Method for calculating lightning induced voltage of overhead line-high-voltage cable sheath

Abstract

The invention discloses an overhead line-high voltage cable sheath lightning stroke induced voltage calculation method. At present, the voltage of a lightning stroke point, a connection point of an overhead line and a cable and a point in a well of each joint along a cable sheath cannot be obtained at the instantaneous moment of lightning stroke of the overhead line on site. According to the method, electromagnetic transient simulation modeling is carried out on actual spatial positions, structural parameters and material parameters of field overhead lines and high-voltage cables, electromagnetic transient simulation modeling is carried out on lightning currents, electromagnetic transient modeling is carried out on normal operation conditions and actual lightning stroke fault conditions of an electric power system, and after the randomness of the fault occurrence moment is considered, the electromagnetic transient simulation modeling is carried out on the actual lightning stroke fault conditions of the electric power system. And the maximum lightning stroke induced voltage value of each point along the cable sheath after lightning stroke is calculated through electromagnetic transient simulation software, so that a reference basis is provided for insulation matching design of the cable sheath of the overhead line-cable mixed line invaded by lightning current, and a foundation is laid for design evaluation of various subsequent voltage limiters and protectors.

Description

Technical Field

[0001] The present invention belongs to the technical field of power grid transmission and transformation, and relates to the calculation of lightning-induced voltage on cable sheaths. Specifically, it is a method for calculating lightning-induced voltage on overhead lines - high-voltage cable sheaths. Background Art

[0002] With the gradual increase in urban electricity consumption in recent years, a power transmission mode mainly based on high-voltage cables and supplemented by overhead lines has gradually formed in the urban center. Urban power transmission channels are developing towards higher voltage levels and larger transmission capacities. Overhead lines are vulnerable to extreme weather during operation, and there are many cases where lightning strikes the line and the lightning current invades the line. The cable lines connected to the overhead lines also have the risk of being invaded by lightning current.

[0003] Because the lightning strike occurs at the microsecond level, the existing on-line monitoring devices cannot always monitor the voltage information such as the lightning strike point, and the large-scale installation of on-site on-line monitoring devices will also cause the decline of the economic efficiency of power grid operation. At present, the characteristics of lightning-induced voltage on the sheaths of overhead line - cable hybrid lines are not clear, and the instantaneous moment of lightning strike on the overhead line, the voltage values at the lightning strike point, the connection point of the overhead line and the cable, and the points in each joint well along the cable sheath cannot be obtained on-site. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to overcome the defects of the above-mentioned existing technologies, and provide a method for calculating lightning-induced voltage on overhead lines - high-voltage cable sheaths. By using electromagnetic transient simulation software, it realizes the construction of electromagnetic transient models of overhead lines, cables, lightning currents, normal operation of the power system, and fault points. After considering the randomness of the lightning current occurrence time, different lightning strike occurrence times are set in the electromagnetic transient simulation software, and electromagnetic transient calculations are performed to obtain the maximum lightning-induced voltage values at each point along the cable sheath, so as to provide a reference basis for the insulation coordination design of the cable sheath when the lightning current invades the overhead line - cable hybrid line, and lay a foundation for the design and evaluation of various subsequent voltage limiters and protectors.

[0005] To this end, the present invention adopts the following technical solution: A method for calculating lightning-induced voltage on overhead lines - high-voltage cable sheaths, which includes the steps of: a) Obtain the actual spatial position and model of the on-site overhead line, obtain the structural parameters and material parameters of the overhead line, and establish an overhead line model in the electromagnetic transient simulation software; b) Obtain the actual spatial position and model of the on-site cable, obtain the structural parameters and material parameters of the cable, and establish a cable model in the electromagnetic transient simulation software; c) According to the normal operation parameters of the power system, establish a normal operation model of the power system in the electromagnetic transient simulation software; d) The overhead line model, cable model, and normal operation model of the power system are connected to the ABC three-phase conductors in the electromagnetic transient simulation software; e) According to the lightning current parameters, establish a lightning current model in the electromagnetic transient simulation software; f) According to the actual lightning strike fault parameters, establish a lightning strike fault point model in the electromagnetic transient simulation software; g) The lightning current model and the lightning strike fault point model are connected to the overhead line model through a single-phase conductor in the electromagnetic transient simulation software, and the lightning current is injected into the normally operating power system through a single-phase conductor; h) Set different lightning strike occurrence times in the electromagnetic transient simulation software, and use the electromagnetic transient simulation software to perform electromagnetic transient calculations to obtain the maximum lightning strike induced voltage at each point along the overhead line - high-voltage cable sheath.

