A method for diagnosing and locating turn-to-turn short circuit fault of air-core reactor based on magnetic field sensor array

Abstract

This invention relates to a method for diagnosing and locating inter-turn short-circuit faults in air-core reactors based on a magnetic field sensor array, belonging to the field of power equipment testing. The method includes the following steps: Step 1: Arranging a magnetic field sensor array at an axial position on the outer side of the air-core reactor to acquire magnetic field distribution data near the reactor; Step 2: Calculating the magnetic field distribution data at the location of the magnetic field sensor array under normal operating conditions and inter-turn short-circuit fault conditions at different locations, and constructing a complete fault feature database; Step 3: Setting an inter-turn short-circuit fault at a determined location on the air-core reactor, and calibrating the data based on the measured data and the data in the fault feature database; Step 4: Calculating the measured data of the air-core reactor using a fault diagnosis algorithm to determine whether a fault has occurred in the reactor and accurately locate the fault location. This invention can diagnose inter-turn short-circuit faults and accurately locate the fault point, improving the safety and reliability of power equipment operation.

Description

Technical Field

[0001] This invention belongs to the field of power equipment testing technology, and relates to a method for diagnosing and locating inter-turn short-circuit faults in hollow reactors based on a magnetic field sensor array. Background Technology

[0002] Air-core reactors, as critical high-voltage primary equipment in power systems, play a vital role in reactive power compensation, system voltage regulation and stabilization, and limiting short-circuit current. Their operating status directly affects the safety and reliability of the power grid. Therefore, ensuring the safe and stable operation of air-core reactors is a crucial aspect of maintaining power system stability.

[0003] Air-core reactors are typically installed outdoors for extended periods, making them susceptible to temperature and humidity fluctuations, pollution, and system overvoltage. Under these conditions, the windings may experience moisture absorption, partial discharge, and localized overheating, leading to a decline or even damage in the inter-turn insulation performance, ultimately inducing inter-turn short circuits. Inter-turn short circuits are not only one of the most common fault types during the operation of air-core reactors, but also pose a significant hazard: if the faulty equipment is not detected and isolated in time, the current distribution near the fault point will be abnormal, the local temperature rise of the coil will be significant, further accelerating insulation aging, causing the fault to gradually expand from a few inter-turn short circuits to multi-turn short circuits. In severe cases, it may cause the reactor to burn out or even catch fire, posing a significant threat to the safe and stable operation of the power system. Therefore, the accurate detection and early identification of inter-turn short circuit faults have important engineering significance and application value.

[0004] Current methods for diagnosing inter-turn short circuits in air-core reactors primarily rely on multi-source signals, including electrical, thermal, mechanical, and vibration signals. Among these, methods based on electrical parameters typically identify faults through changes in characteristics such as voltage, current, power angle, or equivalent impedance. Some studies have also fused electrical signals with environmental information such as temperature, humidity, and wind speed to improve diagnostic reliability. Meanwhile, inter-turn short circuits alter the distribution of electromagnetic forces and cause abnormal structural vibration characteristics; related vibration features have been used in conjunction with machine learning for fault identification and location. However, these methods generally suffer from several common limitations: low sensitivity to early localized faults, susceptibility to environmental noise and fluctuations in operating conditions, and limited ability to accurately locate internal inter-turn short circuits within the reactor.

[0005] From a mechanistic perspective, a large circulating current flows through a short-circuited turn, generating a significantly enhanced local magnetic field around it according to the Biot-Savart law. Therefore, utilizing the magnetic field information around the reactor for fault detection has a clear physical basis. Compared to traditional electrical, thermal, and vibration methods, magnetic field measurement offers advantages such as non-contact operation, high sensitivity, and real-time performance, providing a more promising technical approach for the early identification and location of inter-turn short circuits. Summary of the Invention

[0006] In view of this, the purpose of the present invention is to provide a method for diagnosing and locating inter-turn short-circuit faults in air-core reactors based on a magnetic field sensor array.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] A method for diagnosing and locating inter-turn short-circuit faults in air-core reactors based on a magnetic field sensor array includes the following steps:

