Calculation method for steady-state voltage and loop current of sheath based on multi-loop land cable distributed model

Abstract

This invention discloses a method for calculating the steady-state voltage and circulating current of the sheath based on a distributed model of a multi-loop terrestrial cable. The method includes: 1. Obtaining the factors affecting the steady-state induced voltage and circulating current of the sheath of a multi-loop single-core terrestrial cable; 2. Establishing a distributed parameter model per unit length of the multi-loop single-core terrestrial cable, thereby obtaining the linear equation matrix describing the entire multi-loop terrestrial cable system; 3. Calculating the series impedance of the multi-loop single-core terrestrial cable lines in the system's linear equation matrix; 4. Calculating the parallel admittance between the multi-loop single-core terrestrial cable lines in the system's linear equation matrix; 5. Constructing the impedance matrix and admittance matrix to complete the system's linear equation matrix; 6. Determining the boundary conditions of the system's linear equation matrix; 7. Solving the system's linear equation matrix to obtain the values ​​of the steady-state induced voltage and circulating current; 8. Calculating the steady-state induced voltage and circulating current of the sheath of a multi-loop single-core terrestrial cable with the same arrangement. This invention eliminates repetitive modeling and simulation calculations, improves the model's adaptability, and has significant engineering value.

Description

Technical Field

[0001] This invention relates to a method for calculating the sheath induced voltage and circulating current of a multi-loop single-core terrestrial cable, and more particularly to a rapid method for calculating the sheath steady-state induced voltage and circulating current based on a distributed circuit model of a multi-loop single-core terrestrial cable. Background Technology

[0002] The development of the power industry is crucial to the national economy and people's livelihood. With the sustained and rapid development of my country's economy and the continuous improvement of people's living standards, the demand for electricity is also growing rapidly. This huge social electricity consumption has triggered a massive demand for power transmission. Solving the problem of power transmission channels and delivering large amounts of electricity to users is one of the major issues to be addressed in power development. Currently, the mainstream power transmission methods in China are overhead line transmission and cable transmission. Compared with overhead line transmission, cable transmission has advantages such as not needing to occupy surface corridors, being less affected by climate and environment, high operational reliability, less maintenance workload, and flexible laying. It has been widely used in power plant outgoing lines, cross-river and cross-sea power transmission, internal power supply for industrial and mining enterprises, and urban power supply, covering transmission, distribution, and consumption.

[0003] However, with the continuous increase in urban electricity consumption and the shrinking urban space, the close proximity of three- and four-circuit cable lines is becoming increasingly common, leading to complex electromagnetic coupling relationships between different cable lines. Due to the limited space in cable trenches, asymmetrical cable arrangement can cause three-phase imbalance in line parameters, complicating calculations. High-voltage cables are typically designed as single-core structures. During operation, high-voltage cables inevitably generate an alternating magnetic field. According to Faraday's law of electromagnetic induction, an induced voltage will appear on the metal sheath of the high-voltage cable. If the cable's metal sheath forms a loop, a circulating current will be generated. This circulating current in the cable's metal sheath can cause many problems for high-voltage cable transmission lines, such as significantly reducing the cable's power transmission capacity and generating excessive heat in the metal sheath, leading to a decrease in main insulation capacity and shortening the cable's lifespan. The grounding method of the high-voltage cable's metal sheath is closely related to the circulating current. In long-distance cable transmission lines, direct grounding at both ends of the cross-connection is the most common grounding method. If the three short segments of a cross-connection are close in distance, the circulating current in the metallic sheath can be effectively reduced. However, in actual systems, the three short segments of a cross-connection are not uniform in length. To reduce sheath circulating current losses, based on power grid operation experience, the circulating current ratio in the metallic sheath of cable transmission lines using cross-connection grounding systems generally does not exceed 10%. In actual power engineering, due to factors such as the bends and arrangement of underground tunnels, the lengths of the three short cable segments in a cross-connection cannot be guaranteed to be equal. When the unevenness of the three segments is relatively large, the voltage and current induced in the metallic sheath are large, which may exceed the threshold in severe cases, damaging electrical equipment and even posing safety hazards to maintenance personnel. If the metallic sheath breaks down, it will affect the safe operation of the cable transmission.

