0278-0046 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TIE.2018.2821091, IEEE Transactions on Industrial Electronics IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS Abstract—Among position sensors, resolvers are superior from reliability point of view. However, obtaining lower output voltage harmonics and simple manufacturing process is a challenge in the design and optimization of resolvers. In this paper, a meta-heuristic optimization algorithm is used to minimize total harmonic distortion (THD) of the output signals, and consequently the estimated position error in concentrated coil, wound field resolvers. Meanwhile, to minimize total coil numbers, manufacturing cost and complexity of the winding process, modified objective function and constraints are proposed. In this way, a modified winding function (MWF) method is employed for performance analysis of axial flux resolver. Then, the merits of the optimized winding configuration with respect to fractional slot concentrated windings are shown. The results of the proposed configurations are verified with 3-D time stepping finite element method. Finally, the prototype of the studied axial flux resolver is constructed and tested. Good agreement is obtained between simulation and experimental results, confirming the effectiveness of the optimization process. Index Terms—Position sensors, Axial flux resolver (AFR), modified winding function (MWF), Concentrated winding, Total harmonic distortion (THD), Genetic algorithm (GA), Finite element method (FEM), Permanent Magnet (PM). I. I NTRODUCTION HANKS to the resolvers’ ability to work in the environments that are polluted with dust, fog and oil mist combined with mechanical vibrations and temperature variation, these types of magnetic sensors have found wide use in automation systems, electrical vehicles, drive of PM machines, wind turbines, aerospace and military applications [1]-[5]. However, some challenges exist when the accuracy Manuscript received Month xx, 2xxx; revised Month xx, xxxx; accepted Month x, xxxx. This w ork was supported in part by Research office of Sharif University of Technology and Niroo Research Institute. R. Alipour-Sarabi, Z. Nasiri-Gheidari, and H. Oraee are w ith the Electrical Eng. Department, Sharif University of Technology, Tehran, Iran, (e-mail: ramin.alipoursarabi@gmail.com, znasiri@sharif.edu, oraee@sharif.edu). F. Tootoonchian is w ith the Electrical Eng. Department, Iran University of Science and Technology, Tehran, Iran (e-mail: tootoonchian@iust.ac.ir) and manufacturing difficulties are taken into account [ 6]-[9]. Investigations dealing with resolver-associated problems can be categorized into two groups: Some studies have focused on resolver-to-digital (R/D) converter [10]-[12] that intend to compensate the estimated position error by means of electronic circuits and control loops. On the other hand, to lower electromechanical errors and manufacturing costs, modifications on the machine structure such as rotor contour [13]-[16], rotary transformer [5], [15], slots’ shape [17]-[19], and slot-pole combination [17], [20] have attracted much attention in recent years. Investigation on winding configuration with various degrees of freedom is an appropriate solution to control output voltage harmonic contents in resolvers [17], [21], [22]. To increase torque density and decrease torque ripple, modern PM machines are equipped with high pole numbers [ 23]. Therefore, to have an effective control on stator currents, absolute rotor position estimation is necessary [24]. In this regard, resolvers as position sensors must follow the PM’s pole numbers [22]. As a consequence, resolvers with high pole numbers have attracted attention in many recent investigations [1], [13], [20]. Similar to the conventional electrical machines, resolvers are equipped with distributed or concentrated windings. Distributed winding, leads to lower spatial harmonics [25]. However, when the pole numbers increase, lower value of slot per pole per phase ( ) will result in high harmonic contents in the output voltages [17]. In [26] it is shown that as the inducted harmonics increase, the estimated position error will increase. In fact, since the estimated position is the arc tang of the output signals, as the output signals contain lower harmonic contents, the estimated position will be less damaged. Therefore, the lower THD of output voltages is, the more accurate estimated position is. Although a decrease in  can be compensated by increasing the slots number, manufacturing problems and tooth saturation makes it difficult to use distributed windings in cases with high pole numbers [22]. In order to achieve high pole numbers, variable turn concentrated winding (VTCW) is suggested in [21] and [27] for variable reluctance resolvers and PM machines, respectively. Concentrated winding, offers higher power density, lower end windings, higher efficiency, fault tolerance capability as well as higher sub-harmonics [27]. Furthermore, in VTCW the turn number of coils in each slot Improved Winding Proposal for Wound Rotor Resolver Using Genetic Algorithm and Winding Function Approach R. Alipour-Sarabi, Student Member, IEEE, Z. Nasiri-Gheidari, Member, IEEE, F. Tootoonchian, Member, IEEE, and H. Oraee, Senior Member, IEEE T