sustainability Article Comparison of Coupling Coils for Static Inductive Power-Transfer Systems Taking into Account Sources of Uncertainty Yao Pei 1,2, *, Yann Le Bihan 1,2 , Mohamed Bensetti 1,2 and Lionel Pichon 1,2   Citation: Pei, Y.; Le Bihan, Y.; Bensetti, M.; Pichon, L. Comparison of Coupling Coils for Static Inductive Power-Transfer Systems Taking into Account Sources of Uncertainty. Sustainability 2021, 13, 6324. https:// doi.org/10.3390/su13116324 Academic Editor: Lin Li Received: 28 April 2021 Accepted: 28 May 2021 Published: 2 June 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 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 Université Paris-Saclay, CentraleSupélec, CNRS, Laboratoire de Génie Electrique et Electronique de Paris, 91192 Gif-sur-Yvette, France; yann.lebihan@centralesupelec.fr (Y.L.B.); mohamed.bensetti@centralesupelec.fr (M.B.); lionel.pichon@centralesupelec.fr (L.P.) 2 Sorbonne Université, CNRS, Laboratoire de Génie Electrique et Electronique de Paris, 75252 Paris, France * Correspondence: yao.pei@centralesupelec.fr Abstract: The present work aims at comparing different coupling coils by taking into account sources of uncertainty for static inductive power-transfer (SIPT) systems. Due to the maximum transmission efficiency for the SIPT system related to the mutual inductance between coils, the key point here is to make use of a sparse polynomial chaos expansion (PCE) method to analyze the mutual inductance between the transmitter and the receiver. A fast postprocess-sensitivity analysis allowed the identification of which source of uncertainty was the most influential factor to the mutual inductance for different coupling coils. Furthermore, in view of the relationship between the maximum transmission efficiency and the ratio of the length of wires of a coil and the mutual inductance, circular coupling coils should be recommended for SIPT systems. Keywords: inductive power transfer; uncertainty quantification; polynomial chaos expansion; sensi- tivity analysis 1. Introduction Transportation is facing various challenges due to environmental concerns, including the depletion of fossil fuels, global warming, and local pollutin. In this scenario, electrical vehicles (EVs) can widely help to solve these problems. However, the well-known disad- vantages of EVs are the capacity of the battery, the impact of different penetration levels of plug-in EVs, and so on [1]. So, inductive power transfer (IPT) promises convenient, autonomous, and highly efficient charging of EVs [2]. To achieve affordable and efficient coupling coils for IPT systems, many papers [3–6] present different structures of coils and corresponding distinctive features, such as ro- bustness to misalignment, reduction of the magnetic field pollution, or efficiency. Several books [7,8] present general guidelines for the design of the coils. In [9,10], a simulation study was carried out to explore the variation in the coupling coefficient for different coil configurations, but without considering the influence of the ferrite under different air gaps and coil misalignments. In [11], a comparison of different coupler topologies based on several evaluation criteria was performed. The performances of coupling systems were evaluated and compared for various air gaps and lateral misalignments, but the work did not reveal which factor had the greater influence on the efficiency. In [12], parametric performance evaluations of circular, rectangular, and double-sided winding resonant coils were taken into account separately using finite element modeling (FEM) and comprising air gap variation and longitudinal and lateral misalignment. In [13], circular coils were designed and investigated for planar and angular misalignment through the FEM model. Reference [14] proposed the use of an analytical behavioral model, able to relate mutual inductance to a wide range of misalignment conditions for IPT coil system (axial, lateral, Sustainability 2021, 13, 6324. https://doi.org/10.3390/su13116324 https://www.mdpi.com/journal/sustainability