The most challenging task in protecting transmission lines is detecting faults the power system faces at a reliable performance level. Transmission line faults based on nature in terms of resistance are divided into low-impedance faults (LIFs) and high-impedance faults (HIFs). The main distinction between them is that the increased impedance is within the path of the fault current, limiting the arc current. LIFs comprise single line-to-ground faults, phase-to-phase faults, etc. HIFs result from unwanted contact with power conductors that are poorly connected to surfaces, making it difficult to detect these faults using traditional protection relays (Ghaderi et al., 2017). Like the open conductor (OC), a pathway toward the ground is not always included in HIFs. The open conductor faults (OCFs), like the series HIFs, cause the circuit breaker to not open due to the direct opening bridle. This is followed by the descent of the conductor to the ground (Jeerings and Linders, 1991). In addition, the OC in the transmission lines (TLs) is a challenging problem in power system operation. As a result, the system’s stability suffers as the power transmitted over the line is lowered and healthy phases may be subjected to overloading. Furthermore, if the system is non-earthed, the voltage in the healthy phases may increase (Velez, 2014). Electric shocks and fire hazards generated by open conductor faults (OCFs) are also significant concerns regarding community safety, property failure, and losses. So, first and foremost, fast detection of OCFs is essential to transmission utilities (Abdel-Aziz et al., 2017). Because OCFs do not considerably increase current or voltage drop, distance protective relays, considered the TLs’ principal protection mechanism, cannot detect them. As a result, the distance relay does not trip, and the fault will continue to occur in the open connector until the connector falls to the ground and is detected by another protection relay. In some cases, an earth fault relay can identify this fault-based high value of current when the conductor falls on a surface with meager resistance; however, since it is considered a standby protective for TLs, it will suffer from a delay time.

According to the literature, there are two proposals for identifying OCFs in transmission systems. The negative sequence was the suggested technique for identifying open and down conductor faults, where the negative sequence to the positive sequence current portion is introduced (ALSTOM, 2017). Different artificial intelligence schemes, such as neural networks (Koley et al., 2014) and In (Shukla et al., 2017), utilized the wavelet and naïve Bayes classifier to detect the OCF in six-phase TLs. Most previous schemes, such as thresholds in ALSTOM (2017), do not fully define the OCF problem and offer specific practical implementation challenges. Furthermore, the robustness of the artificial neural network protection scheme proposed by Gilany et al. (2010) has several practical constraints to be fabricated, as the reliability of these systems is highly determined by the nature of the design and the level of changes made to it, such as higher increased loads. In Elmitwally and Ghanem (2021), detecting the fault, selecting the faulty phase, and identifying the fault point depended on measuring the three-phase current at the protective relay in superimposed components of compensated TLs. In Khoshbouy et al. (2022), the ratio for the phase voltage at the sending end to the sum of the ratio for the phase current for two ends in TLs, called pilot superimposed impedance, was used to detect interior and exterior faults competed to a predetermined value, which was estimated based on Thevenin impedance.