[0006] Further, in step a), the actual spatial position of the overhead line includes the heights of the ABC three-phase lines from the ground and the distances from the center crossarm of the tower, as well as the height of the ground wire from the ground and the distance from the center crossarm of the tower; the structural parameters and material parameters of the corresponding model overhead line are obtained through the overhead line model. The structural parameters include: the outer diameter of the conductor of the ABC three-phase lines, the total number of strands, the number of outermost strands, the diameter of a single strand, and the sag, as well as the outer diameter of the conductor and the sag of the ground wire; the material parameters include: the DC resistance and relative magnetic permeability of the conductor of the ABC three-phase lines, as well as the DC resistance and relative magnetic permeability of the conductor of the ground wire.

[0007] Further, in step b), the actual spatial position of the cable includes the heights of the ABC three-phase cables from the ground and the distances from the origin of the abscissa; the structural parameters and material parameters of the corresponding model cable are obtained through the cable model. The structural parameters include: the outer diameter of the conductor core of the ABC three-phase cables, the outer diameter of the XLPE insulation layer, the outer diameter of the metal sheath, and the outer diameter of the outer insulation layer; the material parameters include: the resistivity of the conductor at 90 °C, the relative permittivity of the XLPE insulation layer, the resistivity of the metal sheath at 70 °C, and the relative permittivity of the outer insulation layer.

[0008] Further, in step c), the normal operation parameters of the power system include the effective value of the power system operating power frequency voltage, the equivalent internal inductance value of the power system operation, the active power of the load, and the reactive power of the load; Step d) specifically includes: d1) The normal operation model of the power system is two modules: the module connecting the power system power frequency power supply to the equivalent internal inductance and the power system load module; d2) The power system power frequency power supply, the equivalent internal inductance of the power system operation, the overhead line model, the cable model, and the power system load are connected in series in sequence using ABC three-phase conductors.

[0009] Further, in step e), the lightning current model parameters include the lightning current peak value, the wavefront time, and the half-peak time. The lightning current is described by a double-exponential function model, as shown in the following formula: , where, represents the lightning current; represents the initial lightning current peak value, in kA; is the peak current correction factor; t represents time, in seconds; is the wavefront time coefficient; is the half-wave peak time coefficient; e is the natural constant; , where, is the lightning current peak value, which is jointly determined by , and ; the wavefront time is determined by , and the half-peak time is determined by .

[0010] Further, in step f), the lightning strike fault parameters include the actual position of the fault point and the fault phase.

[0011] Further, step g) is specifically as follows: g1) Connect the lightning current model and the lightning strike fault point model with a single-phase wire; g2) Connect the lightning strike fault point model and the overhead line model with a single-phase wire. The overhead line model is connected to any one of the three-phase wires ABC of the phase selection.

[0012] Further, in step h), the maximum value of the lightning-induced voltage at each point along the overhead line - high-voltage cable sheath is obtained through the following steps: h1) In the cable model described above, set voltage monitoring points at the cable sheath joints of each section; h2) In the electromagnetic transient simulation software, set different fault occurrence times. During one cycle of normal operation of the power system, set the fault occurrence time randomly N times, and record the lightning-induced voltage value of each phase at each point along the cable sheath; h3) After the electromagnetic transient simulation software finishes running repeatedly, compare the lightning-induced voltage values of each phase of ABC at each point along the cable sheath to obtain the maximum value of the lightning-induced voltage; , where, is the maximum value of the lightning-induced voltage; i represents each point along the cable sheath, and 0 is the cable sheath head end; jRepresent the phases of ABC three - phase; is the single - phase voltage value at each point along the cable sheath.

