Bridge steel structure influence-considered calculation method and system for overvoltage of cable along bridge

Abstract

The application discloses a kind of overvoltage calculation method and system of bridge cable considering the influence of bridge steel structure, and the application includes: the steel structure of bridge is included in bridge cable system, the series impedance matrix and shunt admittance matrix of unit length under the influence of steel structure and material are determined, and the node admittance matrix of bridge cable system is obtained;After the node admittance matrix of bridge cable system is simplified and reduced, the simulation modeling of bridge cable system is carried out to obtain the corresponding equivalent resistance inductance capacitance network;According to the equivalent resistance inductance capacitance network obtained, the transient simulation is carried out to obtain the overvoltage distribution result of bridge cable system considering the influence of bridge steel structure.The application can accurately calculate the overvoltage distribution of bridge cable, and the simulation calculation is efficient and fast, can provide basis for the grounding mode design of bridge cable laying system, determine cable segmentation length reference, and can be further expanded to be suitable for various electromagnetic induction effect complex power transmission system.

Description

Technical Field

[0001] This invention relates to the field of power transmission technology, specifically to a method and system for calculating overvoltage of bridge-mounted cables that takes into account the influence of bridge steel structures. Background Technology

[0002] Compared to overhead lines, cable-stayed bridges have characteristics such as high capacitance and low surge impedance. Under transient operating conditions, they exhibit more complex overvoltage phenomena, potentially leading to aging or permanent breakdown of the cable insulation, increasing the difficulty and cost of cable line inspection and maintenance. The grounding system of the cable's metallic sheath is crucial in determining the transient characteristics of the cable-stayed bridge transmission system and is of great significance to the safe and stable operation of the power grid. Therefore, it is necessary to study the transient characteristics of the grounding system of long-distance cable-stayed bridges. An accurate and effective cable transient model is fundamental to analyzing and studying overvoltage protection and insulation coordination in cable transmission systems. During the transient operation of the power system, due to the skin effect between the conductor and the soil, the electrical parameters of the cable exhibit significant frequency-varying characteristics. This not only affects the transmission performance of the cable line but also determines the electromagnetic transient process of the entire transmission system. Therefore, it is necessary to consider the broadband transmission characteristics of the cable in electromagnetic transient simulations and establish an accurate and effective cable model. On the other hand, due to the numerous steel conductors present in bridges, the electromagnetic transient characteristics of the cable system accompanying the bridge under fault conditions will be extremely complex. This not only increases the difficulty of simulation modeling of the transmission system but also places stringent demands on the computational performance of current mainstream electromagnetic transient simulation software. In summary, overvoltage in cable systems accompanying bridges is crucial. Current research on this issue rarely considers the influence of surrounding steel structures on the system, and the transient simulation models of the cables are overly simplistic, resulting in inaccurate calculations. Therefore, there is an urgent need for a method to calculate the overvoltage of cable systems laid along bridges that considers the influence of the bridge's steel structure, providing a computational basis for the grounding design of such systems. Summary of the Invention

[0003] The technical problem to be solved by this invention is to provide a method and system for calculating overvoltage of cables accompanying bridges, taking into account the influence of bridge steel structures. This invention can accurately calculate the overvoltage distribution of cables accompanying bridges, and the simulation calculation is efficient and fast. It can provide a basis for the design of grounding methods for cable systems laid along bridges and for determining the reference length of cable segments. It can also be further extended to be applicable to various power transmission systems with complex electromagnetic induction effects.

[0004] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0005] A method for calculating overvoltage of cable-stayed bridges considering the influence of bridge steel structures includes:

[0006] S1. Incorporate the steel reinforcement structure of the bridge into the cable system, determine the series impedance matrix and parallel admittance matrix per unit length under the influence of the geometric structure and basic material parameters of the steel reinforcement structure of the bridge, and then obtain the node admittance matrix of the cable system based on the series impedance matrix and parallel admittance matrix.

[0007] S2, simplifying and reducing the order of the nodal admittance matrix of the bridge-flying cable system;

[0008] S3. Based on the node admittance matrix of the simplified and reduced-order bridge cable system, the bridge cable system is simulated and modeled to obtain the corresponding equivalent resistance, inductance, and capacitance network.

[0009] S4. Based on the obtained equivalent resistance, inductance, and capacitance network, transient simulation is performed to obtain the overvoltage distribution results of the cable system accompanying the bridge considering the influence of the bridge steel structure.

[0010] Optionally, the bridge-mounted cable system in step S1 includes a power transmission cable, a return cable, and a reinforcing steel conductor arranged sequentially, and the functional expression of the series impedance matrix per unit length is:

[0011]

[0012] In the above formula, Z represents the series impedance matrix per unit length. 11 ~Z 55 In, any Z ii Let Z represent the self-impedance matrix of conductor i, where Z is arbitrary. ik The matrix represents the mutual impedance between conductors i and k, where i and k range from 1 to 5. Values ​​1 and 2 represent transmission cables, value 3 represents return cables, and values ​​4 and 5 represent reinforcing steel conductors. The functional expression for the parallel impedance matrix per unit length determined in step S1 is:

[0013]

[0014] In the above formula, Y represents the parallel impedance matrix per unit length. 11 ~Y 55 In, any Y ii Let i represent the self-admittance matrix of conductor i; the functional expression for the nodal admittance matrix of the bridge-flying cable system obtained in step S1 is:

[0015]

[0016] In the above formula, Y J Let Γ represent the nodal admittance matrix of the cable-stayed bridge system, Γ be the propagation constant matrix, and Y be the nodal admittance matrix. s Y represents the self-admittance part of the nodal admittance matrix. mThe mutual admittance part of the node admittance matrix, l is the length of the cable line accompanying the bridge, Z represents the series impedance matrix per unit length, and Y represents the parallel impedance matrix per unit length.

