Calculation method for the corona onset voltage of UHVDC transmission lines with dirt or water droplets

Abstract

The invention relates to the field of calculating the corona inception voltage of an ultra-high voltage direct current (UHVDC) transmission conductor and discloses a method for calculating the corona inception voltage of an ultra-high voltage direct current (UHVDC) transmission conductor with dirt or water droplets. The method comprises the following steps: a first step: determining the overall shape of dirt or water droplets attached to the conductor by establishing coordinates, and selecting points along the edge of the shape; a second step: calculating the position and charge amount of equivalent line charges by combining a cylindrical mirror method and an electric axis method with a simulated charge method; and a third step: finally obtaining the field intensity around the conductor and obtaining the corona inception voltage through field intensity calculation. The method for calculating the corona inception voltage of an ultra-high voltage direct current (UHVDC) transmission conductor with dirt or water droplets has the advantage of being able to simulate the shape of dirt, water droplets or other foreign matter on the surface of the transmission conductor and calculate the surrounding field intensity, and being able to simulate the shape of the DC transmission conductor with dirt or water droplets attached using multiple points.

Description

Technical Field

[0001] The present invention relates to the field of calculation of the corona onset voltage of an ultra-high voltage direct current (UHVDC) transmission conductor, and in particular to a method for calculating the corona onset voltage of an ultra-high voltage direct current (UHVDC) transmission conductor with dirt or water droplets. Background Art

[0002] Corona discharge occurring on the surface of transmission conductors can cause energy loss and hazards such as radio interference and audible noise. Therefore, conductor corona discharge must be considered in the design and operation of DC transmission lines. However, my country suffers from severe environmental pollution, and operating conditions in some areas are harsh, necessitating research on the impact of contamination on the conductor's corona inception voltage. Furthermore, numerous UHVDC transmission lines have been constructed in the southwestern Yunnan and Guizhou regions, where the climate is highly variable and annual rainfall is high. Water droplets easily condense on the conductor surface under conditions of rain, fog, or high humidity. Raindrops or contamination distort the electric field distribution, reducing its uniformity and the conductor's corona inception voltage, thus affecting the conductor's corona characteristics and causing corona discharge. Therefore, research on how to calculate the corona inception voltage of conductors in the presence of contamination or water droplets is of great significance.

[0003] Traditionally, many Chinese experts and scholars studying the surface corona inception voltage of UHV transmission lines have only been able to simulate smooth conductors. This presents a challenge when dealing with conductors clogged with dirt, water droplets, or other foreign matter. While they can only analyze the field strength around these contaminated UHV transmission lines, they cannot directly calculate the corona inception voltage under specific operating conditions. Therefore, we propose a method for calculating the corona inception voltage of UHVDC transmission lines in the presence of dirt or water droplets. Summary of the Invention

[0004] (1) Technical problems solved

[0005] In view of the deficiencies of the prior art, the present invention provides a method for calculating the corona inception voltage of a UHVDC transmission line with dirt or water droplets, thereby solving the above-mentioned problems.

[0006] (2) Technical solution

[0007] To achieve the above-mentioned objectives, the present invention provides the following technical solution: a method for calculating the corona onset voltage of a UHVDC transmission line with dirt or water droplets, comprising the following steps:

[0008] Step 1: Determine the overall shape of the dirt or water droplets attached to the conductor by establishing coordinates, and select points along the edge of the shape;

[0009] Step 2: Use the combination of the cylindrical mirror method and the electric axis method, combined with the simulated charge method to calculate the position and charge of the equivalent line charge;

[0010] Step 3: Finally, the field strength around the conductor is obtained, and the corona inception voltage is obtained through field strength calculation.

