Method for calculating electromagnetic interference of power grid on buried pipe network

Abstract

The application discloses a kind of power grid to buried pipe network's electromagnetic interference calculation method, comprising the following steps: conductor is divided into a conductor microsection, conductor microsection outer surface two end potential difference is equal to the potential difference of conductor microsection inside, according to this continuity feature equation group is established, according to leakage current the potential difference of conductor microsection outer surface two ends is solved, the impedance of conductor microsection itself and the product of axial current are then solved the potential difference of conductor microsection inside two ends;According to Kirchhoff's law, the relationship between axial current and leakage current on each conductor microsection is obtained, a set of linear algebraic equations is established, and the leakage current distribution on the conductor is obtained by solving the linear algebraic equations.The results of the application are used to evaluate the influence of electromagnetic interference on buried pipe network, so as to control the risk in advance and realize the harmonious coexistence of power grid and oil and gas pipeline network.

Description

TECHNICAL FIELD

[0001] The present application relates to power grid engineering technology, in particular to electromagnetic interference analysis technology of power grid to buried pipe network. BACKGROUND

[0002] Oil and gas pipelines and power grids are lifelines of energy security. In recent years, the rapid economic development has made China's demand for energy increasing. However, the special geographical environment of China has resulted in the reverse distribution of energy layout and power consumption in geography, which makes large-scale and long-distance energy transportation inevitable. So far, there are 160,000 kilometers of oil and gas pipelines in operation in China. In order to fully exert the advantages of limited land resources, power lines and oil and gas pipelines inevitably cross each other. In some land-scarce areas, long-distance pipelines even share the same corridor. A large number of power lines and oil and gas pipelines run in parallel, and the electromagnetic compatibility problem (including magnetic field coupling and electric field coupling) between them is becoming more and more serious. Once the pipeline system is damaged due to this problem, it will cause serious damage to the ecological environment and may also cause major safety accidents. Therefore, the safety influence of large-area power grid on buried metal pipelines has become a very acute problem.

[0003] When the power grid normally transmits power, the alternating electromagnetic field will generate an induced voltage on the nearby oil and gas pipeline. If the AC transmission line is too close to the oil and gas pipeline or the coupling relationship is too strong, it will result in a high voltage to the ground of the pipeline, which may affect the normal work of construction, maintenance or measurement personnel, and even cause corrosion of the pipeline in serious cases.

[0004] Therefore, in order to avoid the alternating electromagnetic field generated by the normal operation of the power grid from having too great an influence on the oil and gas pipeline and inducing serious accidents, the influence of electromagnetic interference on buried pipe network in the normal operation state of the power grid should be analyzed in depth, so as to control the risk in advance and realize the harmonious coexistence of the power grid and the oil and gas pipeline network. SUMMARY

[0005] The technical problem to be solved by the present application is to provide an electromagnetic interference calculation method of power grid to buried pipe network, according to the results, so as to control the risk in advance and realize the harmonious coexistence of the power grid and the oil and gas pipeline network.

[0006] To solve the above technical problems, the present application adopts the following technical scheme: an electromagnetic interference calculation method of power grid to buried pipe network, the calculation results are used to evaluate the influence of electromagnetic interference on buried pipe network, including the following steps:

[0007] The conductor is divided into conductor micro-sections, the potential difference between the two ends of the outer surface of the conductor micro-section is equal to the potential difference between the two ends of the conductor micro-section, equations are established according to the continuity characteristics, the potential difference between the two ends of the outer surface of the conductor micro-section is obtained according to the leakage current, and the potential difference between the two ends of the conductor micro-section itself is multiplied by the axial current to obtain the potential difference between the two ends of the conductor micro-section.

[0008] According to Kirchhoff's law, the relationship between the axial current and the leakage current on each conductor micro-section is obtained, and a set of linear algebraic equations is established, and the leakage current distribution on the conductor is obtained by solving the linear algebraic equations.