[0013] Compared with the prior art, the present invention conducts electromagnetic transient simulation modeling on the actual spatial positions, structural parameters, and material parameters of on - site overhead lines and cables, conducts electromagnetic transient simulation modeling on lightning currents, and conducts electromagnetic transient modeling on the normal operation and actual fault conditions of the power system. After considering the randomness of the fault occurrence time, the electromagnetic transient simulation software calculates the maximum value of the lightning - induced voltage at each point along the cable sheath after a lightning strike, thereby providing a reference basis for the insulation coordination design of the cable sheath of the overhead line - cable hybrid line invaded by lightning current and laying a foundation for the design and evaluation of various subsequent voltage limiters and protectors. Brief Description of the Drawings

[0014] Figure 1 is the flowchart of a method for calculating the lightning - induced voltage of the sheath of an overhead line - high - voltage cable according to the present invention; Figure 2 is the flowchart for obtaining the calculation result of the lightning - induced voltage of the sheath at the cable sectional joint with random fault time according to the present invention; Figure 3 is the diagram of the calculation results of the lightning - induced voltage at each point along the cable sheath at different lightning strike times in the specific embodiment of the present invention. Detailed Embodiment

[0015] The following combines the drawings of the present invention to explain and illustrate the technical solutions of the embodiments of the present invention. However, the following embodiments are only the preferred embodiments of the present invention, not all of them. Based on the embodiments in the implementation manners, other embodiments obtained by those skilled in the art without creative efforts all belong to the protection scope of the present invention.

[0016] This embodiment is a method for calculating the lightning - induced voltage of the sheath of an overhead line - high - voltage cable, as Figure 1 shown. The steps are as follows: a) Obtain the actual spatial position and model of the on - site overhead line, obtain the structural parameters and material parameters of the overhead line, and establish an overhead line model in the electromagnetic transient simulation software; b) Obtain the actual spatial position and model of the on - site cable, obtain the structural parameters and material parameters of the cable, and establish a cable model in the electromagnetic transient simulation software; c) According to the normal operation parameters of the power system, establish a normal operation model of the power system in the electromagnetic transient simulation software; d) Connect the overhead line model, cable model, and normal operation model of the power system to the ABC three - phase conductors in the electromagnetic transient simulation software; e) According to the lightning current parameters, establish a lightning current model in the electromagnetic transient simulation software; f) Establish a lightning fault point model in the electromagnetic transient simulation software according to the actual lightning fault parameters; g) For the lightning current model and the lightning fault point model described above, connect the overhead line model through a single-phase conductor in the electromagnetic transient simulation software, and inject the lightning current into the normally operating power system through the single-phase conductor; h) Set different lightning strike occurrence times in the electromagnetic transient simulation software, and use the electromagnetic transient simulation software to perform electromagnetic transient calculations to obtain the maximum lightning-induced voltage values at various points along the overhead line - high-voltage cable sheath.

[0017] Specifically, in step a), the actual spatial position of the overhead line includes the heights of the ABC three-phase lines from the ground and the distances from the center cross-arm of the tower, as well as the height of the ground wire from the ground and the distance from the center cross-arm of the tower; the structural parameters and material parameters of the corresponding type of overhead line are obtained through the overhead line model. The structural parameters include: the outer diameter of the conductors of the ABC three-phase lines, the total number of strands, the number of outermost strands, the diameter of a single strand, and the sag, as well as the outer diameter of the conductor and the sag of the ground wire; the material parameters include: the DC resistance and relative magnetic permeability of the conductors of the ABC three-phase lines, as well as the DC resistance and relative magnetic permeability of the ground wire.

[0018] Specifically, in step b), the actual spatial position of the cable includes the heights of the ABC three-phase cables from the ground and the distances from the origin of the abscissa (the origin of the abscissa is defined by oneself in the electromagnetic transient simulation software); the structural parameters and material parameters of the corresponding type of cable are obtained through the cable model. The structural parameters include: the outer diameter of the conductor cores of the ABC three-phase cables, the outer diameter of the XLPE insulation layer, the outer diameter of the metal sheath, and the outer diameter of the outer insulation layer; the material parameters include: the resistivity of the conductor at 90 °C, the relative permittivity of the XLPE insulation layer, the resistivity of the metal sheath at 70 °C, and the relative permittivity of the outer insulation layer.

[0019] Specifically, in step c), the normal operating parameters of the power system include the effective value of the power frequency voltage of the power system operation, the equivalent internal inductance value of the power system operation, the active power of the load, and the reactive power of the load; Specifically, step d) includes: d1) The normal operating model of the power system is two modules: the module of the power system power frequency power supply connected to the equivalent internal inductance and the power system load module; d2) The power system power frequency power supply, the equivalent internal inductance of the power system operation, the overhead line model, the cable model, and the power system load are connected in series in sequence by the ABC three-phase conductors.

