Multi-circuit high voltage cable live phase identification method

Abstract

The application relates to a multi-circuit high-voltage cable live phase identification method, which comprises the following specific steps: step one, collecting the sheath current and the core current of the multi-circuit high-voltage cable; step two, combining digital filtering and effective value calculation to perform signal processing; step three, realizing circuit identification by using a clustering analysis technology; step four, determining a phase sequence by analyzing the core current characteristics, and comparing the current variation trends at different positions to track the cable path; and step five, performing data fusion and visual display on the identification result, and automatically generating an intelligent report. The application can effectively distinguish different circuits in a complex channel, determine the cable phase sequence, and track the extension path of the same cable at different positions.

Description

Technical Field

[0001] This application relates to the field of high-voltage cable monitoring, and in particular to a method for energizing and phase-matching multi-circuit high-voltage cables. Background Technology

[0002] Cables (110kV and above) form the backbone of urban power transmission and distribution networks, typically employing a three-phase, three-wire system. In modern, complex power systems, accurately identifying and tracing specific cables remains a crucial and challenging problem. Traditional cable identification methods, such as visual inspection, signal injection, electromagnetic induction, phase comparison, and time-domain reflectometry, often suffer from limitations in complex environments like multi-circuit, long-distance, or underground tunnel situations, including low efficiency, insufficient accuracy, complex operation, or the need for power interruption. With the rapid development of smart grids and the increasing complexity of power systems, the requirements for cable identification and management are rising. Therefore, there is an urgent need to develop a new method that can quickly and accurately identify and trace cables without affecting normal system operation, to meet the needs of modern power system management and improve system reliability and management efficiency. Summary of the Invention

[0003] The purpose of this application is to provide a method for energizing and tracing multi-circuit high-voltage cables, solving the problem of cable identification and tracking in complex power systems, and enabling accurate identification and tracking of specific cables without power interruption or contact.

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

[0005] This application provides a method for live phase comparison of multi-circuit high-voltage cables, including the following specific steps:

[0006] Step 1: Collect the sheath current and core current of the multi-circuit high-voltage cable;

[0007] Step two: Perform signal processing by combining digital filtering and RMS value calculation;

[0008] Step 3: Use cluster analysis techniques to identify loops;

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

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

[0011] The specific steps for collecting the sheath current and core current of multi-circuit high-voltage cables involve establishing equivalent circuit models for leakage and inductive coupling components, calculating the multi-circuit sheath circulating current based on an iterative method, and determining E in the equivalent circuit models for leakage and inductive coupling components. mapE mbp E mcp Let U be the induced voltage generated by the core current of each circuit on the p-th segment of the sheath of the three phases A, B, and C of the m-th circuit, where m = 1, 2, ..., n; p = 1, 2, 3; U map U mbp U mcp These are the induced voltages generated on the p-th segment of the sheath of the three phases A, B, and C of the m-th circuit, respectively, by the induced current components of each circuit; I msap I msbp I mscp These are the sheath circulating currents of the p-th segment of the three sheath circuits of the m-th circuit; I mg11 I mg12 I mg13 I mg21 I mg22 I mg23 For the circulating current in the sheath of the directly grounded box on both sides of the m-th circuit; I mc11 I mc12 I mc13 I mc21 I mc22 I mc23 For the sheath circulating current in the two cross-connection boxes of the m-th loop; I mcap I mcbp I mccp These are the capacitor leakage currents at both ends of the p-th segment of the three-phase circuit A, B, and C in the m-th circuit.

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

[0013]

[0014] First, the initial induced current components of the three sheathed circuits for each loop need to be given. Since the induced voltage generated by the current in each core is not affected by the induced current components, E is set as follows: map E mbp E mcp The generated induced current components serve as the initial values ​​for the induced current components in each sheath circuit; that is, the initial values ​​for iteration are determined by the following formula:

[0015]

[0016] In the formula, 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) sccmThese are the initial values ​​for the induced current components of sheath circuits 1, 2, and 3 in the m-th circuit, respectively; E SAm E SBm E SCm Let E be the total induced voltage generated by the core current of each circuit in the m-th circuit, specifically in the sheath circuits 1, 2, and 3. 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 presence of leakage current in the conductor, multi-circuit cables, like the single-circuit cables described above, have different currents in the conductors of each cross-connected cable segment. Assuming the currents in the conductors of phases A, B, and C of the i-th circuit (i = 1, 2, ..., n) and the p-th segment (p = 1, 2, 3) are respectively 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 using the following formula:

[0018]

[0019] In the formula, LP (p = 1, 2, 3) is the length of the p-th segment of the cable;

[0020] Based on the induced current components of each sheath circuit obtained in the (k-1)th iteration, the induced voltage values ​​generated by the other phase induced current components on each sheath segment of the m-th circuit in the k-th iteration can be calculated, i.e.