[0009] Preferably, the electromagnetic interference of the power grid on the pipe network is realized through electromagnetic field, and therefore Maxwell's equations are followed:

[0010]

[0011] In the formula, H is the magnetic field strength; B is the magnetic flux density; D is the electric displacement vector; E is the electric field strength; ρ is the space charge density; J s is the conduction current density;

[0012] The vector magnetic potential A and the scalar potential function φ are introduced, and B = rot A, then from the second formula of Maxwell's equations, we have:

[0013]

[0014] In the formula, ω is the angular frequency, which is substituted into the first and fourth formulas of Maxwell's equations to obtain the D'Alembert equation:

[0015]

[0016] In the formula, is the phase constant, and μ and ε are the magnetic permeability and dielectric constant respectively;

[0017] The interference of the interference source on the interfered point is given by the following general solution:

[0018]

[0019] In the formula, R is the distance from the interfered point to the interference source;

[0020] The power grid conductor is divided into n s segments, the pipe network conductor is divided into n p segments, the current flowing through the i i th segment of the conductor is I

[0021]

[0022] The induced potential on the kth segment of the pipeline conductor micro-segment is the sum of the potential induced by the current on all the micro-segments of the pipeline conductor, i.e.

[0023]

[0024] Under the action of the induced potential, the pipeline forms a current loop with the anticorrosive layer and the soil, and a certain current field distribution is formed in the ground. After segmentation, the micro-segments of the pipeline conductor have b endpoints. Since the segmented pipeline conductor is short, the potential U i on the ith segment of the pipeline is taken as the average of the voltages V j1 and V j2 of the two adjacent endpoints, i.e.

[0025]

[0026] In matrix form, it is written as:

[0027] U = KV

[0028] Similarly, the current I d of each segment of the conductor is divided into two parts, which flows into the ground from the two nodes connected to it, so:

[0029] J = K T I d

[0030] In the formula, J is the equivalent current of each node.

[0031] For the segmented pipeline conductor, KCL and KVL are:

[0032]

[0033] In the formula, Y is the branch admittance matrix; A is the incidence matrix; I1 is the current flowing through each pipeline conductor;

[0034] Therefore, the node admittance equation is:

[0035] AYA T V = AYE - J

[0036] Using the Green function, the relationship between the potential of each conductor and the current is:

[0037] U = ZI d

[0038] In the formula, Z is the mutual impedance matrix between each micro-segment of the conductor, including inductive and resistive components. The inductive component is:

[0039] The pipeline potential is calculated by combining the above formulas:

[0040] U = K(AYA T+K T Z -1 K) -1 AYE

[0041] Under the lightning condition, the time-domain solution method of electromagnetic coupling between conductors is complex and has large amount of calculation, and the potential distribution of the system under the impulse current is generally calculated by using the time-frequency conversion method. Firstly, the moment method is used to calculate the potential of the grounding grid under the impulse current. The impulse current in the time domain can be described by the following double exponential function:

[0042] I(t)=I m (e -αt -e -βt )

[0043] In the formula: t is time; α is the wave front attenuation index; β is the wave tail attenuation index; I m is the current amplitude.

[0044] By using Fourier transform, the impulse current waveform in the time domain can be converted into the frequency domain response:

[0045]

[0046] In the formula: ω is the angular frequency; I(ω) is the lightning current in the frequency domain.

[0047] The current I(l') linearly changes on the axis l' of the conductor, and the line charge is uniformly distributed on the surface of the conductor, and the scattered electric field strength generated in space is

[0048]

[0049] In the infinite space, there is

[0050]

[0051]

[0052] In the formula: e is the axis direction of the cylindrical conductor line current; A is the vector magnetic potential generated by the axial current I(l'); r is the distance between the field point and the source point in space; φ is the scalar potential generated by the line charge uniformly distributed on the surface of the conductor; μ and ε are the magnetic permeability and dielectric constant of the space where the conductor is located, respectively; k is the wave number.

[0053] The integral equation of the electric field strength can be obtained by combining

[0054]

[0055] Suppose that the entire conductor structure is divided into n segments of conductors, then

[0056] ​

[0057] In the formula: I i and U j is the current on the ith segment of conductor and the potential at the midpoint of the jth segment of conductor respectively; Z ij is the transfer impedance between the ith segment of conductor and the jth segment of conductor

[0058]

[0059] When the lightning current is injected into one end of the conductor, the current injected into one end of the segment of conductor is a known quantity, which can be expressed in a matrix form:

[0060] Z -1 U = I

[0061] Since the current vector I of the injected segment of conductor is known, other unknown currents and branch voltages can be solved. Thus, the spatial current distribution, electromagnetic field and other problems can be solved. Finally, the scalar voltage, electric field intensity and magnetic field intensity in the time domain can be solved through Fourier inverse transform.

