A method for predicting cable fault probability

Abstract

This invention discloses a method for predicting cable failure probability, belonging to the field of XLPE cable condition-based operation and maintenance technology. The method includes: constructing a cable degradation model with segmented degradation characteristics using a Gamma stochastic process, wherein the shape parameters of the model vary segmentally with the degree of degradation to adapt to the nonlinear characteristics of the cable degradation lag and acceleration stages; collecting data on the cable's degradation degree and corresponding operating time during actual operation; determining the shape parameters, inverse scaling parameters, and stage transition parameters in the model using maximum likelihood estimation based on the collected data; and calculating the cable's failure probability at a target time based on the degradation model with determined parameters. This invention can quantify the stochastic and nonlinear stage characteristics of the cable degradation process, achieving accurate prediction of cable remaining life and estimation of failure probability, providing a basis for differentiated cable operation and maintenance decisions.

Description

Technical Field

[0001] This invention relates to the field of XLPE cable condition maintenance technology, and in particular to a method for predicting cable fault probability. Background Technology

[0002] In recent years, XLPE AC cables, with their superior electrical, mechanical, and thermal stability, have seen a continuous increase in their proportion in power lines and a sustained expansion in their installation scale. They have been widely used across various voltage levels, from low-voltage distribution networks to ultra-high-voltage power grids.

[0003] Medium and high voltage XLPE cables, as key equipment in the main power grid lines, bear the important task of power transmission. However, because these cables are mostly laid in underground pipe corridors, tunnels, or directly buried in the soil, they are subjected to long-term electro-thermal-mechanical multi-stress coupling effects, causing their insulation materials to gradually and irreversibly deteriorate. This deterioration process has typical stage characteristics: initially, there is a long performance lag period with no obvious signs of deterioration; later, it enters an accelerated deterioration stage, with insulation performance declining sharply until failure. This nonlinear deterioration characteristic poses a significant challenge to cable condition assessment and remaining life prediction.

[0004] Currently, power companies mainly rely on periodic preventive tests and partial discharge detection to monitor the condition of XLPE cables. These methods have the following limitations: (1) they can only reflect the current state and cannot predict the deterioration trend; (2) the test results are easily affected by environmental interference; and (3) it is difficult to quantify and assess the remaining service life of the cable. Traditional deterministic deterioration models cannot accurately describe the randomness and stage characteristics of cable deterioration, resulting in a large deviation between the predicted results and the actual situation. Summary of the Invention

[0005] The purpose of this invention is to provide a cable fault probability prediction method that can effectively estimate the fault probability of cables, prevent major faults in cables, and rationally allocate cable operation and maintenance measures, thereby ensuring the normal operation of the power system.

[0006] To achieve the above objectives, the present invention provides a cable fault probability prediction method, comprising the following steps: S1. Construct a cable degradation model with segmented degradation characteristics using the Gamma stochastic process; the degradation model includes shape parameters, inverse scale parameters, and stage transition parameters to be determined. S2. Collect data on the degree of cable degradation and the corresponding operating time during actual operation; S3. Using the degradation degree data and runtime data collected in S2, determine the shape parameters, inverse scale parameters, and stage transition parameters in the degradation model through maximum likelihood estimation. S4. Based on the degradation model determined by parameters in S3, calculate the probability of cable failure at the target time.

[0007] Preferably, the specific method for constructing a cable degradation model with segmented degradation characteristics using the Gamma stochastic process described in S1 is as follows: S11. Set the cable degradation level to... The interval, where, This represents the threshold for cable degradation at the time of a fault. A degradation level of 0 indicates the cable is in brand new condition. As the cable is put into use, its degradation level increases until a fault occurs. ; S12. The cable degradation process is described using a Gamma stochastic process, that is, any time during a certain stage of cable degradation... The increase in the degree of degradation over time It follows a Gamma distribution, and its probability density function is: ; In the formula, and These are the shape parameter and inverse scaling parameter of the Gamma distribution, respectively; For indicator functions; For the Gamma function, It is a dummy variable for the Gamma function. It is a natural constant; Shape parameters As the cable deteriorates change: ; In the formula, These are the stage transition parameters. The degree of degradation has not reached Shape parameters at time, For the degree of degradation exceeding Shape parameters at time; when the cable deterioration reaches At this time, the cable transitions from the lag phase to the acceleration phase, and its shape parameters change from... Become .