[0021]

[0022]

[0023] In the formula, 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 Let I be the k-th iteration value of the induced voltage generated by the induced current components of other phases on each small segment of phases A, B, and C in the m-th loop. (k-1) scai I (k -1) scbi I (k-1) scci X represents the (k-1)th iteration value of each induced current component in the i-th loop; AmBi X AmCi X BmCi Let and be the mutual inductance between the sheaths of phase A of the m-th circuit and phase B of the i-th circuit, phase A of the m-th circuit and phase C of the i-th circuit, and phase B of the m-th circuit and phase C of the i-th circuit, respectively. The calculation formula is as follows:

[0024]

[0025] The k-th iteration value of the total induced voltage in each sheath circuit is easily obtained.

[0026]

[0027] The k-th iteration value of each induced current component in the m-th loop can be obtained by the following formula:

[0028]

[0029] The impedance matrix on the right side of equation (9) is the same as that in equation (2), both being 3rd-order constant matrices. Equation (8) can continuously generate a new round of iterative values ​​for the induced current components. The convergence condition of the iteration process is:

[0030]

[0031] In the formula, ε is a given precision value.

[0032] The induced current components of each loop are iterated sequentially. That is, the induced current components of loops 1 to m converge before the iteration process of the induced current components of loop (m+1) is carried out. This continues until the induced current components of all loops converge. When calculating the induced current components using the iterative formula, the latest iteration result of the induced current components of all loops is used each time. When the induced current components of all loops meet the convergence condition, the iteration process is exited and the latest iteration value is taken as the final induced current component of each loop.

[0033] The loop identification using clustering analysis technology specifically involves using a clustering algorithm based on a comprehensive similarity index of the sheath currents of multiple cables to distinguish loops.

[0034] Compared with existing technologies, the beneficial effects of this application are: by non-invasively collecting sheath current and core current, combined with advanced signal processing and cluster analysis technologies, it realizes loop identification, phase sequence determination and cable tracing of complex cable systems, providing an innovative solution for the safe operation and efficient management of power systems. Attached Figure Description

[0035] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the embodiments of this application will be briefly introduced below. It should be understood that the following drawings only show some embodiments of this application and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0036] Figure 1 This is a flowchart of the method in this application;

[0037] Figure 2 The equivalent circuit diagram for calculating the circulating current of the first loop sheath in this application is shown below.

[0038] Figure 3 This is a flowchart illustrating the iterative process of the n-loop induced current components in this application.

[0039] Figure 4 The image shows the waveform of the clustering results in this application. Detailed Implementation

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

[0041] The terms “comprising,” “including,” or any other variations thereof are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase “comprising one…” does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

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

[0043] This invention provides a method for identifying multi-circuit cables in complex power systems. The method non-invasively acquires sheath current and conductor current, performs signal processing combining digital filtering and RMS calculation, and then utilizes cluster analysis to identify the circuit. Phase sequence is determined by analyzing conductor current characteristics, and current change trends are compared at different locations to trace the cable path. Finally, the identification results are fused and visualized, and an intelligent report is automatically generated. This comprehensive method enables efficient and accurate identification and management of complex cable systems without power interruption or contact with the cable itself, providing an innovative solution for the safe operation and optimized maintenance of power systems.

[0044] like Figure 1 As shown in the figure, this application provides a method for energizing and phase-matching a multi-circuit high-voltage cable, including the following specific steps:

[0045] Step 1: Collect the sheath current and core current of the multi-circuit high-voltage cable;

[0046] Step two: Perform signal processing by combining digital filtering and RMS value calculation;

[0047] Step 3: Use cluster analysis techniques to identify loops;

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

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

[0050] The specific steps are as follows: First, a large number of samples are constructed by changing the grounding resistance and the length of the cross-interconnected short segments through a multi-loop sheath current calculation model to verify the accuracy of the clustering algorithm. Then, real test data is substituted for verification. The main steps are: first, the sheath current of multiple cables is collected by a data acquisition device. After obtaining the time series data, the clustering algorithm is used to cluster them. Those clustered into one class are considered a loop. After determining the loop, the core current is collected using a Rogowski coil to determine the phase sequence. The above is the complete step of phase identification. Furthermore, by collecting the current at both ends, if the trend is the same, it can be determined that it is the same cable.

