Fuzzy Inference System Approach for Locating Series, Shunt, and Simultaneous Series-Shunt Faults in Double Circuit Transmission Lines

Many schemes are reported for shunt fault location estimation, but fault location estimation of series or open conductor faults has not been dealt with so far. The existing numerical relays only detect the open conductor (series) fault and give the indication of the faulty phase(s), but they are unable to locate the series fault. The repair crew needs to patrol the complete line to find the location of series fault. In this paper fuzzy based fault detection/classification and location schemes in time domain are proposed for both series faults, shunt faults, and simultaneous series and shunt faults. The fault simulation studies and fault location algorithm have been developed using Matlab/Simulink. Synchronized phasors of voltage and current signals of both the ends of the line have been used as input to the proposed fuzzy based fault location scheme. Percentage of error in location of series fault is within 1% and shunt fault is 5% for all the tested fault cases. Validation of percentage of error in location estimation is done using Chi square test with both 1% and 5% level of significance.


Introduction
In general, the transmission line faults are categorized into series faults and shunt faults. Unlike the shunt faults, which are characterized by substantial increase in current flow, the low magnitude of current following a series fault makes it difficult to be located by conventional approaches based on calculation of impedance and using fundamental component of current and voltage. Series fault is defined as a fault for which the impedances of the three phases are not equal, which is usually caused by the interruption of one or two phases. Series faults in EHV lines may occur due to broken conductor or a circuit breaker malfunction in one or more phases. The broken conductor leads to unbalance and flow of asymmetrical current arising because of the open conductor coming in series with the effected lines. As per field studies, a series fault may occur due to one of the following reasons: (i) Broken conductor(s) due to storm, falling of trees.
(ii) When poles of the circuit breakers fails to open.
(iii) Opening of jumpers at tension tower (angle locations) due to accident and storms. (iv) Mechanical failure of jumpers.
(v) Burning of jumper cones due to local heating at joints because of loose contacts/high contact resistance during prolonged operation.
Although series fault is not dangerous to the system, the operation of the load connected is hampered. The numerical distance relays, which are widely used for protection of transmission lines, only give an alarm that particular phase(s) is/are open, but no trip command is issued to the circuit breaker. Further the distance relays are unable to locate the open conductor (series) fault. Faults in transmission lines affect the power flow and reduce the reliability of transmission system. Fault location estimation is an important task in transmission system for carrying out maintenance work to improve power flow reliability and reduce repairing expenses. Some research has been done to detect the open conductor/series fault. Open phase conductor detector system 2 Computational Intelligence and Neuroscience is described in [1] consisting of transmitters and receiver where transmitter(s) detects the open phase conductor by monitoring the phase conductor voltage using redundant inputs. Carrier communication is used for open conductor detection in [2]. Open conductor fault calculation in four parallel transmission lines using twelve-sequence component methods is discussed in [3]. ANN based techniques are used for enhancement of distance relay performance against open conductor in HV transmission lines in [4]. However these schemes [1][2][3][4] are unable to find the location of series/open conductor fault.
Fault location algorithms for shunt faults are reported by researchers using different soft computing techniques like artificial neural network (ANN) [18][19][20][21], fuzzy [22] and adaptive neurofuzzy inference system (ANFIS) [23], SVM [24], and so forth. Among all the soft computing techniques, fuzzy inference system is used mostly in engineering applications, for example, fault classification [25], due to its easy implementation and less computation work to get accurate results unlike other training based soft computing methods. Moreover there is a chance that simultaneous series and shunt faults may occur in the transmission line as discussed in [26,27] which can lead to incorrect operation of relay. Digital distance relaying scheme which takes care of a simultaneous open conductor and ground fault occurring coincidently on the same phase at the same point on a series-compensated double circuit line is proposed in [28]. But the scheme treats   the simultaneous open conductor and ground fault as single  line to ground fault. Hence, it can be concluded that, hitherto, none of the earlier reported papers  can locate both series and shunt faults and simultaneous series-shunt faults. In this paper, a method is proposed using synchronized phasors and fuzzy logic to classify the fault and estimate fault location of series faults, shunt faults, and simultaneous series and shunt faults. The proposed fuzzy based method works in three stages. In the first stage, the current and voltage signals obtained from both ends of the line are preprocessed to calculate the fundamental components and zero-sequence component of current signals. Thereafter, two fuzzy modules for fault classification have been designed to discriminate the type of fault, that is, whether series fault or shunt fault or simultaneous series and shunt fault has occurred. Further, according to the type of fault, a particular fuzzy module for fault location of series or shunt or simultaneous series or shunt will be activated which finds the location of fault in kilometers from the relaying point.