[0009] Step 1: Arrange a magnetic field sensor array at the axial position on the outer side of the hollow reactor to obtain magnetic field distribution data near the hollow reactor;

[0010] Step 2: Calculate the magnetic field distribution data of the magnetic field sensor array position of the air-core reactor under normal operating conditions and inter-turn short-circuit fault conditions at different locations, and construct a complete fault feature database;

[0011] Step 3: Set up an inter-turn short-circuit fault at the determined location of the air-core reactor, and perform data calibration based on the measured data and the data in the fault characteristic database;

[0012] Step 4: Calculate the measured data of the air-core reactor using a fault diagnosis algorithm to determine whether a fault has occurred in the reactor and accurately locate the fault location. The fault diagnosis algorithm in Step 4 includes three stages:

[0013] The first stage: The magnetic field phase data collected by the magnetic field sensor located at the axial center of the hollow reactor is used as a reference, and the difference is calculated with the magnetic field phase data collected by other magnetic field sensors.

[0014] In the second stage, the fitness function is calculated by comparing the phase difference of the measured magnetic field after calibration with the phase difference under normal operating conditions in the database. If the convergence condition is met, the reactor will work normally; if the convergence condition is not met, the reactor will have an inter-turn short circuit fault.

[0015] In the third stage, a genetic algorithm based on a population competition mechanism is used to calculate the fitness function between the phase difference of the calibrated measured magnetic field and the phase difference of the database. If the convergence condition is met, the calculated fault location result is output.

[0016] Furthermore, the magnetic field sensor array consists of nine TMR magnetic field sensors, and each sensor is arranged at equal intervals from the top to the bottom of the hollow reactor. The sensitive direction of the TMR magnetic field sensor is axial.

[0017] Furthermore, the magnetic field distribution data is phase data extracted from the time-domain signal of the magnetic field collected by the TMR magnetic field sensor. The phase data extraction method is to obtain the phase by sinusoidal fitting of the magnetic field signal using the least squares method.

[0018] Furthermore, in step two, a complete fault feature database is constructed using interpolation, including the following steps:

[0019] Assume the fault location is determined by both the package number and the location parameter, let... x i Indicates the first i The package malfunctioned. y Indicates the location of the fault point in the axial direction of the reactor; for encapsulation x i Two adjacent fault locations Q 1( x i , y 1) and Q 2( x i , y 2) Any fault location during this period Q ( x i , y The magnetic field data is calculated using the following formula:

[0020]

[0021] in, f ( Q 1) and f ( Q 2) Indicate the location of the fault respectively. Q 1( x i , y 1) and Q 2( x i , y 2) Magnetic field distribution data, f ( Q The result is the magnetic field distribution calculated by linear interpolation. In this way, the magnetic field distribution data corresponding to all fault locations are obtained, thereby completing the construction of the fault feature database.

[0022] Furthermore, the data calibration based on measured data and fault characteristic database described in step three includes the following steps:

[0023] Set measured data Data from the fault characteristic database The following linear relationship exists:

[0024]

[0025] Linear regression fitting using the least squares method yields the parameters. a andb .

[0026] Furthermore, the specific calculation process for the first stage is as follows:

[0027] The TMR magnetic field sensors in the magnetic field sensor array are numbered sequentially from bottom to top as 1 to 9. The TMR magnetic field sensor at the axial center of the hollow reactor is numbered 5. Using this sensor as a reference, the phase difference value of the k-th sensor satisfies the following formula:

[0028]

[0029] The phase difference of the measured magnetic field was obtained through calculation. Magnetic field phase difference under normal operating conditions magnetic field phase difference with fault feature database .

[0030] Furthermore, the specific process of the second phase is as follows:

[0031] Measured magnetic field phase difference Phase difference of the magnetic field under normal operating conditions fitness function Satisfy the following formula:

[0032]

[0033] Set convergence criteria parameters ,if This indicates that the air-core reactor is working normally; if This indicates that the air-core reactor has an inter-turn short circuit fault.

