Direct-current cable single-pole grounding fault distance measurement method based on instantaneous power curve slope change

Abstract

The invention discloses a direct-current cable single-pole grounding fault distance measurement method based on instantaneous power curve slope change, relates to the technical field of electrics, and has the advantages that external signal injection is not needed, positioning is realized directly through dynamic slope change of a power curve, the problems of complicated equipment and poor anti-interference performance of a traditional traveling wave method are solved, and the positioning accuracy is improved. According to the technical scheme, the method comprises the following steps that A1, voltage and current signals of conductor layers of a positive electrode and a negative electrode are obtained; a2, calculating a primary slope S0; a3, calculating an equivalent time point tz; a4, the maximum secondary slope pmax is calculated; a5, calculating a constant alpha and correction coefficients lambda and k; a6, an actual secondary slope pavg is obtained; and A7, obtaining a fault distance x. According to the method, the instantaneous power change of the head end of the cable is monitored, and the dynamic change of the power slope is combined, so that the fault position can be accurately identified in real time.

Description

Technical Field

[0001] The present invention relates to the field of electrical technology, and in particular to a method for measuring the distance of a DC cable single-pole grounding fault based on a change in the slope of an instantaneous power curve. Background Art

[0002] Compared to traditional AC cables, DC cables offer advantages such as lower losses, easier maintenance, and greater stability. Medium-voltage DC (MVDC) distribution cables typically operate in harsh environments, and their insulation materials and internal structures are susceptible to aging over time, leading to faults. Faults often occur under complex operating conditions, making it difficult to accurately and quickly locate them. Therefore, effectively locating and troubleshooting faults to reduce outage duration and improve the stability and safety of the entire DC distribution network has become an urgent issue. Minimizing the impact of cable faults on people's production and daily lives has become a key goal for industry development.

[0003] Medium-voltage DC cables are essential transmission channels for flowing electricity in modern power systems, and their performance and reliability directly impact the stability of power supply. However, with the extension of cable lines and the increasing complexity of operating conditions, the probability of cable failures is gradually increasing. Therefore, more accurate fault location solutions are needed to shorten recovery time after a fault occurs and improve the reliability and safety of power grid operation. Through characteristic pattern recognition and analysis of signal frequency characteristics, MVDC distribution cable fault location technology can be greatly improved. This not only improves fault location accuracy but also provides real-time feedback of fault information, providing strong support for the safe and stable operation of the power system.

[0004] The Chinese patent with publication number CN115469187A discloses a method, device and processor for measuring the distance of a cable fault. The invention includes: at a preset port of the faulty cable, controlling a preset pulse wave to be injected into the space formed by the cable core and the shielding layer, and collecting the reflected wave data corresponding to the reflected wave between the cable core and the shielding layer; determining the corresponding traveling wave time difference between the preset pulse wave and the reflected wave based on the preset pulse wave and the reflected wave data; obtaining the traveling wave speed of the preset pulse wave in 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 the traveling wave speed. The present invention solves the technical problems of low ranging accuracy and long ranging time of the fault testing method used in related technologies after a cable fault occurs. In the above method, in complex cable lines, the reflected wave signal is severely attenuated or the waveform is distorted, resulting in inaccurate time difference extraction and the 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 technical problems. Summary of the Invention

[0006] In response to the above-mentioned technical deficiencies, the purpose of the present invention is to provide a DC cable single-pole grounding fault ranging method based on the change of the slope of the instantaneous power curve. It does not require external signal injection and can directly achieve positioning through the dynamic change of the slope of the power curve, solving the problems of complex equipment and poor anti-interference performance of the traditional traveling wave method.

[0007] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0008] The present invention provides a method for measuring the distance between a DC cable single-pole ground fault and a ground fault of a DC cable based on the slope change of an instantaneous power curve, comprising the following steps:

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

[0010] A2. Calculate the slope once;

[0011] A3. Calculate the equivalent time point;

[0012] A4. Calculate the maximum quadratic slope;

[0013] A5. Calculate constants and correction factors;

[0014] A6. Obtain the actual quadratic slope;

[0015] A7. Obtain the fault distance.

[0016] By employing the above technical solution, fault location can be determined by analyzing the slope change of the instantaneous power curve, providing more accurate fault location results. This method can capture subtle changes, thereby improving positioning accuracy, reducing reliance on external equipment, and lowering system complexity, hardware, and maintenance costs. Since no special signal generation device is required, the entire system structure is more concise, easier to deploy, and easier to maintain. Directly utilizing power system data for analysis reduces 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 based on different cable parameters to meet specific application requirements. Therefore, it is not limited to a specific cable type or specification.