[0004] Currently, both domestic and international research primarily utilizes analytical and numerical methods to study induced voltage and circulating current in cable sheaths. Analytical methods involve analyzing the relationships between various factors in a problem, then expressing and solving the problem using concise mathematical language, symbols, and formulas. Analytical methods offer advantages such as high accuracy and fast computation speed for relatively simple problems. However, their application is limited when real-world problems have complex boundary conditions that cannot be accurately expressed analytically. Numerical methods, which emerged with the rapid development of computer technology, are a method for solving engineering electromagnetic field problems. While lacking a clear definition, they mainly include the finite element method, method of moments, boundary element method, and finite difference method. However, numerical methods require system modeling, are cumbersome, and have poor generalization performance. Summary of the Invention

[0005] To address the problems existing in the prior art, the purpose of this invention is to propose a method for calculating the sheath steady-state voltage and circulating current based on a distributed model of a multi-loop terrestrial cable. This method can achieve rapid calculation of the sheath steady-state induced voltage and circulating current by obtaining the distributed circuit parameters of the multi-loop terrestrial cable, eliminating the need for repetitive modeling and simulation calculations, and thus having better adaptability.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A method for calculating the sheath steady-state voltage and circulating current based on a distributed model of multi-loop terrestrial cables includes the following steps:

[0008] Step 1: Obtain the factors affecting the steady-state induced voltage and circulating current of the sheath of multi-loop single-core terrestrial cables through theoretical analysis;

[0009] Step 2: Establish a distributed parameter model per unit length for multi-loop single-core terrestrial cables. The longitudinal coupling between each single-core terrestrial cable is modeled by the impedance Z = R + jLω per unit length. The lateral coupling between multi-loop single-core terrestrial cables and the coupling between the cable core and the sheath are modeled by the admittance Y = G + jCω per unit length. From the distributed parameter model, obtain the linear equations for the steady-state induced voltage and circulating current of a single cable sheath. The voltage between the cable core and ground of the j-th single-core terrestrial cable is:

[0010]

[0011] In the formula, This represents the voltage between the core of the j-th single-core land cable and ground. and These represent the core and sheath currents of the j-th single-core land cable, respectively. This represents the self-impedance of the j-th single-core land cable core. This represents the mutual impedance between the j-th and i-th single-core land cable cores. This represents the mutual impedance between the j-th single-core terrestrial cable core and its sheath. This represents the mutual impedance between the j-th single-core land cable core and the ith single-core land cable sheath.

[0012] The voltage between the sheath and ground of the j-th single-core terrestrial cable is:

[0013]

[0014] In the formula, This represents the voltage between the sheath and ground of the j-th single-core terrestrial cable. This represents the self-impedance of the sheath of the j-th single-core land cable. This represents the mutual impedance between the j-th and i-th single-core land cable cores. This represents the mutual impedance between the j-th single-core terrestrial cable core and its sheath. This represents the mutual impedance between the j-th single-core land cable core and the ith single-core land cable sheath.

[0015] The current in the core of the j-th single-core terrestrial cable is:

[0016]

[0017] In the formula, This represents the self-admittance of the j-th single-core land cable core. This represents the mutual admittance between the core and sheath of the j-th single-core terrestrial cable. This represents the voltage between the j-th cable core and its sheath.

[0018]

[0019] The current in the sheath of the j-th single-core terrestrial cable is:

[0020]

[0021] In the formula, This represents the self-admittance of the j-th single-core land cable core;

[0022] Applying the above four equations to each single-core terrestrial cable in a multi-loop terrestrial cable system yields a set of linear equations describing the entire system. These linear equations can be written in matrix form as follows:

[0023]

[0024] Step 3: Calculate the series impedance of the multi-circuit single-core terrestrial cable line in the linear equation matrix (5) of the multi-circuit terrestrial cable system according to the distributed parameter model, including the mutual impedance between different single-core terrestrial cable cores and sheaths, between cable cores, and the self-impedance between individual cable cores and the mutual impedance between cable cores and sheaths.

