A method for predicting corona power loss in high voltage AC transmission lines

Abstract

The present invention discloses a method for predicting corona energy loss of high-voltage AC transmission lines, including: obtaining a conductor spiral simulation charge; obtaining a conductor corona onset charge using a glow criterion containing a space medium foreign body; obtaining an emission spiral simulation charge based on the obtained conductor spiral simulation charge and the obtained conductor corona onset charge; obtaining an emission spiral charge migration, recombination and motion trajectory based on the obtained emission spiral simulation charge; obtaining a space medium foreign body charge migration process; obtaining the energy consumed in the space movement of the spiral charge migration recombination process and the space medium foreign body charge migration process, which is the corona energy loss. The present invention can accurately predict the corona energy loss of split conductors of ultra-high voltage AC transmission lines in plateau areas under complex environments, and provide technical support for the economic evaluation of overhead transmission lines in plateau areas.

Description

Technical Field

[0001] The invention relates to the technical field of power transmission and transformation engineering, and in particular to a method for predicting corona power loss of a high-voltage AC transmission line. Background Art

[0002] my country's energy and load are inversely distributed, and it is necessary to build a long-distance, large-capacity, high-voltage power grid to meet the needs of national economic development. As the voltage level increases significantly, the electric field on the surface of the conductor and the surrounding space increases significantly, resulting in partial discharge in the air and causing corona discharge. AC corona discharge will produce adverse effects such as corona loss, radio interference and audible noise. Improper control will affect the living environment and the efficient and economical operation of the power grid.

[0003] At present, there has been no systematic research on the corona effect of AC transmission systems above 2000m. Generally, empirical formulas are relied on. For the acquisition of data at different altitudes, single conductor data from two altitude areas are often used for comparison and linear extrapolation, lacking key parameters. In addition, the environmental climate in high-altitude areas is complex, and it is necessary to consider the influence of multiple environmental factors such as low pressure, dust, and rainfall. Corona loss is greatly affected by discharge parameters, and it is difficult to obtain the corona energy loss of multiple split conductors and to achieve accurate evaluation of line economy. In terms of corona loss modeling, if the influence of sag, conductor structure, etc. on the uniformity of the surface electric field is not considered, and the influence of the charge migration process of raindrops and dust particles on the corona energy loss is not considered, there is still a blank in the mathematical and physical model of the synergistic influence of factors such as low pressure, dust, and rainfall. Summary of the invention

[0004] The purpose of the present invention is to provide a method for predicting corona energy loss of high-voltage AC transmission lines, which can accurately predict the corona energy loss of split conductors of ultra-high voltage AC transmission lines in plateau areas under complex environments, and provide technical support for the economic evaluation of overhead transmission lines in plateau areas.

[0005] To achieve the above object, the present invention provides the following solutions:

[0006] A method for predicting corona power loss in a high-voltage AC transmission line comprises the following steps:

[0007] S1, obtain the wire helix simulation charge;

[0008] S2, using the glow criterion of foreign matter in the space medium to obtain the conductor corona charge;

[0009] S3, obtaining an emission spiral simulation charge based on the wire spiral simulation charge obtained in step S1 and the wire corona initiation charge obtained in step S2;

[0010] S4, based on the emitted spiral charges obtained in step S3, obtaining the migration, recombination and movement trajectory of the emitted spiral charges;

[0011] S5, obtaining the charge migration process of foreign matter in the space medium;

[0012] S6, obtaining the energy consumed in the space movement during the spiral charge migration recombination process in step S4 and the space medium foreign matter charge migration process in step S5, which is the corona power loss.

