Single-ended distributed parameter fault location method for ultra-high voltage transmission line

Abstract

This invention relates to a single-end distributed parameter fault location method for ultra-high voltage (UHV) transmission lines, comprising: acquiring the line parameters of the UHV transmission line under test and determining whether a fault has occurred; acquiring the three-line voltage vector and three-phase current vector of the faulty end of the transmission line, establishing a distributed parameter model of the transmission line, and dividing the distributed parameter model of the transmission line into a fault-side segment model, a fault-opposite-side segment model, and a fault branch model according to the fault region; employing a single-end phasor domain centralized parameter fault location method to solve for the initial values ​​of the fault location and fault resistance; based on the fault-opposite-side segment model, constructing a fault location equation with the fault location and fault resistance as variables, and iteratively solving for the fault location and fault resistance as an optimization problem, as the fault location result. Compared with the prior art, this invention significantly improves the fault location accuracy of UHV long-distance transmission lines.

Description

Technical Field

[0001] This invention relates to the field of power transmission line fault location technology, and in particular to a single-end distributed parameter fault location method for ultra-high voltage power transmission lines. Background Technology

[0002] With the continuous growth of electricity demand, the length and voltage level of transmission lines are also constantly increasing. The highest grid voltage level can reach 1100 kV, and the length of transmission lines can reach hundreds or even thousands of kilometers. These transmission lines are called ultra-high voltage (UHV) transmission lines. For example, the East China Power Grid is a typical large receiving-end grid, with a high regional electricity load but relatively low local power generation. In this case, many UHV transmission lines are connected to the East China Power Grid for long-distance transmission of large amounts of electricity. During the operation of UHV transmission lines, faults may occur within the transmission lines. Accurate fault location is crucial for the reliable operation of transmission lines, as it minimizes the time spent locating faults and ensures the reliable operation of the power system.

[0003] There are many fault location methods in the existing literature. These methods mainly include (a) traveling wave-based methods; (b) artificial intelligence-based methods; (c) time-domain fault analysis methods; and (d) phasor-domain fault analysis methods.

[0004] (a) Wave-based method

[0005] Traveling wave-based methods locate faults by detecting the arrival time of the traveling wave. These methods can be further divided into single-ended and double-ended traveling wave fault location methods. Single-ended traveling wave fault location methods determine the fault location by capturing the subsequent arrival time of the traveling wave on the local side. The subsequent arrival time includes the reflected traveling wave from the fault location, providing information for fault location. This class of methods also includes type A, C, E, and F methods. Double-ended traveling wave fault location methods detect the arrival time of the first wavefront at both ends of the line to determine the fault location. These methods also include type B and type D methods. When applied to practical power systems, traveling wave-based methods face the following challenges. First, the reliable detection of the traveling wave front depends on the time of fault occurrence. Therefore, it is possible that the arrival of the fault wavefront may not be detected. Second, the accuracy of these methods depends on the high sampling rate of the measurement, typically on the order of MHz.

[0006] (b) Artificial intelligence-based methods

[0007] With the rapid development of artificial intelligence, data-driven methods are widely used in fields such as computer vision and natural language processing. Researchers have also proposed data-driven fault location methods, including various neural networks such as convolutional neural networks (CNNs), long short-term memory (LSTM), and graph neural networks. Some researchers have also incorporated physical information into the data feature extraction process to improve the accuracy of fault location. A key limiting factor in applying data-driven fault location methods in practical power systems is the availability of field data for training. Because the probability of transmission line faults during operation is very low, the amount of field data is quite limited.

[0008] (c) Time-domain fault analysis method

[0009] The literature proposes time-domain fault analysis methods that directly utilize sampled values ​​for fault location. These methods have the advantage of being compatible with short time windows and complex electrical transient processes during faults. Fault location methods can vary depending on the transmission line model, including RL models, multi-π models, Bergeron models, and distributed parameter models. To handle broadband fault time-domain waveforms, frequency-dependent line models are typically considered to achieve higher line modeling accuracy. The accuracy of time-domain fault analysis methods largely depends on the accuracy of the time-domain line model. Accurate time-domain line models are usually quite complex, posing challenges to the design of time-domain fault location methods.

