Single-ended grounding cable early fault positioning method and system based on sheath impedance

Abstract

The invention relates to the technical field of cable detection, in particular to a sheath impedance-based single-ended grounding cable early-stage fault positioning method and a sheath impedance-based single-ended grounding cable early-stage fault positioning system. The method comprises the following steps: acquiring sheath current at a metal sheath grounding side of a single-ended grounding cable, acquiring sheath voltage at a non-grounding side, and synchronously acquiring voltages at two ends of a main conductor; sheath current and voltage are monitored in real time by adopting a double-threshold strategy combining a fixed threshold and a dynamic probability boundary, and waveform recording is triggered when the sheath current and voltage exceed the threshold; based on a distributed parameter model, fault point voltages are derived from the two sides of a fault point respectively, the two voltages are made to be equal, a quadratic equation about the fault position is established, a sheath impedance parameter and a steady-state component of waveform data are used for solving, and a root with the real part between 0 and 1 is taken to be converted into the actual fault distance. The method is high in detection sensitivity, the positioning result is independent of the fault resistance, the positioning precision is high, and the method is suitable for early fault precise positioning of the single-ended grounding underground cable.

Description

Technical Field

[0001] This invention relates to the field of cable testing technology, specifically to a method and system for locating early faults in single-ended grounded cables based on sheath impedance. Background Technology

[0002] The aging of the insulation of underground power cables can gradually lead to early faults. Detecting and locating these faults before they evolve into permanent interruptions is of great significance for ensuring the stable operation of the power system.

[0003] Existing impedance-based fault location methods typically operate on the dominant conductor, requiring simultaneous voltage and current measurements at both ends of the cable. This involves numerous measurement variables and is complex to implement. Early-stage faults are short-lived and self-extinguishing, causing extremely weak voltage and current disturbances on the dominant conductor, insufficient to trigger conventional protection systems. This results in insufficient sensitivity of existing methods for detecting early-stage faults. Furthermore, existing methods generally rely on fault resistance parameters, which are difficult to accurately obtain in the early stages of faults, introducing additional uncertainties. There is currently limited dedicated research on early-stage fault location in single-ended grounded cables. These cables are short in length and have low impedance, making traditional methods ineffective. Additionally, existing methods use a single fixed threshold for fault detection. For the low-energy, weak signals commonly found in early-stage faults, these signals often do not exceed the fixed threshold, making detection difficult and leading to a high false negative rate. Summary of the Invention

[0004] This invention provides a method and system for locating early faults in single-ended grounded cables based on sheath impedance, in order to improve the detection sensitivity and location accuracy of early faults.

[0005] To achieve the above objectives, the present invention provides the following technical solution: This invention provides a method for early fault location in single-ended grounded cables based on sheath impedance, comprising: S1: Collect the sheath current on the grounded side of the metal sheath of the single-ended grounded cable, collect the sheath voltage on the ungrounded side of the metal sheath, collect the power supply voltage on the main body power supply side, and collect the load voltage on the main body load side. S2: Compare the sheath current and sheath voltage with the corresponding thresholds, which include fixed thresholds set based on safety specifications and dynamic probability boundaries determined by a statistical model based on historical normal operation data. When the sheath current or sheath voltage exceeds the corresponding threshold, record the waveform data of the sheath current, sheath voltage, power supply voltage and load voltage. S3: Based on the distributed parameter model, with the fault location as the unknown, derive the fault point voltage from the power supply side and the load side of the fault point respectively, set the two to be equal, and combine the metal sheath impedance parameter, line capacitance parameter and the waveform data to establish and solve the quadratic equation about the fault location. Take the root with the real part between 0 and 1, and multiply it by the total length of the cable as the actual fault distance.

[0006] As a preferred technical solution of the present invention, in step S1, the sheath current is acquired by a current probe set on the grounding side of the metal sheath, and the sheath voltage is acquired by a voltage sensor set on the non-grounding side of the metal sheath. The sheath current and the sheath voltage are acquired synchronously.

[0007] As a preferred embodiment of the present invention, in step S2, determining the fixed threshold includes: Based on the impedance of the metal sheath, the geometric mean distance of the three-phase cable, the average diameter of the sheath, and the load current, the induced voltage of the metal sheath under normal operating conditions is calculated, and the calculation result is used as the fixed threshold of the sheath voltage. Based on the impedance of the metal sheath and the load current, the induced current of the metal sheath under normal operating conditions is calculated, and the calculation result is used as the fixed threshold for the sheath current.