[0025] Step 4: Calculate the parallel admittance between multi-circuit single-core terrestrial cable lines in the linear equation matrix (5) of the multi-circuit terrestrial cable system according to the distributed parameter model, including the self-admittance between individual cable cores and the mutual admittance between the cable core and the sheath;

[0026] Step 5: Construct the impedance matrix and admittance matrix to obtain the Z matrix in the linear equation system matrix of Step 2. l and Y l This completes the system's linear equation matrix.

[0027] Step 6: Determine the boundary conditions of the linear equation matrix (5) of the multi-loop terrestrial cable system, including the input voltage of the multi-loop single-core terrestrial cable and the location of the grounding box, which are determined by the specific network being studied;

[0028] Step 7: Solve the system's linear equation matrix using the method for solving linear differential equations to obtain the values ​​of steady-state induced voltage and circulating current;

[0029] Step 8: For a new multi-loop single-core land cable with the same arrangement, you only need to modify the size information in the arrangement and the parameter information of the multi-loop single-core land cable to calculate the steady-state induced voltage and circulating current of the sheath.

[0030] In step 1, the factors affecting the steady-state induced voltage and circulating current of the sheath of the multi-loop single-core terrestrial cable are obtained through theoretical analysis, including: the arrangement of the multi-loop single-core terrestrial cable, detailed arrangement cross-sectional dimensions, steady-state load current, sheath geometric radius, sheath unit resistance, grounding resistance at both ends, and soil resistivity; among which the arrangement includes parallel arrangement, right-angle arrangement, and triangular arrangement.

[0031] In step 2, a distributed parameter model per unit length of a multi-loop single-core terrestrial cable is established in the simulation software. The distributed parameter model of the n-loop single-core terrestrial cable consists of 2n+1 distributed transmission line models. In the first 2n transmission line models, the odd-numbered ones represent the cable cores (C) of the multi-loop single-core terrestrial cable. n Even-numbered sections indicate the sheath of a multi-circuit single-core terrestrial cable (S). nThe coupling between each single-core terrestrial cable in the longitudinal direction is modeled by the impedance Z = R + jLω per unit length. The coupling between the transverse directions of the multi-loop single-core terrestrial cables and between the cable core and the sheath is modeled by the admittance Y = G + jCω per unit length. The values ​​of the resistance R, inductance L, conductance G, and capacitance C parameters of the single-core terrestrial cable itself and different terrestrial cables are determined by the internal structure of the single-core terrestrial cable and the laying method of the multi-loop single-core terrestrial cable.

[0032] In step 3, the series impedance of the multi-loop single-core terrestrial cable line in the linear equation matrix of the multi-loop terrestrial cable system is calculated according to the distributed parameter model. This includes the mutual impedance between different cable cores and sheaths, between cable cores, and the self-impedance between individual cable cores, as well as the mutual impedance between cable cores and sheaths. The specific calculation formula is as follows:

[0033]

[0034] In the formula, R represents the self-resistance of the j-th single-core land cable core. g This indicates the resistance between the cable core and ground. L represents the self-inductance of the j-th single-core land cable core. g Indicates the inductance between the cable core and ground. This represents the mutual inductance between the j-th and i-th single-core land cable cores. This represents the mutual inductance between the j-th single-core land cable core and ground. This represents the mutual inductance between the j-th single-core land cable core and its sheath. ω represents the mutual inductance between the j-th single-core land cable core and the ith single-core land cable sheath, ω represents the frequency of the current in the cable, and j represents the imaginary unit. This represents the self-resistance of the sheath of the j-th single-core land cable. This represents the mutual inductance between the j-th and i-th single-core land cable cores. This represents the mutual inductance between the sheath of the j-th single-core land cable and the ground.

[0035] In step 4, the parallel admittance between multiple single-core terrestrial cable lines in the linear equation matrix of the multi-loop terrestrial cable system is calculated according to the distributed parameter model, including the self-admittance between individual single-core terrestrial cable cores and the mutual admittance between the cable core and the sheath; the specific calculation formula is as follows:

[0036]

[0037]

[0038] In the formula, This represents the self-conductivity of the j-th single-core land cable core. This represents the self-susceptance of the j-th single-core terrestrial cable core. This represents the self-conductivity of the sheath of the j-th single-core land cable. This represents the self-susceptance of the sheath of the j-th single-core land cable. This represents the mutual conductance between the j-th and i-th single-core land cable cores.

