A Current Inversion Method for Steel Tape Armored Multicore Cables

Abstract

This invention discloses a current inversion method for steel-tape armored multi-core cables, comprising: S1, setting multiple measurement points at the test location of the multi-core cable, establishing a polar coordinate system with the geometric center of the cable as the origin, and constructing a position coefficient matrix, a conductor current matrix, and an attenuation coefficient matrix; S2, assigning initial values ​​to the unknown variables, and calculating the initial conductor current matrix and the initial attenuation coefficient matrix; S3, finding the local optimum solution of the attenuation coefficient matrix using a stochastic optimization method; S4, constructing a system of linear equations with the conductor current matrix as the unknown variable to solve for the conductor current matrix; S5, after updating the sampled values ​​of the magnetic induction intensity components, solving the system of linear equations to calculate the current values ​​of each conductor in the cable. Based on the time-invariant properties of the magnetization curve, this invention utilizes a stochastic optimization algorithm to solve for the undetermined coefficients of the approximation function, solves for the nonlinear attenuation coefficient of the steel-tape armor of the target cable, corrects the influence of the steel-tape armor on the current inversion results, and improves measurement efficiency and accuracy.

Description

Technical Field

[0001] This invention relates to cable current measurement technology, specifically a current inversion method for steel-tape armored multi-core cables. Background Technology

[0002] In large urban power distribution networks, power cables are the core equipment for power transmission and distribution. When large amounts of power need to be transmitted, multi-core cables are often used in urban power distribution networks to reduce the impact of the skin effect. Cable load current is a core indicator for evaluating cable performance and also a core indicator for monitoring the operating status of the distribution network. Accurate measurement of multi-core cable current provides comprehensive data support for power grid operation monitoring, which is of great practical significance for ensuring the safe operation of cables and supporting the assessment of the operating status and planning decisions of the distribution network.

[0003] However, because the conductors of multi-core cables are enclosed within a multi-layered protective structure, directly measuring the current in the conductors would damage the cable structure, which contradicts the requirements for safe operation. Furthermore, the external magnetic flux of a multi-core cable is a composite flux generated by the currents in each conductor, making it difficult to achieve independent decoupling and measurement of the current in each conductor using traditional non-invasive measurement equipment (such as current transformers and Rogowski coils). Currently, a more effective solution is to reconstruct the current distribution of the multi-core cable using spatial magnetic field inversion technology. Specifically, this involves arranging a magnetic field sensor array on the outer surface of the cable to measure the local magnetic field distribution. Based on the relationship between the field source positions, a set of nonlinear equations incorporating conductor positions and currents is established and solved, thereby achieving non-invasive measurement of the multi-core cable current.

[0004] It is worth noting that most medium-voltage power cables employ armored structures, especially ferromagnetic steel tape armor, to enhance the cable's protection and anti-interference performance. Under the influence of a magnetic field, the steel tape becomes magnetized and generates an additional magnetic field, which causes the measured magnetic field to attenuate compared to the unarmored magnetic field. If the coefficient matrix characterizing the field-source relationship is not corrected, this attenuation will lead to errors in the inversion calculation, thus affecting the accuracy of current measurement. To address this issue, existing methods involve modeling the cable structure, including the steel tape armor and the core conductor, using finite element analysis and solving for the corrected position coefficient matrix. However, this method has two main drawbacks: First, finite element calculation requires extensive mesh generation and solving differential equations in each mesh cell, which not only increases the computational load and time consumption but may also lead to increased complexity, power consumption, and cost of current measurement equipment, affecting the real-time performance of the measurement. Second, the magnetization curve of ferromagnetic materials has nonlinear characteristics, and finite element calculation also requires this information to be known in advance. However, due to differences in raw materials and processes among different manufacturers, the magnetization curve of the steel tape armor of the power cable actually used may not be consistent with the curve used for calculation. The calculation error will limit the suppression effect on the influence of ferromagnetic materials, thus resulting in lower current measurement accuracy for multi-core cables. Summary of the Invention

[0005] The purpose of this invention is to address the problems of poor real-time performance and low current measurement accuracy when using finite element method to correct the coefficient matrix characterizing the field-source relationship in reconstructing the current distribution of multi-core cables through spatial magnetic field inversion technology. This invention provides a current inversion method for steel-tape armored multi-core cables. Based on the time-invariant properties of the magnetization curve, it uses a stochastic optimization algorithm to solve for the undetermined coefficients of the approximation function and the nonlinear attenuation coefficient of the steel-tape armor of the target cable. This corrects the influence of the steel-tape armor on the current inversion results, thereby improving measurement efficiency and accuracy.