Furthermore, many algorithms have been introduced in the literature over the past 20 years to detect OCFs in electric distribution utilities. For instance, voltage unbalance over the feeder was measured to identify the OCFs using sensors (Vieira et al., 2019); however, these sensors need sophisticated communication between these devices. In addition, the proportion of the SC current was inspected in Jayamaha et al. (2017); this requires the installation of current sensors over the line to protect it and deal with numerous challenges that may be difficult to overcome. Other proposed approaches, such as that introduced in Silva et al. (2018), relied on installing a device that measures the second or third harmonics of the current and follows the changes that may occur due to faults. Other schemes of detecting OCFs relied on the data measured from phase-measuring units (Zanjani et al., 2012). However, this necessitated precise management between these units and the control center. The detection strategy presented in Adewole et al. (2020) to identify an open phase was based on the current imbalance prevalent during the occurrence of OCFs; however, it was only suitable for earthed distribution utilities. Additionally, the current arc value changes rapidly over time during HIFs, which presents another challenge for schemes that rely on measuring the variance in frequency components (FCs) of the current due to arcing. The concept behind this is extracting the transient change in the fault (Shukla et al., 2017). In addition, many research works have been published to identify the fault in TLs based on wavelet transform applications, such as discrete wavelet transform, wavelet packet transform, and single-wave entropy schemes. Numerous works used the discrete wavelet transform scheme because time–frequency localization can assess the transients during HIFs (Saravanababu et al., 2013). However, the schemes that rely on high-frequency components, as described in Ashok et al. (2019), result in weak discrimination between LIFs and HIFs. Conversely, algorithms such as those used in Rathore and Shaik (2015) relied on low-frequency components that failed to distinguish HIFs. It should be mentioned that incorporating between low and high frequencies was discussed using predetermined values in Shaik and Pulipaka (2015). However, the fault was not detected when switching a large load case because the value of the low-frequency component primarily relies on the value of the load current. Furthermore, research works (Usama et al., 2014) based on wavelet analysis focused on detecting earth faults, not OCFs. Accordingly, the difficulty in detecting and locating OCFs remarkably affects the state of OCFs on both sides of TL systems. In Asuhaimi Mohd Zin et al. (2015), fault detection and classification utilized discrete wavelet transform and back-propagation neural networks based on Clarke’s parallel-transmission transformation. The fault detection and classification of fault types that are triggered in three-phase TLs using the artificial neural network is described in Assadi et al. (2023). The proposed scheme can detect and classify several faults, including line-to-ground, line-to-line, double-line-to-ground, triple-line, and triple-line-to-ground faults. In Mahanty and Gupta (2007), the methodology for fault analysis uses current samples with the help of fuzzy logic. In this technique, only one end of the three-phase current samples was considered to achieve fault classification. The neural network was utilized for training, and a fuzzy view point was applied to gain an insight into the system and to reduce the complexity of the system (Dash et al., 2000). Jayabharata Reddy and Mohanta (2007) presents a real-time wavelet–Fuzzy combined scheme for digital relaying. The algorithm for fault classification utilizes wavelet multi-resolution analysis to overcome the complications combined with conventional voltage and current-based measurements due to the effect of fault inception angle, fault impedance, and fault distance. No scheme has proven its superiority and effectiveness in all fault scenarios. Thus, new effective solutions are therefore needed.

This work discusses a detection scheme that relies on the Clarke transform conversion for the current signals in TLs, such as the OCF on both sides and the OCF on a single side, followed by an earthed fault on another side through LIFs and HIFs. The sign of all current Clarke components is the primary key for distinguishing between all types of simultaneous LIFs and HIFs. The alternative transient program (ATP) package simulates a 500 kV–150-mile transmission line. The behavior of the proposed schemes is tested and validated considering different fault scenarios with different fault locations, inception angles, fault resistance, and noise.

Furthermore, the proposed schemes are extended to another transmission line, such as the 400 kV–144 km line. The obtained results demonstrated the effectiveness and reliability of the proposed scheme in detecting simultaneous faults, LIFs, and HIFs correctly in 20 mS.

The novelty in the proposed scheme and the essential features that verify the accomplishment achievement of its purpose effectively compared to the preceding approaches are as follows:

• Functionality: It can correctly discriminate between OCFs (series faults), two types of broken conductors together with earth faults (shunt fault) occurring after a short period (simultaneous earth faults), HIFs, and LIFs. These faults are correctly detected at both ends compared to other existing schemes that see these faults at a single end.

The rest of the manuscript is organized as follows: Section 2 clarifies the fundamental problem investigated in this work. The proposed fault detection strategy is introduced in Section 3. In Section 4, the behavior assessment for the proposed scheme is conducted using ATP to examine the ability to identify the fault. In Section 5, a comparison is made between the proposed scheme and other schemes presented in the literature. Finally, Section 6 is dedicated to the conclusion drawn and future work directions. A schematic overview of the proposed scheme’s assessment steps and the work’s organization is given in Figure 1.

The proposed schemes comprise different stages: fault detection, identification, and classification, as declared in Figure 6. As illustrated in Figure 6, the introduced scheme relies on the existing phasor measurement unit at the high-voltage side. Each phasor measurement monitors the three-phase currents’ magnitudes. Phasors are considered the primary tool for analyzing the power system in its steady state or transient situations, so phasor estimation is quite essential for protection applications. Estimating the voltage and current phasor is performed concerning one frequency, which is usually the fundamental power frequency. A phasor measurement unit, or synchrophasor, is a device that measures a power system’s synchronized current phasor. Synchronization among phasor measurement units is achieved by same-time sampling of voltage and current waveforms using a famous synchronizing signal. The ability to calculate synchronized phasors makes the phasor measurement unit one of the most important measuring devices in the future of power system monitoring and control. Precise synchronization of sampling clocks throughout the power system became possible with the advent of the global positioning system (GPS) satellite system. Although the precision of synchronization was not very good in the early years of the system, at present, it is possible to achieve synchronization accuracies of 1 µs or better.

