Method for calculating ground synthetic electric field of direct current transmission line by using equivalent radius lead

Abstract

The invention discloses a method for calculating a ground synthetic electric field of a direct-current power transmission line by adopting an equivalent radius wire, which considers diffusion coefficients of positive and negative ions, and adopts a finite element method to calculate the ground synthetic electric field of the direct-current power transmission line based on a Kaptzov hypothesis in combination with COMSOL Multi-physics and MATLAB. In the modeling process of the power transmission line, the equivalent corona method is utilized, the equivalent corona inception field intensity of the equivalent radius wire is obtained, and calculation is simplified. By using finite element calculation software COMSOLMulti-physics, the convergence speed can be accelerated on the premise of ensuring the calculation precision, and finally a more accurate calculation method of the ground synthetic electric field of the direct current transmission line is obtained. Through field measurement of the ground composite electric field of the direct-current transmission line in actual operation, it is verified that the calculation method has high accuracy and can be applied to calculation of the ground composite electric field of the high-voltage direct-current transmission line in China in future.

Description

Technical Field

[0001] The invention belongs to the field of electromagnetic environment of high voltage power transmission engineering of electric power system, and is specifically applicable to the prediction of synthetic electric field and ion flow density in actual direct current transmission lines. Background Art

[0002] With the rapid development of ultra-high voltage direct current transmission projects in my country, environmental protection issues have also attracted more and more attention. In addition to the corona loss and radio noise interference similar to those of AC transmission lines, direct current transmission lines also have space charge effects that increase the ground field strength and ion flow fields that are unique to direct current transmission lines. The ground synthetic electric field and ion flow density of direct current transmission lines are the main electromagnetic environment parameters in direct current transmission projects. Scientific and reasonable prediction of the ground synthetic electric field of direct current transmission lines is an important prerequisite for tower structure design and conductor selection. At present, the methods for calculating direct current synthetic fields are mainly based on the finite element method-finite volume method based on the Kaptzov hypothesis or the finite element method based on the Deutsch hypothesis. The finite element method based on the Deutsch hypothesis is more convenient and can well predict the synthetic electric field under the DC line. However, since the Deutsch hypothesis believes that the space charge generated by the conductor corona only changes the magnitude of the electric field but not the direction of the electric field, the Deutsch hypothesis can simplify the two-dimensional ion flow field problem into a one-dimensional problem along the electric field line. However, the error between the synthetic ground electric field measured in actual situations at home and abroad (wind speed exists in actual situations) and the result obtained by using the Deutsch hypothesis is more than 20%.

[0003] For example, Chinese patent CN102508964A proposes a finite element method based on the Deutsch hypothesis to predict the calculation method of the ground composite electric field of DC transmission. The coaxial cylindrical electrode is modeled by the simulation software MATLAB, and the calculation accuracy of the electric field strength on the conductor surface is improved by using the subdomain, and the second-order nonlinear partial differential equation is solved to infer the electric field distribution in the presence of space charge, and finally obtain a more accurate calculation method for the ground composite electric field of the DC transmission line. However, as mentioned in the above background technology, this method does not take into account the diffusion of space charge, and when the Deutsch hypothesis is adopted, the calculation error is large when considering the actual wind speed, and it cannot reflect the actual electric field distribution on the ground. Summary of the invention

[0004] In order to overcome the shortcomings of the existing calculation of the ground composite electric field of the DC line, the present invention proposes a method for accurately predicting the ground composite electric field strength of the DC transmission line. In the modeling process, the charge equivalent corona is used to obtain the corona initiation field strength of the equivalent conductor. Based on the Kaptzov hypothesis, the finite element method is used to solve the corona space charge continuity equation and the Poisson equation, and finally a more accurate calculation method for the ground composite electric field of the DC transmission line is obtained.

[0005] In order to achieve the above technical purpose, the technical solution of the present invention is:

[0006] A method for calculating the ground composite electric field of a DC transmission line using an equivalent radius conductor comprises the following steps:

[0007] Step 1, according to the principle of equivalent corona initiation charge, an equivalent corona coefficient is introduced based on the peek formula for calculating the corona initiation field strength of the split conductor, and then the equivalent corona initiation field strength of the equivalent radius conductor is calculated using an empirical formula according to the equivalent corona coefficient;

[0008] Step 2, performing two-dimensional finite element calculation modeling on the DC transmission line, and then assigning an initial value of the surface charge density to the DC transmission line according to the equivalent corona inception field strength calculated in step 1, and then solving using the finite element method to obtain the synthetic electric field strength on the surface of the DC transmission line;

[0009] Step 3, according to the composite electric field strength and surface charge density obtained in step 2, the surface charge density of the conductor is corrected based on the Kaptzov hypothesis using the estimated correction method; then return to step 2, substitute the corrected surface charge density of the conductor and re-solve and iterate until the composite electric field strength satisfies the Kaptzov hypothesis.

