Method for calculating induced voltage of metal sheath of direct-current cable laid in parallel with alternating current and direct current

Abstract

The invention discloses a method for calculating the induced voltage of a metal sheath of a direct-current cable laid in parallel with alternating current and direct current. The method comprises the following steps: calculating the penetration depth of an electromagnetic field in the ground; utilizing a mirror image method to simulate the influence of the ground on the conductor, enabling the ground conductor to be equivalent to a virtual mirror image conductor with a specific depth, and determining the distance from the power transmission conductor to the induced conductor and the mirror image conductor; calculating the magnetic induction intensity based on the distance, and deducing the magnetic flux per unit length of a conductor and a ground loop through magnetic field superposition; calculating induced electromotive force generated by the single wire on the induction conductor; calculating the induced electromotive force generated by each phase on the induction conductor by combining the relative position and the phase difference of the three-phase current; the shielding effect of the metal sheath is considered, a shielding coefficient is introduced, and the total induced electromotive force of the direct-current cable metal sheath is obtained through the superposition principle. The method can effectively improve the accuracy of induced voltage prediction and the engineering application efficiency.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of power transmission and distribution, and particularly relates to a method for calculating induced voltage of a DC cable metal sheath in parallel laying of AC and DC. BACKGROUND

[0002] With the coordinated development of large-scale offshore wind power and flexible DC transmission technology, traditional power transmission methods are facing more and more challenges. In this context, in order to optimize the spatial utilization of urban underground power transmission, AC and DC cable co-tunnel laying methods have been widely used. This laying method not only effectively saves underground space, but also significantly improves the efficiency of power transmission. However, in the case of parallel laying of AC and DC cables, electromagnetic coupling causes adjacent AC cables to generate alternating magnetic fields when transmitting AC current. These alternating magnetic fields induce voltage on the metal sheath of the DC cable, forming induced voltage.

[0003] Especially in the case of parallel laying of AC and DC cables, the generation of induced voltage may cause the voltage on the metal sheath of the DC cable to be too high. This not only threatens the safety of the cable itself, but also can cause great harm to maintenance personnel. If not promptly and effectively monitored and managed, it may cause safety accidents, especially in adverse weather or power system failure conditions, the harm of induced voltage is particularly significant. Therefore, how to accurately and quickly calculate and control the induced voltage on the metal sheath has become a technical problem to be solved in the power system.

[0004] In the prior art, Chinese patent CN114034905B discloses a method for calculating cable metal sheath grounding ring current based on multi-conductor transmission line theory. The method calculates by the following steps: first, taking the ground as the reference conductor, a transmission line unit length equivalent circuit model of n+1 conductors composed of the cable core, the cable metal sheath and the ground loop is established; then, based on the model, the multi-conductor transmission line equation is derived, and then the general solution and the particular solution of the equation are solved, and finally the induced voltage and induced current on the cable metal sheath are calculated. This method can more accurately consider the interaction between the cable metal sheath and the ground, and calculate the induced voltage thereof.

[0005] However, the calculation method used in the prior art also has some technical problems: first, its calculation process is based on a relatively complex multi-conductor transmission line equation, and mainly focuses on the calculation of the circulating current and voltage between the cable metal sheath and the ground loop, and less on the electromagnetic coupling between the AC cable and the DC cable and the induced voltage on the metal sheath. Secondly, the existing method relies on simulation or calculation based on a complex model, which has high accuracy but long calculation time and a complicated calculation process. This makes it difficult to meet the demand for fast calculation in engineering, especially in the process of power system operation and maintenance, where a quick prediction of induced voltage is usually required.

[0006] More importantly, the existing technology usually only considers the induced voltage on the positive and negative conductors of the cable when analyzing the parallel laying of AC and DC cables, ignoring the induced voltage on the metal sheath. However, the metal sheath of the DC cable may generate a significant induced voltage in the electromagnetic field, and this part of the voltage poses a potential threat to the long-term safety of the cable and the safety of maintenance personnel. Due to the shielding effect of the metal sheath on the induced voltage, neglecting this factor may result in an underestimation of the induced voltage, thus underestimating its potential harm to safety.