Fuzzy Inference System (FIS) and
Its Application Fuzzy inference system is chosen to locate the faults in transmission lines in this work because it is easy to implement and it does not require training module to produce outputs. Due to less computation work than other soft computing techniques fuzzy system is chosen. Fuzzy inference system deals with fuzzy logic which starts with the concept of a fuzzy set. A fuzzy set is a set without a crisp, clearly defined boundary. It can contain elements with only a partial degree of membership. A fuzzy set can be defined by the following expression: where represents the universal set, is an element of , is a fuzzy subset in , and ( ) is the membership function of fuzzy set . FIS chosen to be used here is "Mamdani" type because it expects the output membership functions to be fuzzy sets. As fuzzy logic used here is to estimate the location of fault which is not a fixed value, so it is better to use Mamdani method than to use Sugeno method. Membership functions are designed with various membership functions like Gauss, triangular, trapezoidal, and sigmoid functions and so forth. In this work input and output are designed with triangular member function because it has lowest error in location. The triangular membership function is a function of a vector, , and depends on three scalar parameters, , , and , as given by (2) or (3). Consider the following: Computational Intelligence and Neuroscience Fuzzy sets and fuzzy operators are the subjects and verbs of fuzzy logic. If-then rule statements are used to formulate the conditional statements that comprise fuzzy logic. A single fuzzy if-then rule assumes the form as shown in where and are linguistic values defined by fuzzy sets on the ranges and , respectively. From the inputs impedance values their membership values are obtained. This process is called "input fuzzification." From the consequent of each rule (a fuzzy set) and the antecedent value obtained a fuzzy implication operator is applied to obtain a new fuzzy set. Implication method used here is "minimum" which truncates the consequent's membership function and the product which scales it. Then it combines the outputs obtained for each rule into a single fuzzy set, using a fuzzy aggregation operator which is "maximum" in this case. The fuzzy set is then transformed into a single numerical value. Defuzzification method used here is the "centroid" method which returns the centre of the area under the fuzzy set. Center of gravity method is a grade weighted by the areas under the aggregated output functions. The centroid defuzzification method can be given as in * = ∫ ( ) where ∫ ( ) ̸ = 0 for all . By following all these steps described above fuzzy module is designed for fault classification and location estimation module. Detailed fuzzy design of the proposed fault location schemes for series faults, shunt faults, and simultaneous series and shunt faults will be described in next section.

Proposed Fuzzy Based Series, Shunt, and Simultaneous Series and Shunt Faults Classification and Location Estimation
Proposed method uses synchronized phasor measurements and fuzzy inference system to estimate the fault location.
Steps followed in the proposed method are described in Figure 1 for the estimation of fault location and are described in following subsections.

Power System
Network. The utility electrical power plant system selected for modelling is the existing 400 kV transmission line between Korba NTPC to Raipur PGCIL in Chhattisgarh state. Length of the transmission line is 220 km between Korba to Raipur as shown in Figure 2. Power transfer through the double circuit line is 341 MW. Synchronized phasors of currents and voltages are preprocessed using Discrete Fourier Transform (DFT) and sequence analyzer. Fundamental component of current and voltages is obtained using DFT. Zero-sequence currents are obtained using the sequence analyzer in order to determine whether ground is involved in the fault loop or not.

Design of Fuzzy Module for Classification of Series Fault (FIS-CSR) and Shunt Fault (FIS-CSH).
For classification of type of faults, the fundamental components and zerosequence components of currents of both ends are taken. Two different FIS modules are designed, one for classification of series fault (FIS-CSR) and the other for classification of shunt fault (FIS-CSH). In this present study Mamdani type FIS has been used because its outputs are in fuzzy sets.

Fuzzy Module for Classification of Series Fault (FIS-CSR).
A single FIS module has been designed for detecting the presence of fault in a particular phase. The same FIS has been used for the other two phases. Each phase FIS module takes its fundamental phase current as input and provides single output representing the presence of fault in that phase by trip high (TH) or trip low (TL) for no fault condition. The fundamental components of three phase currents of both circuits measured at both ends of the line are used as input for fault classification. Fundamental component of current is set to certain range which corresponds to fault or no fault in each phase. Three ranges of are selected using triangular member function, that is, low, medium, and high. The output trip logic also contains two ranges of triangular member function, that is, trip low (TL) (0) and trip high (TH) (1). The degree of membership functions for input phase fundamental current is shown in Figure 3(a) for series faults. FIS-CSR has six outputs corresponding to the three phases of the parallel lines (double circuit lines). The rules designed for faulty phase identification and fault classification are as follows: (1) If fundamental phase current is low or medium then trip is TH. (2) If fundamental phase current is high then trip is TL.
Fuzzy inference system for fault classification of series fault (FIS-CSR) takes the fundamental current of each phase as input and produces the state of each phase (whether faulty or not) as output.

