A Fusion Calculation Method Considering Cable Grounding Loop Current

Abstract

The invention discloses a fusion calculation method taking into account cable grounding loop current, which relates to the field of cable technology, including: S1, constructing a target entity model of the cable based on the grounding properties of the power cable; S2, constructing an equivalent circuit model of cable cross-interconnection transposition grounding according to the target entity model; S3, establishing a grounding loop current matrix equation based on equivalent resistance and equivalent current of the equivalent circuit model combined with key characteristic parameters of the cable; S4, performing fusion calculation on the grounding loop current matrix equation based on finite element-wavelet gridless hybrid and energy perturbation to obtain numerical calculation results of the grounding loop current; solving the problems that a single finite element method has great limitations in complex calculation scenarios and is difficult to calculate accurate values, and that a single gridless method cannot handle interpolation functions and requires additional conditions to cause calculation complexity, significantly improving the calculation efficiency and reliability of the cable grounding loop current, and realizing that the cable loop current calculation improves the calculation efficiency while taking into account the calculation accuracy.

Description

Technical Field

[0001] The invention relates to the field of cable technology, and in particular to a fusion calculation method taking cable grounding loop current into account. Background Art

[0002] Power cables have been widely used in urban power grid transmission due to their advantages of small footprint and stable performance. When an alternating current passes through the cable core conductor, the core current will generate an alternating electromagnetic field around it, forming a magnetic flux that intersects the core conductor and the metal sheath at the same time. According to Faraday's law of electromagnetic induction, the metal sheath of the cable will inevitably have an induced electromotive force. When the metal sheath of the cable and the earth or the return line form an effective closed loop, a metal sheath loop current will be formed. The existence of ground loop current will affect the service life of the cable and reduce the current carrying capacity of the cable core.

[0003] At present, the calculation methods of grounding loop current of power cables mainly include analytical calculation method and numerical calculation method. When calculating grounding loop current by analytical calculation method, it is first necessary to establish an equivalent circuit model for grounding loop current calculation according to the grounding method of the cable; then, derive the parameter calculation formula of the circuit model based on the relevant electromagnetic field theory; finally, solve the circuit model to obtain the analytical solution of the cable grounding loop current. The numerical method uses numerical methods, such as finite element method, to directly calculate the electromagnetic field and loop current of the cable under grounding conditions. The analytical method has high calculation efficiency, but for power cables with complex laying conditions, the analytical method is difficult to meet engineering requirements in terms of model parameters and the calculation accuracy of loop current. The numerical calculation method has high calculation accuracy, but requires huge computing resources, especially for the calculation of modern power cable loop current. This method has the disadvantages of poor adaptability to complex laying methods, low accuracy, grid distortion, discrete error accumulation, and low solution convergence during parameter numerical calculation.

[0004] The patent "Method for Calculating Ground Loop Current of Cable Metal Sheath Based on Multi-conductor Transmission Line Theory", publication number: CN114034905A, publication date: February 11, 2022, discloses: By taking the earth as the reference conductor No. 0, a unit length equivalent circuit model of the transmission line consisting of n+1 conductors including the cable core, cable metal sheath and earth loop is established; the multi-conductor transmission line equation is derived according to the equivalent circuit model, and the general solution of the multi-conductor transmission line equation is derived; the undetermined constants in the general solution of the multi-conductor transmission line equation are calculated, and the special solution of the multi-conductor transmission line equation is calculated to obtain the induced voltage and induced current of the cable metal sheath. However, this scheme mainly models the cable core and its corresponding cable metal sheath as two independent conductors, which is only suitable for the calculation of ground loop current under simple laying conditions, and has poor adaptability to complex laying methods. Summary of the invention

[0005] The present invention aims at the limitation that conventional cable circulation calculation methods cannot take into account both calculation efficiency and calculation accuracy when dealing with complex laying methods; a fusion calculation method taking into account cable grounding circulation is proposed, by constructing a target entity model of the cable, and then obtaining an equivalent circuit model of cable cross-interconnection and transposition grounding; a grounding circulation matrix equation is established according to the equivalent resistance and equivalent current of the equivalent circuit combined with the key characteristic parameters of the cable; based on the finite element-wavelet gridless hybrid and energy perturbation, the grounding circulation matrix equation is fused and calculated to obtain the numerical calculation result of the grounding circulation, which solves the problems that a single finite element method has great limitations in complex calculation scenarios and is difficult to calculate accurate values, and a single gridless method cannot handle the interpolation function and needs to add additional conditions, resulting in complicated calculations, significantly improves the calculation efficiency and reliability of the cable grounding circulation, and realizes that the cable circulation calculation improves the calculation efficiency while taking into account the calculation accuracy.

