The capability to locate faults in extra high voltage transmission (EHVT) lines is vital for the economic operation of power systems. These faults are classified as shunt, evolving, or cross-country faults. Faults occur starting in one phase after sometime transformed to other phase at all together are named as evolving faults. Faults that occur simultaneously in different phases at different points are known as cross-country faults. The fault location algorithm for cross-country and evolving faults is more complex than that for single-time and location faults because faults occur in various phases at various locations and times. Thus, it is essential to reduce the influence of such faults. This can be completed using a correct, consistent, and fast fault-detection algorithm.

In [1], a fault classification and location scheme for EHVT lines was developed. Researchers have explained the protection of transmission lines using information from only one end of the bus [2,3,5]. Currents and voltages are used to locate shunt faults, as implemented in [6–12]. The faulty location schemes using relaying end voltages and currents were reported in [13–15]. The authors of [16, 17] explained faulty location approaches using a terminal of the fundamental component of the data. In [18], a location strategy for shunt faults using single-end fundamental component voltages and currents was proposed.

The aforementioned algorithms are convenient to implement. However, these involve only shunt faults and complicated training efforts. Therefore, a novel algorithm that provides precise fault locations for EHVT lines during evolving and cross-country faults is required. Fault location methods have mainly been addressed for cross-country faults [19, 20]. Algorithms for non-earthed [21] and ground cross-country faults [22] have been presented. In [23], the authors introduced the location of faults in transmission lines using artificial neural networks (ANNs). The fuzzy algorithm is popular among all the fault-location algorithms. The fuzzy expert system (FES) algorithm is simple and involves only IF-THEN rules. Previous studies have reported the FES in detail [24–33] and is modeled to determine fault locations [34]. The FES was provided for location determination by considering the impedance values as inputs [35]. However, no study has reported a method to locate EHVT lines during cross-country and evolving faults by fuzzy logic and impedances. Thus, an FES algorithm for locating cross-country and evolving faults in EHVT lines has not been reported. To handle the aforementioned location algorithms, an FES was designed to locate cross-country and evolving faults in EHVT lines.

• 1) The speed of this FES is high.

• 2) The purpose of this FES study is to enhance the location error.

• 3) The FES deters the awareness of multiple-terminal data.

• 4) The FES is independent of the variation in fault inception time and actual faulty location.

• 5) FES can be selected to elucidate computational complexity problems.

The remainder of this paper is organized as follows: Section 2 presents a simulation of the EHVT line. Section 3 describes the development of the FES fault location algorithm. Section 4 presents the performance evaluation. Finally, Section 5 concludes the paper.

Figure 1 shows the detailed workflow of the proposed algorithm based on the FES and a schematic of the transmission line setup. The 400-kV, 50-Hz, 100-km transmission line was developed using the toolbox of MATLAB SimPowerSystems. The transmission line was designed using a distributed-parameter block. A three-phase fault breaker was used to simulate various fault types by modifying the inception time and faulty location. The fault impedance increased as the distance of the fault location from the source terminal increased. Various cross-country and evolving faults were generated on the EHVT line. The voltages and currents at the source end were obtained by MATLAB simulations. The waveforms were provided to a second-order Butterworth filter with a cut-off frequency of 480 Hz, and were arranged at a sampling frequency of 1.2 kHz. Furthermore, a discrete Fourier transform (DFT) was used to extract the fundamental components current and voltage. The fundamental component of impedance was then obtained from the ratio of voltage to current. The mean fundamental component of the impedance was determined for 45 post-fault samples. The impedances were used as inputs to the proposed algorithm.

The FES was developed in a MATLAB environment using the fuzzy logic toolbox. MAMDANI was used to implement the FES. Three inputs and three outputs were selected to prepare the FES structure. The inputs to the FES were the fundamental components of the impedance from the relay end in each phase.

The inputs were ZA, ZB, and ZC. The FES inputs were converted into fuzzy sets using triangular membership functions (MFs). Each input was divided into 10 MF partitions: ZF1–ZF10. Similarly, the fault distance in each phase was considered the output of the FES. The outputs were indicated DA, DB, and DC. The MFs were designed for each output as triangular MFs. All the outputs were divided into 10 MF partitions, namely, DF1–DF10. Figures 2 and 3 show the inputs and outputs, respectively. The input (three) and output MFs (three) were selected to develop each rule. The input MFs connected by the “AND” connections. The firing strength was determined using the minimum method. The defuzzification scheme was considered to be of the centroid type. The formulated rules are listed in Table 1.