[0007] Currently, the calculation of induced voltage for AC and DC parallel laying cables often relies on complex simulation software, which has high accuracy but long calculation time and a complex process, and cannot meet the demand for fast and simple calculation in engineering. Therefore, how to use a simple and efficient analytical calculation method to quickly predict the size of the induced voltage has become a technical problem that needs to be solved in engineering applications.

[0008] The existing analytical calculation method usually only considers the loop fundamental frequency voltage of the positive and negative conductors of the DC cable, and does not conduct in-depth analysis on the induced voltage on the metal sheath of the DC cable. This defect may lead to an underestimation of the actual value of the induced voltage on the metal sheath in some cases, thus ignoring the potential safety hazards that this part of voltage may bring. Therefore, there is an urgent need for a new calculation method that can effectively consider the electromagnetic coupling between AC and DC cables and accurately predict the induced voltage on the metal sheath of the DC cable, providing protection for the safe operation of the power system. SUMMARY

[0009] The purpose of the present application is to overcome the defects of the prior art and provide a method for calculating the induced voltage on the metal sheath of a DC cable laid parallel with AC.

[0010] The purpose of the present application can be achieved by the following technical solutions: The present application provides a method for calculating the induced voltage on the metal sheath of a DC cable laid parallel with AC, comprising the following steps: According to the power frequency, ground magnetic permeability and ground conductivity, the penetration depth of the electromagnetic field propagating in the earth is calculated; According to the calculated penetration depth, the influence of the ground on the conductor is simulated using the mirror method, the influence of the earth conductor is equivalent to a virtual mirror conductor at a specific depth, and the distance from the power transmission conductor to the induced conductor and the mirror conductor is calculated; Based on the distance from the power transmission conductor to the induced conductor and the mirror conductor, the magnetic induction intensity generated by the conductor and the virtual mirror conductor on the induced conductor is calculated; Based on the magnetic induction intensity, the unit length magnetic flux constituting the conductor and the earth loop is derived by the superposition method of the magnetic field of the real conductor and the virtual mirror conductor; Based on the unit length magnetic flux and Faraday's law of electromagnetic induction, the induced electromotive force generated by a single conductor on the induced conductor is calculated; According to the relative position and phase difference of the three-phase current, based on the induced electromotive force generated by a single conductor on the induced conductor, the induced electromotive force generated by each phase current on the induced conductor is calculated; Considering the shielding effect of the metal sheath, a shielding coefficient is introduced, and the total induced electromotive force on the DC cable metal sheath is obtained according to the superposition principle and the induced electromotive force caused by the three-phase current.

[0011] Further, the penetration depth of the electromagnetic field propagating in the earth is calculated according to the power frequency, ground magnetic permeability and ground conductivity, and the formula is: Wherein, represents the penetration depth of the electromagnetic field in the earth; represents the frequency of the alternating current power supply; represents the magnetic permeability of the earth; represents the electrical conductivity of the earth.

[0012] Further, according to the calculated penetration depth, the influence of the ground on the conductor is simulated using the mirror method, the influence of the earth conductor is equivalent to a virtual mirror conductor at a specific depth, and the distance from the power transmission conductor to the induced conductor and the mirror conductor is calculated, which specifically includes: Taking the earth surface as the symmetry plane, according to the calculated electromagnetic field penetration depth d , a virtual mirror conductor is set at the penetration depth position below the real conductor; For a real conductor with a height of h from the ground, the actual distance from the induced conductor to the real conductor and the distance from the induced conductor to the virtual mirror conductor are determined.

[0013] Further, the current in the virtual mirror conductor is equal in magnitude and opposite in direction to the current in the real conductor, and is symmetrically arranged in space about the ground and the real conductor.