[0006] In order to solve the above technical problems, the technical solution adopted by the present invention is: a fusion calculation method taking into account the cable grounding loop current, comprising the following steps:

[0007] S1. Construct a target entity model of the cable based on the grounding properties of the power cable;

[0008] S2. constructing an equivalent circuit model of cable cross-connection transposition grounding according to the target entity model;

[0009] S3, establishing a ground loop current matrix equation based on the equivalent resistance and equivalent current of the equivalent circuit model combined with key characteristic parameters of the cable;

[0010] S4. Based on finite element-wavelet meshless hybrid and energy perturbation, a fusion calculation is performed on the ground circulation matrix equation to obtain a numerical calculation result of the ground circulation.

[0011] In this scheme, by constructing the target entity model of the cable, the structure of the cable system can be intuitively presented, providing a specific object for subsequent circuit equivalence and calculation; by constructing an equivalent circuit model of cable cross-interconnection and transposition grounding, the complex physical cable system can be converted into a circuit model that is easy to analyze, and the relationship between electrical parameters such as current and voltage can be more easily established, providing a basis for the subsequent establishment of mathematical equations; by establishing the ground loop matrix equation, the coupling relationship and quantitative relationship between the various electrical parameters of the cable can be comprehensively considered, and the mathematical relationship between the ground loop and other electrical parameters can be accurately described, providing a mathematical model basis for the accurate calculation of the ground loop; by combining the finite element method with the wavelet meshless method, the finite element method can be effectively avoided in dealing with complex When complex geometric shapes and boundary conditions are encountered, mesh division may become very complicated, and the mesh quality will affect the calculation accuracy. It also avoids the problems of low calculation efficiency and poor calculation stability of the meshless method, significantly improving the calculation efficiency of cable circulation. At the same time, through energy perturbation, it can handle the changes in circulation caused by small energy changes in the cable electromagnetic field, ensuring more accurate grounding circulation values. The grounding circulation matrix equation is solved by a hybrid method, which achieves the goal of improving calculation efficiency while taking into account calculation accuracy, overcoming the limitations of conventional cable circulation calculation methods in dealing with complex laying methods, such as grid distortion, cumulative increase of discrete errors, and the inability to take into account both calculation efficiency and calculation accuracy, further ensuring the reliability of cable circulation calculations.

[0012] Preferably, S1 comprises the following sub-steps:

[0013] Establish a cable model based on the actual structure, actual grounding method and grounding position of the power cable;

[0014] The cable model is meshed and an electromagnetic field distribution simulation is performed, and the cable model is adjusted and optimized according to the simulation results to obtain a target entity model of the cable.

[0015] Preferably, S2 comprises the following sub-steps:

[0016] Draw the electrical wiring diagram corresponding to the cross-connection and grounding of the cables based on the target entity model and the key characteristic parameters of the cables;

[0017] An equivalent circuit diagram is established according to the electrical wiring diagram to obtain an equivalent circuit model.

[0018] Preferably, S3 includes the following sub-steps:

[0019] The self-impedance of the metal sheath of each cable segment is calculated based on the self-inductance per unit length of the loop formed by the metal sheath of each cable segment and the ground, the metal sheath resistance and the angular frequency;

[0020] Constructing a grounding loop current equation group of the cable metal sheath according to the self-impedance and induced voltage of each section of the cable metal sheath combined with the equivalent resistance and equivalent current of the equivalent circuit model;

[0021] A grounding circulation matrix equation is established based on the grounding circulation loop equation group.

[0022] Preferably, the calculation formula of the grounding loop equation group is as follows:

[0023] ;

[0024] In the formula, It represents the induced voltage generated by the current of the i-th section of the core conductor of phase A on the metal sheath. It represents the induced voltage generated by the current of the i-th section of the core conductor of phase B on the metal sheath. It represents the induced voltage generated by the current of the core conductor of the i-th section of the C phase on the metal sheath; is the induced voltage generated by the circulating current of the B-phase and C-phase metal sheaths on the i-th metal sheath, is the induced voltage generated by the circulating current of phase A and phase C on the metal sheath of the i-th section, is the induced voltage generated by the circulating current of the metal sheath of phase A and phase B on the i-th section of the metal sheath; i represents the first, second and third sections of the cable line in the metal sheath cross-connection system, and the corresponding values ​​are 1, 2 and 3; is the self-impedance of the metal sheath of the i-th section of the A-phase cable, is the self-impedance of the metal sheath of the i-th section of the B-phase cable, is the self-impedance of the metal sheath of the i-th section of the C-phase cable; is the ground loop current of the metal sheath of phase A, is the ground loop current of the B-phase metal sheath, is the ground loop current of the C phase metal sheath; is the equivalent current of the equivalent circuit model; is the equivalent resistance of the equivalent circuit model.

[0025] Preferably, establishing a grounding circulation matrix equation based on the grounding circulation loop equation group includes:

[0026] Establishing a grounding loop current column vector based on the grounding loop current of each phase metal sheath;

[0027] Construct the self-impedance coefficient matrix based on the self-impedance on the cable metal sheath;

[0028] The induced electromotive force column vector is constructed based on the induced voltage generated by the core conductor current on the metal sheath of each phase cable;

[0029] A grounding circulation matrix equation is constructed by fusing the grounding circulation column vector, the self-impedance coefficient matrix and the induced electromotive force column vector.