[0017] Furthermore, in step A1,

[0018] The positive conductor current i1(t), positive metal shield layer current i2(t), positive armor layer current i3(t), negative conductor current i4(t), negative metal shield layer current i5(t), negative armor layer current i6(t), as well as the positive conductor-to-ground voltage u1(t), positive metal shield layer-to-ground voltage u2(t), positive armor layer-to-ground voltage u3(t), negative conductor-to-ground voltage u4(t), negative metal shield layer-to-ground voltage u5(t), negative armor layer-to-ground voltage u6(t) are obtained from the sampling points.

[0019] By employing the above technical solution, current and voltage data from multiple layers (conductor layer, metal shielding layer, and armor layer) at both the positive and negative poles can be collected, providing a more comprehensive understanding of the cable's internal operating conditions. This multi-layered data provides more detailed information, helping to more accurately locate faults. Current and voltage signals at different layers respond differently to different fault types. For example, a problem in the conductor layer may cause significant changes in conductor current, while a problem in the shielding layer or armor layer may primarily manifest as current changes at the corresponding layer. Therefore, collecting multi-layered information helps distinguish different fault types, such as short circuits, broken wires, and ground faults. This multi-dimensional data input makes subsequent calculations (such as primary and secondary slopes) 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 inevitable. By acquiring data from multiple layers, the system can compensate for interference from a single signal source to a certain extent, thereby improving the overall system stability and anti-interference capabilities.

[0020] Furthermore, in step A2,

[0021] When the DC cable is operating normally, the average slope of the instantaneous power curve in the period before reaching the peak, that is, the primary slope S0, is calculated as follows:

[0022] in, Used to calculate the maximum value during the change process.

[0023] By adopting the above technical solution, by analyzing the primary slope of the instantaneous power curve, the changing trends in the cable's operating status can be more accurately captured. This is critical for identifying early faults or abnormal conditions, as these changes often appear in the data before obvious fault symptoms. Using the primary slope as an indicator can help develop more scientific and reasonable preventive maintenance plans. When an abnormal change in the slope is detected, inspections and repairs can be scheduled in advance to avoid service interruptions caused by sudden failures. Detailed analysis of the instantaneous power curve helps to promptly identify potential problems, allowing measures to be taken to prevent small problems from escalating into major failures. This not only improves the reliability of the power transmission system but also reduces the economic losses caused by unplanned downtime.

[0024] Furthermore, in step A3, the equivalent time point t of the average slope of the monotonically increasing process of the instantaneous power curve in the case of a DC cable fault after the fault occurs and before it reaches the second peak is calculated. z , and its calculation formula is:

[0025]

[0026] Where Δp k To calculate the power increment, M max is the maximum mutual inductance of the cable, which represents the coupling between conductors in different layers. argmax() is used to find the time point with the largest rate of change after a fault occurs.

[0027] By adopting the above technical solution, by analyzing the changing characteristics of the instantaneous power curve after the fault occurs, especially finding the time point with the largest rate of change, the physical location of the fault can be more accurately located. This is crucial for rapid response and repair. Determining the equivalent time point helps identify specific problems within the cable, allowing the maintenance team to prepare the necessary materials and tools in a targeted manner, thereby improving repair efficiency and reducing downtime. Using these calculation results, potential safety hazards can be discovered and addressed in a timely manner, preventing small faults from evolving into major accidents, and ensuring the safe and stable operation of the power system. Quantifying the coupling between conductors in different layers (for example, through the maximum mutual inductance coefficient) can help understand the electromagnetic environment inside the cable, thereby optimizing daily operating strategies and avoiding similar faults from recurring.

[0028] Furthermore, in step A4, by refining the influence of system structure parameters on energy transmission and electromagnetic process in the cable, t z The maximum slope at the moment, that is, the maximum quadratic slope The calculation formula is as follows:

[0029]

[0030] in, When the fault location is infinitely close to the cable head end, t z The maximum value that the slope of the instantaneous power curve can take under various fault conditions, M ij represents the mutual inductance between the i-th and j-th layers of the cable, R i Represents the self-resistance of the i-th layer of the cable.