[0010] (d) Phasor Domain Fault Analysis Method

[0011] Phasor domain fault analysis methods are the most widely used methods in practical power systems. Existing methods can be divided into single-ended and double-ended methods. Compared with double-ended fault location methods, single-ended methods do not require remote measurements. Therefore, single-ended fault location methods are more attractive in practical applications. Existing single-ended methods include the simple reactance method, the Takagi method, and the Eriksson method. Currently, some methods also utilize circuit breaker operating information or renewable energy characteristics to implement single-ended fault location.

[0012] Ultra-high voltage (UHV) long-distance transmission lines present additional challenges to fault location. On the one hand, the extremely high voltage levels of these lines lead to more complex transients and larger parallel capacitive currents during faults. On the other hand, the length of the transmission lines amplifies the impact of distributed parameters on the accuracy of line modeling. Among all faults, single-phase grounding faults have the highest probability of occurrence: statistically, 70% to 80% of faults are single-phase grounding faults. Furthermore, high fault resistance is a well-known challenge in single-phase grounding faults, contributing significantly to accurate fault location.

[0013] The Eriksson method is a single-ended phasor domain fault location method based on a transmission line impedance model, widely used in practice as it requires only local measurement information. However, the Eriksson method utilizes a lumped parameter model of the transmission line. With increasing voltage levels and transmission line lengths, the influence of distributed capacitance becomes significant, and using a lumped parameter model in ultra-high voltage long-line fault location reduces location accuracy. Summary of the Invention

[0014] The purpose of this invention is to overcome the shortcomings of the existing fault location methods, which utilize lumped parameter models of transmission lines and reduce location accuracy, and to provide a single-end distributed parameter fault location method for ultra-high voltage transmission lines.

[0015] The objective of this invention can be achieved through the following technical solutions:

[0016] A method for locating single-end distributed parameter faults in ultra-high voltage transmission lines includes the following steps:

[0017] S1: Obtain the line parameters of the ultra-high voltage transmission line under test and determine whether the line has a fault. If a fault occurs, proceed to step S2.

[0018] S2: Obtain the three-line voltage vector and three-phase current vector at the faulty end of the transmission line, establish a distributed parameter model of the transmission line, and divide the distributed parameter model of the transmission line into a fault-side segment model, a fault-side segment model, and a fault branch model according to the fault area.

[0019] S3: Based on the three-line voltage vector and three-phase current vector at this end of the transmission line, the single-end phasor domain centralized parameter fault location method is used to solve for the initial value of the fault location and fault resistance.

[0020] S4: Based on the segmented model opposite the fault point, with the fault location and fault resistance as variables, construct the fault location equation and use it as an optimization problem. Based on the initial values ​​of the fault location and fault resistance, solve to obtain the iterative values ​​of the fault location and fault resistance for the next step.

[0021] S5: Based on the next iteration value of the fault location and fault resistance, iteratively solve the optimization problem until the preset termination condition is met, and obtain the final fault location and fault resistance as the fault location result.

[0022] Furthermore, the expression for the distributed parameter model of the transmission line is:

[0023]

[0024] In the formula, Let Z be the voltage vector at position y, where y is the distance relative to side M; Z is the impedance matrix per unit length of the line; and Y is the admittance matrix per unit length of the line. Let be the current vector at position y. This is the voltage vector at the starting point of the line. and Let M and N represent the voltage vectors on the M and N sides of the line, respectively. Let be the voltage vector at the end of the line, and l be the line length. Let be the current vector at the starting point of the line. This represents the current vector at the end of the line. and These represent the current vectors on the M side and the N side of the line, respectively. The M side is the line itself, and the N side is the opposite side of the line.

[0025] The corresponding expression for the relationship between the voltage and current phasors at both ends of the transmission line, calculated accordingly, is as follows:

[0026]

[0027] In the formula, K 11 ,K 12 ,K 21 and K 22 Both are functions of l.

[0028] Furthermore, the expression for the fault point local segmentation model is:

[0029]

[0030] In the formula, Where is the voltage at the fault point, and p is the fault location. This refers to the current flowing into the fault point.