[0030] Preferably, each element in the self-impedance coefficient matrix is ​​calculated based on the angular frequency of the cable, the equivalent resistance of the equivalent circuit model, and the inductance parameters.

[0031] Preferably, the ground loop current matrix equation calculation formula is as follows:

[0032] ;

[0033] In the formula, represents the self-impedance coefficient matrix, represents the ground loop current column vector, represents the induced electromotive force column vector.

[0034] In this scheme, the self-impedance on the cable metal sheath reflects the metal sheath's own resistance to current. The mutual influence relationship between the metal sheaths of each phase can be described by constructing a self-impedance coefficient matrix. In matrix form, the current distribution and circulating current changes caused by the self-impedance in the cable, as well as the correlation with other inductance parameters, can be systematically considered, providing important parameter basis for accurately establishing the grounding loop current equation; by combining the induced voltage generated by the core conductor current on the metal sheath into a column vector, the electromagnetic induction effect of the core conductor current on the metal sheath can be quantified, so that the grounding loop current matrix equation can more accurately consider the influence of the electromagnetic induction effect on the circulating current, thereby ensuring the accuracy of the grounding loop current calculation results; by comprehensively considering the influence of various physical factors such as the cable's self-impedance and electromagnetic induction on the circulating current, an accurate mathematical model is provided for solving the grounding loop current.

[0035] Preferably, S4 includes the following sub-steps:

[0036] Taking the self-impedance coefficient matrix as the quantity to be determined, multi-scale decomposition is performed on it to obtain the function to be determined including the finite element shape function;

[0037] The function to be determined is transformed based on wavelet transform and finite element interpolation to establish a discrete algebraic equation group of finite element-wavelet meshless method;

[0038] Solving the discrete algebraic equations of the finite element-wavelet meshless method to obtain the magnetic field intensity and magnetic induction intensity of the cable;

[0039] Based on the energy perturbation method, the inductance parameter value is calculated by the magnetic field strength and the magnetic induction strength;

[0040] Substitute the inductance parameter value into the ground loop current matrix equation, and solve the ground loop current matrix equation to obtain the ground loop current value.

[0041] In this scheme, by multi-scale decomposition of the self-impedance coefficient matrix, the characteristics of self-impedance can be analyzed from different scales, which helps to have a deeper understanding of the electromagnetic characteristics of the cable system, so as to better use the finite element method to accurately calculate the inductance parameters. By introducing the finite element shape function, the physical field distribution in the cable system can be more accurately described, laying the foundation for subsequent accurate calculations. Wavelet transform has good time-frequency localization characteristics and can effectively deal with local mutations and complex boundary problems. Finite element interpolation has high calculation accuracy in regular areas. Combining the two to transform the function to be calculated is to comprehensively utilize the advantages of wavelet transform and finite element interpolation to establish a discrete algebraic equation group that is more in line with the actual situation of the cable system. Compared with a single method, it reduces the error in numerical calculation and improves the accuracy and reliability of calculation. Combined with the energy perturbation method, the inductance parameter value can be calculated more accurately to more accurately reflect the inductance characteristics of the cable under actual operating conditions, and then improve the accuracy of ground loop current calculation through accurate inductance parameters, which helps to achieve more effective evaluation of the operating status and safety of the cable.

[0042] Preferably, the transforming of the function to be solved based on wavelet transform and finite element interpolation to establish a discrete algebraic equation system of finite element-wavelet meshless method includes:

[0043] The interpolation projection operator is used to project the function to be determined in the finite element space to obtain the interpolation scaling function to be determined;

[0044] Establishing a wavelet function based on the interpolation scale function to be determined, and constructing a wavelet basis function to be determined by fusing the interpolation scale function to be determined with the wavelet function;

[0045] Constructing a wavelet transform of the wavelet basis function to be determined based on a connection scaling method, and obtaining a refined basis expression of the wavelet basis function to be determined;

[0046] The refined basis expression is interpolated by using the standard finite element method, and the refined basis expression and the corresponding interpolation function are substituted into the weighted residual expression to obtain a discrete algebraic equation group of the finite element-wavelet meshless method.

[0047] In this scheme, the cable electromagnetic field is analyzed by hybrid finite element and wavelet meshless method, which overcomes the shortcomings of existing numerical calculation methods such as grid distortion, accumulation of discrete errors and low convergence of solutions during numerical calculation of parameters. It solves the problems of excessive demand for computing resources, limited applicable occasions and inability to balance computing efficiency and accuracy of single finite element or single wavelet meshless calculation method, and significantly improves the reliability, adaptability, computing accuracy and efficiency of cable grounding loop current calculation.

[0048] Beneficial effects of the present invention:

[0049] 1. By combining the finite element and wavelet meshless methods, the meshless method can effectively avoid the difficulties in meshing the finite element method due to complex geometric conditions such as cable cross-interconnection transposition and irregular grounding positions. The high computational efficiency of the finite element method in regular areas can be used to overcome the low computational efficiency of the meshless method and the computational stability problems that may be encountered when dealing with some large-scale problems. Finally, the advantages of the two methods are combined to make the calculation results more stable and accurate, and to achieve a better balance between computational efficiency and accuracy.