[0039] Compared with the prior art, the present invention has the following advantages:

[0040] 1. By incorporating actual parameter information from multi-circuit single-core terrestrial cables, the electrical characteristics of the cable sheath can be simulated more accurately. Furthermore, the establishment of a distributed parameter model for multi-circuit single-core terrestrial cables improves upon the inaccuracies of lumped parameter models in calculating long-distance power transmission, making it more suitable for refined steady-state induced voltage and circulating current analysis.

[0041] 2. Because the distributed parameter model takes into account the loop structure, the coupling within a single cable, and the coupling between cables when it is established, it can handle the electromagnetic coupling relationships between complex multi-loop cable systems.

[0042] 3. Since the differential equations of the system are established in advance, and the model only needs to deal with one-dimensional spatial changes along the cable length, it is possible to quickly calculate the steady-state induced voltage and circulating current of the sheath, eliminating the need for repetitive modeling and simulation calculations.

[0043] In summary, the method of this invention solves the problems of heavy and repetitive modeling and simulation work in existing technologies, and has great engineering value. Attached Figure Description

[0044] Figure 1 A flowchart is shown for a fast calculation method of sheath steady-state induced voltage and circulating current based on a distributed circuit model of a multi-loop single-core terrestrial cable.

[0045] Figure 2 A schematic diagram of the distributed parameter model per unit length of a multi-loop single-core terrestrial cable is shown. Detailed Implementation

[0046] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0047] The purpose of this invention is to propose a method for calculating the sheath steady-state induced voltage and circulating current based on a distributed model of a multi-loop terrestrial cable. This method can quickly calculate the sheath steady-state induced voltage and circulating current by obtaining the distributed circuit parameters of the multi-loop terrestrial cable, eliminating the need for repetitive modeling and simulation calculations, and thus having better adaptability.

[0048] To achieve the above objectives, the present invention provides a method for calculating the sheath steady-state induced voltage and circulating current based on a multi-loop terrestrial cable distributed model, comprising the following steps:

[0049] Step 1: Through theoretical analysis, obtain the factors affecting the steady-state induced voltage and circulating current of the sheath of multi-loop single-core terrestrial cables. These factors mainly include: the arrangement of the multi-loop single-core terrestrial cables, detailed cross-sectional dimensions, steady-state load current, sheath geometric radius, sheath unit resistance, grounding resistance at both ends, and soil resistivity. The arrangement methods include parallel arrangement, right-angle arrangement, and triangular arrangement.

[0050] Step 2: Establish a distributed parameter model for the unit length of multi-loop single-core terrestrial cables. For example... Figure 2 As shown, the distributed parameter model of an n-loop single-core terrestrial cable consists of 2n+1 distributed transmission line models. In the first 2n transmission line models, odd-numbered ones represent the cable cores (C) of the multi-loop single-core terrestrial cable. n Even-numbered sections indicate the sheath of a multi-circuit single-core terrestrial cable (S). n The 2n+1th transmission line represents ground (g). The longitudinal coupling between each single-core land cable is modeled by the impedance Z = R + jLω per unit length. The lateral coupling between multi-loop single-core land cables, and between the cable core and the sheath, is modeled by the admittance Y = G + jCω per unit length. The values ​​of resistance R, inductance L, conductance G, and capacitance C between a single-core land cable and different land cables are determined by the internal structure of the single-core land cable and the laying method of the multi-loop single-core land cable. Voltage v(x,t) and current i(x,t) are functions of time t and distance x. A linear equation set of sheath induced voltage and circulating current is obtained from the distributed parameter model. Under steady-state conditions, the effective values ​​of voltage and current are only functions of distance. The voltage between the cable core and ground of the j-th single-core land cable is:

[0051]

[0052] In the formula, This represents the voltage between the core of the j-th single-core land cable and ground. and These represent the core and sheath currents of the j-th single-core land cable, respectively. This represents the self-impedance of the j-th single-core land cable core. This represents the mutual impedance between the j-th and i-th single-core land cable cores. This represents the mutual impedance between the j-th single-core terrestrial cable core and its sheath. This represents the mutual impedance between the j-th single-core land cable core and the ith single-core land cable sheath.