[0031] Furthermore, the expression for the fault point-side segmentation model is:

[0032]

[0033] In the formula, This refers to the current flowing out of the fault point.

[0034] Furthermore, the process of constructing the fault location equation is as follows:

[0035] Based on the expression of the segmented model opposite the fault point, we can obtain and For p, and The function; based on the expression of the segmented model of the fault point on this side, we can obtain for and functions of p for and functions of p; according to and Relationship, and R F and The relational expression is obtained. Available p and R F express, and Ultimately, it can be represented as And the fault location p and the fault resistance R F The function is used to obtain the fault location equation.

[0036] Furthermore, the aforementioned and The relation is:

[0037]

[0038] In the formula, The current flowing out of the fault point. The current flowing into the fault point, This refers to the fault point current.

[0039] The R F and The relation is:

[0040]

[0041] In the formula, R F This is the fault resistor.

[0042] Furthermore, the fault location equation is constructed using a positive-order fault network, a negative-order fault network, or a zero-order fault network.

[0043] Furthermore, the expression for the fault location equation constructed using a positive-sequence fault network is as follows:

[0044]

[0045] In the formula, f FL (x) represents the fault location result, x = [p, R]. F ] T , The positive-sequence voltage fault component of the segmented model opposite the fault point. Z represents the positive-sequence current fault component of the segmented model opposite the fault point. R1 This represents the positive-sequence fault impedance component of the segmented model opposite the fault point.

[0046] Furthermore, the expression for the optimization problem is:

[0047]

[0048] In the formula, F(x) represents the result of the optimization problem, f real (x) and f imag (x) represents the real and imaginary parts of the formula for calculating the fault location result, respectively, x = [p,R] F ] T p is the fault location, R F The fault resistor is l, and the line length is l.

[0049] The optimization problem is solved iteratively using the Gauss-Newton method, and the corresponding calculation expression is:

[0050]

[0051] In the formula, J f (x) is the Jacobian matrix, and ki is the number of iterations;

[0052] The termination condition is:

[0053] ||d (ki) ||2≤ε

[0054] In the formula, ε is a given threshold.

[0055] Furthermore, the single-ended phasor domain centralized parameter fault location method is the Eriksson method.

[0056] Compared with the prior art, the present invention has the following advantages:

[0057] (1) This invention proposes a precise fault location method for ultra-high voltage long-distance transmission lines using single-end electrical quantities. This method only requires local measurement information with a sampling rate of 4kHz and does not require measurement information at the opposite end of the line. Therefore, it does not require communication technology or synchronous sampling at both ends of the transmission line, and has the advantages of low cost and ease of practical application. Compared with the existing Eriksson method, the proposed fault location method utilizes a distributed parameter line model. Taking the fault point as the boundary, the long-distance transmission line model is divided into three parts. The two sides of the fault point are two healthy line models, which adopt the distributed parameter model; the fault point adopts the fault branch model. The above three models constitute the complete line model after the fault; it can accurately compensate for the parallel capacitor current when there is a fault in the ultra-high voltage long line. In addition, this method measures the single-end voltage and current of the transmission line, and expresses the voltage vector and circuit vector on the opposite side as functions of the measured value, fault location and fault resistance on the local side, to obtain a precise optimized model for single-end fault location considering grounding resistance. Furthermore, through an iterative method, the above optimized model is solved to obtain the actual fault location and achieve precise fault location.

[0058] (2) Simulation experiments conducted in PSCAD / EMTDC show that, compared with the existing Eriksson method, the method proposed in this invention significantly improves the fault location accuracy of ultra-high voltage long-distance transmission lines, which is of great significance for accurately determining the fault location and quickly restoring the operation of the power grid. Attached Figure Description

[0059] Figure 1 This is a schematic diagram of an AG fault occurring in a double-ended transmission line system provided in an embodiment of the present invention;

[0060] Figure 2 This is a schematic diagram of an equivalent network for positive-order fault components provided in an embodiment of the present invention;

[0061] Figure 3 This is a schematic diagram of a distributed parameter model for a power transmission line provided in an embodiment of the present invention;