[0013] Furthermore, the step S1, obtaining the wire spiral simulation charge, specifically includes:

[0014]

[0015] in,

[0016]

[0017]

[0018]

[0019] Where x, y, and z are the three component data of the wire spiral simulation charge in the rectangular coordinate system, L p is the pitch, θ is the rotation angle, δ0 is the arc vertical stress, γ is the gravity section ratio per unit length, l h is the horizontal spacing, h is the vertical spacing, r0 is the radius of the sub-conductor;

[0020]

[0021]

[0022]

[0023] E x =E x1 cosδcosβ+E y1 sinβ+E z1 sinδcosβ (8)

[0024] E y =E x1 cosδsinβ+E y1 cosβ+E z1 sinδsinβ (9)

[0025] E z =E x1 sinδ+E z1 cosδ (10)

[0026] Among them, E x1 is the electric field strength generated by the spiral charge of the wire, Ey1 is the electric field strength generated by the space spiral charge, E z1 is the electric field strength generated by the mirror spiral charge, B(1) is the first row element of the matrix [B], B(2) is the second row element of the matrix [B], B(3) is the third row element of the matrix [B], U is the voltage applied to the wire, E x 、E y 、E z To consider the three electric field components of the actual space coordinate point in the rectangular coordinate system after coordinate transformation, δ is the angle between the spiral charge and xoy, β is the angle between the spiral charge and xoz, and ε0 is the vacuum dielectric constant;

[0027] Then the wire helix simulated charge number Q cond，r for:

[0028]

[0029] Furthermore, the step S2, using the glow criterion of foreign matter in the space medium to obtain the conductor corona charge, specifically includes:

[0030]

[0031] Among them, N eph is the total number of electrons excited on the cathode surface by the photons released by the initial electron avalanche, γ ph is the surface photoelectron emission coefficient of steel core aluminum conductor, d is the distance between conductor and dielectric particles, r and ξ are virtual integral variables, α is the impact ionization coefficient, η is the electron adsorption coefficient, g is the area factor of photon geometric absorption function, and μ is the absorption coefficient of photons in air;

[0032] When N eph When ≥1, it is determined that the glow discharge containing foreign matter in the space medium is self-sustaining. At this time, the corona initiation field strength of the split conductor is calculated using formula (13):

[0033]

[0034] Among them, E c is the corona initiation field strength of the split conductor, m is the roughness coefficient considering meteorological factors, δ′ is the relative air density, and n is the split number;

[0035] Based on the split conductor corona initiation field strength, the conductor corona initiation charge is calculated:

[0036] Q c，r =ε0E c (14)

[0037] Where ε0 is the dielectric constant of vacuum, Q c，r It is the corona charge of the wire.

[0038] Furthermore, in step S3, based on the wire spiral simulation charge obtained in step S1 and the wire corona charge obtained in step S2, the emission spiral simulation charge Q is obtained. s，r , specifically including:

[0039] Q s，r =Q cond，r -Q c，r (15)

[0040] Furthermore, the step S4, based on the emitted spiral charges obtained in step S3, obtains the migration, recombination and movement trajectory of the emitted spiral charges, specifically including:

[0041] Δd i =μE i Δt (16)

[0042]

[0043]

[0044] Where, Δd i is the distance that the i-th spiral charge moves in space within Δt time, μ is the ion mobility, E i is the electric field strength of the ith spiral charge in space, n i0 is the space charge density, q i0 Space charge, e is the electron charge, Δv i is the control volume of the charge, γ is the recombination coefficient, q i is the charge of the i-th spiral after Δt time;

[0045] Average positive ion mobility μ + :μ + =1.74·e 0.07·RH +46.17·e -0.01·P +1.38-4.306·10 -5 ·RH·P;

[0046] Average negative ion mobility μ - :μ - =5.25·e 0.05·RH +8.09·e -0.04·P +1.19-5.29·10 -5 ·RH·P;

[0047] Among them, RH is relative humidity and P is air pressure.

[0048] Furthermore, the step S5, obtaining the charge migration process of foreign matter in the space medium, specifically includes:

[0049]

[0050]

[0051] Among them, d p is the particle diameter of the medium, ρ p is the density of medium particles, g is the acceleration of gravity, v is the velocity of medium particles, t is the movement time of medium particles, F D is the viscous resistance of the medium particles, F e is the electric field force on the medium particles, F g is the gravity acting on the particles of the medium, q is the normalized charge of the medium particles, t is the normalized charging time of the medium particles, i is the normalized resistive current, q c is the normalized characteristic charge of the medium particles.

