Method for calculating the corona initiation voltage of a positive DC conductor with foreign objects

Abstract

This invention relates to the field of calculating the corona initiation voltage of high-voltage transmission lines, and discloses a method for calculating the corona initiation voltage of a positive DC transmission line when foreign objects are present. The method includes the following steps: First, simulating the presence of foreign objects on the surface of the DC transmission line using multiple infinitely long cylindrical conductors; Second, using the electric axis method to represent each small cylindrical conductor as an infinitely long line charge, determining the position of each line charge, and then calculating the charge amount of each line charge using the simulated charge method; Third, finally determining the corona initiation voltage of the DC transmission line based on the method for calculating the corona initiation voltage of the conductor. This method for calculating the corona initiation voltage of a positive DC transmission line when foreign objects are present can simulate any shape of foreign object on the surface of the transmission line, effectively and conveniently calculating the surrounding electric field strength.

Description

Technical Field

[0001] This invention relates to the field of calculating the corona initiation voltage of high-voltage transmission lines, specifically a method for calculating the corona initiation voltage of a positive DC transmission line when foreign objects are present. Background Technology

[0002] my country has a vast territory and complex terrain, with uneven distribution of energy resources and productivity. Therefore, vigorously developing large-capacity and long-distance power transmission is a necessity given my country's unique national conditions at this stage. Direct current (DC) transmission has advantages such as large transmission capacity, long transmission distance, and reduced transmission losses. In the future, my country plans to construct multiple DC lines. Because excessively high voltage in transmission lines can sometimes cause corona discharge, and conductors with foreign objects on their surface are more prone to corona discharge than smooth conductors, corona discharge can cause a series of hazards, such as interference with wireless communication equipment, energy loss, and chemical reactions that can corrode and damage metal electrodes. Therefore, studying the corona initiation voltage of high-voltage transmission lines is an extremely important part of high-voltage transmission engineering and has significant implications for national development. Currently, many domestic experts and scholars, when studying the corona initiation condition when foreign objects are present on the surface of high-voltage transmission lines, are often troubled by how to calculate the electric field strength around the conductor.

[0003] Currently, there is no particularly effective and convenient method in China for calculating the electric field strength around a conductor when foreign objects are present, especially when there are irregular foreign objects on the conductor surface, making the calculation of the electric field strength around the conductor particularly difficult. The calculation of the electric field strength around a conductor often relies on foreign simulation software such as ANSYS. There is no good domestic simulation software or calculation method that can effectively solve this problem and break the shackles of foreign software. Therefore, we propose a method for calculating the corona initiation voltage of a positive DC conductor when foreign objects are present. Summary of the Invention

[0004] (a) Technical problems to be solved

[0005] To address the shortcomings of existing technologies, this invention provides a method for calculating the corona initiation voltage when a foreign object is present in a positive DC conductor, thus solving the aforementioned problems.

[0006] (II) Technical Solution

[0007] To achieve the above-mentioned objectives, the present invention provides the following technical solution: a method for calculating the corona initiation voltage of a positive DC conductor when a foreign object is present, comprising the following steps:

[0008] Step 1: Simulate the situation where there are foreign objects on the surface of DC transmission lines using multiple infinitely long cylindrical conductors;

[0009] Step 2: Use the electric axis method to represent each small cylindrical wire as an infinitely long line charge, determine the position of each line charge, and then use the simulated charge method to calculate the charge of each line charge.

[0010] Step 3: Finally, calculate the corona initiation voltage of the DC transmission line based on the method for calculating the corona initiation voltage of the conductor.

[0011] Preferably, the specific content of the first step is as follows: based on the shape and size of the actual wire and the foreign object, select an appropriate infinitely long cylindrical wire with a radius of a, determine the number of small cylindrical wires, and simulate their shape.

