*2.5. LTS with Superconducting Induction Motors*

When it comes to LTSs, superconductivity can not only be used for levitation but also for generating a tractive effort [10,21–26]. Superconducting motors have their windings made of low-temperature, conventional, or high-temperature superconductors. A typical linear induction motor with an iron core and copper winding can produce only a limited thrust because of the flux saturation of the iron core. High-temperature superconducting windings can generate a strong magnetic field and, consequently, large thrust. High flux density and high thrust can be produced over a wide gap range because of extremely high ampere turns (see Section 4.5).

Some general problems connected with the electromagnetic fields related to highspeed LTSs driven by different linear motors (synchronous, induction, superconducting) were described in [27].

### **3. Linear Transportation Systems Using Induction Motors**

A LIM can be obtained from its rotary counterpart, the induction motor, by an imaginary process of cutting the rotary's stator and rotor in a radial plane and unrolling it, at the same time as replacing a cage or a winding with a conducting sheet, as in Figure 1.

**Figure 1.** Conversion of rotary machine into LIM.

Should the second primary be added to the single-sided LIM in Figure 1, a doublesided LIM would be formed. Depending on the relative length of the secondary and primary, the LIM can be categorized as a short-secondary (Figure 2) or a short-primary LIM.

**Figure 2.** Short-primary LIM (**a**); short-secondary LIM (**b**).

The rotary motor can be thought of as "infinite" in that its primary winding generated magnetic field is continuous and has no beginning or end around its circumference. Unlike the rotary, the short-primary LIM has a finite length. Thus, only the part of the secondary side that is immediately below the primary is subjected to a primary generated magnetic field. During motion, the new unexcited parts of the secondary side equivalent "rotor" continually enter under the LIM primary magnetic field generated by a distributed Magnetomotive Force (MMF). This process generates a continuous electromagnetic response in the new incoming segments of the secondary, the Reaction Rail (RR), in a form of induced MMF, thereby resisting the immediate establishment of the magnetic flux under the front end of the LIM primary. Subsequently, the reaction rail MMF decays but at a lower rate dictated by the "rotor time constant" of the motor. Figure 3a shows a short-primary LIM, and Figure 3b shows the reaction rail. The RR consists of a series of aluminum top cap

(**a**) (**b**)

segments, connected for electric continuity, and underlying iron bars, the Back Iron (BI), corresponding to the conventional rotor winding and rotor laminations, respectively.

**Figure 3.** LIM primary (supplied part) (**a**); LIM secondary (reaction rail) (**b**) [28].

LIMs can be further classified into a number of other topologies, but so far only the single-sided, short-primary linear induction machine has been successfully used in urban transportation systems [1,2,15]. It seems to be a natural choice since the cost of building an active multiphase primary along a multikilometer guideway would render such systems uneconomical. In most existing urban applications, the primary is suspended under the bogie, over a track-installed reaction rail consisting of either solid or laminated mild steel BI covered with an aluminum extrusion supported on an assembly that permits the transfer of forces to the guideway. In most current applications, mainly in South-East Asia, Canada, and the USA, the guideway is of an elevated, right-of-way type requiring a minimal footprint and does not affect other modes of ground transportation.

As already mentioned, the relative motion between the finite-length primary and the infinite secondary induces a dynamic end effect by creating end-effect currents in the aluminum top cap that demagnetize the oncoming end of the motor. The currents produce additional forces and losses that exist even at synchronous speed and increase with vehicle velocity. The static end effect, another LIM-related phenomenon, occurs because of the phase impedance imbalance caused by the finite length of the phase winding. The effect is amplified by the dynamic end effect, which distorts the air-gap magnetic flux density, having a direct effect on the flux linked to the phase windings. The transverse edge effect is yet another phenomenon characteristic of LIMs. Its major source is the longitudinal component of the top cap induced current. The two major impacts of the transverse edge effect are an increase of the equivalent secondary resistance and an uneven flux distribution across the LIM's primary. Because of the dynamics of the vehicle as well as the RR's limited construction accuracy, the reaction rail is usually offset from the longitudinal symmetry line of the primary side of the LIM, leading to decentralized transverse forces and potential lateral instability. The asymmetrical construction of the reaction rail necessitated by the vicinity of switches aggravates this effect.

Many constraints exist in the high-speed urban electric traction LIM application, which requires a large distance between the LIM primary and the secondary side RR. Running rail and truck deflection, rail canting, and wheel wear are the major reasons for using a large air gap with the LIM. For a gap length of ten to fifteen millimeters, the ratio between the air-gap width and the pole pitch is significant and leakage flux is considerable. The values of up to 100 Hz are not uncommon in today's applications of urban traction LIMs. At the operational slip of around 10–15%, the skin effect in the aluminum cap is not completely negligible. Finally, there are unbalanced normal forces, attractive and repulsive, that add additional complexity in the analysis of the optimal gap and the construction of the motor, as they affect the distance between the lowest point of the primary and the top of the reaction rail top cap.

Because of the differences between the LIM and the rotary machine, unconventional analysis techniques and modeling methods have been developed in an attempt to account for the number and magnitude of LIM-characteristic phenomena.

Many methods of LIM calculation, optimization, and control are identical (or very similar) with the methods applicable to rotating induction machines. The electromagnetic calculations of the rotary motor are reasonably simple because of the motor's "infinite" character and the possibility of applying symmetry boundary conditions, thus limiting the solution region and speeding up the calculations even further. Two dimensional calculations assure sufficient accuracy for the performance prediction of a standard rotary motor. However, the LIM is not symmetrical. The phenomena occurring in the front end of the motor are different than in the receding end and therefore the symmetry boundaries cannot be used, which leads to longer calculation times.