[0006] The objective of this invention is mainly achieved through the following technical solutions:

[0007] A current inversion method for steel-tape armored multi-core cables includes the following steps:

[0008] Step S1: Set up multiple measurement points evenly distributed circumferentially along the outer surface of the multi-core cable to be tested. Establish a polar coordinate system with the geometric center of the multi-core cable as the origin. Construct a position coefficient matrix based on the magnetic field measured by the magnetic field sensor at the measurement points of the conductors in the multi-core cable to be tested. Construct a conductor current matrix by calculating the current of each conductor of the multi-core cable at different times based on the magnetic field measurement values ​​at different times. Construct an attenuation coefficient matrix based on the influence of the steel armor magnetization at each measurement point on the magnetic field distribution when there is no steel armor.

[0009] Step S2: Assign initial values ​​to the unknown variables in the position coefficient matrix, conductor current matrix, and attenuation coefficient matrix, and calculate the initial conductor current matrix and initial attenuation coefficient matrix based on the initial variable values;

[0010] Step S3: Calculate the objective function value based on the current variable values ​​of the unknown variables in the position coefficient matrix, conductor current matrix, and attenuation coefficient matrix, combined with the sampled value matrix of the magnetic induction intensity components near the outer surface of the multi-core cable. Compare the calculated objective function value with a first set judgment threshold. If it is less than the first set judgment threshold, substitute the current variable value into the position coefficient matrix and attenuation coefficient matrix to calculate the iterated position coefficient matrix and attenuation coefficient matrix, and proceed to step S4. If it is greater than or equal to the first set judgment threshold, use a random optimization algorithm to calculate a new variable that minimizes the objective function value, and then calculate the objective function value based on the iterated new variable. Repeat this step until the objective function value is less than the first set judgment threshold, and then proceed to step S4.

[0011] Step S4: Construct a system of linear equations with the conductor current matrix as the unknown variable, and substitute the initial conductor current matrix and the initial attenuation coefficient matrix to solve the least squares solution of the system of linear equations. Then, solve the attenuation coefficient matrix of the current iteration based on the least squares solution. Then, determine whether the ratio of the F-norm of the difference between the attenuation coefficient matrix calculated in the current iteration and the attenuation coefficient matrix calculated in the previous iteration to the F-norm of the attenuation coefficient matrix calculated in the previous iteration is less than or equal to the second set judgment threshold. If it is greater than, return to step S3; otherwise, record the final calculation results of the current attenuation coefficient matrix and the position coefficient matrix.

[0012] Step S5: Substitute the final calculation results of the current attenuation coefficient matrix and position coefficient matrix into the system of linear equations with the conductor current matrix as the unknown variable. After the sampled values ​​of the magnetic induction intensity components are updated, solve the system of linear equations with the conductor current matrix as the unknown variable to calculate the current values ​​of each conductor in the cable. In specific implementation of this invention, the center of the multiple measurement points surrounding the test area is the same point. In step S3 of this invention, a stochastic optimization algorithm is used, implemented through existing stochastic optimization algorithms such as gradient descent, genetic algorithm, and evolutionary algorithm. In step S4 of this invention, the least squares solution of the system of linear equations can be obtained by applying regularization methods such as Moore-Penrose generalized inverse (SVD decomposition) and Tikhonov regularization.

[0013] Furthermore, the position coefficient matrix constructed in step S1 is represented as a position coefficient matrix. P Its elements p ij Representative located at j The unit current at the conductor location at the measurement point iThe generated magnetic field components, in which the element p ij The calculation formula is as follows:

[0014]

[0015] In the formula, r i Indicates measurement point i Radial coordinates in polar coordinates i i Indicates measurement point i Angular coordinates in polar coordinates r' j Indicates conductor j The radial coordinates of the center in polar coordinates, I will j Indicates conductor j The angular coordinates of the center in polar coordinates. Represents the permeability of free space. j Indicates the conductor number in a multi-core cable. i Indicates the measurement point number; r i and i i Given quantities r' j and I will j It is an unknown quantity.

[0016] Furthermore, the conductor current matrix constructed in step S1 is a conductor current matrix. I c It is represented as:

[0017]

[0018] in, n Indicates the number of conductors in a multi-core cable. N Indicates the total number of sampling points. n and N All of these are known quantities.

[0019] Furthermore, the attenuation coefficient matrix constructed in step S1 is an attenuation coefficient matrix. F It is represented as:

[0020]

[0021] The `diag` function converts a row vector into a diagonal matrix. J 1×n It is a row vector consisting entirely of 1s, with dimensions of . n , n Indicates the number of conductors in a multi-core cable. Ic For conductor current matrix; For nonlinear functions, it represents a nonlinear mapping from matrix to matrix; with x Replace nonlinear functions Medium variables Using the BH curve approximation function or To represent nonlinear functions f(x) Relationship, in the formula, a 1 , a 2 , a 3 For unknown quantities, it is a description f(x) The constant coefficient of the curve.

