One of the unique properties of the power system operation is that the electrical speed of all generating units must be the same (Padiyar, 2004). This is known as the synchronous operation of the power system. However, any disturbance to the power system operation can affect the rotating speeds of rotors, i.e., the network frequency (Kundur, 1994; Anderson and Fouad, 2003; Kundur et al., 2004; Padiyar, 2004; Grigsby, 2012). The transient stability (large-disturbance rotor angle stability) is defined as “the ability of the power system to maintain synchronism when subjected to a severe disturbance, such as a short circuit on transmission facilities, loss of generation, or loss of a large load” where the small-signal stability is defined as “the ability of the power system to maintain synchronism when subjected to small disturbances, such as switching of small loads, generators or transmission line tripping, for which the equations that describe the dynamics of the power system may be linearized for analytical purposes.” (Kundur, 1994), (Kundur et al., 2004; Das, 2007; Machowski et al., 2008). It is essential to note that the transient stability is dependent on the operating condition and the perturbation, which makes the analysis of the transient stability more complicated. Also, the linearization analysis does not apply to transient stability analysis (Padiyar, 2004). Under a transient event, the system response involves large excursions of generator rotor angles, power flows, bus voltages, and other system variables. If the resulting angular separation between the machines in the power system remains within certain bounds, the system maintains synchronism. Loss of synchronism because of transient instability, if it occurs, will usually be evident within 2–3 s of the initial disturbance (Kundur, 1994).

The fault levels in the power system drastically increased due to various reasons. For example, the integration of multiple energy sectors (Zheng et al., 2020), the continuous increase in electricity demands, the massive scale of the power plants either conventional or renewable generation, and the expansion of power grid (Koyama and Yanabu, 2009; Sung et al., 2009; Li et al., 2014). Therefore, the stresses caused by excessive fault currents led to high mechanical, electrical, and thermal instabilities of electric networks (Lee et al., 2008). Consequently, the electrical apparatus might be damaged and cause a partial blackout or even a major blackout if the existing switch gears are not upgraded (Anderson and Fouad, 2003), (Grigsby, 2012), (Miyashita et al., 2005; Kodle et al., 2016; Glover et al., 2017). These changes are the main concerns for the transmission system operators because an increase in the fault levels negatively impacts the power system in terms of security and reliability (Ravindranath and Chander, 1977). Therefore, fault-limiting techniques are required. Many effective methods were used, for instance, bus splitting, current limiting reactors, and others. However, each of these has its own limiting factors. For example, using bus splitting will reduce the reliability of the interconnected system. Also, series reactors have drawbacks such as constant high reactive losses, bulky, and contributing to grid voltage drops. Therefore, a new technique should be utilized to overcome the disadvantages (Blair et al., 2012; Son et al., 2012; Jain et al., 2016). Different methods were used to mitigate the transient instability, such as flexible AC transmission system (FACTS) controller, which includes static VAR Compensator (SVC), thyristor-controlled series capacitor (TCSC), static synchronous series compensator (STATCOM) and unified power flow controller (UPFC) (Kamarposhti et al., 2021), (Wang et al., 2020).

Superconducting fault current limiters are superconducting power equipment whose impedance is small in steady-state condition and large in a fault condition. Therefore, SFCLs do not deteriorate power system stability in steady-state conditions and effectively limit the short-circuit currents in a fault condition (Sjostrom et al., 1999). Different types of SFCL are available in the market; resistive SFCLs, shielded Core FCL, SFCL bridge, and saturated iron core FCL. The Resistive SFCLs have been the primary choice for SFCL field experiments. Its popularity due to its simple concept, compact size and weight, and resistant nature (Blair, 2013). The shielded iron core SCFCL, or often called inductive SCFCL advantageous is that there is no current lead to cryogenic temperatures and that the superconductor is exhibited to large currents but low voltages. Like resistive SCFCLs, a quench takes place in the superconductor and therefore a recovery time of several seconds is needed. However, A major drawback of this type is the large volume and weight which is similar to a transformer of the same power rating (Noe and Steurer, 2007). SCFCL bridge rectifiers are made up of diodes or thyristors arranged in a complete bridge configuration. This SFCL type is undesirable because it no longer controls short-circuit current if, for example, one of the semiconductors fails and causes a short circuit. Furthermore, the total losses are rather substantial.

