A method for locating single-pole grounding faults in DC cables based on the slope variation of instantaneous power curves

Abstract

This invention discloses a method for locating single-pole grounding faults in DC cables based on the slope change of the instantaneous power curve. Relating to the field of electrical technology, this method achieves fault location directly through the dynamic change of the power curve slope without requiring external signal injection. It solves the problems of complex equipment and poor anti-interference capability of traditional traveling wave methods. The key technical points are: the method includes the following steps: A1. Acquiring the voltage and current signals of each conductor layer of the positive and negative poles; A2. Calculating the primary slope; A3. Calculating the equivalent time point; A4. Calculating the maximum secondary slope; A5. Calculating the constant α and correction coefficients λ and k; A6. Obtaining the actual secondary slope; A7. Obtaining the fault distance. This invention, by monitoring the instantaneous power change at the cable end and combining it with the dynamic change of the power slope, can accurately and in real-time identify the fault location.

Description

Technical Field

[0001] This invention relates to the field of electrical technology, specifically to a method for locating single-pole grounding faults in DC cables based on the slope change of the instantaneous power curve. Background Technology

[0002] Compared to traditional AC cables, DC cables offer advantages such as lower loss, easier maintenance, and higher stability. Medium-voltage DC (MVDC) distribution cables typically operate in harsh environments, where their insulation materials and internal structures are prone to aging over time, leading to faults. Faults often occur under complex operating conditions, making accurate and rapid fault location difficult. Therefore, effectively locating and eliminating faults to reduce power outage time and improve the stability and security of the entire DC distribution network has become a pressing issue. Minimizing the impact of cable faults on people's lives and work has become a key objective for the industry.

[0003] Medium-voltage DC cables, as crucial transmission channels for flowing electricity in modern power systems, directly impact the stability of power supply. However, with the extension of cable lines and the complexity of operating conditions, the probability of cable faults gradually increases. Therefore, more precise fault location schemes are needed to shorten recovery time after a fault and improve the reliability and safety of power grid operation. Through feature pattern recognition and signal frequency characteristic analysis, MVDC distribution cable fault location technology can be significantly improved. This not only enhances fault location accuracy but also provides real-time fault information feedback, offering strong support for the safe and stable operation of the power system.

[0004] Chinese Patent Publication No. CN115469187A discloses a method, device, and processor for locating cable faults. The invention includes: injecting a preset pulse wave into the space formed by the cable core and shielding layer at a preset port of the faulty cable, and collecting reflected wave data corresponding to the reflected waves between the cable core and shielding layer; determining the traveling wave time difference between the preset pulse wave and the reflected wave based on the preset pulse wave and reflected wave data; obtaining the traveling wave velocity of the preset pulse wave within the faulty cable; and determining the distance between the fault point in the faulty cable and the preset port based on the traveling wave time difference and traveling wave velocity. This invention solves the technical problems of low locating accuracy and long locating time in related technologies for fault testing methods after cable faults occur. In complex cable lines, the above methods suffer from severe attenuation or waveform distortion of the reflected wave signal, leading to inaccurate time difference extraction and inability to accurately identify the fault location.

[0005] Therefore, the applicant has developed a new technical solution in the actual production process to solve the above-mentioned technical problems. Summary of the Invention

[0006] To address the aforementioned technical shortcomings, the purpose of this invention is to provide a method for locating single-pole grounding faults in DC cables based on the slope change of the instantaneous power curve. This method eliminates the need for external signal injection and achieves location directly through the dynamic change of the slope of the power curve, thus solving the problems of complex equipment and poor anti-interference capability of traditional traveling wave methods.

[0007] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0008] This invention provides a method for locating single-pole grounding faults in DC cables based on the slope change of instantaneous power curves, comprising the following steps:

[0009] A1. Obtain the voltage and current signals of each conductor layer of the positive and negative electrodes;

[0010] A2. Calculate the first slope;

[0011] A3. Calculate the equivalent time point;

[0012] A4. Calculate the maximum quadratic slope;

[0013] A5. Calculate the constants and correction factors;

[0014] A6. Obtain the actual quadratic slope;

[0015] A7. Obtain the distance to the fault.