[0062] Figure 4 This is a schematic diagram of a single-line diagram model of a power transmission line provided in an embodiment of the present invention;

[0063] Figure 5 This is a flowchart illustrating a single-end fault location method for an ultra-high voltage transmission line provided in an embodiment of the present invention. Detailed Implementation

[0064] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0065] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0066] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0067] Introduction to the Eriksson method:

[0068] The Eriksson method is a single-ended phasor domain lumped parameter fault location method based on the transmission line impedance model, and it is widely used in practice. Since single-phase grounding faults are the most common type of fault, without loss of generality, this paper derives the fault location expression using an A-phase grounding fault (denoted as AG) as an example.

[0069] Figure 1 This is a schematic diagram of a two-terminal (MN) transmission system. In this invention, the M-terminal is uniformly referred to as the local side, and the N-terminal as the opposite side. In the diagram, and These are the three-phase voltages on this side. and These are the three-phase currents on this side. Z s Z is the self-impedance per unit length of the line. m Z is the mutual impedance per unit length of the line. L1 =Z s –Z m and Z L0 =Z s +2Z m These represent the positive (negative) sequence impedance and zero sequence impedance per unit length of the line, respectively. F It is a faulty resistor. It is the voltage at the fault point. This is the current flowing through the fault resistor. The total length of the transmission line is denoted as l, and the distance from the fault to this side is denoted as p.

[0070] According to Kirchhoff's Voltage Laws (KVLs), the voltage of phase A on this side can be expressed as follows:

[0071]

[0072] The above equation can be rearranged into the following equation:

[0073]

[0074] In the formula: k=(Z L0 -Z L1 ) / Z L1 It is the zero-order compensation coefficient. It is the zero-sequence current on this side.

[0075] For an AG fault, the A-phase fault current of the faulty branch... and positive sequence fault current Should meet:

[0076]

[0077] The fault component can be obtained by subtracting the voltage and current before the fault from the voltage and current after the fault. Figure 2 for Figure 1 The positive-sequence fault component equivalent network, in the figure, Z S1 and Z R1 These are the equivalent positive-sequence impedances of the local system and the opposite system, respectively. and These are the fault components of the voltage and current on this side, respectively.

[0078] In the above equivalent network of positive-sequence fault components, the positive-sequence current of the fault branch... and the sudden change in current on this side satisfy:

[0079]

[0080] By combining equations (2)–(4), the fault location p and fault resistance R can be obtained. F satisfy:

[0081] p 2 -k1p+k2-k3R F =0 (5)

[0082] The specific expression for the coefficients k1-k3 in the formula is as follows:

[0083]

[0084] Expanding the real and imaginary parts of equation (5) respectively, the fault location p can be obtained:

[0085]

[0086] p has two solutions. The solution that is greater than 0 and less than the total length l of the line is taken as the correct solution.

[0087] Fault resistor R F The following can also be obtained accordingly:

[0088]

[0089] As can be seen from the above, the Eriksson method only requires local measurement information and is widely used in practice. However, the Eriksson method utilizes a lumped parameter model of the transmission line. With the increase of voltage level and transmission line length, the influence of its distributed capacitance cannot be ignored. Using a lumped parameter model in fault location of ultra-high voltage long lines will reduce the location accuracy. Therefore, this invention performs accurate modeling of long-distance transmission lines and proposes an accurate fault location method.

[0090] Example 1

[0091] like Figure 5 As shown in the figure, this embodiment provides a method for locating single-end distributed parameter faults in ultra-high voltage transmission lines, including the following steps:

[0092] S1: Obtain the line parameters of the ultra-high voltage transmission line under test and determine whether the line has a fault. If a fault occurs, proceed to step S2.

[0093] S2: Obtain the three-line voltage vector and three-phase current vector at the faulty end of the transmission line, establish a distributed parameter model of the transmission line, and divide the distributed parameter model of the transmission line into a fault-side segment model, a fault-side segment model, and a fault branch model according to the fault area.

[0094] S3: Based on the three-line voltage vector and three-phase current vector at this end of the transmission line, the single-end phasor domain centralized parameter fault location method is used to solve for the initial value of the fault location and fault resistance.