[0008] As a preferred embodiment of the present invention, in step S2, the determination of the dynamic probability boundary includes: A normal distribution statistical model of sheath current and sheath voltage is established using historical normal operation data. The dynamic threshold boundary is determined based on the preset confidence level, and the product of the mean plus or minus the confidence coefficient and the standard deviation is used as the dynamic probability boundary.

[0009] As a preferred embodiment of the present invention, it further includes: The sheath voltage waveform is sliced ​​using the fundamental period as a window, and the mean square error of the positive half-cycle and negative half-cycle compared with the standard sine wave is calculated respectively. The ratio of the absolute value of the difference between the two to the sum of the two is used as the asymmetric waveform distortion index. The zero-sequence component of sheath current, the zero-sequence component of sheath voltage, high-frequency transient energy, and harmonic distortion rate are used to form a feature vector, which is then input into a pre-trained random forest classifier to identify and distinguish early faults from system noise. When the asymmetric waveform distortion index exceeds the preset judgment value, the fixed threshold and dynamic probability boundary in step S2 are dynamically reduced.

[0010] As a preferred embodiment of the present invention, in step S3, the establishment and solution of the quadratic equation regarding the fault location is performed using the fundamental component, specifically including: Extract the fundamental components of sheath current, sheath voltage, power supply voltage, and load voltage from the waveform data. Substitute the fundamental components into the quadratic equation and take the root with the real part between 0 and 1 as the normalized fault location. Multiply the normalized fault location by the total cable length as the actual fault distance.

[0011] As a preferred embodiment of the present invention, in step S3, the establishment and solution of the quadratic equation regarding the fault location is performed using zero-sequence components, specifically including: The zero-sequence components of sheath current, sheath voltage, power supply voltage, and load voltage are extracted from the waveform data respectively. The zero-sequence components are substituted into the quadratic equation, and the root with the real part between 0 and 1 is taken as the normalized fault location. The product of the normalized fault location and the total length of the cable is taken as the actual fault distance.

[0012] As a preferred technical solution of the present invention, the fundamental component or zero-sequence component is taken from the steady-state segment of the waveform data; the steady-state segment is determined after analyzing the time-varying resistance characteristics of the early fault arc based on the improved Schwarz model; when establishing the quadratic equation about the fault location, the coefficients of the equation are corrected by the distributed parameters based on the inductance per unit length of the metal sheath, the line capacitance, the total length of the cable and the field calibration coefficient.

[0013] This invention also proposes an early fault location system for single-ended grounded cables based on sheath impedance, comprising: The signal acquisition module is used to acquire the sheath current on the grounded side of the metal sheath of the single-ended grounded cable, the sheath voltage on the ungrounded side of the metal sheath, the power supply voltage on the main body power supply side, and the load voltage on the main body load side. The threshold monitoring module is used to compare the sheath current and sheath voltage with the corresponding thresholds, including fixed thresholds set based on safety specifications and dynamic probability boundaries determined by a statistical model based on historical normal operation data. When the sheath current or sheath voltage exceeds the corresponding threshold, the module records the waveform data of the sheath current, sheath voltage, power supply voltage and load voltage. The fault location module is used to derive the fault point voltage from the power supply side and the load side of the fault point according to the distributed parameter model, with the fault location as the unknown quantity. The voltage is made equal to the voltage of the fault point. The module combines the metal sheath impedance parameter, the line capacitance parameter and the waveform data to establish and solve a quadratic equation about the fault location. The root with the real part between 0 and 1 is taken and multiplied by the root with the total length of the cable as the actual fault distance.

[0014] The beneficial effects of this invention are: This invention applies an impedance-based location method to metal sheaths, replacing load-end current measurement with the voltage on the ungrounded side of the sheath, thus reducing measurement variables. A quadratic equation is established by bidirectionally deriving the fault point voltage, naturally decoupling the location result from the fault resistance. A dual-threshold mechanism combining a fixed threshold and a dynamic probability boundary, along with an asymmetric waveform distortion index and a random forest classifier, significantly improves the detection sensitivity for low-energy early faults. Solving for zero-sequence and steady-state components effectively filters out noise interference and eliminates the influence of time-varying fault resistance characteristics. The location accuracy is significantly better than the traditional dominant double-ended impedance method, making it suitable for early fault detection and location in single-ended grounded underground cables. Attached Figure Description