[0017] Optionally, the self-impedance Z of conductor i ii The expression for the computation function is:

[0018]

[0019] In the above formula, z cci It is the self-impedance per unit length of the core of the power transmission cable i, z csi Let z be the mutual impedance per unit length between the core and the metal sheath of the power transmission cable i. ssi It is the self-impedance per unit length of the metal sheath of the power transmission cable i, z ii Let be the impedance of the return cable or the reinforcing conductor, and we have:

[0020] z cci =z co +z in1 +z s1 ,

[0021]

[0022] z ssi =z s2 +z in2 +z g ,

[0023] In the above formula, z co Z represents the internal impedance per unit length of the cable core. in1 z is the series impedance per unit length of the inner insulation layer caused by the time-varying magnetic field. s1 ρ3 is the impedance per unit length of the inner surface of the sheath, and m is the resistivity of the cable's metallic sheath. s R2 is the reciprocal of the composite penetration depth of the cable's metallic sheath, R3 is the inner insulation radius of transmission cable i, sh is a trigonometric function, and z is the radius of the metallic sheath of transmission cable i. in2 The series impedance per unit length of the outer insulation layer caused by the time-varying magnetic field, z s2 Z is the impedance per unit length of the outer surface of the sheath. g The earth return impedance per unit length of the power transmission cable;

[0024] The mutual impedance matrix Z between conductor i and conductor k ik The expression for the computation function is:

[0025]

[0026] In the above formula, Z ki Let z be the mutual impedance matrix between conductor k and conductor i.ik Y represents the unit-length mutual impedance between conductor i and conductor k; Y is the self-admittance matrix of conductor i. ii The expression for the computation function is:

[0027]

[0028] In the above formula, y csi Let y be the mutual admittance per unit length between the core and the metal sheath of the power transmission cable i. sgi Let y be the mutual admittance per unit length between the metal sheath of transmission cable i and the ground. ii Let be the self-admittance per unit length between the core of the transmission cable i and the return cable.

[0029] Optionally, the internal impedance z per unit length of the cable core co The series impedance per unit length of the inner insulation layer caused by the time-varying magnetic field z in1 and the impedance per unit length z of the inner surface of the sheath s1 The expression for the computation function is:

[0030]

[0031] In the above formula, ρ1 is the resistivity of the cable core, m c m is the reciprocal of the composite penetration depth of the cable core. s ρ is the reciprocal of the composite penetration depth of the cable's metallic sheath, j is the imaginary unit, ω is the angular frequency, R1 is the core radius of transmission cable i, R2 is the inner insulation radius of transmission cable i, R3 is the metallic sheath radius of transmission cable i, μ1 is the permeability of the cable core, μ2 is the permeability of the inner insulation, μ3 is the permeability of the metallic sheath, ρ3 is the resistivity of the metallic sheath, and z is the series impedance per unit length of the outer insulation layer caused by the time-varying magnetic field. in2 The impedance per unit length z of the outer surface of the sheath s2 And the earth return impedance per unit length of the transmission cable z g The expression for the computation function is:

[0032]

[0033] In the above formula, m g h is the reciprocal of the composite penetration depth of the earth. i μ is the vertical distance from the center of the transmission cable i to the ground. g ρ is the magnetic permeability of the earth. g Ri is the resistivity of the earth, R4 is the outer insulation radius of the transmission cable i, and z is the internal impedance per unit length of the return cable core. hco The series impedance per unit length of the insulating layer caused by the time-varying magnetic field z hin And the earth return impedance per unit length of the return cable zhg The expression for the computation function is:

[0034]

[0035] In the above formula, m hc h is the reciprocal of the composite penetration depth of the return cable core. i R5 is the vertical distance from the center of the return cable to the ground; R6 is the radius of the return cable core; μ5 is the permeability of the return cable core; μ6 is the permeability of the return cable insulation; ρ5 is the resistivity of the return cable core; e is the natural logarithm constant; z is the impedance per unit length of the reinforcing conductor. eco And the earth return impedance per unit length of the reinforcing conductor z eg The expression for the computation function is:

[0036]

[0037] In the above formula, m ec h is the reciprocal of the composite penetration depth of the reinforcing conductor. i R7 is the vertical distance from the center of conductor i to the ground, R7 is the radius of conductor i, μ7 is the permeability of conductor i; and z is the mutual impedance per unit length between conductor i and conductor k. ik The expression for the computation function is:

[0038]

[0039] In the above formula, d ik h is the axial distance between conductor i and conductor k. i and h k Let be the vertical distances from the ground to the axes of conductors i and k, respectively.

[0040] Optionally, the mutual admittance y per unit length between the core and the metal sheath of the power transmission cable i csi The expression for the computation function is:

[0041]

[0042] The mutual admittance per unit length y between the metal sheath of the power transmission cable i and the ground sgi The expression for the computation function is:

[0043]

[0044] Self-admittance per unit length of return cable y ii The expression for the computation function is:

[0045]

[0046] Wherein, ε2 is the dielectric constant of the inner insulation layer of transmission cable i, ε4 is the dielectric constant of the outer insulation layer of transmission cable i, and ε5 is the dielectric constant of the insulation layer of return cable.

[0047] Optionally, the simplified and reduced-order function expression for the nodal admittance matrix of the bridge-attached cable system in step S2 is as follows:

[0048] Y eq =T A Y J T B ,

[0049] In the above formula, Y eq To simplify the nodal admittance matrix of the reduced-order bridge-fed cable system, Y J T represents the nodal admittance matrix of the cable-stayed bridge system. A and T B Let be the introduced nodal admittance transformation matrix, and we have:

[0050]

[0051] In the above formula, T1 is an intermediate variable, and T 11 T is an identity matrix of order 2a+1, where a is the number of transmission cables in the bridge cable system; 12 It is a 1×n matrix with all elements equal to 1, where n is the number of reinforcing conductors. The nodal admittance matrix Y of the bridge cable system is... J The nodal admittance matrix Y of the bridge-flying cable system is of order 2a+n+1. eq It is of order 2a+1.

