Rearrangement method of reducing fault location error in tied uncompleted parallel lines

In Tied Uncompleted Parallel (TUP) line, locating faults via single-ended fault location algorithm leads to a considerable final error yielding unacceptable outage time. On the other hand, utilizing modern techniques such as Two-ended Protection method, in these temporarily transmission lines are not economically justified. This paper proposes a rearrangement method of tied uncompleted transmission lines to improve the protection coordination and fault location via single ended fault location. This novel method aims to reduce the error of fault location in the line without imposing an unnecessary financial burden or installing new devices. The proposed technique can locate a fault online, resulting less outage time and more reliability of the network. The simulation results, as well as those of field test, indicate the effectiveness of the proposed method in locating fault according to different constraints such as the protection coordination. This method has already been implemented in the Fars-Iran power system since 2018, and it has yielded outstanding results in practice. The technique is easy to execute and considerably reduces the fault location error and the outage time. Having derived the factors of fault location error, the rearrangement technique suggests a new arrangement based on the fault location error factor reduction. In this paper, it is approved that the proposed algorithm can effectively locate faults in uncompleted transmission lines via simulation results as well as practical experience.

Single phase short circuit currents measured by the relay P (kA) T0, TN Dead-end towers' label TM The dead-end Tower under calculation IKSS_R, IKSS_P The short circuit power at terminal R and P (mVA)

I. INTRODUCTION
Transmission lines are one of the most essential elements of power system deliveries. The accuracy of fault locating is a critical element in restoring power services, reducing the outage times as well as increasing the reliability and decreasing the maintenance cost.
Various types of techniques have been proposed for finding the location of the faults. Among those, there are some measures using single-ended fault location algorithms [1][2][3][4][5][6]. Being economical, simplicity of installation and lowcost maintenance are the main reasons that these techniques are widely applied in power systems. On the other hand, they can be affected by variations in source impedance, fault impedance, and angle. Nevertheless, due to economic factors, they are still widely used in power systems. Moreover, by using Global Positioning Systems (GPS) and Phasor Measurement Units (PMUs), it is now possible to monitor synchronous voltage and current of all ends of the transmission line to calculate the exact place of fault occurrence [7]. Afrasiabi used the features extracted from the signals measured by PMUs to train a Gabor Filter Convolutional Neural Network and developed a robust and accurate algorithm for fault localization system [8]. Guha developed a real time fault locating algorithm based on the complex voltage data derived from PMUs and the network topology. He et al. could locate the closest bus to the fault location without carrying out any computationally expensive calculations [9]. Moreover, an error model of the measurement chain including instrument transformers and PMUs developed to design measuring errors covariance matrix in the state estimation formulation. Using the state station calculation and the solution algorithm of Weighted Least Square [10]. On the other hand, Kezunovc used synchronized voltage and current samples at both ends of transmission line to estimate fault location yet it requires a significant high rate [11,12]. Lee et al. used an algorithm based on zero and positive sequence with synchronized data at both ends of the line [13], but this method had error on three phase faults. Liu used a novel technique to locate the fault position in a multi-section line by online or offline data [14]. Moreover, Minambres et al. used the unsynchronized data to simply detect the fault in three terminal transmission lines [15]. Girgis et al. [16] developed a three-terminal fault location algorithm by using synchronized and unsynchronized voltages and currents to estimate the fault location. He [17] developed a dynamic fault locator for threeterminal lines based on Newton iterative technique but these methods [16,17] are supposed to be computationally complex ones. Izykowski [18] developed a non-iterative algorithm using of unsynchronized measurements without considered the effect of high resistance inter-phase faults. However, due to the high cost of using the PMUs and GPS system, these techniques cannot be applied in all stations, let alone in temporary schemes.
Furthermore, there are some papers investigating Artificial Intelligence methods in fault locating problem. Parsi studied four different techniques, time domain, impedance, visual inspection and wavelet-based technique applied to the travelling fault wave [19]. Dashtdar extracted the fault characteristics from zero-sequence current using discrete wavelet transform to train an artificial neural network [20]. By the trained network, he could estimate the fault distance based on the type of the fault in different conditions. Kumar proposed a Neural Network approach using the voltage and current of single end of line processed by Discrete Fourier Transform and trained using Levenberg-Marquardt method [21]. Mukherjee deployed a Principle Component Analysis (PCA)-based method using fault signals of ten different types of seven intermediate locations [22].
Meanwhile, some have developed phase-based methods to locate the fault in power grids. By introducing the fault location as an additional state of the overall model and using state estimation algorithm to identify the fault location, Liu developed a phase-based method in fault location problem for non-homogeneous transmission lines [23].
A Significant number of power grid expansion projects in Fars province in Iran have not been completed due to several reasons, mainly economic issues. A typical scheme of these uncompleted projects is illustrated in Fig. 1. Although there is no certain time to complete the future scopes, the completed sections, which are mainly the transmission line, are currently under operation as shown in Fig. 1. These TUP lines are connected to the main power transmission line using jumpers as shown in Fig. 1, so as to reduce power loss. However, it can provoke a protection error in detecting the accurate place of the fault occurrence. This problem can increase not only the outage time but also the expenses of repairing the power line, especially those installed in harsh environments such as mountains or valleys. On the other hand, in the majority of cases, using PMUs and GPS in such temporarily schemes impose a considerable financial burden. The main contributions of this paper are as follows:  Proposing a novel and practical rearrangement method in a TUP line to reduce the inaccuracy of fault location in the single-ended fault location algorithms.  Online fault locating without installing high expensive devices.  Reducing the outage time as well as the maintenance cost by easing finding the fault location which accordingly, will increases the reliability.
This paper is organized as follows: In section II, fault locating problems in TUP lines using single-ended fault location techniques, as well as previous fault locating ones are described. Section III discusses the proposed rearrangement method, which is evaluated using the practical network described in section IV. The experimental results are illustrated in section V, and a comparative study is conducted in section VI. Finally the conclusion is reached in section VII.