[0020] Specifically, in step e), the parameters of the lightning current model include the peak value of the lightning current, the wavefront time, and the half-peak time. The lightning current is described by a double-exponential function model, as shown in the following formula: , Among them, represents the lightning current; represents the initial lightning current peak value, kA; is the peak current correction factor; t represents time, in seconds; is the wavefront time coefficient; is the half-peak time coefficient; e is the natural constant; , Among them, is the lightning current peak value, determined jointly by , and ; The wavefront time is determined by , and the half-peak time is determined by .

[0021] Specifically, in step f), the lightning strike fault parameters include the actual position of the fault point and the fault phase.

[0022] Specifically, step g) is specifically as follows: g1) Connect the lightning current model and the lightning strike fault point model with a single-phase wire; g2) Connect the lightning strike fault point model and the overhead line model with a single-phase wire. The overhead line model is connected to any one of the ABC three-phase wires of the phase selection.

[0023] Specifically, in step h), the maximum value of the lightning-induced voltage at each point along the overhead line - high-voltage cable sheath is obtained through the following steps, as Figure 2 shown: h1) In the cable model described above, set voltage monitoring points at the cable sheath joints of each segment; h2) In the electromagnetic transient simulation software, set different fault occurrence times. During one cycle (20 ms) of normal operation of the power system, set the fault occurrence time randomly N times, and record the lightning-induced voltage value of each phase at each point along the cable sheath; h3) After the electromagnetic transient simulation software finishes running repeatedly, compare the lightning-induced voltage values of each phase of ABC at each point along the cable sheath to obtain the maximum value of the lightning-induced voltage; , Among them, is the maximum value of the lightning-induced voltage; i represents each point along the cable sheath, 0 is the cable sheath head end; j represents the ABC three-phase phases; is the single-phase voltage value at each point along the cable sheath.

[0024] Taking a 220 kV lightning strike line fault occurring on-site as an example, the lightning-induced voltage value of the cable sheath connected to this line is obtained below by applying the lightning-induced voltage calculation method for overhead line - high-voltage cable sheath of the present invention. The specific steps are as follows: 1) Obtain the structural parameters and material parameters of the overhead line according to the actual spatial position and type of the on-site overhead line.

[0025] 1.1) Obtain the actual spatial position of the overhead line, including: the heights of the ABC three-phase lines from the ground are 66.45 m, 54.4 m, and 43.2 m respectively, and the distances from the center cross-arm of the tower are 18.4 m, 23.5 m, and 20.0 m respectively; and the height of the ground wire from the ground is 69.15 m, and the distance from the center cross-arm of the tower is 22.8 m.

[0026] 1.2) Obtain that the actual overhead line conductor type on-site is LGJ - 630 / 45, and obtain the structural parameters and material parameters of the overhead line of the corresponding type. The structural parameters include: the outer diameters of the conductors of the ABC three-phase lines are 0.014636 m, the total number of strands is 45, the number of strands in the outermost layer is 7, the diameter of a single strand is 0.00211 m, and the sag is 12 m; and the outer diameter of the conductor of the ground wire is 0.00166 m, and the sag is 12 m. The material parameters include: the DC resistance of the conductors of the ABC three-phase lines is 0.0459 Ω / km, and the relative magnetic permeability is 1.0; and the DC resistance of the conductor of the ground wire is 0.045 Ω / km and the relative magnetic permeability is 1.0.

[0027] 1.3) Establish an overhead line model in the simulation software PSCAD.

[0028] 2) Obtain the structural parameters and material parameters of the cable according to the actual spatial position and type of the on-site cable.

[0029] 2.1) Obtain the actual spatial position of the cable, including that the heights of the ABC three-phase cables from the ground are 0.5 m, 0.64 m, and 0.5 m, and the distances of the three-phase cables from the abscissa origin (the abscissa origin is taken as the center of the A-phase cable) are 0, 0.1 m, and 0.2 m.