[0052] Optionally, step S3 includes:

[0053] S3.1, regarding the nodal admittance matrix Y of the bridge-mounted cable system J Each element in the complex frequency domain can be written in the following form:

[0054]

[0055] In the above formula, f(s) is the complex frequency domain form of the elements, s is the independent variable, and c j Let a be the j-th residue. j Let c be the j-th pole and the j-th residue. j and the j-th pole a j Let be a real number or a pair of conjugate complex numbers, d and h be constants to be solved, and N be the fitting order, which is equal to the number of poles;

[0056] S3.2, the complex frequency domain form of the summation elements is obtained by the least squares method as shown in the following equation:

[0057]

[0058] In the above formula, σ(s) is the nodal admittance matrix Y. J The approximation of an Nth-order rational function, the nodal admittance matrix Y J The approximation σ(s) of the Nth order rational function shares the same poles as the approximation σ(s)f(s), and both approach 1 at high frequencies. For the specified initial pole, Let s be the unknown quantity to be determined, s be the independent variable, and h be a constant;

[0059] S3.3, multiply both sides of the unknown Nth-order rational function σ(s) and its approximation by f(s):

[0060]

[0061] Then, rearranging the terms in the above equation, we get:

[0062]

[0063] S3.4, the nodal admittance matrix Y of the bridge-mounted cable system. J Substituting the data at various frequencies and rearranging the terms, we obtain the following system of linear equations:

[0064] AX = B,

[0065] In the above formula, A is the pole matrix, X is the parameter matrix to be determined, and B is the nodal admittance matrix Y. J The frequency response matrix at multiple frequencies is given by:

[0066]

[0067]

[0068] In the above formula, M is the number of frequency points sampled, and s1~s M The complex frequency domain representation of M frequency points, s k For the complex frequency domain representation of the k-th frequency point, There are N initial poles, f(s1)~f(s) M Y represents the nodal admittance matrix. J The M frequency response values ​​of the internal element, f(s) k Y is the nodal admittance matrix. J The k-th frequency response value of the internal element, d and h are constants to be solved, N is the fitting order, and c1~c N Given N initial residues, The N residues are the corrected values; the initial residues c1 to c2 are obtained by solving the linear equations using the least squares method. Nconstant d, constant h, and corrected residue

[0069] S3.5, Based on the solved linear equation system, the nodal admittance matrix Y is... J The approximation of the Nth-order rational function σ(s) is transformed into the corresponding time-domain circuit network, and the equivalent resistance, inductance, and capacitance network of the time-domain circuit network is obtained.

[0070] Optionally, step S4 includes: importing the obtained equivalent resistance, inductance, and capacitance network into simulation software to establish a power system component model within the simulation software; electrically connecting the power system component model with the power supply and surge arrester; and then performing transient simulation through the simulation software to obtain the overvoltage distribution results of the cable system accompanying the bridge considering the influence of the bridge steel structure.

[0071] Furthermore, the present invention also provides a system for calculating overvoltage of cable-stayed bridges that takes into account the influence of bridge steel structures, including a microprocessor and a memory interconnected thereto, wherein the microprocessor is programmed or configured to execute the method for calculating overvoltage of cable-stayed bridges that takes into account the influence of bridge steel structures.

[0072] Furthermore, the present invention also provides a computer-readable storage medium storing a computer program, the computer program being programmed or configured by a microprocessor to execute the method for calculating the overvoltage of the cable accompanying the bridge considering the influence of the bridge steel structure.

[0073] Compared with the prior art, the present invention has the following main advantages:

[0074] 1. This invention considers the influence of bridge steel structure on overvoltage of cable traveling on the bridge, and derives the node admittance matrix of the electrical system of cable traveling on the bridge, thereby enabling accurate calculation of overvoltage distribution of cable traveling on the bridge.

[0075] 2. This invention can simplify and reduce the order of the node admittance matrix of the bridge cable system, thereby making the overvoltage simulation calculation results of the bridge cable more efficient.

[0076] 3. Based on the simplified and reduced-order nodal admittance matrix of the bridge-fed cable system, this invention performs simulation modeling of the bridge-fed cable system to obtain the corresponding equivalent resistance, inductance, and capacitance network. Based on the obtained equivalent resistance, inductance, and capacitance network, transient simulation is performed to obtain the overvoltage distribution results of the bridge-fed cable system considering the influence of the bridge steel structure. Various types of overvoltage simulations of bridge-fed cable systems can be carried out, which can provide a basis for the design of grounding methods for bridge-fed cable systems and the determination of cable segment length references.

[0077] 4. This invention can not only accurately predict the impact of bridge steel structure on overvoltage of cable transmission system laid with bridge, but also can be further extended to be applicable to various transmission systems with complex electromagnetic induction effects. Attached Figure Description

[0078] Figure 1 This is a flowchart illustrating the method of an embodiment of the present invention.

[0079] Figure 2 This is a simplified schematic diagram of the bridge-flying cable power transmission system in an embodiment of the present invention.

[0080] Figure 3 This is a simplified simulation diagram of the bridge-flying cable power transmission system in an embodiment of the present invention.

[0081] Figure 4 This is a simplified simulation result of lightning-induced overvoltage in a bridge-fed cable transmission system according to an embodiment of the present invention.

[0082] Figure 5 This is a schematic diagram of the cross-sectional structure of a typical bridge-mounted cable system in an embodiment of the present invention.

[0083] Figure 6 This is a schematic diagram of the overall circuit structure of a typical bridge-mounted cable system in an embodiment of the present invention.

[0084] Figure 7 This is a schematic diagram of the overvoltage simulation results of a typical bridge-fed cable system in an embodiment of the present invention. Detailed Implementation

[0085] like Figure 1 As shown, the overvoltage calculation method for the cable accompanying the bridge, considering the influence of the bridge steel structure, in this embodiment includes:

[0086] S1. Incorporate the steel reinforcement structure of the bridge into the cable system, determine the series impedance matrix and parallel admittance matrix per unit length under the influence of the geometric structure and basic material parameters of the steel reinforcement structure of the bridge, and then obtain the node admittance matrix of the cable system based on the series impedance matrix and parallel admittance matrix.

[0087] S2, simplifying and reducing the order of the nodal admittance matrix of the bridge-flying cable system;

[0088] S3. Based on the node admittance matrix of the simplified and reduced-order bridge cable system, the bridge cable system is simulated and modeled to obtain the corresponding equivalent resistance, inductance, and capacitance network.