[0062]

[0063]

[0064]

[0065] In the formula: U0(ω), E0(ω) and H0(ω) are respectively the scalar voltage, electric field intensity and magnetic field intensity in the frequency domain generated by a unit current source.

[0066] The technical scheme adopted by the present application is based on the method of calculating the electromagnetic interference of the power transmission line on the pipeline, and the influence of the electromagnetic interference on the buried pipeline network is evaluated according to the result, so as to pre-control the risk and realize the harmonious coexistence of the power grid and the oil and gas pipeline network.

[0067] The specific technical scheme adopted by the present application and the beneficial effects brought by the specific technical scheme will be described in detail in the specific embodiments below in combination with the drawings. BRIEF DESCRIPTION OF DRAWINGS

[0068] The present application will be further described below in combination with the drawings and specific embodiments:

[0069] Figure 1 It is a circuit diagram of the buried pipeline-ground equivalent loop model;

[0070] Figure 2 It is a schematic diagram of overhead line;

[0071] Figure 3 It is a schematic diagram of underground cable;

[0072] Figure 4 Model diagram of overhead conductor and buried conductor for uniform soil;

[0073] Figure 5 Equivalent circuit diagram for single-phase grounding short circuit;

[0074] Figure 6 Schematic diagram of pipe network conductor segment magnetic field diffusion. DETAILED DESCRIPTION

[0075] The electromagnetic interference problem of an AC transmission line on a nearby buried metal pipeline is mainly caused by the spatial electromagnetic field and the ground current of the AC current in the line. From the mechanism level, it can be divided into three categories: inductive coupling effect, resistive coupling effect, and capacitive coupling effect. The analysis of the electromagnetic influence mechanism is the basis for determining the electromagnetic influence object and the calculation method, and it is also helpful for formulating relevant limits, determining safety distances, and implementing protection measures.

[0076] Inductive coupling: the alternating current in the transmission line will produce an alternating magnetic field around it, which will induce a voltage on the buried metal pipeline. This alternating magnetic field exists not only in the air but also in the ground. When the buried metal pipeline is close to the transmission line, the magnetic field is stronger, which will produce a longitudinal electromotive force on both sides of the pipeline. The pipeline is usually coated with a corrosion-resistant layer, and the corrosion-resistant layer material is not an absolute insulating material, but a substance with a certain electrical conductivity, i.e., there is a leakage current between the pipe and the ground. The longitudinal electromotive force acting on the pipe and the ground forms a loop that produces a longitudinal current and a leakage current, and generates a potential difference on both sides of the pipeline coating, i.e., a coating voltage.

[0077] Capacitive coupling: high-voltage is applied to the conductor of a high-voltage AC transmission line, and there is a strong electric field around it. Due to the principle of electrostatic induction, a potential to ground will be induced on the pipeline. However, the ground generally has good shielding effect on the electric field, and the capacitive coupling effect of the transmission line on the buried pipeline is small.

[0078] Resistive coupling: when a single-phase grounding short circuit fault occurs in the line, the short-circuit current flows into the ground through the tower grounding device. The large short-circuit current will greatly raise the ground potential in the vicinity of the fault point. When there is a buried oil and gas pipeline near the tower, the metal pipeline will remain at a lower potential due to the high resistivity of the pipeline coating. Thus, a high potential difference is formed between the metal pipeline and the ground around the pipeline.

[0079] Calculation method of the influence of the power grid on the pipeline network

[0080] Theoretical basis

[0081] By regarding the ground as a reference conductor and treating the long-distance oil and gas pipeline as an infinitesimal, an equivalent model of the pipeline-ground loop transmission line can be established, and the equivalent circuit of the pipeline-ground loop is shown in Figure 1 .

[0082] The corresponding frequency domain telegraph equation is:

[0083]

[0084]

[0085] Where U, I are voltage and current along the pipeline respectively; Z, Y are unit length series impedance and shunt admittance of the pipeline-ground return transmission line model respectively; E is the induced electromotive force generated by the transmission line on the unit length pipeline. The above equations can be obtained by simultaneous equations:

[0086]

[0087]

[0088] Assuming that the induced electromotive force generated by the transmission line on each pipeline element does not change with the coordinate x, i.e. E is a constant, the general solution can be obtained:

[0089] U(x) = Ae γx + Be -γx

[0090]

[0091] Where Z C is the characteristic impedance of the pipeline-ground return transmission line model, γ is the propagation constant, α and β are the attenuation constant and phase constant respectively.