[0051] Multi-circuit cable sheath circulating current also includes two components: induced current and leakage current. The difference between multi-circuit and single-circuit systems lies in the fact that the calculation of the induced voltage in the sheath requires consideration of the influence of other circuits, including the conductor load current and the sheath circulating current. This leads to a different calculation method for the induced current component in multi-circuit systems.

[0052] Currently, the impedance matrix method is mainly used to calculate the induced current components in multi-loop systems. 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 the superposition of leakage current and inductive coupling current components. Therefore, to accurately analyze the characteristics of such cables, it is necessary to establish equivalent circuit models for the leakage and inductive coupling components separately. This separate modeling approach helps to gain a deeper understanding of the current distribution within the cable.

[0054] 3) Calculation of multi-loop sheath circulation based on iterative method

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

[0056] For ease of representation, a multi-loop cable spacing matrix is ​​formed based on the phase spacing and loop spacing of the cables. This spacing matrix is ​​a 3n-order square matrix (n is the number of loops) and is symmetric. The spacing between each cable can be easily read from the spacing matrix, which is beneficial for the development of calculation programs. Taking a double loop as an example, the spacing matrix S is...

[0057]

[0058] First, the initial induced current components of the three sheathed circuits for each loop need to be given. Since the induced voltage generated by the current in each core is not affected by the induced current components, E can be used as the initial induced current component. map E mbp E mcp The generated induced current components serve as the initial values ​​for the induced current components in each sheath circuit; that is, the initial values ​​for iteration are determined by the following formula:

[0059]

[0060] In the formula, 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 These are the initial values ​​for the induced current components of sheath circuits 1, 2, and 3 in the m-th circuit, respectively; E SAm E SBm E SCm Let E be the total induced voltage generated by the core current of each circuit in the m-th circuit, specifically in the sheath circuits 1, 2, and 3. 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 presence of leakage current in the conductor, multi-circuit cables, like the single-circuit cables described above, have different currents in the conductors of each cross-connected cable segment. Assume the conductor currents of phases A, B, and C of the p-th segment (p = 1, 2, 3) of the i-th circuit (i = 1, 2, ..., n) are Ii, ... 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 using the following formula:

[0062]

[0063] In the formula, LP (p = 1, 2, 3) is the length of the p-th segment of the cable.

[0064] Based on the induced current components of each sheath circuit obtained in the (k-1)th iteration, the induced voltage values ​​generated by the other phase induced current components on each sheath segment of the m-th circuit in the k-th iteration can be calculated, i.e.

[0065]

[0066] In the formula, 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 Let I be the k-th iteration value of the induced voltage generated by the induced current components of other phases on each small segment of phases A, B, and C in the m-th loop. (k-1) scai I (k -1) scbi I (k-1) scci X represents the (k-1)th iteration value of each induced current component in the i-th loop; AmBi X AmCi X BmCi Let and be the mutual inductance between the sheaths of phase A of the m-th circuit and phase B of the i-th circuit, phase A of the m-th circuit and phase C of the i-th circuit, and phase B of the m-th circuit and phase C of the i-th circuit, respectively. The calculation formula is as follows:

[0067]

[0068] The k-th iteration value of the total induced voltage in each sheath circuit is easily obtained.