[0016] By employing the aforementioned technical solution, analyzing the slope changes of the instantaneous power curve to determine the fault location can provide more accurate fault location results. This method can capture subtle changes, thereby improving the accuracy of location, reducing reliance on external equipment, and lowering system complexity, hardware, and maintenance costs. Since no special signal generation device is required, the overall system structure is simpler, easier to deploy and maintain. It directly utilizes data from the power system itself for analysis, reducing the impact of the external environment on measurement results, enhancing system stability and reliability. It is applicable to various types of DC cables and can be adjusted according to different cable parameters to adapt to specific application scenarios. Therefore, it is not limited to a specific type or specification of cable.

[0017] Further, in step A1,

[0018] Obtain the positive conductor current from the sampling point. Positive metal shielding layer current Positive electrode armor layer current Negative conductor current Negative electrode metal shielding layer current Negative electrode armor layer current and the voltage of the positive conductor to ground Positive metal shielding layer voltage to ground Positive electrode armor layer voltage to ground Voltage of negative conductor to ground The voltage of the negative metal shielding layer to ground Negative electrode armor layer to ground voltage .

[0019] By employing the aforementioned technical solution and collecting current and voltage data from multiple layers (conductor layer, metal shielding layer, and armor layer) of the positive and negative poles, a more comprehensive understanding of the cable's internal operating status can be achieved. This multi-layered data provides more detailed information, helping to pinpoint fault locations more accurately. Different layers of current and voltage signals respond differently to different types of faults. For example, a problem in the conductor layer may cause significant changes in conductor current, while a problem in the shielding or armor layer may primarily manifest as changes in current at that corresponding layer. Therefore, collecting multi-layered information helps distinguish different fault types, such as short circuits, open circuits, and grounding faults. Multi-dimensional data input makes subsequent calculations (such as primary slope, secondary slope, etc.) more accurate, thereby improving the performance of the entire fault location algorithm. This high-precision data foundation is a prerequisite for complex data analysis and processing. In complex real-world environments, external interference and noise are unavoidable. By acquiring data from multiple layers, the system can compensate for the interference affecting a single signal source to a certain extent, thereby improving the overall system's stability and anti-interference capability.

[0020] Further, in step A2,

[0021] Under normal operating conditions of a DC cable, the average slope of the instantaneous power curve during the period before reaching its peak value, i.e., the primary slope. The calculation formula is as follows:

[0022] (1);

[0023] in, Used to calculate the maximum value during this change process.

[0024] By employing the aforementioned technical solution and analyzing the primary slope of the instantaneous power curve, the changing trends of cable operating conditions can be captured more accurately. This is crucial for identifying early faults or anomalies, as these changes often appear in the data before obvious fault phenomena. Using the primary slope as an indicator helps in developing more scientific and reasonable preventative maintenance plans. When an abnormal change in the slope is detected, inspections and repairs can be arranged in advance, avoiding service interruptions caused by sudden faults. Detailed analysis of the instantaneous power curve helps to identify potential problems in a timely manner, thereby taking measures to prevent small problems from developing into major faults. This not only improves the reliability of the power transmission system but also reduces economic losses caused by unexpected downtime.

[0025] Furthermore, in step A3, the equivalent time point of the average slope of the instantaneous power curve during the monotonically increasing process of the DC cable in the event of a fault, before reaching the second peak, is calculated. The calculation formula is as follows:

[0026] (2);

[0027] in, To calculate the power increment, It is the maximum mutual inductance of the cable, representing the coupling effect between different layers of conductors. This is used to find the time point with the largest rate of change after the fault occurred. It is the resistance of the load.