[0053] The voltage between the sheath and ground of the j-th single-core terrestrial cable is:

[0054]

[0055] In the formula, This represents the voltage between the sheath and ground of the j-th single-core terrestrial cable. This represents the self-impedance of the sheath of the j-th single-core land cable. This represents the mutual impedance between the j-th and i-th single-core land cable cores. This represents the mutual impedance between the j-th single-core terrestrial cable core and its sheath. This represents the mutual impedance between the j-th single-core land cable core and the ith single-core land cable sheath.

[0056] The current in the core of the j-th single-core terrestrial cable is:

[0057]

[0058] In the formula, This represents the self-admittance of the j-th single-core land cable core. This represents the mutual admittance between the core and sheath of the j-th single-core terrestrial cable. This represents the voltage between the j-th cable core and its sheath.

[0059]

[0060] The current in the sheath of the j-th single-core terrestrial cable is:

[0061]

[0062] In the formula, This represents the self-admittance of the j-th single-core land cable core.

[0063] Formulas (1), (2), (3), and (4) form a set of linear equations describing the induced voltage and circulating current in the sheath of a single-core terrestrial cable. Applying these four formulas to each single-core terrestrial cable in a multi-loop terrestrial cable system yields the set of linear equations describing the entire multi-loop terrestrial cable system. The set of linear equations for the multi-loop terrestrial cable system can be written in matrix form as follows:

[0064]

[0065] In the formula, V represents the voltage and current of the cable core, V = [V c V s ] T I represents the voltage and current of the sheath, I = [I c I s ] T Z l and Y l These are the impedance matrix and the admittance matrix. Z c Z represents the self-impedance and mutual impedance between cable cores. s Z represents the self-impedance and mutual impedance between the sheaths. cs Y represents the mutual impedance between the cable core and the sheath. c Y represents the self-admittance and mutual admittance between cable cores.s Y represents the self-admittance and mutual admittance between the sheathing layers. cs It represents the mutual admittance between the cable core and the sheath.

[0066] Step 3: Calculate the series impedance of the multi-circuit single-core terrestrial cable line in the linear equation matrix (5) of the multi-circuit terrestrial cable system according to the distributed parameter model, including the mutual impedance between different cable cores and sheaths, between cable cores, and the self-impedance between individual cable cores and the mutual impedance between cable cores and sheaths.

[0067]

[0068]

[0069] In the formula, R represents the self-resistance of the j-th single-core land cable core. g This indicates the resistance between the cable core and ground. L represents the self-inductance of the j-th single-core land cable core. g Indicates the inductance between the cable core and ground. This represents the mutual inductance between the j-th and i-th single-core land cable cores. This represents the mutual inductance between the j-th single-core land cable core and ground. This represents the mutual inductance between the j-th single-core land cable core and its sheath. ω represents the mutual inductance between the j-th single-core land cable core and the ith single-core land cable sheath, ω represents the frequency of the current in the cable, and j represents the imaginary unit. This represents the self-resistance of the sheath of the j-th single-core land cable. This represents the mutual inductance between the j-th and i-th single-core land cable cores. This represents the mutual inductance between the sheath and ground of the j-th single-core land cable. The sheath's self-resistance and self-inductance can be determined by the cable's manufacturing parameters and cable arrangement. The cable core's self-resistance and self-inductance, the mutual resistance and inductance between cable cores, the mutual resistance and inductance between the cable core and the sheath, and the mutual resistance and inductance between the cable core, sheath, and ground can all be determined by the cable's manufacturing parameters and cable arrangement.

[0070] Step 4: Calculate the parallel admittance between multiple single-core cable lines in the linear equation matrix (5) of the multi-circuit terrestrial cable system according to the distributed parameter model, including the self-admittance between individual cable cores and the mutual admittance between the cable core and the sheath.

[0071]

[0072] In the formula, This represents the self-conductivity of the j-th single-core land cable core. This represents the self-susceptance of the j-th single-core terrestrial cable core. This represents the self-conductivity of the sheath of the j-th single-core land cable. This represents the self-susceptance of the sheath of the j-th single-core land cable. This represents the mutual conductance between the j-th and i-th single-core land cable cores.