[0022] Furthermore, in the specific implementation of step S2, it is first assumed that the current in each conductor of the multi-core cable has no harmonic components, and the equally spaced sampling values ​​of the current time-domain waveform of a single conductor satisfy the following formula:

[0023]

[0024] In the formula, A This represents the amplitude of the current's time-domain waveform. f The initial phase angle represents the current time-domain waveform. f The frequency of the current time-domain waveform is represented. f s This indicates the sampling frequency of the current waveform during the test. N Indicates the total number of sampling points. k Indicates the sampling point number; where, A and f For unknown quantities, f , f s and k The quantity is known;

[0025] Initial current matrix I c (0) It can be represented in the following form:

[0026]

[0027] in, A t Indicates the sequence number t The amplitude of the time-domain waveform of the current in conductor number. f t Indicates the sequence number t The initial phase angle of the time-domain waveform of the current in conductor number 1. A t and ft All are unknown quantities. t =1, 2, … , n , n Indicates the number of conductors in a multi-core cable;

[0028] The unknown variables in the position coefficient matrix include the radial coordinates of the centers of each conductor in the multi-core cable in polar coordinates. r'={r' 1 , r' 2 ,…,r' n } And the angular coordinates of the centers of each conductor in a multi-core cable in polar coordinates. θ'={θ' 1 ,i ' 2 ,…,θ' n } The unknown variables in the attenuation coefficient matrix include constants. a={a 1 , a 2 , a 3 } ;

[0029] For unknown variables r '={ r '1, r '2, … , r ' n}、 i '={ i '1, i '2, … , i ' n}、 A ={ A 1, A 2, … , A n}、 f ={ f 1, f 2, … , f n}、 a ={ a 1, a 2, a 3) Assign initial values ​​to obtain the initial variable values. r ', i ', A , f , a )=( r ' (0) , i' (0) , A (0) , f (0) , a (0) ); where, when initial values ​​are assigned, the above unknown variables satisfy the following constraints:

[0030]

[0031] In the formula, R c The given quantity represents the inner diameter of the cable's steel armor. R s Given a known quantity, representing the radius of the cable conductor; A max The maximum value of the measured current amplitude;

[0032] In step S2, when calculating the initial conductor current matrix and the initial attenuation coefficient matrix based on the initial variable values, the initial variable values ​​are first used ( A (0) , f (0) The initial conductor current matrix was calculated. I c (0) The specific values ​​are then determined based on the initial conductor current matrix. I c (0) The initial attenuation coefficient matrix is ​​calculated. F (0) This invention calculates current by measuring the magnetic field value, and the sampling frequency of the current waveform during testing... f s Essentially, it refers to the sampling frequency of the magnetic field waveform, which can be defined according to different measurement requirements. In this invention, the initial value can be set manually with reference to experience; if experience cannot be referenced, it can be set to a random value within the constraints.

[0033] Furthermore, the unknown variables in the position coefficient matrix include the radial coordinates of the centers of each conductor in the multi-core cable in polar coordinates. r'={r' 1 , r' 2 ,…,r' n } And the angular coordinates of the centers of each conductor in a multi-core cable in polar coordinates. θ'= {i' 1 ,th' 2 ,…,θ' n }The unknown variables in the conductor current matrix include the amplitude of the conductor current time-domain waveform. A ={ A 1, A 2,…, A n}, and the initial phase angle of the conductor current time-domain waveform. f ={ f 1, f 2, … , f n The unknown variables in the attenuation coefficient matrix include constants. a={a 1 , a 2 , a 3 } ;in, n Indicates the number of conductors in a multi-core cable;

[0034] In step S3, the current variable value ( r ', i ', A , f , a Substitute these values ​​into the objective function and calculate the function value. The objective function is:

[0035]

[0036] In the formula, ||M|| ∞ Let L∞ be the L-norm of matrix M, defined as the maximum sum of the absolute values ​​of the elements in each row of the matrix.

[0037]

[0038] B mea The sampled matrix of the magnetic flux density components near the outer surface of the multi-core cable is shown below:

[0039]

[0040] in, m This represents the total number of magnetic field measurement points. N M represents the total number of sampling points, and M refers to any matrix.

[0041] Furthermore, each conductor has 4 unknown variables to be solved, and the nonlinear function has 3 unknown variables to be solved, for a total of 4n+3 unknowns. Each measurement point can be used to formulate an equation, and the number of equations is equal to the number of measurement points. m To ensure that the linear equation system has a least-squares solution, the number of equations must be greater than the number of unknowns. The total number of magnetic field measurement points set in step S1... mWith the number of conductors n The following condition must be met: m > 4n + 3. This ensures the uniqueness and stability of the solution to the nonlinear equation system.