[0050] 2. By constructing the ground loop current matrix equation, the influence of various physical factors such as cable self-impedance and electromagnetic induction on the loop current is comprehensively considered. It can quantitatively analyze the ground loop current size of each phase metal sheath under given cable structure and operating parameters, providing an accurate mathematical model for solving the ground loop current. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Other features, objects and advantages of the present invention will become more apparent by reading the detailed description of non-limiting embodiments made with reference to the following drawings. The drawings are only for the purpose of illustrating preferred embodiments and are not to be considered as limiting the present invention. Also, the same reference symbols are used throughout the drawings to represent the same parts.

[0052] Figure 1 The present invention is a flowchart of a fusion calculation method taking into account cable grounding loop current according to an embodiment of the present invention.

[0053] Figure 2 A schematic diagram of a target entity model according to an embodiment of the present invention.

[0054] Figure 3 The present invention is a schematic diagram of electrical wiring when cables are cross-connected and grounded.

[0055] Figure 4 The figure is a schematic diagram of an equivalent circuit model of an embodiment of the present invention. DETAILED DESCRIPTION

[0056] 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 the accompanying drawings and embodiments. It should be understood that the specific implementation method described herein is only an optimal embodiment of the present invention, which is only used to explain the present invention and does not limit the scope of protection of the present invention. All other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0057] Some nouns or terms that appear in the description of the embodiments of the present application are subject to the following interpretations:

[0058] Bridging scale term: represents a bridging scale, which is used in multi-scale computing methods and is a technical means to connect calculations at different scales. When calculating at a refined scale, there will be a solution set that cannot be approximated by the current function space, which requires a mechanism to coordinate calculations at different scales. The core idea is to establish a reasonable connection between basis functions at different scales to ensure the consistency and linear independence of all basis functions after introducing refined basis functions, including finite element shape functions and wavelet bases.

[0059] Example 1: Figure 1 As shown, a fusion calculation method taking into account cable grounding loop current includes steps S1-S4, wherein:

[0060] S1. Build the target entity model of the cable based on the grounding properties of the power cable, where: Figure 2 As shown,

[0061] Establish a cable model based on the actual structure, actual grounding method and grounding position of the power cable;

[0062] The cable model is meshed and an electromagnetic field distribution simulation is performed, and the cable model is adjusted and optimized according to the simulation results to obtain a target entity model of the cable.

[0063] S2. Construct an equivalent circuit model of cable cross-connection transposition grounding according to the target entity model, wherein: Figure 3 and Figure 4 As shown,

[0064] Based on the target entity model and the key characteristic parameters of the cables, a corresponding electrical wiring diagram is drawn when the cables are cross-connected and grounded; an equivalent circuit diagram is established according to the electrical wiring diagram to obtain an equivalent circuit model.

[0065] Among them, the key characteristic parameters of the cable include at least the induced voltage, the metal sheath impedance, the metal sheath resistance, the self-inductance per unit length of the loop formed by the metal sheath and the earth, and the length of the section cable line.

[0066] S3. Establish a ground loop current matrix equation based on the equivalent resistance and equivalent current of the equivalent circuit model combined with key characteristic parameters of the cable.

[0067] Specifically, S3 includes the following sub-steps:

[0068] The self-impedance of the metal sheath of each cable segment is calculated based on the self-inductance per unit length of the loop formed by the metal sheath of each cable segment and the ground, the metal sheath resistance and the angular frequency;

[0069] Constructing a grounding loop current equation group of the cable metal sheath according to the self-impedance and induced voltage of each section of the cable metal sheath combined with the equivalent resistance and equivalent current of the equivalent circuit model;

[0070] A grounding circulation matrix equation is established based on the grounding circulation loop equation group.

[0071] Specifically, the calculation formula of the grounding loop equation group is as follows:

[0072] (1)

[0073] In the formula, It represents the induced voltage generated by the current of the i-th section of the core conductor of phase A on the metal sheath. It represents the induced voltage generated by the current of the i-th section of the core conductor of phase B on the metal sheath. It represents the induced voltage generated by the current of the core conductor of the i-th section of the C phase on the metal sheath; is the induced voltage generated by the circulating current of the B-phase and C-phase metal sheaths on the i-th metal sheath, is the induced voltage generated by the circulating current of phase A and phase C on the metal sheath of the i-th section, is the induced voltage generated by the circulating current of the metal sheath of phase A and phase B on the i-th section of the metal sheath; i represents the first, second and third sections of the cable line in the metal sheath cross-connection system, and the corresponding values ​​are 1, 2 and 3; is the self-impedance of the metal sheath of the i-th section of the A-phase cable, is the self-impedance of the metal sheath of the i-th section of the B-phase cable, is the self-impedance of the metal sheath of the i-th section of the C-phase cable; is the ground loop current of the metal sheath of phase A, is the ground loop current of the B-phase metal sheath, is the ground loop current of the C phase metal sheath; is the equivalent current of the equivalent circuit model; is the equivalent resistance of the equivalent circuit model.