[0034] Furthermore, the specific calculation process for the third stage is as follows:

[0035] First, determine the location of the fault within the envelope, and then, based on the location of this envelope, determine the axial location of the specific inter-turn short circuit fault in the air-core reactor; let the number of envelopes be... i Each package is set as an initial population 1. i Population size set to 100, fitness function Satisfy the following formula:

[0036]

[0037] i Each population was iteratively calculated three times using a genetic algorithm to obtain its optimal fitness function: and the corresponding axial position ; i The optimal fitness function of each population competes with the others to select the best population. x The following equation is satisfied:

[0038]

[0039] x That is, the envelope number where the inter-turn short-circuit fault is located;

[0040] exist x If the encapsulation fails, a genetic algorithm is used to continue iterative optimization calculations, with convergence criteria parameters set. ,if If the algorithm converges, then the position of the output is calculated. y The axial location where the final fault occurred is now determined, and fault location is complete.

[0041] The beneficial effects of this invention are as follows: This invention arranges a magnetic field sensor array on the outside of the hollow reactor to collect and analyze the surrounding magnetic field in real time in a non-contact manner, so as to realize online diagnosis and location of inter-turn short circuits. It has the advantages of non-contact, high sensitivity, fast response and strong real-time performance.

[0042] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0043] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0044] Figure 1 This is a flowchart of the inter-turn short-circuit fault diagnosis and location method for hollow reactors based on magnetic field array sensors in this invention;

[0045] Figure 2 A flowchart illustrating the construction of a complete fault feature database in this invention;

[0046] Figure 3 This is a flowchart of the fault diagnosis and location algorithm in this invention. Detailed Implementation

[0047] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0048] It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Therefore, the drawings only show the components related to the present invention and are not drawn according to the actual number, shape and size of the components in the actual implementation. In the actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0049] In the following description, numerous details are explored to provide a more thorough explanation of embodiments of the invention. However, it will be apparent to those skilled in the art that embodiments of the invention may be practiced without these specific details. In other embodiments, well-known structures and devices are shown in block diagram form rather than in detail to avoid obscuring embodiments of the invention.

[0050] Example 1:

[0051] like Figure 1-3 As shown, this invention provides a method for diagnosing and locating inter-turn short-circuit faults in air-core reactors based on a magnetic field sensor array, comprising the following steps:

[0052] Step 1: Arrange a magnetic field sensor array at the axial position on the outer side of the hollow reactor to obtain magnetic field distribution data near the hollow reactor.

[0053] The magnetic field sensor array consists of nine TMR magnetic field sensors, and each sensor is evenly spaced from the top to the bottom of the hollow reactor. The sensitive direction of the TMR magnetic field sensor is axial.

[0054] The acquired magnetic field distribution data is phase data extracted from the time-domain signal of the magnetic field collected by the TMR magnetic field sensor. The phase data extraction method is to obtain the phase by sinusoidal fitting of the magnetic field signal using the least squares method.

[0055] Step 2: Calculate the magnetic field distribution data of the magnetic field sensor array position of the air-core reactor under normal operating conditions and inter-turn short-circuit fault conditions at different locations, and construct a complete fault feature database;

[0056] The acquired magnetic field distribution data is phase data extracted from the time-domain signal of the magnetic field collected by the TMR magnetic field sensor. The phase data extraction method is to obtain the phase by sinusoidal fitting of the magnetic field signal using the least squares method.

[0057] Calculating the magnetic field distribution data of the magnetic field sensor array locations under all different inter-turn short-circuit fault conditions requires significant computational resources and time. To improve computational efficiency, the fault locations are discretized at certain step intervals, and magnetic field distribution calculations are performed only for a subset of fault conditions. For the magnetic field distribution data between adjacent fault locations, a linear interpolation method is used for estimation. The specific process is as follows:

[0058] Assume the fault location is determined by both the package number and location parameters, where x i Indicates the first i The package malfunctioned. y This indicates the location of the fault point along the axial direction of the reactor. (For encapsulation...) x i Two adjacent fault locations Q 1( x i , y 1) and Q 2( x i , y 2) Any fault location during this period Q ( x i , y The magnetic field data is calculated using the following formula:

[0059]

[0060] in, f ( Q 1) and f ( Q 2) Indicate the location of the fault respectively. Q 1( x i , y 1) and Q 2( x i , y 2) Magnetic field distribution data, f ( Q The result is the magnetic field distribution calculated by linear interpolation. Using this method, magnetic field distribution data corresponding to all fault locations are obtained, thus completing the construction of the fault feature database.

