High-voltage cable impedance parameter calculation method

Abstract

The invention provides a high-voltage cable impedance parameter calculation method, and relates to the technical field of high-voltage cable impedance parameter calculation, and the method comprises the steps: constructing a sample set covering a plurality of typical laying conditions, and carrying out the calculation of a high-fidelity electromagnetic field simulation and analysis formula for each condition to obtain a reference and theoretical impedance matrix; a three-dimensional tensor representing an impedance deviation rule is formed through systematic comparison; the method comprises the following steps of: obtaining a tensor, decomposing the tensor to obtain a core tensor and a factor matrix, constructing a low-dimensional correction subspace taking theoretical impedance as a reference point by extracting a base vector matched with a target working condition, then obtaining an impedance measurement value of the target working condition based on rapid simplified simulation, and optimally solving an optimal coordinate system number in the subspace by taking the measurement value as a target. And finally, a complete impedance matrix is synthesized through linear combination of the coefficient and the basis vector, and an impedance parameter calculation result with high precision and high efficiency is output.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of cable parameter calculation, in particular to a high-voltage cable impedance parameter calculation method. BACKGROUND

[0002] In high-voltage power transmission systems, especially in scenarios where multiple cables are operated in parallel, accurate calculation of cable impedance parameters is a key prerequisite for ensuring system current distribution, avoiding local overheating and insulation aging. The accuracy of impedance parameters directly affects the reliability, operation efficiency and life assessment of cable system design. With the growth of urban power grid expansion and new energy grid connection demand, the underground cable laying environment is becoming increasingly complex, such as uneven soil structure, cable spacing variation and parallel laying, which makes impedance calculation must consider the adaptability of complex working conditions and the efficiency of engineering design, which poses a severe challenge to traditional calculation methods.

[0003] Currently, the industry mainly relies on analytical formulas combined with multi-conductor transmission line equivalent circuit technology in engineering practice. Specifically, first, the self-impedance and mutual impedance of the cable are calculated based on the Carson-Clem formula based on idealized assumptions, and then the obtained impedance matrix is substituted into the equivalent circuit model to solve the current distribution. This method is widely used because of its fast calculation speed and ease of implementation, and has become the mainstream means for electrical analysis of cable systems. However, this method has inherent limitations when dealing with complex laying conditions commonly encountered in actual engineering, as the theoretical assumptions often differ significantly from the actual situation. The shortcomings of the prior art are mainly reflected in its difficulty in achieving high-precision adaptation to complex working conditions while ensuring calculation efficiency. On the one hand, the idealized assumptions of homogeneous earth and uniform current distribution relied on by analytical formulas make it impossible to accurately depict the impedance deviation caused by uneven soil, proximity effect and three-dimensional electromagnetic coupling in the actual environment, resulting in systematic errors between theoretical calculation results and true values. On the other hand, while high-precision finite element simulation can improve accuracy, it is costly and time-consuming, and cannot effectively transfer the deviation pattern of the calculated working condition to the new target working condition, making it difficult to support the rapid design and parameter calibration needs of batch cable projects. Therefore, the existing technical system lacks a method of calculating impedance parameters that can combine the reliability of high-precision simulation with the efficiency of analytical formulas and have cross-working-condition adaptive capability.

[0004] The above information disclosed in the BACKGROUND section is only intended to strengthen the understanding of the background of the present disclosure, and therefore it can include information that does not constitute prior art known to those of ordinary skill in the art. SUMMARY

[0005] The application aims to provide a high-voltage cable impedance parameter calculation method to solve the problems in the background art.

[0006] To achieve the above-mentioned purpose, the application provides the following technical solutions. A high-voltage cable impedance parameter calculation method, the specific steps include: Step 1: constructing a high-voltage cable condition set of multiple typical laying conditions in a computer, extracting a reference impedance matrix of each typical laying condition based on high-fidelity electromagnetic field simulation, calculating the theoretical impedance matrix thereof through an analytical formula, calculating the deviation matrix of the two, and stacking the deviation matrices of all typical laying conditions to form a three-dimensional impedance deviation tensor; Step 2: performing tensor decomposition on the three-dimensional impedance deviation tensor to obtain a core tensor and multiple factor matrices, determining a target condition based on a high-voltage cable to be measured, calculating the theoretical impedance matrix of the target condition through an analytical formula, extracting a basis vector associated with the characteristics of the target condition from the factor matrices, and dynamically constructing a low-dimensional correction subspace in combination with the theoretical impedance matrix as a reference point; Step 3: obtaining an impedance measurement value of the high-voltage cable to be measured through rapid simplified simulation, minimizing the error between the candidate impedance matrix generated in the correction subspace and the impedance measurement value as an optimization target to perform rapid optimization, and solving the optimal coordinate coefficient; Step 4: substituting the optimal coordinate coefficient into the generation expression of the correction subspace to synthesize a complete impedance matrix, which is output as the final high-precision impedance parameter calculation result.