[0095] S4: Based on the segmented model opposite the fault point, with the fault location and fault resistance as variables, construct the fault location equation and use it as an optimization problem. Based on the initial values ​​of the fault location and fault resistance, solve to obtain the iterative values ​​of the fault location and fault resistance for the next step.

[0096] S5: Based on the next iteration value of the fault location and fault resistance, iteratively solve the optimization problem until the preset termination condition is met, and obtain the final fault location and fault resistance as the fault location result.

[0097] The specific process of step S2 is as follows:

[0098] Figure 3 This is a distributed parameter model (single-line diagram) for a transmission line, where the line length is l, y is the distance relative to side M, Z is the impedance matrix per unit length of the line, and Y is the admittance matrix per unit length of the line. and These represent the voltage vectors on the M and N sides of the line, respectively. and These represent the current vectors on the M and N sides of the line, respectively.

[0099] Its distributed parameter model can then be expressed as the following differential equation:

[0100]

[0101] Solving equation (9) yields the relationship between the voltage and current phasors at both ends of the transmission line, as shown in equation (10). In the equation, I is the identity matrix, O is the zero matrix; K 11 ,K 12 ,K 21 and K 22 All are functions of l. The matrices Z, Y, I, O, K above... 11 ,K 12 ,K 21 ,K 22 All dimensions are 3×3.

[0102]

[0103] In the formula:

[0104] The following is based on Figure 4 The equivalent single-line diagram system shown derives the fault location expression. In the diagram, the transmission line model where the fault occurs is divided into three parts: the mf segment model to the left of the fault point, the nf segment model to the right of the fault point, and the fault branch model. The mf segment and the nf segment both adopt the sound line model of Equation (10). and These are the three-phase voltage and current on this side, respectively. and These are the three-phase voltages and currents on the opposite side, respectively. and These are the voltage and current of the faulty branch, respectively. The current flowing into the fault point from this side. This refers to the current flowing from the fault point to the opposite side.

[0105] This invention only requires local measurement information (measured voltage). and measuring current This allows for fault location. The derivation is as follows.

[0106] Based on the distributed parameter model of transmission lines according to equation (9), for the mf segment line located on this side, the fault point voltage and the current flowing into the fault point It can be expressed as a function of the fault location p, as shown in equations (11)-(12):

[0107]

[0108] At the point of failure, and satisfy:

[0109]

[0110] According to Kirchhoff's Current Laws (KCLs), the following equation holds true at the fault point:

[0111]

[0112] The distributed parameter model of the transmission line in equation (10) is then applied to the nf segment line located on the opposite side. The voltage on the opposite side is then... and current Satisfying equations (15)-(16):

[0113]

[0114] The specific processes of steps S4 and S5 are as follows:

[0115] In equations (15)-(16), and For p, and The function. And according to equation (11), Available And p represents; according to equation (12) Available And p represents, according to equation (14) yes and The function is then combined into equations (11)-(13). Available p and R F This indicates that the opposite side... and The final value can be expressed as the measured value on this side. And the fault location p and the fault resistance R F The function.

[0116] Let the two unknowns p and R be... F Let it be vector x = [p, R] F ] TEstablish the positive-sequence fault component network of the nf segment line on the opposite side, and denote its voltage and current fault components as follows: and Then, in this positive-sequence fault component network, the following fault location equation exists:

[0117]

[0118] Obviously, when x is correctly solved, the above expression should equal 0.

[0119] It is worth noting that this invention is not limited to the positive-order fault network described above. Similar fault location equations can also be established using negative-order or zero-order fault networks.

[0120] It should be emphasized again that although the opposite electrical quantity appears in equation (17) and However, this invention only requires measuring the electrical quantities on the local side; as can be seen from the above analysis, the electrical quantities at the opposite end in equation (17) are all derived from the measured values ​​on the local side.

[0121] Expand equation (17) into the real part f real (x) and the imaginary part f imag (x), and construct the following fault location problem:

[0122]

[0123] This problem is a constrained optimization problem, which can be solved iteratively using the Gauss-Newton method as follows:

[0124]

[0125] Where: Jacobian matrix ki represents the number of iterations.