[0092] To solve the equation, two terminal constraints are also required. According to the transmission line end constraints U(0) = -Z1I(0) and U(L) = Z2I(L), the following can be obtained:

[0093]

[0094]

[0095] Where

[0096] The actual situation encountered in engineering is that the pipeline is parallel to the line and approaches one end distance, and then extends to the far distance at both ends, which is reflected in the mathematical model as the pipeline at both ends is connected to the matching impedance,

[0097] That is, Z1 = Z2 = Z C , ρ1 = ρ2 = 0.

[0098] The ground return impedance is an important parameter for calculating the induced voltage on buried oil and gas pipelines by power transmission lines. For a complex conductor system composed of overhead conductors and buried conductors, the ground return impedance can be divided into three types:

[0099] As shown in Figure 2 , the first type is the self-impedance and mutual impedance of the overhead conductor system. The Carson formula is the most classical one, but it is only applicable to uniform soil and contains an infinite integral in the correction term, which is inconvenient to calculate. Therefore, the formula for calculating the impedance of a unit length of overhead line on layered soil based on the concept of "complex depth" proposed by Dubanton is introduced. The formulas for self-impedance Z s and mutual impedance Z m are as follows:

[0100]

[0101]

[0102] In the formula, p is the complex transmission depth of electromagnetic waves in soil.

[0103] As shown in Figure 3 , the second type is the self-impedance and mutual impedance of the buried conductor system. For calculating the self-impedance and mutual impedance of buried conductors, the Pollaczek formula is usually used:

[0104]

[0105]

[0106] where,

[0107]

[0108]

[0109] α = ωμ0 / ρ e

[0110] In the above formula, h m = (h i + h j ) / 2, d jk is the distance between cable j and cable k, d jk' is the distance between the mirror images of cable j and cable k, and x jk is the horizontal distance between cable j and cable k.

[0111] The third type is the mutual impedance between the overhead conductor and the buried conductor, and the mutual impedance between the transmission line and the buried oil pipeline. The mutual impedance between the transmission line and the buried oil pipeline can also be calculated using the Pollaczek formula. Due to the complexity of some functions in the formula, it is usually simplified to obtain an approximate formula.

[0112] The model of the overhead conductor and the buried conductor is shown in Figure 4 The mutual impedance Z jm12 between the overhead conductor 1 and the buried conductor 2 is expressed as follows:

[0113] The formula is as follows:

[0114]

[0115] where h1 is the height of the overhead conductor from the ground, h2 is the buried depth of the buried conductor, y 12 is the horizontal distance between them, μ0 is the air permeability, w is the complex penetration depth, and w is the angular frequency.

[0116] The loop impedance formed by the conductor and the ground is called the "ground return self-impedance", and the mutual impedance between the loop formed by different conductors and the ground return channel is called the "ground return mutual impedance". If a unit current flows through the conductor, the ground return mutual impedance is the longitudinal induced voltage generated on the conductor. When a single-phase grounding fault occurs in the transmission line, the non-fault phase and the fault phase produce overvoltage on the pipeline through inductive coupling, and part of the short-circuit current enters the ground through the tower grounding net and produces electromagnetic interference on the pipeline through resistive coupling. When the two effects act together, the pipeline coating may be damaged due to excessive withstand voltage, and in severe cases, the pipeline may even explode. The schematic diagram of the inductive coupling calculation model in the case of single-phase grounding fault is shown in Figure 5 .

[0117] Calculation principle

[0118] The interference of the transmission line on the pipeline will be studied based on the method of moments. First, the conductor is divided into a plurality of conductor segments, the potential difference between the outer surfaces of the conductor segments is equal to the potential difference between the inner surfaces of the conductor segments, and a set of equations is established based on this continuity characteristic. The potential difference between the outer surfaces of the conductor segments is obtained based on the leakage current, and the product of the impedance of the conductor segment itself and the axial current is used to obtain the potential difference between the inner surfaces of the conductor segment. According to Kirchhoff's law, the relationship between the axial current and the leakage current on each conductor segment is obtained, and a set of linear algebraic equations is established to obtain the leakage current distribution on the conductor. The specific implementation process is as follows:

[0119] Since the electromagnetic interference of the power grid on the pipeline network is realized through electromagnetic fields, it follows Maxwell's equations:

[0120]

[0121] where H is the magnetic field intensity; B is the magnetic flux density; D is the electric displacement vector; E is the electric field intensity; p is the space charge density; J s is the conduction current density.