[0073] Step 5: Construct the impedance matrix and admittance matrix to obtain Z in the linear equation matrix (5) of the multi-loop terrestrial cable system from Step 2. l and Y l This completes the linear equation set matrix (5) for the multi-loop terrestrial cable system:

[0074]

[0075] Step 6: Determine the boundary conditions of the linear equation matrix (5) of the multi-loop terrestrial cable system, such as the input voltage of the multi-loop single-core terrestrial cable and the location of the grounding box. These are determined by the specific network being studied.

[0076] Step 7: Solve the matrix (5) of the linear equation system of the multi-loop land cable system using the solution method of the linear differential equation system, and then obtain the values ​​of steady-state induced voltage and circulating current.

[0077] Step 8: For new multi-loop single-core land cables with the same arrangement, only the size information in the arrangement and the parameter information of the multi-loop single-core land cable need to be modified to calculate the steady-state induced voltage and circulating current of the sheath, saving the process of remodeling and simulation.

Claims

1. A method for calculating the sheath steady-state voltage and circulating current based on a distributed model of a multi-loop terrestrial cable, characterized in that: Includes the following steps: Step 1: Obtain the factors affecting the steady-state induced voltage and circulating current of the sheath of multi-loop single-core terrestrial cables through theoretical analysis; Step 2: Establish a distributed parameter model per unit length for multi-loop single-core terrestrial cables. The longitudinal coupling between each single-core terrestrial cable is modeled by the impedance Z = R + jLω per unit length. The lateral coupling between multi-loop single-core terrestrial cables and the coupling between the cable core and the sheath are modeled by the admittance Y = G + jCω per unit length. From the distributed parameter model, obtain the linear equations for the steady-state induced voltage and circulating current of a single cable sheath. The voltage between the cable core and ground of the j-th single-core terrestrial cable is: In the formula, This represents the voltage between the core of the j-th single-core land cable and ground. and These represent the core and sheath currents of the j-th single-core land cable, respectively. This represents the self-impedance of the j-th single-core land cable core. This represents the mutual impedance between the j-th and i-th single-core land cable cores. This represents the mutual impedance between the j-th single-core terrestrial cable core and its sheath. This represents the mutual impedance between the j-th single-core land cable core and the ith single-core land cable sheath. The voltage between the sheath and ground of the j-th single-core terrestrial cable is: In the formula, This represents the voltage between the sheath and ground of the j-th single-core terrestrial cable. This represents the self-impedance of the sheath of the j-th single-core land cable. This represents the mutual impedance between the j-th and i-th single-core land cable cores. This represents the mutual impedance between the j-th single-core terrestrial cable core and its sheath. This represents the mutual impedance between the j-th single-core land cable core and the ith single-core land cable sheath. The current in the core of the j-th single-core terrestrial cable is: In the formula, This represents the self-admittance of the j-th single-core land cable core. This represents the mutual admittance between the core and sheath of the j-th single-core terrestrial cable. This represents the voltage between the j-th cable core and its sheath. The current in the sheath of the j-th single-core terrestrial cable is: In the formula, This represents the self-admittance of the j-th single-core land cable core; Applying the above four equations to each single-core terrestrial cable in a multi-loop terrestrial cable system yields a set of linear equations describing the entire system. These linear equations can be written in matrix form as follows: Step 3: Calculate the series impedance of the multi-circuit single-core terrestrial cable line in the linear equation matrix (5) of the multi-circuit terrestrial cable system according to the distributed parameter model, including the mutual impedance between different single-core terrestrial cable cores and sheaths, between cable cores, and the self-impedance between individual cable cores and the mutual impedance between cable cores and sheaths. Step 4: Calculate the parallel admittance between multi-circuit single-core terrestrial cable lines in the linear equation matrix (5) of the multi-circuit terrestrial cable system according to the distributed parameter model, including the self-admittance between individual cable cores and the mutual admittance between the cable core and the sheath; Step 5: Construct the impedance matrix and admittance matrix to obtain the Z matrix in the linear equation system matrix of Step 2. l and Y l This completes the system's linear equation matrix. Step 6: Determine the boundary conditions of the linear equation matrix (5) of the multi-loop terrestrial cable system, including the input voltage of the multi-loop single-core terrestrial cable and the location of the grounding box, which are determined by the specific network being studied; Step 7: Solve the system's linear equation matrix using the method for solving linear differential equations to obtain the values ​​of steady-state induced voltage and circulating current; Step 8: For a new multi-loop single-core land cable with the same arrangement, you only need to modify the size information in the arrangement and the parameter information of the multi-loop single-core land cable to calculate the steady-state induced voltage and circulating current of the sheath.