[0074] Specifically, the calculation formula for the induced voltage generated by the current of the i-th section of the core conductor of each phase is as follows:

[0075] (2)

[0076] (3)

[0077] (4)

[0078] In the formula, is the induced current of phase A, is the induced current of phase B, is the C phase induced current; The inductance of the loop formed by the metal sheath of phase A and the earth. The inductance of the loop formed by the B-phase metal sheath and the ground. is the inductance of the loop formed by the C-phase metal sheath and the ground, j is an imaginary unit, express The length of the cable line segment, is the angular frequency.

[0079] Specifically, when the metal sheaths at both ends of the cable line are cross-connected and grounded, the induced voltage generated by the circulating current of the other two phases on the metal sheath of the i-th cable is , the calculation formula is as follows:

[0080] (5)

[0081] (6)

[0082] (7)

[0083] In the formula, Indicated in The mutual inductance per unit length of the loop formed by the metal sheath of phase A and phase B in the cable segment and the ground, Indicated in The mutual inductance per unit length of the loop formed by the metal sheath of phases B and C in the cable segment and the ground, Indicated in The mutual inductance per unit length of the loop formed by the metal sheath of phase A and phase C in a cable segment and the ground.

[0084] Specifically, the calculation formula of the self-impedance on the metal sheath of the i-th section of each phase cable is as follows:

[0085] (8)

[0086] (9)

[0087] (10)

[0088] In the formula, Phase A Cable metal sheath resistance, Phase B Cable metal sheath resistance, Phase C Resistance of metal sheath of cable segment; Phase A The self-inductance per unit length of the loop formed by the metal sheath of the cable segment and the ground. Phase B The self-inductance per unit length of the loop formed by the metal sheath of the cable segment and the ground. Phase C The self-inductance per unit length of the loop formed by the metal sheath of the cable segment and the ground; Phase A The self-inductance of the loop formed by the metal sheath of the cable segment and the ground. Phase B The self-inductance of the loop formed by the metal sheath of the cable segment and the ground. Phase C The self-inductance of the loop formed by the metal sheath of a cable segment and the ground.

[0089] Specifically, establishing a grounding circulation matrix equation based on the grounding circulation loop equation group includes:

[0090] Establishing a grounding loop current column vector based on the grounding loop current of each phase metal sheath;

[0091] Construct the self-impedance coefficient matrix based on the self-impedance on the cable metal sheath;

[0092] The induced electromotive force column vector is constructed based on the induced voltage generated by the core conductor current on the metal sheath of each phase cable;

[0093] A grounding circulation matrix equation is constructed by fusing the grounding circulation column vector, the self-impedance coefficient matrix and the induced electromotive force column vector.

[0094] Specifically, each element in the self-impedance coefficient matrix is ​​calculated based on the angular frequency of the cable, the equivalent resistance of the equivalent circuit model, and the inductance parameters.

[0095] Specifically, the ground loop current matrix equation calculation formula is as follows:

[0096] (11)

[0097] In the formula, represents the self-impedance coefficient matrix, represents the ground loop current column vector, represents the induced electromotive force column vector.

[0098] Furthermore, the calculation formula of the self-impedance coefficient matrix is ​​as follows:

[0099] (12)

[0100] (13)

[0101] (14)

[0102] (15)

[0103] (16)

[0104] (17)

[0105] In the formula, Indicates the current The length of the segment, is the length of the first section of cable phase A, is the length of the second section of cable phase A, is the length of the third section of cable phase A; is the length of the first section of cable phase B, is the length of the second section of cable phase B, is the length of the third section of cable phase B; is the length of the first section of cable phase C, is the length of the second section of cable phase C, is the length of the third section of cable phase C; is the resistance of the first section of cable phase A, is the resistance of the second section of cable phase A, is the resistance of the third section of cable phase A; is the resistance of the first section of cable phase B, is the resistance of the second section of cable phase B, is the resistance of the third section of cable phase B; is the resistance of the first section of cable phase C, is the resistance of the second section of cable phase C, is the resistance of the third section of cable phase C.

[0106] In this embodiment, the grounding circulation matrix equation uses the grounding circulation column vector when the metal sheaths of phases A, B, and C are cross-connected and grounded as the unknown quantity. The self-impedance on the metal sheath of the cable reflects the metal sheath's own resistance to current. By constructing a self-impedance coefficient matrix, the mutual influence relationship between the metal sheaths of each phase can be described. In the form of a matrix, the current distribution and circulation changes caused by the self-impedance in the cable, as well as the correlation with other inductance parameters, can be systematically considered, providing important parameter basis for accurately establishing the grounding circulation equation; by combining the induced voltage generated by the core conductor current on the metal sheath into a column vector, the electromagnetic induction effect of the core conductor current on the metal sheath can be quantified, so that the grounding circulation matrix equation can more accurately consider the influence of the electromagnetic induction effect on the circulation, thereby ensuring the accuracy of the grounding circulation calculation results; by comprehensively considering the influence of various physical factors such as the self-impedance and electromagnetic induction of the cable on the circulation, an accurate mathematical model is provided for solving the grounding circulation.