[0015] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings: Figure 1 This is a flowchart illustrating the early fault location method for single-ended grounded cables based on sheath impedance according to the present invention. Figure 2 A schematic diagram of the structure and measurement points of a single-ended grounding cable; Figure 3 This is a waveform diagram of the metal sheath voltage under normal operating conditions. Figure 4 This is a waveform diagram of the metal sheath current under normal operating conditions. Figure 5 This is a schematic diagram of the early fault location system for single-ended grounded cables based on sheath impedance according to the present invention. Figure 6 This is a waveform diagram of the dominant voltage under phase-to-ground fault conditions; Figure 7 The waveform of the dominant current under phase-to-ground fault conditions; Figure 8 This is a waveform diagram of the metal sheath voltage under phase-to-ground fault conditions; Figure 9 The waveform of the metal sheath current under phase-to-ground fault conditions; Figure 10 Comparison of positioning errors between the main conductor and the metal sheath; Figure 11 The waveform of the sheath voltage with zero sequence component under phase-to-ground fault conditions; Figure 12 The waveform of the zero-sequence component sheath current under phase-to-ground fault conditions is shown. Detailed Implementation

[0016] The preferred embodiments of the present invention will be described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0017] Example 1: As Figure 1 As shown in the flowchart, the present invention provides a method for early fault location of single-ended grounded cables based on sheath impedance, comprising: S1: Collect the sheath current on the grounded side of the metal sheath of the single-ended grounded cable, collect the sheath voltage on the ungrounded side of the metal sheath, collect the power supply voltage on the main body power supply side, and collect the load voltage on the main body load side. Furthermore, the metal sheath of the single-ended grounded cable is grounded only on the power supply side, while the non-grounded side remains open and no sheath voltage limiter is provided.

[0018] Further, in step S1, the sheath current is acquired by a current probe located on the grounded side of the metal sheath, and the sheath voltage is acquired by a voltage sensor located on the ungrounded side of the metal sheath. The sheath current and sheath voltage are acquired synchronously.

[0019] Specifically, this invention relates to a medium-voltage insulated single-core cable, the structure of which, from the inside out, includes a main body, a semi-conductive layer, an insulation layer, and a metal sheath. The equivalent structure of the cable is as follows: Figure 2 As shown. The metal sheath, acting as a conductor parallel to the main conductor, serves as a return path for phase-to-ground fault current. In the single-ended grounding cable to which this invention applies, the metal sheath is grounded only near the power supply side, while the ungrounded side remains open and no sheath voltage limiter is installed.

[0020] Based on the above structure, a high-sensitivity current probe is installed on the grounding side of the metal sheath to collect the current of the metal sheath. A precision voltage sensor is installed on the ungrounded side of the metal sheath to collect the voltage of the metal sheath. The power supply voltage is collected from the power supply side of the main body. Load voltage is collected on the load side of the main body. .in and Synchronous acquisition must be maintained, and the sampling rate of the measurement system should not be less than 2 GSa / s to ensure that short-term transient signals are accurately captured.

[0021] The physical meanings of the four measured quantities are as follows: This refers to the voltage relative to ground on the power supply side of the cable. This is the voltage relative to ground on the load side of the cable. The total current flowing through the metal sheath. This is the voltage relative to ground on the non-grounded side of the metal sheath.

[0022] Compared to the traditional two-terminal impedance method, which requires simultaneous measurement of the power supply current... and load-side current The present invention uses the voltage on the ungrounded side of the metal sheath. Instead of the two current measurements mentioned above, the algorithm input variables are simplified to: , , , Four, which decouples the direct impact of system load on the positioning algorithm.

[0023] S2: Compare the sheath current and sheath voltage with the corresponding thresholds, which include fixed thresholds set based on safety specifications and dynamic probability boundaries determined by a statistical model based on historical normal operation data. When the sheath current or sheath voltage exceeds the corresponding threshold, record the waveform data of the sheath current, sheath voltage, power supply voltage and load voltage. Further, in step S2, determining the fixed threshold includes: Based on the impedance of the metal sheath, the geometric mean distance of the three-phase cable, the average diameter of the sheath, and the load current, the induced voltage of the metal sheath under normal operating conditions is calculated, and the calculation result is used as the fixed threshold of the sheath voltage. Based on the impedance of the metal sheath and the load current, the induced current of the metal sheath under normal operating conditions is calculated, and the calculation result is used as the fixed threshold for the sheath current.

[0024] Specifically, according to national cable standards, the fixed threshold value for induced voltage in the metal sheath under normal operating conditions is... Calculate using the following formula: ; in, Fixed threshold voltage for sheath, in V / km; Load current, in amperes (A); The geometric mean distance of the three-phase cable is expressed in mm. The average diameter of the sheath is in mm. This calculation result is used as the fixed threshold for the sheath voltage.