[0007] Further, the multiple-condition impedance deviation tensor is constructed and tensor decomposition is performed, specifically including: The high-voltage cable condition set of multiple typical laying conditions is constructed, and the high-voltage cable condition set is a sample set composed of multiple typical laying conditions, wherein each typical laying condition is uniquely determined by a group of characteristic parameters, and the characteristic parameters include soil resistivity, cable spacing and laying depth; For each typical laying condition in the high-voltage cable condition set, a reference impedance matrix is extracted through high-fidelity electromagnetic field simulation, and the high-fidelity electromagnetic field simulation includes: 1) based on the geometric parameters and material properties of the high-voltage cable, and introducing the electromagnetic environment defined by the soil resistivity, cable spacing and laying depth of the typical laying condition, establishing a three-dimensional model including the cable core, insulation layer, metal shielding layer, outer sheath and surrounding soil domain, 2) setting ideal electric conductor boundary conditions and absorbing boundary conditions to simulate an infinite region, 3) using a frequency domain solver to solve Maxwell equations at power frequency; based on the electromagnetic field distribution data obtained by solving, the open-short circuit method is used to calculate and extract the self-impedance and mutual impedance per unit length to form the reference impedance matrix; Based on the high-voltage cable geometry parameters and material properties used in the above high-fidelity electromagnetic field simulation, a theoretical impedance matrix is calculated for each typical laying condition by an analytical formula; For each typical laying condition, the reference impedance matrix is subtracted from the corresponding theoretical impedance matrix to obtain the deviation matrix of the typical laying condition. The deviation matrices of all typical laying conditions are stacked according to the condition index to form a three-dimensional impedance deviation tensor, wherein the three dimensions of the tensor correspond to the row index, column index and condition index of the deviation matrix, respectively. The three-dimensional impedance deviation tensor is decomposed using a tensor decomposition algorithm to obtain a core tensor and three factor matrices, which are respectively: a condition characteristic factor matrix representing the correlation of deviation modes between different typical laying conditions, a row characteristic factor matrix representing the correlation between row elements of the deviation matrix, and a column characteristic factor matrix representing the correlation between column elements of the deviation matrix.

[0008] Further, constructing a low-dimensional correction subspace specifically includes: Receiving the characteristic parameters of the target condition as input data, calculating the theoretical impedance matrix of the target condition by an analytical formula, and setting this theoretical impedance matrix as a reference point; According to the characteristic parameters of the target condition, selecting the associated column vectors from the condition characteristic factor matrix as weights reflecting the deviation mode, and combining the selected weights with the row characteristic factor matrix and the column characteristic factor matrix to generate a set of basis vectors for the target condition; Taking the reference point as the origin, the linear space spanned by the set of basis vectors is the low-dimensional correction subspace. For any candidate impedance matrix in the correction subspace, it is generated by linearly combining the reference point and the set of basis vectors with a set of coordinate coefficients.

[0009] Further, the fast optimization to solve the optimal coordinate coefficients specifically includes: Obtaining the impedance measurement value by performing a fast simplified simulation on the high-voltage cable to be measured, wherein the fast simplified simulation refers to solving a two-dimensional axisymmetric model of the cable, and the calculation speed is higher than that of the high-fidelity electromagnetic field simulation; In the low-dimensional correction subspace, the coordinate coefficients are used as optimization variables to construct an objective function, which is used to measure the difference between the candidate impedance matrix and the impedance measurement value; the objective function also includes a regularization constraint term based on the coordinate coefficients. In the low-dimensional parameter space composed of coordinate coefficients, a numerical optimization algorithm is executed for iterative search to minimize the objective function, and finally a set of optimal coordinate coefficients is solved.

[0010] Further, synthesizing and outputting a high-precision impedance matrix specifically includes: The optimal coordinate coefficients obtained by solving are substituted into the generating expression of the correction subspace, linearly combined with the basis vectors, and superimposed on the reference point to synthesize a complete and high-precision impedance matrix, and the synthesized impedance matrix is subjected to physical constraint inspection, and the physical constraint includes checking the symmetry of the matrix and the positive definiteness of the main diagonal elements. The impedance matrix passing the inspection is output as the final high-precision impedance parameter calculation result of the target working condition.

[0011] Further, the specific mode of the tensor decomposition processing includes: The tensor decomposition adopts a Tucker decomposition algorithm, which decomposes the three-dimensional impedance deviation tensor into the product form of a core tensor and three factor matrices, wherein each row of the working condition characteristic factor matrix corresponds to a typical laying working condition, and each column represents a deviation mode of a potential typical laying working condition. The row characteristic factor matrix and the column characteristic factor matrix jointly represent the variation law of the internal elements of the deviation matrix under various deviation modes.

[0012] Further, the construction mode of the optimization objective function includes: The weighted Frobenius norm between the candidate impedance matrix generated in the correction subspace and the impedance measurement value of the target working condition is taken as the main optimization objective, and the L2 norm of the coordinate coefficient vector is introduced as a regularization constraint term to jointly constitute the objective function for fast optimization and solving.

[0013] Compared with the prior art, the present application has the following beneficial effects: The present application quantifies and encapsulates the systematic errors in the complex laying environment by systematically obtaining the impedance deviation between the high-fidelity simulation and the analytical formula calculation under multiple typical laying working conditions and constructing a three-dimensional impedance deviation tensor, thereby realizing the quantification and encapsulation of systematic errors in a complex laying environment for the first time; then, by performing tensor decomposition on the deviation tensor, low-dimensional basis vectors representing the main deviation modes are extracted, so that a low-dimensional correction subspace can be dynamically constructed with the theoretical impedance of the target working condition as the reference point, which not only retains the physical credibility of high-precision simulation but also constrains the problem to be solved in a very low-dimensional parameter space. The present application uses the local impedance measurement value of the target working condition obtained by the introduced fast and simplified simulation to perform fast optimization in the aforementioned low-dimensional subspace with the measurement value as the target, and solve the optimal coordinate coefficients, which makes the method unnecessary to perform full-order high-cost simulation for each new working condition, and only a small amount of online calculation is needed to realize the accurate migration of the general deviation model to the specific scene, and finally the optimal coefficients and the basis vectors are linearly combined to synthesize the final impedance matrix, thereby fusing the efficiency of the analytical formula and the precision of the approximate real simulation in the output result; The application realizes accurate, rapid and adaptive calculation of cable impedance parameters in complex and changeable engineering environment without greatly increasing the calculation cost, and provides key technical support for standardized design and reliable operation of batch cable engineering. BRIEF DESCRIPTION OF DRAWINGS

