Flexible alternating current transmission system (FACTS) controllers are a family of power electronics-based controllers that have become increasingly popular in electrical power and transmission systems. Recently, FACTS controllers have been established as a feasible transmission choice to accomplish effective utility of rights of way and enhanced transmission capacity to meet growing electrical demand. Among the different FACTS controllers, the thyristor-controlled series-compensated transmission line (TCSCTL) is a promising option for transferring control power [1]. It offers various functionalities, such as enhanced damping of power oscillations, active power flow, transient stability, mitigating the sub-synchronous resonance issue, and limiting the short-circuit current. Nonetheless, the protection of TCSCTL is more difficult and complicated than the protection of an uncompensated transmission line because of voltage and current inversions, reaching, and ferroresonance problems. Moreover, there are problems with mho relay functionalities in such applications.

TCSCTL is now a main part of the FACTS device group, and it is widely identified as an economical and effective means of solving the issues related to long transmission lines, such as, voltage and transient stability issues and FACTS controllers based optimal power flow control, in deregulation of the electrical power market to reduce losses and improve congestion management in transmission systems. Therefore, it is crucial to identify the specific fault issue in a transmission line so that the FACTS device is leveraged fully.

Numerous studies have addressed the distance estimation of shunt faults (single location faults) in TCSCTL applications. Some the significant research include neural network-based distance estimation [2,3], genetic algorithm tuned support vector machine and artificial intelligence based faulty classifications [4,5], fuzzy-based section identification [6], fault detection [7], and fault analysis [8,9] for TCSCTL. The majority of studies have been validated on shunt faults, while only a few have addressed the issues related to the multi-location (two-location) faults in TCSCTLs. The popular computational approaches used in the development of multi-location fault models include neural networks [10,11], fuzzy rule-based systems (FRS) [12,13], and support vector machines [14]. Among these methods, FRS is proven to be the most suitable method, followed by support vector machines and neural network techniques.

The most recent fault distance methods based on FRS are reported in [15–18], which draw current from the relay terminal. FRS fault diagnosis for TCSCTLs is reported in studies [19–23]. However, this technique does not locate multi-location faults in TCSCTLs. Furthermore, the techniques mentioned in [19–23] require simplicity. Therefore, a suitable method needs to be investigated with a simple process; however, this is not provided in the abovementioned studies. As a result, our research focuses on the issue mentioned above utilizing FRS in the LabVIEW software. In this context, this study utilizes a concept based on the FRS, whose objectives are stated as follows:

• 1) The main purpose of FRS study is to boost error (%).

• 2) The speed of FRS is very high.

• 3) The FRS has no significant impact on instants (Φ), resistances (R), multi-location faults, and distance in each phase (D1, D2, D3).

• 4) It directly utilizes the current information without performing communication links.

The remainder of this paper is as follows: Section 3 explains the TCSCTL, and technical inputs used for obtaining the distance of multi-location faults. Section 4 describes the FRS technique in detail. In Section 5, the experimental evaluation of FRS using various data samples to verify its performance is illustrated. Finally, the obtained result are summarized in Section 6.

A schematic representation of the TCSCTL considered in this study is demonstrated in Figure 1. This line operates at 500 kV voltage, 100 km length, and 60 Hz frequency. The TCSCTL consists of one capacitor that is used in the line for compensation. The capacitor is connected in parallel with an air gap arrangement, a metal oxide varistor (MOV) that protects it from overvoltage. Furthermore, it is also in parallel with the series connected inductor and anti-parallel thyristor combination. The 3-phase time-domain currents (IA, IB, and IC) are extracted from the relay terminal. B-1 is considered a relay terminal because here the behavior of the TCSCTL with respect to varying currents is studied, which is simulated using the MATLAB/Simulink software environment. Figure 2 shows a flow chart of the proposed framework.