[0011] Preferably, the specific contents of the mirror image method and the electric axis method in the second step are as follows:

[0012] The calculation formula of the electric axis position is:

[0013] R 2 +b 2 =h 2 ;

[0014] Then the coordinates of the equivalent line charge are:

[0015]

[0016] The distance parameter is:

[0017]

[0018] According to the distance formula, the distance between the point P to be determined and the electric axis is obtained, where one is the original charge point and the other is its mirror charge point;

[0019] The potential coefficient P to be determined is obtained:

[0020]

[0021] in

[0022]

[0023] Preferably, the specific steps of calculating the linear charge using the simulated charge method in the second step are:

[0024] Assume that there are n line charges, and the coordinates of each line charge are (x i ,y i ), set n matching points at the boundary of the wire with dirt attached, and set the coordinates of each matching point to (x j ,y j ), the potential at each matching point Equal, the value is equal to the voltage U on the wire, based on the combination of the cylindrical mirror method and the electric axis method, the coordinates of each line charge (x i ,y i ), and ε is the dielectric constant, ε0=8.85×10 -12 F / m;

[0025] It represents the electric potential generated by the i-th line charge at the j-th matching point:

[0026]

[0027] Pij for The corresponding potential coefficient:

[0028]

[0029] Then we have:

[0030]

[0031] Substituting into the solution, we can find the charge Q of each line charge i , and thus calculate the field strength in the space around the wire.

[0032] Preferably, the surrounding field strength in the third step is calculated as follows:

[0033] Let any point outside the wire be A(x,y), then the distance from a single line charge to point A and the distance from its image charge to point A are:

[0034]

[0035] The electric field strength generated by a single line charge at point A is:

[0036]

[0037] So the electric field strength at point A in the x direction is:

[0038]

[0039] The electric field strength at point A in the y direction is:

[0040]

[0041] The electric field strength at point A is

[0042]

[0043] Preferably, the calculation steps of the corona inception voltage are as follows:

[0044] S1: Calculate the spatial electric field distribution based on the initial voltage value;

[0045] S2: Calculated collision ionization coefficient α and adhesion coefficient η parameters;

[0046] S3: Calculate N eph ;

[0047] S4: When N eph When ≥1, the corona inception voltage is obtained. When the above conditions are not met, the calculation of the spatial electric field distribution is restarted.

[0048] Preferably, the parameter of α is:

[0049]

[0050] Parameters of η:

[0051]

[0052] Where Pw is the water vapor partial pressure in the air, Pd is the dry vapor partial pressure in the air, and Ptotal is the total air pressure.

[0053] (3) Beneficial effects

[0054] Compared with the prior art, the present invention provides a method for calculating the corona onset voltage of UHVDC transmission lines with dirt or water droplets, which has the following beneficial effects:

[0055] 1. This method for calculating the corona inception voltage of ultra-high voltage direct current transmission conductors with dirt or water droplets has the advantage of simulating the shape of dirt, water droplets, or other foreign matter on the surface of the transmission conductor and calculating the surrounding electric field strength. It can also simulate the shape of the DC transmission conductor with dirt or water droplets using multiple points.

[0056] 2. This method for calculating the corona onset voltage of a UHVDC transmission line with dirt or water droplets is based on the electric axis method, where each point is represented by an infinitely long linear charge. This method uses multiple linear charges distributed within the conductor contour to simulate the actual conductor conditions.

[0057] 3. This method for calculating the corona inception voltage of a UHVDC transmission line with dirt or water droplets determines the location of each linear charge and then uses a charge simulation method to calculate the charge magnitude of each linear charge, thereby calculating the overall field strength. Finally, based on the method for calculating the corona inception voltage, the field strength is used to derive the conductor's corona inception voltage. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 This is a schematic diagram of the field strength calculation process;

[0059] Figure 2 Create a schematic diagram for the coordinates;

[0060] Figure 3 Schematic diagram of the electric axis method;

[0061] Figure 4 Select a schematic diagram for the electrical axis;

[0062] Figure 5 is a schematic diagram of equivalent line charges;

[0063] Figure 6 Schematic diagram of the calculation steps of negative DC corona inception voltage;

[0064] Figure 7 Schematic diagram of the electric field distribution of a smooth wire;

[0065] Figure 8 Schematic diagram of the electric field distribution on the wire after the water droplet is electrically attached. DETAILED DESCRIPTION

[0066] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. 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 making creative efforts are within the scope of protection of the present invention.

