A submarine cable fault identification and section location method based on multi-modulus collaborative analysis

Abstract

This invention belongs to the field of cable fault identification technology and discloses a method for fault identification and segment location of submarine cables based on multi-modulus collaborative analysis. First, it obtains the measured values ​​of voltage and current at the beginning and end of a three-core armored submarine cable, along with line parameters. Second, it establishes and decouples a distributed parameter model of the three-core armored submarine cable based on the line parameters. Utilizing the difference between measured and calculated values, and combining the decoupled modulus, it identifies faults in both cracking and short-circuit scenarios. Finally, it calculates the voltage at the cable segment joint location using the modulus to locate the short-circuit fault segment. This invention is applicable to fault identification and segment location of high-voltage, long-distance, segmented AC submarine cables. It offers high calculation accuracy and speed, is unaffected by the power supply at both ends, fault type, and transition resistance, facilitates measurement value acquisition, and has low implementation cost, making it highly significant in engineering practice.

Description

Technical Field

[0001] This invention belongs to the field of cable fault identification technology, specifically relating to a method for fault identification and section location of three-core armored submarine cables using decoupled multi-modulus collaborative analysis. Background Technology

[0002] Submarine cables, as a crucial component of offshore wind power systems, play a vital role in power transmission. However, their harsh operating environment, constantly threatened by biological organisms, tides, and maritime activities, easily leads to damage to the armor, insulation, and conductors, causing cable cracking, short circuits, and other faults. These faults not only affect the normal operation of offshore wind power equipment but may also trigger power system anomalies or even safety accidents, resulting in economic losses. Therefore, accurate and rapid fault identification and distance measurement are of great significance for ensuring the efficient operation of the power system and effectively protecting the stability and safety of the operating environment.

[0003] Currently, cable modeling methods can be broadly categorized into lumped parameter models and distributed parameter models. Lumped parameter models are only suitable for describing the electrical characteristics of short cables, while distributed parameter models are more applicable to long-distance submarine cables. Fault location methods for cables can be broadly classified into traveling wave methods and impedance methods. The traveling wave method utilizes the traveling wave information generated by the fault to achieve fault location, but it is easily affected by factors such as wavefront identification and noise. The impedance method achieves fault location based on the relationship between steady-state measured phasors, line parameters, and fault distance, yielding relatively accurate results, but the computational load is large for long-distance submarine cables. Furthermore, most of the above methods are designed for short-circuit faults, with little coverage of the identification of cracking and short-circuit faults. Therefore, based on distributed parameter models, rapid and accurate fault identification and segment location for submarine cables is of great significance. Summary of the Invention

[0004] To address the aforementioned technical challenges and enable rapid and accurate identification and segment location of submarine cable faults, this invention proposes a method for submarine cable fault identification and segment location based on multi-modulus collaborative analysis. This method boasts high computational accuracy, fast speed, and is unaffected by the power supply at both ends, fault type, and transition resistance. It also facilitates the acquisition of measurement values ​​and has practical engineering significance.

[0005] To achieve the above objectives, the present invention is implemented through the following technical solution:

[0006] This invention is a method for fault identification and segment location of submarine cables based on multi-modulus collaborative analysis, comprising the following steps:

[0007] Step 1: Measure the voltage and current at both ends of the three-core armored submarine cable in steady state. The subscripts i = A, SA, B, SB, C, SC, M represent phase A conductor, phase A shield, phase B conductor, phase B shield, phase C conductor, phase C shield, and armor layer, respectively. The superscripts S and R represent the quantities at the beginning and end of the cable, respectively. The current and three-phase conductor voltage are obtained through direct measurement, while the voltage of the shield and armor layer are calculated from the grounding resistance and the current flowing through them.

[0008]

[0009] in R g To determine the grounding resistance, based on the cable parameters, obtain the impedance matrix Z, admittance matrix Y, and cable length L per unit length of the three-core armored submarine cable.

[0010] Step 2: Based on the distributed parameter model, write the 7th order matrix equations of voltage and current with respect to distance x. Decouple the U, I, Z, and Y matrices in the equations to obtain the voltage modulus equation and the current modulus equation.