[0031] By adopting the above technical solution and calculating the maximum quadratic slope, the specific time when the fault occurs and its severity can be identified more accurately. This technology is particularly important when the fault location is close to the head end of the cable. Parameters such as the mutual inductance and self-resistance between the conductors of each layer can help to more accurately determine the location of the fault point, thereby improving the speed and efficiency of troubleshooting. A deep understanding of how different structural parameters affect energy transmission and electromagnetic processes will help optimize cable design solutions and formulate more scientific and reasonable maintenance plans to extend the service life of cables. This mathematical model-based method can be integrated into a real-time monitoring system to achieve continuous monitoring of the cable's operating status and issue timely warnings when an anomaly is detected to prevent potential risks.

[0032] Furthermore, in step A5, the constant α and the correction coefficients λ and k are calculated using the system and cable structural parameters. The calculation formula is as follows:

[0033]

[0034] Among them, the constant α is related to the cable material, and the correction coefficients λ and k are used to adjust the response of the cable characteristics to different loads and power capacity. load is the resistance of the load, l is the length of the cable, μ0 is the magnetic permeability of free space (4π×10 -7 H / m), D is the horizontal distance between conductors in each layer, and r is the radius of the circuit core.

[0035] By employing the above technical solution, constants related to cable materials and correction factors used to adjust cable characteristics are calculated. These calculation results can help designers more precisely adjust cable designs to better adapt them to different load conditions and power capacities. By accurately calculating the cable's electrical parameters, such as the load resistance (R), cable length (L), free space permeability (μ0), the horizontal distance between conductor layers (d), and the radius of the line core (r), the performance of the cable in actual applications can be effectively predicted, thereby improving the reliability of the entire power transmission system. Understanding the cable's performance under different operating conditions helps select the most appropriate cable material and design parameters, avoiding over- or under-design issues. This can reduce construction and maintenance costs while ensuring system performance. In-depth analysis of cable structural parameters and their application in practical problem-solving can provide new ideas and technical means for cable design and manufacturing, promoting technological advancement in related fields.

[0036] Furthermore, in step A6, after the DC cable fault occurs, the instantaneous power curve of the measurement unit at the head end of the fault line cell is collected, and the slopes before and after each time point are compared to obtain the curve at t z The slope at the moment, that is, the actual quadratic slope The calculation formula is as follows:

[0037]

[0038] Among them, Δt is the time interval, μ1 and μ2 are correction coefficients used to adjust the weights of different slopes.

[0039] By employing the above technical solution, calculating the actual quadratic slope can help more accurately assess the severity of a fault. Different slope changes may indicate different types of faults or different stages of fault development, helping to develop targeted maintenance strategies. Using this analytical method, power maintenance teams can predict possible future problems based on historical data, thereby optimizing maintenance plans and resource allocation, improving system reliability and efficiency. Timely detection and accurate location of faults not only helps reduce power outages but also prevents potential safety risks such as fires or other accidents caused by electrical faults. Detailed analysis of the instantaneous power curve and its slope changes can provide clues to the root cause of the fault. This is very helpful for improving design, construction, and daily operating procedures, helping to prevent similar problems from recurring.

[0040] Further, in step A7, by the maximum quadratic slope Actual quadratic slope The constant α and the correction coefficients k and λ are used to calculate the fault location x, which is calculated as follows:

[0041]

[0042] Among them, Z is the impedance matrix of the cable line, Y is the admittance matrix of the cable line, R0 is the line resistance per unit length, L0 is the line inductance per unit length, G0 is the line conductance per unit length, and C0 is the line length per unit length.

[0043] By adopting the above technical solution, the electrical parameters of the cable line combined with quadratic slope analysis are used to determine the location of the fault point, which can provide more accurate positioning results than traditional methods. This is crucial for quickly repairing cable faults. Accurate fault location reduces the time and resources required to find the fault point, improving the efficiency of maintenance work. This helps to quickly restore power supply services and reduce the inconvenience caused by power outages to users. Precisely locating the fault point means that the maintenance team can go directly to the exact location for repair, avoiding unnecessary excavation 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, and the occurrence of large-scale power outages caused by faults can be reduced.

[0044] Beneficial effects of the present invention:

[0045] 1. By monitoring instantaneous power changes at the cable headend and combining them with the dynamic changes in power slope, this method can accurately and real-timely identify the fault location. Compared with traditional fault location methods based on current, voltage fluctuations, or impedance changes, this method can avoid errors caused by the fault location being far from the measurement point, thereby improving the accuracy and real-time performance of fault location.