[0089] S4. Based on the obtained equivalent resistance, inductance, and capacitance network, transient simulation is performed to obtain the overvoltage distribution results of the cable system accompanying the bridge considering the influence of the bridge steel structure.

[0090] The bridge-mounted cable system in step S1 includes power transmission cables, return cables, and reinforcing conductors arranged sequentially; the quantity can be selected according to actual needs. For example... Figure 2As shown, the bridge cable system in step S1 of this embodiment includes two power transmission cables (labeled as 1 and 2), one return cable (labeled as 3), and two steel conductors (labeled as 4 and 5). The power transmission cables have a metal sheath in addition to the current-carrying conductor core, which is a double conductor structure. The return cable is similar to the steel conductor structure, but has only one current-carrying conductor, which is a single conductor structure. Figure 2 In the middle, d 12 d 23 d 34 and d 45 The numbers h1, h2, h3, h4, and h5 represent the spacing between transmission cable 1 and transmission cable 2, the spacing between transmission cable 2 and return cable 3, the spacing between return cable 3 and reinforcing conductor 4, and the spacing between reinforcing conductor 4 and reinforcing conductor 5, respectively. h1, h2, h3, h4, and h5 represent the heights of transmission cable 1, transmission cable 2, return cable 3, reinforcing conductor 4, and reinforcing conductor 5, respectively. R1 represents the core radius of transmission cable i, R2 represents the inner insulation radius of transmission cable i, R3 represents the metal sheath radius of transmission cable i, and R4 represents the outer insulation radius of transmission cable i; R5 represents the core radius of return cable 3, R6 represents the insulation radius of return cable 3, R7 represents the insulation radius of return cable 3, and R7 represents the radius of reinforcing conductor 5. μ g ρ is the magnetic permeability of the earth. g The resistivity of the earth.

[0091] Based on conductor structure classification, the bridge-fed cable system can be simplified to two transmission cables, one return cable, and two reinforcing conductors. This simplified system encompasses the self-impedance characteristics of two conductors, the self-impedance characteristics of a single conductor, the mutual impedance characteristics between two conductors, the mutual impedance characteristics between two conductors and a single conductor, and the mutual impedance characteristics between single conductors. In this embodiment, the bridge-fed cable system in step S1 includes the transmission cable, the return cable, and the reinforcing conductors arranged sequentially, and the functional expression of the series impedance matrix per unit length is:

[0092]

[0093] In the above formula, Z represents the series impedance matrix per unit length. 11 ~Z 55 In, any Z ii Let Z represent the self-impedance matrix of conductor i, where Z is arbitrary. ik The matrix represents the mutual impedance between conductors i and k, where i and k range from 1 to 5. Values ​​1 and 2 represent transmission cables, value 3 represents return cables, and values ​​4 and 5 represent reinforcing steel conductors. The functional expression for the parallel impedance matrix per unit length determined in step S1 is:

[0094]

[0095] In the above formula, Y represents the parallel impedance matrix per unit length. 11 ~Y 55 In, any Y ii Let i represent the self-admittance matrix of conductor i, where the subscript i of the matrix elements is an integer. i = 1 and 2 represent transmission cables, i = 3 represents return cables, and i = 4 and 5 represent reinforcing conductors. The functional expression of the nodal admittance matrix of the bridge-fed cable system obtained in step S1 is:

[0096]

[0097]

[0098] In the above formula, Y J Let Γ represent the nodal admittance matrix of the cable-stayed bridge system, Γ be the propagation constant matrix, and Y be the nodal admittance matrix. s Y represents the self-admittance part of the nodal admittance matrix. m The mutual admittance part of the node admittance matrix, l is the length of the cable line accompanying the bridge, Z represents the series impedance matrix per unit length, and Y represents the parallel impedance matrix per unit length.

[0099] In this embodiment, the self-impedance Z of conductor i ii The expression for the computation function is:

[0100]

[0101] In the above formula, z cci It is the self-impedance per unit length of the core of the power transmission cable i, z csi Let z be the mutual impedance per unit length between the core and the metal sheath of the power transmission cable i. ssi It is the self-impedance per unit length of the metal sheath of the power transmission cable i, z ii (i=3) represents the impedance of the return cable or reinforcing conductor, and we have:

[0102] z cci =z co +z in1 +z s1 ,

[0103]

[0104] z ssi =z s2 +z in2 +z g ,

[0105] In the above formula, z co Z represents the internal impedance per unit length of the cable core. in1 The series impedance per unit length of the inner insulation layer caused by the time-varying magnetic field, z s1ρ3 is the impedance per unit length of the inner surface of the sheath, and m is the resistivity of the cable's metallic sheath. s R2 is the reciprocal of the composite penetration depth of the cable's metallic sheath, R3 is the inner insulation radius of transmission cable i, sh is a trigonometric function, and z is the radius of the metallic sheath of transmission cable i. in2 The series impedance per unit length of the outer insulation layer caused by the time-varying magnetic field, z s2 Z is the impedance per unit length of the outer surface of the sheath. g The earth return impedance per unit length of the power transmission cable;

[0106] The mutual impedance matrix Z between conductor i and conductor k ik The expression for the computation function is:

[0107]

[0108] In the above formula, Z ki Let z be the mutual impedance matrix between conductor k and conductor i. ik Y represents the unit-length mutual impedance between conductor i and conductor k; Y is the self-admittance matrix of conductor i. ii The expression for the computation function is:

[0109]

[0110] In the above formula, y csi Let y be the mutual admittance per unit length between the core and the metal sheath of the power transmission cable i. sgi Let y be the mutual admittance per unit length between the metal sheath of transmission cable i and the ground. ii Let be the self-admittance per unit length between the core of the transmission cable i and the return cable.