[0042] Furthermore, the formula for determining whether the ratio of the F-norm of the difference between the attenuation coefficient matrix calculated in the current iteration and the attenuation coefficient matrix calculated in the previous iteration to the F-norm of the attenuation coefficient matrix calculated in the previous iteration is less than or equal to the second set judgment threshold in step S4 is as follows:

[0043]

[0044] In the formula, l For the number of iterations, This is the attenuation coefficient matrix calculated in the current iteration. ε1 is the attenuation coefficient matrix calculated in the previous iteration; ε2 is the second set judgment threshold.

[0045] || M ||2 represents a matrix M The F-norm of a matrix is ​​defined as the square root of the sum of the squares of all its elements, i.e.

[0046]

[0047] n Indicates the number of conductors in a multi-core cable. m This represents the total number of magnetic field measurement points. m ij Let be the element in the i-th row and j-th column of matrix M.

[0048] Furthermore, the system of linear equations constructed in step S4, with the conductor current matrix as the unknown variable, is expressed as follows:

[0049]

[0050] in, P This is the position coefficient matrix. I c For conductor current matrix, F This is the attenuation coefficient matrix. B mea This is a matrix of sampled values ​​of the magnetic induction intensity components near the outer surface of the multi-core cable.

[0051] In summary, compared with existing technologies, this invention has the following advantages: Compared with the finite element method, this invention eliminates the need for complex mesh generation and differential equation solving, resulting in a lower complexity of the solution model, significantly reducing computational load and hardware requirements, thus improving measurement efficiency. Based on the time-invariant nature of the magnetization curve, this invention fits the nonlinear attenuation caused by the steel strip armor using a function and utilizes a stochastic optimization algorithm to solve for the undetermined coefficients. It does not require prior acquisition of the steel strip material's BH curve data, allowing for adaptive calculations tailored to the target object, improving measurement accuracy, and possessing greater universality. Attached Figure Description

[0052] The drawings described herein are used to provide a further understanding of the embodiments of the present invention, constitute a part of this application, and do not constitute a limitation of the embodiments of the present invention. In the drawings:

[0053] Figure 1 This is a schematic diagram showing the structure of the steel-tape armored multi-core power cable under test and the arrangement of magnetic field measurement points.

[0054] Figure 2 This is a flowchart of a specific embodiment of the present invention. Detailed Implementation

[0055] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with examples and drawings. The exemplary embodiments of the present invention and their descriptions are only used to explain the present invention and are not intended to limit the present invention.

[0056] Example:

[0057] A current inversion method for a steel-tape armored multi-core cable includes the following steps: Step S1: Set multiple measurement points uniformly distributed circumferentially along the outer surface of the multi-core cable to be tested at the test location. Establish a polar coordinate system with the geometric center of the multi-core cable as the origin. Construct a position coefficient matrix based on the magnetic field measurements generated by the conductors at the measurement points by the magnetic field sensor. Obtain the current values ​​of each conductor of the multi-core cable at different times based on the current calculated from the magnetic field measurements at different times to construct a conductor current matrix. Construct an attenuation coefficient matrix based on the influence of the steel armor magnetization at each measurement point on the magnetic field distribution without steel armor. Step S2: ... Initial values ​​are assigned to the unknown variables in the position coefficient matrix, conductor current matrix, and attenuation coefficient matrix, and the initial conductor current matrix and initial attenuation coefficient matrix are calculated based on the initial variable values; Step S3: Based on the current variable values ​​of the unknown variables in the position coefficient matrix, conductor current matrix, and attenuation coefficient matrix, and combined with the sampled value matrix of the magnetic induction intensity components near the outer surface of the multi-core cable, the objective function value is calculated; The calculated objective function value is compared with a first set judgment threshold. If it is less than the first set judgment threshold, the current variable value is substituted into the position coefficient matrix and attenuation coefficient matrix to calculate the iterated position coefficient matrix and attenuation coefficient matrix. The attenuation coefficient matrix is ​​calculated, and the process proceeds to step S4. If the attenuation coefficient matrix is ​​greater than or equal to the first set judgment threshold, a stochastic optimization algorithm is used to calculate a new variable that minimizes the objective function value. The objective function value is then calculated based on the new variable after iteration. This step is repeated until the objective function value is less than or equal to the first set judgment threshold, and then the process proceeds to step S4. Step S4: A system of linear equations is constructed with the conductor current matrix as the unknown variable. The initial conductor current matrix and the initial attenuation coefficient matrix are substituted into the system of linear equations, and the least squares solution of the system of linear equations is obtained. The attenuation coefficient matrix for the current iteration is then calculated based on the least squares solution. Finally, the attenuation coefficient matrix calculated in the current iteration is judged. The ratio of the F-norm of the difference between the attenuation coefficient matrix and the attenuation coefficient matrix calculated in the previous iteration to the F-norm of the attenuation coefficient matrix calculated in the previous iteration is checked against a second set threshold. If the ratio is greater than the threshold, the process returns to step S3; otherwise, the final calculation results of the current attenuation coefficient matrix and position coefficient matrix are recorded. Step S5: Substitute the recorded final calculation results of the current attenuation coefficient matrix and position coefficient matrix into a system of linear equations with the conductor current matrix as the unknown variable. After the sampled values ​​of the magnetic induction intensity components are updated, the system of linear equations with the conductor current matrix as the unknown variable is solved to calculate the current current values ​​of each conductor in the cable. Figure 1 As shown, in a specific implementation of the present invention, the center of the multiple measurement points surrounding the same point is the same as the center of the part to be measured. Figure 1 The corresponding names of the symbols in the attached diagram are as follows: 1. Cable conductor, 2. Insulation filler, 3. Steel tape armor, 4. Outer sheath, 5. Measuring point.