[0069]

[0070] The k-th iteration value of each induced current component in the m-th loop can be obtained by the following formula:

[0071]

[0072] The impedance matrix on the right side of equation (9) is the same as that in equation (2), both being 3rd-order constant matrices. Equation (8) can continuously generate a new round of iterative values ​​for the induced current components. The convergence condition of the iteration process is:

[0073]

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

[0075] The iterative process of the n-loop induced current component is as follows: Figure 3 As shown. During the iteration process, since the induced current components of the n loops cannot simultaneously meet the convergence condition, if equation (10) is used to simultaneously determine whether the induced current components of the n loops meet the convergence requirement, 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 sequentially. That is, when the induced current components of loops 1 to m converge, the iteration process of the induced current components of the (m+1)th loop is carried out until the induced current components of all loops converge. When using the iterative formula to calculate the induced current components, the latest iteration result of the induced current components of all loops is used each time. When the induced current components of all loops meet the convergence condition, 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 nucleus phase algorithm based on CLARA clustering

[0077] Given the convergence of sheath currents in three-phase cables within the same circuit, a clustering algorithm is proposed to distinguish circuits based on the sheath currents of multiple cables. To eliminate the impact of outliers on the clustering effect, improve the robustness and accuracy of clustering, and reduce time complexity to improve the efficiency of large-scale data clustering, we adopted the Clustering Application Based on Comprehensive Similarity Index (CLARA) algorithm to cluster daily CLP data. The CLARA algorithm repeatedly applies PAM to a subset 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 reconstruct 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 number of data points, and c is the data point identified as a medium. Finding the global optimum for the k-mediooids problem is an NP-hard problem. Kaufmann cleverly incorporated the sampling concept into the PAM method and proposed the efficient CLARA clustering method to reduce the time complexity of PAM in solving large-scale clustering problems. The CLARA algorithm repeatedly applies PAM to a subset of data 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 reconstruct 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 the cross-interconnection segment through the multi-loop sheath current calculation model to verify the accuracy of the clustering algorithm. Then, real test data is substituted into the sample for verification. The main steps are to first collect the sheath current of multiple cables through the data acquisition device, obtain the time series data, and then use the clustering algorithm to cluster them. The clusters are considered as one loop. After the loop is determined, the phase sequence can be determined by collecting the core current using a Rogowski coil.

[0081] like Figure 4 This image shows twelve waveforms, representing the sheath current waveforms of twelve cables. It can be seen that the changing trends differ significantly every three cables, primarily used to distinguish cable loops. This method involves collecting current data from cable connector leads and conductors, and conducting a series of detailed analyses. First, the collected current waveforms are filtered and their RMS values ​​are calculated. Then, clustering techniques are used to distinguish different loops within complex cable tunnels. By analyzing the conductor currents of each three-phase cable loop, the phase sequence can be determined. Furthermore, by simultaneously sampling conductor currents in two tunnels and comparing their changing trends, the extension of the same cable at different locations can be identified.

[0082] The above description is merely an embodiment of this application and is not intended to limit the scope of protection of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A method for energizing and phase-matching multi-circuit high-voltage cables, characterized in that, The specific steps include the following: Step 1: Collect the sheath current and core current of the multi-circuit high-voltage cable; Step two: Perform signal processing by combining digital filtering and RMS value calculation; Step 3: Use cluster analysis techniques to identify loops; Step four: Determine the phase sequence by analyzing the core current characteristics, and compare the current change trends at different locations to trace the cable path; Step 5: Perform data fusion and visualization of the recognition results, and automatically generate an intelligent report; The induced current components of each loop are iterated sequentially. That is, the induced current components of loops 1 to m converge before the iteration process of the induced current components of loop (m+1) is carried out. This continues until the induced current components of all loops converge. When calculating the induced current components using the iterative formula, the latest iteration result of the induced current components of all loops is used each time. When the induced current components of all loops meet the convergence condition, the iteration process is exited and the latest iteration value is taken as the final induced current component of each loop. The loop identification using clustering analysis technology specifically involves using a clustering algorithm based on a comprehensive similarity index of the sheath currents of multiple cables to distinguish loops. Specifically, a multi-loop nucleus phase algorithm based on CLARA clustering. Given the convergence of sheath currents in three-phase cables within the same circuit, a clustering algorithm is proposed to distinguish circuits based on the sheath currents of multiple cables. To eliminate the impact of outliers on the clustering effect, improve the robustness and accuracy of clustering, and reduce time complexity to improve the efficiency of large-scale data clustering, the CLARA algorithm, based on a comprehensive similarity index, is used to cluster daily CLP data. The CLARA algorithm repeatedly applies PAM to a subset 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 reconstruct the original data information within the allowable deviation range. (10) Where n is the number of data points, k is the number of clusters, p is the number of data points, and c is the number of data points identified as mediod. First, the grounding resistance is changed by using a multi-loop sheath current calculation model. A large number of samples are constructed by cross-interconnecting small segments to verify the accuracy of the clustering algorithm. Then, real test data is substituted for verification. The steps are as follows: first, the sheath current of multiple cables is collected by a data acquisition device. After obtaining the time sequence data, the clustering algorithm is used to cluster them. The clusters are considered as one loop. After determining the loop, the phase sequence can be determined by collecting the core current using a Rogowski coil.

