysis. *Math. Comput. Appl.* **2019**, *24*, 67. [CrossRef]

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