[0058] The specific implementation steps for this embodiment when applied to a YJLV22-3×300 steel-tape armored three-core cable are as follows: Figure 2 As shown, the specific steps include:

[0059] Step S1: Set multiple measurement points evenly distributed circumferentially along the outer surface of the multi-core cable to be tested. Establish a polar coordinate system with the geometric center of the multi-core cable as the origin, and define the calculation model. The calculation model definition in step S1 includes the following sub-steps:

[0060] Step S11, define the position coefficient matrix P Its elements p ij Representative located at j The unit current at the conductor location at the measurement point i The generated magnetic field components, in which elements p ij Calculate according to formula (1):

[0061] (1)

[0062] In the formula,

[0063] r i The known quantity represents the measurement point. i In this embodiment, the radial coordinates are in polar coordinates. r i =45 mm (i=1,2, …, 24).

[0064] i i The known quantity represents the measurement point. i In this embodiment, the angular coordinates are in polar coordinates. i i =(15× i )°(i=1,2, …, 24).

[0065] r ' j The unknown quantity represents the conductor. j The radial coordinates of the center in polar coordinates, in this embodiment, are... j =1, 2, 3.

[0066] i ' j The unknown quantity represents the conductor. j The angular coordinates of the center in polar coordinates.

[0067] Represents the permeability of free space. j Indicates the conductor number in a multi-core cable.i Indicates the measurement point number.

[0068] Step S12, define the conductor current matrix I c , representing the current value of each conductor in the cable at different times.

[0069]

[0070] in, n The quantity is known, representing the number of cable conductors. In this embodiment... n =3.

[0071] N The known quantity represents the total number of sampling points. Since the current is calculated from the magnetic field measurement value, it is essentially the total number of sampling points of the magnetic field waveform involved in the calculation. In this embodiment... N =160.

[0072] Step S13, define the attenuation coefficient matrix as shown in equation (2). F .

[0073] (2)

[0074] In the formula, F This is the attenuation coefficient matrix, representing the effect of the steel armor magnetization at each sampling point on the magnetic field distribution without steel armor.

[0075] The diag function converts a row vector into a diagonal matrix.

[0076] J 1×n Let be a row vector of all 1s with dimension . n .

[0077] It is a nonlinear function, representing a nonlinear mapping from matrix to matrix.

[0078] by x Replace nonlinear functions Medium variables In this embodiment, the function approximation is performed using equation (3).

[0079] (3)

[0080] In the formula, a 1. a 2. a 3 is an unknown quantity, which describes f ( x The constant coefficient of the curve.

[0081] Step S2: Generate or calculate initial parameter values. Step S2 includes the following sub-steps:

[0082] Step S21: Assume that the current in each conductor of the cable has no harmonic components, and the equally spaced sampling values ​​of the current time domain waveform of a single conductor satisfy formula (4).

[0083] (4)

[0084] In the formula, A The unknown quantity represents the amplitude of the current time-domain waveform.

[0085] φ is an unknown quantity, representing the initial phase angle of the current time-domain waveform.

[0086] f Given a known quantity, representing the frequency of the current time-domain waveform, in this embodiment, f =50Hz.

[0087] f s The known quantity represents the sampling frequency of the current waveform during the test. Since the current is calculated by measuring the magnetic field value, it is essentially the sampling frequency of the magnetic field waveform. In this embodiment, it is 4kSPS, which means 4000 points are collected per second.

[0088] k For known quantities, represent the sampling point number.

[0089] Based on equation (4), the initial current matrix I c (0) It can be expressed in the form of equation (5).

[0090] (5)

[0091] in, A t ( t =1, 2, 3) are unknowns, representing the sequence number. t The amplitude of the time-domain waveform of the current in conductor number 1.

[0092] f t ( t =1, 2, 3) are unknowns, representing the sequence number. t The initial phase angle of the time-domain waveform of the current in conductor number 1.