[0011] Step 3: Based on the modulus equation obtained in Step 2, use the measured voltage and current at the beginning and end of the three-core armored submarine cable as initial conditions to solve the voltage modulus equation, obtaining the voltage modulus at any distance x. 7 Decoupled Voltage Magnitude Expressions

[0012]

[0013] Where m represents the decoupled modulus, and the numbers correspond to the ordinal numbers of the decoupled modulus. This represents the voltage modulus obtained using the decoupled first-end quantity as the initial condition. This represents the voltage modulus obtained by using the decoupled terminal quantity as the initial condition.

[0014] Step 4: Based on the voltage modulus obtained in Step 3 Calculate the seven voltage moduli at the end of the three-core armored submarine cable, and substitute them into the decoupling formula to obtain the calculated values ​​of the three-phase voltage at the end.

[0015] Step 5: Calculate the terminal three-phase voltage based on the value obtained in Step 4. The voltage measurement value at the end of the three-core armored submarine cable obtained in step 1. Substitute the calculated and measured values ​​of the three-phase voltage at the end into the fault criterion to determine whether a fault has occurred.

[0016] Step 6: Based on the judgment result of Step 5, if a fault is determined to have occurred, calculate the decoupled first-end voltage amplitude corresponding to the fourth voltage modulus in steady state after the fault, substitute it into the cracking criterion, and determine whether the fault type is cracking or short circuit, thereby realizing fault identification.

[0017] Step 7: Based on the judgment result of Step 6, if a short circuit fault is determined to have occurred, then use the voltage modulus... Calculate the voltage modulus at the cable segment joint locations separately, and substitute it into the decoupling formula to obtain the calculated value of the voltage at the faulty phase joint.

[0018] Step 8: Based on the calculated voltage at the faulty phase connector obtained in Step 7, the faulty section is determined by comparing the calculated voltage values ​​at different connector locations.

[0019] A further improvement of the present invention is that: in step 4, the voltage modulus formula obtained in step 3 is used... Let x = L, calculate the seven voltage moduli at the cable end, and substitute them into the decoupling formula to obtain the calculated values ​​of the three-phase voltage at the end.

[0020]

[0021] Where V is the calculated value obtained by calculating the voltage modulus separately and then substituting it into the decoupling formula, and α i β i γ i These are the i-th elements of the row vectors in rows 1, 3, and 5 of the voltage decoupling matrix, respectively.

[0022] A further improvement of the present invention lies in: the calculated value of the terminal three-phase voltage obtained in step 4. The voltage measurement value at the end of the three-core armored submarine cable obtained in step 1. Substitute the calculated and measured amplitudes of the three-phase voltages at the end into the fault criterion:

[0023]

[0024] Where peak is the amplitude, and j = A, B, C, "nor" indicates normal operation. If the criterion condition is met, it is determined that a fault has occurred and the faulty phase is identified as phase j; otherwise, it is determined that there is no fault.

[0025] A further improvement of the present invention is that, in step 6, the method for fault identification is as follows: calculate the decoupled first-end voltage amplitude corresponding to the fourth voltage modulus in the steady state after the fault, and substitute it into the cracking criterion:

[0026]

[0027] in, U is the measured value of the decoupled start-up voltage corresponding to the fourth voltage modulus in steady state after the fault. S P is a column vector composed of the measured voltage values ​​at the first end. u4 The row vector is formed by taking the modulus values ​​of the elements in the 4th row of the voltage decoupling matrix. `peak` represents the amplitude, and `K` is the threshold. To prevent false judgments and ensure the reliability of the criterion, the threshold value `K` is obtained through calculation and analysis under the conditions of slight cracking and short circuit with large transition resistance. If the criterion condition is met, it is determined that a cracking fault has occurred in phase j, and the result is obtained from step 5. The magnitude of the fault determines the severity of the fault; otherwise, it is determined to be a short circuit fault. At this point, the fault identification is complete.

[0028] A further improvement of the present invention is that, in step 7, the voltage modulus at the cable segment joint locations is calculated respectively, and the calculated voltage value is obtained by substituting it into the decoupling formula.

[0029]

[0030] Where x1, x2, ..., x N Let η be the position of N connectors from the beginning. i This is the i-th element of the row vector containing the faulty phase in the voltage decoupling matrix. These are the i-th voltage modulus calculated using the decoupled first-end and last-end quantities as initial conditions, where i ranges from 1 to 7, and L is the cable length.