2. The method for live phase comparison of multi-circuit high-voltage cables according to claim 1, characterized in that, The specific steps for collecting the sheath current and core current of multi-circuit high-voltage cables involve establishing equivalent circuit models for leakage and inductive coupling components, calculating the multi-circuit sheath circulating current based on an iterative method, and determining E in the equivalent circuit models for leakage and inductive coupling components. map E mbp E mcp Let U be the induced voltage generated by the core current of each circuit on the p-th segment of the sheath of the three phases A, B, and C of the m-th circuit, where m = 1, 2, ..., n; p = 1, 2, 3; map U mbp U mcp These are the induced voltages generated on the p-th segment of the sheath of the three phases A, B, and C of each circuit, respectively, by the induced current components of each circuit; I msap I msbp I mscp These are the sheath circulating currents of the p-th segment of the three sheath circuits of the m-th circuit; I mg11 I mg12 I mg13 I mg21 I mg22 I mg23 For the circulating current in the sheath of the directly grounded box on both sides of the m-th circuit; I mc11 I mc12 I mc13 I mc21 I mc22 I mc23 For the sheath circulating current in the two cross-connection boxes of the m-th loop; I mcap I mcbp I mccp These are the capacitor leakage currents at both ends of the p-th segment of the three-phase circuit A, B, and C in the m-th circuit.

3. The method for live phase comparison of a multi-circuit high-voltage cable according to claim 2, characterized in that, Based on the phase spacing and loop spacing of the cable, a multi-loop cable spacing matrix is ​​formed. This spacing matrix is ​​a 3n-order square matrix, where n is the number of loops, and it is a symmetric matrix. The spacing matrix S is... (1) First, the initial induced current components of the three sheathed circuits for each loop need to be given. Since the induced voltage generated by the current in each core is not affected by the induced current components, E is set as follows: map E mbp E mcp The generated induced current components serve as the initial values ​​for the induced current components in each sheath circuit; that is, the initial values ​​for iteration are determined by the following formula: (2) In the formula, 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 These are the initial values ​​for the induced current components of sheath loops 1, 2, and 3 in the m-th loop, respectively; E SAm E SBm E SCm Let E be the total induced voltage generated by the core current of each circuit in the m-th circuit, specifically in the sheath circuits 1, 2, and 3. 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 presence of leakage current in the conductor, multi-circuit cables, like single-circuit cables, have different currents in the conductors of each cross-connected cable segment. Assuming the conductor currents of phases A, B, and C of the i-th circuit (i=1,2,...n) and the p-th segment (p=1,2,3) are respectively 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 using the following formula: (3) In the formula, LP (p=1,2,3) is the length of the p-th segment of the cable; Based on the induced current components of each sheath circuit obtained in the (k-1)th iteration, the induced voltage values ​​generated by the other phase induced current components on each sheath segment of the m-th circuit in the k-th iteration can be calculated, i.e. (4) (5) (6) In the formula, 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 I represents the k-th iteration value of the induced voltage generated by the induced current components of other phases on each small segment of phases A, B, and C in the m-th loop. (k-1) scai I (k-1) scbi I (k-1) scci X represents the (k-1)th iteration value of each induced current component in the i-th loop; AmBi X AmCi X BmCi Let and be the mutual inductance between the sheaths of phase A of the m-th circuit and phase B of the i-th circuit, phase A of the m-th circuit and phase C of the i-th circuit, and phase B of the m-th circuit and phase C of the i-th circuit, respectively. The calculation formula is as follows: (7) The k-th iteration value of the total induced voltage in each sheath circuit is easily obtained. (8) The k-th iteration value of each induced current component in the m-th loop can be obtained by the following formula: (9) The impedance matrix on the right side of equation (9) is the same as that in equation (2), both being 3rd-order constant matrices. Equation (8) can continuously generate a new round of iterative values ​​for the induced current components. The convergence condition of the iteration process is: (10) In the formula, ε is a given precision value.

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