[0093] Step S22, for unknown variables r '={ r '1, r '2, r ' 3}、 i '={ i '1, i '2, i ' 3}、 A ={ A 1, A 2, A 3}、 f ={ f 1, f 2, f 3}、 a ={ a 1, a 2, a 3) Assign initial values ​​to obtain the initial variable values. r ', i ', A , f , a )=( r ' (0) , i ' (0) , A (0) , f (0) , a (0) ),in r ' (0) ={16, 16, 16}、 i ' (0) ={-30, 90, 210}、 A (0) ={200, 200, 200}、 f (0) ={0, 120, 240}、 a (0)) ={0.01, 50, 0.1}

[0094] The above variable values ​​should satisfy the inequality constraints as shown in equation (6).

[0095] (6)

[0096] In the formula, R c This is a known quantity, representing the inner diameter of the cable's steel armor.

[0097] R s is a known quantity, representing the radius of the cable conductor.

[0098] A max This represents the maximum value of the measured current amplitude.

[0099] Amax The amplitude corresponding to the maximum value of the measured current is determined based on operating data or experience.

[0100] Step S23, initial variable values ​​( A (0) , f (0) Substituting into equation (6), the initial conductor current matrix is ​​calculated. I c = I c (0) .

[0101] Step S24, initialize the conductor current matrix. I c (0) Substitute into equation (2) to calculate the initial attenuation coefficient matrix. F = F (0) .

[0102] Step S3: Find the attenuation coefficient matrix using a stochastic optimization method. F Local optimal solution. Step S3 includes the following sub-steps:

[0103] Step S31, set the current variable value ( r ', i ', A , f , a Substitute the result into the objective function of equation (7) and calculate the function value.

[0104] (7)

[0105] In the formula, ||M|| ∞ Let L∞ norm represent the matrix M, defined as the maximum sum of the absolute values ​​of the elements in each row of the matrix, i.e.

[0106] (8)

[0107] in, m ij Let be the element in the i-th row and j-th column of matrix M.

[0108] B mea Given a known quantity, the matrix represents the sampled values ​​of the tangential component of the magnetic induction intensity near the outer surface of the multi-core cable, as shown below.

[0109]

[0110] In this embodiment, the total number of magnetic field measurement points is 24.

[0111] Step S32, determine the objective function value g < e 1. Check if the condition is true. If not, proceed to step S33; if true, change the current variable value ( r ', i ', A , f , a Substituting into equations (1) and (2), the attenuation coefficient matrix after iteration is calculated respectively. F *(0) and position coefficient matrix P *(0) .

[0112] in, e 1 represents the first preset judgment threshold. In this embodiment, e 1 = 0.01.

[0113] Step S33, in this embodiment, an evolutionary algorithm called the covariance matrix adaptive evolutionary strategy is applied to calculate a new variable that may minimize equation (7). r ' (1) , i ' (1) , A (l) , f (1) , a (1) Return to step S31, substitute the iterated variables into equation (7) to calculate the objective function value, until the judgment condition in step S32 is met.

[0114] Step S4: Construct and solve a system of linear equations. I c Iterative optimization of the attenuation coefficient matrix F Step S4 includes the following sub-steps:

[0115] Step S41, build I c The system of linear equations with unknown variables is shown in equation (9), and is substituted into... P=P *(0) , F = F *(0) .

[0116] (9)

[0117] Step S42, find the least squares solution of the linear system of equations (9). I c = I c (1)In this embodiment, Moore-Penrose generalized inverse (SVD decomposition) is used to solve the equations to suppress the effects of measurement disturbances caused by the magnetic field sensor.

[0118] Step S43, will I c = I c (1) Substituting into equation (3), we obtain F = F (1) .

[0119] Step S44, determine F (l) - F* (l-1) Does it satisfy condition (11)? If not, return to step S31 and... I c = I c (1) , F = F (1) Substitute into the objective function of equation (7), and reassign the variables ( r ', i ', a Assign initial values ​​and iteratively calculate the attenuation coefficient matrix after iteration using the methods in steps S32 and S33. F *(l) and position coefficient matrix P *(l) Then return to step S41; if successful, record. F *(l) , P *(l) These are the final calculation results for the attenuation coefficient matrix and the position coefficient matrix, respectively.

[0120] (10)

[0121] In the formula, l denoted as the number of iterations in step S4.

[0122] e 2 represents the second set judgment threshold. In this embodiment, e 2 = 0.01.

[0123] || M ||2 represents a matrix M The F-norm (Frobenius norm) of a matrix is ​​defined as the square root of the sum of the squares of all its elements, i.e.

[0124] (11)

[0125] Step S5, will F = F *(l) , P = P *(l) Substituting into equation (9), when the sampling value matrix of the magnetic induction intensity component... B mea After the update, solve the linear equation system (9) to calculate the current values ​​of each conductor in the current cable. I c .