[0031] A further improvement of the present invention is that, in step 8, based on the calculated voltage value at the faulty phase connector obtained in step 7, the faulty section is determined by sequentially comparing the voltage amplitude at different connector locations, specifically:

[0032] Step 8.1: Substitute the positions of the N connectors from the beginning into the criterion formula sequentially. Where n = 1, 2, ..., N, k2 is a threshold selected based on the calculation error. This value represents the maximum calculation error at different transition resistances and different connector positions, with a certain margin. If the criterion is met, the fault is determined to occur near the nth connector. Let x ∈ (x n -Δx,x n +Δx), where Δx is the maximum ranging error under different conditions with a certain margin. If all x n If none of the criteria formulas are met, the fault is considered to occur at a non-joint location, and the subsequent steps are executed.

[0033] Step 8.2: If the criterion is met... The fault is determined to occur between the cable head and the first connector, i.e., x∈(0,x1);

[0034] Step 8.3: If the criterion is met... The fault is determined to occur between the cable end and the Nth connector, i.e., x∈(x N ,L);

[0035] Step 8.4: If the two criteria in Steps 8.2 and 8.3 are not met, then calculate the values ​​at the positions of two adjacent joints in sequence. and The value, if

[0036]

[0037] Where n = 1, 2, ..., N-1, then let n = n+1, and repeat the above calculation until...

[0038]

[0039] The fault is determined to occur between the nth and (n+1)th joints of the cable, i.e., x∈(x n ,x n+1 With this, the location of the faulty section is complete.

[0040] The beneficial effects of this invention are: Based on the distributed parameter model of a three-core armored submarine cable, this invention improves the calculation accuracy by decoupling the three-phase cores, shielding layer and armor layer;

[0041] This invention utilizes the decoupled modulus to identify the type of fault; it also pre-locates the faulty section before precise ranging, greatly improving the speed and accuracy of calculation.

[0042] This invention is applicable to high-voltage, long-distance segmented AC submarine cables, and is not affected by the power supply at both ends, fault type, or transition resistance. It is easy to obtain measurement values, has low implementation cost, and has high engineering practical significance. Attached Figure Description

[0043] Figure 1 This is a flowchart of the present invention.

[0044] Figure 2 This is a schematic diagram of the distributed parameter model for a three-core armored submarine cable.

[0045] Figure 3 This is a schematic diagram of the segmented structure of a three-core armored submarine cable with two connectors. Detailed Implementation

[0046] The embodiments of the present invention will be disclosed below with reference to the drawings. For clarity, many practical details will be described in the following description. However, it should be understood that these practical details are not intended to limit the invention. That is, in some embodiments of the invention, these practical details are not essential.

[0047] A schematic diagram of the distributed parameter model of a three-core armored submarine cable is shown below. Figure 2 As shown, the electromagnetic coupling between conductors is represented by impedance and admittance. Impedance consists of the self-impedance of a single phase conductor, the mutual impedance between different phase conductors, and the mutual impedance between corresponding phase conductors and the shielding and armor layers. Similarly, admittance consists of the self-admittance of a single phase conductor, the mutual admittance between different phase conductors, and the mutual admittance between corresponding phase conductors and the shielding and armor layers. A schematic diagram of the segmented structure of a three-core armored submarine cable with two joints is shown below. Figure 3 As shown, the measurement points are set at the beginning and end of the cable, the total length of the cable L is 30km, and there is a joint every 10km.

[0048] like Figure 1 As shown, the present invention provides a method for fault identification and segment location of submarine cables based on multi-modulus collaborative analysis, comprising the following steps:

[0049] Step 1: Measure the voltage and current at both ends of the three-core armored submarine cable in steady state. The subscripts i = A, SA, B, SB, C, SC, M represent phase A conductor, phase A shield, phase B conductor, phase B shield, phase C conductor, phase C shield, and armor layer, respectively. The superscripts S and R represent the quantities at the beginning and end of the cable, respectively. The current and three-phase conductor voltage are obtained through direct measurement, while the voltage of the shield and armor layer are calculated from the grounding resistance and the current flowing through them.