[0122] Introducing the vector magnetic potential A and the scalar potential function φ, such that B = rot A, then from the second equation of Maxwell's equations we have:

[0123]

[0124] where ω is the angular frequency. Substituting it into the first and fourth equations of Maxwell's equations, we get the D'Alembert equations:

[0125]

[0126] where is the phase constant, and μ, ε are the magnetic permeability and the dielectric constant, respectively.

[0127] The interference of the interference source to the interfered point is given by the following general solution:

[0128]

[0129] where R is the distance from the interfered point to the interference source.

[0130] Since the inductive coupling component is much larger than the capacitive coupling component, the influence of the capacitive coupling component is ignored. The power grid conductor is segmented into n s segments, and the pipe network conductor is segmented into n p segments. The current flowing through the i i th segment of the conductor is I

[0131]

[0132] The induced potential on the k th segment of the pipe network conductor is the sum of the potentials induced by the currents on all the power grid conductor segments on the conductor, i.e.,

[0133]

[0134] Under the action of the induced potential, the pipe network will form a through-flow loop with the anticorrosion layer and the soil, and a certain current field distribution will be formed in the ground. The current dispersion diagram of the segmented pipe network conductor is shown in Figure 6 .

[0135] If there are b endpoints in the segmented pipe network, then since the segmented pipe network conductor is relatively short, the potential U i on the i j1 th segment of the pipe can be taken as the voltage V j2 and VThe average value of the current is:

[0136]

[0137] The matrix form is:

[0138] U = KV

[0139] Similarly, the current I d of each segment of the conductor is divided into two parts, which flows into the ground from the two nodes connected to it, so:

[0140] J = K T I d

[0141] In the formula, J is the equivalent current of each node.

[0142] Using KCL and KVL on the segmented pipe network conductor has:

[0143]

[0144] In the formula, Y is the branch admittance matrix; A is the incidence matrix; I1 is the current flowing through each pipe network conductor.

[0145] Therefore, the node admittance equation can be established as:

[0146] AYA T V = AYE - J

[0147] Using the Green function, the relationship between the potential of each conductor and the current is:

[0148] U = ZI d

[0149] In the formula, Z is the mutual impedance matrix between each conductor segment, including inductive and resistive components, inductive components. The above formula can be used to calculate the pipe potential:

[0150] U = K(AYA T + K T Z -1 K) -1 AYE

[0151] Under lightning conditions, due to the complexity of the time-domain solution method of electromagnetic coupling between conductors and the large amount of calculation, the potential distribution of the system under the impulse current is generally calculated using the time-frequency conversion method. First, the impulse current under the lightning current is calculated using the moment method. The impulse current in the time domain can be described by the following double exponential function:

[0152] I(t) = I m (e -αt -e -βt )

[0153] where t is time; a is the wave front attenuation index; β is the wave tail attenuation index; I m is the current amplitude.

[0154] By Fourier transform, the impulse current waveform in time domain can be converted into frequency domain response:

[0155]

[0156] where ω is the angular frequency; I(ω) is the lightning current in frequency domain.

[0157] The current I(l′) linearly changes along the conductor axis l′ and the line charge uniformly distributes along the conductor surface The scattered electric field intensity generated in space is

[0158]

[0159] where, in infinite space,

[0160]

[0161]

[0162] where e is the axis direction of the cylindrical conductor line current; A is the vector magnetic potential generated by the axial current I(l′); r is the distance between the field point and the source point in space; φ is the line charge uniformly distributed on the conductor surface The generated scalar potential; μ and ε are the magnetic permeability and dielectric constant of the space where the conductor is located; k is the wave number.

[0163] The integral equation of electric field intensity can be obtained by combining

[0164]

[0165] Suppose the entire conductor structure is divided into n segments of conductors, then

[0166]

[0167] where I i and U j are the current on the i-th segment of conductor and the potential at the midpoint of the j-th segment of conductor respectively; Z ij is the transfer impedance between the i-th segment of conductor and the j-th segment of conductor

[0168]

[0169] When the lightning current is injected into one end of the conductor, the current injected into one end of the segment of conductor is a known quantity, which can be expressed in matrix form:

[0170] Z -1 U = I

[0171] Since the injected conductor segment current vector I is known, other unknown currents and branch voltages can be solved. Thus, the problems of spatial current distribution, electromagnetic field, etc. can be solved. Finally, the scalar voltage, electric field intensity and magnetic field intensity in the time domain can be solved by Fourier inverse transform.