[0052] Furthermore, the step S6, obtaining the energy consumed in the space movement during the spiral charge migration recombination process in step S4 and the space medium foreign matter charge migration process in step S5, namely the corona power loss, specifically includes:

[0053]

[0054] Among them, P is the corona energy loss value of the unit length wire, f is the power frequency cycle, cycle is the acquisition time step, N sc is the single-step spiral charge number, is the electric field strength vector of the i-th spiral charge in space, is the distance vector of the ith spiral charge moving in space, is the electric field force vector acting on the medium particles, is the distance vector of the migration of i medium particles in space, l cond is the wire length.

[0055] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects: the method for predicting corona power loss of high-voltage AC transmission lines provided by the present invention analyzes the influence of sub-conductor radius, splitting number, conductor surface field strength, dust concentration, dust particle size and rainfall rate on corona loss, and combines the entire process of corona discharge initiation, ion migration recombination, and medium particle charge migration to establish a three-dimensional AC power loss acquisition method based on spiral charge and considering factors such as sag, altitude, dust and rain. The deviation is 20% compared with the internationally general BPA formula, filling the gap in prediction methods for altitudes above 2000m and considering the influence of dust. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0057] Figure 1 is a schematic diagram of a spiral charge arrangement containing sag according to an embodiment of the present invention;

[0058] Figure 2 is a radial cross-sectional view of an embodiment of the present invention;

[0059] Figure 3 is an axial cross-sectional view of an embodiment of the present invention;

[0060] Figure 4 is a schematic diagram of the corona morphology of foreign matter in the medium according to an embodiment of the present invention;

[0061] Figure 5 is a discharge parameter variation curve of an embodiment of the present invention;

[0062] Figure 6 is a schematic diagram of the charge emission process of an embodiment of the present invention;

[0063] Figure 7 This is a schematic diagram of ion motion trajectories according to an embodiment of the present invention;

[0064] Figure 8a Schematic diagram of charging characteristics of foreign matter in a dielectric medium during a power frequency cycle according to an embodiment of the present invention;

[0065] Figure 8b is a schematic diagram of the motion characteristics of a charge medium foreign body according to an embodiment of the present invention;

[0066] Fig. 9 is a schematic diagram of the corona loss prediction results under high altitude rain conditions according to an embodiment of the present invention;

[0067] Fig.10 is a schematic diagram of corona loss prediction results under high altitude dust conditions according to an embodiment of the present invention;

[0068] Fig.11 The present invention is a flow chart of a method for predicting corona power loss in a high-voltage AC transmission line. DETAILED DESCRIPTION

[0069] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0070] The purpose of the present invention is to provide a method for predicting corona power loss of high-voltage AC transmission lines, which can accurately predict the corona power loss of split conductors of ultra-high voltage AC transmission lines in plateau areas under complex environments such as sunny, dusty and rainy conditions, and provide technical support for the economic evaluation of overhead transmission lines in plateau areas.

[0071] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0072] like Fig.11 As shown, the method for predicting corona power loss of high-voltage AC transmission lines provided by the present invention comprises the following steps:

[0073] S1, obtain the wire spiral simulation charge, including:

[0074]

[0075] in,

[0076]

[0077]

[0078]

[0079] Where x, y, and z are the three component data of the wire spiral simulation charge in the rectangular coordinate system, L p is the pitch, θ is the rotation angle, δ0 is the arc vertical stress, y is the unit length gravity section ratio, l h is the horizontal spacing, h is the vertical spacing, r0 is the radius of the sub-conductor;

[0080]

[0081]

[0082]

[0083] E x =E x1 cosδcosβ+E y1 sinβ+Ez1 sinδcosβ (8)

[0084] E y =E x1 cosδsinβ+E y1 cosβ+E z1 sinδsinβ (9)

[0085] E z =E x1 sinδ+E z1 cosδ (10)

[0086] Among them, E x1 is the electric field strength generated by the spiral charge of the wire, E y1 is the electric field strength generated by the space spiral charge, E z1 is the electric field strength generated by the mirror spiral charge, B(1) is the first row element of the matrix [B], B(2) is the second row element of the matrix [B], B(3) is the third row element of the matrix [B], U is the voltage applied to the wire, E x 、E y 、E z To consider the three electric field components of the actual space coordinate point in the rectangular coordinate system after coordinate transformation, δ is the angle between the spiral charge and xoy, β is the angle between the spiral charge and xoz, and ε0 is the vacuum dielectric constant;