[0050]

[0051] in R g The grounding resistance is 1Ω. The actual measured value is close to 0 during normal operation. To facilitate subsequent steps, this value is taken as 0 during normal operation. Based on the parameters of the HYJQF41-F 127 / 220kV cable, the impedance matrix Z, admittance matrix Y, and cable length L per unit length of the three-core armored submarine cable are obtained.

[0052] Step 2: Based on the distributed parameter model, write the 7th order matrix equations of voltage and current with respect to distance x. Decouple the U, I, Z, and Y matrices in the equations to obtain the modulus equations of voltage and current.

[0053] Step 3: Decouple the measured start-up and end-up quantities using the method in Step 2. Use the decoupled start-up and end-up quantities as initial conditions to solve the voltage modulus equation in Step 2, resulting in seven decoupled voltage modulus expressions.

[0054]

[0055] Where the subscript m represents the decoupled modulus, and the number corresponds to the ordinal number of the decoupled modulus. This represents the expression for calculating the voltage modulus using the decoupled first-end quantity as the initial condition. The expression for calculating the voltage modulus using the decoupled terminal quantity as the initial condition is given. The specific values ​​of the row vector in the 4th row of the voltage decoupling matrix for the HYJQF41-F 127 / 220kV three-core armored submarine cable are as follows:

[0056] σ=[0.0465-0.0441i,-0.3137+0.0465i,0.0465-0.0441i,-0.3137+0.0465i,

[0057] 0.0465-0.0441i,-0.3137+0.0465i,0.8277]

[0058] Step 4: Based on the voltage modulus expression obtained in Step 3 Let x = L, calculate the seven voltage moduli at the cable end, and substitute them into the decoupling formula to obtain the calculated values ​​of the three-phase voltage at the end.

[0059]

[0060] Where V represents the calculated value obtained by calculating the voltage modulus separately and then substituting it into the decoupling formula, and α i β i γ i These are the i-th elements of the row vectors in rows 1, 3, and 5 of the voltage decoupling matrix, respectively.

[0061] Step 5: Based on the calculated values ​​of the three-phase voltages at the end in Step 4. The voltage measurement value at the end of the three-core armored submarine cable obtained in step 1. Substitute the calculated and measured amplitudes of the three-phase voltages at the end into the fault criterion:

[0062]

[0063] Where peak represents the amplitude, and j = A, B, C, "nor" indicates normal operation. After multiple calculations, it is known that the threshold value k1 of the HYJQF41-F 127 / 220kV three-core armored submarine cable is 0.00275kV. If the criterion condition is met, it is determined that a fault has occurred and the faulty phase is determined to be phase j; otherwise, it is determined that there is no fault.

[0064] Step 6: Based on the judgment result of Step 5, if a fault is determined to have occurred, calculate the decoupled first-terminal voltage amplitude corresponding to the fourth voltage modulus in steady state after the fault, and substitute it into the cracking criterion:

[0065]

[0066] in U is the measured value of the decoupled first-terminal voltage corresponding to modulus 4 in steady state after the fault. S P is a column vector composed of the measured voltage values ​​at the first end. u4 The row vector is formed by taking the modulus values ​​of the elements in the 4th row of the voltage decoupling matrix. The subscript 'peak' indicates the amplitude, and K is the threshold. To prevent false judgments and ensure the reliability of the criterion, calculations and analyses are performed for 0.1Ω cracking and 1000Ω transition resistance short circuits. The threshold K is set to 0.15kV. If the criterion condition is met, it is determined that a cracking fault has occurred in phase j, and the result is obtained from step 5. The magnitude of the fault determines the severity of the fault; otherwise, it is determined to be a short circuit fault. At this point, the fault identification is complete.

[0067] Step 7: Based on the judgment result of Step 6, if a short circuit fault is determined to have occurred, calculate the voltage modulus at the locations of the two cable segment joints x1 = 10km and x2 = 20km respectively, and substitute them into the decoupling formula to obtain the calculated voltage value.

[0068]

[0069] Where η i This is the i-th element of the row vector containing the faulty phase in the voltage decoupling matrix. These are the i-th voltage modulus calculated using the decoupled first-end and last-end quantities as initial conditions, where i ranges from 1 to 7, and L is the cable length.