[0014] Figure 1 It is a whole method flowchart of the application; Figure 2 It is a candidate impedance matrix norm-coordinate coefficient absolute value mean scatter plot of the application; Figure 3 It is a base vector norm mean-optimal coordinate coefficient vector norm-final high-precision impedance parameter norm column point line plot of the application; Figure 4 It is a coordinate coefficient absolute value mean-candidate impedance matrix norm fitting curve plot of the application; Figure 5 It is an optimal coordinate coefficient vector norm-final high-precision impedance parameter norm column point line fitting curve plot of the application. DETAILED DESCRIPTION

[0015] In order to make the purpose, technical scheme and advantages of the application clearer and more apparent, the application will be further described in detail below in combination with specific embodiments.

[0016] It should be noted that, unless otherwise defined, the technical terms or scientific terms used in the application should be understood as the usual meaning understood by those skilled in the art to which the application belongs. The "first", "second" and similar words used in the application do not represent any order, quantity or importance, but are only used to distinguish different components. "Include" or "contain" and similar words mean that the elements or objects before the word cover the elements or objects listed after the word and their equivalents, and do not exclude other elements or objects. "Connected" or "connected" and similar words are not limited to physical or mechanical connection, but can include electrical connection, whether direct or indirect. "Up", "down", "left", "right" and the like only represent relative positional relationship, when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0017] EMBODIMENT: Please refer to Figures 1-5 The application provides a technical scheme: A high-voltage cable impedance parameter calculation method, the specific steps include: Step 1: Construct a high-voltage cable condition set of multiple typical laying conditions in a computer, extract a reference impedance matrix of each typical laying condition based on high-fidelity electromagnetic field simulation, and calculate a theoretical impedance matrix thereof through an analytical formula, calculate a deviation matrix of the two, and stack the deviation matrices of all typical laying conditions to form a three-dimensional impedance deviation tensor; Constructing a multi-condition impedance deviation tensor and performing tensor decomposition, specifically comprising: Constructing a high-voltage cable condition set of multiple typical laying conditions, which is a sample set composed of multiple typical laying conditions, wherein each typical laying condition is uniquely determined by a set of characteristic parameters, including soil resistivity, cable spacing, and laying depth; For each typical laying condition in the high-voltage cable condition set, a reference impedance matrix is extracted through high-fidelity electromagnetic field simulation, which includes: 1) based on the geometric parameters and material properties of the high-voltage cable, and introducing the electromagnetic environment defined by the soil resistivity, cable spacing, and laying depth of its typical laying condition, establishing a three-dimensional model containing the cable core, insulation layer, metal shielding layer, outer sheath, and surrounding soil domain, 2) setting ideal electrical conductor boundary conditions and absorbing boundary conditions to simulate an infinite region, 3) using a frequency domain solver to solve Maxwell's equations at power frequency; based on the electromagnetic field distribution data obtained by solving, the open-short circuit method is used to calculate and extract the self-impedance and mutual impedance per unit length, forming the reference impedance matrix; Based on the same high-voltage cable geometric parameters and material properties used in the above high-fidelity electromagnetic field simulation, a theoretical impedance matrix is calculated for each typical laying condition through an analytical formula; For each typical laying condition, subtract its reference impedance matrix from its corresponding theoretical impedance matrix to obtain the deviation matrix of the typical laying condition. Stack the deviation matrices under all typical laying conditions according to the condition index to form a three-dimensional impedance deviation tensor, wherein the three dimensions of the tensor correspond to the row index, column index, and condition index of the deviation matrix, respectively; The three-dimensional impedance deviation tensor is decomposed using a tensor decomposition algorithm to obtain a core tensor and three factor matrices, the three factor matrices being: a condition characteristic factor matrix representing the correlation of deviation patterns between different typical laying conditions, a row characteristic factor matrix representing the correlation between row elements of the deviation matrix, and a column characteristic factor matrix representing the correlation between column elements of the deviation matrix.