2. The method for calculating sheath steady-state voltage and circulating current based on a multi-loop terrestrial cable distributed model according to claim 1, characterized in that: In step 1, the factors affecting the steady-state induced voltage and circulating current of the sheath of the multi-loop single-core terrestrial cable are obtained through theoretical analysis, including: the arrangement of the multi-loop single-core terrestrial cable, detailed arrangement cross-sectional dimensions, steady-state load current, sheath geometric radius, sheath unit resistance, grounding resistance at both ends, and soil resistivity; among which the arrangement includes parallel arrangement, right-angle arrangement, and triangular arrangement.

3. The method for calculating the sheath steady-state induced voltage and circulating current based on a multi-loop terrestrial cable distributed model according to claim 1, characterized in that: In step 2, a distributed parameter model per unit length of a multi-loop single-core terrestrial cable is established in the simulation software. The distributed parameter model of the n-loop single-core terrestrial cable consists of 2n+1 distributed transmission line models. In the first 2n transmission line models, the odd-numbered ones represent the cable cores (C) of the multi-loop single-core terrestrial cable. n Even-numbered sections indicate the sheath of a multi-circuit single-core terrestrial cable (S). n The coupling between each single-core terrestrial cable in the longitudinal direction is modeled by the impedance Z = R + jLω per unit length. The coupling between the transverse directions of the multi-loop single-core terrestrial cables and between the cable core and the sheath is modeled by the admittance Y = G + jCω per unit length. The values ​​of the resistance R, inductance L, conductance G, and capacitance C parameters of the single-core terrestrial cable itself and different terrestrial cables are determined by the internal structure of the single-core terrestrial cable and the laying method of the multi-loop single-core terrestrial cable.

4. The method for calculating sheath steady-state voltage and circulating current based on a multi-loop terrestrial cable distributed model according to claim 1, characterized in that: In step 3, the series impedance of the multi-loop single-core terrestrial cable line in the linear equation matrix of the multi-loop terrestrial cable system is calculated according to the distributed parameter model. This includes the mutual impedance between different cable cores and sheaths, between cable cores, and the self-impedance between individual cable cores, as well as the mutual impedance between cable cores and sheaths. The specific calculation formula is as follows: In the formula, R represents the self-resistance of the j-th single-core land cable core. g This indicates the resistance between the cable core and ground. L represents the self-inductance of the j-th single-core land cable core. g Indicates the inductance between the cable core and ground. This represents the mutual inductance between the j-th and i-th single-core land cable cores. This represents the mutual inductance between the j-th single-core land cable core and ground. This represents the mutual inductance between the j-th single-core land cable core and its sheath. ω represents the mutual inductance between the j-th single-core land cable core and the ith single-core land cable sheath, ω represents the frequency of the current in the cable, and j represents the imaginary unit; This represents the self-resistance of the sheath of the j-th single-core land cable. This represents the mutual inductance between the j-th and i-th single-core land cable cores. This represents the mutual inductance between the sheath of the j-th single-core land cable and the ground.

5. The method for calculating the sheath steady-state voltage and circulating current based on a multi-loop terrestrial cable distributed model according to claim 1, characterized in that: In step 4, the parallel admittance between multiple single-core terrestrial cable lines in the linear equation matrix of the multi-loop terrestrial cable system is calculated according to the distributed parameter model, including the self-admittance between individual single-core terrestrial cable cores and the mutual admittance between the cable core and the sheath; the specific calculation formula is as follows: In the formula, This represents the self-conductivity of the j-th single-core land cable core. This represents the self-susceptance of the j-th single-core terrestrial cable core. This represents the self-conductivity of the sheath of the j-th single-core land cable. This represents the self-susceptance of the sheath of the j-th single-core land cable. This represents the mutual conductance between the j-th and i-th single-core land cable cores.

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