[0046] 2. By analyzing the changing trend of power slope, this method does not rely on complex sensor arrangements. It only requires a power measurement device at the head end of the cable, reducing equipment and installation costs. Combined with the power change curve after a fault occurs, this method can quickly locate the fault point, significantly shorten power outage recovery time, and improve the operational reliability of the medium-voltage DC distribution network.

[0047] 3. The present invention extracts the dynamic variation characteristics of the slope of the instantaneous power curve, combines cable structural parameters with correction coefficients to dynamically adjust the slope weight under different working conditions, and calculates the fault location based on the coupling of the impedance matrix and the admittance matrix. This breaks through the traditional traveling wave method's reliance on the integrity of the reflected wave signal, and solves the problems of low ranging accuracy, long time consumption, and high cost caused by reflected wave attenuation, manual intervention delays, equipment complexity, and electromagnetic interference in traditional methods. It achieves high-precision real-time positioning without the need for external pulse injection, and is particularly suitable for complex scenarios such as arc faults and high-impedance aging cables, significantly improving the fault recovery efficiency and operational reliability of medium-voltage DC distribution systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0049] Figure 1 Flow chart of the method of the present invention.

[0050] Figure 2 Schematic diagram of the simulated power distribution network. DETAILED DESCRIPTION

[0051] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0052] A DC cable single-pole grounding fault location method based on the slope change of the instantaneous power curve, such as Figure 1 As shown, the following steps are included:

[0053] A1. Obtain voltage and current signals of each conductor layer of the positive and negative electrodes;

[0054] A2. Calculate the slope once;

[0055] A3. Calculate the equivalent time point;

[0056] A4. Calculate the maximum quadratic slope;

[0057] A5. Calculate constants and correction factors;

[0058] A6. Obtain the actual quadratic slope;

[0059] A7. Obtain the fault distance.

[0060] Among them, A1, first obtain the positive conductor current i1(t), positive metal shield layer current i2(t), positive armor layer current i3(t), negative conductor current i4(t), negative metal shield layer current i5(t), negative armor layer current i6(t) and positive conductor to ground voltage u1(t), positive metal shield layer to ground voltage u2(t), positive armor layer to ground voltage u3(t), negative conductor to ground voltage u4(t), negative metal shield layer to ground voltage u5(t), negative armor layer to ground voltage u6(t) from the sampling point;

[0061] A2. Calculate the average slope of the instantaneous power curve in the period before reaching the peak value under normal working conditions according to formula (1), i.e., the primary slope S0;

[0062] A3. According to formula (2), calculate the equivalent time point t of the average slope of the instantaneous power curve in the monotonically increasing process after the fault occurs and before it reaches the second peak. z ;

[0063] A4. Calculate t according to formula (3) z The maximum slope at the moment, that is, the maximum quadratic slope

[0064] A5. Calculate the constant α and the correction coefficients λ and k using the system and cable structure parameters according to equations (4), (5) and (6);

[0065] A6. After the fault occurs, collect the instantaneous power curve of the measurement unit at the head end of the fault line cell, compare the slopes before and after each time point, and obtain the curve at t by formula (7). z The slope at the moment, that is, the actual quadratic slope

[0066] A7. The maximum quadratic slope obtained in the previous step Actual quadratic slope Substitute the constant α and the correction coefficients k and λ into equation (8) to calculate the fault location x.

[0067] In step A2, according to formula (1), the average slope of the instantaneous power curve in a period of time before reaching the peak under normal working conditions, that is, the primary slope S0, is calculated as follows:

[0068] in Used to calculate the maximum value during the change process.

[0069] In step A3, the equivalent time point t of the average slope of the instantaneous power curve in the monotonically increasing process after the fault occurs and before it reaches the second peak is calculated according to formula (2). z , and its calculation formula is:

[0070]

[0071] Where Δp k To calculate the power increment, M maxis the maximum mutual inductance of the cable, which represents the coupling between conductors in different layers. argmax() is used to find the time point with the largest rate of change after a fault occurs.

[0072] In step A4, by refining the influence of system structure parameters on energy transmission and electromagnetic process in the cable, t is obtained through formula (3): z The maximum slope at the moment, that is, the maximum quadratic slope The calculation formula is as follows:

[0073]

[0074] in, When the fault location is infinitely close to the cable head end, t z The maximum value that the slope of the instantaneous power curve can take under various fault conditions, M ij represents the mutual inductance between the i-th and j-th layers of the cable, R i Represents the self-resistance of the i-th layer of the cable.

