Multi-loop high-voltage cable electrified nuclear phase method

Abstract

The invention relates to a multi-loop high-voltage cable electrified phase checking method. The method comprises the following specific steps: step 1, collecting sheath current and wire core current of a multi-loop high-voltage cable; 2, performing signal processing by combining digital filtering and effective value calculation; thirdly, loop identification is achieved through the clustering analysis technology; 4, determining a phase sequence by analyzing current characteristics of the wire core, and comparing current change trends at different positions to track a cable path; and 5, carrying out data fusion and visual display on the identification result, and automatically generating an intelligent report. According to the invention, different loops in a complex channel can be effectively distinguished, the phase sequence of the cable is determined, and the extension path of the same cable is tracked at different positions.

Description

Technical Field

[0001] The present application relates to the field of high-voltage cable monitoring, and in particular to a method for checking the phase of a multi-circuit high-voltage cable under energization. Background Art

[0002] High-voltage cables (110kV and above) are the backbone of urban transmission and distribution networks, and generally adopt a three-phase three-wire system. In modern complex power systems, accurately identifying and tracing specific cables has always been an important and challenging problem. Traditional cable identification methods, such as visual inspection, signal injection, electromagnetic induction, phase comparison, and time domain reflection, often have limitations such as low efficiency, insufficient accuracy, complex operation, or the need to interrupt power supply when facing complex environments such as multi-circuit, long distance, or underground tunnels. With the rapid development of smart grids and the continuous improvement of the complexity of power systems, the requirements for cable identification and management are increasing. Therefore, there is an urgent need to develop a new method that can quickly and accurately identify and track cables without affecting the normal operation of the system, so as to meet the needs of modern power system management and improve the reliability and management efficiency of the system. Summary of the invention

[0003] The purpose of the embodiments of the present application is to provide a method for live phase verification of multi-circuit high-voltage cables, so as to solve the problem of cable identification and tracking in complex power systems and to accurately identify and track specific cables without power outage or contact.

[0004] To achieve the above objectives, this application provides the following technical solutions:

[0005] The present invention provides a method for checking phases of a multi-circuit high-voltage cable under energization, including the following specific steps:

[0006] Step 1: collecting sheath current and core current of multi-circuit high-voltage cables;

[0007] Step 2: Signal processing is performed by combining digital filtering and effective value calculation;

[0008] Step 3: Use cluster analysis technology to realize loop identification;

[0009] Step 4: Determine the phase sequence by analyzing the core current characteristics and compare the current change trends at different locations to track the cable path;

[0010] Step 5: Perform data fusion and visualization on the recognition results and automatically generate an intelligent report.

[0011] The method of collecting the sheath current and core current of the multi-circuit high-voltage cable is specifically to establish an equivalent circuit model of the leakage component and the inductive coupling component, and calculate the multi-circuit sheath circulating current based on the iteration method. In the equivalent circuit model of the leakage component and the inductive coupling component, E map、E mbp 、E mcp are the induced voltages generated by the core currents of each circuit on the pth section sheath of the three phases A, B, and C of the mth circuit, m = 1, 2, ... n; p = 1, 2, 3; U map , U mbp , U mcp are the induced voltages generated by the induced current components of each loop on the p-th section sheath of the three-phase A, B, and C of the m-th loop; I msap ,I msbp ,I mscp I is the sheath circulation of the pth section of the three sheath loops of the mth loop; mg11 ,I mg12 ,I mg13 ,I mg21 ,I mg22 ,I mg23 is the sheath circulating current in the directly grounded boxes on both sides of the mth loop; I mc11 ,I mc12 ,I mc13 ,I mc21 ,I mc22 ,I mc23 I is the sheath circulation in the two cross-connected boxes of the mth circuit; mcap ,I mcbp ,I mccp They are the capacitor leakage currents at both ends of the pth section of the three-phase electricity of A, B, and C in the mth loop.