[0008] Preferably, the specific method for collecting data on the degree of cable degradation and the corresponding operating time during actual operation in step S2 is as follows: Collect actual degradation data from at least 20 cables, with each data point including at least the initial degree of degradation. Initial degradation time Current degree of degradation and the current deterioration moment The method for obtaining the degree of cable degradation remains consistent.

[0009] Preferably, the specific method for determining the shape parameter, inverse scaling parameter, and stage transition parameter in the degradation model through maximum likelihood estimation as described in S3 is as follows: Let the set of parameters be undetermined ,in, and For shape parameters, For inverse scaling parameters, For the stage transition parameters; for the first Each sample, based on its degree of degradation and The likelihood probability is calculated for three different scenarios: Scenario 1: When At that time, the first The likelihood probability of each sample is: ; in, For the case At that time, the first The likelihood probability of a sample. , In time The cumulative amount of degradation, In time The cumulative amount of degradation; Scenario 2: When At that time, the first The likelihood probability of each sample is: ; Scenario 3: When At that time, the first The likelihood probability of each sample is: ; In the formula, Indicates the first The degree of degradation of each sample starts from the initial degree of degradation. Growth to stage transition parameters The duration of the experience; Considering the above three scenarios, the first... The likelihood probability of each sample is: ; in, This is an indicator function.

[0010] Preferably, the optimal parameters of the degradation model Obtained through the following formula: ; in, This represents the total number of cable samples collected.

[0011] Preferably, the specific method for calculating the cable's failure probability at the target time based on the degradation model with parameters determined in S3, as described in S4, is as follows: For the current moment Current degree of degradation The cable, calculate thereafter Failure probability at any time There are two scenarios: Scenario 1: When At that time, the equipment was The probability of failure at time t is: ; in, Indicates the target time The degree of degradation is a random variable. Indicates the current time The degree of degradation is a random variable; Scenario 2: When At that time, the cable is at the target time The failure probability is: ; In the formula, Indicates the degree of degradation from the current level. Growth to stage transition parameters The duration of the experience; Combining the above two equations, the cable at the target time The failure probability is: ; in, This is an indicator function.

[0012] Preferably, the stage transition parameters The range of values ​​is ,in, This is the threshold for the degree of degradation when a cable fails.

[0013] Preferably, when the shape parameters The time characterizes the cable in the lag phase of degradation, where the degree of degradation increases slowly; when the shape parameters The time indicates that the cable is in an accelerated deterioration stage, and the rate of increase in the degree of deterioration is rising.

[0014] Therefore, the cable fault probability prediction method described above in this invention has the following beneficial effects: (1) This invention sets the shape parameter of the Gamma stochastic process to vary piecewise with the degree of degradation, so that the model in Automatically adapts to the slow growth characteristics of cable degradation during the lag phase. It automatically adapts to the rapid degradation characteristics of the acceleration phase, solving the problem that traditional single distribution models cannot characterize the nonlinear phase transition of the degradation process; (2) Based on maximum likelihood estimation, this invention calibrates model parameters using actual degradation data and calculates the failure probability at any target time in combination with the current state of the equipment, thereby achieving an improvement from qualitative state assessment to quantitative failure probability prediction, overcoming the limitation of existing detection methods that can only reflect the current state and cannot predict the degradation trend. (3) By collecting actual degradation data of multiple cables, the present invention estimates the model parameters, which can quantitatively describe the random fluctuations in the cable degradation process and make up for the shortcomings of traditional deterministic models that regard degradation as a fixed curve and cannot describe the random differences between individual samples.