[0018] In the specific embodiment, the purpose of constructing the multi-prototype laying condition impedance deviation tensor and performing tensor decomposition is to systematically capture and quantify the systematic deviation between the theoretical analytical model and the real electromagnetic response of the high-voltage cable under different laying environments. By establishing a high-voltage cable working condition set covering different soil resistivities, cable spacings, and laying depths, a representative sample space is constructed to ensure that the deviation patterns extracted later can widely cover the main working condition types encountered in actual projects, thereby improving the generalization ability and engineering applicability of the impedance parameter correction method. The reason for performing high-fidelity electromagnetic field simulation for each typical laying condition to extract the reference impedance matrix is that the impedance parameters of the high-voltage cable are significantly affected by the surrounding complex electromagnetic environment, and it is difficult to accurately reflect the electromagnetic coupling effect under actual laying conditions relying solely on analytical formulas. Specifically, the high-fidelity electromagnetic field simulation includes the following steps: first, according to the actual structural parameters of the high-voltage cable, such as the core radius, the insulation layer thickness, the shielding layer size, and the soil resistivity, cable spacing, and laying depth of the specific typical laying condition, a three-dimensional entity model including the cable body and the surrounding soil domain is established in a finite element simulation software, such as COMSOL Multiphysics; second, to accurately simulate the infinite space boundary, ideal conductor boundary conditions and scattering boundary conditions are set on the outer surface of the model; third, a frequency domain solver is used to solve the Maxwell equations at the power frequency (50 Hz) to obtain the spatial electromagnetic field distribution; finally, based on the mature method of open-short circuit method, the self-impedance and mutual impedance per unit length are calculated and extracted from the simulation results to form the reference impedance matrix under the same working condition, which is considered as the real reference; Based on the same cable body parameters used in the above high-fidelity simulation, the theoretical impedance matrix for the same typical laying condition is calculated using Carson-Clem and other analytical formulas. The purpose is to establish a theoretical reference under simplified assumptions (such as homogeneous earth and regular arrangement). The reference impedance matrix is subtracted from the theoretical impedance matrix element by element to obtain the deviation matrix reflecting the theoretical model error under the same typical laying condition. By stacking the deviation matrices of all typical laying conditions along the third dimension according to the working condition index, a three-dimensional impedance deviation tensor is formed. This data structure organizes the error information from each independent typical laying condition in a unified and structured manner, facilitating the extraction of common patterns and correlation rules of errors from a system level; The specific way of tensor decomposition processing includes: The tensor decomposition adopts the Tucker decomposition algorithm, which decomposes the three-dimensional impedance deviation tensor into the product of a core tensor and three factor matrices. Each row of the working condition characteristic factor matrix corresponds to a typical laying condition, and each column represents a potential deviation pattern of the typical laying condition. The column vector represents the weight of the deviation pattern in different typical laying conditions. The row characteristic factor matrix and the column characteristic factor matrix jointly represent the variation law of the internal elements of the deviation matrix under various deviation modes. It should be noted that the tensor decomposition (Tucker decomposition) of the three-dimensional impedance deviation tensor is the core knowledge extraction step, and the tensor decomposition can decompose high-dimensional data into a set of low-dimensional factor matrices and a core tensor, thereby realizing data dimension reduction and feature extraction. In the present application, three factor matrices are obtained after decomposition: each row of the working condition characteristic factor matrix corresponds to a specific typical laying working condition, and each column represents a potential deviation mode automatically learned from the overall data, such as a mode dominated by soil unevenness or a mode mainly enhanced by the proximity effect. The reason for using the tensor decomposition as a specific mathematical tool to process the stacked deviation data is that traditional principal component analysis and other methods cannot effectively mine the rich associated information contained in the three-dimensional data structure. The deviation matrix of a single working condition is obtained by comparing COMSOL high-fidelity simulation with Carson-Clem formula, but this is only a single point data. When the deviation matrices of hundreds or thousands of such working conditions are stacked into a three-dimensional tensor, an associated network along the working condition, matrix row, and matrix column directions is naturally formed in the interior. The tensor decomposition can simultaneously and cooperatively mine the potential laws in these three directions, which cannot be achieved by matrix decomposition methods. It should be noted that the three factor matrices obtained by decomposition each have a clear physical and functional direction. Each row of the working condition characteristic factor matrix corresponds to a specific typical laying working condition, and each column represents a potential common deviation mode learned from the global data, such as a mode dominated by soil unevenness, a mode enhanced by proximity electromagnetic coupling, or a mode affected by the sheath loop current. The values in this matrix quantify the correlation between each specific historical working condition and these common deviation modes. The row characteristic factor matrix and the column characteristic factor matrix jointly and finely depict how each common deviation mode is specifically manifested in each row index and column index position of the impedance matrix. In other words, the three factor matrices jointly constitute a set of deviation mode dictionary and its instruction manual. The row characteristic factor matrix and the column characteristic factor matrix jointly depict the specific manifestation of each deviation mode in the row and column structure of the impedance matrix. Through this decomposition, the complex deviation law originally implied in a large amount of data is explicitly represented as several explainable deviation modes and their combination relationships, which lays a data-driven theoretical foundation for subsequent rapid construction of correction subspaces for any new working condition.