[0172]

[0173]

[0174]

[0175] In the formula, U0(ω), E0(ω) and H0(ω) are respectively the scalar voltage, electric field intensity and magnetic field intensity in the frequency domain generated by a unit current source.

[0176] The calculation software used in the above-mentioned electromagnetic interference calculation method of the power grid to the buried pipe network is CDEGS. CDEGS (Current Distribution, Electromagnetic Interference, Grounding and Soil Structure Analysis) is an integrated engineering software package developed by Safe Engineering Services & technologies Ltd. in Canada. The software is written on the basis of electromagnetic theory and has a series of functions such as grounding system design analysis, electromagnetic interference research, etc. The core of the software is mainly to calculate the electromagnetic field distribution around the network composed of any shape conductor on the ground or underground and the conductor and ground surface potential distribution under steady state and fault, lightning and other transient conditions.

[0177] The theoretical basis of the programming and analysis program of the CDEGS software is various related electromagnetic theories. Since these are not constrained by various frequencies, the results obtained by processing are more accurate, and the software can research and design various grounding system analysis and processing electromagnetic interference and other related problems. The main purpose of the CDEGS software package is to calculate the electromagnetic field distribution around the network composed of any shape conductor on the ground or underground and the conductor and ground surface potential distribution under various steady state and transient conditions such as short circuit fault, lightning strike, etc. The software is powerful in calculating the electromagnetic influence of high-voltage transmission lines on adjacent buried oil and gas pipelines, and is recommended for use by the International Large Grid Conference

[0178] CDEGS software is widely used in oil and gas pipeline overvoltage calculation, it can analyze the influence law of various operating conditions of transmission lines on pipeline overvoltage. At the same time, by establishing different working condition models, the potential distribution of aboveground or underground conductor can be calculated, and it can also be applied to gradient control line and electromagnetic interference elimination problem. CDEGS mainly contains 8 engineering modules. In the pipeline overvoltage protection, mainly use MALZ module, HIFREQ module and FFTSES module. MALZ module can analyze the frequency domain grounding of any soil structure, calculate the grounding resistance value of different types of grounding grid, HIFREQ module can analyze the electromagnetic field generated by any charged conductor network in frequency domain, can establish the model of overhead transmission tower line and simplified grounding grid underground, and carry out calculation and analysis. FFTSES module is also called fast Fourier transform, mainly cooperates with HIFREQ module to carry out simulation calculation under lightning transmission line condition.

[0179] The above is only a specific embodiment of the present application, but the protection scope of the present application is not limited to this, and those skilled in the art should understand that the present application includes but is not limited to the contents described in the drawings and the above specific embodiment. Any modification without deviating from the functional and structural principles of the present application will be included in the scope of the claims.

Claims

1. A method for calculating electromagnetic interference from a power grid to a buried pipeline network, the calculation results of which are used to evaluate the influence of electromagnetic interference on the buried pipeline network, characterized in that, It comprises the following steps: The conductor is divided into conductor micro-sections, the potential difference between the two ends of the outer surface of the conductor micro-section is equal to the potential difference between the two ends of the conductor micro-section, an equation group is established according to the continuity, the potential difference between the two ends of the conductor micro-section is obtained according to the leakage current, and the potential difference between the two ends of the conductor micro-section itself is multiplied by the axial current to obtain the potential difference between the two ends of the conductor micro-section; According to Kirchhoff's law, the relationship between the axial current and the leakage current on each conductor micro-section is obtained, a set of linear algebraic equations is established, and the leakage current distribution on the conductor is obtained by solving the linear algebraic equations; If the entire conductor structure is divided into n conductor sections, then where: I i and U j are the current on the ith segment of conductor and the potential at the midpoint of the jth segment of conductor, respectively; Z ij is the transfer impedance between the ith segment of conductor and the jth segment of conductor When the lightning current is injected into one end of the conductor, the current injected into one end of the conductor section is a known quantity, which is represented in matrix form: Z -1 U = I The injection current vector I of the conductor micro-section is known, the other unknown currents and branch voltages are obtained, and finally the scalar voltage, electric field intensity and magnetic field intensity in the time domain are obtained through Fourier inverse transform In the formula: U0(ω), E0(ω) and H0(ω) are the scalar voltage, electric field intensity and magnetic field intensity in the frequency domain generated by the unit current source respectively.

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