Abstract: The working principle of the long stator synchronous linear motor used in maglev trains is introduced, and its electromagnetic design features are pointed out, especially the differences from the design of general rotating motors. An electromagnetic design program is compiled to provide a basis for the calculation of the long stator synchronous linear motor. Keywords: maglev train; long stator synchronous linear motor; electromagnetic design Foreign transportation research reports point out that medium and long distance transportation between large cities with a distance of about 800 km is too far for cars and trains and too close for airplanes, which is very uneconomical in terms of cost. However, this distance is very suitable for maglev trains. Maglev trains can fill the transportation gap between cars, trains and airplanes with a running speed of up to 500 km/h, and can also reduce the pollution of cars and airplanes to the environment [1]. Therefore, maglev trains will become a powerful supplement to the existing transportation system and make it possible to solve the problem of high-speed long-distance transportation in industrial countries. High-speed maglev railway transportation has two major systems: EMS and EDS. EMS (carriage and rolling stock side drive) is an attraction electromagnetic levitation system, and EDS (track side drive) is a repulsion electric levitation system. The development of German maglev trains has gone through the process from EDS with long stator synchronous linear motors, to EMS with short stator asynchronous linear motors, and then to EMS with long stator synchronous linear motors, and finally determined the development route of long stator EMS. German high-speed maglev trains have opened up new prospects for railway transportation with their contactless electromagnetic levitation, drive and guidance systems. Maglev trains have a speed of up to 500 km/h. Although the operating speed is very high, the energy consumption is not large. There is no friction loss during operation, the comfort is good, and the impact on the environment is very small [2]. In addition, its levitation and guidance system surrounds the guide rail (that is, the vehicle wraps around the road surface from the outside), and the levitation, guidance and braking functions are designed to be both redundant and different, so the operation is very safe. After decades of development, the technology of German maglev trains has become mature. At present, several countries such as Germany, the United States and China are considering putting long stator maglev trains into use. In the United States, Las Vegas has decided to use German high-speed maglev trains on its transportation line between the city and Los Angeles; Germany has also launched a large-scale survey on the application of maglev trains domestically, considering the Rhine Corridor/Main-Rhine/Ruhr region as well as northern and southern Germany; Shanghai, China, is building a maglev railway using German high-speed maglev train TR-08 technology, striving to become the world's first practically applied maglev railway. 1 Long Stator Synchronous Linear Motor 1.1 Working Principle The contactless traction technology of the German TR-type maglev train requires the use of a long stator synchronous linear motor for drive. The stator core of the motor is made of 0.15 mm thick electrical steel sheets stacked together and fixed to the lower part of the guide rail; the three-phase stator windings are composed of protective cables, pre-formed, and embedded in the stator slots on both sides of the guide rail by a cable laying machine. After the three-phase stator windings are energized, a moving magnetic field is generated, which interacts with the levitation (excitation) magnets arranged on the vehicle to achieve traction. Its working principle is shown in Figure 1. [align=center] Figure 1 Working principle diagram of long stator synchronous linear motor[/align] In order to obtain constant levitation force, the German TR type maglev train adopts the attraction electromagnetic levitation principle, which generates levitation force by forming an air gap magnetic flux between the stator core of the synchronous motor and the levitation magnet on the vehicle. Its levitation and traction system are combined into one, which is also the advantage of the German TR type maglev train. In order to meet the requirements of high-speed operation of the train, the TR type maglev train adopts an independent guidance system. Steel plates (guide and brake rails) are arranged vertically on both sides of the line, and guide magnets are arranged on both sides of the vehicle, which form a closed loop with the steel plates of the line. After the electromagnet coil is energized, it can generate sufficient lateral guiding force, but the independent guidance system increases the weight of the vehicle and the cost of the line [3]. Because the line is very long, in order to avoid energy loss, the long stator line is divided into independent sections, and the power supply is only connected in the section where the vehicle is located. The power supply is supplied from the substation to the stator three-phase windings installed on both sides of the line. By changing the frequency of the three-phase AC current, the traction force can be continuously adjusted from the standstill to the running speed range. 1. 2 Electromagnetic Design Characteristics Compared with general rotating motors, the design calculation of long stator synchronous linear motors is roughly the same, requiring several parts: magnetic circuit calculation, parameter calculation, rated excitation magnetomotive force calculation, excitation data calculation, loss and efficiency calculation [4]. The difference is that when designing a long stator synchronous linear motor, the characteristics of the long stator linear motor and the differences from general rotating motors must be considered. The main characteristics are: (1) The rotor of a rotating motor is subjected to centrifugal force, while the rotor of a linear motor is not subjected to centrifugal force. (2) The radial unilateral magnetic pull of a rotating motor cancels each other out, leaving only the tangential force, which generates electromagnetic torque; the unilateral magnetic pull of a linear motor does not cancel out, and it is used as a levitation force. (3) The linear motor has edge effect. (4) The stator winding of a general rotating motor works for a long time, and current always flows in the winding; while the stator winding of a long stator linear motor is energized for a short time and works for a short time. In summary, it can be seen that the long stator synchronous linear motor has its own electromagnetic design characteristics, which are summarized as follows: (1) The motor has many poles, Take the number of slots per pole per phase as q = 1; to facilitate the arrangement of windings, the long stator adopts a single-layer winding and is directly buried with cable. (2) The long stator winding works for a short time, so the stator winding current density j1 can