The applicability and feasibility of the proposed schemes are clear. Nevertheless, the proposed scheme needs communication links between both ends (sending and receiving end) to detect, identify, and classify the fault. This communication link between both ends is used to send and receive three-phase currents’ magnitudes for sending and receiving ends in the proposed fault detection (PFD) unit at both ends. The presented scheme is embedded in the PFD unit on both ends to detect and identify these faults when one or two conditions are verified. In the sending end PFD unit, the first condition is proving if the obtained sending end current for phase a at fault is equal to or less than (10–15) % of the sending end current for phase A at normal operation. The second condition is verifying if the obtained receiving end current for phase A at fault is equal to or more than (140–160) % of the receiving end current for phase A at normal operation. Furthermore, in the receiving end PFD unit, the first condition is verifying if the obtained receiving end current for phase A at fault is equal to or less than (10–15) % of the receiving end current for phase A at normal operation. The second condition is verifying if the obtained sending end current for phase A at fault is equal to or more than (140–160) % of the sending end current for phase A at normal operation. The security attribute for the presented algorithm is achieved under unbalanced load conditions. Thus, the obtained sending end or receiving end current for phase A at fault is more than (140–160) % of the sending end or receiving end for phase A at normal operation. According to the proposed detection scheme, this is the second condition monitoring if the first condition is verified.

Consequently, the proposed scheme is not affected by unbalanced load conditions. On the other hand, the presented algorithm is susceptible to consideration because the computed current signal significantly increases to specific high ratios according to the fault type. The threshold values ((10–15) % and (140–160) %) are selected based on the detail analysis under all possible fault conditions in Section 2. The expected threshold values under these faults are as follows:

In the PFC units, the formula of the suggested fault classification is examined under some critical insights into un-transposed and transposed TLs. In this regard, the impedance matrix is symmetrical in the un-transposed case (symmetrical space between the conductors). In a symmetrical space between the conductors, the self or diagonal terms are generally unequal, and neither is the mutual or off-diagonal term in the impedance matrix. The current flowing in any one conductor will induce voltage drops in the other two conductors, which may be unequal even if the currents are balanced. Asymmetric voltage drops caused by the mutual impedances are unequal. This issue can be solved by making the TLs a perfectly transposed line in which the three sections have equal lengths. The perfect transposition results in the same total voltage drop for each phase conductor and equal average series self-impedance of each phase conductor. This effect applies to the average series phase mutual impedance and the average shunt phase mutual susceptance. Consequently, the phase impedance for a perfectly transposed single circuit is symmetric. Applying an entire transpose scheme suffers from expensive costs and inconvenience. Accordingly, the line may be transposed at one or two locations along the line route. This configuration provides a symmetrical impedance matrix.

In the proposed fault classification procedure, the output of the Clarke matrix is reflected in signals of the phase currents to detect various OCFs in un-transposed and transposed TLs precisely. The time-domain transformation is used with Clarke components, denoted as α, β, and 0, which are extracted as follows: I α I β I 0 = 2 / 3 − 1 / 3 − 1 / 3 0 1 /   3 − 1 / 3 1 / 3 1 / 3 1 / 3 I a I b I C . (1)

The Clarke components are represented by Eq. 1, considering phase a as a reference, and two other Clarke components concerning phases b and c. In general, the same zero “0” component exists for any reference, whereas phases a, b, and c have three “β” components. These components are called aerial modes 1, 2, and 3 when OCFs or simultaneous earth faults occur. First, when conductor a opens, as shown in Figure 2B, one can note the following for Clarke’s components: I α = 2 3 I a − 1 3 I b − 1 3 I c , (2) I β = 1 3 I b − I c , (3) I 0 = 1 3 I a + I b + I c . (4)

Second, when the simultaneous earth fault at phase a happens, as shown in Figure 2C or Figure 2D, one can find that Clarke’s matrix components change as follows: I α = 2 3 I a − 1 3 I b − 1 3 I c , (5) I β = 1 3 I b − I c , (6) I 0 = 1 3 I a + I b + I c . (7)

Evaluating the three components of the Clarke matrix shows that aerial modes 1 and 2 best identify OCFs and simultaneous earth faults. The values of aerial modes 1 and 2 are 0 under healthy conditions. If OCFs occur, analysis of Clarke’s matrix components reveals that the value of aerial mode 1 is negative and the value of aerial mode 2 is positive, as shown in Figure 7.