[0012] According to the phase spacing and loop spacing of the cable, a multi-loop cable spacing matrix is ​​formed. The spacing matrix is ​​a 3n-order square matrix, where n is the number of loops, and is a symmetric matrix. The spacing matrix S is

[0013]

[0014] First, the initial induced current components of the three sheath loops of each loop need to be given. Since the induced voltage generated by the current of each core is not affected by the induced current component, E map 、E mbp 、E mcp The generated induced current component is used as the initial value of the induced current component of each sheath loop, that is, the iterative initial value is determined by the following formula:

[0015]

[0016] Where, Zs = Zs1 + Zs2 + Zs3; Rt is the sum of the grounding resistance at both ends of the sheath and the equivalent resistance of the earth; I (0) scam ,I (0) scbm ,I (0) sccmare the initial values ​​of the iteration of the induced current components of sheath loops 1, 2, and 3 in the mth loop; E SAm 、E SBm 、E SCm are the total induced voltages generated by the core current of each circuit on the sheath circuits 1, 2, and 3 in the mth circuit, that is, E SAm =E ma1 +E mb2 +E mc3 E SBm =E mb1 +E mc2 +Ema3,E SCm =E mc1 +E ma2 +E mb3 ;

[0017] Due to the existence of leakage current in the core, the multi-circuit cable is the same as the single-circuit cable mentioned above. The current in the core of each cross-connected cable is different. Assume that the core currents of the A, B, and C phases of the i-th circuit i=1, 2, ···n and the p-th section p=1, 2, 3 are I iap ,I ibp ,I icp According to electromagnetic theory, E map 、E mbp 、E mcp m=1, 2, ···n;p=1, 2, 3 are calculated by the following formula:

[0018]

[0019] Where LP (p = 1, 2, 3) is the length of the pth section of the cable;

[0020] According to the induced current components of each sheath loop obtained in the k-1th iteration, the k-th iteration value of the induced voltage generated by the induced current components of other phases on each sheath section of the mth loop can be calculated, that is,

[0021]

[0022]

[0023] Where U (k) ma1 , U (k) ma2 , U (k) ma3 , U (k) mb1 , U (k) mb2 U (k) mb3 U (k) mc1 , U(k) mc2 , U (k) mc3 are the k-times iterative values ​​of the induced voltage generated by the induced current components of other phases on each small segment of the three phases A, B, and C of the mth loop, I (k-1) scai ,I (k -1) scbi ,I (k-1) scci are the k-1 iteration values ​​of the induced current components of the i-th loop respectively; X AmBi , X AmCi , X BmCi , are the mutual inductances between the sheaths of the mth loop A phase and the ith loop B phase, the mth loop A phase and the ith loop C phase, and the mth loop B phase and the ith loop C phase, respectively. The calculation formula is as follows:

[0024]

[0025] It is easy to obtain the k-th iteration value of the total induced voltage of each sheath loop:

[0026]

[0027] Then the kth iteration value of each induced current component of the mth loop can be obtained by the following formula:

[0028]

[0029] The impedance matrix on the right side of equation (9) is the same as equation (2), both of which are third-order constant matrices. Equation (8) can continuously generate a new round of iterative values ​​of the induced current component. The convergence condition of the iterative process is:

[0030]

[0031] Where ε is the given accuracy value.

[0032] The induced current components of each loop are iterated in turn, that is, when the induced current components of loops 1 to m converge, the iterative process of the induced current components of the m+1th loop is performed until the induced current components of all loops converge. When the iterative formula is used to calculate the induced current components, the latest iteration results of the induced current components of all loops are used each time. When the induced current components of all loops meet the convergence conditions, the iterative process is exited and the latest iteration value is used as the final induced current component of each loop.

[0033] The clustering analysis technology is used to realize loop identification. Specifically, a clustering application algorithm with a comprehensive similarity index is used to distinguish the loops of multiple cable sheath currents.

[0034] Compared with the existing technology, the beneficial effects of this application are: through non-invasive collection of sheath current and core current, combined with advanced signal processing and cluster analysis technology, loop identification, phase sequence determination and cable tracking of complex cable systems are realized, providing innovative solutions for the safe operation and efficient management of power systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required for use in the embodiments of the present application will be briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present application and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without paying creative work.

[0036] Figure 1 A flow chart of the method of this application;

[0037] Figure 2 This is the equivalent circuit diagram for calculating the sheath circulating current of the first loop of the present application;

[0038] Figure 3 It is an iterative flow chart of the n-loop induced current component of the present application;

[0039] Figure 4 This is a waveform diagram of the clustering results of this application. DETAILED DESCRIPTION

[0040] The technical solutions in the embodiments of the present application will be described below in conjunction with the drawings in the embodiments of the present application. It should be noted that similar reference numerals and letters represent similar items in the following drawings, so once an item is defined in one drawing, it does not need to be further defined and explained in the subsequent drawings.