[0030] 2.2) Obtain that the actual cable type on-site is YJLW - 127 / 220 kV - 1×2500 mm 2 , and obtain the structural parameters and material parameters of the cable of the corresponding type. The structural parameters include: the outer diameters of the conductor cores of the ABC three-phase cables are 0.0310 m, the outer diameter of the XLPE insulation layer is 0.0580 m, the outer diameter of the metal sheath is 0.0730 m, and the outer diameter of the outer insulation layer is 0.0790 m; the material parameters include: the resistivity of the conductor at 90 °C is 2.1*10 -8Ω·m, the relative permittivity of the XLPE insulation layer is 2.3, the resistivity of the metal sheath at 70 °C is 2.5×10 -7 Ω·m, and the relative permittivity of the outer insulation layer is 2.3.

[0031] 2.3) Establish a cable model in the simulation software PSCAD.

[0032] 3) Select typical lightning current parameters: peak value -30 kA, wavefront / half-peak time 2.6 / 50 μs, wave impedance 300 Ω. Establish a lightning current model at the lightning strike point in the simulation software PSCAD.

[0033] 4) In the normal operation state of the power system, the effective value of the power system power frequency line voltage is taken as 1.05 p.u. (231 kV), the equivalent internal inductance of the power system operation is taken as 20 mH, the three-phase load active power is taken as 200 MW, and the load reactive power is taken as 0. The power system reaches a steady state after operating for 0.1 s. Establish a normal operation model of the power system in the simulation software PSCAD.

[0034] 5) In the actual fault situation, the actual position of the fault point is on the overhead line, 500 m away from the cable head. The fault phase is phase B. Establish a lightning strike fault point model in the simulation software PSCAD.

[0035] 6) Considering the randomness of the lightning current occurrence time, set different lightning strike occurrence times in the simulation software PSCAD. The calculation results of the lightning-induced voltage at each point along the cable sheath under different lightning strike times are as Figure 3 shown.

[0036] It can be seen that the sheath induced overvoltage invaded when the power frequency of the power supply runs to the trough of the wave reaches the minimum, and the induced voltage level in the single-end grounding mode is 131.36 kV; the sheath induced overvoltage invaded when the power frequency runs to the peak reaches the maximum, and the overvoltage levels are 322.22 kV respectively. Compared with the invasion at the peak moment, the overvoltage levels generated by the same lightning current invading at the trough moment of the power frequency operation are reduced by 60% respectively in the two grounding modes, which has an obvious reduction effect. Through electromagnetic transient calculation, the maximum value of the lightning-induced voltage of the cable sheath is 322.22 kV.

[0037] The above description of the embodiments is to facilitate the understanding and application of the present invention by ordinary technical personnel in the technical field. Those who are familiar with the technology in this field can obviously make various modifications to the above embodiments easily, and apply the general principles described here to other embodiments without creative labor. Therefore, the present invention is not limited to the above embodiments, and all improvements and modifications made by those skilled in the art according to the disclosure of the present invention should be within the protection scope of the present invention.

Claims

1. A calculation method for the induced lightning voltage of the overhead line - high voltage cable sheath, characterized in that, Including the steps: a) Obtain the actual spatial position and model of the on-site overhead line, get the structural parameters and material parameters of the overhead line, and establish an overhead line model in the electromagnetic transient simulation software; b) Obtain the actual spatial position and model of the on-site cable, get the structural parameters and material parameters of the cable, and establish a cable model in the electromagnetic transient simulation software; c) According to the normal operation parameters of the power system, establish a normal operation model of the power system in the electromagnetic transient simulation software; d) The above-mentioned overhead line model, cable model and normal operation model of the power system are connected to the ABC three-phase conductors in the electromagnetic transient simulation software; e) According to the lightning current parameters, establish a lightning current model in the electromagnetic transient simulation software; f) According to the actual lightning strike fault parameters, establish a lightning strike fault point model in the electromagnetic transient simulation software; g) The above-mentioned lightning current model and lightning strike fault point model are connected to the overhead line model through a single-phase conductor in the electromagnetic transient simulation software, and the lightning current is injected into the normally operating power system through a single-phase conductor; h) Set different lightning strike occurrence times in the electromagnetic transient simulation software, and use the electromagnetic transient simulation software to perform electromagnetic transient calculations to obtain the maximum lightning induction voltage at each point along the overhead line - high-voltage cable sheath.

2. The method for calculating the lightning-induced voltage of the overhead line - high-voltage cable sheath according to claim 1, characterized in that, In step a), the actual spatial position of the overhead line includes the heights of the ABC three-phase lines from the ground and the distances from the center cross-arm of the tower, as well as the height of the ground wire from the ground and the distance from the center cross-arm of the tower.