[0070] Step 8: Based on the calculated voltage value at the faulty phase connector obtained in Step 7, the faulty section is determined by sequentially comparing the voltage amplitude at different connector locations. The specific steps are as follows:

[0071] (a) Substitute the positions of the two joints from the beginning into the criterion formula in turn. Where n = 1, 2, and k2 is a threshold selected based on calculation error. Based on multiple calculations, k2 is set to 0.05 kV. If the criterion is met, the fault is determined to occur near the nth connector. Let x ∈ (xn -Δx,x n +Δx), where, based on the maximum distance measurement error under different conditions, let Δx = 0.3km, if all x n If none of the criteria formulas are met, the fault is considered to occur at a non-joint location, and the subsequent steps are executed.

[0072] (b) If the criterion is satisfied The fault is determined to occur between the cable head and the first connector, i.e., x∈(0,10), in km;

[0073] (c) If the criterion is satisfied The fault is determined to occur between the end of the cable and the second joint, i.e., x∈(20,30), in km;

[0074] (d) If neither of the above two criteria is met, then calculate the positions of the two adjacent joints. and The value, if

[0075]

[0076] The fault was determined to occur between the first and second cable joints, i.e., x∈(10,20), in km. At this point, the fault section location was completed.

[0077] Simulation verification

[0078] To verify the effectiveness and reliability of this invention, a transmission model of a three-core armored submarine cable was built on PSCAD / EMTDC. Two fault scenarios were simulated: core cracking and a short circuit between the core and the shield. Fault simulations were performed under different fault types, fault distances, and fault resistance. Based on the method of this invention, relevant parameters and fault sections were calculated using MATLAB. The fault identification results are shown in Table 1, and the fault section location results are shown in Table 2, where x... r R represents the actual fault distance. f Indicates the fault resistance.

[0079] Table 1 Fault identification results under different fault conditions

[0080]

[0081] Table 2. Fault section location results under different fault conditions

[0082]

[0083] As can be seen from the data in Tables 1 and 2, the present invention has high calculation accuracy and speed, is not affected by the power supply at both ends, fault type and transition resistance, and the measured values ​​are easy to obtain.

[0084] The above description is merely an embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principle of the present invention should be included within the scope of the claims of the present invention.

Claims

1. A method for fault identification and segment location of submarine cables based on multi-modulus collaborative analysis, characterized in that: The method for identifying and locating faults in submarine cables includes the following steps: Step 1: Measure the voltage and current at the beginning and end of the three-core armored submarine cable. Based on the cable parameters, obtain the impedance matrix Z, admittance matrix Y, and cable length L per unit length of the three-core armored submarine cable. Step 2: Based on the distributed parameter model, write the 7th order matrix equations of voltage and current with respect to distance x. Decouple the U, I, Z, and Y matrices in the equations to obtain the voltage modulus equation and the current modulus equation. Step 3: Based on the modulus equation obtained in Step 2, use the measured voltage and current at the beginning and end of the three-core armored submarine cable as initial conditions to solve the voltage modulus equation, obtaining the voltage modulus at any distance x. Where S and R represent the cable head end and end end quantities respectively, and m represents the decoupled modulus; Step 4: Based on the voltage modulus obtained in Step 3 Calculate the seven voltage moduli at the end of the three-core armored submarine cable, and substitute them into the decoupling formula to obtain the calculated values ​​of the three-phase voltage at the end. Step 5: Calculate the terminal three-phase voltage based on the value obtained in Step 4. The voltage measurement value at the end of the three-core armored submarine cable obtained in step 1. Substitute the calculated and measured values ​​of the three-phase voltage at the end into the fault criterion to determine whether a fault has occurred. Step 6: Based on the judgment result of Step 5, if a fault is determined to have occurred, calculate the decoupled first-end voltage amplitude corresponding to the fourth voltage modulus in steady state after the fault, substitute it into the cracking criterion, and determine whether the fault type is cracking or short circuit, thereby realizing fault identification. Step 7: Based on the judgment result of Step 6, if a short circuit fault is determined to have occurred, then use the voltage modulus... Calculate the voltage modulus at the cable segment joint locations separately, and substitute it into the decoupling formula to obtain the calculated value of the voltage at the faulty phase joint. Step 8: Based on the calculated voltage at the faulty phase junction obtained in Step 7, the faulty section is determined by comparing the calculated voltage values ​​at different junction locations. Specifically, in Step 4, the voltage modulus formula obtained in Step 3 is used... Let x = L, calculate the seven voltage moduli at the cable end, and substitute them into the decoupling formula to obtain the calculated values ​​of the three-phase voltage at the end. Where V is the calculated value obtained by calculating the voltage modulus separately and then substituting it into the decoupling formula, and α i β i γ i These are the i-th elements of the row vectors in rows 1, 3, and 5 of the voltage decoupling matrix, respectively. 7 Decoupled Voltage Magnitude Expressions Where m represents the decoupled modulus, and the numbers correspond to the ordinal numbers of the decoupled modulus. This represents the voltage modulus obtained using the decoupled first-end quantity as the initial condition. This represents the voltage modulus obtained by using the decoupled terminal quantity as the initial condition.