[0012] Preferably, for the conductor portion: based on calculation accuracy and according to the actual conductor size, the radius 'a' of the small cylindrical conductor is selected as one-hundredth of the original conductor radius 'r'. First, 100 small cylindrical conductors are arranged along the diameter direction of the conductor perpendicular to the ground. Then, a small circle is tangent between every two small circles on both sides of the first column, forming the second and third columns, and so on, until the small circles are tangent to the boundary of the large circle, or until another column of small circles cannot be accommodated.

[0013] Foreign object section: Select the small cylindrical wire with radius 'a' as defined above. Based on the dimensions of each boundary of the foreign object, select the maximum number of small circles whose length does not exceed the boundary length. Start arranging them inward from the point tangent to the boundary until the foreign object is filled.

[0014] Preferably, determining the location of each line charge includes the following steps:

[0015] Calculate the location of the equivalent line charge:

[0016]

[0017] The coordinates of the equivalent line charge are (0, b). Once the position of the line charge is determined, the electric potential of the line charge with respect to any point in space can be calculated.

[0018] Let there be an arbitrary point p(x,y) outside the conductor, with distances from the positions of the line charges +τ and -τ, respectively:

[0019]

[0020] The electric potential at point p is:

[0021]

[0022] Preferably, the second step of calculating the charge amount of each line charge using the simulated charge method includes the following steps:

[0023] Establish the following coordinate system: the x-axis is located on the ground, and the y-axis is perpendicular to the ground and pointing upwards. N small cylindrical wires are used to simulate the shape of the foreign object. Based on the actual model, the center position of each small cylindrical wire is (x... k ,y k The positions of the corresponding N equivalent line charges are determined using the electric axis method, with coordinates (x, y, y).i ,y i N matching points are set at the boundary between the wire and the foreign object. The position coordinates of the matching points are represented by (x, y). j ,y j ) represents the potential at each matching point. They are equal, and their values ​​are equal to the voltage U across the conductor.

[0024] Equivalent line charge location:

[0025] x i =x k ;

[0026]

[0027] The potential generated by the i-th line charge at the j-th matching point is:

[0028]

[0029] Let the potential coefficient be:

[0030]

[0031] Generating matrix:

[0032]

[0033] [P ij ] is an N×N potential coefficient matrix, [τ i [ ] is a column vector consisting of N line charges. A column vector consisting of the potentials of N matching points;

[0034] By substituting the values ​​into the solution, the charge τ of each line charge can be calculated. i Then, based on the amount of charge of the line charge, the electric field strength in the space around the conductor can be calculated.

[0035] Preferably, the corona initiation voltage calculation in the third step includes the following steps:

[0036] S1: Determine the initial voltage value;

[0037] S2: Calculate the spatial electric field distribution;

[0038] S3: Calculate the values ​​of the collision ionization coefficient α and the adhesion coefficient η;

[0039] S4: Calculate the number of primary and secondary electron avalanches, N1 and N2;

[0040] S5: Determine N1 and N2.

[0041] (III) Beneficial Effects

[0042] Compared with the prior art, the present invention provides a method for calculating the corona initiation voltage when a foreign object is present in a positive DC conductor, which has the following beneficial effects:

[0043] 1. The method for calculating the corona initiation voltage when there are foreign objects on the positive DC conductor can simulate any shape of foreign object on the surface of the transmission conductor and effectively and conveniently calculate the surrounding electric field strength. Attached Figure Description

[0044] Figure 1 This is a schematic diagram of the electric field strength calculation process;

[0045] Figure 2 This is a schematic diagram of the shape simulation;

[0046] Figure 3 This is a schematic diagram of the electric axis method;

[0047] Figure 4 This is a schematic diagram of the equivalent line charge;

[0048] Figure 5 A schematic diagram illustrating the steps for calculating the negative DC corona initiation voltage;

[0049] Figure 6 This is a schematic diagram of the calculation structure. Detailed Implementation

[0050] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0051] Please see Figure 1-6 The method for calculating the corona initiation voltage when a foreign object is present in a positive DC conductor includes the following steps:

[0052] S1: Calculation of electric field strength

[0053] The shape was simulated using multiple infinitely long cylindrical wires.

