2656 IEEE TRANSACTIONS ON MAGNETICS, VOL. 46, NO. 7, JULY 2010 Modeling and Analysis of Linear Synchronous Motors in High-Speed Maglev Vehicles Monir Sadat Hosseini and Sadegh Vaez-Zadeh Advanced Motion Systems Research Lab, School of Electrical and Computer Engineering, College of Engineering, The Center of Excellence on Applied Electromagnetic Systems, University of Tehran, Tehran, Iran Accurate knowledge of magnetic field distribution and thrust and normal force calculation in linear synchronous motors are essential for assessing performances and design of the motors. In this paper, two-dimensional field distribution produced by dc excitation of sec- ondary and ac currents of primary of a high-speed single-sided wound secondary linear synchronous motor is obtained by an analytical method solving Maxwell equations in the motor layers. Further, the determination of electromagnetic forces of this type of motor is pre- sented. The results are compared with those obtained from an adopted base model and the finite-element method (FEM). Anisotropy, field harmonics and primary slot effects are investigated. Good correlations between the results obtained by the proposed method and the finite-element method confirm the superiority of the former method over the base method. Index Terms—Electromagnetic analysis, electromagnetic fields, electromagnetic forces, finite-element analysis, linear synchronous motors, modeling. I. INTRODUCTION E XTRA high-speed rail transportation has progressed by different Maglev technologies for decades [1]. Two major competing technologies are German Transrapid and Japanese superconducting systems [2]. The former uses electromagnetic levitation while the latter enjoys a totally different electro- dynamic levitation. However, both systems are propelled by wound secondary linear synchronous motors due to salient features of this type of motor [3], [4]. A linear synchronous motor (LSM) enjoys high efficiency due to a lack of slip losses and high magnetizing current. In Maglev applications the motor does not require contactless high power transmission as it is essential for induction motors. Also, the machine power factor can be controlled to higher values than a fixed power factor which is obtained by a comparable induction motor at the same output power and speed. Higher efficiency and power factor lead to a significant reduction of in- verter rating, resulting in a substantial cost saving. Many aspects of LSMs have been studied in the literature, including their modeling, analysis, design and control [5]–[10]. Among these studies the machine modeling plays a fundamental role since it is required for all other studies. Early attempts on LSM modeling are just marginal modifications of rotary syn- chronous machine modeling in which a rotational speed is re- placed by a translational velocity [11]. This type of modeling ig- nores the essential topology of LSMs, i.e., the machine flatness and its consequences like the phenomenon of end effect. This phenomenon in particular, has significant effect on machine per- formance especially at high speeds. Therefore, the traditional LSM modeling is not appropriate to high-speed applications. Manuscript received March 02, 2009; revised June 22, 2009 and September 04, 2009; accepted December 10, 2009. First published March 04, 2010; current version published June 23, 2010. Corresponding author: S. Vaez-Zadeh (e-mail: vaezs@ut.ac.ir). Digital Object Identifier 10.1109/TMAG.2009.2039999 Recent efforts overcome the shortcoming of early modeling methods by finite element method (FEM), taking into account the linear topology of the machines [5]–[7]. However, a FEM model although accurate in studying machine performance, lacks analytical studies. Therefore, they face limitations in tasks like design optimization of machines. A FEM analysis can evaluate a final design but it is not time efficient during design procedures, since it needs many long iterations to reach a desirable design. The thrust and levitation force characteristics of an electrodynamically levitated linear synchronous motor are calculated analytically [8]. However, the field distribution of the motor is assumed to be known for example from a FEM model. Some researchers have presented approximated - models of LSMs [9], [10]. These rather simple models are useful for machine analysis and control. However, they are not accurate enough for design and optimization purposes. More recently an analysis and design of a short primary linear syn- chronous motor for high-speed applications has been presented, ignoring the effect of permeability of the iron core of elec- tromagnets on the field distribution [12]. Many recent studies have focused heavily on permanent-magnet LSMs [13]–[26]. Different analytical and numerical methods for such machines have been presented [27]–[29]. However, permanent-magnet LSMs are mainly used in low-power automation applications. They still are not considered heavily in high-power high-speed applications like Maglev. This paper aims at presenting a full analytical model of wound secondary linear synchronous motors (WSLSMs) con- sidering some features of the motors missing in the existing literature, e.g., the field harmonics and anisotropy. A primary attention is paid to the field and force calculations by taking into account the flatness of machines. A layer model approach is followed and rather accurate expressions are obtained for the machine characteristics. The main contribution of this paper is modeling of a wound secondary motor instead of a machine with a coreless or a permanent-magnet secondary as reported in the literature [30], [31]. Therefore, the iron core of the secondary is taken into account. A second model is also 0018-9464/$26.00 © 2010 IEEE