[0014] Further, the magnetic induction intensity generated by the real conductor and the virtual mirror conductor on the induced conductor is calculated based on the distance from the power transmission conductor to the induced conductor and the mirror conductor, and the formula is: wherein, B represents the magnetic induction intensity at the induced conductor; μ0 represents the vacuum permeability; I represents the effective value of the current passing through the real conductor; D represents the distance from the induced conductor to the real conductor; D' represents the distance from the induced conductor to the virtual mirror conductor.

[0015] Further, the unit length magnetic flux is calculated according to the formula: wherein, Φ represents the unit length magnetic flux; μ0 represents the vacuum permeability; I represents the effective value of the current passing through the real conductor; D represents the actual distance from the power transmission conductor to the induced conductor; D' represents the distance from the power transmission conductor to the virtual mirror conductor.

[0016] Further, the induced electromotive force generated by a single conductor on the induced conductor is calculated based on the unit length magnetic flux and the Faraday's law of electromagnetic induction, and the formula is: wherein, E represents the induced electromotive force generated by a single conductor on the induced conductor; j represents the imaginary unit; ω represents the angular frequency of the three-phase power supply; Φ represents the unit length magnetic flux; μ0 represents the vacuum permeability; I represents the effective value of the current passing through the real conductor; D represents the actual distance from the power transmission conductor to the induced conductor; D' represents the distance from the power transmission conductor to the virtual mirror conductor.

[0017] Further, the induced electromotive force generated by each phase current on the induced conductor is calculated based on the induced electromotive force generated by a single conductor on the induced conductor according to the relative position and phase difference of the three-phase current, and specifically includes: The conductor is three infinite straight conductors, and an alternating three-phase current is passed through, and the three-phase current is: wherein, , , respectively represent the complex phasor of A, B, C three-phase current; represents the effective value of current in the real conductor; represents the imaginary unit; According to the three-phase current, the induced electromotive force generated by each phase current on the induced conductor is calculated based on the induced electromotive force generated by a single conductor on the induced conductor, and the formula is: wherein, , , respectively represent the induced electromotive force generated by A, B, C three-phase current on the induced conductor; , respectively represent the mirror distance of the virtual mirror conductor from A, B, C three-phase cable, , , respectively represent the actual distance of the positive pole of the DC cable from A, B, C three-phase cable.

[0018] Further, the mirror distance, the formula is: The actual distance, the formula is wherein, represents the actual distance of the three-phase cable i to the real conductor; represents the distance of the three-phase cable i to the virtual mirror conductor, ; respectively represent the horizontal position coordinates of the real conductor and the induced conductor; respectively represent the vertical height coordinates of the real conductor and the induced conductor; represents the electromagnetic field penetration depth.

[0019] Further, the shielding effect of the metal sheath is considered, and a shielding coefficient is introduced. According to the induced electromotive force caused by the three-phase current, the total induced electromotive force on the metal sheath of the DC cable is obtained, and the formula is: wherein, E represents the total induced electromotive force on the DC cable metal sheath, K represents the shielding coefficient, , respectively represent the mirror distance of the virtual mirror conductor from the A, B and C three-phase cables, , , respectively represent the actual distance of the positive pole of the DC cable from the A, B and C three-phase cables; I represents the effective value of the current in the real conductor; j represents the imaginary unit; μ0 represents the vacuum permeability.

[0020] Compared with the prior art, the present application has the following advantages: (1) In the prior art, when calculating the induced voltage on the metal sheath of the AC / DC cable, it is usually dependent on complex simulation software and calculation methods based on multi-conductor transmission line equations, although the induced voltage can be accurately predicted, the calculation process is complex and requires a long time, which is difficult to meet the demand for rapid calculation in engineering. In view of this technical problem, the present application proposes a simple analytical calculation method, which simulates the influence of the ground on the cable based on the electromagnetic field penetration depth and the mirror method, and quickly calculates the induced voltage on the metal sheath of the cable. This method not only improves the calculation efficiency, but also avoids the cumbersome steps caused by complex models in traditional simulation methods, so that the induced voltage can be more efficiently predicted and managed in actual engineering, thereby ensuring the safety of the power system.