[0028] By employing the aforementioned technical solutions and analyzing the instantaneous power curve changes after a fault occurs, particularly identifying the time point with the largest rate of change, the physical location of the fault can be pinpointed more accurately. This is crucial for rapid response and repair. Determining the equivalent time point helps identify specific problems within the cable, enabling maintenance teams to prepare the necessary materials and tools accordingly, thereby improving maintenance efficiency and reducing downtime. Utilizing these calculation results, potential safety hazards can be identified and addressed promptly, preventing minor faults from escalating into major accidents and ensuring the safe and stable operation of the power system. Quantifying the coupling effects between different conductor layers (e.g., through the maximum mutual inductance coefficient) helps in understanding the electromagnetic environment inside the cable, thereby optimizing daily operating strategies and preventing similar faults from recurring.

[0029] Furthermore, in step A4, by refining the influence of system structural parameters on energy transfer and electromagnetic processes in the cable, the following conclusions are drawn. The maximum slope at time t, i.e., the maximum quadratic slope. The calculation formula is as follows:

[0030] (3);

[0031] in, This means that when the fault location is infinitely close to the beginning of the cable, The maximum value that the slope of the instantaneous power curve can take under various fault conditions. Representing the cable number Layer and first Mutual inductance between layers Representing the cable number The self-resistance of the layer.

[0032] By adopting the above technical solution and calculating the maximum quadratic slope, the specific time and severity of the fault can be identified more accurately. This technology is particularly important when the fault location is close to the cable head. Utilizing parameters such as mutual inductance and self-resistance between conductor layers can help to more accurately determine the location of the fault point, thereby improving the speed and efficiency of fault diagnosis. A deeper understanding of how different structural parameters affect energy transmission and electromagnetic processes helps to optimize cable design and develop more scientific and reasonable maintenance plans, extending cable lifespan. This mathematical model-based method can be integrated into a real-time monitoring system to achieve continuous monitoring of cable operating status and issue timely warnings when anomalies are detected, preventing potential risks.

[0033] Furthermore, in step A5, constants are calculated using system and cable structure parameters. and correction factor and The calculation formula is as follows:

[0034] (4);

[0035] (5);

[0036] (6);

[0037] Where, constant The correction factor is related to the cable material. and Used to adjust the cable characteristics in response to different loads and power capacities. The resistance of the load, The length of the cable. Take the permeability of free space as H / m, The horizontal distance between each conductor layer. The radius of the circuit cell.

[0038] By employing the above technical solutions, constants related to cable materials and correction factors for adjusting cable characteristics are calculated. These calculations help designers more accurately adjust cable designs to better adapt to different load conditions and power capacities. This is achieved by accurately calculating cable electrical parameters, such as load resistance (R), cable length (… ), free space permeability ( ), the horizontal distance between each conductor layer (d), and the radius of the circuit cell ( Factors such as [missing information] can effectively predict the performance of cables in practical applications, thereby improving the reliability of the entire power transmission system. Understanding the performance of cables under different operating conditions helps in selecting the most suitable cable materials and design parameters, avoiding over- or under-design. This allows for reduced construction and maintenance costs while ensuring system performance. In-depth analysis of cable structural parameters and their application in solving practical problems can provide new ideas and technical means for cable design and manufacturing, promoting technological progress in related fields.

[0039] Further, in step A6, after a DC cable fault occurs, the instantaneous power curve of the measuring unit at the beginning of the faulty line cell is acquired, and the slope before and after each time point is compared to obtain the curve at... The slope at time step 1, i.e., the actual quadratic slope. The calculation formula is as follows:

[0040] (7);

[0041] in, For time intervals, , This is a correction coefficient used to adjust the weights for different slopes.

[0042] By employing the aforementioned technical solutions, calculating the actual secondary slope can help more accurately assess the severity of faults. Different slope changes may indicate different types of faults or different stages of fault development, aiding in the development of targeted maintenance strategies. Using this analytical method, power maintenance teams can predict potential future problems based on historical data, thereby optimizing maintenance plans and resource allocation, improving system reliability and efficiency. Timely detection and accurate fault location not only help reduce power outage time but also prevent potential safety risks, such as fires or other accidents caused by electrical faults. Detailed analysis of instantaneous power curves and their slope changes can provide clues to the root cause of faults. This is highly helpful for improving design, construction, and daily operating procedures, helping to prevent similar problems from recurring.