[0061] Step 3: Artificially set an inter-turn short-circuit fault at a determined location on the air-core reactor, and perform data calibration based on measured data and data from the fault characteristic database.

[0062] The specific process of linearly fitting the data measured under this fault condition with the data at that location in the database to determine the calibration parameters and calibrate the measured data is as follows:

[0063] Set measured data Data from the fault characteristic database The following linear relationship exists:

[0064]

[0065] Linear regression fitting using the least squares method yields the parameters. a and b .

[0066] The main reason for calculating calibration parameters is that the actual operating reactor is subject to interference from surrounding metallic substances. According to Lenz's theorem, these metallic substances induce eddy currents that affect the original magnetic field distribution. Therefore, the actual operating reactor will deviate from the simulation calculation results under ideal conditions, necessitating calibration using measured data.

[0067] Step 4: Calculate the measured data of the air-core reactor using a fault diagnosis algorithm to determine whether the reactor has failed and to accurately locate the fault location.

[0068] This fault diagnosis algorithm mainly consists of three stages:

[0069] In the first stage, the magnetic field phase data collected by the magnetic field sensor located at the axial center of the hollow reactor is used as a benchmark, and the difference is calculated with the magnetic field phase data collected by other magnetic field sensors to avoid phase deviation caused by the uncertainty of the actual measurement start time. The specific calculation process is as follows:

[0070] The TMR magnetic field sensors in the magnetic field sensor array are numbered sequentially from bottom to top as 1 to 9. The TMR magnetic field sensor at the axial center of the hollow reactor is numbered 5. Using this sensor as a reference, the phase difference value of the k-th sensor satisfies the following formula:

[0071]

[0072] The phase difference of the measured magnetic field was obtained through calculation. Magnetic field phase difference under normal operating conditions magnetic field phase difference with fault feature database .

[0073] In the second stage, the fitness function is calculated by comparing the phase difference of the calibrated measured magnetic field with the phase difference under normal operating conditions in the database. If the convergence condition is met, the reactor operates normally. If the convergence condition is not met, the reactor has an inter-turn short-circuit fault. The specific process is as follows:

[0074] Measured magnetic field phase difference Phase difference of the magnetic field under normal operating conditions fitness function Satisfy the following formula:

[0075]

[0076] Set convergence criteria parameters ,if This indicates that the air-core reactor is working normally; if This indicates that the air-core reactor has an inter-turn short circuit fault.

[0077] In the third stage, a genetic algorithm based on a population competition mechanism is used to calculate the fitness function between the phase difference value of the calibrated measured magnetic field and the phase difference value in the database. If the convergence condition is met, the calculated fault location result is output. The specific calculation process is as follows:

[0078] To pinpoint the exact location of an inter-turn short-circuit fault in an air-core reactor, it is first necessary to determine the envelope containing the fault, and then, based on the location of that envelope, determine the specific axial position of the fault. Let the number of envelopes be... i Each package is set as an initial population 1. i Population size set to 100, fitness function Satisfy the following formula:

[0079]

[0080] i Each population was iteratively calculated three times using a genetic algorithm to obtain its optimal fitness function: and the corresponding axial position .Then i The optimal fitness function of each population competes with the others to select the best population. x ,in x ∈(1,2,..., i ), satisfying the following formula:

[0081]

[0082] x This refers to the envelope number where the inter-turn short-circuit fault is located. Further calculation of the axial location of the fault is needed. y .exist xIf the encapsulation fails, a genetic algorithm is used to continue iterative optimization. Convergence criteria parameters are set. ,if If the algorithm converges, then the position of the output is calculated. y The axial location where the final fault occurred is now determined, and fault location is complete.

[0083] Example 2:

[0084] An electronic device, comprising a memory and a processor;

[0085] The memory is used to store computer programs;

[0086] The processor is configured to implement the method described in Embodiment 1 when executing the computer program.