[0021] (2) The present application proposes a method for calculating the induced voltage on the metal sheath of the AC / DC parallel laid DC cable, which is based on Maxwell's equations and equivalent to a virtual mirror conductor of a certain depth to simulate the influence of the finite conductivity ground. The induced electromotive force generated by the change of magnetic flux is analyzed by the law of electromagnetic induction, and the three-phase system is processed by using the complex phasor method and the superposition principle. The model converts the complex electromagnetic field problem into an engineering calculation formula based on the geometry and medium characteristics by introducing the shielding coefficient. The present application method can quickly and accurately calculate the induced voltage on the metal sheath of the DC cable in the AC / DC cable co-tunnel laying environment, accurately evaluate its numerical level and distribution characteristics, and has important significance for the safety design and reliable operation of the project.

[0022] (3) In the prior art, when analyzing the parallel laying of AC and DC, only the induced voltage on the positive and negative conductors of the cable is considered, and the induced voltage on the metal sheath of the DC cable is ignored. Since the metal sheath of the DC cable may generate a relatively significant induced voltage in the electromagnetic field, this part of the voltage poses a potential threat to the safety of the cable and the maintenance personnel. To solve this problem, the present application accurately calculates the induced voltage on the metal sheath of the DC cable, considers the electromagnetic coupling effect of three-phase current and the shielding effect of the metal sheath on the induced voltage, and proposes a more comprehensive induced voltage prediction method. This method not only solves the problem of ignoring the induced voltage on the metal sheath in the prior art, but also ensures accurate assessment of the overall safety of the cable system.

[0023] (4) Most existing calculation methods ignore the influence of the electromagnetic shielding effect of the metal sheath of the DC cable on the induced voltage. The metal sheath of the DC cable not only shields part of the induced voltage, but also changes the electromagnetic field distribution between the cables, thereby affecting the size of the induced voltage. To effectively solve this problem, the present application introduces the concept of shielding coefficient and makes superposition correction to the induced electromotive force caused by three-phase current according to the shielding effect. In this way, the present application can more realistically simulate the shielding effect of the metal sheath of the cable and calculate more accurate induced voltage values, avoiding calculation deviations that may be caused by ignoring the shielding effect.

[0024] (5) Traditional calculation methods often rely on multi-conductor transmission line theory and use complex circuit models to derive and calculate induced voltage. This method not only has a complex calculation process, but also requires a long calculation time, making it difficult to meet the demand for real-time calculation and rapid feedback in engineering. To solve this technical problem, the present application uses an analytical calculation method based on a single conductor and a virtual mirror conductor to significantly simplify the calculation process while ensuring calculation accuracy. This method can give the calculation result of the induced voltage in a short time, providing real-time support for safety monitoring and emergency handling in engineering sites, and solving the efficiency bottleneck of existing technologies in engineering applications. BRIEF DESCRIPTION OF DRAWINGS

[0025] Figure 1 The flow chart of the DC cable metal sheath induced voltage calculation method of the embodiment of the present application; Figure 2 The simulation schematic diagram of the parallel laying of AC and DC in single-phase AC of the embodiment of the present application; Figure 3 The comparison chart of test, simulation and analytical data under different single-phase AC current sizes of the embodiment of the present application; Figure 4 The simulation schematic diagram of the parallel laying of AC and DC in three-phase AC of the embodiment of the present application. DETAILED DESCRIPTION

[0026] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work should fall within the protection scope of the present application.