A. Review of single-ended fault location techniques
Single-ended impedance-based fault location algorithms estimate the location of a fault based on the voltage and the current of one terminal. Consider the two-terminal transmission network shown in Fig. 2, where the positive sequence impedance is ZL1 between two terminals R and P. where, the form taken by VR and IR depends on the fault type which are expressed in table 1 [1].
The apparent impedance to the fault ZRelay can be expressed as: The fundamental equation that governs single-ended impedance-based fault location is equation (2)

1) SIMPLE REACTANCE METHOD
This technique gains advantage from the fact that RF is naturally resistive [1]. Furthermore, by assuming that IR and IP are in phase, the impact of RF (IF/IR) can be ignored. This result can be derived by considering the imaginary components of (2) as: However, this technique can be affected by various reasons such as load current and difference between the phases of IR and IP.

2) TAKAGI METHOD
This technique improves the Simple Reactance Method by subtracting out the load current from the total fault current. This technique uses the superposition principle and estimates the fault Current IF. Having estimated IF, an angle ß can be derived so as to reduce the impact of RF (IF/IR) by changing the angle of IF. However, if the system is not uniformed or the load model is not a constant current, the results might not be valid [2].

3) MODIFIED TAKAGI METHOD
Depending on the relay types, the availability of the pre-fault current is under question. Having considered this fact, the modified Takagi method uses IR0 to change the phase of IF current so as to reduce the impact of RF (IF/IR) in fault location finding process. Although this technique has superior performance over Takagi method [3][4][5], it is highly dependent on accurately knowing the source impedance.

4) ERIKSSON METHOD
Eriksson method uses the source impedance parameters to eliminate the effect of any reactance errors such as load or fault resistance with high accuracy. This technique can calculate the value of RF, which is not possible in any other methods, but is unable to estimate the fault location in 3 terminals line or in TUP lines. [6]

B. Fault location error in TUP lines using single-ended technique protection scheme
First, we consider the described TUP line in which the parallel lines are connected at both ends shown in Fig. 3. In both terminals R and P, distance relays are installed, and their short circuit current is IR and IP, respectively. Moreover, m is the percentage of L'P, where the fault takes place. The conventional arrangement of TUP line leads to a non-uniform line impedance due to its arrangement, and it is of great importance to calculate the error in fault location in the single-ended fault technique. For calculating this error, assume a fault takes place in the location of m. The IR, VR and IP and VP are measured by relays in terminals R and P, respectively. The IR and IP are divided into IRʹ, IRʺ, IPʹ, and IPʺ in the branches. The measuring fault location relay error in the relay located at terminal R is calculated according to Fig.  3: And the calculated impedance by the relay is: By applying (5) and (8) into (10) it will be: It is noteworthy to mention that the distance relays indicate the location of the fault based on the calculated reactance and the initial data of the line's parameters, such as X0, X1, R0, R1.
Since the distance relays can only receive one line's parameters, the impedance of the parallel line is assumed as a uniform line with half of its impedance. Assuming a uniform line, the impedance that the relay should calculate, ZCorrect, is as follows: and ZError, which can be interpreted as the difference between the actual impedance that the relay must calculate and the apparent impedance that the relay sees, is derived as: where, ZError is an error that might lead to miscoordination, as the relay apparent impedance might become bigger than 120% (ZLN+ ZLP/2 + ZLM) [25].
Moreover, another fault location related error is the difference between exact distances of the fault location and the one that the relay is programmed to calculate, which is called Distance Error, ZError_Distance. While there is an error in precisely locating the fault, the dispatched linemen have to patrol through the line to find the exact fault point. This is a time-consuming process and leads to a more outage time of the line. The distance error can be derived as: As shown in (14) and (16) the proportion of IP/IR leads to a considerable error, where IP is much bigger than IR. It is therefore obvious that the error of the relay installed in one end could be much higher than that of the other side. Moreover, the length of ZLP is another dominant factor in both miscoordination and ZError-Distance, as the impedance of fault that the relay calculates could be more than 120% ZTotal [25].