Fuzzy Module for Classification of Shunt Fault (FIS-CSH).
The shunt faults are classified into phase to ground (LG), double phase to ground (LLG), phase to phase (LL), and three-phase (LLL) faults. As discussed in Section 2, for faulty phase identification, the fundamental components of three phase currents are taken as input to FIS-CSH for classification of phases. Further, for ground identification, separate FIS module has been designed which takes the zero-sequence current signals of the two circuits 1 and 2 as input. Each input's signals are distributed in three ranges with triangular member function, that is, low, medium, and high. There are six outputs for faulty phase identification corresponding to the three phases of circuit 1: A1, B1, and C1 and A2, B2, and C2 of circuit 2 which becomes high (1) in case of fault and otherwise remains low (0). The degree of membership functions for input current is shown in Figure 3(b) for shunt fault phase identification and in Figure 3(c) for ground identification. The rules designed for faulty phase identification are as follows: (1) If fundamental phase current is low or medium then trip is TL.
(2) If fundamental phase current is high then trip is TH.
Further the rules used for ground identification are as follows: (1) If zero-sequence current is low or medium then trip is TL.
(2) If zero-sequence current is high then trip is TH.

Design of Fuzzy Module for Fault Location.
Once the fault is detected and its type is identified, then the next task of protective relaying scheme is to estimate the fault location from the relaying point. In this study, two separate FIS modules have been designed for series fault (FIS-LSR) and shunt fault (FIS-LSH). Based on type of fault that has occurred in the monitored transmission line, that is, whether series fault or shunt fault or simultaneous series-shunt fault, the corresponding fuzzy module for fault location will be activated which estimates the location of fault.

Fuzzy Module for Series Fault Location (FIS-LSR).
During  Figure 4(a). Fundamental components of current values are divided into ranges like 1 , 2 , 3 , . . . , 112 using triangular member functions. Output represents the fault location in kilometers which is divided into 111 ranges using triangular member  (1) If input is 1 then location is 1 .
(111) If input is 111 then location is 111 .
(112) If input is 112 then location is 1 . inference system, the phase impedance is calculated for faulty phase(s) from

Fuzzy Module for Shunt Fault Location (FIS-LSH).
where is fundamental component of voltage and is fundamental component of current. is taken as input to the fuzzy module for fault location estimation of shunt faults. Different fuzzy modules for different types of fault (LG, LLG, LL, and LLL) for fault location estimation are designed. Based on type of fault which has occurred in the system identified by fault classification module, the corresponding FIS-LSH will be activated and fault location will be estimated. Figure 4(b) shows the fuzzy based fault location modules (FIS-LSH) of different types of shunt fault; impedance ( ) of faulty phase is taken as input to fuzzy module and fault location is estimated. In Figure 4(b), it is clear that for LG faults there will be only one input as only one phase is faulty. Fundamental components of impedance ( ) are divided into a number of ranges like 1 , 2 , 3 , . . . , 56 using triangular member functions. Output fault location is also divided into ranges using triangular member function like 1 , 2 , 3 , . . . , 55 . Total number of rules made for LG shunt fault location is 56. The rules are given below: (1) If input is 1 then location is 1 .
(2) If input is 2 then location is 2 .
(55) If input is 55 then location is 55 .
(56) If input is 56 then location is 1 .
For LLG and LL faults, there are two inputs to the fuzzy module as shown in Figure 4(b). Fundamental components of impedance values for faulty phase 1 ( i ) and phase 2 ( ii ) are divided into ranges like i1 , i2 , i3 , . . . , i56 and ii1 , ii2 , ii3 , . . . , ii56 using triangular member functions. Output fault location is also divided into ranges using triangular member function like 1 , 2 , 3 , . . . , 55 . The rules for LLG faults are given hereunder. Similarly LLL fault location module is designed using three inputs for location estimation as shown in Figure 4 (1) If input 1 is i1 and input 2 is ii1 then location is 1 .
(2) If input 1 is i2 and input 2 is ii2 then location is 2 .
(3) If input 1 is i3 and input 2 is ii3 then location is 3 .
(55) If input 1 is i55 and input 2 is ii55 then location is 55 . (56) If input 1 is i56 and input 2 is ii56 then location is 1 .

Simultaneous Series and Shunt Fault Location. If both series and shunt fault classification FIS modules (FIS-CSH
and FIS-CSR) detect the presence of fault, then simultaneous series and shunt fault has occurred. In case of simultaneous series and shunt faults, location of series fault will be obtained using one-end measurement and that of shunt fault will be obtained using remote end measurement. For simultaneous series and shunt faults, FIS-LSR is activated for series fault end and FIS-LSH is activated for shunt fault end, which determines the location of respective fault.