The same components are examined when LIFs are involved in the investigation. Aerial mode 1 is found to have a positive sign, while aerial mode 2 has a negative sign. This means that OCFs and LIFs are entirely different when compared to each other. Moreover, the sign of aerial modes 1 and 2 is positive, and their values are low if HIFs occur. In addition, if an OCRE/EFSE fault occurs, it will be found that the sign of aerial mode 1 changes from negative to positive, and the sign of aerial mode 2 changes from positive to negative. Furthermore, the sign of aerial mode 1 is negative, and its value increases, while the sign of aerial mode 2 is positive, and its value increases when an OCSE/EFRE fault occurs.

Distinctive fault types across the TL length were evaluated through various fault situations (locations, inception angles, and fault resistance values) to explain the efficacy of the suggested schemes in detecting simultaneous OCSE/EFRE and OCSE/EFRE. The cases can be organized as follows to detect and classify faults successively:

Case 1:

OCFs at different locations and fault time occurrence (inception angle ϕ in degrees).

Case 2:

OCRE/EFSE at different locations and fault time occurrence considering fault resistance effects.

Case 3:

OCSE/EFRE at different locations and fault time occurrence considering fault resistance effects.

Case 4:

LIF and HIF at a specific location and specific fault time occurrence considering fault resistance effects.

The proposed fault detection, identification, and fault classification schemes can also be generalized for any transmission system. Figure 14A shows the single-line diagram of 400 kV, 144 km TL simulated in the ATP/EMTP program. The ATPDraw software is an interface to implement the system (Prikler and Høidalen, 2009). This TL model is a benchmark in the ATPDraw software, and it is represented using the three-phase JMARTI frequency dependence model in the ATPDraw field using the line/cable module (Prikler and Høidalen, 2009). The JMARTI representation is a frequency-fitted model in a specific frequency range. The JMARTI model is utilized to apply the simulated line and, therefore, take waveforms for the fault case in evaluating the proposed schemes. For simultaneous series and shunt earth fault detection and classification using Clarke transform for TLs under different fault scenarios, the line parameters have been extracted, and results show that the self-impedance of this line, for a length of 144 km, is 0.3382 + j1.6009 Ω, while that of the mutually linked one is 0.3282 + j 0.8493 Ω, according to the retrieved line parameters. Using a mutually linked RL circuit, Thevenin’s equivalent impedance at buses S and R are expressed as R ₁ = 1.0185 Ω and L ₁ = 50.929 mH, and zero sequences are R ₀ = 2.037 Ω, L ₀= 101.85 mH at bus S and R ₁ = 0.6366 Ω, L ₁ = 31.83 mH, R ₀= 1.2732 Ω, L ₀= 63.66 mH at bus R. The TL configuration is illustrated in Figure 14B, where the dc resistance is 0.0522 Ω/km, and the outer diameter of the conductor is 3.18 cm. The sky wires are solid, their dc resistance is 0.36 Ω/mile, and the outer diameter is 1.46 cm. The resistivity of the soil is equal to 200 Ω. Similarly, a small error in simulation for 400 kV TL is found using system verification in the ATPDraw software program.

The proposed fault detection, identification, and classification schemes are also examined using another TL data, considering several fault types. In this case, the values of Clarke components for the investigated scenarios are shown in Table 9. In addition, the DWT-based algorithm was examined in the same scenarios, as shown in Table 10, where the values of (M _a , M _b , and M _c ), (H _a , H _b , and H _c ), and (R _a , R _b , R _c ) were calculated. As presented in these tables, considering the OCRE/EFSE occurred, the values of M _a > M _th and M _c > M _th caused by small fault resistances were unmet. In addition, the values are H _a > H _th and R _a >1. Furthermore, the proposed fault detection, identification, and fault classification schemes provided precise fault detection, identification, and fault classification for the investigated types of faults.

The proposed schemes’ challenge is their performance if the current transformers’ saturation occurs. The current transformers must correctly provide the protection relays with the stepped-down fault current level. Proper means to detect current transformer saturation are essential for digital signal processing. Esmail et al. (2015) suggested an effective method for detecting current transformer saturation with a universal distinction index without a necessity for setting a definition. For this point, the instantaneous sample-based multiplication of the secondary current by its derivative is individually employed to distinguish between saturated and unsaturated wave portions.

Reconstructing the detected saturated secondary current is accomplished using Kalman filtering to obtain the phasor quantities of the unsaturated current portion professionally.