[0027] Embodiment 1 The embodiment provides a method for calculating induced voltage of a DC cable metal sheath laid in parallel with an AC cable, as shown in the formula (1), comprising the following steps: Figure 1 Step S1: calculating the penetration depth of electromagnetic field propagation in the ground according to the power frequency, ground magnetic permeability and ground conductivity; The distance at which the electromagnetic field intensity is attenuated to 1 / e of the surface value is called the penetration depth. As can be seen from the skin effect, when the time-varying electromagnetic field propagates in the ground conductor, the electromagnetic field intensity decreases with the increase of the penetration depth, and the formula is as follows: wherein, represents the penetration depth of the electromagnetic field in the ground; represents the frequency of the AC power supply; represents the magnetic permeability of the ground; represents the conductivity of the ground.

[0028] Step S2: simulating the influence of the ground on the conductor by using the mirror image method according to the calculated penetration depth, equivalent the influence of the ground conductor to a virtual mirror image conductor at a certain depth, calculating the distance from the power transmission conductor to the induced conductor and the mirror image conductor, specifically including: Taking the ground surface as the symmetry plane, according to the calculated electromagnetic field penetration depth d , a virtual mirror image conductor is arranged at the penetration depth position below the real conductor; For the real conductor with a height of h from the ground, the actual distance from the induced conductor to the real conductor and the distance from the induced conductor to the virtual mirror image conductor are determined.

[0029] The current in the virtual mirror image conductor is equal in size and opposite in direction to that in the real conductor, and is symmetrically arranged in space with respect to the ground and the real conductor.

[0030] Step S3: calculating the magnetic induction intensity generated by the conductor and the virtual mirror image conductor on the induced conductor based on the distance from the power transmission conductor to the induced conductor and the mirror image conductor. ​When the conductor and the ground form a loop, the ground effect is handled using the mirror method, placing a mirror conductor below the symmetric position of the real conductor about the ground surface at a depth d, the current in the mirror conductor is equal in magnitude and opposite in direction to the real conductor, removing the ground and only considering the joint action of the real conductor and the mirror conductor. For a single infinite straight wire with a height of h from the ground, with a current I, using the mirror method, the magnetic induction intensity at a distance r from the wire is the superposition of the real conductor and the mirror conductor, the formula is: wherein, B represents the magnetic induction intensity at the inducted conductor; μ0 represents the vacuum permeability; I represents the effective value of the current passing through the real conductor; r represents the distance from the inducted conductor to the real conductor; r' represents the distance from the inducted conductor to the virtual mirror conductor.

[0031] Step S4: Based on the magnetic induction intensity, the unit length magnetic flux of the conductor and the ground loop is derived by the superposition method of the magnetic field of the real conductor and the virtual mirror conductor, the formula is: wherein, Φ represents the unit length magnetic flux; μ0 represents the vacuum permeability; I represents the effective value of the current passing through the real conductor; r represents the actual distance from the transmission wire to the inducted conductor; r' represents the distance from the transmission wire to the virtual mirror conductor.

[0032] Step S5: Based on the unit length magnetic flux and the Faraday's law of electromagnetic induction, the induced electromotive force generated by the single wire on the inducted conductor is calculated, the formula is: wherein, E represents the induced electromotive force generated by the single wire on the inducted conductor; j represents the imaginary unit; ω represents the angular frequency of the three-phase power supply; Φ represents the unit length magnetic flux; μ0 represents the vacuum permeability; I represents the effective value of the current passing through the real conductor; r represents the actual distance from the transmission wire to the inducted conductor; r' represents the distance from the transmission wire to the virtual mirror conductor.