[0075] In step A5, according to equations (4), (5), and (6), the constant α and the correction coefficients λ and k are calculated using the system and cable structure parameters. The calculation formulas are as follows:

[0076]

[0077] Among them, the constant α is related to the cable material, and the correction coefficients λ and k are used to adjust the response of the cable characteristics to different loads and power capacity. load is the resistance of the load, l is the length of the cable, μ0 is the magnetic permeability of free space (4π×10 -7 H / m), D is the horizontal distance between conductors in each layer, and r is the radius of the circuit core.

[0078] In step A6, after the fault occurs, the instantaneous power curve of the measurement unit at the head end of the fault line cell is collected, and the slopes before and after each time point are compared. The curve at t is obtained by formula (7). z The slope at the moment, that is, the actual quadratic slope The calculation formula is as follows:

[0079]

[0080] Among them, Δt is the time interval, μ1 and μ2 are correction coefficients used to adjust the weights of different slopes.

[0081] In step A7, the maximum quadratic slope obtained in the previous step is Actual quadratic slope The constant α and the correction coefficients k and λ are substituted into formula (8) to calculate the fault location x, which is calculated as follows:

[0082]

[0083] Among them, Z is the impedance matrix of the cable line, Y is the admittance matrix of the cable line, R0 is the line resistance per unit length, L0 is the line inductance per unit length, G0 is the line conductance per unit length, and C0 is the line susceptance per unit length.

[0084] In one embodiment, PSCAD / EMTDC is used to establish an experimental model of a ±10kV radial MVDC distribution cable network. Figure 2 As shown, DCT in the figure is the load-side DC transformer (±10kV / ±0.4kV);

[0085] The cable type is YJV22-80mm2; two distributed generation (DGs) are integrated in the network;

[0086] Tables 1, 2, and 3 list the cable length, load size, and number of measurement units in the experimental model, respectively, where n s and n r Represents the sending node number and receiving node number of the cable;

[0087] L represents the length of the cable;

[0088] P + and P - Represents the load of the positive electrode and the negative electrode respectively; n MU Represents the number of MUs.

[0089] 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 fault cable segment, R f , t f and x f They represent 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 distribution cable network shown in the figure are fde represents the error rate of fault distance estimation;

[0090] exist Figure 2In the simulation, the main power supply (AC / DC) is the core power source, directly connected to the ±10kV busbar. The main power supply is responsible for converting alternating current (AC) or direct current (DC) into the required power form for the system, while the busbar collects and distributes power, ensuring stable power transmission to each branch line. Five fault points (Fault1-Fault5) were set at different nodes in the simulation experiment. Each fault point is located on a corresponding line and connected to other components or busbars. When a fault occurs, it will disrupt the normal conductivity of the line and affect the power transmission of the line. DG1 and DG2 are distributed power sources, each connected to the system line through a specific node. Under normal circumstances, they assist the main power supply. In the event of a fault, such as after Fault 2, DG1 can provide emergency power to some lines to improve system reliability.

[0091] Table 1 Cable lengths in the experimental model

[0092]

[0093] Table 2 Loads in the experimental model

[0094]

[0095] Table 3 Number of MUs in the experimental model

[0096]

[0097]

[0098] Table 4 Fault information and fault distance estimation results under different situations

[0099]

[0100] From Tables 1, 2, 3, and 4, we can see that the algorithm of the present invention can correctly identify the faulty cable in all five cases. In the five cases, the maximum error rate of the fault distance estimation is 1.225% and the minimum is 0.053%.

[0101] Working Principle: When a DC cable fault occurs, the electromagnetic energy transmission path within the cable suddenly changes, causing a significant change in the slope of the instantaneous power curve at the head end. By capturing the slope change trend, the fault location can be directly associated. Parameters such as the mutual inductance and self-resistance between cable layers are used to correct the theoretical maximum slope. The weight is dynamically adjusted based on the actual slope to eliminate interference from line branches, arc noise, and other interference, improving anti-interference capabilities. Without injecting high-voltage pulse signals, the method relies solely on head-end power measurement data, locating faults in real time through algorithmic analysis. This avoids the equipment complexity and signal attenuation issues of traditional traveling wave methods, which rely on the time difference of reflected waves and are susceptible to sudden changes in line impedance.

[0102] The present invention is based on the dynamic characteristics of power and directly maps the fault location through slope changes, with higher accuracy and faster response. It is particularly suitable for high-impedance aging cables and complex electromagnetic environments.