[0019] Step 2: tensor decomposition is performed on the three-dimensional impedance deviation tensor to obtain a core tensor and a plurality of factor matrices, a target working condition is determined based on the to-be-tested high-voltage cable, a theoretical impedance matrix of the target working condition is calculated through an analytical formula, and a basis vector associated with a feature of the target working condition is extracted from the factor matrices to dynamically construct a low-dimensional correction subspace in combination with the theoretical impedance matrix as a reference point; In the specific embodiment, the core purpose of this step is to efficiently apply the systematic deviation mode knowledge learned in the historical typical laying working conditions to any new target working condition to realize rapid and high-precision correction of the impedance parameters. This method avoids repeatedly performing high-computational-cost simulation analysis for each new target working condition, but instead converts the correction problem into a rapid optimization problem in a low-dimensional space by constructing a low-dimensional correction subspace with clear physical meaning, thereby greatly improving the computational efficiency while ensuring accuracy. The reason for performing tensor decomposition on the three-dimensional impedance deviation tensor and extracting the factor matrices therefrom is that the factor matrices obtained by decomposition actually constitute a deviation mode knowledge base. Among them, the working condition feature factor matrix encodes the association between different typical laying working conditions and potential deviation modes; and the row feature factor matrix and the column feature factor matrix jointly describe the specific spatial distribution form of each deviation mode in the impedance matrix. The construction of the low-dimensional correction subspace specifically includes: The characteristic parameters of the target working condition are received as input data, the theoretical impedance matrix of the target working condition is calculated through an analytical formula, and this theoretical impedance matrix is set as a reference point. Specifically, the characteristic parameters of the target working condition to be analyzed are received, which are completely identical to the categories defining the typical laying working conditions, including soil resistivity, cable spacing, and laying depth. Subsequently, the same electromagnetic analytical formula, such as the Carson-Clem formula, is called, the cable body parameters (geometric size, material properties) of the target working condition and the above characteristic parameters are input, and the theoretical impedance matrix of the target working condition is calculated, denoted as This theoretical impedance matrix represents the initial estimate of the impedance of the target working condition under the assumption of a simplified model, and is established as the reference point for subsequent correction. According to the characteristic parameters of the target working condition, the associated column vectors are selected from the working condition feature factor matrix as weights reflecting the deviation modes, and the selected weights are combined with the row feature factor matrix and the column feature factor matrix for combination operation to generate a group of basis vectors for the target working condition. Specifically, the characteristic parameter vector of the target working condition is The similarity is calculated with each row of the working condition feature factor matrix , such as cosine similarity, and the indices of the top typical laying working conditions with the highest similarity are selected; according to the an index, from the working condition characteristic factor matrix corresponding column vectors , each column vector represents the weight of a potential deviation mode; The column vectors of the weights of these deviation modes are combined with the obtained row characteristic factor matrix and column characteristic factor matrix which describe how the deviation modes are distributed inside the impedance matrix, to dynamically synthesize a set of base vectors for the current target working condition , and the mathematical formula is: wherein, is the element of the column vector , indicating the association strength between the related typical laying working condition matched according to the target working condition characteristics and the potential deviation mode, and are the and column vectors of , respectively, describing the spatial form of the deviation mode in the row and column directions of the impedance matrix, represents the outer product operation, which is used to combine the row and column characteristics into a complete matrix form of the base vector; is the total number of potential deviation modes, which is determined by the decomposition rank preset when the three-dimensional impedance deviation tensor is decomposed in step 1, representing the number of independent deviation modes learned from all typical laying working condition data, which determines the fineness of the knowledge base, The larger the value is, the stronger the description ability of the deviation is, but the calculation complexity also increases accordingly; is the index of the potential deviation mode, indicating the potential deviation mode, and the value range is from 1 to , in the summation process, all potential deviation modes are combined according to the weights; is the index of the base vector, indicating the related typical laying working condition matched according to the target working condition characteristics, and the value range is from 1 to ( is the number of selected related typical laying working conditions, ) ; is a complex matrix, which reflects the main deviation mode contained in the rth correlated typical laying condition, and its spatial distribution form on the specific structure (row, column position) of the impedance matrix, The larger the value is, the more significant the rth deviation mode in the correlated typical laying condition is, and the greater its contribution weight is when synthesizing the basis vector; The linear space spanned by the set of basis vectors with the reference point as the origin is the low-dimensional modified subspace, and any candidate impedance matrix in the modified subspace is generated by linear combination of the reference point and the set of basis vectors with a set of coordinate coefficients; The weighted Frobenius norm between the candidate impedance matrix generated in the modified subspace and the impedance measurement value of the target condition is taken as the main optimization target, and the L2 norm of the coordinate coefficient vector is introduced as a regularization constraint term to jointly constitute the objective function for fast optimization and solution; Specifically, with the reference point as the origin, the linear space spanned by the above-synthesized basis vectors is defined as the low-dimensional modified subspace under the target condition, Any candidate impedance matrix in the modified subspace can be generated by the following linear combination formula: wherein, is called the coordinate coefficient, represents a modified candidate impedance matrix, and the difference between the modified candidate impedance matrix and the reference point is completely determined by This decision, the coordinate coefficient reflects the intensity of the basis vector generated by the rth correlated typical laying condition being activated in the current modification; is the number of correlated typical laying conditions and basis vectors, and this value is the number of typical laying conditions most relevant to the target condition selected according to the similarity threshold or the preset number in the feature matching link of step 2, which determines the dimension of the low-dimensional modified subspace constructed for the current target condition; It should be particularly noted that the larger the absolute value of the coordinate coefficient is, the greater the contribution of the deviation mode to the final modified result is, and the positive or negative sign indicates whether the deviation increases or decreases the impedance value, is a fixed basis, and is a free variable to be optimized; by optimizing only these low-dimensional Instead of all elements of the whole impedance matrix, so as to ensure the high efficiency of the calculation, the physical credibility of the results and the strong adaptability to new working conditions at the same time.