[0033] Using the logarithmic property, we can get: Step S6: Based on the relative position and phase difference of the three-phase currents, and the induced electromotive force generated by a single conductor on the induction conductor, calculate the induced electromotive force generated by each phase current on the induction conductor. If the conductors are three infinitely long straight wires, carrying three-phase alternating current, let the three-phase currents be: The formulas for the induced electromotive force generated in each phase on the induced conductor are: in, , , These represent the complex phasors of the three-phase currents A, B, and C, respectively. This represents the effective value of the current in a real conductor; Represents the imaginary unit; , , These represent the induced electromotive forces generated on the conductor by the three-phase currents A, B, and C, respectively. , These represent the mirror distances of the virtual mirror conductor from the three-phase cables A, B, and C, respectively. , , These represent the actual distances from the positive terminal of the DC cable to the three phases A, B, and C, respectively.

[0034] Mirror distance, the formula is: The actual distance is calculated using the formula: in, Indicates three-phase cable i The actual distance to the real conductor; Indicates three-phase cable i Distance to the virtual mirror conductor, ; These represent the horizontal position coordinates of the real conductor and the induced conductor, respectively; These represent the vertical height coordinates of the actual conductor and the induced conductor, respectively; This indicates the depth to which the electromagnetic field penetrates.

[0035] Step S7: Considering the shielding effect of the metal sheath, a shielding coefficient is introduced, and the total induced electromotive force on the DC cable metal sheath is obtained according to the superposition principle and the induced electromotive force caused by the three-phase current.

[0036] According to the shielding effect of the metal sheath, a shielding coefficient is introduced k ph For a 50Hz system, , , it is obtained: wherein, E represents the total induced electromotive force on the DC cable metal sheath, K represents the shielding coefficient, , respectively represent the mirror image distance of the virtual mirror conductor from the A, B and C three-phase cables, , , respectively represent the actual distance of the DC cable positive electrode from the A, B and C three-phase cables; I represents the effective value of the current in the real conductor; j represents the imaginary unit; μ0 represents the vacuum permeability.

[0037] Example 2: To verify the correctness of the calculation method of the induced voltage of the DC cable metal sheath under single-phase alternating current, two YJV22-8.7 / 15 3x400 parallel cables are used for testing and simulation. In this embodiment, one metal sheath is grounded at one end and grounded at the other end through a protector, and the other cable is used as a non-current-carrying cable as a DC cable model. The other cable as an AC circuit is applied with a single-phase alternating current through a through-core transformer to simulate the electromagnetic induction environment. Modeling is carried out through simulation, and the simulation is shown in Figure 2 .

[0038] Since the DC cable has a length of about 3m on one side and a coupling distance of 5m from the AC cable in the test, the approximate DC and AC cable real coupling length is 12m. Different single-phase alternating currents are applied to the AC cable, and the test, simulation and analytical calculation data are shown in Figure 3 and Table 1.

[0039] Table 1 Test, simulation and analytical induced voltage under different single-phase alternating current As shown in Table 1, when the single-phase current is 218.9A, the maximum error between the test and the analysis is 17.69%; when the single-phase current is 1037A, the maximum error between the simulation and the analysis is 12.49%. Although the analysis method mentioned in the application has certain error in precision compared with the test and the simulation calculation, the order of magnitude and the trend are consistent with the simulation, and the model construction is simple and does not depend on the simulation software.

[0040] To verify the correctness of the calculation method of the induced voltage of the DC cable metal sheath under three-phase alternating current, two YJV22-8.7 / 15 3x400mm 2 parallel laying, one metal sheath is grounded at one end and grounded at the other end through a protector, and the other cable is used as the AC loop, and the distance between the DC cable and the AC cable is 0.8m to simulate the electromagnetic induction environment, and the modeling is simulated as shown in Figure 4 Table 2 shows the simulation and the analytical induced voltage under different three-phase alternating current.

[0041] Table 2 shows the simulation and the analytical induced voltage under different three-phase alternating current. As shown in Table 2, when the three-phase current is 749A, the maximum error between the simulation and the analysis is 6.5%. Although the analysis method mentioned in the application has certain error in precision compared with the simulation calculation, the order of magnitude and the trend are consistent with the simulation, and the model construction is simple and does not depend on the simulation software.

