Gyuláné Vincze, Gergely György Balázs
Budapest University of Technology and Economics Department of Electric Power Engineering
Most of the modern high-speed vehicles are driven by linear synchronous motor (LSM). The operating principle of the linear synchronous motor is the same as the rotating synchronous motor and the control method - described in chapter 6.1.1. – can be also applied.
The plane unfolded stator coils of the linear motor are equivalent to the stator of the common synchronous machine, while the linear structure - consist of alternating polarity magnets placed an even distance - is equivalent to the permanent magnet rotor. The magnets can be permanent magnets or excited electro magnets. Basically there are two types of the linear synchronous motor vehicle drives:
linear motor drive with short stator coil, when the active coil of the motor is on the vehicle with the inverter supply and the control, and the alternating polarity magnets are installed along the whole track,
linear motor drive with long stator coil, when the motor coils are embedded in the track, the inverter supply and the control is performed outside the vehicle, only the magnets are on the vehicle.
From these types the B./ solution is preferable at high speed, magnetic levitated vehicles especially in those solutions, where the magnets - built in the vehicle - are also for levitating the vehicle. Although the installation of the track is expensive, this solution has a great advantage: the inverter supply is performed outside the vehicle; the high power electric energy transmission to the moving vehicle would cause difficulties.
The linear motor drive of the Transrapid vehicle is an example for the B./ type solution. The specialty of the Transrapid solution is that the magnets for the traction are the same with the levitating (holder) magnets, therefore these cannot be permanent magnets. The excitation current of the holder magnets are not constant because of the levitation distance control (presented in chapter 7) consequently the flux of the magnets is not constant. At synchronous motor, the alternation of the pole flux appears as a disturbing signal in the traction force control.
Fig.6.8 presents the linear motor drive structure of the Transrapid vehicle. The winding is embedded in the bottom of the track; the levitating magnets are mounted on arms and reach under the track. The holder magnets are a series of electro magnets which are mounted a row in τp pole pitch with alternating N-S-N-S magnetic poles. The figure also represents the winding of the linear generator for the power supply of the auxiliaries.
The three phase winding is installed in the track iron core slots, every third slot belongs to the same phase, which is equivalent to the holder magnets – installed in the vehicle - τp pole pitch, that is shifted electrically with 180°. The a, b, c phase coils follow each other with 2-2 slot shift, that is equivalent to 120° shift in electrical angle. Differently from the common rotating machine, the winding is concentrated (one phase, one slot) and wave winding. The winding of each phase is threaded in every third slot with alternating, back and forth current direction (Fig.6.8.b and c.). The phase winding is single-turn, cable-like with insulated casing, and it consists of three parallel threads to reduce the skin effect.
The stator winding of the three phase linear motor drive is distributed to segments along the track, therefore only those segments should be supplied where the train is running, the whole truck does not need to be supplied. The length of the sectors is different; it varies between 300…2080m. The selection of the length is depending on the energy demand of the given segment, e.g by acceleration or uphill the energy demand increases, and therefore it has a shorter segment. The current supply of each segment is performed by cabling installed under the track.
The tractive force control of the linear synchronous vehicle drive should be achieved with the similar principles that of the rotating synchronous motor drives torque control, that were described in chapter 6.1, by considering that the pole flux field is moving in the direction of the movement referred to the stator winding. To reach optimal tractive force development, the stator winding current time function should be synchronized to this motion, so that resultant stator field – generated by the three phase current - would run together with the pole field and shift ratio would be optimal. The normal motor mode – shown in Fig.6.1.b and 6.3 (sign I) - can be developed if the three phase current generated moving waved stator field is leading to the holder magnet pole field with τ p /2, i.e. electrically 90°. In field weakening mode the leading should be controlled larger than τ p /2 (in accordance to Fig.6.3). For braking -τ p /2 shift, i.e. lagging must be applied. At linear motor d= ± τ p /2 shift current wave is equivalent to the J p=±90° current vector control, to the optimal (energy efficient) mode as it is described in chapter 6.1.
The Fig.6.9 represents the red stator field in such time instant when the symmetry axis of the magnetic flux positive pole is getting close position to the a+ coil side. Based on the projections of the current vector in Fig.6.9.b, the required i a, i b, i c phase currents for a given tractive force and for this time instant can be defined. In dt time intreval the vehicle is moving ds=vdt distance. For generating the same tractive force, the current vector should be turned with ds(180°/τ p ) electric angle, to keep the ϑp electric angle unchanged. The time functions of the phase current should be varied depending on the vehicle motion.
For accelerating the vehicle and increasing the traction force, the current vector magnitude should be increased, keeping the previous phase position. If the vehicle is running with constant speed, then similarly to the rotating machines the currents of the stator coils are three phase, shifted with 120° in time and symmetrical sinusoidal AC currents. If the vehicle is accelerating, then the frequency of synchronized moving wave should be increased in the stator coils. The fundamental frequency of the three phase current is f=v/λ, where v: vehicle speed, λ=2τ p : wavelength. f=270Hz fundamental frequency belongs to 500km/h speed (~140m/s) if we calculate with τ p=25,8cm pole pitch of the magnets applied in the TR 08 type vehicle. Consequently such inverter is required for supplying the stator coils which can vary the fundamental frequency of the supplying voltage in 0-270Hz range. (ds/dt)(180°/τ p )=v(π/τ p )=2πf electric angular frequency belongs to v=ds/dt vehicle speed (Fig.6.9.b).
Similarly to the rotating synchronous drives, the regenerative braking of the vehicle can be reached if the displacement angle of the stator excitation wave is changed to negative (lagging instead of leading), that reverses the tractive force direction. In such cases the linear motor is operating as a generator. The braking is completed with eddy current brake can be found on the side of the vehicle at the height of the side guiding magnets.
The winding of the linear generator of the vehicle auxiliaries’ energy supply can be seen in the crown of the magnetic poles (Fig.6.8). The linear generator uses that the slots of the track iron core distort the flux density fundamental component, therefore magnetic harmonics are also generated in the air gap. The linear generator detects the change of the harmonic flux density caused by the vehicle motion, and the generated induced voltage supply the auxiliaries.
Besides the vehicle drive the described structure of the track allows the vertical levitation also. The ferromagnetic laminated iron core – the stator winding is installed into its slots - consists of parts connected tightly to each other and it is continuous along the whole track in each side. The stator winding can be discontinuous but the iron core cannot. The continuity is important because attractive force is exerted to this iron core by the levitating magnet that controls the vertical position of the vehicle. The strength of the tractive force exerting moving wave stator field is much lower than the strength of the holder magnet. Since the locomotive is running on air cushion without friction, the tractive force demand is lower than the force required for the levitation. The levitation methods of the vehicles are presented in chapter 7.
(The literature used for this chapter: …)