[0111] In this embodiment, the internal impedance z per unit length of the cable core is... co The series impedance per unit length of the inner insulation layer caused by the time-varying magnetic field z in1 and the impedance per unit length z of the inner surface of the sheath s1 The expression for the computation function is:

[0112]

[0113] In the above formula, ρ1 is the resistivity of the cable core, m c m is the reciprocal of the composite penetration depth of the cable core. sρ is the reciprocal of the composite penetration depth of the cable's metallic sheath, j is the imaginary unit, ω is the angular frequency, R1 is the core radius of transmission cable i, R2 is the inner insulation radius of transmission cable i, R3 is the metallic sheath radius of transmission cable i, μ1 is the permeability of the cable core, μ2 is the permeability of the inner insulation, μ3 is the permeability of the metallic sheath, ρ3 is the resistivity of the metallic sheath, and z is the series impedance per unit length of the outer insulation layer caused by the time-varying magnetic field. in2 The impedance per unit length z of the outer surface of the sheath s2 And the earth return impedance per unit length of the transmission cable z g The expression for the computation function is:

[0114]

[0115] In the above formula, m g h is the reciprocal of the composite penetration depth of the earth. i μ is the vertical distance from the center of the transmission cable i to the ground. g ρ is the magnetic permeability of the earth. g Ri is the resistivity of the earth, R4 is the outer insulation radius of the transmission cable i, and z is the internal impedance per unit length of the return cable core. hco The series impedance per unit length of the insulating layer caused by the time-varying magnetic field z hin And the earth return impedance per unit length of the return cable z hg The expression for the computation function is:

[0116]

[0117] In the above formula, m hc h is the reciprocal of the composite penetration depth of the return cable core. i R5 is the vertical distance from the center of the return cable to the ground; R6 is the radius of the return cable core; μ5 is the permeability of the return cable core; μ6 is the permeability of the return cable insulation; ρ5 is the resistivity of the return cable core; e is the natural logarithm constant; z is the impedance per unit length of the reinforcing conductor. eco And the earth return impedance per unit length of the reinforcing conductor z eg The expression for the computation function is:

[0118]

[0119] In the above formula, m ec h is the reciprocal of the composite penetration depth of the reinforcing conductor. i R7 is the vertical distance from the center of conductor i to the ground, R7 is the radius of conductor i, μ7 is the permeability of conductor i; and z is the mutual impedance per unit length between conductor i and conductor k. ik The expression for the computation function is:

[0120]

[0121] In the above formula, d ik h is the axial distance between conductor i and conductor k. i and h k Let be the vertical distances from the ground to the axes of conductors i and k, respectively.

[0122] In this embodiment, the mutual admittance per unit length between the cable core and the metal sheath of the power transmission cable i is y. csi The expression for the computation function is:

[0123]

[0124] The mutual admittance per unit length y between the metal sheath of the power transmission cable i and the ground sgi The expression for the computation function is:

[0125]

[0126] Self-admittance per unit length of return cable y ii The expression for the computation function is:

[0127]

[0128] Wherein, ε2 is the dielectric constant of the inner insulation layer of transmission cable i, ε4 is the dielectric constant of the outer insulation layer of transmission cable i, and ε5 is the dielectric constant of the insulation layer of return cable.

[0129] In this embodiment, the simplified and reduced-order function expression for the nodal admittance matrix of the bridge-fed cable system in step S2 is as follows:

[0130] Y eq =T A Y J T B ,

[0131] In the above formula, Y eq To simplify the nodal admittance matrix of the reduced-order bridge-fed cable system, Y J T represents the nodal admittance matrix of the cable-stayed bridge system. A and T B Let be the introduced nodal admittance transformation matrix, and we have:

[0132]

[0133] In the above formula, T1 is an intermediate variable, and T 11 T is an identity matrix of order 2a+1, where a is the number of transmission cables in the bridge cable system; 12It is a 1×n matrix with all elements equal to 1, where n is the number of reinforcing conductors. The nodal admittance matrix Y of the bridge cable system is... J The nodal admittance matrix Y of the bridge-flying cable system is of order 2a+n+1. eq It is of order 2a+1, which reduces the computation time.

[0134] In this embodiment, step S3 specifically involves building a simulation model of the bridge-flying cable that considers the frequency-varying characteristics of the transmission line based on the vector matching algorithm and the PSCAD programming language. Specifically, step S3 includes:

[0135] S3.1, regarding the nodal admittance matrix Y of the bridge-mounted cable system J Each element in the complex frequency domain can be written in the following form:

[0136]

[0137] In the above formula, f(s) is the complex frequency domain form of the elements, s is the independent variable, and c j Let a be the j-th residue. j Let c be the j-th pole and the j-th residue. j and the j-th pole a j Let be a real number or a pair of conjugate complex numbers, d and h be constants to be solved, and N be the fitting order, which is equal to the number of poles;

[0138] S3.2, the complex frequency domain form of the summation elements is obtained by the least squares method as shown in the following equation:

[0139]

[0140] In the above formula, σ(s) is the nodal admittance matrix Y. J The approximation of an Nth-order rational function, the nodal admittance matrix Y J The approximation σ(s) of the Nth order rational function shares the same poles as the approximation σ(s)f(s), and both approach 1 at high frequencies. For the specified initial pole, Let s be the unknown quantity to be determined, s be the independent variable, and h be a constant;

[0141] S3.3, multiply both sides of the unknown Nth-order rational function σ(s) and its approximation by f(s):

[0142]

[0143] Then, rearranging the terms in the above equation, we get:

[0144]

[0145] S3.4, the nodal admittance matrix Y of the bridge-mounted cable system.J Substituting the data at various frequencies and rearranging the terms, we obtain the following system of linear equations:

[0146] AX = B,

[0147] In the above formula, A is the pole matrix, X is the parameter matrix to be determined, and B is the nodal admittance matrix Y. J The frequency response matrix at multiple frequencies is given by:

[0148]

[0149] B = [f(s1)...f(s)] k )…f(s M )] T ,

[0150] In the above formula, M is the number of frequency points sampled, and s1~s M The complex frequency domain representation of M frequency points, s k For the complex frequency domain representation of the k-th frequency point, There are N initial poles, f(s1)~f(s) M Y represents the nodal admittance matrix. J The M frequency response values ​​of the internal element, f(s) k Y is the nodal admittance matrix. J The k-th frequency response value of the internal element, d and h are constants to be solved, N is the fitting order, and c1~c N Given N initial residues, The N residues are the corrected values; the initial residues c1 to c2 are obtained by solving the linear equations using the least squares method. N constant d, constant h, and corrected residue

[0151] S3.5, Based on the solved linear equation system, the nodal admittance matrix Y is... J The approximation σ(s) of the Nth-order rational function is transformed into the corresponding time-domain circuit network, and the equivalent resistance, inductance, and capacitance network of the time-domain circuit network is obtained. It should be noted that the method used in step S3.5 is an existing method (see reference: Gustavsen B. Computer code forrational approximation of frequency dependent admittance matrices[J].IEEE Transactions on Power Delivery,2002,17(4):1093-1098.). This embodiment only involves the application of the method and does not involve the improvement of the method, so its implementation details will not be described here.