The performance of the FES was tested for the 400-kV, 50-Hz, EHVT line. The FES in MATLAB was developed for faulty locations. The verification of the FES performance at various inception times and fault locations was crucial. MATLAB simulations of the EHVT line were conducted to demonstrate the feasibility of the proposed algorithm. For the simulations, all the feasible faults, inception times, and fault locations of the EHVT line were considered. The results for the cross-country faults obtained by modifying the fault inception angle from 0 to 130 ms are summarized in Tables 2 and 3. The evolving faults at various locations are listed in Tables 4 and 5.

The test results for the shunt faults are listed in Table 6. The maximum absolute error (MAE) was computed using Eq. (1): the MAE at the faulty location was below 0.41% for all the test cases. The proposed algorithm is precise, robust, and requires only source terminal impedances to determine the fault location without the information of the fault type. The fault locations and phases were identified correctly in all the cases. The proposed algorithm successfully classified the fault types based on the fault location results. Although the faulty location algorithm used data from the relaying end, it precisely located all the fault types and did not misidentify the faults. The results noticed if any of DA, DB, DC values are between [0.3 99.7] and |DA-DB|, |DB-DA|, |DC-DA| is more than 0.7 then fault is cross country fault while it is lower than 0.7 then the fault is evolving fault while all outputs DA, DB, DC is between 99.7 and 100, and then there is No-fault. Figures 4 and 5 explain the test results for the evolving and cross-country faults, respectively, in the fuzzy logic toolbox.

where FLa is an actual fault location, FLe is the estimated fault location, and L is the total line length.

Figure 6(a) indicates the output of the FES in which the “A” phase goes to 81 at 41 ms, and the “C” phase goes to 81 at 61 ms. The other output “B” remains at 100 giving there is AC-evolving fault. Figure 6(b) exemplifies the output of FES in which the “A” phase goes to 61 at 61 ms and “C” goes to 81 at 61 ms. The other output “B” remains at 100 giving there is AC-cross country fault. Figure 6(c) represents the output of the FES in which the “A” and “C” phases go to 81 at 41 ms. The other output “B” remains at 100 km giving there is AC-shunt fault.

The FES algorithm was compared with previously reported algorithms, as shown in Table 7. It can be concluded that the MAE of the proposed algorithm is less than those of the algorithms published in [8, 15, 17, 18, 20, 23], which is beneficial over earlier fault location techniques. Furthermore, in previous studies, both current and voltage were selected [2, 8, 17, 18, 23], whereas the proposed FES algorithm uses a one-terminal impedance. In addition, the proposed FES is independent of communication links. Previous authors published support vector machine (SVM), adaptive neuro-fuzzy inference system (ANFIS), and ANN-based location algorithms [2, 8, 17, 18]. Meanwhile, the proposed algorithm was implemented without training effort or complexity. As described above, the proposed algorithm provided satisfactory results for the detection of cross-country and evolving faults. Therefore, the FES algorithm is the best option for fault locations. Hence, an accurate, fast, efficient, stable, and reliable approach was

This paper presents a fault-location algorithm for cross-country and evolving faults using an FES. The FES is structured by considering impedance variables. The results for the EHVT line confirm the MAE to be below 0.41% for all the fault cases. The proposed approach does not require classification methods for fault classification. The investigations demonstrate that the proposed algorithm is precise and convenient to develop. It is independent of the variation in fault inception time and actual fault location. The proposed algorithm identifies all the faults regardless of the classification algorithm and does not require complex consumption.

Table 1. Rules for FES.

Table 2. Test results of FES during two-location faults for various inception times.

Table 3. Test results of FES during three-location faults for various inception times.

Table 4. Test results of FES during evolving for various fault locations.

Table 5. Test results of FES during evolving faults for various fault locations.

Table 6. Test results of FES during shunt faults for various inception times and faulty locations.

Table 7. Comparison of the proposed algorithm with other algorithms.