3. The method for calculating the lightning-induced voltage of the overhead line - high-voltage cable sheath according to claim 1, wherein, In step a), the structural parameters and material parameters of the corresponding model overhead line are obtained through the overhead line model. The structural parameters include: the outer diameter of the conductors of the ABC three-phase lines, the total number of strands, the number of outermost strands, the diameter of a single strand and the sag, as well as the outer diameter of the conductor and the sag of the ground wire; the material parameters include: the DC resistance and relative magnetic permeability of the conductors of the ABC three-phase lines, as well as the DC resistance and relative magnetic permeability of the ground wire.

4. The method for calculating the lightning strike induced voltage of the overhead line - high voltage cable sheath according to claim 1, characterized in that, In step b), the actual spatial position of the cable includes the height of the ABC three-phase cables from the ground and the distance from the origin of the abscissa.

5. The method for calculating the lightning-induced voltage of the overhead line - high-voltage cable sheath according to claim 1, characterized in that, In step b), the structural parameters and material parameters of the corresponding model cable are obtained through the cable model. The structural parameters include: the outer diameter of the conductor cores of the ABC three-phase cables, the outer diameter of the XLPE insulation layer, the outer diameter of the metal sheath and the outer diameter of the outer insulation layer; the material parameters include: the resistivity of the conductor at 90 °C, the relative permittivity of the XLPE insulation layer, the resistivity of the metal sheath at 70 °C and the relative permittivity of the outer insulation layer.

6. The method for calculating the lightning-induced voltage of the overhead line - high-voltage cable sheath according to claim 1, wherein In step c), the normal operation parameters of the power system include the effective value of the power system operating power frequency voltage, the equivalent internal inductance value of the power system operation, the active power of the load and the reactive power of the load; Step d) specifically includes: d1) The normal operation model of the power system is two modules: the module of the power system power frequency power supply connected to the equivalent internal inductance and the power system load module; d2) The power system power frequency power supply, the power system operation equivalent internal inductance, the overhead line model, the cable model and the power system load are connected in series in sequence by the ABC three-phase conductors.

7. The method for calculating the lightning-induced voltage of the overhead line - high-voltage cable sheath according to claim 1, characterized in that, In step e), the lightning current model parameters include the peak value of the lightning current, the front time, and the half-peak time. The lightning current is described by a double-exponential function model, as shown in the following formula: ， Among them, represents the lightning current; represents the initial lightning current peak value, kA; is the peak current correction factor; t represents time, in seconds; is the wavefront time coefficient; is the half-peak time coefficient; e is the natural constant; ， Among them, is the peak value of lightning current, which is jointly determined by , and ; the wavefront time is determined by , and the half-peak value time is determined by .

8. The method for calculating the lightning strike induced voltage of the overhead line - high voltage cable sheath according to claim 1, wherein, In step f), the lightning strike fault parameters include the actual location of the fault point and the fault phase.

9. The method for calculating the induced lightning voltage of the overhead line - high voltage cable sheath according to claim 1, wherein Step g) is specifically as follows: g1) Connect the lightning current model and the lightning strike fault point model using a single-phase wire; g2) Connect the lightning strike fault point model and the overhead line model using a single-phase wire. The overhead line model is connected to any one of the ABC three-phase wires for the selected phase.

10. The method for calculating the lightning strike induced voltage of the overhead line - high voltage cable sheath according to claim 1, characterized in that, In step h), the maximum value of the lightning-induced voltage at each point along the overhead line - high-voltage cable sheath is obtained through the following steps: h1) In the cable model described above, set voltage monitoring points at the cable sheath joints of each segment; h2) In the electromagnetic transient simulation software, set different fault occurrence times. During one cycle of normal operation of the power system, set the fault occurrence time randomly N times, and record the lightning-induced voltage value of each phase at each point along the cable sheath; h3) After the electromagnetic transient simulation software has finished running repeatedly, compare the lightning-induced voltage values of each phase of ABC at each point along the cable sheath to obtain the maximum value of the lightning-induced voltage; ， Among them, is the maximum value of the lightning strike induced voltage; i represents each point along the cable sheath, and 0 is the beginning end of the cable sheath; j represents the ABC three-phase phases; is the single-phase voltage value of each point along the cable sheath.

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