## 3 Numerical Modeling and Novel Technologies and Materials
### Superconducting Material Based Electrical Machines  
Superconducting materials have a set of particular electromagnetic properties. Under a certain critical temperature, their resistivity is negligible, and the magnetic flux density is expelled from the material. This perfect diamagnetism is called the Meissner effect, i.e., the exclusion of the magnetic field from the core of the superconducting material. High Temperature Superconducting (HTS) materials for power applications, such as electrical machines, are commercially available under the form of bulks and tapes. Bulks, mostly made of Yttrium-Barium-Copper-Oxide (YBCO) alloys, are obtained by a process known as Top-Seeded Melt Growth (TSMG), which consists of a method to fabricate single or multiple grain superconductors. The seeds, which act as nucleation centers, are placed on the top surface of YBCO compacted pellets and subjected to heat treatment processes, followed by melt texture growth heating cycles in order to meet the bulks. Unfortunately, the TSMG process is confined to small-scale and simple material geometries [265; 266; 267]. Besides scale limitations, bulks are susceptible to cracking due to irregular thermal expansion of their body, and therefore, long-term operation can be compromised [268]. In the case of tapes, most adequate for large-sized machines due to the long length of tape available and mechanical robustness, the most common compounds are Bismuth-Strontium-Calcium-Copper-Oxide (BSCCO), i.e., First-Generation (1G) tape, and YBCO, i.e., Second-Generation (2G) tape. The latter are best suited for working in higher magnetic fields than 1G tapes [269]. When compared to 1G tapes, 2G tapes take advantage of their improved properties, such as mechanical robustness, operation at a higher magnetic field, and critical current. These 2G coated conductors are manufactured by a continuous process using thin film deposition techniques in order to apply the superconducting material to buffered metal substrates. The manufacturing steps include electroplating, sputtering, electro-polishing, Ion Beam Assisted Deposition (IBAD), and Metal Organic Chemical Vapor Deposition (MOCVD). The IBAD process consists of the sputtering of a stack of buffer layers that develop a texture for the superconductor material's deposition. MOCVD is the deposition of the superconductor, based on Rare-Earth elements with Barium-Copper-Oxide (REBCO) materials. Further details concerning the manufacturing process can be found in [269; 270; 271]. On the other hand, Magnesium Diboride (MgB2) presents an alternative to YBCO and BSCCO [272]. Despite not being the natural choice since it requires lower cooling temperatures than YBCO or BSCCO, the MgB2 superconducting material benefits from lower prices. Commercial MgB2 is fabricated by a Powder-In-Tube (PIT) process. The manufacturing process was addressed in [273]. The wide availability of raw materials and decreasing fabrication costs lead to a trade-off between material price and cooling costs, and it is expected to compete with YBCO and BSCCO. One of the main advantages of superconductors is the possibility of generating high magnetic flux densities with smaller amounts of material, when compared to conventional materials, such as copper coils or PMs [274]. Therefore, the design of electrical machines can benefit from these superconducting materials, allowing us to build smaller and lighter machines when compared to conventional ones. From DC machines (i.e., commutator and homopolar types) to AC machines (i.e., induction, homopolar, and synchronous), superconducting materials can be employed in every machine type [268]. By using a superconducting material for the excitation winding, field winding losses are practically negligible in DC conditions. In AC conditions, losses are reduced, but not negligible, mainly due to the AC loss phenomenon [275; 276]. On the other hand, cryogenics can also present a design challenge since it can increase the size and costs of the device [277].