be selected to be larger. (3) Since the number of slots per pole per phase is q = 1 and a uniform air gap is adopted, the stator tooth harmonic magnetomotive force is large. The first and second order tooth harmonic magnetic fields generated by it interact with the linear generator winding mounted on the surface of the rotor excitation magnetic pole, inducing AC current in the linear generator winding and outputting electrical power. When the train running speed exceeds 100 km/h, the necessary excitation magnetic energy, air conditioning, lighting devices and auxiliary devices of the vehicle are all provided by the linear generator. (4) The rotor is not affected by centrifugal force and the air gap is uniform, so the main pole no longer needs molded pole shoes. (5) Using the unilateral magnetic pull force as the levitation force, the linear motor needs to calculate the levitation force in addition to the thrust. (6) The edge effect should be calculated using the finite element method. The parameters such as the direct-axis synchronous reactance xd, quadrature-axis synchronous reactance xq and direct-axis transient reactance xd′, as well as the thrust, should be appropriately corrected. (7) The formula for calculating the skin effect coefficient KF of the rotating synchronous motor cannot be used for the linear motor. When the frequency f > 30 Hz, the coefficient of the linear motor with frequency change is taken as KF = 1 + 0.004(f - 30). In addition, due to the different structures, the formulas for calculating the mechanical loss and temperature rise of the rotating synchronous motor are not applicable to the linear motor, and a new calculation formula needs to be adopted. (8) The suspension and traction systems are combined into one, and the excitation required for the motor magnetic circuit can be determined according to the weight of the train. First, the magnitude of the suspension force is determined by the weight of the train, and then the air gap magnetic flux density and air gap magnetic flux are calculated, so that the excitation magnetomotive force required for the magnetic circuit can be determined. (9) The weight of the train can be approximated as a constant during operation. Therefore, the levitation force and the air gap magnetic flux density that generate the levitation force are basically constant. During operation, the excitation current is adjusted to keep the air gap magnetic flux density constant. It can be seen that the thrust is proportional to the stator winding current. (10) From the speed formula v=2fτ, it can be seen that when the frequency increases, the speed increases and the running resistance will definitely increase. Therefore, the required thrust and current must increase accordingly. That is, the running resistance is the greatest when the frequency is the maximum, and the steady-state values ​​of the corresponding thrust and current will also be the maximum. [align=center] Figure 2 Main program flowchart[/align] (12) If the air gap magnetic flux is kept constant during operation, the magnetic flux density of each part of the motor magnetic circuit will also remain unchanged. Therefore, the required excitation magnetomotive force of the magnetic circuit is constant and independent of the frequency. (13) The armature reaction occurs at the location of the train. The calculation of the armature reaction reactance and armature reaction magnetomotive force is the same as that of a general rotating motor. Where there is no train, the stator winding only generates leakage flux and leakage electromotive force. (14) Since the iron loss is approximately 1.3 times the frequency. The iron loss is directly proportional to the power of the frequency and also directly proportional to the square of the air gap magnetic flux density. Since the air gap magnetic flux density remains constant for a given train weight, the iron loss only varies with frequency, reaching its maximum at the highest frequency. Furthermore, since the copper loss is directly proportional to the square of the current, and the steady-state current value is largest at the highest frequency, the copper loss during steady-state operation is also largest at the highest frequency. 1.3 Electromagnetic Design Program Flowchart Based on the electromagnetic design characteristics of the long stator synchronous linear motor, its electromagnetic design program was developed. The main program flowchart is shown in Figure 2. 2 Calculation Example The long stator synchronous linear motor was calculated using this program. The dimensions of the calculation example are shown in Figure 3. The train consists of two cars, with a total length of 54.2 m, a total weight of 108.4 t, a maximum speed of 400 km/h, and a running resistance of 60.4 kN (at 400 km/h). The motor is Y-connected, with a maximum phase voltage of 4500 V and a maximum phase current of 1200 A. The power supply frequency is 0–215 Hz, the number of main pole pairs is 160, the pole pitch is 258 mm, and the air gap is 10 mm. [align=center]Figure 3 Dimensions of a long stator synchronous linear motor[/align] The calculated parameters are: at 75 ℃ and 215 Hz, the stator phase resistance in the 300 m power supply section is 0.2838 Ω, the stator leakage reactance is 210218 Ω, the direct-axis synchronous reactance is 1.1958 Ω, the quadrature-axis synchronous reactance is 0.9433 Ω, the excitation winding resistance is 0.8155 Ω, and the excitation winding leakage reactance is 0.1729 Ω. Other key calculated data are: air gap magnetic potential drop is 11967 A, the required excitation magnetomotive force under no-load is 12630 A, and the required excitation magnetomotive force under rated load is 1 2280 A. The current density of the excitation winding under no-load conditions is 1.79 A/mm2, and the current density of the excitation winding under rated load conditions is 1.74 A/mm2. The rated voltage of the excitation device is 295 V, the rated current is 307 A, and the rated capacity is 90 kW. Within the 300 m power supply section, when the train runs at a constant speed of 400 km/h, the rated phase voltage of the motor is 4441 V, the rated phase current is 758 A, the total loss is 647 W, and the rated efficiency is 91%. 3 Conclusion The working principle of the long stator synchronous linear motor is introduced, its electromagnetic design characteristics are pointed out, and the electromagnetic design program is compiled, providing a basis for the calculation of the long stator synchronous linear motor. References: [1] Liu Huaqing et al. Transrapid Maglev Train: A New Choice for Travelers [M]. Chengdu: University of Electronic Science and Technology Press, 1995. [2] Meins J, Miller L, Mayer WJ. The high speed Maglev Transportation System Transrapid[J]. IEEE Trans. Magnetics, 1998, 24(2): 808-811. [3] Lian Jisan. Principle and technical characteristics of maglev trains[J]. Electric Locomotive Technology, 2001, 24(3): 23-26. [4] Electromagnetic calculation formula for salient pole synchronous motor[D]. Beijing: First Ministry of Machine Building Industry of the People's Republic of China, 1965.