[0015] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the cable fault probability prediction method of the present invention; Figure 2 This is a schematic diagram of the XLPE cable degradation model for a cable fault probability prediction method according to the present invention. Detailed Implementation

[0017] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0018] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, 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.

[0019] Example like Figure 1 As shown, a cable fault probability prediction method includes the following steps: S1. Construct a cable degradation model with segmented degradation characteristics using the Gamma stochastic process; the degradation model includes shape parameters, inverse scale parameters, and stage transition parameters to be determined. The specific method for constructing a cable degradation model with piecewise degradation characteristics using the Gamma stochastic process is as follows: S11. Set the cable degradation level to... The interval, where, This represents the threshold for cable degradation at the time of a fault. A degradation level of 0 indicates the cable is in brand new condition. As the cable is put into use, its degradation level increases until a fault occurs. ; S12. The cable degradation process is described using a Gamma stochastic process, that is, any time during a certain stage of cable degradation... The increase in the degree of degradation over time It follows a Gamma distribution, and its probability density function is: ; In the formula, and These are the shape parameter and inverse scaling parameter of the Gamma distribution, respectively; For indicator functions; For the Gamma function, It is a dummy variable for the Gamma function. It is a natural constant; Shape parameters As the cable deteriorates change: ; In the formula, For stage transition parameters ( The range of values ​​is , (This is the threshold for the degree of degradation when a cable fails). The degree of degradation has not reached Shape parameters at time, For the degree of degradation exceeding Shape parameters at time; when the cable deterioration reaches At this time, the cable transitions from the lag phase to the acceleration phase, and its shape parameters change from... Become .

[0020] S2. Collect data on the degree of cable degradation and the corresponding operating time during actual operation; To ensure the statistical significance of the parameter estimates, actual degradation data from at least 20 cables were collected, with each data point including at least the initial degree of degradation of the cable. Initial degradation time Current degree of degradation and the current deterioration moment The method for obtaining the degree of cable degradation remains consistent.

[0021] S3. Using the degradation degree data and runtime data collected in S2, determine the shape parameters, inverse scale parameters, and stage transition parameters in the degradation model through maximum likelihood estimation. Specifically: Let the set of parameters be undetermined ,in, and For shape parameters, For inverse scaling parameters, For the stage transition parameters; for the first Each sample, based on its degree of degradation and The likelihood probability is calculated for three different scenarios: Scenario 1: When At that time, the first The likelihood probability of each sample is: ; in, For the case At that time, the first The likelihood probability of a sample. , In time The cumulative amount of degradation, In time The cumulative amount of degradation; Scenario 2: When At that time, the first The likelihood probability of each sample is: ; Scenario 3: When At that time, the first The likelihood probability of each sample is: ; In the formula, Indicates the first The degree of degradation of each sample starts from the initial degree of degradation. Growth to stage transition parameters The duration of the experience; Considering the above three scenarios, the first... The likelihood probability of each sample is: ; in, This is an indicator function.

[0022] Optimal parameters of the degradation model Obtained through the following formula: ; in, This represents the total number of cable samples collected.

[0023] S4. Based on the degradation model determined by parameters in S3, calculate the probability of cable failure at the target time.

[0024] Specifically: For the current moment Current degree of degradation The cable, calculate thereafter Failure probability at any time There are two scenarios: Scenario 1: When At that time, the equipment was The probability of failure at time t is: ; in, Indicates the target time The degree of degradation is a random variable. Indicates the current time The degree of degradation is a random variable; Scenario 2: When At that time, the cable is at the target time The failure probability is: ; In the formula, Indicates the degree of degradation from the current level. Growth to stage transition parameters The duration of the experience; Combining the above two equations, the cable at the target time The failure probability is: ; in, This is an indicator function.

[0025] The following combination Figure 2 The degradation model and failure probability prediction principle of the present invention will be further explained.