[0103] Obviously, those skilled in the art may make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if such changes and modifications fall within the scope of the claims and their equivalents, the present invention is intended to include such changes and modifications.

Claims

1. A method for measuring the distance between a DC cable and a single-pole ground fault based on the slope change of an instantaneous power curve, characterized in that: The following steps are involved: A1. Obtain voltage and current signals of each conductor layer of the positive and negative electrodes; A2. Calculate the slope once; A3. Calculate the equivalent time point; A4. Calculate the maximum quadratic slope; A5. Calculate constants and correction factors; A6. Obtain the actual quadratic slope; A7. Obtain the fault distance.

2. A DC cable single-pole grounding fault location method based on instantaneous power curve slope change according to claim 1, characterized in that: In step A1, The positive conductor current i1(t), positive metal shield layer current i2(t), positive armor layer current i3(t), negative conductor current i4(t), negative metal shield layer current i5(t), negative armor layer current i6(t), as well as the positive conductor-to-ground voltage u1(t), positive metal shield layer-to-ground voltage u2(t), positive armor layer-to-ground voltage u3(t), negative conductor-to-ground voltage u4(t), negative metal shield layer-to-ground voltage u5(t), negative armor layer-to-ground voltage u6(t) are obtained from the sampling points.

3. The method for measuring the DC cable single-pole grounding fault location based on the slope change of the instantaneous power curve according to claim 2, characterized in that: In step A2, When the DC cable is operating normally, the average slope of the instantaneous power curve in the period before reaching the peak, that is, the primary slope S0, is calculated as follows: in, Used to calculate the maximum value during the change process.

4. The method for measuring the distance between a DC cable single-pole ground fault based on the slope change of an instantaneous power curve according to claim 1, characterized in that: In step A3, the equivalent time point t is calculated as the average slope of the monotonically increasing instantaneous power curve in the case of a DC cable fault after the fault occurs and before it reaches the second peak. z , and its calculation formula is: Where Δp k To calculate the power increment, M max is the maximum mutual inductance of the cable, which represents the coupling between conductors in different layers. argmax() is used to find the time point with the largest rate of change after a fault occurs.

5. The method for measuring the distance between a DC cable single-pole ground fault based on the slope change of an instantaneous power curve according to claim 1, characterized in that: In step A4, by refining the influence of system structure parameters on energy transmission and electromagnetic process in the cable, t z The maximum slope at the moment, that is, the maximum quadratic slope The calculation formula is as follows: in, When the fault location is infinitely close to the cable head end, t z The maximum value that the slope of the instantaneous power curve can take under various fault conditions, M ij represents the mutual inductance between the i-th and j-th layers of the cable, R i Represents the self-resistance of the i-th layer of the cable.

6. The method for measuring the distance between a DC cable single-pole ground fault based on the slope change of an instantaneous power curve according to claim 1, characterized in that: In step A5, the constant α and the correction coefficients λ and k are calculated using the system and cable structure parameters. The calculation formula is as follows: Among them, the constant α is related to the cable material, and the correction coefficients λ and k are used to adjust the response of the cable characteristics to different loads and power capacity. load is the resistance of the load, l is the length of the cable, μ0 is the magnetic permeability of free space (4π×10 -7 H / m), D is the horizontal distance between conductors in each layer, and r is the radius of the circuit core.

7. The method for measuring the DC cable single-pole grounding fault location based on the change in the slope of the instantaneous power curve according to claim 1, characterized in that: In step A6, after the DC cable fault occurs, the instantaneous power curve of the measurement unit at the head end of the fault line cell is collected, and the slopes before and after each time point are compared to obtain the curve at t z The slope at the moment, that is, the actual quadratic slope The calculation formula is as follows: Among them, Δt is the time interval, μ1 and μ2 are correction coefficients used to adjust the weights of different slopes.

8. The method for measuring the distance between a DC cable single-pole ground fault based on the slope change of an instantaneous power curve according to claim 1, characterized in that: In step A7, the maximum quadratic slope Actual quadratic slope The constant α and the correction coefficients k and λ are used to calculate the fault location x, which is calculated as follows: Among them, Z is the impedance matrix of the cable line, Y is the admittance matrix of the cable line, R0 is the line resistance per unit length, L0 is the line inductance per unit length, G0 is the line conductance per unit length, and C0 is the line length per unit length.

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