[0043] Further, in step A7, after a DC cable fault occurs, the instantaneous power curve of the measuring unit at the beginning of the faulty line cell is acquired, and the slope before and after each time point is compared to obtain the curve at... The slope at time;

[0044] A7. Through the maximum quadratic slope Actual quadratic slope ,constant and correction factor and The fault location was calculated. The calculation formula is as follows:

[0045] ;

[0046] in, This is the impedance matrix of the cable line. This is the admittance matrix of the cable line. The resistance per unit length of the line. Inductance per unit length of the line, The conductivity per unit length of the line, For the unit length of the line, a constant The correction factor is related to the cable material. and Used to adjust the cable characteristics in response to different loads and power capacities.

[0047] By employing the aforementioned technical solutions, and utilizing the electrical parameters of cable lines combined with quadratic slope analysis to determine the location of faults, more accurate positioning results can be provided than traditional methods. This is crucial for the rapid repair of cable faults. Accurate fault location reduces the time and resources required to locate fault points, improving the efficiency of maintenance work. This helps to quickly restore power supply services, reducing inconvenience caused to users by power outages. Precise fault location means that maintenance teams can go directly to the exact location for repairs, avoiding unnecessary digging or inspection work, thereby reducing maintenance costs and resource consumption. By efficiently identifying and resolving power system faults, the reliability and stability of the entire power supply network can be significantly improved, reducing the occurrence of large-scale power outages caused by faults.

[0048] The beneficial effects of this invention are:

[0049] 1. This invention can accurately and in real time identify the fault location by monitoring the instantaneous power change at the cable head end and combining it with the dynamic change of the power slope. Compared with traditional fault location methods based on current, voltage fluctuations or impedance changes, this invention can avoid the error caused by the fault location being far away from the measurement point, thus improving the accuracy and real-time performance of fault location.

[0050] 2. This invention analyzes the changing trend of the power slope. This method does not rely on complex sensor arrangements, but only requires the installation of a power measurement device at the beginning of the cable, which reduces equipment and installation costs. Combined with the power change curve after the fault occurs, this method can quickly locate the fault point, significantly shorten the power outage recovery time, and improve the operational reliability of the medium-voltage DC distribution network.

[0051] 3. This invention extracts the dynamic change characteristics of the slope of the instantaneous power curve, dynamically adjusts the slope weight under different operating conditions by combining cable structure parameters and correction coefficients, and calculates the fault location based on the coupling of the impedance matrix and admittance matrix. It breaks through the dependence of the traditional traveling wave method on the integrity of the reflected wave signal and solves the problems of low ranging accuracy, long time consumption and high cost caused by the attenuation of reflected waves, delay of manual intervention, complex equipment and electromagnetic interference in traditional methods. It realizes high-precision real-time positioning without external pulse injection, and is especially suitable for complex scenarios such as arc faults and high impedance aging cables. It significantly improves the fault recovery efficiency and operational reliability of medium voltage DC power distribution systems. Attached Figure Description

[0052] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0053] Figure 1 This is a flowchart of the method of the present invention.

[0054] Figure 2 This is a schematic diagram simulating a power distribution network. Detailed Implementation

[0055] 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. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0056] A method for locating single-pole grounding faults in DC cables based on the slope change of the instantaneous power curve, such as... Figure 1 As shown, the steps include the following steps:

[0057] A1. Obtain the voltage and current signals of each conductor layer of the positive and negative electrodes;

[0058] A2. Calculate the first slope;

[0059] A3. Calculate the equivalent time point;

[0060] A4. Calculate the maximum quadratic slope;

[0061] A5. Calculate the constants and correction factors;

[0062] A6. Obtain the actual quadratic slope;

[0063] A7. Obtain the distance to the fault.