[0026] like Figure 2 As shown, the horizontal axis of the model represents the degradation time (years), indicating the length of time the cable has been in operation, ranging from approximately 0 to 30 years; the vertical axis represents the degree of degradation, indicating the severity of aging of the cable insulation layer, ranging from 0 (brand new / completely healthy) to 100 (complete failure / breakdown).

[0027] The horizontal red dashed line marks as =100 represents the limit value / fault threshold of the degree of degradation. When the cable degradation reaches... When this occurs, it means the cable's insulation has completely failed, its lifespan is over, and an electrical breakdown or short circuit fault has occurred. This is marked by a horizontal blue dashed line. ≈45 is the stage transition parameter in this embodiment, representing the critical threshold for the degradation stage transition. In practical engineering, when the cable degradation reaches... When the cable reaches a certain point, it signifies that the cable has transitioned from the stagnant growth stage to the accelerated deterioration stage, at which point intensive monitoring or maintenance and replacement plans should be initiated.

[0028] Figure 2 The image shows two typical cable degradation curves, representing the degradation process under two different operating conditions: the solid line (sample 1) degrades faster, reaching the end of its service life around year 18. (100) means that the cable failed at approximately 18 years; the dashed line (sample 2) deteriorated more slowly and steadily, reaching the end of its lifespan at approximately 29 years. (100), its service life is significantly longer than that of sample 1. The difference between the two curves shows that the degradation model constructed in this invention can effectively distinguish the differences in degradation rate between different individual cables under the same operating environment.

[0029] Both curves exhibit a "stepped" characteristic, rather than a smooth upward trend. This characteristic reflects that the degradation of XLPE cables in actual operation is not a linear process, but rather a physical phenomenon characterized by staged abrupt changes. Specifically, these steps may correspond to physical events such as a sudden intensification of partial discharge, a breakthrough growth of water trees, or accelerated aging of insulation materials caused by sudden changes in ambient temperature / load. During the plateau phase (horizontal segment), degradation is relatively stable, and the degree of degradation increases slowly; during the rising phase (vertical abrupt change), insulation performance declines rapidly. Figure 2 The stepped degradation characteristic shown precisely verifies the use of shape parameters in this invention. Variations in stages according to the degree of degradation ( <1 corresponds to a prolonged plateau period. The rationality and engineering practicality of the modeling approach (>1 corresponds to the accelerated mutation period).

[0030] In practical engineering applications, Figure 2 The degradation model shown can be used to guide power companies' operation and maintenance decisions. On the one hand, the current degree of cable degradation is obtained through on-site testing (such as dielectric loss factor testing, partial discharge testing, etc.), and the model is used to determine whether the cable is currently in a stagnant or accelerating phase. On the other hand, based on the fault probability calculation formula in step S4, the fault probability of the cable at the target time is predicted, achieving a quantitative assessment of the remaining life. For cables with a rapid degradation rate (such as...), Figure 2 For cables in sample 1), the testing cycle needs to be shortened or replacement should be arranged in advance; for cables with a slower rate of degradation (such as...), the testing cycle needs to be shortened or replacement should be arranged in advance. Figure 2 The high-quality cables in sample 2) can continue to operate safely, thereby saving maintenance costs and realizing differentiated operation and maintenance management of cable assets.

[0031] Therefore, this invention employs the aforementioned cable fault probability prediction method. Based on maximum likelihood estimation to determine model parameters, it can quantitatively calculate the fault probability of a cable at any target time, achieving accurate prediction of remaining lifespan and providing a scientific basis for developing differentiated maintenance strategies. This method can effectively reduce the risk of sudden cable faults, extend equipment lifespan, optimize the allocation of operation and maintenance resources, and ensure the safe and reliable operation of the power grid.

[0032] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for predicting cable fault probability, characterized in that, Includes the following steps: S1. Construct a cable degradation model with segmented degradation characteristics using the Gamma stochastic process; the degradation model includes shape parameters, inverse scale parameters, and stage transition parameters to be determined. S2. Collect data on the degree of cable degradation and the corresponding operating time during actual operation; S3. Using the degradation degree data and runtime data collected in S2, determine the shape parameters, inverse scale parameters, and stage transition parameters in the degradation model through maximum likelihood estimation. S4. Based on the degradation model determined by parameters in S3, calculate the probability of cable failure at the target time.