[0087] Example 3:

[0088] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the method described in Embodiment 1.

[0089] Example 4:

[0090] A computer program product includes a computer program that, when executed by a processor, implements the method described in Example 1.

[0091] In the above embodiments, the reference to "this embodiment" in the specification indicates that a specific feature, structure, or characteristic described in connection with the embodiment is included in at least some embodiments, but not necessarily all embodiments. Multiple appearances of "this embodiment" do not necessarily refer to the same embodiment.

[0092] In the above embodiments, although the invention has been described in conjunction with specific embodiments thereof, many substitutions, modifications, and variations of these embodiments will be apparent to those skilled in the art from the foregoing description. For example, other memory structures (e.g., dynamic RAM (DRAM)) may be used with the embodiments discussed. The embodiments of the invention are intended to cover all such substitutions, modifications, and variations falling within the broad scope of the appended claims.

[0093] As will be understood by those skilled in the art, the computer-readable storage medium described in this embodiment allows for the implementation of all or part of the steps in the above method embodiments by computer program-related hardware. The aforementioned computer program can be stored in a computer-readable storage medium. When executed, the program performs the steps of the above method embodiments; and the aforementioned storage medium includes various media capable of storing program code, such as ROM, RAM, magnetic disks, or optical disks.

[0094] The electronic terminal provided in this embodiment includes a processor, a memory, a transceiver, and a communication interface. The memory and the communication interface are connected to the processor and the transceiver and complete communication between them. The memory is used to store computer programs, the communication interface is used to perform communication, and the processor and the transceiver are used to run the computer programs, so that the electronic terminal performs the steps of the above method.

[0095] In this embodiment, the memory may include random access memory (RAM) and may also include non-volatile memory, such as at least one disk storage device.

[0096] The processors mentioned above can be general-purpose processors, including central processing units (CPUs), network processors (NPs), etc.; they can also be digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components.

[0097] This invention can be used in a wide range of general-purpose or special-purpose computing system environments or configurations. Examples include: personal computers, server computers, handheld or portable devices, tablet devices, multiprocessor systems, microprocessor-based systems, set-top boxes, programmable consumer electronics, network PCs, minicomputers, mainframe computers, and distributed computing environments including any of the above systems or devices, etc.

[0098] This invention can be described in the general context of computer-executable instructions, such as program modules, that are executed by a computer. Generally, program modules include routines, programs, objects, components, data structures, etc., that perform a specific task or implement a specific abstract data type. This invention can also be practiced in distributed computing environments where tasks are performed by remote processing devices connected via a communication network. In distributed computing environments, program modules can reside in local and remote computer storage media, including storage devices.

[0099] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. 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 be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for diagnosing and locating inter-turn short-circuit faults in air-core reactors based on a magnetic field sensor array, characterized in that: Includes the following steps: Step 1: Arrange a magnetic field sensor array at the axial position on the outer side of the hollow reactor to obtain magnetic field distribution data near the hollow reactor; Step 2: Calculate the magnetic field distribution data of the magnetic field sensor array position of the air-core reactor under normal operating conditions and inter-turn short-circuit fault conditions at different locations, and construct a complete fault feature database; Step 3: Set up an inter-turn short-circuit fault at the determined location of the air-core reactor, and perform data calibration based on the measured data and the data in the fault characteristic database; Step 4: Calculate the measured data of the air-core reactor using a fault diagnosis algorithm to determine whether a fault has occurred in the reactor and accurately locate the fault location. The fault diagnosis algorithm in Step 4 includes three stages: The first stage: The magnetic field phase data collected by the magnetic field sensor located at the axial center of the hollow reactor is used as a reference, and the difference is calculated with the magnetic field phase data collected by other magnetic field sensors. In the second stage, the fitness function is calculated by comparing the phase difference of the measured magnetic field after calibration with the phase difference under normal operating conditions in the database. If the convergence condition is met, the reactor will work normally. If the convergence condition is not met, the reactor has an inter-turn short circuit fault. In the third stage, a genetic algorithm based on a population competition mechanism is used to calculate the fitness function between the phase difference of the calibrated measured magnetic field and the phase difference of the database. If the convergence condition is met, the calculated fault location result is output.