[0126] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A current inversion method for a steel-tape armored multi-core cable, characterized in that, Includes the following steps: Step S1: Set up multiple measurement points evenly distributed along the circumference of the outer surface of the multi-core cable to be tested. Establish a polar coordinate system with the geometric center of the multi-core cable to be tested as the origin. Construct a position coefficient matrix based on the magnetic field measurement values ​​generated by the conductors in the multi-core cable at the measurement points by the magnetic field sensor. Calculate the current values ​​of each conductor of the multi-core cable at different times based on the magnetic field measurement values ​​at different times and construct a conductor current matrix. An attenuation coefficient matrix is ​​constructed based on the influence of steel armor magnetization at each measurement point on the magnetic field distribution without steel armor. Step S2: Assign initial values ​​to the unknown variables in the position coefficient matrix, conductor current matrix, and attenuation coefficient matrix, and calculate the initial conductor current matrix and initial attenuation coefficient matrix based on the initial variable values; Step S3: Calculate the objective function value based on the current variable values ​​of the unknown variables in the position coefficient matrix, conductor current matrix, and attenuation coefficient matrix, combined with the sampled value matrix of the magnetic induction intensity components near the outer surface of the multi-core cable. The calculated objective function value is compared with the first set judgment threshold. If it is less than the first set judgment threshold, the current variable value is substituted into the position coefficient matrix and the attenuation coefficient matrix to calculate the iterated position coefficient matrix and the attenuation coefficient matrix, and then proceed to step S4. If it is greater than or equal to the first set judgment threshold, a random optimization algorithm is used to calculate a new variable that minimizes the objective function value. The objective function value is then calculated based on the iterated new variable. This step is repeated until the objective function value is less than the first set judgment threshold, and then proceed to step S4. Step S4: Construct a system of linear equations with the conductor current matrix as the unknown variable, and substitute the initial conductor current matrix and the initial attenuation coefficient matrix to solve the least squares solution of the system of linear equations. Then, solve the attenuation coefficient matrix of the current iteration based on the least squares solution. Then, determine whether the ratio of the F-norm of the difference between the attenuation coefficient matrix calculated in the current iteration and the attenuation coefficient matrix calculated in the previous iteration to the F-norm of the attenuation coefficient matrix calculated in the previous iteration is less than or equal to the second set judgment threshold. If it is greater than, return to step S3; otherwise, record the final calculation results of the current attenuation coefficient matrix and the position coefficient matrix. Step S5: Substitute the final calculation results of the current attenuation coefficient matrix and position coefficient matrix into the linear equation system with the conductor current matrix as the unknown variable. After the sampled value of the magnetic induction intensity component is updated, solve the linear equation system with the conductor current matrix as the unknown variable to calculate the current value of each conductor of the cable. The attenuation coefficient matrix constructed in step S1 is the attenuation coefficient matrix. F It is represented as: The `diag` function converts a row vector into a diagonal matrix. J 1×n It is a row vector consisting entirely of 1s, with dimensions of . n , n Indicates the number of conductors in a multi-core cable. I c For conductor current matrix; It is a nonlinear function, representing a nonlinear mapping from matrix to matrix; by x Replace nonlinear functions Medium variables Using the BH curve approximation function or To represent nonlinear functions f(x) Relationship, in the formula, a 1 , a 2 , a 3 For unknown quantities, it is a description f(x) The constant coefficient of the curve.

2. The current inversion method for a steel-tape armored multi-core cable according to claim 1, characterized in that, The position coefficient matrix constructed in step S1 is represented as the position coefficient matrix. P Its elements p ij Representative located at j The unit current at the conductor location at the measurement point i The generated magnetic field components, in which the element p ij The calculation formula is as follows: Where, r i Indicates measurement point i Radial coordinates in polar coordinates θ i Indicates measurement point i Angular coordinates in polar coordinates r' j Indicates conductor j The radial coordinates of the center in polar coordinates, θ' j Indicates conductor j The angular coordinates of the center in polar coordinates. Represents the permeability of free space. j Indicates the conductor number in a multi-core cable. i Indicates the measurement point number; r i and θ i Given quantities r' j and θ' j It is an unknown quantity.

3. The current inversion method for a steel-tape armored multi-core cable according to claim 1, characterized in that, The conductor current matrix constructed in step S1 is the conductor current matrix. I c It is represented as: in, n Indicates the number of conductors in a multi-core cable. N Indicates the total number of sampling points. n and N All of these are known quantities.