[0152] In this embodiment, step S4 includes: importing the obtained equivalent resistance, inductance, and capacitance network into simulation software to establish a power system component model within the simulation software; electrically connecting the power system component model to the power supply and surge arresters; and then performing transient simulation through the simulation software to obtain the overvoltage distribution results of the cable system accompanying the bridge considering the influence of the bridge steel structure. Specifically, in this embodiment, the obtained equivalent resistance, inductance, and capacitance network is imported into PSCAD simulation software. Using the Branch scripting language of PSCAD, a power system component model is established within the simulation software. The power system component model is electrically connected to the power supply and surge arresters. Then, transient simulation is performed through the simulation software to obtain the overvoltage distribution results of the cable system accompanying the bridge considering the influence of the bridge steel structure. Figure 3 This is a simplified simulation diagram of a cable-stayed power transmission system. In the diagram, the total line length is 5km, R1 is 1Ω, R2 is 50Ω, and U... in For voltage excitation applied to the first high-voltage single-core cable, S1 is a timer switch, the cable's metal sheath is grounded at one end, and A is the ungrounded end of the metal sheath. Figure 4 The figure shows the simulation results of overvoltage under lightning excitation in the simplified bridge-mounted cable transmission system. As can be seen from the figure, although the voltage simulation results of the equivalent model established by the vector matching method maintain good consistency with the voltage simulation results of the PSCAD built-in model under lightning excitation, the most significant deviations occur at the reflection and refraction points of the voltage waveform. That is, for more complex simplified bridge-mounted cable lines, the equivalent circuit model obtained by the vector matching method has very accurate transient response characteristics. Figure 5 This is a schematic diagram of the cross-sectional structure of a typical bridge-mounted cable system. Figure 5 Three 220kV high-voltage single-core cables are laid horizontally, with a return cable laid parallel to the A-phase cable. Cable supports, serving as the cable laying channels, are located on the side web of the concrete box girder. The steel structure inside the concrete box girder is simplified to 255 cylindrical steel conductors, with a spacing of 0.1m between adjacent conductors. The spacing between adjacent two-phase high-voltage single-core cables is 0.35m, and the horizontal distance between the A-phase high-voltage single-core cable and the return cable is 1m. The vertical height of the bridge bottom above sea level is 10m. The equivalent radius of the steel conductor is 5mm. Figure 6 This is a schematic diagram of the overall circuit structure of a typical bridge-mounted cable system.

[0153] Figure 6The total length of the cable line in the Zhongsui Bridge is 6790m. The grounding method for the cable's metal sheath is single-end grounding at both ends, with three cross-interconnected grounding sections in the middle. The single-end grounding section is 560m long, and the cross-interconnected section is 630m long. Each grounding point of the high-voltage single-core cable maintains electrical connection through a return cable, and finally, grounding is achieved at the location of the bored piles of the bridge. The length of each set of reinforcing steel conductors (SR) is consistent with the concrete box girder, taken as 70m, and grounded in parallel at both ends. F1 and F8 represent the metal sheaths of the A-phase cable at the ungrounded positions of the single-end grounding sections at the beginning and end, respectively, while F2 to F7 represent the metal sheaths of the A-phase cable at the cross-interconnected joints. Figure 7 This is a schematic diagram of the overvoltage simulation results for a typical cable-on-bridge system. It can be seen that, considering the bridge steel structure, the oscillation start time of the overvoltage waveform at different locations on the metal sheath of the cable-on-bridge varies. The closer to the beginning of the cable, the earlier the oscillation start time of the overvoltage waveform. The overvoltage waveform of the metal sheath of the cable-on-bridge at different locations oscillates more severely in the early stage of a lightning strike fault, and tends to level off in the later stage.

[0154] In summary, the method in this embodiment considers the influence of the bridge steel structure on the overvoltage of the cable accompanying the bridge, derives the node admittance matrix of the cable accompanying electrical system, and thus can accurately calculate the overvoltage distribution of the cable accompanying the bridge. This method simplifies and reduces the order of the node admittance matrix of the cable accompanying system, making the overvoltage simulation calculation results more efficient. Based on the simplified and reduced-order node admittance matrix of the cable accompanying system, this method performs simulation modeling of the cable accompanying system to obtain the corresponding equivalent resistance, inductance, and capacitance network. Transient simulation is performed based on the obtained equivalent resistance, inductance, and capacitance network to obtain the overvoltage distribution results of the cable accompanying system considering the influence of the bridge steel structure. This allows for the simulation of various types of overvoltage in cable accompanying systems, providing a basis for the design of grounding methods for cable accompanying cable systems and determining cable segment length references. This method not only accurately predicts the influence of the bridge steel structure on the overvoltage of cable transmission systems accompanying bridges, but can also be further extended to various transmission systems with complex electromagnetic induction effects.

[0155] Furthermore, this embodiment also provides a system for calculating the overvoltage of cables traveling on bridges, taking into account the influence of bridge steel structures. This system includes a microprocessor and a memory interconnected, wherein the microprocessor is programmed or configured to execute the aforementioned method for calculating the overvoltage of cables traveling on bridges, taking into account the influence of bridge steel structures. Additionally, this embodiment also provides a computer-readable storage medium storing a computer program that is programmed or configured by the microprocessor to execute the aforementioned method for calculating the overvoltage of cables traveling on bridges, taking into account the influence of bridge steel structures.

[0156] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-readable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create a machine for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The functions specified in one or more boxes. These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable apparatus for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0157] The above description is merely a preferred embodiment of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should also be considered within the scope of protection of the present invention.