[0107] It can be understood that by combining the above-mentioned ground loop column vector, self-impedance coefficient matrix and induced electromotive force column vector to construct a matrix equation, the generation mechanism and mutual relationship of the cable ground loop can be described in a systematic and accurate mathematical form, providing an accurate mathematical model for solving the ground loop; the ground loop matrix equation physically describes the generation principle of the ground loop of each phase metal sheath in the cable system, and can quantitatively analyze the size of the ground loop of each phase metal sheath under given cable structure and operating parameters. In cable engineering design and operation and maintenance, it is of great significance to accurately calculate the ground loop. Excessive ground loop will cause the cable metal sheath to heat up and increase the loss, and may even affect the service life and operation safety of the cable. Through the ground loop matrix equation, the size of the ground loop can be predicted in the cable design stage, and the grounding method and structural parameters of the cable can be optimized to reduce the ground loop. In the operation and maintenance stage, this equation can be used to monitor and evaluate the operation status of the cable, and timely discover and solve problems caused by abnormal ground loop.

[0108] S4. Based on finite element-wavelet meshless hybrid and energy perturbation, a fusion calculation is performed on the ground circulation matrix equation to obtain a numerical calculation result of the ground circulation.

[0109] Specifically, the S4 includes the following sub-steps:

[0110] Taking the self-impedance coefficient matrix as the quantity to be determined, multi-scale decomposition is performed on it to obtain the function to be determined including the finite element shape function;

[0111] The function to be determined is transformed based on wavelet transform and finite element interpolation to establish a discrete algebraic equation group of finite element-wavelet meshless method;

[0112] Solving the discrete algebraic equations of the finite element-wavelet meshless method to obtain the magnetic field intensity and magnetic induction intensity of the cable;

[0113] Based on the energy perturbation method, the inductance parameter value is calculated by the magnetic field strength and the magnetic induction strength;

[0114] Substitute the inductance parameter value into the ground loop current matrix equation, and solve the ground loop current matrix equation to obtain the ground loop current value.

[0115] It is understandable that since the finite element method is a discrete algorithm constructed on the basis of a series of meshes, as its application areas continue to expand and engineering problems become increasingly complex, this method often encounters some difficulties in solving practical engineering problems. Figure 2 When calculating the electromagnetic field of the cable warehouse shown in the figure, the drastic changes in the geometric model parameters often lead to mesh distortion, which causes a sharp increase in the discrete solution error or even invalid solutions. Therefore, it is necessary to use adaptive meshing technology to ensure that the mesh is coordinated with the geometric shape changes. However, the application of adaptive meshing technology has undoubtedly aggravated the excessive demand for computing resources. Therefore, in order to avoid the adaptive meshing problem that finite element algorithms must deal with when solving such problems, a new type of numerical calculation method: meshless method came into being in the field of computational mechanics. The significant feature of this type of method is different from that of finite element algorithms: the shape function is constructed on a series of discrete points in the solution domain, and there is no need to give the relationship between these discrete nodes. Therefore, this type of method is very suitable for problems where the field geometry and parameters change during the calculation process, such as shape optimization or non-destructive testing. However, the obvious disadvantage of the meshless method is that the shape function is non-interpolation type, and special methods are required to deal with imposed boundary conditions and internal boundary conditions of different media, which increases the computational complexity.

[0116] In this embodiment, by mixing the finite element and wavelet meshless methods, the meshless method can be used to effectively avoid the difficulties in meshing the finite element method due to complex geometric conditions such as cable cross-interconnection transposition and irregular grounding positions; the finite element method has high computational efficiency in regular areas to overcome the low computational efficiency of the meshless method and the computational stability problems that may be encountered when dealing with some large-scale problems; and finally, the advantages of the two methods are combined to make the calculation results more stable and accurate, and achieve a better balance between computational efficiency and accuracy.

[0117] Specifically, the function to be solved is transformed based on wavelet transform and finite element interpolation to establish a discrete algebraic equation set of finite element-wavelet meshless method, including:

[0118] The interpolation projection operator is used to project the function to be determined in the finite element space to obtain the interpolation scaling function to be determined;

[0119] Establishing a wavelet function based on the interpolation scale function to be determined, and constructing a wavelet basis function to be determined by fusing the interpolation scale function to be determined with the wavelet function;

[0120] Constructing a wavelet transform of the wavelet basis function to be determined based on a connection scaling method, and obtaining a refined basis expression of the wavelet basis function to be determined;

[0121] The refined basis expression is interpolated by using the standard finite element method, and the refined basis expression and the corresponding interpolation function are substituted into the weighted residual expression to obtain a discrete algebraic equation group of the finite element-wavelet meshless method.