SFCLs are used to minimize the short circuit current to a definite value and have the ability to decrease the levels of fault current within the electricity grid by factors of 3–10 times (Baldan et al., 2007), (Egorova et al., 2013). Under normal circumstances, SFCL is quenched to a temperature of approximately −200°C, which can be accomplished in a cost-efficient way by using liquid nitrogen (Blair et al., 2012), (Sjostrom et al., 1999), (Lee, 2011), (Vojenčiak et al., 2016). This will minimize the material’s resistivity, which means that it will not have any influence on the network under normal conditions (Matsumoto et al., 2010), (Yonemura et al., 2015). However, if the current goes above the nominal, the materials instantaneously lose their properties of superconductivity and work as a typical resistor. During that situation, the current will be reduced to a predefined value (Lee et al., 2008), (Wang et al., 2014). These properties make superconductors work as a self-triggered current limiter. Moreover, significant features introduced by the superconductors, such as negligible voltage drop and energy losses during steady-state operating conditions, enable higher grid loads without upgrading the equipment in the power system (Kovalsky et al., 2005; Zhang et al., 2015; Kumar et al., 2016).

The normalized non-linear relationship between current flow in a superconductor and its resistance is demonstrated in Figure 1. It can be seen from Figure 1 that when a fault develops, the current rises, causing the superconductor to quench and exponentially increase its resistance. Most SFCL designs consider the above behavior to limit the fault current in the first cycle [Electric Power Research Institute (EPRI), 2009], (Khatibi and Bigdeli, 2014). Under normal grid operation, resistive SFCLs use superconducting material as the main current-carrying conductor. The principle of operation is shown in the single-line diagram in the upper half of Figure 1. As mentioned before, the lower plot is a normalized performance of the voltage across R _sc as a function of the ratio of the current through the SFCL device (I _Line )to the critical current (I _c ) of the superconducting element. The level of the current at which the quench happens is identified by the operating temperature, the size, and the category of the superconductor. The quick rise in resistance produces a voltage across the superconductor and leads the current to convey to a shunt, a combination of resistor and inductor. The shunt’s role is to limit the voltage increase across the superconductor in the quench situation. In essence, the superconductor works like a switch with a millisecond response that stimulates the transition of the load current to the shunt impedance. Theoretically, the initial fault current is restricted to less than one cycle [Electric Power Research Institute (EPRI), 2009].

Eq. 1 describes the characteristics of the resistive type of SFCL behavior (Chen et al., 2016a), (Moon et al., 2011). R t = 0 t < t 0 R n 1 − e − t − t 0 T 1 / 2 t 0 ≤ t < t 1 C 1 t − t 1 + D 1 t 1 ≤ t < t 2 C 2 t − t 2 + D 2 t 2 ≤ t < t 3 (1)

R _n denotes the SFCL’s normal-state resistance; T is the time constant. The SFCL’s time-domain characteristics of t0, t1, and t2 indicate the quench-starting time, the first recovery-starting time, and the secondary recovery-starting time, respectively, as shown in Figure 2. The function coefficients are C1, D1, C2, and D2, as stated in Eq. 1 (Sung et al., 2009), (Chen et al., 2016a), (Elshiekh et al., 2013), (Lim et al., 2009).