[0064] Among them, A1, firstly, obtain the positive conductor current from the sampling point. Positive metal shielding layer current Positive electrode armor layer current Negative conductor current Negative electrode metal shielding layer current Negative electrode armor layer current and the voltage of the positive conductor to ground Positive metal shielding layer voltage to ground Positive electrode armor layer voltage to ground Voltage of negative conductor to ground The voltage of the negative metal shielding layer to ground Negative electrode armor layer to ground voltage ;

[0065] A2. Calculate the average slope of the instantaneous power curve during the period before reaching its peak value under normal operating conditions, i.e., the first slope, according to equation (1). ;

[0066] A3. Calculate the equivalent time point of the average slope of the instantaneous power curve during the monotonically increasing process in the period between the time of the fault occurrence and the time before the second peak, according to equation (2). ;

[0067] A4. Calculate according to formula (3) The maximum slope at time t, i.e., the maximum quadratic slope. ;

[0068] A5. Based on equations (4), (5), and (6), calculate the constants using system and cable structure parameters. and correction factor and ;

[0069] A6. After the fault occurs, the instantaneous power curve of the battery cell at the beginning of the faulty line is collected, and the slope before and after each time point is compared. The curve at the beginning of the fault is obtained by equation (7). The slope at time step 1, i.e., the actual quadratic slope. ;

[0070] A7. The maximum quadratic slope obtained in the preceding steps. Actual quadratic slope ,constant and correction factor and The fault location is calculated by substituting into equation (8). .

[0071] In step A2, the average slope of the instantaneous power curve during the period before reaching its peak value under normal operating conditions is obtained according to equation (1), i.e., the primary slope. The calculation formula is as follows:

[0072] (1);

[0073] in, Used to calculate the maximum value during this change process.

[0074] In step A3, according to equation (2), the equivalent time point of the average slope of the instantaneous power curve during the monotonically increasing process in the period between the time of the fault occurrence and the time before the second peak is calculated. The calculation formula is as follows:

[0075] (2)

[0076] in, To calculate the power increment, It is the maximum mutual inductance of the cable, representing the coupling effect between different layers of conductors. This is used to find the time point with the largest rate of change after the fault occurred. It is the resistance of the load.

[0077] In step A4, by refining the influence of system structural parameters on energy transmission and electromagnetic processes in the cable, equation (3) is derived. The maximum slope at time t, i.e., the maximum quadratic slope. The calculation formula is as follows:

[0078] (3)

[0079] in, This means that when the fault location is infinitely close to the beginning of the cable, The maximum value that the slope of the instantaneous power curve can take under various fault conditions. Representing the cable number Layer and first Mutual inductance between layers Representing the cable number The self-resistance of the layer.

[0080] In step A5, constants are calculated using system and cable structure parameters. and correction factor and The calculation formula is as follows:

[0081] (4);

[0082] (5);

[0083] (6);

[0084] Where, constant The correction factor is related to the cable material. and Used to adjust the cable characteristics in response to different loads and power capacities. The resistance of the load, The length of the cable. Take the permeability of free space as H / m, The horizontal distance between each conductor layer. The radius of the circuit cell.

[0085] In step A6, after the fault occurs, the instantaneous power curve of the measuring unit at the beginning of the faulty cell is collected, and the slope before and after each time point is compared. The curve at the beginning of the fault is obtained through equation (7). The slope at time step 1, i.e., the actual quadratic slope. The calculation formula is as follows:

[0086] (7);

[0087] in, For time intervals, , This is a correction coefficient used to adjust the weights for different slopes.

[0088] In step A7, the maximum quadratic slope Actual quadratic slope ,constant and correction factor and The fault location was calculated. The calculation formula is as follows:

[0089] ;

[0090] in, This is the impedance matrix of the cable line. This is the admittance matrix of the cable line. The resistance per unit length of the line. Inductance per unit length of the line, The conductivity per unit length of the line, For the unit length of the line, a constant The correction factor is related to the cable material. and Used to adjust the cable characteristics in response to different loads and power capacities.