[0067] See also Figure 1-8 A method for calculating the corona inception voltage of a UHVDC transmission line with dirt or water droplets includes the following steps:

[0068] S1: Calculation of field strength

[0069] 1. Establish a coordinate system for the wire. According to the shape and size of the actual wire and foreign object, establish the coordinate system with the center of the circle as the origin.

[0070] 2. Simulate the wire as a line charge using the electric axis method

[0071] When calculating the corona inception voltage of a DC transmission line, the mirror image method and the electric axis method can be used based on the uniqueness theorem. These two methods treat the actual non-uniform distribution of the medium as uniform, thus replacing the original two-dimensional conductor cross-section model with a simple line charge.

[0072] The mirror method is that when setting a charge point, it is still necessary to consider the influence of the ground plane on the electric field distribution. It is necessary to set up a charge point below the ground plane with an opposite charge to the initial charge, so that the potential on the ground plane can be zero.

[0073] The electric axis method is primarily used to analyze two parallel cylindrical conductors. It's particularly well-suited for transmission lines. In practice, transmission lines are long, so calculations can be simplified by assuming them to be infinitely long straight wires. A cross-section of the unit charge can be taken to simplify the calculations, assuming the charges on the wire are +τ and -τ, respectively.

[0074] The calculation formula of the electric axis position is:

[0075] R 2 +b 2 =h 2 ;

[0076] Then the coordinates of the equivalent line charge are:

[0077]

[0078] The distance parameter is:

[0079]

[0080] After determining the position of the electric axis, the distance from the point P to the electric axis is obtained according to the above distance formula, where one is the original charge point and the other is its mirror charge point.

[0081] Then we can get the potential coefficient P to be determined:

[0082]

[0083] in

[0084]

[0085] For the actual situation of the wire, such as Figure 4 After establishing the coordinate system, select an appropriate location based on the conductor radius, keeping close to the conductor edge. If dirt or water droplets are present on the conductor, use appropriate coordinates in the coordinate system to simulate the shape of the dirt or water droplets. After determining the arrangement of the electric axis, the position of the line charge can be determined. In actual calculations, the electric axis density must be appropriately arranged according to the situation. Generally, for a conductor with a radius of 2 mm, it is recommended to select at least 300 points to obtain a relatively accurate calculation result.

[0086] 3. Determine the amount of line charge by simulating charge method

[0087] Taking the attached triangle pollution as an example, suppose there are n line charges. The position of the n line charges is determined by the electric axis method, and the coordinates of each line charge are (x i ,y i Then set n matching points at the boundary of the wire with dirt attached, and set the coordinates of each matching point to (x j ,y j ), the potential at each matching point Equal, the value is equal to the voltage U on the wire. Through the calculations of 1 and 2, the coordinates of each line charge (x i ,y i ), and ε is the dielectric constant, ε0=8.85×10 -12 F / m.

[0088] It represents the electric potential generated by the i-th line charge at the j-th matching point:

[0089]

[0090] P ij for The corresponding potential coefficient:

[0091]

[0092] Then there is

[0093]

[0094] Substituting into the solution, we can find the charge Q of each line charge i , and thus calculate the field strength in the space around the wire.