[0041] The terms "comprises," "comprising," or any other variation thereof are intended to encompass non-exclusive inclusion, such that a process, method, article, or apparatus that includes a list of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or apparatus. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of additional identical elements in the process, method, article, or apparatus that includes the element.

[0042] The terms "first", "second", etc. are only used to distinguish one entity or operation from another entity or operation, and should not be understood as indicating or implying relative importance, nor should they be understood as requiring or implying any such actual relationship or order between these entities or operations.

[0043] The present invention provides a multi-circuit cable identification method in a complex power system. The method collects sheath current and core current in a non-invasive manner, combines digital filtering and effective value calculation for signal processing, and then uses cluster analysis technology to achieve circuit identification. The phase sequence is determined by analyzing the core current characteristics, and the current change trend is compared at different locations to track the cable path. Finally, the identification results are data fused and visualized, and an intelligent report is automatically generated. This comprehensive method realizes efficient and accurate identification and management of complex cable systems without power outages or contact with the cable body, providing an innovative solution for the safe operation and optimized maintenance of power systems.

[0044] like Figure 1 As shown, the embodiment of the present application provides a method for checking phases of a multi-circuit high-voltage cable under power-on conditions, including the following specific steps:

[0045] Step 1: collecting sheath current and core current of multi-circuit high-voltage cables;

[0046] Step 2: Signal processing is performed by combining digital filtering and effective value calculation;

[0047] Step 3: Use cluster analysis technology to realize loop identification;

[0048] Step 4: Determine the phase sequence by analyzing the core current characteristics and compare the current change trends at different locations to track the cable path;

[0049] Step 5: Perform data fusion and visualization on the recognition results and automatically generate an intelligent report.

[0050] The specific steps are to first change the grounding resistance through the multi-loop sheath current calculation model, construct a large number of samples, verify the accuracy of the clustering algorithm, and then substitute the real test data for verification. The main steps are to first collect the sheath current of multiple cables through the collector, and use the clustering algorithm to cluster the time series data after obtaining it. The data that are clustered together are a loop. After the loop is determined, the core current is collected by Rogowski coil to determine the phase sequence. The above is the complete step of the phase core, and by collecting the current at the front and back ends, if the trend is the same, it can be determined that it is the same cable.

[0051] The metal sheath circulating current of multi-circuit cables also includes two components: induced current and leakage current. Compared with a single circuit, the special feature of a multi-circuit system is that when calculating the induced voltage of the metal sheath, it is necessary to consider the influencing factors of other circuits, including the core load current and the sheath circulating current. This leads to a different calculation method for the induced current component of a multi-circuit system.

[0052] At present, the impedance matrix method is mainly used to calculate the inductive current components of multiple loops. For an n-loop system, a 3n-order matrix equation needs to be solved. This method can effectively handle complex multi-loop systems.

[0053] In cross-connected high-voltage cables, the sheath current is a superposition of the leakage current component and the inductive coupling current component. Therefore, in order to accurately analyze the characteristics of such cables, it is necessary to establish equivalent circuit models for the leakage component and the inductive coupling component separately. This separate modeling method helps to gain a deeper understanding of the current distribution in the cable.

[0054] 3) Multi-circuit sheath circulation calculation based on iteration method

[0055] like Figure 2 As shown in the figure, when E map 、E mbp 、E mcp (m=1, 2, ...n; p=1, 2, 3) are the induced voltages generated by the core currents of each circuit on the p-th section sheath of the three phases A, B, and C of the m-th circuit; U map , U mbp , U mcp are the induced voltages generated by the induced current components of each loop on the p-th section sheath of the three-phase A, B, and C of the m-th loop; I msap ,I msbp ,I mscp I is the sheath circulation of the pth section of the three sheath loops of the mth loop; mg11 ,I mg12 ,I mg13 ,I mg21 ,I mg22 ,I mg23 is the sheath circulating current in the directly grounded boxes on both sides of the mth loop; I mc11 ,I mc12 ,I mc13 ,I mc21 ,I mc22 ,I mc23 I is the sheath circulation in the two cross-connected boxes of the mth loop; mcap ,I mcbp ,I mccp They are the capacitor leakage currents at both ends of the pth section of the three-phase electricity of A, B, and C in the mth loop.