[0091] In one embodiment, an experimental model of a ±10kV radial MVDC distribution cable network is established using PSCAD / EMTDC. A schematic diagram of the model is shown below. Figure 2 As shown in the figure, DCT is the load-side DC transformer (±10kV / ±0.4kV);

[0092] The cable type is YJV22-80mm2; two distributed power sources (DGs) are integrated into the network;

[0093] Tables 1, 2, and 3 list relevant information such as cable length, load size, and number of measurement units in the experimental model, where n s and n r Represents the sending node number and receiving node number of the cable;

[0094] L represents the length of the cable;

[0095] P + and P - These represent the loads at the positive and negative terminals, respectively; n MU This represents the number of MUs.

[0096] Five different fault conditions were selected for testing. The basic information of these cases and the corresponding fault distance estimation results are shown in Table 4, where FC represents the faulty cable section, R... f t f and x f These represent the fault resistance, fault start time, and fault distance, respectively; n L and n R express Figure 2 The left and right node numbers of a cable in the radial MVDC power distribution cable network shown, r fde This represents the error rate in fault distance estimation;

[0097] exist Figure 2In this system, the main power supply (AC / DC) serves as the core power source, directly connected to the ±10kV bus. The main power supply converts AC or DC power into the required form of electrical energy for the system, while the bus collects and distributes this energy, ensuring a stable supply to each branch line. Five fault points (Fault1-Fault5) are set at different nodes in the simulation test. Each fault point is located on a corresponding line and connected to other components or the bus. When a fault occurs, it disrupts the normal conductivity of the line, affecting the power transmission on that line. DG1 and DG2, as distributed power sources, are connected to the system lines through specific nodes. Normally, they assist the main power supply. In case of a fault, such as after fault 2, DG1 can provide emergency power to some lines to improve system reliability.

[0098] Table 1. Cable lengths in the experimental model

[0099]

[0100] Table 2 Load in the experimental model

[0101]

[0102] Table 3. Number of MUs in the experimental model

[0103]

[0104] Table 4. Fault information and fault distance estimation results under different conditions.

[0105]

[0106] Tables 1, 2, 3, and 4 show that the algorithm of this invention can correctly identify faulty cables in all five cases. The error rate for fault distance estimation ranges from a maximum of 1.225% to a minimum of 0.053% across the five cases.

[0107] Working principle: When a fault occurs in a DC cable, the electromagnetic energy transmission path inside the cable changes abruptly, causing a significant slope change in the instantaneous power curve at the beginning. By capturing the slope change trend, the fault location can be directly correlated. The theoretical maximum slope is corrected using parameters such as interlayer mutual inductance and self-resistance of the cable, and the weights are dynamically adjusted based on the actual slope to eliminate interference from line branches, arc noise, and other sources, thereby improving anti-interference capability. It does not require the injection of high-voltage pulse signals, relying solely on the power measurement data at the beginning. Through algorithmic analysis, the fault is located in real time, avoiding the equipment complexity and signal attenuation problems of the traditional traveling wave method. The traditional traveling wave method relies on the time difference of reflected waves and is easily affected by sudden changes in line impedance.

[0108] Based on power dynamic characteristics, this invention directly maps the fault location through slope changes, resulting in higher accuracy and faster response. It is especially suitable for high-impedance aging cables and complex electromagnetic environments.