[0010] The method, in step 1, the equivalent corona coefficient includes the split conductor coefficient k1 and the equivalent radius conductor coefficient k2, and the calculation formulas are:

[0011]

[0012] Where E0 represents the corona initiation field strength of the positive and negative poles of the split conductor, E max Indicates the maximum surface field strength of the positive and negative poles of the split wire; E 0eq It represents the corona initiation field strength of the positive and negative electrodes of the equivalent wire, E maxeq Indicates the maximum surface field strength of the positive and negative poles of the equivalent radius wire.

[0013] The method, in step 1, the peek formula for calculating the wire field strength includes the following formulas for calculating the positive split wire field strength E0 + And the negative pole split wire field strength E0 － The calculation formula is:

[0014]

[0015] Where r represents the conductor radius, which is obtained based on the radius parameter of the actual line.

[0016] The method, in step 1, the empirical formula is

[0017] k2=0.1059+1.192k1-0.323k1 2 .

[0018] The equivalent corona induction field strength of the positive and negative electrodes of the equivalent radius conductor is calculated according to the above formula.

[0019] The method described above performs two-dimensional finite element calculation modeling on the DC transmission line as follows:

[0020]

[0021]

[0022] Among them, ▽ is the gradient operator, E is the electric field intensity, ρ + , ρ - is the space charge density, K + , K - is the mobility of positive and negative ions, D p , D n is the diffusion coefficient of positive and negative ions, qe is the charge carried by the electron, R is the recombination coefficient of positive and negative ions, J + , J - is the positive and negative ion flow density, and W is the wind speed.

[0023] In the method, in step 3, the estimated correction method is used, which is calculated by the following formula:

[0024]

[0025] Where Es represents the surface field strength of the conductor, Ec represents the corona initiation field strength of the conductor, and ρ represents the charge density on the surface of the conductor.

[0026] In the method, in the step 3, satisfying the Kaptzov assumption means that after the transmission line corona initiation, the surface field strength of the conductor maintains the conductor corona initiation field strength unchanged.

[0027] The technical effect of the present invention is that the present invention takes into account the diffusion coefficient of positive and negative ions, adopts the finite element method, based on the Kaptzov hypothesis, and combines COMSOL Multi-physics and MATLAB to calculate the synthetic electric field on the ground of the DC transmission line. In the modeling process of the transmission line, the equivalent corona method is used to obtain the equivalent corona initiation field strength of the equivalent radius conductor, which simplifies the calculation. The finite element calculation software COMSOL Multi-physics can accelerate the convergence speed under the premise of ensuring the calculation accuracy, and finally obtain a more accurate calculation method for the ground synthetic electric field of the DC transmission line. And through the field measurement of the ground synthetic electric field of the DC transmission line in actual operation, it is verified that the calculation method of the present invention has high accuracy and can be applied to the calculation of the ground synthetic electric field of my country's high-voltage DC transmission line in the future. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 It is a flow chart of the present invention.

[0029] Figure 2 It is a decomposition diagram after modeling a real DC line.

[0030] Figure 3 This is the spatial charge distribution diagram at t = 0.05s.

[0031] Figure 4 It is the distribution diagram of space charge in steady state.

[0032] Figure 5 It is the distribution map of the ground synthetic electric field along the line. DETAILED DESCRIPTION

[0033] The embodiments of the present invention are further described in detail below in conjunction with the accompanying drawings, but this embodiment does not limit the present invention. All characteristic parameters and evaluation methods that use the same characteristics as the present invention should be included in the protection scope of the present invention.

