*1.1. Characteristics of Superconducting Cables*

In recent years, the deployment of Superconducting Cables (SCs) in power system applications has become widely accepted due to their unique characteristics. Several prototype projects have been carried out worldwide which proposed the utilization of different configurations of SCs as a viable solution for bulk power transmission [7–12].

Compared to conventional cables, SCs are characterized by a plethora of technically-attractive features, such as higher current-carrying capability [13], higher power transfer at lower operating voltages and over longer distances [1,14], lower losses due to their lower resistance compared to that of overhead transmission lines [15], and more compact size due to their high current density. Therefore, the installation of SCs is considered a promising solution against congestion, especially in high power density areas such as metropolitan meshed networks. Furthermore, their fundamental property of transferring power over long distances, at low voltage levels, renders them the most effective way to interconnect renewable energy sources, such as offshore wind farms, to the power grid.

The superconducting behavior appears after cooling down the superconductor below a characteristic temperature, known as critical temperature *TC*, which has a specific value for each superconducting material [16–19]. The maximum value of the current that can be conducted through the superconductor without encountering increase in the resistance value is called critical current *IC*. However, superconductors lose their superconductivity if the magnetic field reaches its critical value *HC* or in case the temperature increases beyond *TC*. This phenomenon is called quench. These remarkable physical properties of SCs make them capable of conducting currents with approximately zero electrical resistance during steady state, while their variable resistance, which is dependent on the load current, in conjunction with the introduction of a high resistive layer into the superconducting wire, such as copper, result in fault current limitation in short-circuit situations. The contribution of SCs to fault current limitation is determined by the design.

#### *1.2. Challenges Associated with the High Temperature Superconducting Cables Installation and the Superconducting Cables (SCs)*

The discovery of HTS materials created the opportunity of applying the superconductivity principles to electric power devices such as, superconducting machines and SCs. The major advantage

of the HTS materials is that their high critical temperature values, *TC*, are attainable using liquid nitrogen, *LN*2, as coolant with a boiling temperature of 77 K [20–22]. For the presented case studies, the Yttrium Barium Copper Oxide (YBCO) material has been chosen with *TC*(*YBCO*) = 93 K, which belongs to the 2nd generation of HTS tapes (2G), as its transition from the superconducting state to normal state lasts for a few milliseconds, which makes it attractive considering the fault current limitation capability [8].

In addition, one of the most challenging tasks to be achieved is the connection between HTS cables and existing conventional circuits [23–25]. It is important to understand that the direction and the magnitude of power flows could be a ffected by the installation of HTS cables, due to their low impedance. During steady state conditions, HTS cables operate at the superconducting state, presenting the current path with approximately zero resistance and as a consequent, attracting naturally the power flow. These significant changes in the current distribution and the rearrangements of power flows must be considered in order to maintain power system stability.

Furthermore, the installation of HTS power cables impacts on the short-circuit level of the power system. The changes in the short-circuit level, and as a consequence the changes in the fault currents, affect the performance and design of power system protection schemes. The incorporation of the copper parallel layer and fault current limiting features in SCs cables have made them increasingly appealing for power system applications [26,27]. In steady state condition SCs transmit bulk power with low losses. Under fault conditions, when the fault current flowing through the HTS tapes exceeds the critical current *IC*, the superconducting tapes will automatically quench and switch to normal resistive state. As the fault current increases, the resistance and the temperature of the cable increase as well, as interdependent variables. The transition from the superconducting state to the normal resistive state during short circuit conditions can occur within milliseconds (i.e., within a single AC cycle). Consequently, the integration of the fault current limiting feature into the HTS cable can limit the short-circuit current to a certain point, helping towards protecting the system [27]. This property of the SCs creates new challenges for the power system protection, as the calculation of the expected short-circuit level must be conducted in accordance with the variable resistance of the installed SCs.

The paper is organized as follows: Section 2 presents the detailed mathematical development of the utilized cable based on well-known equations which explain the behavior of superconductors. The model is developed using Matlab and Simulink software and is applied to a power system which contains wind farms and synchronous generators. In Section 3, di fferent fault scenarios are carried out which aim to investigate the cable performance during transients and verify the practical feasibility of the proposed SCs model.

#### **2. Modelling of SCs with 2G HTS Wires**

Various numerical models of HTS cables have been recently proposed, which use the Finite Element Method (FEM) or finite-di fference time-domain (FDTD) analysis to understand the non-linear electromagnetic properties of the superconductors [28–31]. The investigation of the electromagnetic and thermal properties of the HTS cables is an e ffective way to predict and optimize the cable performance under di fferent operating conditions. However, for power system studies such as fault analysis, the performance of the numerical models using FEM and FDTD is compromised due to the computational complexity [30]. Thus, a simplified time-dependent model of a multilayer HTS cable will be analyzed in this research, providing a solid foundation for the utilization of SCs in power system applications.