[0025] Fixed threshold of induced current in metal sheath under normal operating conditions Calculate using the following formula: ; in, Fixed threshold for sheath current, in amperes (A); The fixed threshold for the sheath voltage calculated by the above formula; Sheath resistance, unit: Ω; The value represents the sheath reactance, in Ω. This calculation result is used as the fixed threshold for the sheath current.

[0026] Further, in step S2, the determination of the dynamic probability boundary includes: A normal distribution statistical model of sheath current and sheath voltage is established using historical normal operation data. The dynamic threshold boundary is determined based on the preset confidence level, and the product of the mean plus or minus the confidence coefficient and the standard deviation is used as the dynamic probability boundary.

[0027] Specifically, using historical normal operation data, the sheath current was analyzed. and sheath voltage Establish a normal distribution statistical model with the following probability density function: ; in, This is the average of historical normal operating data. The standard deviation of historical normal operating data. Dynamic probability boundary based on preset confidence levels. for: ; in This represents the confidence coefficient corresponding to the confidence level.

[0028] During online monitoring, the system triggers waveform recording and records synchronously when any of the following conditions are met. Complete waveform data: ; ; in, These are the mean and standard deviation of the historical normal operating data for sheath current, respectively. These are the mean and standard deviation of the historical normal operating data for the sheath voltage, respectively. The corresponding confidence coefficient; These are fixed threshold values ​​for sheath current and sheath voltage, respectively, calculated using the formulas described above. If neither exceeds the corresponding threshold, the system is considered to be in normal operating condition, and no action is taken; monitoring continues. The waveforms of sheath voltage and sheath current under normal operating conditions are shown below. Figure 3 and Figure 4 As shown.

[0029] Furthermore, it also includes: The sheath voltage waveform is sliced ​​using the fundamental period as a window, and the mean square error of the positive half-cycle and negative half-cycle compared with the standard sine wave is calculated respectively. The ratio of the absolute value of the difference between the two to the sum of the two is used as the asymmetric waveform distortion index. The zero-sequence component of sheath current, the zero-sequence component of sheath voltage, high-frequency transient energy, and harmonic distortion rate are used to form a feature vector, which is then input into a pre-trained random forest classifier to identify and distinguish early faults from system noise. When the asymmetric waveform distortion index exceeds the preset judgment value, the fixed threshold and dynamic probability boundary in step S2 are dynamically reduced.

[0030] Specifically, based on the trigger determination, the sheath voltage waveform is sliced ​​using the fundamental period as a window, and the mean square error of the positive half-cycle waveform and the standard sine wave is calculated respectively. The mean square error between the negative half-cycle waveform and the standard sine wave Asymmetric waveform distortion index Defined as: ; in, This represents the mean square error between the positive half-cycle waveform and the standard sine wave; This represents the mean square error between the negative half-cycle waveform and the standard sine wave. To prevent extremely small positive numbers with a denominator of zero.

[0031] Simultaneously, the zero-sequence component of the sheath current is extracted. Zero-sequence component of sheath voltage High-frequency transient energy and harmonic distortion rate , constitute the feature vector A pre-trained random forest classifier is input to identify and distinguish early faults from system noise. The pre-trained random forest classifier is trained offline based on historical early fault sample data and normal operation sample data, using the zero-sequence component of the sheath current. Zero-sequence component of sheath voltage High-frequency transient energy and harmonic distortion rate The eigenvectors formed As input, the output is the classification result of early faults or system noise.

[0032] when When the threshold is exceeded, the system identifies it as an early-stage high-impedance fault and dynamically lowers the fixed threshold. and dynamic probability boundary This improves detection sensitivity and prevents the failure to detect weak transient waveforms.

[0033] S3: Based on the distributed parameter model, with the fault location as the unknown, the fault point voltage is derived from the power supply side and the load side of the fault point respectively. The two are made equal. Combining the metal sheath impedance parameter, the line capacitance parameter and the waveform data, a quadratic equation about the fault location is established and solved. The root with the real part between 0 and 1 is taken, and its product with the total length of the cable is taken as the actual fault distance.

[0034] Specifically, after triggering waveform recording, the cable is modeled based on a distributed parameter model. The cable considers inductance, capacitance, and resistance per unit length. The metal sheath is modeled using its own impedance (including resistance and inductance) as the return path for phase-to-ground fault current. The insulation layer is modeled as a dielectric with capacitance per unit length. It is assumed that early faults occur at a normalized distance from the power source. place ( The total impedance of the metal sheath is (including total resistance) Unit: Ω; Total inductance (Unit: H), total cable capacitance is , unit F.