[0109] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A DC cable single pole earth fault location method based on instantaneous power curve slope change, characterized in that, The method comprises the following steps: A1. obtaining voltage and current signals of each conductor layer of the positive and negative electrodes; A2. calculating a first slope: average slope of the instantaneous power curve in a period of time before reaching the peak value under normal operation of the DC cable; A3. The equivalent time point of the average slope of the instantaneous power curve in the monotonically increasing process within a time period after the time of fault occurrence until before the second peak value is reached in the case of a fault of the DC cable ; A4. Calculate the maximum quadratic slope: By distilling the impact of system structure parameters on energy transfer and electromagnetic processes in the cable, it is derived that the maximum slope at the instant A5. calculating constant α and correction factors λ and k using system and cable structure parameters; A6. Obtain actual quadratic slope: after the occurrence of DC cable fault, collect the instantaneous power curve in the fault line core first end measurement unit, compare the slopes before and after each time point, and obtain the slope of the curve at the time point . A7. The fault location is calculated by the maximum quadratic slope , the actual quadratic slope , the constant and the correction factor and The calculation formula is:​ ； wherein Z is the impedance matrix of the cable line, Y is the admittance matrix of the cable line, R is the line resistance per unit length, L is the line inductance per unit length, G is the line conductance per unit length, C is the line capacitance per unit length, a constant K is a correction factor related to the cable material, and is used to adjust the response of the cable characteristics to different loads and power supply capacities.

2. A DC cable single earth fault location method based on the slope change of instantaneous power curve according to claim 1, characterized in that, In step A1, positive conductor current , positive metal shield layer current , positive armor layer current , negative conductor current , negative metal shield layer current , negative armor layer current , and positive conductor voltage to ground , positive metal shield layer voltage to ground , positive armor layer voltage to ground , and negative conductor voltage to ground , negative metal shield layer voltage to ground , negative armor layer voltage to ground .

3. A DC cable single earth fault location method based on the slope change of instantaneous power curve according to claim 2, characterized in that, In step A2, The average slope of the instantaneous power curve in the time period before it reaches its peak value, i.e. the first derivative, in the case of a normal operation of the direct current cable The formula for which is: （1）； wherein, to calculate the maximum value in the course of the change, denotes the total length of the cable line.

4. A DC cable single earth fault location method based on the slope change of instantaneous power curve according to claim 1, characterized in that, In step A3, the equivalent time point of the average slope of the monotone increasing process of the instantaneous power curve in the time period after the time of fault occurrence until the time before the second peak is calculated in the case of fault of the DC cable The calculation formula is: （2）； wherein, is the calculated power increment, is the maximum mutual inductance coefficient of the cable, indicating the coupling effect between different layer conductors, is used to find the time point with the largest change rate after the fault occurs, wherein is the resistance of the load, represents the total length of the cable line.

5. A DC cable single earth fault location method based on the slope change of instantaneous power curve according to claim 1, characterized in that, In step A4, the influence of the refined system structure parameters on the energy transfer and electromagnetic processes in the cable is derived the maximum slope at the time instant, i.e. the maximum quadratic slope which is calculated as follows: （3）； wherein, represents the case when the fault location is infinitely close to the cable head end, represents the maximum value that the slope of the momentary power curve can take under various fault conditions, represents the mutual inductance between the layers of the cable, layers of the cable, represents the self-resistance of the layer of the cable, represents the total length of the cable line.

6. A DC cable single earth fault location method based on the slope change of instantaneous power curve according to claim 1, characterized in that, In step A5, the system and cable structure parameters are used to calculate constants and correction factors and with the following formulas: （4）； （5）； （6）； wherein the constant Related to the cable material, the correction factor and for adjusting the response of the cable characteristics to different loads and power supply capacities, is the resistance of the load, is the length of the cable, is the permeability of free space taken H / m, is the horizontal distance between the conductors of each layer, is the radius of the line core.

7. A DC cable single earth fault location method based on the slope change of instantaneous power curve according to claim 1, characterized in that, In step A6, after the occurrence of the DC cable fault, the instantaneous power curve in the fault line core first end measuring unit is collected, the slopes before and after each time point are compared, the slope of the curve at the time is obtained, i.e. the actual quadratic slope , and the calculation formula is as follows: . （7）； wherein, is a time interval, , is a correction factor for adjusting the weight of different slopes.

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