energies Article A Complex Study of Stator Tooth-Coil Winding Thermal Models for PM Synchronous Motors Used in Electric Vehicle Applications Lukáš Veg 1 , Jan Kaska 2, * , Martin Skalický 1 and Roman Pechánek 1, *   Citation: Veg, L.; Kaska, J.; Skalický, M.; Pechánek, R. A Complex Study of Stator Tooth-Coil Winding Thermal Models for PM Synchronous Motors Used in Electric Vehicle Applications. Energies 2021, 14, 2395. https://doi.org/10.3390/en14092395 Academic Editors: Federico Barrero and Sergio Cruz Received: 1 March 2021 Accepted: 19 April 2021 Published: 23 April 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional afﬁl- iations. Copyright: c  2021 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 (https:// creativecommons.org/licenses/by/ 4.0/). 1 Department of Power Electronics and Machines, Faculty of Electrical Engineering, University of West Bohemia, Univerzitní 26, 301 00 Pilsen, Czech Republic; vegl@fel.zcu.cz (L.V.); skalickm@fel.zcu.cz (M.S.) 2 Department of Electrical and Computational Engineering, Faculty of Electrical Engineering, University of West Bohemia, Univerzitní 26, 301 00 Pilsen, Czech Republic * Correspondence: kaskaj@fel.zcu.cz (J.K.); rpechane@fel.zcu.cz (R.P.) Abstract: The operational reliability and high efﬁciency of modern electrical machines depend on the ability to transfer heat in the construction parts of the machine. Therefore, many authors study various thermal models and work on the development of effective heat dissipation. New insights and methods lead to improved techniques for the thermal design of electrical machines. This paper presents an experimentally validated thermal model of a permanent magnet synchronous motor (PMSM) with an improved slot winding model. It also deals with various approaches to homoge- nization and equivalent material properties of a tooth-coil winding sub-model. First, an algorithm for building a lumped-parameter thermal network (LPTN) of PMSM is described and its properties and problems are discussed. Subsequently, a sub-model of a slot with a winding based on the ﬁnite element method (FEM) is introduced. This sub-model is able to generate different conductor distributions based on probabilistic methods for a speciﬁed ﬁll factor. This allows the veriﬁcation of various homogenization approaches and at the same time it is a tool that automatically calculates thermal resistances for the LPTN. Keywords: electrical motor; synchronous machine; winding model; ﬁll factor; thermal model; modeling; probability; measurement 1. Introduction Today, especially with regard to climate challenges, higher energy efﬁciency and power density of electrical machines are required. This fact brings new challenges in the design of an electrical motor especially for traction applications and electric vehicles (EV). In this day, new types or modiﬁed designs of electrical machines are widely analyzed and researched. One of the most utilized types of electrical motors in the automotive industry is a permanent magnet synchronous motor (PMSM). In recent years, research and devel- opment of PMSM for automotive electric traction machines have greatly intensiﬁed [1–4]. One of the commonly used construction typologies of PMSM in the automotive industry is a machine with tooth-coil winding or a machine with concentrated winding. This brings the advantage of low-cost production, high torque density and high efﬁciency [5–7]. On the other hand, the manufacturing process brings new challenges to the thermal design of a PMSM [8]. Randomly wound windings mean great uncertainties and the manufactured winding can thus differ signiﬁcantly from the winding modeled by conventional methods. The current technical literature divides electric motor thermal analysis and design into two main categories [9]: the thermal design and analyses based on the numerical methods and those based on analytical methods [10,11]. The numerical methods include the ﬁnite element method (FEM) and computational ﬂuid dynamics (CFD). These methods Energies 2021, 14, 2395. https://doi.org/10.3390/en14092395 https://www.mdpi.com/journal/energies