[0020] Step 3: Through the quick and simplified simulation of the high-voltage cable to be measured to obtain its impedance measurement value, the error minimization between the candidate impedance matrix generated in the correction subspace and the impedance measurement value is taken as the optimization target to perform quick optimization, and the optimal coordinate coefficient is solved; The quick optimization to solve the optimal coordinate coefficient specifically includes: Through the quick and simplified simulation of the high-voltage cable to be measured to obtain its impedance measurement value, the quick and simplified simulation refers to solving by establishing a two-dimensional axisymmetric model of the cable, and the calculation speed is higher than that of the high-fidelity electromagnetic field simulation; In the low-dimensional correction subspace, a target function is constructed by taking the coordinate coefficient as the optimization variable, and the target function is used to measure the difference between the candidate impedance matrix and the impedance measurement value; the target function simultaneously contains a regularization constraint term based on the coordinate coefficient; in the low-dimensional parameter space composed of the coordinate coefficient, a numerical optimization algorithm is executed to perform iterative search, so as to minimize the target function, and finally a set of optimal coordinate coefficients is solved; Specifically, the measurement value of part of the impedance elements under the target working condition of the high-voltage cable to be measured is obtained by performing quick and simplified simulation on the target working condition, and is denoted as ; The reason why the quick and simplified simulation is introduced to obtain the impedance measurement value instead of directly using the high-fidelity simulation is the pragmatic consideration based on engineering efficiency, and the quick and simplified simulation refers to establishing a two-dimensional axisymmetric model of the cable in the professional software or performing calculation by using the quasi-static electromagnetic field approximation. This model ignores the complex full three-dimensional coupling effects in the actual laying, such as strict electromagnetic interference between cables, irregular ground boundary, etc., but due to the extremely simplified model geometry and calculation grid, the solving speed is several orders of magnitude faster than that of the high-fidelity three-dimensional full coupling simulation, and it can be completed within several seconds to several minutes. Although the result is slightly inferior to the high-fidelity simulation in absolute accuracy, it can quickly provide valuable impedance reference data reflecting the main electromagnetic trend of the current working condition; In the low-dimensional correction subspace, the optimization target is to find a set of optimal coordinate coefficients to form the coordinate coefficient vector , so that the candidate impedance matrix generated by the formula is as consistent as possible with the impedance measurement value obtained by the quick simulation; In order to achieve this goal, a target function for quick optimization is constructed, and the formula is as follows: , wherein To measure the mapping operator, since fast simplified simulation can only provide reliable values of partial impedance elements (e.g. self-impedance of main cable core), The role is to extract the matrix elements corresponding to the effective data from the complete candidate matrix , so as to ensure that the comparison is carried out on the same element set; The Frobenius norm of the matrix is used to measure the sum of the squares of the differences of all corresponding elements of the two matrices, and the smaller the value, the higher the overall consistency of the candidate matrix with the measured data; The value of the fitting term in the formula directly reflects the degree of deviation of the candidate impedance matrix from the measured data, and the smaller the value, the more consistent the corrected impedance prediction with the fast simulation result; The L2 norm of the vector, i.e. the Euclidean norm, is used to measure the size of the coordinate coefficient vector, The regularization parameter is used to control the strength of the regularization term; the regularization term acts as a stabilizer to prevent the optimization process from producing an over-fitted solution that is physically unreasonable or numerically unstable due to excessive matching of limited measured data containing noise or errors; The L2 norm (Euclidean norm) of the coordinate coefficient vector measures the size of the vector, and the fitting term drives the optimization solution to match the generated impedance matrix to the measured data of the target working condition, ensuring the accuracy of the correction result for the current working condition, and the regularization term restricts the amplitude of the coordinate coefficient vector , which includes preventing excessive fitting of limited measured data containing noise or errors, and implicitly assuming that the true deviation should be combined by a moderate coefficient rather than an extreme combination; The larger the regularization parameter , the stronger the restriction on the amplitude of the coefficient, and the more conservative the optimization result tends to be small correction; The smaller, the larger the correction amplitude is allowed to better fit the data, and the regularization parameter needs to be selected according to the data quality and engineering experience of the specific problem, and its value range is between 0.01 and 1.0 for debugging, in order to achieve the best balance between avoiding overfitting and fully fitting the data; Since the optimization variable is only a low-dimensional coordinate coefficient vector , whose dimension is much smaller than 10, numerical optimization algorithms such as conjugate gradient method or quasi-Newton method can be efficiently executed in low-dimensional parameter space, and the whole optimization process aims to minimize the objective function , and finally outputs the value that makes ​Minimum or optimal coordinate coefficient vector that satisfies the convergence condition .

[0021] Step 4: Substitute the optimal coordinate coefficients into the generation expression of the modified subspace to synthesize the complete impedance matrix, which is then output as the final high-precision impedance parameter calculation result. The synthesis and output of a high-precision impedance matrix specifically includes: The optimal coordinate coefficients obtained by the solution are substituted into the generation expression of the modified subspace, linearly combined with the basis vectors, and the results are superimposed on the reference point to synthesize a complete and high-precision impedance matrix. The synthesized impedance matrix is ​​then subjected to physical constraint verification, which includes checking the symmetry of the matrix and the positive definiteness of the main diagonal elements. The impedance matrix that passes the test will be output as the final high-precision impedance parameter calculation result for the target working condition. The reason why a rigorous physical constraint check must be performed after synthesizing the impedance matrix is ​​that any impedance parameter used for actual power grid analysis must obey the basic laws of electromagnetics and circuit theory. A physically realizable impedance matrix representing a passive cable system must satisfy two core characteristics: first, complex symmetry, that is, the matrix should be equal to its own conjugate transpose, which reflects the principle of electromagnetic reciprocity; second, the positive definiteness of its real matrix, that is, all eigenvalues ​​are positive, which ensures that the cable system behaves as an energy-consuming element rather than an energy-supplying element, which conforms to the law of conservation of energy. If this check is ignored and the mathematically synthesized result is directly output, it will lead to physical paradoxes or numerical non-convergence in the subsequent calculation of current distribution, loss and temperature rise, thereby causing engineering design risks. Specifically, the following logic applies: First, the optimal coordinate coefficients obtained by rapid optimization are linearly combined with the basis vectors dynamically generated for the target working condition according to the definition of subspace to calculate the total correction amount. Then, this correction amount is superimposed on the established reference point, i.e., the theoretical impedance matrix of the target working condition. The specific process includes solving the optimal coordinate coefficient vector. Substitute the already defined modified subspace generation expression: Calculate the correction amount Each item Indicates activation The calculated correction amount With reference point By adding them together, we obtain the final high-precision impedance parameters. ; Table 1 shows the specific data for some operating condition numbers and the final high-precision impedance parameter norms.