[0054] Based on the actual shape and size of the conductor and the foreign object, select an infinitely long cylindrical conductor with a suitable radius 'a', determine the number of such small cylindrical conductors, and simulate their shape, such as... Figure 2 As shown.

[0055] For the conductor section: To ensure calculation accuracy, based on the actual conductor dimensions, the radius 'a' of the small cylindrical conductor is selected as one-hundredth of the original conductor radius 'r'. First, 100 small cylindrical conductors are arranged along the diameter direction of the conductor perpendicular to the ground. Then, a small circle is tangent between every two small circles on both sides of the first column, forming the second and third columns, and so on, until the small circles are tangent to the boundary of the large circle, or until another column of small circles cannot be accommodated.

[0056] Foreign object section: Select the small cylindrical wire with radius 'a' as defined above. Based on the dimensions of each boundary of the foreign object, select the maximum number of small circles whose length does not exceed the boundary length. Start arranging them inward from the point tangent to the boundary until the foreign object is filled.

[0057] Determining the position of equivalent line charge using the electric axis method

[0058] Using the ground as the x-axis and the center of the cylindrical conductor as the y-axis position, the equivalent line charge of a cylindrical conductor of radius *a* above the ground is located at (0, b), with a charge of τ. A mirror image of this cylindrical conductor lies below the x-axis. Figure 3 As shown.

[0059] Calculate the location of the equivalent line charge:

[0060]

[0061] The coordinates of the equivalent line charge are (0, b). Once the position of the line charge is determined, the electric potential of the line charge with respect to any point in space can be calculated.

[0062] Let there be an arbitrary point p(x,y) outside the conductor, with distances from the positions of the line charges +τ and -τ, respectively:

[0063]

[0064] The electric potential at point p is:

[0065]

[0066] Finding the linear charge τ using the simulated charge method

[0067] Establish the following coordinate system: the x-axis is located on the ground, and the y-axis is perpendicular to the ground and pointing upwards. N small cylindrical wires are used to simulate the shape of the foreign object. Based on the actual model, the center position of each small cylindrical wire is (x... k ,y k The positions of the corresponding N equivalent line charges are determined using the electric axis method, with coordinates (x, y, y). i ,y i N matching points are set at the boundary between the wire and the foreign object. The position coordinates of the matching points are represented by (x, y). j ,y j ) represents the potential at each matching point. They are equal, and their values ​​are equal to the voltage U on the conductor.

[0068] Equivalent line charge location:

[0069] x i =x k ;

[0070]

[0071] The potential generated by the i-th line charge at the j-th matching point is:

[0072]

[0073] Let the potential coefficient

[0074]

[0075] Generating matrix

[0076]

[0077] [P ij ] is an N×N potential coefficient matrix, [τ i [ ] is a column vector consisting of N line charges. It is a column vector consisting of the potentials of N matching points.

[0078] By substituting the values ​​into the solution, the charge τ of each line charge can be calculated. i Then, based on the amount of charge of the line charge, the electric field strength in the space around the conductor can be calculated.

[0079] Calculate the electric field strength around the conductor

[0080] The distance from a single line charge to point P, and the distance from its mirror charge to point P, are respectively:

[0081]

[0082] The electric field strength produced by a single line charge at point P is:

[0083]

[0084] The electric field strength at point P in the X direction:

[0085]

[0086] The electric field strength at point P in the y-direction is:

[0087]

[0088] The electric field strength at point P is

[0089]

[0090] The above calculation method can be used to calculate the electric field strength at any point in the space around the conductor. Since the conductor is more likely to corona when there are foreign objects, we only need to select an appropriate number of calculation points below the foreign objects of the conductor with an appropriate step size to calculate the electric field strength.