[0087] Then the wire helix simulated charge number Q cond，r for

[0088]

[0089] S2, using the glow criterion of foreign matter in the space medium to obtain the conductor corona charge, specifically including:

[0090]

[0091] Among them, N eph is the total number of electrons excited on the cathode surface by the photons released by the initial electron avalanche, γ ph is the surface photoelectron emission coefficient of steel core aluminum conductor, d is the distance between conductor and dielectric particles, r and ξ are virtual integral variables, α is the impact ionization coefficient, η is the electron adsorption coefficient, g is the area factor of photon geometric absorption function, and μ is the absorption coefficient of photons in air;

[0092] When N eph When ≥1, it is determined that the glow discharge containing foreign matter in the space medium is self-sustaining. At this time, the corona initiation field strength of the split conductor is calculated using formula (13):

[0093]

[0094] Among them, Ec is the corona initiation field strength of the split conductor, m is the roughness coefficient considering meteorological factors, δ′ is the relative air density, and n is the split number;

[0095] Based on the split conductor corona initiation field strength, the conductor corona initiation charge is calculated:

[0096] Q c，r =ε0E c (14)

[0097] Where ε0 is the dielectric constant of vacuum, Q c，r It is the corona charge of the wire.

[0098] S3, based on the wire spiral simulation charge obtained in step S1 and the wire corona charge obtained in step S2, obtain the emission spiral simulation charge Q s，r , specifically including:

[0099] Q s，r =Q cond，r -Q c，r (15)

[0100] S4, based on the emitted spiral charges obtained in step S3, obtaining the migration, recombination and movement trajectory of the emitted spiral charges, specifically including:

[0101] Δd i =μE i Δt (16)

[0102]

[0103]

[0104] Where, Δd i is the distance that the i-th spiral charge moves in space within Δt time, μ is the ion mobility, E i is the electric field strength of the ith spiral charge in space, n i0 is the space charge density, q i0 Space charge, e is the electron charge, Δv i is the control volume of the charge, γ is the recombination coefficient, q i is the charge of the i-th spiral after Δt time;

[0105] Average positive ion mobility μ + :μ + =1.74·e 0.07·RH +46.17·e -0.01·P +1.38-4.306·10 -5· RH·P;

[0106] Average negative ion mobility μ - :μ- =5.25·e 0.05·RH +8.09·e -0.04·P +1.19-5.29·10 -5 ·RH·P;

[0107] Among them, RH is relative humidity and P is air pressure.

[0108] S5, obtaining the charge migration process of foreign matter (raindrops, sand and dust, etc.) in the space medium, specifically including:

[0109]

[0110]

[0111] Among them, d p is the particle diameter of the medium, ρ p is the density of medium particles, g is the acceleration of gravity, v is the velocity of medium particles, t is the movement time of medium particles, F D is the viscous resistance of the medium particles, F e is the electric field force on the medium particles, F g is the gravity acting on the particles of the medium, q is the normalized charge of the medium particles, t is the normalized charging time of the medium particles, i is the normalized resistive current, q c is the normalized characteristic charge of the medium particles.

[0112] S6, obtaining the energy consumed in the space movement of the spiral charge migration composite process in step S4 and the space medium foreign matter charge migration process in step S5, namely, the corona power loss, specifically including:

[0113]

[0114] Among them, P is the corona energy loss value of the unit length wire, f is the power frequency cycle, cycle is the acquisition time step, N sc is the single-step spiral charge number, is the electric field strength vector of the i-th spiral charge in space, is the distance vector of the ith spiral charge moving in space, is the electric field force vector acting on the medium particles, is the distance vector of the migration of i medium particles in space, l cond is the wire length.