[0034] In order to simplify the calculation, the present embodiment first obtains the equivalent corona initiation field strength of the DC transmission line in the case of an equivalent radius conductor; then, the DC line is two-dimensionally modeled in the finite element calculation software COMSOL Multi-physics, and the current continuity equation and the electrostatic field Poisson equation are solved by the finite element method. Based on the Kaptzov hypothesis (after the transmission line corona initiation, the surface field strength maintains the corona initiation field strength unchanged), the surface charge density of the transmission line is iterated by using MATLAB until the Kaptzov hypothesis is satisfied, and then it is determined in MATLAB whether the spatial charge distribution reaches a steady-state distribution, and finally a more accurate DC line ground synthetic electric field calculation method can be obtained.

[0035] The specific steps are:

[0036] Step 1: Calculate the equivalent radius of the transmission line according to the actual line parameters, and calculate the corona initiation field strength of the positive and negative polarity conductors according to the positive and negative polarity Pic's formula. Then, based on the principle of equivalent corona initiation charge, use the empirical formula to calculate the equivalent corona initiation field strength of the equivalent radius conductor.

[0037] Step 2: Perform finite element calculation modeling, and assign initial values ​​of surface charge density of positive and negative polarity wires based on the empirical formula for the distribution of positive and negative charges in coaxial cylindrical electrodes, and use the finite element method to solve the current continuity equation and Poisson's equation.

[0038] Step 3: Use iteration to obtain the surface field strength of the conductor under steady-state conditions and determine whether the Kaptzov assumption is satisfied. If it is satisfied, it is a steady-state result. If not, complete the iteration and then perform the second step again.

[0039] Specifically, the first step of this embodiment is as follows: Figure 1 As shown, in the calculation of the overall synthetic electric field, the equivalent radius conductor is used to replace the split conductor, and equations (1) and (2) are used to obtain the corona initiation field strength of the split conductor, while what we are concerned about now is the equivalent corona initiation field strength of the equivalent radius conductor. For this purpose, the equivalent corona coefficients k1 and k2 are introduced; as shown in equations (3) and (4), and then the equivalent corona initiation field strength of the transmission line can be obtained by equation (5): The Pico formula of the positive and negative conductors is shown in equations (1) and (2):

[0040]

[0041] In formulas (1) and (2), r represents the wire radius.

[0042]

[0043] k2=0.1059+1.192k1-0.323k1 2 (5)

[0044] In formula (3) and (4), E0 represents the corona initiation field strength of the positive and negative split conductors, and E max Indicates the maximum surface field strength of the positive and negative split wires, E 0eq It represents the positive and negative equivalent wire corona initiation field strength, E maxeq It indicates the maximum surface field strength of the positive and negative poles with equivalent radius wires.

[0045] The second step is to use the finite element method to solve the current continuity equation and Poisson's equation. From Gauss's theorem, we know that:

[0046]

[0047] From the relationship between potential gradient and potential, we can know that:

[0048]

[0049] From the mechanism of electric charge forming current, we can know that:

[0050]

[0051] From the current continuity equation, we know that:

[0052]

[0053] j=j + +j - (12)

[0054]

[0055] Combining equations (8)(9)(10)(11) we can get:

[0056]

[0057] In the above formulas (6)-(15), E is the electric field intensity, ρ + , ρ - is the space charge density, K + , K - is the mobility of positive and negative ions, D p , D n is the diffusion coefficient of positive and negative ions, qe is the charge carried by the electron, R is the recombination coefficient of positive and negative ions, J + , J - is the positive and negative ion flow density, and W is the wind speed.

[0058] In COMSOL Multi-physics, the wire is modeled by using equivalent radius wires instead of split wires and considering the radius of the entire computational domain, such as Figure 2 As shown, it is more than 4 times the distance between the positive and negative conductors. The present invention takes into account the diffusion of positive and negative ions. Equations (14) and (15) are second-order nonlinear partial differential equations. The present invention uses the built-in electrostatic module and rare species transfer module of COMSOL Multi-physics to set boundary conditions and couple the solution of multi-physics field equations. A discrete method is used to disperse the solution domain into a series of interrelated small units to form a discrete algebraic equation group. In the specific solution process, in order to reduce oscillation and excessive iteration, an anisotropic streamline artificial diffusion method is added, and the Poisson equation is solved by electrostatics. The standard Gaussian quadrature method built into COMSOL Multi-physics is used for spatial integration.