In this paper, the resistive SCFL is used to verify that the fault current can be minimized significantly. Also, the transient stability of the power system can be enhanced without tuning the PSS. There are difficulties in tuning the PSS because the technique used, simulation study, field implementation, and the number of standard tests to be undertaken for its evaluation differ from utility to utility and vendor to vendor. As a result, the power system planner and the operator must examine and evaluate the efficiency of PSS tuning following the stated criteria for the specific power system. Nevertheless, many power plants have been reported to have tuned their PSS at unit commissioning, during automatic voltage regulator (AVR) modernization, or based on system operator observation/feedback (Wang et al., 2019).

It should be noted that refs (Miyashita et al., 2005), (Pawar and Chavan, 2017), (Mohamed, 2012), and (Wang et al., 2018a) used a single-machine infinite bus (SMIB) to study the improvement of the transient stability by using SCFL. However, each area contributes to the short circuit within the interconnected network in the interconnected power system. Therefore, this paper uses a two-area system with four synchronous machines to analyze the impact of resistive SCFL on angle stability. Different fault locations and fault types are considered in the analysis. Also, the optimal location and value of the resistive SFCL were analyzed.

To design a resistive SCFL, five parameters need to be defined (Sung et al., 2009), (Zhang et al., 2015), (Alaraifi et al., 2013), (Wang et al., 2018a):

1 The triggering current (the value at which the SFCL will be stimulated).

All these parameters have been taken into consideration in designing SFCL. The design of the single phase of the step resistance SFCL model is shown in Figure 3. The principle of operation can be described as follows: firstly, the current measurement is used to measure the current of each phase to compute the absolute and RMS values of the phase line current by RMS block. If the RMS current is less than the triggering current, then the model will consider the SFCL in the normal operating state (superconductivity situation), and the SFCL will take a resistive value of 0.0 L Ω (the minimum resistance). Otherwise, if the RMS value of the line current is higher than the triggering current, then the model will lose the superconductivity state and increase rapidly to the maximum predefined value. Lastly, the fault current drops below the triggering current because the fault was cleared, and the SFCL restores the superconducting condition after recovery. The transport delay block is installed to implement the maximum resistance for 1 s from the moment the fault occurs. The resistive SFCL is connected in series with the transmission line in the event of a short circuit. According to the above-mentioned, the summary of the parameters used in the SFCL modeling can be represented in Table 1.

The interconnected two-area system is shown in Figure 4. The system consists of two similar areas connected via a weak tie line (230 kV lines of 220 km length (Kundur, 1994)). Each area has two synchronous generators, and there are 967 MW, and 1767 MW loads at area 1 and area 2, respectively, and the system operates with area 1 exporting 400 MW to area 2; detailed parameters in the Appendix A1. Figure 4 shows the proposed locations of the resistive type SFCL in the interconnected power system, case 1 in Figure 4A, and case 2 in Figure 4B. The power system has been modeled in MATLAB and SIMULINK software to perform different scenarios. In the simulation studies, different types of faults are applied in different locations on line one to demonstrate the performance of SFCLs.

The short circuit current at bus i can be calculated as follows I s c = E i Z i i (2) where is Z i i bus impedance from i , which includes the SFCL impedance as well, and E i is the pre-fault voltage of bus i .

Increasing the critical clearing time or angle typically improves angular stability. Critical clearance time for a machine can be improved by avoiding active power changes during faults, according to the swing equation for a synchronous machine. d ω k d t = 1 M k P m k − P e k (3) ω k = d δ k d t (4) H = ω 0 2 M k (5) Where M k is the inertia consatant of machine k , ω k is the rotor speed of machine k , δ k is the rotor angle of machine k , P m k is the mechanical power of machine k , and P e k is the electrical power delevied machine k . Hence, By subsituting Eqs 4, 5 into Eq. 3, the swing equation will be formulated in Eq. 6 2 H k ω 0 d 2 δ k d t 2 = P m k − P e k (6)

In this section, the system will be tested under different scenarios to verify that the SFCL can not only limit the fault current but also improve the power system’s transient stability without tuning PSSs. Two kinds of PSS have been used: simplified PSS and conventional PSS. The simplified PSS is MB-PSS designed to introduce intermediate phase advance at all oscillation frequencies of interest, compensating for the inherent lag between field excitation and electrical torque (Zheng et al., 2020), (Leiva Roca et al., 2022). Therefore, only six parameters are required to be tuned. In contrast, the conventional PSS uses the measured electrical power and its relationship to shaft speed as an input signal (Leiva Roca et al., 2022), (Wang et al., 2018b).