2. The method for submarine cable fault identification and segment location based on multi-modulus collaborative analysis according to claim 1, characterized in that: The calculated values ​​of the terminal three-phase voltages obtained in step 4 The voltage measurement value at the end of the three-core armored submarine cable obtained in step 1. Substitute the calculated and measured amplitudes of the three-phase voltages at the end into the fault criterion: Where peak is the amplitude, and j = phases A, B, and C. "nor" indicates normal operation. If the criterion condition is met, it is determined that a fault has occurred and the faulty phase is identified as phase j; otherwise, it is determined that there is no fault.

3. The method for submarine cable fault identification and segment location based on multi-modulus collaborative analysis according to claim 2, characterized in that: In step 6, the method for fault identification is as follows: calculate the decoupled first-terminal voltage amplitude corresponding to the fourth voltage modulus in steady state after the fault, and substitute it into the cracking criterion: in, U is the measured value of the decoupled start-up voltage corresponding to the fourth voltage modulus in steady state after the fault. S P is a column vector composed of the measured voltage values ​​at the first end. u4 The row vector is formed by taking the modulus values ​​of the elements in the 4th row of the voltage decoupling matrix. `peak` represents the amplitude, and `K` is the threshold. The value of the threshold `K` is obtained through calculation and analysis under cracking and short-circuit conditions. If the criterion condition is met, it is determined that a cracking fault has occurred in phase j, and the result is determined in step 5. The magnitude of the fault determines the severity of the fault; otherwise, it is determined to be a short circuit fault. At this point, the fault identification is complete.

4. The method for submarine cable fault identification and segment location based on multi-modulus collaborative analysis according to claim 1, characterized in that: In step 7, the voltage modulus at the cable segment joint locations is calculated, and the calculated voltage value is obtained by substituting it into the decoupling formula. Where x1, x2, ..., x N Let η be the position of N connectors from the beginning. i This is the i-th element of the row vector containing the faulty phase in the voltage decoupling matrix. These are the i-th voltage modulus calculated using the decoupled first-end and last-end quantities as initial conditions, where i ranges from 1 to 7, and L is the cable length.

5. The method for submarine cable fault identification and segment location based on multi-modulus collaborative analysis according to claim 4, characterized in that: In step 8, based on the calculated voltage value at the faulty phase connector obtained in step 7, the faulty section is determined by sequentially comparing the voltage amplitude at different connector locations. Specifically: Step 8.1: Substitute the positions of the N connectors from the beginning into the criterion formula sequentially. Where n = 1, 2, ..., N, k2 is a threshold selected based on the calculation error. This value represents the maximum calculation error at different transition resistances and different connector positions, with a margin. If the criterion is met, the fault is determined to occur near the nth connector. Let x ∈ (x n -Δx,x n +Δx), where Δx is the maximum ranging error under different conditions with a margin, if all x n If none of the criteria formulas are met, the fault is considered to occur at a non-joint location, and the subsequent steps are executed. Step 8.2: If the criterion is met... The fault is determined to occur between the cable head and the first connector, i.e., x∈(0,x1); Step 8.3: If the criterion is met... The fault is determined to occur between the cable end and the Nth connector, i.e., x∈(x N ,L); Step 8.4: If the two criteria in Steps 8.2 and 8.3 are not met, then calculate the values ​​at the positions of two adjacent joints in sequence. and The value, if Where n = 1, 2, ..., N-1, then let n = n+1, and repeat the above calculation until... The fault is determined to occur between the nth and (n+1)th joints of the cable, i.e., x∈(x n ,x n+1 With this, the location of the faulty section is complete.

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