[0035] Further, in step S3, deriving the fault point voltage from the power supply side and the load side of the fault point respectively specifically includes: From the power supply side, based on the power supply voltage, sheath current, and the metal sheath impedance and line capacitance of the section from the power supply side to the fault point, calculate the line capacitance current of the section from the power supply side to the fault point, and derive the first expression for the fault point voltage. From the load side, based on the load voltage, sheath voltage, and the metal sheath impedance and line capacitance of the section from the load side to the fault point, the line capacitance current of the section from the load side to the fault point is calculated, and the second expression for the fault point voltage is derived.

[0036] Specifically, starting from the power supply side, The pressure drop of the sheath of the section is: ; in, The voltage at the fault point is expressed in volts (V). The normalized distance from the fault point to the power supply terminal ( ), dimensionless; The total impedance of the metal sheath ( ), unit Ω; The sheath current is measured on the grounding side of the metal sheath, in amperes (A).

[0037] Expanded to: ; in, The total resistance of the metal sheath is expressed in Ω. The total inductance of the metal sheath is expressed in ohms (H), and the current is expressed as... Deduction for power supply side sheath current Value after capacitor current: ; in, The total capacitance of the cable insulation layer, in F; Voltage relative to ground on the power supply side of the main conductor (power supply voltage), unit: V; For distributed parameter model The equivalent concentrated capacitance of the insulation layer.

[0038] Will Substituting the values, we obtain the first expression for the fault point voltage: ; The meanings of the symbols are the same as above; in this expression The highest-order term is the quadratic term, and its coefficient is determined by... , , and measurement quantity They are jointly determined, and all are known quantities.

[0039] From the load side, The pressure drop of the sheath of the section is: ; in, The sheath voltage is measured on the ungrounded side of the metal sheath, in volts (V). This is the normalized distance from the fault point to the load end, which is dimensionless. This represents the capacitor branch current from the load side to the fault point, in amperes (A).

[0040] Expanded to: ; The capacitive current from the load side to the fault point for: ; in, The voltage relative to ground on the load side of the main conductor (load voltage), in V; Voltage on the ungrounded side of the metal sheath, in volts (V). The potential difference between the load-side main body and the sheath drives the... The capacitance current of the insulation layer; This is the equivalent concentrated capacitance of the insulation layer.

[0041] Will Substituting the values, we obtain the second expression for the fault point voltage: ; The meanings of the symbols are the same as above; in this expression The highest-order term is also a quadratic term, and its coefficient is determined by... , , and measurement quantity , They are jointly determined, and all are known quantities.

[0042] Equaling the first and second expressions, we obtain the information about the fault location. The quadratic equation is of the form: ; Where the coefficient Depends on the electrical parameters of the metal sheath ( ) and total cable capacitance These parameters are all known quantities. The coefficients of this equation do not include fault resistance because the fault current... The flow to the grounding terminal is conducted through the metal sheath and is already included in... In this process, the fault resistance is naturally decoupled from the equation, and the location result is independent of the fault resistance value.

[0043] To more accurately describe the dynamic behavior of early faults, an improved Schwarz model is introduced to simulate the time-varying characteristics of early fault resistance, and the fault resistance is... Defined as time Arc voltage and arc current Functions: ; in The properties are described by the improved Schwarz equation: ; in, For arc conductivity, It is a time constant. The arc voltage constant is denoted by . This model can more realistically reproduce the early fault development process, providing a theoretical basis for the extraction of steady-state components. and Typical values ​​can be referenced from arc discharge experimental data. For early faults in medium-voltage cables, Typically on the order of microseconds to milliseconds Typically in the hundreds of volts range, the specific value can be determined through experimental calibration based on the cable insulation material and operating environment.

[0044] Furthermore, considering the capacitance of the cable's metal sheath to ground... With angular frequency The fault location equation is related to the transient response at the fault point. Distributed parameter corrections are applied to the equation coefficients, resulting in the following form: ; in For distribution parameter correction factor, This is a nonlinear characteristic factor for early faults. It utilizes a hyperbolic sine function. The Taylor series expansion takes the first two terms as corrections: ; ; in, Total cable length, in meters (m). Let be the propagation constant. The conductivity per unit length of the insulation layer, measured in S / m, reflects the leakage current characteristics of the insulation layer. For medium-voltage cables in normal operation, The value is extremely small and can usually be approximated as zero; and This is the field calibration coefficient, determined by the cable laying environment. For direct burial scenarios, and The typical values ​​are close to 1. For air-laid scenarios, there may be slight deviations due to different heat dissipation conditions. The specific values ​​can be obtained by substituting the measured data into the equation under the condition of known fault location.