[0022] Table 1 Statistical data Through the analysis of the updated data, the high-voltage cable impedance calculation presents a clearer mathematical relationship between the parameters and the engineering trend. The norm of the reference point is used as the starting point for correction, and its size basically determines the order of magnitude of the final high-precision impedance parameter norm. For example, in working condition 8, the final impedance norm is also at a high level because the norm of the reference point is high. In working condition 5, the final impedance norm is also relatively low because the norm of the reference point is low. This confirms that the theoretical impedance estimation is the physical basis of the correction process. When analyzing the influence of the number of basis vectors on the correction amplitude, the data shows that when the number of basis vectors is large (such as working conditions 4 and 8), the difference between the final impedance norm and the reference point norm is larger, meaning that the correction that integrates more deviation modes can make more significant adjustments to the theoretical value. Conversely, when the number of basis vectors is small (such as working conditions 5 and 11), the difference is relatively small, and the correction amplitude is more conservative. This reflects the correlation between the dimension of the correction subspace and the adjustment capability. The mean of the absolute values of the coordinate coefficients directly reflects the integrated activation strength of the deviation modes. The data shows that there is an obvious cooperative change trend between this mean and the difference between the final impedance norm and the reference point norm. For example, in working conditions with a larger mean (such as working conditions 2 and 4), the correction amplitude is also more significant. In working conditions with a smaller mean (such as working conditions 5 and 15), the correction amplitude is relatively limited. This shows that the optimal coordinate coefficients obtained by optimization effectively quantify the specific contribution of each deviation mode to the current target working condition, thereby achieving precise and nonlinear deviation compensation.

[0023] After synthesizing the complete matrix, the system automatically performs the above physical constraint verification. For symmetry, the difference norm between the matrix and its conjugate transpose is calculated for judgment. For positive definiteness, the eigenvalues of the real part matrix are checked. Once a violation of the constraint is found, the fine-tuning mechanism is triggered (such as the nearest symmetric positive definite projection of the matrix) to ensure the physical reliability of the output results. In the specific implementation, if the synthesized impedance matrix fails to pass the physical constraint verification, it indicates that the current correction result is mathematically optimal but physically unachievable. The specific processing follows the diagnosis and iteration process. First, automatically diagnose the violation type: if the difference between the impedance matrix and its conjugate transpose exceeds the threshold, it is determined that the complex symmetry is not satisfied. If there is a significant negative eigenvalue in the real part matrix, it is determined that the positive definiteness is not satisfied. According to the diagnosis result, perform hierarchical processing: for slight deviations, prefer automated numerical correction, such as enforcing Hermite symmetry through symmetric projection or eliminating negative eigenvalues through nearest positive semi-definite projection of the real part matrix, and re-verify after correction. If the deviation is serious or the automatic correction is invalid, it indicates that the current construction of the correction subspace is insufficient to accurately cover the real physical state of the target working condition, at which time the iterative reconstruction process is triggered: the subspace dimension is expanded, i.e. the number of relevant basis vectors is increased, the subspace is reconstructed again, and the fast optimization is performed again in the subspace to solve new optimal coordinate coefficients, and then the synthesis and verification are performed again, and the process can continue until the result passes the physical constraints; Finally, the impedance matrix that passes the verification is converted into a standardized and structured data format (such as a common data file or a database entry) as the final high-precision impedance parameter calculation result of the target working condition, which is directly imported into the cable system design software, the power flow calculation program or the short-circuit analysis tool for accurate calculation of the current distribution of the parallel cable, evaluation of the current sharing effect, prediction of the line loss and temperature rise, thereby providing key inputs for engineering design and operation decision-making.

[0024] The above formulas are dimensionless numerical calculations, and the formulas are obtained by software simulation of a large amount of data to obtain a formula closest to the real situation, and the preset parameters in the formula are set by a person skilled in the art according to the actual situation.

[0025] The above embodiments can be realized wholly or partially by software, hardware, firmware or any combination thereof. When realized by software, the above embodiments can be realized wholly or partially in the form of a computer program product. Those skilled in the art can realize that the units and algorithm steps of the examples described in connection with the embodiments disclosed herein can be realized by electronic hardware or a combination of computer software and electronic hardware. Whether the functions are realized by hardware or software methods depends on the specific application and design constraints of the technical solutions.

[0026] The units described as separate components can or can not be physically separated, and the components shown as units can or can not be physical units, which can be located in one place or distributed on multiple network units. Part or all of the units can be selected to achieve the purpose of the embodiments according to actual needs.

[0027] The above is merely a specific implementation of the present application, but the protection scope of the present application is not limited thereto, and any person skilled in the art can easily think of changes or replacements within the technical range disclosed in the present application, which should be covered within the protection scope of the present application.

Claims

1. A method of calculating impedance parameters of a high voltage cable, characterized by, The specific steps include: Step 1: Construct a high-voltage cable condition set of multiple typical laying conditions in a computer, extract a reference impedance matrix of each typical laying condition based on high-fidelity electromagnetic field simulation, calculate a theoretical impedance matrix thereof through an analytical formula, calculate a deviation matrix of the two, and stack the deviation matrices of all typical laying conditions to form a three-dimensional impedance deviation tensor; Step 2: Tensor decomposition is performed on the three-dimensional impedance deviation tensor to obtain a core tensor and multiple factor matrices, a target condition is determined based on a high-voltage cable to be measured, a theoretical impedance matrix of the target condition is calculated through an analytical formula, a basis vector associated with a characteristic of the target condition is extracted from the factor matrices, and a low-dimensional correction subspace is dynamically constructed in combination with the theoretical impedance matrix as a reference point; Step 3: A fast and simplified simulation is performed on the high-voltage cable to be measured to obtain an impedance measurement value, a fast optimization is performed with minimization of an error between a candidate impedance matrix generated in the correction subspace and the impedance measurement value as an optimization objective, and optimal coordinate coefficients are solved; Step 4: The optimal coordinate coefficients are substituted into a generated expression of the correction subspace to synthesize a complete impedance matrix, which is output as a final high-precision impedance parameter calculation result.