[0122] As an implementation method, in the multi-scale refinement calculation process, in order to ensure the consistency and linear independence of all basis functions after the introduced refinement basis function, including the finite element shape function and the wavelet basis, in this embodiment, the vector magnetic potential in the cable is taken as the quantity to be determined by the wavelet basis refinement calculation method. , perform multi-scale, i.e. coarse and fine scale decomposition, and introduce fine scale function , using the invariance of multiple projections of the projection operator P, that is, satisfying , and further transform the function to be solved Written as:

[0123] (18)

[0124] in, It is the bridging scale item.

[0125] The purpose of introducing the bridging scale term is to convert the field quantity to be determined coarse-scale projection Some variables represented by fine-scale projection This ensures that the required field quantity Multi-scale decomposition of

[0126] Multiplying both sides of formula (18) by the projection operator P yields:

[0127] (19)

[0128] The above algorithm realizes the specific area The refined expression under the finite element interpolation scale, using the interpolation projection operator P to project the function to be determined in the finite element space, can obtain the interpolation scale function to be determined:

[0129] (20)

[0130] The wavelet function can be further expressed as:

[0131] (twenty one)

[0132] Among them is Resolution / Scale Among the classical wavelets, Daubechies wavelet has many advantages such as compact support and orthogonality. Therefore, Daubechies wavelet is applied in this embodiment. The scaling function of Daubechies wavelet is constructed by a double scaling equation:

[0133] (twenty two)

[0134] in is the wavelet approximation spatial low-pass filter coefficient, is an even integer.

[0135] According to the bridging scale term expression, the interpolation scale function and wavelet function to be determined are substituted into the bridging scale term expression to construct the wavelet basis function to be determined, where:

[0136] The bridging scale term expression is as follows:

[0137] (twenty three)

[0138] Substituting the interpolation scaling function and wavelet function to be determined, and replacing the summation subscripts with j, k, and i, we can obtain:

[0139] (twenty four)

[0140] Substituting formula (20), formula (21) and formula (24) into formula (18), we can obtain the wavelet basis function to be determined:

[0141] (25)

[0142] Based on the connection scale method to construct the wavelet transform, the refined basis expression can be further obtained as follows:

[0143] (26)

[0144] Therefore, in In the refined area, formula (18) can be written as:

[0145] (27)

[0146] In other sub-regions, the standard finite element method is used to Interpolation yields:

[0147] (28)

[0148] Substituting the interpolation functions of formula (27) and formula (28) into the standard Galerkin weighted residual expression, we can get the discrete algebraic equations of the finite element-wavelet meshless method. Solving this algebraic equations can get the numerical solution of the electromagnetic field problem. The magnetic field intensity H and magnetic induction intensity B can be further calculated. Then, according to the energy perturbation method, the inductance parameter value in the circuit model can be calculated. The specific calculation formula is as follows:

[0149] The self-inductance per unit length of the coil is: ,

[0150] Coil Mutual inductance per unit length: ,

[0151] After the inductance parameter value is calculated, it is substituted into the ground loop current matrix equation, the ground loop current is calculated and solved, and finally the value of the ground loop current is obtained.

[0152] In this embodiment, the self-impedance coefficient matrix reflects the interaction relationship between the various parts of the cable system. By performing multi-scale decomposition on it, the characteristics of the self-impedance can be analyzed from different scales, which is helpful for a deeper understanding of the electromagnetic characteristics of the cable system. By introducing the finite element shape function, the physical field distribution in the cable system can be more accurately described, laying the foundation for subsequent precise calculations. Wavelet transform has good time-frequency localization characteristics and can effectively deal with local mutations and complex boundary problems. Finite element interpolation has a higher calculation accuracy in regular areas. Combining the two to transform the function to be calculated is to comprehensively utilize the advantages of wavelet transform and finite element interpolation to establish a discrete algebraic equation group that is more in line with the actual situation of the cable system. Compared with a single method, it reduces the error in numerical calculation and improves the accuracy and reliability of calculation. Combined with the energy perturbation method, the inductance parameter value can be calculated more accurately to more accurately reflect the inductance characteristics of the cable under actual operating conditions, and then improve the accuracy of ground loop current calculation through accurate inductance parameters, which helps to achieve more effective evaluation of the operating status and safety of the cable.

[0153] The above specific embodiments are preferred embodiments of the present invention, and are not intended to limit the specific implementation scope of the present invention. The scope of the present invention includes but is not limited to the present specific embodiments. All equivalent changes made in accordance with the shape, structure, and method of the present invention are within the protection scope of the present invention.