There are still obstacles to the large-scale application of resistive-type SFCL. Although it is compact in structure, simple to implement (directly connected to the transmission line), has no control required, is rapid in response, and has minimal impact on the power grid, it requires a significant number of superconducting tapes (high in cost). In addition, it has higher AC loss generated during the current limiting period. There are still other issues, such as the costly material and production costs, the high cost of low-temperature operation and maintenance, and the operation’s dependability not yet shown. Furthermore, the cryogenic system’s capacity will rise with the number of superconductors. Therefore, the cryogenic system must be inspected and replaced regularly. As a result, cryogenic system stability and extended life expectancy should be necessary for the stable and safe operation of SFCLs.

From a protection point of view, when SFCLs were added to existing electric networks, the amount of the maximum fault current might change, affecting the protection coordination system between protective relays. To examine protection coordination with fault current limiters, the triggering level of the fault current limiters, the installation site, and the amount of impedance caused by the fault current limiter should also be considered.

Despite the superior current limiting capabilities achieved by SFCLs, commercialization and installation of superconducting fault limiters have been delayed due to technical and economic concerns as mentioned above. Table 2 shows three resistive SFCL implemented in England, Germany and Italy.

The transmission network in Qatar consists of 8 power plants that use natural gas and one PV power plant, and above 400 substations with different voltage levels (400 kV, 220 kV, 132 kV, 66 kV, 33 kV, 22 kV, and 11 kV) (Alashqar et al., 2022). As a result, the transmission and distribution expansion meshed the national grid, and the fault level increased. Figure 13 shows the comparison between 2020 and 2021 subject to the total number of tripping the transmission network, and these tripping due to several reasons such as joint cable failure, protection maloperation, fault in the OHL, third-party damage, etc.,

Figures 14, 15 show a real measurement for the system behavior after a phase-phase fault occurred in the 400 kV OHL circuit. The fault happened during the minimum time on 16th January 2021 when the number of running machines was less than the peak in summer. As a result, the system peak on the day of incidence is 50% less compared to the system peak in summer. Figure 14 illustrates that the fault current reached around 23 kA in both phase a and phase b. Also, Figure 15A shows the voltage behavior, and it can be seen clearly that a voltage dip occurred, and the voltage reached 308 kV and normalized within 71 m. Furthermore, as shown in Figure 15B, the system frequency fluctuated to reach around 50.4 Hz maximum and approximately 49.6 Hz minimum.

Traditional techniques are used to limit the fault current, such as splitting busbars, restricting generations in some locations, opening circuits (cable, OHL, and transformers), installing series reactors, and for future generations, high-impedance transformers are required. The SFCL is not preferable from a planning perspective due to the high cost compared to the other solution. For example, the cost of a series reactor in the 400 kV level costs 3.2 M$ (excluding the modification cost in the line), whereas a SFCL unit costs three times the series reactor. However, the SFCL is still developing, and the cost will decline with time.

Stability is a great concern of the power system operations, which needs to be maintained under any operating condition. However, the growth in the electricity supply and the sophistication in the electrical networks leads to an increase in fault current levels, threatening the power system stability. Therefore, a SFCL becomes a promising solution to overcome these challenges. This paper shows a comprehensive analysis of the influence of the SFCL in an interconnected power system. The key findings are:

1) The resistive value of the SFCL needs to be adjusted to avoid voltage drop during normal and abnormal operation conditions.