2. The method for diagnosing and locating inter-turn short-circuit faults in air-core reactors based on a magnetic field sensor array according to claim 1, characterized in that: The magnetic field sensor array consists of nine TMR magnetic field sensors, and each sensor is arranged at equal intervals from the top to the bottom of the hollow reactor. The sensitive direction of the TMR magnetic field sensor is axial.

3. The method for diagnosing and locating inter-turn short-circuit faults in air-core reactors based on a magnetic field sensor array according to claim 2, characterized in that: The magnetic field distribution data is phase data extracted from the time-domain signal of the magnetic field collected by the TMR magnetic field sensor. The phase data extraction method is to obtain the phase by sinusoidal fitting of the magnetic field signal using the least squares method.

4. The method for diagnosing and locating inter-turn short-circuit faults in air-core reactors based on a magnetic field sensor array according to claim 3, characterized in that: In step two, a complete fault feature database is constructed using interpolation, including the following steps: Assume the fault location is determined by both the package number and the location parameter, let... x Indicates the package number where the fault occurred. y Indicates the location of the fault point in the axial direction of the reactor; for encapsulation x Two adjacent fault locations Q 1( x , y 1) and Q 2( x , y 2) Any fault location during this period Q ( x , y The magnetic field data is calculated using the following formula: in, f ( Q 1) and f ( Q 2) Indicate the location of the fault respectively. Q 1( x , y 1) and Q 2( x , y 2) Magnetic field distribution data, f ( Q The result is the magnetic field distribution calculated by linear interpolation. In this way, the magnetic field distribution data corresponding to all fault locations are obtained, thereby completing the construction of the fault feature database.

5. The method for diagnosing and locating inter-turn short-circuit faults in air-core reactors based on a magnetic field sensor array according to claim 4, characterized in that: Step three, which involves data calibration based on measured data and the fault characteristic database, includes the following steps: Assume measured data Data from the fault characteristic database The following linear relationship exists: Linear regression fitting using the least squares method yields the parameters. a and b .

6. The method for diagnosing and locating inter-turn short-circuit faults in air-core reactors based on a magnetic field sensor array according to claim 5, characterized in that: The specific calculation process for the first stage is as follows: The TMR magnetic field sensors in the magnetic field sensor array are numbered sequentially from bottom to top as 1 to 9. The TMR magnetic field sensor at the axial center of the hollow reactor is numbered 5. Using this sensor as a reference, the phase difference value of the k-th sensor satisfies the following formula: The phase difference of the measured magnetic field was obtained through calculation. Magnetic field phase difference under normal operating conditions magnetic field phase difference with fault feature database .

7. The method for diagnosing and locating inter-turn short-circuit faults in air-core reactors based on a magnetic field sensor array according to claim 6, characterized in that: The specific process for the second stage is as follows: Measured magnetic field phase difference Phase difference of the magnetic field under normal operating conditions fitness function Satisfy the following formula: Set convergence criteria parameters ,if This indicates that the air-core reactor is working normally; if This indicates that the air-core reactor has an inter-turn short circuit fault.

8. The method for diagnosing and locating inter-turn short-circuit faults in air-core reactors based on a magnetic field sensor array according to claim 7, characterized in that: The specific calculation process for the third stage is as follows: First, determine the location of the fault within the enclosure; then, based on this enclosure location, determine the axial location of the specific inter-turn short-circuit fault in the air-core reactor; let the number of enclosures be... i Each package is individually set as the initial population 1~ i Population size set to 100, fitness function Satisfy the following formula: i Each population was iteratively calculated three times using a genetic algorithm to obtain its optimal fitness function: and the corresponding axial position ; i The optimal fitness function of each population competes with the others to select the best population. x The following equation is satisfied: x That is, the envelope number where the inter-turn short-circuit fault is located; exist x Under the premise of encapsulation failure, a genetic algorithm is used to continue iterative optimization calculation, with convergence criteria parameters set. ,if If the algorithm converges, then the position of the output is calculated. y The axial location where the final fault occurred is now determined, and fault location is complete.

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