[0126] The iteration terminates when the following condition is met:

[0127] ||d (ki) ||2≤ε (20)

[0128] In the formula: ε is a given threshold.

[0129] Since the Gauss-Newton method requires iteration, choosing appropriate initial values ​​is crucial to ensuring the convergence of the algorithm. In this invention, the Eriksson method is first used to calculate the optimization variables p and R. F The initial value of .

[0130] Finally, it should be noted that although the above derivation process of the present invention is only for AG fault type, it can also be solved in a similar way for other fault types of transmission lines.

[0131] Implementation example:

[0132] A 1000 kV, 800 km transmission line was constructed in PSCAD / EMTDC. The system and transmission line parameters are shown in Table 1. S1 ,R S0 ,L S1 and L S0 These are the positive-sequence and zero-sequence resistances and inductances of the equivalent power supply at terminal M (this side), R. R1 ,R R0 ,L R1 and L R0 The parameters are the positive-sequence and zero-sequence resistance and positive-sequence and zero-sequence inductance of the equivalent power supply at the N-terminal, respectively. r1, r0, L1, L0, C1 and C0 are the positive-sequence and zero-sequence resistance, positive-sequence and zero-sequence inductance and positive-sequence and zero-sequence capacitance per unit length of the transmission line, respectively.

[0133] Since the IEC 61850 standard specifies that the sampling frequency of the merging unit in a smart substation is 4kHz, the same sampling frequency was used in the simulation in this paper.

[0134] Table 1 System parameters for the example

[0135] parameter value parameter value <![CDATA[R S1 ]]> 1.0515Ω <![CDATA[R S0 ]]> 0.6Ω <![CDATA[L S1 ]]> 0.13743H <![CDATA[L S0 ]]> 0.0926H <![CDATA[R S1 ]]> 26Ω <![CDATA[R S0 ]]> 20Ω <![CDATA[L S1 ]]> 0.14298H <![CDATA[L S0 ]]> 0.11927H <![CDATA[r1]]> 0.0343Ω / km <![CDATA[r0]]> 0.2913Ω / km <![CDATA[L1]]> 0.0013H / km <![CDATA[L0]]> 0.0037H / km <![CDATA[C1]]> 0.0087μF / km <![CDATA[C0]]> 0.0060μF / km

[0136] To comprehensively verify and compare the effectiveness of this method, simulations were performed for fault location under different fault distances (100, 200, 300, 400, 500, 600, and 700 km) and different fault resistances (2, 5, 10, 50, 100, and 300 Ω). The results are shown in Tables 2 and 3. It can be seen that the fault location error of the Eriksson method increases with the increase of the actual fault location. This is because the model error of lumped parameters becomes increasingly significant with the increase of the transmission line length. However, when using this method, the fault location error is not greatly affected by the actual fault location. This is because even for ultra-high voltage long transmission lines, the accurate line model based on distributed parameters used in this invention can guarantee the accuracy of fault location.

[0137] Table 2. Fault location results (km) when grounded via low fault resistance (AG)

[0138]

[0139] Table 3. Fault location results (km) when grounded via high fault resistance (AG).

[0140]

[0141] Table 4 summarizes and compares the average fault location errors of different methods. It is evident that the location accuracy of our proposed method is significantly higher than that of the Eriksson method. This demonstrates the importance of employing a more accurate distributed parameter model for ultra-high voltage long-distance transmission lines and the effectiveness of our proposed method.

[0142] Table 4. Average Fault Location Error (%)

[0143] <![CDATA[Fault resistance R F (Ω)]]> 2 5 10 50 100 300 Eriksson method 4.617 4.457 4.275 3.753 5.587 3.561 This method 0.032 0.020 0.009 0.009 0.012 0.018