[0091] S2: Calculation of corona initiation voltage

[0092] When the voltage of a positive direct current transmission line increases to a certain level, the electric field in the vicinity of the line increases. This causes the electron collision ionization coefficient α to exceed the adhesion coefficient η (the region where α > η is called the ionization region). Free electrons in this region move towards the line under the influence of the applied electric field, colliding with air molecules and causing ionization, resulting in an initial electron avalanche. Simultaneously, the collisions and ionization of air molecules excite them, causing them to radiate photons. Air molecules absorb these photons and undergo photoionization. The resulting photons, under the influence of the electric field, move towards the positively charged conductor, colliding with and ionizing air molecules to form a secondary electron avalanche.

[0093] When the number of secondary electron avalanches N2 is not less than the number of primary electron avalanches N1, the positive DC corona can be self-sustaining. The voltage across the conductor at this point is the corona initiation voltage. The calculation process is as follows: Figure 5 :

[0094] Determine the initial voltage value

[0095] Choose a suitable voltage range, determine the appropriate initial voltage value and maximum voltage value, and then determine an appropriate voltage increment step ΔU to ensure that the calculation is within a reasonable range.

[0096] Calculate the spatial electric field distribution

[0097] Following the above method for calculating electric field strength, select a suitable number of infinitely long cylindrical wires to simulate the shapes of the wires and the foreign object. Then, use the electric axis method to determine the position of the equivalent line charge of each small cylindrical infinitely long wire. Select matching points at the boundary between the wire and the foreign object, with the same number of equivalent line charges, whose potential value is equal to the voltage U on the wire. Then, solve for the charge τ of each equivalent line charge using the simulated charge method. i Then, the electric field strength at the selected calculation point is calculated.

[0098] (3) Calculate the values ​​of the collision ionization coefficient α and the adhesion coefficient η.

[0099] When α > η, a region is formed where electron avalanches occur; this region is called the ionization region. The formula for calculating the collisional ionization coefficient α is as follows:

[0100]

[0101] The formula for calculating the adhesion coefficient η is:

[0102]

[0103] α d and α w These are the ionization coefficients in dry air and humid air, respectively; η d and η w These are the adhesion coefficients in dry air and humid air, respectively; p d and p w These are the partial pressures of dry air and water vapor, respectively. Their relationship with the electric field strength is as follows (N is the total number of molecules in air at pressure p):

[0104] For the ionization coefficient:

[0105] hour,

[0106]

[0107] hour,

[0108]

[0109] For the adhesion coefficient:

[0110] hour;

[0111]

[0112] hour;

[0113]

[0114] hour;

[0115] η d =1.0681×10 4 ;

[0116] hour;

[0117]

[0118] hour;

[0119]

[0120] Calculate the number of primary and secondary electron avalanches, N1 and N2.

[0121]

[0122] The electron avalanche head is spherical in shape, with a radius of:

[0123]

[0124] y i The coordinates, D, are at the boundary of the ionized region. e V is the electron diffusion coefficient. e This represents the electron drift velocity.

[0125] After calculating the number of positive ions produced by a single collisional ionization, this value is applied to the number of positive ions in a secondary electron avalanche. The calculations up to the middle result are:

[0126]

[0127] f1 is the number of photoelectrons produced during a single collisional ionization, μ is the photon absorption coefficient, and g y Let be the electrode coefficient. The ionization region is divided into layers, with the thickness of each layer being dy. Let the coordinate of a certain layer be y'. Then the total number of photoelectrons produced in this layer is...

[0128] Determine N1 and N2

[0129] When N2≥N1, the corona can be self-sustaining, and the voltage on the conductor is the corona initiation voltage. Otherwise, the voltage is increased according to the voltage step size ΔU set in the first step, and the process is repeated in the second step until the condition N2≥N1 is met.

[0130] S3: Calculation Results

[0131] Assume the air pressure is at standard atmospheric pressure, the absolute humidity is maintained at 10%, the relative humidity is maintained at 58.1%, and the temperature is 273K.

[0132] According to the calculation method of this invention, the electric field strength of a conductor with a radius of 0.01m and a height of 4m above the ground is calculated when a spherical foreign object with a radius of 3mm is attached. During the calculation, 10,000 calculation points are selected below the foreign object in a step size of 1E-5m. The electric field strength distribution is as follows: Figure 6 As shown, according to the calculation process of the corona initiation voltage, its corona initiation voltage value is 185KV.