[0042] If the above functions are realized in the form of software function units and sold or used as independent products, they can be stored in a computer readable storage medium. Based on this understanding, the technical solutions of the application or the parts of the application that essentially contribute to the prior art or the parts of the technical solutions can be embodied in the form of software products, and the computer software products are stored in a storage medium, including a plurality of instructions for causing a computer device (which can be a personal computer, a server, or a network device) to execute all or part of the steps of the method described in the embodiments of the application. The foregoing storage medium includes a U disk, a mobile hard disk, a read-only memory (ROM, Read-Only Memory), a random access memory (RAM, Random Access Memory), a magnetic disk or an optical disk, and various storage medium that can store program codes.

[0043] The above merely illustrates the specific embodiments of the present application, but the protection scope of the present application is not limited thereto, and any skilled person in the art can easily think of various equivalent modifications or replacements within the technical range disclosed by the present application, and these modifications or replacements shall be covered within the protection scope of the present application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.

Claims

1. A method for calculating the induced voltage of the metal sheath of a parallel AC / DC DC cable, characterized in that, Includes the following steps: Calculate the penetration depth of the electromagnetic field in the earth based on the power frequency, ground magnetic permeability, and ground electrical conductivity. Based on the calculated penetration depth, the influence of the ground on the conductor is simulated using the mirror method. The influence of the earth conductor is equivalent to a virtual mirror conductor at a specific depth, and the distance from the transmission line to the induced conductor and the mirror conductor is calculated. The magnetic flux density generated on the induced conductor by the conductor and the virtual mirror conductor is calculated based on the distance from the transmission line to the induced conductor and the mirror conductor. Based on magnetic induction intensity, the magnetic flux per unit length that constitutes the circuit between the conductor and the earth is derived by superimposing the magnetic fields of the real conductor and the virtual mirror conductor. Based on the magnetic flux per unit length and Faraday's law of electromagnetic induction, calculate the induced electromotive force generated by a single wire on an induction conductor. Based on the relative positions and phase differences of the three-phase currents, and the induced electromotive force generated by a single conductor on the induction conductor, the induced electromotive force generated by each phase current on the induction conductor is calculated. Considering the shielding effect of the metal sheath, a shielding coefficient is introduced. Based on the superposition principle and the induced electromotive force caused by the three-phase current, the total induced electromotive force on the metal sheath of the DC cable is obtained.

2. The method for calculating the induced voltage of the metal sheath of a parallel AC / DC cable according to claim 1, characterized in that, The penetration depth of the electromagnetic field in the earth is calculated based on the power supply frequency, ground magnetic permeability, and ground electrical conductivity, using the following formula: in, This indicates the depth to which an electromagnetic field penetrates the earth. Indicates the frequency of the AC power supply; It represents the magnetic permeability of the earth; It represents the electrical conductivity of the earth.

3. The method for calculating the induced voltage of the metal sheath of a parallel AC / DC DC cable according to claim 1, characterized in that, Based on the calculated penetration depth, the influence of the ground on the conductor is simulated using the mirror method, which equates the influence of the earth conductor to a virtual mirror conductor at a specific depth. The distance from the transmission line to the induced conductor and the mirror conductor is calculated, specifically including: Taking the Earth's surface as the plane of symmetry, based on the calculated electromagnetic field penetration depth... d A virtual mirror conductor is set at a depth position below the real conductor; For a height above the ground of h The real conductor, determining the actual distance from the induced conductor to the real conductor. and the distance to the virtual mirror conductor .

4. The method for calculating the induced voltage of the metal sheath of a parallel AC / DC cable according to claim 1, characterized in that, The current in the virtual mirror conductor is equal in magnitude and opposite in direction to that in the real conductor, and is arranged symmetrically with respect to the ground in space.