[0144] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A method for locating single-ended distributed parameter faults in ultra-high voltage transmission lines, characterized in that, Includes the following steps: S1: Obtain the line parameters of the ultra-high voltage transmission line under test and determine whether the line has a fault. If a fault occurs, proceed to step S2. S2: Obtain the three-phase voltage vector and three-phase current vector at the faulty end of the transmission line, establish a distributed parameter model of the transmission line, and divide the distributed parameter model of the transmission line into a fault-side segment model, a fault-side segment model, and a fault branch model according to the fault area. S3: Based on the three-phase voltage vector and three-phase current vector at this end of the transmission line, the single-ended phasor domain centralized parameter fault location method is used to solve for the initial value of the fault location and fault resistance. S4: Based on the segmented model opposite the fault point, with the fault location and fault resistance as variables, construct the fault location equation and use it as an optimization problem. Based on the initial values ​​of the fault location and fault resistance, solve to obtain the iterative values ​​of the fault location and fault resistance for the next step. S5: Based on the next iteration value of the fault location and fault resistance, iteratively solve the optimization problem until the preset termination condition is met, and obtain the final fault location and fault resistance as the fault location result. The expression for the optimization problem is: In the formula, The calculation results for the optimization problem, and These represent the real and imaginary parts of the formula for calculating the fault location result. , Location of the fault. The fault resistor, This refers to the line length; The optimization problem is solved iteratively using the Gauss-Newton method, and the corresponding calculation expression is: In the formula, For Jacobian matrices, ki This represents the number of iterations. The termination condition is: In the formula, The given threshold.

2. The single-end distributed parameter fault location method for ultra-high voltage transmission lines according to claim 1, characterized in that, The expression for the distributed parameter model of the transmission line is: In the formula, for y Voltage vector at position, y The distance relative to side M. This is the impedance matrix per unit length of the line. The admittance matrix per unit length of the line is... for y The current vector at the location, This is the voltage vector at the starting point of the line. and Let M and N represent the voltage vectors on the M and N sides of the line, respectively. This is the voltage vector at the end of the line. l For line length, Let be the current vector at the starting point of the line. This represents the current vector at the end of the line. and These represent the current vectors on the M side and the N side of the line, respectively. The M side is the line itself, and the N side is the opposite side of the line. The corresponding expression for the relationship between the voltage and current phasors at both ends of the transmission line, calculated accordingly, is as follows: In the formula, , , and All are l The function.

3. The single-end distributed parameter fault location method for ultra-high voltage transmission lines according to claim 2, characterized in that, The expression for the fault point local segmentation model is: In the formula, The voltage at the fault point. Location of the fault. The current flowing into the fault point, , , and All are The function.

4. The single-end distributed parameter fault location method for ultra-high voltage transmission lines according to claim 3, characterized in that, The expression for the segmented model opposite the fault point is: In the formula, This refers to the current flowing out of the fault point.

5. The single-end distributed parameter fault location method for ultra-high voltage transmission lines according to claim 4, characterized in that, The specific process of constructing the fault location equation is as follows: Based on the expression of the segmented model opposite the fault point, we can obtain and for p , and The function; based on the expression of the segmented model of the fault point on this side, we can obtain for , and p functions, for , and p The function; according to and Relationship, and , and The relational expression is obtained. Available , , p as well as R F express, and Ultimately, it can be represented as , and the location of the fault p and fault resistor R F The function is used to obtain the fault location equation.

6. The single-end distributed parameter fault location method for ultra-high voltage transmission lines according to claim 5, characterized in that, The and The relation is: In the formula, The current flowing out of the fault point. The current flowing into the fault point, The fault current; The , and The relation is: In the formula, This is the fault resistor.

7. The single-end distributed parameter fault location method for ultra-high voltage transmission lines according to claim 5, characterized in that, The fault location equation is constructed using a positive-sequence fault network, a negative-sequence fault network, or a zero-sequence fault network.

8. The single-end distributed parameter fault location method for ultra-high voltage transmission lines according to claim 7, characterized in that, The expression for the fault location equation constructed using a positive-sequence fault network is as follows: In the formula, For the fault location results, , The positive-sequence voltage fault component of the segmented model opposite the fault point. The positive-sequence current fault component of the segmented model opposite the fault point. This represents the positive-sequence fault impedance component of the segmented model opposite the fault point.

9. The single-end distributed parameter fault location method for ultra-high voltage transmission lines according to claim 1, characterized in that, The single-ended phasor domain centralized parameter fault location method is the Eriksson method.

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