[0045] To address the issue that early-stage faults typically manifest as unstable insulation breakdown, a correction term based on harmonic distortion rate is introduced: ; in, The amplitude of the third harmonic component of the sheath current, in amperes (A). The amplitude of the fundamental component of the sheath current, in amperes (A). The empirical weighting coefficient reflects the degree of influence of harmonic correction on the positioning results. Its value ranges from 0 to 1 and can be determined through simulation or experimental calibration based on the actual harmonic level of the cable system. The above correction transforms the equation from a lumped parameter model to a semi-distributed parameter model, which is beneficial for long cables (…). The positioning error (2km) can be reduced from 5% to less than 1%.

[0046] Furthermore, in step S3, the establishment and solution of the quadratic equation regarding the fault location is performed using the fundamental component, specifically including: When using the fundamental component for solving, extract the waveform data from the steady-state segment of the recorded waveform data. The fundamental component is substituted into the above quadratic equation using the fundamental phasor, and the root with the real part between 0 and 1 is taken as the normalized fault location. ,Will Total cable length The product of these is used as the actual fault distance.

[0047] Furthermore, in step S3, the establishment and solution of the quadratic equation regarding the fault location is performed using zero-sequence components, specifically including: According to the symmetrical component method, the zero-sequence component only appears when a single-phase ground fault occurs in the system, and is calculated from the three-phase current and three-phase voltage using the following formulas: ; ; in and ( ( ) represent the current and phase voltage of each phase, respectively. Extract the phase voltage from the steady-state segment of the recorded waveform data. The zero-sequence component is used as the basis for substituting into the above quadratic equation, and the root with the real part between 0 and 1 is taken as the normalized fault location. ,Will Total cable length The product of these is used as the actual fault distance.

[0048] The advantage of the zero-sequence component solution method lies in its inherent filtering characteristics. The zero-sequence measurement originates from the sum of phase components, which can effectively cancel the balanced and symmetrical components in the system, filter out noise, harmonics and transient disturbances that are unrelated to the fault, and make the zero-sequence signal more sensitive to the asymmetric conditions caused by the fault, thereby providing clearer and more reliable fault characteristics. Its positioning accuracy is better than that of the fundamental component solution method.

[0049] In summary, this invention simplifies the measurement configuration by applying an impedance-based location method to metal sheaths and replacing load-end current measurement with the voltage on the ungrounded side of the sheath. It significantly improves the detection sensitivity for low-energy early faults by combining a dual threshold mechanism with an asymmetric waveform distortion index and a random forest classifier. The location results are independent of the fault resistance, and the influence of the time-varying characteristics of the fault resistance is further eliminated by using steady-state component solutions. This invention is suitable for early fault detection and location in single-end grounded underground cables.

[0050] Example 2: This example uses, as follows Figure 5 The present invention, based on the sheath impedance-based early fault location system for single-ended grounded cables, uses a 1000m long medium-voltage single-core underground cable as an example to verify the location accuracy and technical advantages of the method of the present invention.

[0051] The cable's metallic sheath is grounded only on the power supply side, with the ungrounded side open and no sheath voltage limiter installed. According to national cable standards, the resistance of the metallic sheath... Sheath reactor .

[0052] First, the threshold values ​​for sheath voltage and sheath current under normal operating conditions are established according to the method described in Example 1. Fixed threshold values ​​are calculated based on national cable standards. Simultaneously, a normal distribution statistical model for sheath current and sheath voltage is established using historical operating data under normal conditions to determine the dynamic probability boundary. Under normal operating conditions, the sheath voltage is proportional to the cable length, is zero at the grounding end, and increases linearly towards the open circuit end. The waveforms of the sheath voltage and sheath current are as follows: Figure 3 and Figure 4 As shown, this serves as a benchmark for judging early failures.

[0053] To verify the fault location accuracy, a three-phase cable simulation model was used, with the circuit consisting of ten... The equivalent circuit module indicates that each module covers a 100m segment length, with a fault resistance set at 200Ω. Fault points are sequentially set along the cable at 100m intervals: 100m, 200m, 300m, 400m, 500m, 600m, 700m, 800m, 900m, and 1000m. The fault initiation time is set at the positive half-cycle of phase A. The duration is 1 / 4 of a cycle (0.0042 s).