Claims

1. A method for calculating overvoltage of cable-stayed bridges considering the influence of bridge steel structure, characterized in that, include: S1, incorporate the bridge's steel reinforcement structure into the bridge-mounted cable system, such that the bridge-mounted cable system includes power transmission cables, return cables, and steel reinforcement conductors arranged in sequence. Determine the series impedance matrix and parallel impedance matrix per unit length under the influence of the geometric structure and basic material parameters of the bridge's steel reinforcement structure, and then obtain the nodal admittance matrix of the cable system accompanying the bridge based on the series impedance matrix and parallel impedance matrix. S2, simplifying and reducing the order of the nodal admittance matrix of the bridge-flying cable system; S3. Based on the node admittance matrix of the simplified and reduced-order bridge cable system, the bridge cable system is simulated and modeled to obtain the corresponding equivalent resistance, inductance, and capacitance network. S4. Based on the obtained equivalent resistance, inductance and capacitance network, transient simulation is performed to obtain the overvoltage distribution of the cable system accompanying the bridge considering the influence of the bridge steel structure. The simplified and reduced-order function expression for the nodal admittance matrix of the bridge-mounted cable system in step S2 is as follows: ， In the above formula, Y eq To simplify the nodal admittance matrix of the reduced-order bridge-fed cable system, Y J T represents the nodal admittance matrix of the cable-stayed bridge system. A and T B Let be the introduced nodal admittance transformation matrix, and we have: ， ， In the above formula, T1 is an intermediate variable, and T 11 2 a +1 order identity matrix a T represents the number of power transmission cables in the bridge cable system. 12 It is of order 1× n A matrix whose elements are all 1s. n The number of reinforcing conductors, along with the nodal admittance matrix Y of the bridge cable system. J 2 a + n +1 order, simplified reduced nodal admittance matrix Y of the bridge-flying cable system eq 2 a +1 level; Step S3 includes: S3.1, regarding the nodal admittance matrix Y of the bridge-mounted cable system J Each element in the complex frequency domain can be written in the following form: In the above formula, f ( s ) represents the complex frequency domain form of the element. s As the independent variable, c j For the first j Residual number, a j For the first j The first extreme point, the second j Individual Residuals c j and the j Extreme points a j For real numbers or pairs of conjugate complex numbers, d and h Let be the constant to be solved. N The fitting order is the order of the fit. N The number of poles is equal to the number of poles; S3.2, the complex frequency domain form of the summation elements is obtained by the least squares method as shown in the following equation: In the above formula, σ ( s Y is the nodal admittance matrix. J The approximation of an Nth-order rational function, the nodal admittance matrix Y J Approximation of Nth-order rational functions σ ( s )and σ ( s ) f ( s The approximations of ) share the same poles and approach 1 at high frequencies; n For the specified initial pole, Let s be the unknown quantity to be determined, and let s be the independent variable. h It is a constant; S3.3, in an unknown Nth-order rational function σ ( s Multiply both sides of the expression and its approximation by f ( s ): ， Then, rearranging the terms in the above equation, we get: ， S3.4, the nodal admittance matrix Y of the bridge-mounted cable system. J Substituting the data at various frequencies and rearranging the terms, we obtain the following system of linear equations: ， In the above formula, A is the pole matrix, X is the parameter matrix to be determined, and B is the nodal admittance matrix Y. J The frequency response matrix at multiple frequencies is given by: ， ， ， In the above formula, M is the number of frequency points sampled. ~ The complex frequency domain representations are given for M frequency points. For the first k Complex frequency domain representation of a frequency point ~ They are respectively N An initial pole, ~ The nodal admittance matrix Y is respectively J The M frequency response values ​​of the internal element, Y is the nodal admittance matrix J The first internal element k Each frequency response value, d and h Let be the constant to be solved. N The fitting order is... ~ for N An initial residue, ~ For the revised version N The initial residues are obtained by solving the system of linear equations using the least squares method. ~ ,constant d ,constant h and the corrected residue ~ ; S3.5, Based on the solved linear equation system, the nodal admittance matrix Y is... J Approximation of Nth-order rational functions σ ( s The circuit is transformed into a corresponding time-domain circuit network, and the equivalent resistance, inductance, and capacitance network of the time-domain circuit network is obtained.

2. The method for calculating overvoltage of bridge-mounted cables considering the influence of bridge steel structure according to claim 1, characterized in that, In step S1, the functional expression for the series impedance matrix of unit length is: ， In the above formula, Z represents the series impedance matrix per unit length. 11 ~Z 55 In, any Z ii Let Z represent the self-impedance matrix of conductor i, where Z is arbitrary. ik The matrix represents the mutual impedance between conductors i and k, where i and k range from 1 to 5. Values ​​1 and 2 represent transmission cables, value 3 represents return cables, and values ​​4 and 5 represent reinforcing steel conductors. The functional expression for the parallel impedance matrix per unit length determined in step S1 is: ， In the above formula, Y represents the parallel impedance matrix per unit length. 11 ~Y 55 In, any Y ii Let i represent the self-admittance matrix of conductor i; the functional expression for the nodal admittance matrix of the bridge-flying cable system obtained in step S1 is: ， ， In the above formula, Y J Let Γ represent the nodal admittance matrix of the cable-stayed bridge system, Γ be the propagation constant matrix, and Y be the nodal admittance matrix. s Y represents the self-admittance part of the nodal admittance matrix. m The mutual admittance portion of the nodal admittance matrix, l Z represents the length of the cable line accompanying the bridge, Z represents the series impedance matrix per unit length, and Y represents the parallel impedance matrix per unit length.