[0115] In the embodiment of the present invention, the corona loss varies linearly with the square of the sub-conductor radius, the corona loss varies approximately linearly with the splitting number, the corona loss varies approximately linearly with the square of the field strength, the corona loss varies approximately exponentially with the dust concentration, the corona loss varies approximately exponentially with the dust particle size, the corona loss is independent of the wind speed, the corona loss varies approximately exponentially with the altitude, and the corona loss varies approximately linearly with the logarithm of the rainfall rate. In step S1, the wire spiral simulation charge and boundary point coordinates are obtained, and the sag spiral charge is arranged as follows: Figure 1 , radial cross section diagram see Figure 2 , axial cross section diagram see Figure 3 As can be seen from the figure, the spiral charge can not only accurately reproduce the sag characteristics of the actual overhead line, but also take into account the outer strands of the actual steel-core aluminum conductor and its spiral winding structure, and can obtain a more accurate three-dimensional electric field distribution. In step S2, the glow discharge process at the beginning of the corona containing foreign matter in the space is simulated. Figure 4 The variation law of discharge parameters in the ionization region is obtained. Figure 5 , which provides a basis for the corona charge criterion in step S3. In step S3, the emission process of the simulated charge is shown in Figure 6 As can be seen from the figure, the emission process takes into account the surface structure and morphological parameters of the wire, which is closer to the real physical process. In step S4, the migration and recombination process of the ions is obtained, and the ion movement trajectory is shown in Figure 7 As can be seen from the figure, in one power frequency cycle, positive and negative ions move back and forth in the space around the conductor under the alternating electric field, and produce ion energy loss, that is, ion kinetic energy loss. In step S5, the charge migration motion characteristics of the space medium foreign matter in the AC space charge region are obtained. Figure 8a and 8b It can be seen that the charging process of dielectric particles in space within one power frequency cycle can be divided into four characteristics. The charged dielectric particles in the space charge region are affected by gravity, electric field force and air drag and show irregular motion characteristics. In step S6, the energy consumed by the spatial motion of ions and charged particles under the action of the electric field is obtained, which is the corona energy loss. The corona energy loss under the conditions of dust and rain in the plateau area is obtained. Figure 9-10 , where the data points in the figure are test values, and the curves are obtained values. It can be seen from the figure that the test values ​​are in good agreement with the obtained values, which verifies the accuracy of the proposed method for predicting corona energy loss in high-voltage AC transmission lines, and can provide support for corona energy loss in overhead transmission lines under complex environments at high altitudes.

[0116] The present invention provides a method for predicting corona power loss of a high-voltage AC transmission line. By analyzing the influence of the sub-conductor radius, the number of splits, the surface field strength of the conductor, the dust concentration, the dust particle size and the rainfall rate on the corona loss, and combining the whole process of corona discharge initiation, ion migration recombination and medium particle charge migration, a three-dimensional AC power loss acquisition method based on spiral charge and considering factors such as sag, altitude, dust and rain is established. The acquisition deviation is reduced by 20% compared with the internationally general BPA formula, filling the gap in the prediction method for altitudes above 2000m and considering the influence of dust.

[0117] The principles and implementation methods of the present invention are described in this article using specific examples. The description of the above embodiments is only used to help understand the method and core idea of ​​the present invention. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting the present invention.

Claims

1. A method for predicting corona power loss in high voltage AC transmission lines, characterized in that: The following steps are involved: S1, obtain the wire helix simulation charge; S2, using the glow criterion of foreign matter in the space medium to obtain the conductor corona charge; S3, based on the wire spiral simulation charge obtained in step S1 and the wire corona charge obtained in step S2, obtain the emission spiral simulation charge Q s,r , specifically: Q s，r =Q cond，r -Q c，r (15); In the formula, Q c,r is the corona charge of the wire, Q cond,r Simulate the charge number for the wire helix; S4, based on the emitted spiral charge obtained in step S3, obtaining the migration, recombination and movement trajectory of the emitted spiral charge, specifically: Δd i =μE i Δt (16) Where, Δd i is the distance that the i-th spiral charge moves in space within Δt time, μ is the ion mobility, E i is the electric field strength of the ith spiral charge in space, n i0 is the space charge density, q i0 Space charge, e is the electron charge, Δv i is the control volume of the charge, γ is the recombination coefficient, q i is the charge of the i-th spiral after Δt time; Average positive ion mobility μ + :μ + =1.74·e 0.07·RH +46.17·e -0.01·P +1.38-4.306·10 -5 ·RH·P; Average mobility of negative ions μ - :μ - =5.25·e 0.05·RH +8.09·e -0.04·P +1.19-5.29·10 -5 ·RH·P; Where RH is relative humidity and P is air pressure; S5, obtaining the charge migration process of foreign matter in the space medium, specifically: Among them, x, y, and z are the three component data of the wire spiral simulation charge in the rectangular coordinate system, and d p is the particle diameter of the medium, ρ p is the density of medium particles, g is the acceleration of gravity, v is the velocity of medium particles, t is the movement time of medium particles, F D is the viscous resistance of the medium particles, F e is the electric field force on the medium particles, F g is the gravity acting on the particles of the medium, q is the normalized charge of the medium particles, t is the normalized charging time of the medium particles, i is the normalized resistive current, q c is the normalized characteristic charge of the medium particles; S6, obtaining the energy consumed in the space movement during the spiral charge migration recombination process in step S4 and the space medium foreign matter charge migration process in step S5, which is the corona power loss.