[0054] In the early stages of a fault, the voltage and current of the dominant conductor experience only minor disturbances, such as Figure 6 and Figure 7 As shown, this type of disturbance does not trigger conventional protection systems, nor does it affect the continuous operation of the load. However, the voltage and current of the metal sheath change significantly, such as... Figure 8 and Figure 9 As shown, the instantaneous peak voltage of the sheath is approximately 860V, and the peak current of the sheath is approximately -40A, showing significant changes compared to normal operating conditions. In the dual threshold determination mechanism, both the fixed threshold and the dynamic probability boundary are triggered, and the system immediately starts waveform recording and enters the fault location calculation process. Simultaneously, the asymmetric waveform distortion index... A significant asymmetry was detected in the positive and negative half-cycles of the sheath voltage waveform. After the feature vector was input into a random forest classifier, it was accurately identified as an early fault rather than system noise. This comparison demonstrates that the metal sheath is highly sensitive to early faults, which is the technical basis for this invention's use of metal sheath parameters as the core criterion for fault localization.

[0055] The location calculations for each fault point were performed using both the fundamental component and the zero-sequence component. All components were taken from the steady-state segment of the waveform data. The results were compared with those obtained using the traditional two-terminal impedance method (based on the dominant body parameters). The error was defined by the following formula: ; in This represents the actual distance to the early fault location. The estimated fault distance calculated by the algorithm. This represents the total length of the line; all parameters are in meters.

[0056] The location error of each fault location is compared to the example. Figure 10 As shown. The traditional method based on the dominant body has a relative error range of 0.03% to 0.50%, while the method based on the metal sheath of this invention has an error range of 0.00% to 0.16%, resulting in significantly higher positioning accuracy and stability at all fault locations.

[0057] Furthermore, the waveform of the zero-sequence component is analyzed. Under phase-to-ground fault conditions, the zero-sequence component is completely confined within the metal sheath. The zero-sequence component waveforms of the sheath voltage and sheath current are as follows: Figure 11 and Figure 12 As shown. Compared with the fundamental component, the inherent filtering characteristics of the zero-sequence component can effectively cancel the balanced and symmetrical components in the system, filter out noise, harmonics and transient disturbances, and are more sensitive to asymmetric conditions caused by faults. Therefore, the positioning accuracy of the zero-sequence component solution is further superior to that of the fundamental component solution.

[0058] The verification results of this embodiment show that by applying the impedance-based location method to the metal sheath, the present invention achieves accurate location of early faults in single-ended grounded underground cables without the need to measure the dominant current; the dual threshold mechanism combined with the asymmetric waveform distortion index and random forest classifier effectively improves the detection sensitivity for low-energy early faults; the location result is independent of the fault resistance, and the influence of the time-varying characteristics of the fault resistance is eliminated by solving the steady-state component, thus possessing both high accuracy and strong practicality.

[0059] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for early fault location of single-ended grounded cables based on sheath impedance, characterized in that, include: S1: Collect the sheath current on the grounded side of the metal sheath of the single-ended grounded cable, collect the sheath voltage on the ungrounded side of the metal sheath, collect the power supply voltage on the main body power supply side, and collect the load voltage on the main body load side. S2: Compare the sheath current and sheath voltage with the corresponding thresholds, which include fixed thresholds set based on safety specifications and dynamic probability boundaries determined by a statistical model based on historical normal operation data. When the sheath current or sheath voltage exceeds the corresponding threshold, record the waveform data of the sheath current, sheath voltage, power supply voltage and load voltage. S3: Based on the distributed parameter model, with the fault location as the unknown, derive the fault point voltage from the power supply side and the load side of the fault point respectively, set the two to be equal, and combine the metal sheath impedance parameter, line capacitance parameter and the waveform data to establish and solve the quadratic equation about the fault location. Take the root with the real part between 0 and 1, and multiply it by the total length of the cable as the actual fault distance.

2. The method for early fault location of a single-ended grounded cable based on sheath impedance according to claim 1, characterized in that, In step S1, the sheath current is acquired by a current probe located on the grounded side of the metal sheath, and the sheath voltage is acquired by a voltage sensor located on the ungrounded side of the metal sheath. The sheath current and sheath voltage are acquired synchronously.

3. The method for early fault location of a single-ended grounded cable based on sheath impedance according to claim 1, characterized in that, In step S2, determining the fixed threshold includes: Based on the impedance of the metal sheath, the geometric mean distance of the three-phase cable, the average diameter of the sheath, and the load current, the induced voltage of the metal sheath under normal operating conditions is calculated, and the calculation result is used as the fixed threshold of the sheath voltage. Based on the impedance of the metal sheath and the load current, the induced current of the metal sheath under normal operating conditions is calculated, and the calculation result is used as the fixed threshold for the sheath current.