[0056] For the convenience of representation, a multi-circuit cable spacing matrix is ​​formed according to the phase spacing and loop spacing of the cable. The spacing matrix is ​​a 3n-order square matrix (n is the number of loops) and is a symmetrical matrix. The spacing matrix can be easily read out from the spacing matrix, which is conducive to the preparation of the calculation program. Taking a double loop as an example, the spacing matrix S is

[0057]

[0058] First, the initial induced current components of the three sheath loops of each loop need to be given. Since the induced voltage generated by the current of each core is not affected by the induced current component, E map 、E mbp 、E mcp The generated induced current component is used as the initial value of the induced current component of each sheath loop, that is, the iterative initial value is determined by the following formula:

[0059]

[0060] Where, Zs = Zs1 + Zs2 + Zs3; Rt is the sum of the grounding resistance at both ends of the sheath and the equivalent resistance of the earth; I (0) scam ,I (0) scbm ,I (0) sccm are the initial values ​​of the iteration of the induced current components of sheath loops 1, 2, and 3 in the mth loop; E SAm 、E SBm 、E SCm are the total induced voltages generated by the core current of each circuit on the sheath circuits 1, 2, and 3 in the mth circuit, that is, E SAm =E ma1 +E mb2 +E mc3 E SBm =E mb1 +E mc2 +Ema3,E SCm =E mc1 +E ma2 +E mb3 .

[0061] Due to the existence of leakage current in the core, the current in each cross-connected cable core of the multi-circuit cable is different, just like the single-circuit cable mentioned above. Assume that the core currents of the A, B, and C phases of the pth segment (p=1, 2, 3) of the i-th circuit (i=1, 2, ···n) are I iap ,I ibp ,I icp According to electromagnetic theory, E map 、E mbp 、E mcp (m=1, 2, ···n; p=1, 2, 3) can be calculated by the following formula:

[0062]

[0063] Wherein, LP (p=1, 2, 3) is the length of the pth section of the cable.

[0064] According to the induced current components of each sheath loop obtained in the k-1th iteration, the k-th iteration value of the induced voltage generated by the induced current components of other phases on each sheath section of the mth loop can be calculated, that is,

[0065]

[0066] Where U (k) ma1 , U (k) ma2 , U (k) ma3 , U (k) mb1 , U (k) mb2 U (k) mb3 U (k) mc1 , U (k) mc2 , U (k) mc3 are the k-times iterative values ​​of the induced voltage generated by the induced current components of other phases on each small segment of the three phases A, B, and C of the mth loop, I (k-1) scai ,I (k -1) scbi ,I (k-1) scci are the k-1 iteration values ​​of the induced current components of the i-th loop respectively; X AmBi , X AmCi , X BmCi , are the mutual inductances between the sheaths of the mth loop A phase and the ith loop B phase, the mth loop A phase and the ith loop C phase, and the mth loop B phase and the ith loop C phase, respectively. The calculation formula is as follows:

[0067]

[0068] It is easy to obtain the k-th iteration value of the total induced voltage of each sheath loop:

[0069]

[0070] Then the kth iteration value of each induced current component of the mth loop can be obtained by the following formula:

[0071]

[0072] The impedance matrix on the right side of equation (9) is the same as equation (2), both of which are third-order constant matrices. Equation (8) can continuously generate a new round of iterative values ​​of the induced current component. The convergence condition of the iterative process is:

[0073]

[0074] In the formula, ε is a given precision value, which is usually taken as 0.001.

[0075] The iteration process of the inductive current component of the n loop is as follows Figure 3 As shown. During the iteration process, since the induced current components of n loops cannot meet the convergence conditions at the same time, if formula (10) is used to simultaneously judge whether the induced current components of n loops meet the convergence requirements, the program will fall into a state of non-convergence. Therefore, in the actual iteration process, the induced current components of each loop are iterated in turn, that is, when the induced current components of loops 1 to m converge, the iterative process of the induced current components of the m+1th loop is performed downward until the induced current components of all loops converge. When using the iterative formula to calculate the induced current components, the latest iteration results of the induced current components of all loops are used each time. When the induced current components of all loops meet the convergence conditions, the iteration process is exited, and the latest iteration value is used as the final induced current component of each loop.