A. Rearrangement Technique
The main goal of the proposed method is to reduce ZError and ZError-Distance not only to ease the procedure of finding the exact location of the fault but to prevent miscoordination. The proposed method consists of two steps. The first one (as shown in Fig. 4) is to disconnect the points A or B, which leads to new ZR as: According to the new topology, and as the line is now uniform, ZError and ZError-Distance can be derived as: (if B is disconnected): ZError-Distance= ZError = +R I (20) It is obvious that if a fault occurs at the sections LN, LM, or LP in Fig. 4, the problem can be addressed as described by equation (2), and the effect of the other side's current on the impedance of the relays is negligible. Another advantage of this step is that the impedance of the line is uniformed regardless of the location of the fault. Moreover, in the conventional scheme of connecting TUP lines, there would always be an error due to the settings of the relays, whether the fault occurs at sections LN, LM, or LP. However, by disconnecting one side the uniformity of the line will eliminate this error. Nevertheless, whether A or B is disconnected two different ZError-Distance can be derived according to equations (20) and (25). The best solution, thus, for minimizing the error of ZError-Distance is to discard the result of one relay. Discarding a relay result is according to the Ishort-circuit of both ends, in a way that the relay associated with the lower Ishort-circuit will be ignored. The policy taken to discard any relay results is described in table 2.
It is important to note that the short circuit current is highly dependent on the type of the fault, and since a majority of fault's type are SLG ones, the rearrangement should be calculated accordingly. Consequently, for other types of faults, where the proportion of . 3 . ⁄ < 1 the ZError-Distance might not satisfy all the constraints. In the next step of the proposed rearrangement, two main goals under two constraints are considered. The first goal is to minimize ZError-Distance to be lower than the sight range of the linemen teams, and the other one is to maintain protection coordination. In the proposed algorithm, to reach these goals, ZLP' is reduced by dividing into multiple sections being briefly described in Fig. 6; yet, it is vitally important to describe the constraints described in the following.

1) PROTECTION CONSTRAINT (P.C)
Assume that a fault occurs at TN shown in Fig. 5, and IR is much bigger than IP. It is obvious that ZError-Distance in the Relay (R) is less than that of Relay (P). However, the impedance calculated by Relay (R) and (P), which are described in equations (18) and (22), should not exceed 120% (ZLN+ ZLP + ZLM) to prevent miscoordination for all fault types [25].

2) VISUAL CONSTRAINT (V.C):
Any linemen team whose job is to locate and repair the failed equipment of lines has a sight range depending on some factors. These factors root from environmental conditions of the line's surroundings and their equipment such as binoculars, drones and etc. If ZError-Distance is less than this sight range, it is highly probable that the linemen team can locate the exact place of the fault occurrence as soon as they patrol to the point that the relay had determined.

3) LINE TOPOLOGY CONSTRAINT:
As the second step of the proposed rearrangement, it is suggested to divide the TUP line into multiple sections, yet these changes can merely occur in dead-end towers, where donated as Ni in Fig. 5. The second step of the rearrangement method starts from the first point of the TUP line near to the terminal, where . 1 . is bigger than the other side. An example of this process is illustrated in Fig. 5. This procedure is described as follows: connect B. (Fig 5-A) If B is connected then rename terminal P as R and terminal R as P for a fault at T0. (Fig 5-

