*2.1. Configuration and Design Specifications*

Several design topologies of SCs have been developed to minimize the capital and operating costs. The di fferent configurations can be classified based on the superconducting layer layout for each phase and the voltage level. One design, known as triaxial configuration involves three di fferent phases attached onto a single former, contained in a single cryostat [1] as shown in Figure 1. The three phases are separated by a dielectric layer which provides electric insulation. The circulating liquid

nitrogen flows between the copper screen and the inner cryostat wall to cool down the entire cable to a temperature range of 65–77 K [31]. This configuration offers higher carrying current capacity, and has the lowest inductance compared to other cable designs. Regarding the position of the insulation layer, SCs can be separated into two categories, namely the warm dielectric (WD) and the cold dielectric (CD), with the latter to be the most preferred design due to low losses and higher current capacity [32]. In this paper, a CD triaxial SCs with YBCO wires has been modelled. The detailed structure of the SCs tape is demonstrated in Figure 2.

**Figure 1.** Configuration of triaxial SCs cable.

**Figure 2.** Configuration of SCs tape.

The typical structure of the YBCO tape consists of the YBCO layer, the copper stabilizer layer, the silver stabilizer layer, the Hastelloy substrate and the buffer layer which is placed between the substrate and the YBCO layer [33]. The YBCO layer, which is the only layer responsible for conducting the load current during the steady state operation, is manufactured as a film with very small thickness, protected by copper stabilizer layers on both sides. In the superconducting wire, a stabilizer layer (such as copper) is connected in parallel with the HTS layer to maintain stability, reduce the heat generation and the temperature during high current faults, and protect the cable from thermal-induced damage. This technique has been introduced and adopted by major manufacturers [34–37]. For the fault analysis, due to the parallel structure of the layers, the total fault current flowing through each phase must meet Equation (1),

$$I\_{\text{total}} = I\_{HTS} + I\_{\text{Copper}} \tag{1}$$

where *Itotal* is the total current, *IHTS* is the current in YBCO layer and *ICopper* is the current flowing in the copper layer. Specifically, as it is illustrated in Figure 3, in steady state, during which the HTS tapes are in the superconducting state, the load current only flows through the HTS layer (i.e., as presented by Equation (2)), due to its very low impedance compared to that of the copper stabilizer,

$$I\_{\text{total}} = I\_{\text{HTS}} \tag{2}$$

**Figure 3.** Operation of HTS cable during (**a**) steady state (**b**) fault.

In this case, during the steady state, the *ICopper* is approximately zero.

In transient conditions, once the fault current exceeds the value of the critical current *IC* the HTS tapes quench and their resistivity increases exponentially. Furthermore, the temperature of the HTS tapes is affected by the generated heat. The temperature increases gradually and exceeds the value of the critical temperature *TC*, indicating the transition to the normal state. Once the HTS tapes enter the normal state, the variable resistance, which is a function of the current density *J* and the temperature *T*, reaches values which are much higher than that of the copper layer. Hence, the transient current is diverted into the copper stabilizer layer, as expressed in Equation (3), which acts as a by-pass circuit. Thus, the effect of the stabilizer layer is important for the transient studies,

$$I\_{total} = I\_{Copper} \tag{3}$$

where *ICopper* is the diverted fault current, flowing through the stabilizer layers, while a very small current (approximately zero) flowing through the HTS layers.

Based on the analysis presented above and according to the study conducted in [37], the boundary of the critical current *IC* determines whether or not the superconducting tape quenches. Thus, exceeding the threshold of *IC* can be considered as the impelling factor that leads to quench, while the threshold of the critical temperature *TC* determines if the superconductor will enter the highly resistive normal state. Therefore, it can be defined as a criterion for the degree of quenching. To further study the performance of the integrated HTS cables, it is of major importance to investigate in more detail the transition period from the superconducting to the normal state. To study the quenching process, special focus should be given to the current distribution among the layers and the resistance variations with respect to the accumulated heat and the current amplitude. In the following part, the proper design of a simplified model of multilayer HTS power cable will be presented.