[0059] (3) MATLAB iterative wire surface charge density

[0060] Since the present invention is based on the Kaptzov hypothesis, it is necessary to adjust the surface charge density of the wire according to the Kaptzov hypothesis until the assumption condition is met. Therefore, it is necessary to use the interface between COMSOL Multi-physics and MATLAB, set up in MATLAB to obtain the surface field strength and surface charge density of the wire, and use the estimation-correction method, that is, formula (16), to correct the surface charge density of the wire in MATLAB until the Kaptzov hypothesis is met under steady-state conditions.

[0061]

[0062] Where Es is the surface field strength of the conductor, Ec is the corona initiation field strength of the conductor, and ρ is the charge density on the surface of the conductor.

[0063] After iterating the surface charge density in MATLAB, the iterative surface charge density is brought into COMSOL Multi-physics for recalculation using the interface between COMSOL Multi-physics and MATLAB, and it is again determined whether the surface field strength of the conductor satisfies the Kaptzov hypothesis. If the steady-state result satisfies the Kaptzov hypothesis, it is considered that the ground synthetic electric field distribution under steady-state conditions is obtained.

[0064] like Figure 3 The figure shows the space charge distribution at t = 0.05s. Figure 4 The figure shows the space charge distribution in the steady state. Figure 5 The figure shows the distribution of the ground composite electric field along the radial direction of the conductor under steady-state conditions.

[0065] Parts not described in detail in this specification belong to the prior art known to professionals in the field.

Claims

1. A method for calculating the ground synthetic electric field of a DC transmission line using an equivalent radius conductor, characterized in that: The following steps are involved: Step 1, according to the principle of equivalent corona initiation charge, an equivalent corona coefficient is introduced based on the peek formula for calculating the corona initiation field strength of the split conductor, and then the equivalent corona initiation field strength of the equivalent radius conductor is calculated using an empirical formula according to the equivalent corona coefficient; Step 2, performing two-dimensional finite element calculation modeling on the DC transmission line, and then assigning an initial value of the surface charge density to the DC transmission line according to the equivalent corona inception field strength calculated in step 1, and then solving using the finite element method to obtain the synthetic electric field strength on the surface of the DC transmission line; Step 3, according to the composite electric field strength and surface charge density obtained in step 2, the surface charge density of the conductor is corrected based on the Kaptzov hypothesis using the estimated correction method; then return to step 2, substitute the corrected surface charge density of the conductor and re-solve and iterate until the composite electric field strength satisfies the Kaptzov hypothesis.

2. The method according to claim 1, characterized in that In step 1, the equivalent corona coefficient includes the split conductor coefficient k1 and the equivalent radius conductor coefficient k2, and the calculation formulas are: Where E0 represents the corona initiation field strength of the positive and negative poles of the split conductor, E max Indicates the maximum surface field strength of the positive and negative poles of the split wire; E 0eq It represents the corona initiation field strength of the positive and negative electrodes of the equivalent wire, E maxeq Indicates the maximum surface field strength of the positive and negative poles of the equivalent radius wire.

3. The method according to claim 2, characterized in that In step 1, the peek formula for calculating the conductor field strength includes the following formulas for calculating the positive split conductor field strength E0 + And the negative pole split conductor field strength E0 － The calculation formula is: Where r represents the conductor radius, which is obtained based on the radius parameter of the actual line.

4. The method according to claim 3, characterized in that In step 1, the empirical formula is k2=0.1059+1.192k1-0.323k1 2 。 The equivalent corona induction field strength of the positive and negative electrodes of the equivalent radius conductor is calculated according to the above formula.

5. The method according to claim 2, characterized in that: The two-dimensional finite element calculation modeling of the DC transmission line is: in, is the gradient operator, E is the electric field intensity, ρ + , ρ - is the space charge density, K + , K - is the mobility of positive and negative ions, D p , D n is the diffusion coefficient of positive and negative ions, qe is the charge carried by the electron, R is the recombination coefficient of positive and negative ions, J + , J - is the positive and negative ion flow density, and W is the wind speed.

6. The method according to claim 5, characterized in that In step 3, the estimated correction method is used, which is calculated by the following formula: Where Es represents the surface field strength of the conductor, Ec represents the corona initiation field strength of the conductor, and ρ represents the charge density on the surface of the conductor.

7. The method according to claim 6, characterized in that In the step 3, satisfying the Kaptzov hypothesis means that after the transmission line corona initiation, the surface field strength of the conductor maintains the conductor corona initiation field strength unchanged.

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