3. The method for calculating overvoltage of bridge-mounted cables considering the influence of bridge steel structure according to claim 2, characterized in that, Self-impedance Z of conductor i ii The expression for the computation function is: ， In the above formula, z cci It is a power transmission cable i The self-impedance per unit length of the cable core, z csi For power transmission cables i The mutual impedance per unit length between the cable core and the metal sheath. z ssi It is a power transmission cable i The self-impedance per unit length of the metal sheath, Let be the impedance of the return cable or the reinforcing conductor, and we have: ， ， ， In the above formula, z co This represents the impedance per unit length of the cable core. z in1 This refers to the series impedance per unit length of the inner insulation layer caused by the time-varying magnetic field. z s1 The impedance per unit length of the inner surface of the sheath. ρ 3 represents the resistivity of the cable's metallic sheath. m s It is the reciprocal of the composite penetration depth of the cable's metallic sheath. R 2 represents the inner insulation radius of transmission cable i. R 3 represents the radius of the metal sheath of power transmission cable i. For trigonometric functions, z in2 This refers to the series impedance per unit length of the outer insulation layer caused by the time-varying magnetic field. z s2 The impedance per unit length of the outer surface of the sheath. z g The earth return impedance per unit length of the power transmission cable; The mutual impedance matrix Z between conductor i and conductor k ik The expression for the computation function is: ， In the above formula, Z ki Let z be the mutual impedance matrix between conductor k and conductor i. ik For conductor i and conductor k The mutual impedance per unit length between them; The self-admittance matrix Y of conductor i ii The expression for the computation function is: ， In the above formula, y csi For power transmission cables i The mutual admittance per unit length between the cable core and the metal sheath y sgi For power transmission cables i The mutual admittance per unit length between the metal sheath and the ground. y ii For power transmission cables i The self-admittance per unit length between the cable core and the return cable.

4. The method for calculating overvoltage of bridge-mounted cables considering the influence of bridge steel structure according to claim 3, characterized in that, Impedance per unit length of cable core z co Series impedance per unit length of the inner insulation layer caused by the time-varying magnetic field z in1 and the impedance per unit length of the inner surface of the sheath z s1 The expression for the computation function is: ， ， In the above formula, ρ 1 represents the resistivity of the cable core. m c It is the reciprocal of the composite penetration depth of the cable core. m s It is the reciprocal of the composite penetration depth of the cable's metallic sheath. The imaginary unit, Angular frequency, R 1 represents the core radius of power transmission cable i. R 2 represents the inner insulation radius of transmission cable i. R 3 represents the radius of the metal sheath of power transmission cable i. μ 1 represents the permeability of the cable core. μ 2 represents the permeability of the cable's internal insulation. μ 3 represents the permeability of the cable's metallic sheath. ρ 3 represents the resistivity of the cable's metallic sheath; the series impedance per unit length of the outer insulation layer caused by the time-varying magnetic field. z in2 impedance per unit length of the outer surface of the sheath z s2 and the earth return impedance per unit length of the transmission cable. z g The expression for the computation function is: ， In the above formula, m g It is the reciprocal of the composite penetration depth of the earth. h i For power transmission cables i The vertical distance of the axis from the ground, μ g The magnetic permeability of the earth. ρ g The resistivity of the earth. R 4 is a power transmission cable i The outer insulation radius; the internal impedance per unit length of the return cable core. z hco Series impedance per unit length of the insulating layer caused by time-varying magnetic field z hin and the earth return impedance per unit length of the return cable. z hg The expression for the computation function is: ， ， In the above formula, m hc It is the reciprocal of the composite penetration depth of the return cable core. h i This is the vertical distance from the center of the return cable to the ground. R 5 represents the core radius of the return cable. R 6 represents the insulation radius of the return cable. μ 5 represents the permeability of the return cable core. μ 6 represents the permeability of the return cable insulation. ρ 5 represents the resistivity of the return cable core. e It is the natural logarithm constant; Resistance per unit length of reinforced conductor z eco and the earth return impedance per unit length of the reinforcing conductor. z eg The expression for the computation function is: ， ， In the above formula, m ec It is the reciprocal of the composite penetration depth of the reinforcing steel conductor. h i For steel conductor i The vertical distance of the axis from the ground, R 7 represents the radius of the reinforcing conductor. μ 7 represents the magnetic permeability of the steel conductor; conductor i and conductor k The unit length mutual impedance z between ik The expression for the computation function is: ， In the above formula, d ik For conductor i and conductor k The axial distance between them h i and h k The conductors are respectively i and conductor k The vertical distance of the axis from the ground.

5. The method for calculating overvoltage of bridge-mounted cables considering the influence of bridge steel structure according to claim 3, characterized in that, power transmission cables i Mutual admittance per unit length between the cable core and the metal sheath y csi The expression for the computation function is: ， power transmission cables i Mutual admittance per unit length between the metal sheath and the ground y sgi The expression for the computation function is: ， Self-admittance per unit length of return cable y ii The expression for the computation function is: ， in, The imaginary unit, Angular frequency, R 1 represents the core radius of power transmission cable i. R 2 represents the inner insulation radius of transmission cable i. R 3 represents the radius of the metal sheath of power transmission cable i. R 4 is a power transmission cable i The outer insulation radius, R 5 represents the core radius of the return cable. R 6 represents the insulation radius of the return cable. ε 2 is a power transmission cable i The dielectric constant of the inner insulating layer, ε 4 is a power transmission cable i The dielectric constant of the outer insulating layer, ε 6 represents the dielectric constant of the insulation layer of the return cable.

6. The method for calculating overvoltage of bridge-mounted cables considering the influence of bridge steel structure according to claim 5, characterized in that, Step S4 includes: importing the obtained equivalent resistance, inductance, and capacitance network into the simulation software to establish a power system component model within the simulation software; electrically connecting the power system component model with the power supply and surge arrester; and then performing transient simulation through the simulation software to obtain the overvoltage distribution results of the bridge-mounted cable system considering the influence of the bridge steel structure.

7. A system for calculating overvoltage of cable-stayed bridges considering the influence of bridge steel structures, comprising a microprocessor and a memory interconnected, characterized in that, The microprocessor is programmed or configured to execute the method for calculating overvoltage of bridge-mounted cables considering the influence of bridge steel structures as described in any one of claims 1 to 6.

8. A computer-readable storage medium storing a computer program, characterized in that, The computer program is used to be programmed or configured by a microprocessor to execute the method for calculating overvoltage of bridge-mounted cables considering the influence of bridge steel structures as described in any one of claims 1 to 6.

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