IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 24, NO. 2, APRIL 2014 3600609 Proposed FEM-Based Optimization Method for Economical Design of Long Permanent-Magnet Guideways With HT c Superconductors Arsalan Hekmati Abstract—The levitation force between a superconductor disk and a permanent magnet (PM) is the origin for possible industrial applications. The PMs form the most costly part of the permanent- magnet guideways (PMGs), particularly for longer distances. A heuristic optimization method based on simulated annealing has been proposed for the determination of the optimum arrangement and dimensions of PMs in several PMG structures. This optimum design is the most economical PMG design that guarantees the satisfactory levitation performance of the PMG. As part of the optimization process, a FEM-based method has been used, based on the estimation of penetration depth and self-inductance of the superconductor disk, for the calculation of the levitation force. The optimization results contain the PMG structure with minimum PM consumption for a specified levitation height and supercon- ductor disk characteristics and the variation of the most important PMG features, such as its cost and width, versus those distinctive system parameters. These results will provide basic analysis for the design of HTS-PMG levitation systems. Several guideways have been fabricated based on the optimization process outputs and have shown satisfactory results. Index Terms—Guideway, high temperature, optimization, per- manent magnet (PM), superconductor. I. I NTRODUCTION T HE LEVITATION between high-temperature supercon- ductors (HTS) and permanent magnets (PMs) has re- sulted in a wide range of applications, such as the fields of bearings [1]–[3] and transportation systems [4]–[8], with the main advantages of high or super-high speed, low maintenance, and low energy consumption. Among these devices, there is a large interest in Maglev systems where the levitation of vehicles above PM tracks is attained by the bulk HTS, such as transportation and launching systems, such that, due to their great potential and vast applications, improving the levitation performance of these Maglev systems is particularly important. As the levitation and guidance are the result of the interaction between permanent-magnet guideways (PMGs) and onboard HTS bulk, the PMG plays an outstanding role in Maglev systems, and its optimization is a direct and influential approach Manuscript received July 28, 2013; revised October 17, 2013; accepted December 11, 2013. Date of publication December 23, 2013; date of current version January 15, 2014. This paper was recommended by Associate Editor P. J. Masson. The author is with the Department of Electrical and Computer En- gineering, Shahid Beheshti University, Tehran 1983963113, Iran (e-mail: A_Hekmati@sbu.ac.ir). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TASC.2013.2295840 to improving the levitation performance of the vehicle. Some arrays of PMs such as the Halbach array have been proposed [9]–[11] and applied in electrical machines, magnet bearings, particle accelerators, and Maglev designs [12]–[15]. Works have been done on the modeling of the levitated superconductor [16]–[18], analysis of the applied magnetic field’s impact on the levitation and guidance force [19], [20], and the experimental and numerical evaluations of the levitation force [3], [21]–[28]. In recent years, studies have been performed on the design op- timization of different types of PMGs, changing the orientation or size of the magnets [3], [8], [10], [14], [15], [20], [25]– [27], [29]–[31], modifying the dimensions or arrangements of the superconducting bulks [20], [27], [29], [32]–[35], studying the influence of the cooling process of the superconductor [3], [20], [25], [31], [36]–[41], or analyzing the superconducting levitation and its stability [3], [11], [28], [42]–[50]. In this paper, the application of a heuristic method for the optimization of the PMG design has been studied to make better use of the PMs and the superconductor. In this paper, Bean’s critical-state model has been utilized for the distribution of the current density inside the superconductor disk, and the penetration depth of the magnetic flux is estimated by the method in [51]. The levitation force of the YBaCuO bulk above a NdFeB guideway has been studied in zero-field cooling [32], [52] and is calculated by Ampere’s force density [53], through the calculation of the self-inductance of the superconductor bulk by the formula of Lorenz [54]. The magnetic flux density of the PMG has been calculated via the 3-D simulation of the PMG, which has been implemented using FLUX3D. Considering the influence of the magnet arrangement on the levitation force, a method for the determination of the optimum PMG arrangement is presented, which, being the most economical design, guarantees the satisfactory levitation oper- ation. With the results of this work, we want to establish some guidelines on what the characteristics of the superconductor and magnets of the system should be to achieve a desired levitation force with minimum PM consumption, which is particularly important in lengthy PMGs for long-distance transportation. In the proposed optimization algorithm, the levitation forces are calculated in different PMG structures, and the dimensions of the PMG with minimum PM consumption are determined for specific levitation heights and superconductor disk dimen- sions, for each PMG structure. Based on these optimization outputs, the influence of the distinctive parameters of the sys- tem, such as the levitation height and the superconductor disk characteristics, on the important PMG features, such as its cost 1051-8223 © 2013 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.