[0076] 5) Multi-loop kernel phase algorithm based on CLARA clustering

[0077] The sheath currents of three-phase cables in the same loop have the characteristic of convergence. It is planned to use a clustering algorithm to distinguish the loops of multiple cable sheath currents. In order to eliminate the influence of outliers on the clustering effect, improve the robustness and accuracy of clustering, and reduce the time complexity to improve the efficiency of large-scale data clustering, we use the Clustering Application Based on Comprehensive Similarity Index (CLARA) algorithm to cluster daily CLP. The CLARA algorithm repeatedly applies PAM to a sub-dataset of n'<<n objects, and then assigns the remaining objects to the media closest to them. When the sampling method is completely random and the sample size meets certain requirements, the extracted data can restore the original data information within the allowable deviation range.

[0078]

[0079] Where n is the number of data points, k is the number of clusters, p is the data point, and c is the data point identified as a medioid. Finding the global optimum for the k-medioids problem is an NP-hard problem. Kaufmann cleverly added sampling ideas to the PAM method and proposed an effective CLARA clustering method to reduce the time complexity of PAM in solving big data clustering problems. The CLARA algorithm repeatedly applies PAM to a sub-dataset of n'<<n objects, and then assigns the remaining objects to the media closest to them. When the sampling method is completely random and the sample size meets certain requirements, the extracted data can restore the original data information within the allowable deviation range.

[0080] First, a large number of samples are constructed by changing the grounding resistance and the length of cross-connected small sections through the multi-loop sheath current calculation model to verify the accuracy of the clustering algorithm, and then the real test data is substituted for verification. The main steps are to first collect the sheath currents of multiple cables through the collector, and then use the clustering algorithm to cluster the time series data. The data that are clustered together are one loop. After the loop is determined, the phase sequence can be determined by using the Rogowski coil to collect the core current.

[0081] like Figure 4 , there are twelve waveforms in this picture, representing the sheath current waveforms of twelve cables. It can be seen that the change trends of every three cables are quite different, and the cable loops are mainly distinguished by the change trends. This method collects the current data of the lead wires and cores of the cable connectors and carries out a series of sophisticated analysis processes. First, the collected current waveforms are filtered and the effective value is calculated, and then clustering technology is used to distinguish different loops in complex cable channels. By analyzing the core current of each three-phase cable, the phase sequence can be determined. Furthermore, by sampling the core currents in two tunnels at the same time and comparing their change trends, the extension of the same cable at different locations can be identified.

[0082] The above description is only an embodiment of the present application and is not intended to limit the protection scope of the present application. For those skilled in the art, the present application may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for checking the phase of a multi-circuit high-voltage cable under energization, characterized in that: The specific steps include: Step 1: collecting sheath current and core current of multi-circuit high-voltage cables; Step 2: Signal processing is performed by combining digital filtering and effective value calculation; Step 3: Use cluster analysis technology to realize loop identification; Step 4: Determine the phase sequence by analyzing the core current characteristics and compare the current change trends at different locations to track the cable path; Step 5: Perform data fusion and visualization on the recognition results and automatically generate an intelligent report.

2. A method for checking phase of a multi-circuit high-voltage cable under energization according to claim 1, characterized in that: The method of collecting the sheath current and core current of the multi-circuit high-voltage cable is specifically to establish an equivalent circuit model of the leakage component and the inductive coupling component, and calculate the multi-circuit sheath circulating current based on the iteration method. In the equivalent circuit model of the leakage component and the inductive coupling component, E map 、E mbp 、E mcp are the induced voltages generated by the core currents of each circuit on the pth section sheath of the three phases A, B, and C of the mth circuit, m = 1, 2, ... n; p = 1, 2, 3; U map , U mbp , U mcp are the induced voltages generated by the induced current components of each loop on the p-th section sheath of the three-phase A, B, and C of the m-th loop; I msap ,I msbp ,I mscp I is the sheath circulation of the pth section of the three sheath loops of the mth loop; mg11 ,I mg12 ,I mg13 ,I mg21 ,I mg22 ,I mg23 is the sheath circulating current in the directly grounded boxes on both sides of the mth loop; I mc11 ,I mc12 ,I mc13 ,I mc21 ,I mc22 ,I mc23 I is the sheath circulation in the two cross-connected boxes of the mth circuit; mcap ,I mcbp ,I mccp They are the capacitor leakage currents at both ends of the pth section of the three-phase electricity of A, B, and C in the mth loop.