4. The current inversion method for a steel-tape armored multi-core cable according to claim 1, characterized in that, In the specific implementation of step S2, it is first assumed that the current in each conductor of the multi-core cable has no harmonic components, and the equally spaced sampling values ​​of the current time-domain waveform of a single conductor satisfy the following formula: Where, A This represents the amplitude of the current's time-domain waveform. φ The initial phase angle represents the current time-domain waveform. f The frequency of the current time-domain waveform is represented. f s This indicates the sampling frequency of the current waveform during the test. N Indicates the total number of sampling points. k Indicates the sampling point number; where, A and φ For unknown quantities, f , f s and k The quantity is known; Initial current matrix I c (0) It can be represented in the following form: in, A t Indicates the sequence number t The amplitude of the time-domain waveform of the current in conductor number. φ t Indicates the sequence number t The initial phase angle of the time-domain waveform of the current in conductor number 1. A t and φ t All are unknown quantities. t =1, 2, … , n , n Indicates the number of conductors in a multi-core cable; The unknown variables in the position coefficient matrix include the radial coordinates of the centers of each conductor in the multi-core cable in polar coordinates. r'= {r' 1 , r' 2 , … ,r' n } And the angular coordinates of the centers of each conductor in a multi-core cable in polar coordinates. θ'={θ' 1 , θ' 2 , … ,θ' n } The unknown variables in the attenuation coefficient matrix include constants. a={a 1 , a 2 , a 3 } ; For unknown variables r '={ r '1, r '2, … , r ' n }、 θ '={ θ '1, θ '2, … , θ ' n }、 A ={ A 1, A 2, … , A n }、 φ ={ φ 1, φ 2, … , φ n }、 a ={ a 1, a 2, a 3} Assign initial values ​​to obtain initial variable values ​​( r ', θ ', A , φ , a )=( r ' (0) , θ ' (0) , A (0) , φ (0) , a (0) ); where, when initial values ​​are assigned, the above unknown variables satisfy the following constraints: Where, R c The given quantity represents the inner diameter of the cable's steel armor; R s Given a known quantity, representing the radius of the cable conductor; A max The maximum value of the measured current amplitude; In step S2, when calculating the initial conductor current matrix and the initial attenuation coefficient matrix based on the initial variable values, the initial variable values ​​are first used ( A (0) , φ (0) The initial conductor current matrix was calculated. I c (0) The specific values ​​are then determined based on the initial conductor current matrix. I c (0) The initial attenuation coefficient matrix is ​​calculated. F (0) .

5. The current inversion method for a steel-tape armored multi-core cable according to claim 1, characterized in that, The unknown variables in the position coefficient matrix include the radial coordinates of the centers of each conductor in the multi-core cable in polar coordinates. r'={r' 1 , r' 2 , … ,r' n } And the angular coordinates of the centers of each conductor in a multi-core cable in polar coordinates. θ'={θ' 1 , θ' 2 , … ,θ' n } ; The unknown variables in the conductor current matrix include the amplitude of the conductor current time-domain waveform. A ={ A 1, A 2, …, A n }, and the initial phase angle of the conductor current time-domain waveform. φ ={ φ 1, φ 2, … , φ n The unknown variables in the attenuation coefficient matrix include constants. a={a 1 , a 2 , a 3 } ;in, n Indicates the number of conductors in a multi-core cable; In step S3, the current variable value ( r ', θ ', A , φ , a Substitute these values ​​into the objective function and calculate the function value. The objective function is: In the formula, ||M|| ∞ The L∞ norm of matrix M is defined as the maximum sum of the absolute values ​​of the elements in each row of the matrix. B mea The sampled matrix of the magnetic flux density components near the outer surface of the multi-core cable is shown below: in, m This represents the total number of magnetic field measurement points. N This indicates the total number of sampling points.

6. The current inversion method for a steel-tape armored multi-core cable according to claim 5, characterized in that, The total number of magnetic field measurement points set in step S1 m With the number of conductors n The following condition must be met: m > 4n + 3.

7. The current inversion method for a steel-tape armored multi-core cable according to claim 1, characterized in that, In step S4, the formula for determining whether the ratio of the F-norm of the difference between the attenuation coefficient matrix calculated in the current iteration and the attenuation coefficient matrix calculated in the previous iteration to the F-norm of the attenuation coefficient matrix calculated in the previous iteration is less than or equal to the second set judgment threshold is as follows: Where, l For the number of iterations, This is the attenuation coefficient matrix calculated in the current iteration. ε1 is the attenuation coefficient matrix calculated in the previous iteration; ε2 is the second set judgment threshold. || M ||2 represents a matrix M The F-norm of a matrix is ​​defined as the square root of the sum of the squares of all its elements, i.e. n Indicates the number of conductors in a multi-core cable. m This represents the total number of magnetic field measurement points. m ij Let be the element in the i-th row and j-th column of matrix M.

8. A current inversion method for a steel-tape armored multi-core cable according to any one of claims 1 to 7, characterized in that, The system of linear equations constructed in step S4, with the conductor current matrix as the unknown variable, is expressed as follows: in, P This is the position coefficient matrix. I c For conductor current matrix, F This is the attenuation coefficient matrix. B mea This is a matrix of sampled values ​​of the magnetic induction intensity components near the outer surface of the multi-core cable.

Images