When a fault occurs in two phases of TCSCTL at two distances simultaneously, is known as a multi-location fault. The TCSCTL is simulated for a simulation time of 200 ms, and the waveform of the instantaneous currents during the multi-location fault situation, that is, the B fault at 58 km and C fault at 15 km, are shown in Figure 3. Here, the 3rd level Haar wavelet transform is used for extracting features from currents obtained via the TCSCTL simulations. To estimate the multi-location fault distance, input signals are simulated according to various fault scenarios. Following feature extraction, a generally suitable computational scheme is adopted by the proposed technique to perform the distance estimation task regarding multi-location faults. The Haar wavelet transforms are the easiest wavelet transforms. The main benefits of the Haar wavelet transform are the investigation of signals with sudden transitions, that is, monitoring of tool failures in machines, and rapid computation. The Haar wavelet transforms can be expressed as

Fuzzy logic was introduced by Lofty Zadeh in 1965 based on the theory of “partial truth,” that is the truth values lied between “absolutely false” and “absolutely true”. Fuzzy logic provides a structure to design the uncertainty, perception process, and human way of reasoning. It is also based on natural language, and through a set of IF-THEN rules, an expert system is created, which is a function of fuzzy computations. Fuzzy logic has many benefits: first, it is applicable to many systems; furthermore, it can be understood simply owing to being mostly flexible; and finally, it can be used to design nonlinear functions of arbitrary complexities. The FRS components are depicted in Figure 4.

The FRS used in this study is of the Mamdani type. The input, outputs, and their membership functions are reported in Figure 5. The membership function is obtained by dividing the input and output gaps into separate parts in a triangular format. The IF-THEN rules have two components: an antecedent component and a consequent component. For each rule in the FRS, Haar wavelet currents are the antecedent of the rule, and the distance in each phase is the consequent. Each rule is then evaluated on these variables using the fuzzy AND operator to produce another value. The number of rules in the FRS scheme used here is 27, as shown in Figure 6. Each output parameter is a crisp value, which indicates the location in a range of 0–100. Here, we used the most applicable method of defuzzification, the center of gravity method, to defuzzify the outputs.

In this section, the adopted FRS scheme is examined on the widely studied 500 V, 60 Hz, TCSCTL. The FRS scheme has been assessed with respect to different dynamic fault parameters, such as instants (Φ), resistances (R), multi-location faults, and distance in each phase (D1, D2, D3), where a total of 25,000 fault cases have been examined. The effects of varying R, Φ, shunt faults, distances, and types, and corresponding test results are reported in Tables 1–4. The FRS applications in multi-location and shunt faults in the LabVIEW fuzzy software are depicted in Figures 7 and 8, respectively. The error in the distance estimation of multi-location faults is calculated using Eq. (2).

It is important to test the FRS application for close-in (1–5 km) and remote-end (95–99 km) multi-location faults because in such cases the voltage and current magnitudes are different, which leads to relay failures. The results of the FRS for close-in and remote-end multi-location faults are listed in Table 5. The FRS application during close-in and remote-end multi-location faults in the LabVIEW fuzzy software is shown in Figure 9. This confirms that the proposed scheme is not affected by the addition of close-in and remote-end multi-location faults. Moreover, observe that most fault cases are located below the 0.258 error value.

To assess the FRS performance, multi-location fault-based algorithms presented in [3,10–12,14] are chosen. The comparison results support the computational ones presented in Table 6. The results of the FRS technique compared to those obtained by the algorithms presented in [3,10–12], achieve excellent distance estimation accuracy and track the output values well for all data sets. The FRS scheme designed in LabVIEW simulations outperforms the benchmark algorithms without planning complex techniques, such as those adopted in [3,10,11,14]. Therefore, we can conclude that more test samples are recommended than those used in [12,14]. To the best of our knowledge, no implementation has described the enhancement of multi-location fault distance estimation in TCSCTL, as we have in this study.

This study presented an FRS technique for the distance estimation of multi-location faults in TCSCTLs. In addition, the proposed research is independent of the Haar wavelet voltage and communication links. The standard deviation values of the Haar wavelet current coefficients were considered for distance estimation of TCSCTL in multi-location faults. The drastic change in different faults provided significant results during the FRS validation. In addition, the FRS achieved high efficacy with respect to errors against line parameters. Furthermore, the enactment of the proposed FRS was compared to that of the other techniques. The proposed FRS scheme detected all types of multi-location faults with cycle time range between 0.01 to 0.46 seconds.

Table 1. Effect of varying φ in multi-location fault scenario (A fault at 11 km and C fault at 78 km).

Table 2. Effect of varying R in multi-location fault scenario (A fault at 92 km and B fault at 21 km).

Table 3. Effect of varying distances and types.

Table 4. Effect of varying shunt faults.

Table 5. Effect of close-in and remote-end multi-location faults.

Table 6. Comparison of FRS to established techniques.