E) 2) Calculate ZError-distance for Relay (S) and ZError All Faults
Type for Relay (R and P). (Fig 5-B) 3) Compare ZError-distance and ZError All Faults Type with visual constraints and protection constraint respectively. 4) If the constraints are satisfied disconnect T from the rest of TUP line. (Fig 5-C) If the entire line is totally energized finish the process. (Fig 5-F) If the entire line is not energized, Set T0 =TM and start the processing from stage 1. (Fig 5-C) 5) If the constraints are not satisfied set TM to the previous dead-end tower and start the processing from stage 2. (Fig 5-C) If the visual and protection constraints cannot be both satisfied, only consider the protection constraint. In the second step, the impact of ZLP' is reduced on the exact fault location error, while maintaining protection coordination. As mentioned before, in the faults occurring between terminal R and T0 in Fig. 7, the relay (R) shows better results compared to the one on the other side. Similarly, for locations between T0 and terminal P, relay (P)'s fault locator shows more accurate results for SLG faults compared to that of the other side. Moreover, in the faults occurring on the main line (section A in Fig. 7), both relays can show reliable answers for the fault location regardless of the fault type. In contrast, in the conventional arrangement schemes in the entire part of these sections, there is a considerable error causing both relays to show unreliable results for fault location with the possibility of miscoordination. The flow chart of the proposed algorithm is shown in Fig. 6. According to Fig. 5 it is assumed that Terminal R is close to point A and Terminal P is close to point B, moreover the dead-end towers are named as T0 to TN.

B. Selecting the Correct Fault Location
As it is mentioned in 3.1 both relays might not indicate the correct fault location and it is of great importance to detect which relay is showing the reliable fault location under various conditions. This analysis is summarized in the table (2) for a single line diagram shown in Fig. 7.   Fig. 7 Fig. 9.

FIGURE 8. A single line diagram of the rearrangement TUP line in Fars network
In Fig. 9 the error-distance for SLG faults is compared with the result of relay P and R in the conventional scheme. The error of rearrangement method is calculated for the faults occurring at the sections LBR and LBP. However, for the faults occurring at the section A, regardless of the fault type and with RF = 0, the rearrangements method has no error-distance. VOLUME XX, 2017 9 Although for 3PH faults at sections LBR and LBP the rearrangement results violate the Visual Constraint, they still yield better results compared with that of the conventional schemes. Since the relays are experiencing an overreach, the worse-case is when the RF is equal to zero.
The results of rearrangement method on sections LBR and LBP for SLG faults with different RF are compared with each other and indicated that they do not violate Visual Constraints and its results are illustrated in Fig.  10.
The results shown in Fig. 9 and 10, indicates that in all sections of the new rearrangement scheme, the protection constraints are satisfied for both relays. Although in section LBP and merely for 3PH and 2PH faults our proposed technique might violate visual constraint, for all the other types of errors in the entire sections at least one relay can estimate an acceptable fault location and can significantly reduce the errordistance.    Although, according to table 6, synchronized phasor measurements methods have the best results in finding the fault locations, they impose high financial burden to the project for two main reason. The first one roots from this point that a considerable number of TUP lines are temporarily and they can correctly be protected by using single-ended based techniques after the installation period of the whole project. The second one is, however, using high technological devises such as PMUs or GPS system, making them highly expensive. Yet, despite the fact that, single-ended based techniques are the most affordable ones, they cannot fulfill the desired accuracy for fault locating. On the other hand, in spite of being slightly more costly than single-ended based techniques, the proposed method can have a significant impact on the accuracy of fault locating.
Comparing the final results with those of similar works, one can simply conclude that the novel proposed rearrangement technique not only can reduce the outage time, but also might discard the need of installing high technologic devices such as PMUs, GPS and even numeric relays for finding the exact location of the faults.

VII. CONLUSION
Single-ended fault location methods could be accurate if the transmission line is uniform, while in uncompleted tied transmission line reveal unreliable fault location. Connecting parallel section of the uncompleted transmission lines make the line nonuniformed.
On the other hand, Multi-ended fault location algorithms can greatly improve the fault location accuracy, yet a majority of these algorithms require the transfer of large amounts of data, alignment of the data sets, and complicated solutions to calculate the distance to the fault point. These algorithms are prone to the risk of time-consuming fault location determination in online applications, while imposing considerable costs.
Moreover, financial investigation to implement such techniques are supposed to be unnecessary in temporary transmission line schemes. The proposed novel and economic rearrangement technique has many advantages over existing methods in that it can calculate the location of the fault much faster, maintain the protection coordination constraint compared with conventional techniques. Furthermore, it does not require advanced digital relays, let alone data transfer. In the case of multi-section or hybrid lines, our proposed method can still yield acceptable answers with some considerations. In fact, the relay's fault location has to be modified by considering the impedance of different sections.
In the conventional arrangement of these types of transmission lines, in cases, the relays could not locate the fault location. However, implementing the proposed technique, most of the time, relays can calculate the actual fault location and present the data to operations personnel in real-time. It is noteworthy to mention that the proposed technique is applied to the Fars-Iran power system in 2018 and yield excellent performance in practice since then.