2. The method according to claim 1, characterized in that, The specific method for constructing a cable degradation model with piecewise degradation characteristics using the Gamma stochastic process described in S1 is as follows: S11. Set the cable degradation level to... The interval, where, This represents the threshold for cable degradation at the time of a fault. A degradation level of 0 indicates the cable is in brand new condition. As the cable is put into use, its degradation level increases until a fault occurs. ; S12. The cable degradation process is described using a Gamma stochastic process, that is, any time during a certain stage of cable degradation... The increase in the degree of degradation over time It follows a Gamma distribution, and its probability density function is: ； In the formula, and These are the shape parameter and inverse scaling parameter of the Gamma distribution, respectively; For indicator functions; For the Gamma function, It is a dummy variable for the Gamma function. It is a natural constant; Shape parameters As the cable deteriorates change: ； In the formula, These are the stage transition parameters. The degree of degradation has not reached Shape parameters at time, For the degree of degradation exceeding Shape parameters at time; when the cable deterioration reaches At this time, the cable transitions from the lag phase to the acceleration phase, and its shape parameters change from... Become .

3. The method according to claim 1, characterized in that, The specific method for collecting data on the degree of cable degradation and the corresponding operating time during actual operation, as described in S2, is as follows: Collect actual degradation data from at least 20 cables, with each data point including at least the initial degree of degradation. Initial degradation time Current degree of degradation and the current deterioration moment The method for obtaining the degree of cable degradation remains consistent.

4. The method according to claim 3, characterized in that, The specific method described in S3 for determining the shape parameters, inverse scaling parameters, and stage transition parameters in the degradation model using maximum likelihood estimation is as follows: Let the set of parameters be undetermined ,in, and For shape parameters, For inverse scaling parameters, For the stage transition parameters; for the first Each sample, based on its degree of degradation and The likelihood probability is calculated for three different scenarios: Scenario 1: When At that time, the first The likelihood probability of each sample is: ； in, For the case At that time, the first The likelihood probability of a sample. , In time The cumulative amount of degradation, In time The cumulative amount of degradation; Scenario 2: When At that time, the first The likelihood probability of each sample is: ； Scenario 3: When At that time, the first The likelihood probability of each sample is: ； In the formula, Indicates the first The degree of degradation of each sample starts from the initial degree of degradation. Growth to stage transition parameters The duration of the experience; Considering the above three scenarios, the first... The likelihood probability of each sample is: ； in, This is an indicator function.

5. The method according to claim 4, characterized in that, The optimal parameters of the degradation model Obtained through the following formula: ； in, This represents the total number of cable samples collected.

6. The method according to claim 1, characterized in that, The specific method described in S4 for calculating the cable's failure probability at the target time based on the degradation model with parameters determined in S3 is as follows: For the current moment Current degree of degradation The cable, calculate thereafter Failure probability at any time There are two scenarios: Scenario 1: When At that time, the equipment was The probability of failure at time t is: ； in, Indicates the target time The degree of degradation is a random variable. Indicates the current time The degree of degradation is a random variable; Scenario 2: When At that time, the cable is at the target time. The failure probability is: ； In the formula, Indicates the degree of degradation from the current level. Growth to stage transition parameters The duration of the experience; Combining the above two equations, the cable at the target time The failure probability is: ； in, This is an indicator function.

7. The method according to claim 6, characterized in that, The stage transition parameters The range of values ​​is ,in, This is the threshold for the degree of degradation when a cable fails.

8. The method according to claim 2, characterized in that, When shape parameters The time characterizes the cable in the lag phase of degradation, where the degree of degradation increases slowly; when the shape parameters The time indicates that the cable is in an accelerated deterioration stage, and the rate of increase in the degree of deterioration is rising.

Images