Claims

1. A fusion calculation method taking into account cable grounding loop current, characterized in that: The steps include: S1. Construct a target entity model of the cable based on the grounding properties of the power cable; S2. constructing an equivalent circuit model of cable cross-connection transposition grounding according to the target entity model; S3, establishing a ground loop current matrix equation based on the equivalent resistance and equivalent current of the equivalent circuit model combined with key characteristic parameters of the cable; S4, performing fusion calculation on the grounding circulation matrix equation based on finite element-wavelet meshless hybrid and energy perturbation to obtain numerical calculation results of the grounding circulation; The S2 comprises the following sub-steps: Draw the electrical wiring diagram corresponding to the cross-connection and grounding of the cables based on the target entity model and the key characteristic parameters of the cables; Establish an equivalent circuit diagram according to the electrical wiring diagram to obtain an equivalent circuit model; The S3 comprises the following sub-steps: The self-impedance of the metal sheath of each cable segment is calculated based on the self-inductance per unit length of the loop formed by the metal sheath of each cable segment and the ground, the metal sheath resistance and the angular frequency; Constructing a grounding loop current equation group of the cable metal sheath according to the self-impedance and induced voltage of each section of the cable metal sheath combined with the equivalent resistance and equivalent current of the equivalent circuit model; Establishing a grounding circulation matrix equation based on the grounding circulation loop equation group; The calculation formula of the ground loop current equation group is as follows: ； In the formula, Indicates the A phase on the metal sheath i The induced voltage generated by the current in the core conductor of the segment line is Indicates the B phase on the metal sheath i The induced voltage generated by the current in the core conductor of the segment line is Indicates the C phase on the metal sheath i The induced voltage generated by the current in the core conductor of the segment line; For the i The induced voltage on the metal sheath of the segment is generated by the circulating current of the metal sheath of phases B and C. For the i The induced voltage on the metal sheath of the segment is generated by the circulating current of the metal sheath of phase A and phase C. For the i The induced voltage on the metal sheath of the segment is generated by the circulating current of the metal sheath of phase A and phase B; i Indicates the first, second and third cable lines in the metal sheath cross-connection system, and the corresponding values ​​are 1, 2, and 3; Phase A land cable i The self-impedance of the metal sheath, for B Phase Land Cable i The self-impedance of the metal sheath, is the self-impedance of the metal sheath of the i-th section of the C-phase land cable; is the ground loop current of the metal sheath of phase A, is the ground loop current of the B-phase metal sheath, is the ground loop current of the C phase metal sheath; is the equivalent current of the equivalent circuit model; is the equivalent resistance of the equivalent circuit model; Construct the self-impedance coefficient matrix based on the self-impedance on the cable metal sheath; The S4 comprises the following sub-steps: Taking the self-impedance coefficient matrix as the quantity to be determined, multi-scale decomposition is performed on it to obtain the function to be determined including the finite element shape function; The function to be determined is transformed based on wavelet transform and finite element interpolation to establish a discrete algebraic equation group of finite element-wavelet meshless method; Solving the discrete algebraic equations of the finite element-wavelet meshless method to obtain the magnetic field intensity and magnetic induction intensity of the cable; Based on the energy perturbation method, the inductance parameter value is calculated by the magnetic field strength and the magnetic induction strength; Substitute the inductance parameter value into the ground loop current matrix equation, and solve the ground loop current matrix equation to obtain the ground loop current value.

2. The fusion calculation method taking into account cable grounding loop current according to claim 1 is characterized in that: The S1 comprises the following sub-steps: Establish a cable model based on the actual structure, actual grounding method and grounding position of the power cable; The cable model is meshed and an electromagnetic field distribution simulation is performed, and the cable model is adjusted and optimized according to the simulation results to obtain a target entity model of the cable.

3. The fusion calculation method taking into account cable grounding loop current according to claim 1 is characterized in that: The establishing of a grounding circulation matrix equation based on the grounding circulation loop equation group includes: Establishing a grounding loop current column vector based on the grounding loop current of each phase metal sheath; The induced electromotive force column vector is constructed based on the induced voltage generated by the core conductor current on the metal sheath of each phase cable; A grounding circulation matrix equation is constructed by fusing the grounding circulation column vector, the self-impedance coefficient matrix and the induced electromotive force column vector.

4. The fusion calculation method taking into account cable grounding loop current according to claim 3 is characterized in that: Each element in the self-impedance coefficient matrix is ​​calculated based on the angular frequency of the cable, the equivalent resistance of the equivalent circuit model, and the inductance parameters.

5. The fusion calculation method taking into account cable grounding loop current according to claim 3 is characterized in that: The calculation formula of the ground loop current matrix equation is as follows: ； In the formula, represents the self-impedance coefficient matrix, represents the ground loop current column vector, represents the induced electromotive force column vector.

6. The fusion calculation method taking into account cable grounding loop current according to claim 1 is characterized in that: The method of transforming the function to be solved based on wavelet transform and finite element interpolation to establish a discrete algebraic equation group of finite element-wavelet meshless method includes: The interpolation projection operator is used to project the function to be determined in the finite element space to obtain the interpolation scaling function to be determined; Establishing a wavelet function based on the interpolation scale function to be determined, and constructing a wavelet basis function to be determined by fusing the interpolation scale function to be determined with the wavelet function; Constructing a wavelet transform of the wavelet basis function to be determined based on a connection scaling method, and obtaining a refined basis expression of the wavelet basis function to be determined; The refined basis expression is interpolated by using the standard finite element method, and the refined basis expression and the corresponding interpolation function are substituted into the weighted residual expression to obtain a discrete algebraic equation group of the finite element-wavelet meshless method.

Images