4. The method for early fault location of a single-ended grounded cable based on sheath impedance according to claim 1, characterized in that, In step S2, the determination of the dynamic probability boundary includes: A normal distribution statistical model of sheath current and sheath voltage is established using historical normal operation data. The dynamic threshold boundary is determined based on the preset confidence level, and the product of the mean plus or minus the confidence coefficient and the standard deviation is used as the dynamic probability boundary.

5. The method for early fault location of a single-ended grounded cable based on sheath impedance according to claim 1, characterized in that, Also includes: The sheath voltage waveform is sliced ​​using the fundamental period as a window, and the mean square error of the positive half-cycle and negative half-cycle compared with the standard sine wave is calculated respectively. The ratio of the absolute value of the difference between the two to the sum of the two is used as the asymmetric waveform distortion index. The zero-sequence component of sheath current, the zero-sequence component of sheath voltage, high-frequency transient energy, and harmonic distortion rate are used to form a feature vector, which is then input into a pre-trained random forest classifier to identify and distinguish early faults from system noise. When the asymmetric waveform distortion index exceeds the preset judgment value, the fixed threshold and dynamic probability boundary in step S2 are dynamically reduced.

6. The method for early fault location of a single-ended grounded cable based on sheath impedance according to claim 1, characterized in that, In step S3, deriving the fault point voltage from the power supply side and the load side of the fault point respectively specifically includes: From the power supply side, based on the power supply voltage, sheath current, and the metal sheath impedance and line capacitance of the section from the power supply side to the fault point, calculate the line capacitance current of the section from the power supply side to the fault point, and derive the first expression for the fault point voltage. From the load side, based on the load voltage, sheath voltage, and the metal sheath impedance and line capacitance of the section from the load side to the fault point, the line capacitance current of the section from the load side to the fault point is calculated, and the second expression for the fault point voltage is derived.

7. The method for early fault location of a single-ended grounded cable based on sheath impedance according to claim 1, characterized in that, In step S3, the establishment and solution of the quadratic equation regarding the fault location is performed using the fundamental component, specifically including: Extract the fundamental components of sheath current, sheath voltage, power supply voltage, and load voltage from the waveform data. Substitute the fundamental components into the quadratic equation and take the root with the real part between 0 and 1 as the normalized fault location. Multiply the normalized fault location by the total cable length as the actual fault distance.

8. The method for early fault location of a single-ended grounded cable based on sheath impedance according to claim 1, characterized in that, In step S3, the establishment and solution of the quadratic equation regarding the fault location is performed using zero-sequence components, specifically including: The zero-sequence components of sheath current, sheath voltage, power supply voltage, and load voltage are extracted from the waveform data respectively. The zero-sequence components are substituted into the quadratic equation, and the root with the real part between 0 and 1 is taken as the normalized fault location. The product of the normalized fault location and the total length of the cable is taken as the actual fault distance.

9. The method for early fault location of a single-ended grounded cable based on sheath impedance according to claim 7 or 8, characterized in that, The fundamental component or zero-sequence component is taken from the steady-state segment of the waveform data; the steady-state segment is determined after analyzing the time-varying resistance characteristics of the early fault arc based on the improved Schwarz model; when establishing the quadratic equation about the fault location, the coefficients of the equation are corrected by the distributed parameters based on the inductance per unit length of the metal sheath, the line capacitance, the total length of the cable, and the field calibration coefficient.

10. An early fault location system for single-ended grounded cables based on sheath impedance, characterized in that, The system is used to perform the early fault location method for single-ended grounded cables based on sheath impedance as described in any one of claims 1-9, the system comprising: The signal acquisition module is used to acquire the sheath current on the grounded side of the metal sheath of the single-ended grounded cable, the sheath voltage on the ungrounded side of the metal sheath, the power supply voltage on the main body power supply side, and the load voltage on the main body load side. The threshold monitoring module is used to compare the sheath current and sheath voltage with the corresponding thresholds, including fixed thresholds set based on safety specifications and dynamic probability boundaries determined by a statistical model based on historical normal operation data. When the sheath current or sheath voltage exceeds the corresponding threshold, the module records the waveform data of the sheath current, sheath voltage, power supply voltage and load voltage. The fault location module is used to derive the fault point voltage from the power supply side and the load side of the fault point according to the distributed parameter model, with the fault location as the unknown quantity. The voltage is made equal to the voltage of the fault point. The module combines the metal sheath impedance parameter, the line capacitance parameter and the waveform data to establish and solve a quadratic equation about the fault location. The root with the real part between 0 and 1 is taken and multiplied by the root with the total length of the cable as the actual fault distance.

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