*4.5. Superconductig LIM*

A typical linear induction motor with an iron core and copper windings can only produce limited thrust because of the saturation of the iron core and, in particular, its teeth. Superconducting Linear Induction Motors (SLIMs) are a promising alternative to conventional traction solutions. A novel high-temperature superconducting (HTSC) SLIM was proposed in [26]. This SLIM uses stacks of second generation (2G) superconducting tapes. Such a SLIM, capable of high ampere turns, can generate a strong magnetic field and, consequently, exceptionally large thrust as it can achieve high flux densities over wide air gaps. Commercial 2G HTS tapes utilizing yttrium- and gadolinium-based ceramics (YBCO) can operate up to critical temperatures of 77 K, which can be provided by liquid nitrogen refrigerants. They can carry a critical current of 600 A at 77 K and self-field. These properties make 2G tapes a promising material for use in power electric equipment, including rotating and linear induction machines [23–25].

The conventional variant of such a SLIM has already been analyzed in [29,61,70]. The only additional component of the SLIM is the cryostat, as in [24].

To determine all the crucial parameters of the SLIM, the FEA has been applied. One of the challenges that must be solved is a proper evaluation of penetration of the strong electromagnetic field into the moving and conducting reaction rail. Such modeling and analysis can be extremely difficult and time consuming as it requires a proper choice of the FE mesh (depending on the velocity and slip) [70]. Because of the strong saturation of the laminated magnetic core, classical LIM construction methods may be put into question.

The current density within the HTSC coil was modeled according to the power law for superconducting windings [14]. Figure 17a shows an example of the magnetic field distribution within the subject SLIM, and Figure 17b shows the thrust characteristics for different speeds.

**Figure 17.** Magnetic field distribution within the end part of the SLIM (**a**). SLIM characteristics for different speeds (**b**) [26].

As can be seen from the figures above, the superconducting LIM has significantly increased thrust values compared to a conventional solution. An important computational problem here is the correct modeling of the superconducting windings in the LIM, as well as the correct consideration of the strong saturation of the magnetic circuit.

#### **5. Conclusions**

The paper provides an overview of different linear transportation systems and focuses on the applications that use linear induction motors. Against this background, the authors have presented and discussed new practical methodologies capable of solving some important transportation LIM problems. Despite the LIM's lower efficiency, when compared with the rotary motor, for many applications the LIM system is a superior transport solution that successfully competes against the conventional, rotary-motor-based alternative. This is because the efficiency is a broader concept and the efficiency of a transportation system must be analyzed in the context of the application. For elevated, driverless automated

systems, the LIM is indeed a superior solution because it does not rely on adhesion, has no moving parts, and provides the lowest life cycle and operation and maintenance costs.

Based upon the experience gathered in the subject area of LIMs, the authors believe that future research work should concentrate on increasing the motor efficiency by improving the construction materials and production technology and researching the application of high-temperature superconductivity. This progress must be accompanied by the improvement in efficiency of predictive algorithms and more efficient FEA methods.

LIMs have been known and widely researched by the scientific community but mostly as standalone electric motors. However, LIMs often work as parts of an overly complex transportation system. Thus, future research should take into account the complex interaction of the LIM with its specific system environment.

**Author Contributions:** Conceptualization, R.P. and K.W.; investigation, R.P. and K.W.; resources, R.P. and K.W.; writing—original draft preparation, R.P. and K.W.; writing—review and editing, R.P. and K.W. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.