[0133] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for calculating the corona initiation voltage of a positive DC conductor when a foreign object is present, characterized in that, Includes the following steps: Step 1: Simulate the situation where there are foreign objects on the surface of DC transmission lines using multiple infinitely long cylindrical conductors; Step 2: Use the electric axis method to represent each small cylindrical wire as an infinitely long line charge, determine the position of each line charge, and then use the simulated charge method to calculate the charge of each line charge. Step 3: Finally, calculate the corona initiation voltage of the DC transmission line based on the method for calculating the corona initiation voltage of the conductor; among which, The second step of determining the location of each line charge includes the following steps: Calculate the location of the equivalent line charge: The coordinates of the equivalent line charge are (0, b). After determining the position of the line charge, calculate the electric potential of the line charge with respect to any point in space. Let there be an arbitrary point p(x,y) outside the conductor, with distances from the line charge +τ and -τ respectively: The electric potential at point p is: The second step, calculating the charge amount of each line charge using the simulated charge method, includes the following steps: Establish the following coordinate system: the x-axis is located on the ground, and the y-axis is perpendicular to the ground and pointing upwards. N small cylindrical wires are used to simulate the shape of the foreign object. Based on the actual model, the center position of each small cylindrical wire is (x... k ,y k The positions of the corresponding N equivalent line charges are determined using the electric axis method, with coordinates (x, y, y). i ,y i N matching points are set at the boundary between the wire and the foreign object. The position coordinates of the matching points are represented by (x, y). j ,y j ) represents the potential at each matching point. They are equal, and their values ​​are equal to the voltage U across the conductor. Equivalent line charge location: x i =x k ; The potential generated by the i-th line charge at the j-th matching point is: Let the potential coefficient be: Generating matrix: [P ij ] is an N×N potential coefficient matrix, [τ i [ ] is a column vector consisting of N line charges. A column vector consisting of the potentials of N matching points; Substitute the values ​​into the equations to solve for the charge τ of each line charge. i Then, the electric field strength in the space around the conductor can be calculated based on the amount of charge of the line charge.

2. The method for calculating the corona initiation voltage of a positive DC conductor when foreign matter is present, as described in claim 1, is characterized in that: The specific content of the first step is as follows: based on the shape and size of the actual wire and the foreign object, select an appropriate infinitely long cylindrical wire with a radius of a, determine the number of small cylindrical wires, and simulate their shape.

3. The method for calculating the corona initiation voltage of a positive DC conductor when foreign matter is present, as described in claim 2, is characterized in that: The simulation of the conductor section, based on the accuracy of the calculation, takes into account the actual conductor size. The radius 'a' of the small cylindrical conductor is selected as one-hundredth of the original conductor radius 'r'. First, 100 small cylindrical conductors are arranged along the diameter direction of the conductor perpendicular to the ground. Then, a small circle is tangent between every two small circles on both sides of the first column to form the second and third columns, and so on, until the small circle is tangent to the boundary of the large circle, or there is no room for another column of small circles.

4. The method for calculating the corona initiation voltage of a positive DC conductor when foreign matter is present, as described in claim 2, is characterized in that: The foreign object simulation involves selecting a small cylindrical wire with a radius of a, as defined above. Based on the dimensions of each boundary of the foreign object, the maximum number of small circles with an arrangement length not exceeding the boundary length is selected. The arrangement starts from the point tangent to the boundary and proceeds inward until the foreign object is filled.

5. The method for calculating the corona initiation voltage of a positive DC conductor when foreign matter is present, as described in claim 1, is characterized in that: The calculation of the corona initiation voltage in the third step includes the following steps: S1: Determine the initial voltage value; S2: Calculate the spatial electric field distribution; S3: Calculate the values ​​of the collision ionization coefficient α and the adhesion coefficient η; S4: Calculate the number of primary and secondary electron avalanches, N1 and N2; S5: Determine N1 and N2.

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