5. The method for calculating the induced voltage of the metal sheath of a parallel AC / DC cable according to claim 1, characterized in that, The magnetic flux density generated on the induced conductor by the conductor and the virtual mirror conductor is calculated based on the distance from the transmission line to the induced conductor and the mirror conductor, using the following formula: in, This represents the magnetic flux density at the point where the conductor is induced. Indicates the permeability of free space; It represents the effective value of the current passing through a real conductor; It represents the distance from the induced conductor to the actual conductor; This represents the distance from the induced conductor to the virtual mirror conductor.

6. The method for calculating the induced voltage of the metal sheath of a parallel AC / DC DC cable according to claim 1, characterized in that, The magnetic flux per unit length is given by the following formula: in, This represents the magnetic flux per unit length. Indicates the permeability of free space; It represents the effective value of the current passing through a real conductor; This is the actual distance between the transmission line and the induced conductor; This represents the distance between the transmission line and the virtual mirror conductor.

7. The method for calculating the induced voltage of the metal sheath of a parallel AC / DC cable according to claim 1, characterized in that, The formula for calculating the induced electromotive force generated by a single wire on an inductive conductor, based on the magnetic flux per unit length and Faraday's law of electromagnetic induction, is as follows: in, This represents the induced electromotive force generated in the conductor by a single wire. Represents the imaginary unit; This represents the angular frequency of a three-phase power supply. This represents the magnetic flux per unit length. Indicates the permeability of free space; This represents the effective value of the current in a real conductor; This is the actual distance between the transmission line and the induced conductor; This represents the distance between the transmission line and the virtual mirror conductor.

8. The method for calculating the induced voltage of the metal sheath of a parallel AC / DC DC cable according to claim 1, characterized in that, The calculation of the induced electromotive force (EMF) generated by each phase current on the induction conductor based on the relative position and phase difference of the three-phase currents and the induced EMF generated by a single conductor on the induction conductor specifically includes: The conductors are three infinitely long straight wires carrying three-phase alternating currents. Let the three-phase currents be: in, , , These represent the complex phasors of the three-phase currents A, B, and C, respectively. This represents the effective value of the current in a real conductor; Represents the imaginary unit; Based on the three-phase current, and the induced electromotive force generated by a single conductor in the induction conductor, the induced electromotive force generated by each phase current in the induction conductor is calculated using the following formula: in, , , These represent the induced electromotive forces generated on the conductor by the three-phase currents A, B, and C, respectively. , These represent the mirror distances of the virtual mirror conductor from the three-phase cables A, B, and C, respectively. , , These represent the actual distances from the positive terminal of the DC cable to the three phases A, B, and C, respectively.

9. The method for calculating the induced voltage of the metal sheath of a parallel AC / DC cable according to claim 8, characterized in that, The mirror distance is calculated using the following formula: The actual distance is calculated using the formula: in, Indicates three-phase cable i The actual distance to the real conductor; Indicates three-phase cable i Distance to the virtual mirror conductor, ; These represent the horizontal position coordinates of the real conductor and the induced conductor, respectively; These represent the vertical height coordinates of the actual conductor and the induced conductor, respectively; This indicates the depth to which the electromagnetic field penetrates.

10. The method for calculating the induced voltage of the metal sheath of a parallel AC / DC DC cable according to claim 1, characterized in that, Considering the shielding effect of the metal sheath, a shielding coefficient is introduced. Based on the superposition principle and the induced electromotive force caused by the three-phase current, the total induced electromotive force on the metal sheath of the DC cable is obtained, as shown in the formula: in, This represents the total induced electromotive force on the metal sheath of a DC cable. Indicates the shielding coefficient. , These represent the mirror distances of the virtual mirror conductor from the three-phase cables A, B, and C, respectively. , , These represent the actual distances from the positive terminal of the DC cable to the three-phase cables A, B, and C, respectively. This represents the effective value of the current in a real conductor; Represents the imaginary unit; It represents the vacuum permeability.

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