2. The method of claim 1, wherein: The three-dimensional impedance deviation tensor is constructed and tensor decomposition is performed, specifically including: A high-voltage cable condition set of multiple typical laying conditions is constructed, and the high-voltage cable condition set is a sample set composed of multiple typical laying conditions, wherein each typical laying condition is uniquely determined by a set of characteristic parameters, and the characteristic parameters include soil resistivity, cable spacing and laying depth; For each typical laying condition in the high-voltage cable condition set, a reference impedance matrix is extracted through high-fidelity electromagnetic field simulation, and the high-fidelity electromagnetic field simulation includes: 1) based on the geometric parameters and material properties of the high-voltage cable, and by introducing the electromagnetic environment defined by the soil resistivity, cable spacing and laying depth of the typical laying condition, a three-dimensional model including the cable core, insulation layer, metal shielding layer, outer sheath and surrounding soil domain is established, 2) ideal electric conductor boundary conditions and absorption boundary conditions are set to simulate an infinite region, and 3) a frequency domain solver is used to solve Maxwell equations at power frequency; based on the electromagnetic field distribution data obtained by solving, the open-short circuit method is used to calculate and extract the self-impedance and mutual impedance per unit length to form the reference impedance matrix; Based on the geometric parameters and material properties of the high-voltage cable used in the above high-fidelity electromagnetic field simulation, a theoretical impedance matrix is calculated for each typical laying condition through an analytical formula; For each typical laying condition, the reference impedance matrix thereof is subtracted from the corresponding theoretical impedance matrix to obtain a deviation matrix of the typical laying condition, and the deviation matrices under all typical laying conditions are stacked according to the condition index to form a three-dimensional impedance deviation tensor, wherein the three dimensions of the tensor correspond to the row index, the column index and the condition index of the deviation matrix, respectively. The three-dimensional impedance deviation tensor is decomposed by using a tensor decomposition algorithm to obtain a core tensor and three factor matrices, the three factor matrices being a work condition characteristic factor matrix representing the correlation between deviation modes in different typical laying conditions, a row characteristic factor matrix representing the correlation between row elements of the deviation matrix, and a column characteristic factor matrix representing the correlation between column elements of the deviation matrix.

3. The method of claim 2, wherein: The construction of the low-dimensional correction subspace specifically comprises: Receiving the characteristic parameters of the target work condition as input data, calculating the theoretical impedance matrix of the target work condition by using an analytical formula, and setting the theoretical impedance matrix as a reference point; According to the characteristic parameters of the target work condition, selecting the associated column vectors from the work condition characteristic factor matrix as weights reflecting the deviation modes, and performing combination operation on the selected weights and the row characteristic factor matrix and the column characteristic factor matrix to generate a set of basis vectors for the target work condition; Taking the reference point as the origin, the linear space spanned by the set of basis vectors is the low-dimensional correction subspace, and any candidate impedance matrix in the correction subspace is generated by linear combination of the reference point and the set of basis vectors with a set of coordinate coefficients.

4. The method of claim 3, wherein: The fast optimization to solve the optimal coordinate coefficients specifically comprises: Obtaining the impedance measurement value of the high-voltage cable to be measured by performing fast simplified simulation on the high-voltage cable, the fast simplified simulation being to establish a two-dimensional axisymmetric model of the cable for solving, and the calculation speed being higher than that of high-fidelity electromagnetic field simulation; In the low-dimensional correction subspace, taking the coordinate coefficients as optimization variables to construct an objective function, the objective function being used to measure the difference between the candidate impedance matrix and the impedance measurement value; the objective function simultaneously contains a regularization constraint term based on the coordinate coefficients, and a numerical optimization algorithm is executed in the low-dimensional parameter space composed of the coordinate coefficients to iteratively search to minimize the objective function, and finally a set of optimal coordinate coefficients is solved.

5. A method of calculating impedance parameters of a high voltage cable according to claim 4, characterized in that: Synthesizing and outputting the high-precision impedance matrix specifically comprises: Substituting the solved optimal coordinate coefficients into the generation expression of the correction subspace, performing linear combination with the basis vectors, and superimposing the result on the reference point to synthesize a complete high-precision impedance matrix, performing physical constraint verification on the synthesized impedance matrix, the physical constraints including checking the symmetry of the matrix and the positive definiteness of the main diagonal elements; The impedance matrix that passes the verification is output as the final high-precision impedance parameter calculation result of the target work condition.

6. The method of claim 2, wherein: The specific manner of tensor decomposition processing comprises: The tensor decomposition adopts a Tucker decomposition algorithm, the Tucker decomposition algorithm decomposes the three-dimensional impedance deviation tensor into a product form of a core tensor and three factor matrices, wherein each row of the work condition characteristic factor matrix corresponds to a typical laying condition, and each column represents a deviation mode of a potential typical laying condition; The row characteristic factor matrix and the column characteristic factor matrix jointly represent the variation law of the internal elements of the deviation matrix under various deviation modes.

7. The method of claim 4, wherein: The construction manner of the optimization objective function comprises: The weighted Frobenius norm between the generated candidate impedance matrix in the modified subspace and the impedance measurement value of the target working condition is taken as the main optimization target, and the L2 norm of the coordinate coefficient vector is introduced as a regularization constraint term to jointly constitute the objective function for fast optimization solution.

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