2. The method for predicting corona power loss in high voltage AC transmission lines according to claim 1, characterized in that: The step S1, obtaining the wire spiral simulation charge, specifically includes: in, Where x, y, and z are the three component data of the wire spiral simulation charge in the rectangular coordinate system, L p is the pitch, θ is the rotation angle, δ0 is the arc vertical stress, γ is the gravity section ratio per unit length, l h is the horizontal spacing, h is the vertical spacing, r0 is the radius of the sub-conductor; AND x =And x1 cosδcosβ+E y1 sinβ+E z1 sinδcosβ (8) AND y =And x1 cosδsinβ+E y1 cosβ+E z1 sinδsinβ (9) AND z =And x1 sinδ+E z1 cosδ (10) Among them, E x1 is the electric field strength generated by the spiral charge of the wire, E y1 is the electric field strength generated by the space spiral charge, E z1 is the electric field strength generated by the mirror spiral charge, B(1) is the first row element of the matrix [B], B(2) is the second row element of the matrix [B], B(3) is the third row element of the matrix [B], U is the voltage applied to the wire, E x 、E y 、E z To consider the three electric field components of the actual space coordinate point in the rectangular coordinate system after coordinate transformation, δ is the angle between the spiral charge and xoy, β is the angle between the spiral charge and xoz, and ε0 is the vacuum dielectric constant; Then the wire helix simulated charge number Q cond,r for:

3. The method for predicting corona power loss in high voltage AC transmission lines according to claim 2, characterized in that: The step S2, using the glow criterion of foreign matter in the space medium to obtain the conductor corona charge, specifically includes: Among them, N eph is the total number of electrons excited on the cathode surface by the photons released by the initial electron avalanche, γ ph is the surface photoelectron emission coefficient of steel core aluminum conductor, d is the distance between conductor and dielectric particles, r and ξ are virtual integral variables, α is the impact ionization coefficient, η is the electron adsorption coefficient, g is the area factor of photon geometric absorption function, and μ is the absorption coefficient of photons in air; When N eph When ≥1, it is determined that the glow discharge containing foreign matter in the space medium is self-sustaining. At this time, the corona initiation field strength of the split conductor is calculated using formula (13): Among them, E c is the corona initiation field strength of the split conductor, m is the roughness coefficient considering meteorological factors, δ is the relative air density, and n is the split number; Based on the split conductor corona initiation field strength, the conductor corona initiation charge is calculated: Q c,r =ε0E c (14) Where ε0 is the dielectric constant of vacuum, Q c,r It is the corona charge of the wire.

4. The method for predicting corona power loss in high voltage AC transmission lines according to claim 3, characterized in that: The step S6, obtaining the energy consumed in the space movement of the spiral charge migration composite process in step S4 and the space medium foreign matter charge migration process in step S5, is the corona power loss, which specifically includes: Among them, P is the corona energy loss value of the unit length wire, f is the power frequency cycle, cycle is the acquisition time step, N sc is the single-step spiral charge number, is the electric field strength vector of the i-th spiral charge in space, is the distance vector of the ith spiral charge moving in space, is the electric field force vector acting on the medium particles, is the distance vector of the migration of i medium particles in space, l cond is the wire length.

Images