3. A method for checking phases of multi-circuit high-voltage cables under energization according to claim 2, characterized in that: According to the phase spacing and loop spacing of the cable, a multi-loop cable spacing matrix is ​​formed. The spacing matrix is ​​a 3n-order square matrix, where n is the number of loops, and is a symmetric matrix. The spacing matrix S is First, the initial induced current components of the three sheath loops of each loop need to be given. Since the induced voltage generated by the current of each core is not affected by the induced current component, E map 、E mbp 、E mcp The generated induced current component is used as the initial value of the induced current component of each sheath loop, that is, the iterative initial value is determined by the following formula: Where, Zs = Zs1 + Zs2 + Zs3; Rt is the sum of the grounding resistance at both ends of the sheath and the equivalent resistance of the earth; I (0) scam ,I (0) scbm ,I (0) sccm are the initial values ​​of the iteration of the induced current components of sheath loops 1, 2, and 3 in the mth loop; E SAm 、E SBm 、E SCm are the total induced voltages generated by the core current of each circuit on the sheath circuits 1, 2, and 3 in the mth circuit, that is, E SAm =E ma1 +E mb2 +E mc3 E SBm =E mb1 +E mc2 +Ema3,E SCm =E mc1 +E ma2 +E mb3 ; Due to the existence of leakage current in the core, the multi-circuit cable is the same as the single-circuit cable mentioned above. The current in the core of each cross-connected cable is different. Assume that the core currents of the A, B, and C phases of the i-th circuit i=1, 2, ···n and the p-th section p=1, 2, 3 are I iap ,I ibp ,I icp According to electromagnetic theory, E map 、E mbp 、E mcp m=1, 2, ···n;p=1, 2, 3 are calculated by the following formula: Where LP (p = 1, 2, 3) is the length of the pth section of the cable; According to the induced current components of each sheath loop obtained in the k-1th iteration, the k-th iteration value of the induced voltage generated by the induced current components of other phases on each sheath section of the mth loop can be calculated, that is, Where U (k) ma1 , U (k) ma2 , U (k) ma3 , U (k) mb1 , U (k) mb2 U (k) mb3 U (k) mc1 , U (k) mc2 , U (k) mc3 are the k-times iterative values ​​of the induced voltage generated by the induced current components of other phases on each small segment of the three phases A, B, and C of the mth loop, I (k-1) scai ,I (k-1) scbi ,I (k-1) scci are the k-1 iteration values ​​of the induced current components of the i-th loop respectively; X AmBi , X AmCi , X BmCi , are the mutual inductances between the sheaths of the mth loop A phase and the ith loop B phase, the mth loop A phase and the ith loop C phase, and the mth loop B phase and the ith loop C phase, respectively. The calculation formula is as follows: It is easy to obtain the k-th iteration value of the total induced voltage of each sheath loop: Then the kth iteration value of each induced current component of the mth loop can be obtained by the following formula: The impedance matrix on the right side of equation (9) is the same as equation (2), both of which are third-order constant matrices. Equation (8) can continuously generate a new round of iterative values ​​of the induced current component. The convergence condition of the iterative process is: In the formula, ε is a given accuracy value. The multi-loop current calculation model is established through the iteration method to construct a large number of samples to verify the accuracy of the algorithm.

4. A method for checking phases of multi-circuit high-voltage cables under energization according to claim 3, characterized in that: The induced current components of each loop are iterated in turn, that is, when the induced current components of loops 1 to m converge, the iterative process of the induced current components of the m+1th loop is performed until the induced current components of all loops converge. When the iterative formula is used to calculate the induced current components, the latest iteration results of the induced current components of all loops are used each time. When the induced current components of all loops meet the convergence conditions, the iterative process is exited and the latest iteration value is used as the final induced current component of each loop.

5. A method for checking phases of multi-circuit high-voltage cables under energization according to claim 4, characterized in that: The clustering analysis technology is used to realize loop identification. Specifically, a clustering application algorithm with a comprehensive similarity index is used to distinguish the loops of multiple cable sheath currents.

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