Series Fault Classification and Location Estimation.
The proposed scheme involves two stages; first is fault classification and then location estimation. In the first stage, both the FIS modules FIS-CSR and FIS-CSH are tested to detect the fault and classify the fault type, that is, whether the fault is series or shunt fault. For example, a series fault in A1 phase has occurred at 60 ms time and 64 km away from the relaying point; the test result of both the FIS is shown in Figure 5. Figure 5(a) shows the six outputs of FIS-CSR which become high (1) after 80.5 ms for phase A1 only depicting that the fault is series fault in A1 phase of circuit 1 while Figure 5(b) shows that the outputs of FIS-CSH are all low (0) confirming that there is no shunt fault in the system. Once the fault type is classified as series fault, the corresponding FIS module for series fault location estimation is activated and the output of FIS-LSR during a series fault in phase A1 at 64 km at 60 ms time is shown in Figure 6. The estimated fault location is 63 km after 88 ms time as shown in Figure 6. Further the proposed scheme is also tested for different series faults with varying fault location and inception angle and some of the results of proposed fault location scheme are given in Table 1. The test result shows the high accuracy in determining the fault location with much less % of error.

Shunt Fault Classification and Location Estimation.
The proposed scheme can simultaneously detect the presence of fault and also classify the fault whether it is series or shunt fault as, during no fault or normal condition, all outputs of both the fuzzy modules FIS-CSR and FIS-CSH are low (zero), and in case of any type of fault the corresponding fuzzy classification module output changes its state from low to high after some time. This can be clearly seen from the test results shown in Figure 7 during A1B1G shunt fault in circuit 1 at 50 km at 60 ms time. Figure 7(a) shows that all the outputs of FIS-CSR are low throughout the simulation time (0-160 ms) and Figure 7(b) shows the outputs of FIS-CSH fault module which become high for phases A1, B1, and G1 after 73.54 ms time verifying that it is A1B1G shunt fault in circuit 1. As the fault type classified is LLG type of shunt fault, LLG shunt fault locator estimates the fault location as 50.69 km as shown in Figure 8. Few more other types of shunt fault are tested and results are reported in Table 2.     Figure 9 it can be seen that the proposed scheme correctly identifies the fault type and the faulty phase and its location. Proposed fuzzy based method is tested for some other simultaneous series and shunt faults and results are given in Table 3, which corroborate that the proposed scheme works equally well during simultaneous series and shunt faults situation also, as compared to existing schemes which fails.   Figure 10 shows the percentage of fault cases in which the shunt fault location error is within 0 to ±2.0% and ±2.1 to ±5% ranges.
The computed value of 2 must equal or exceed the appropriate critical value to justify rejection of the null hypothesis at 0.05 or 0.01 level of significance. It shows whether the apparent differences or relationships are true differences/relationships or whether they merely result from sampling error [29]. Chi square test results are shown in Table 4. Fault cases for different range of error according to fault type are the calculated ones which is the observed frequency of error distribution ( ). Expected frequency of  occurrence of error for each of the cells (column or row) for all types of fault is calculated from the observed frequency of the error using (8). 2 is calculated for all types of fault for all the ranges of error and shown in Table 4 by using (9). Different levels of significance for different degrees of freedom are shown in Table 5. Degree of freedom can be calculated as per (10). Consider where is the expected frequency of error, is observed frequencies in columns, is observed frequencies in rows, and total is the sum of all the frequencies = 2100. Consider where is the observed frequency of error. Consider = (Rows − 1) * (Columns − 1) , where is the degree of freedom.
In this method there are 4 rows and 2 columns, so degree of freedom is 3. From Table 5, with degree of freedom 3, calculated 2 value is less for both 5% and 1% significant levels for all types of fault. This shows that null hypothesis is accepted and the error for fault location will not be the same for replication of experiment. Thus the proposed fuzzy based fault location scheme is accurate and can be used for series and shunt fault location estimation.

Conclusion
This paper proposes a new approach using synchronized phasor measurement and fuzzy system to classify the series, shunt, and simultaneous series-shunt faults and predict the fault location in a double circuit transmission lines. Proposed method is effective in determining accurate fault location because it is not affected by variation in fault type, fault inception angle, fault distance, and so forth. Fuzzy inference system used for series and shunt fault location estimation is "Mamdani" type. Fault location error in case of series fault is within 1%, while in case of shunt fault it is up to 5%. So error validation of shunt faults is done using Chi square test. The major contribution of the proposed scheme is that it classifies the fault type (both series and shunt) correctly and estimates the correct value of fault location of series faults and simultaneous series-shunt faults which has not been reported to date.