[0095] 4. Calculate the field strength around the conductor

[0096] S1: Let any point outside the wire be A(x,y). The distances from a single line charge to point A and the distances from its image charge to point A are:

[0097]

[0098] The electric field strength generated by a single line charge at point A is:

[0099]

[0100] So the electric field strength at point A in the x direction is:

[0101]

[0102] The electric field strength at point A in the y direction is:

[0103]

[0104] The electric field strength at point A is

[0105]

[0106] The above calculation method can be used to calculate the field strength at any point in the space around the conductor. Usually, dirt or water droplets attached to the conductor will make the conductor more prone to dizziness. Therefore, it is only necessary to select an appropriate step size and choose an appropriate calculation point below the point where the dirt or raindrops are attached to the conductor to obtain the field strength.

[0107] S2: Calculation of corona onset voltage

[0108] For high-voltage transmission lines, there are usually two transmission modes: positive and negative DC. Their corona inception mechanisms and calculation methods are slightly different. Here, the calculation of the corona inception voltage of a negative DC conductor is taken as an example.

[0109] The specific calculation process is as follows Figure 5 As shown:

[0110] Corona discharge is a self-sustaining discharge in a bipolar unbalanced electric field across a gap. The corona generated by negative DC contains an electromagnetic pulse known as "Trichel," which forms an initial electron avalanche. This electron avalanche moves along the electric field, triggering a negative DC corona discharge at the boundary of the ionized region. This discharge is inextricably linked to electron emission from the cathode surface. Whether a negative DC corona discharge can sustain itself depends primarily on whether the initial electron avalanche emitted from the electrode surface can generate a free electron on the cathode surface. Many researchers studying the mechanism of corona discharge have proposed several mechanisms for secondary electron emission from the cathode surface.

[0111] Photoelectron emission: When the initial electron avalanche moves toward the cathode surface, some of the photons generated reach the cathode surface and cause the emission of photoelectrons.

[0112] Ion collisions cause electrons to be generated on the cathode surface: In a very non-uniform electric field, there are some positively charged ions. The kinetic energy generated by the electric field on the cathode surface collides with unstable molecules in the air or unstable metastable molecules on the cathode surface to generate free electrons.

[0113] The cathode surface is not smooth or has burrs, which can cause electrons to scatter. The cathode surface is inevitably rough, and these areas may have burrs or surface defects, which can cause local electric field distortion. In this distorted electric field, free electrons are emitted, causing a self-sustaining negative DC corona. Because the cathode surface electric field emission mechanism does not fully reflect the actual situation, the mechanism of photoelectron emission and ion collision is used. These two mechanisms are collectively referred to as the photoionization model. This is combined with gas discharge theory to perform calculations for the most severe load case.

[0114] Corona is a process of change of microscopic particles.

[0115]

[0116] StdNumberParticle is the number of particles in one cubic meter of gas under standard conditions, StdTemperature is the standard thermodynamic temperature, StdPressure is the standard atmospheric pressure, Potal and Temperature are the set atmospheric pressure and thermodynamic temperature values.

[0117] Using a Cartesian coordinate system, let the origin be the geodetic plane, the y-axis be the vertical downward direction, and the x-axis be the direction along the geodetic plane. Assume that there is a free electron on the electrode surface moving toward the geodetic plane to form an electron avalanche. Where N1 is the number of initial electron avalanches:

[0118]

[0119] α(y) is the electron impact ionization coefficient, η(y) is the electron adhesion coefficient, and y is the distance to the boundary of the ionization region, that is, the region where the difference between the impact ionization coefficient and the adhesion coefficient is zero. Factors affecting the above two coefficients include the gap electric field distribution, air pressure, ambient temperature, and the distance between the gaps.

[0120] The effective ionization coefficient is obtained by integrating the electron impact ionization coefficient and the attachment coefficient in the ionization region. The degree of ionization in the gap region can be reflected by the effective ionization coefficient.

[0121]

[0122] During the development of the electron avalanche, when it reaches a distance of Δy, photons will be generated and radiated outward as free electrons collide.

[0123] Δn1(y)=f * (y)·N1·Δy;

[0124] f*(y) is the probability of photon generation, which is directly proportional to the electron impact ionization coefficient, with the proportional coefficient being k.

[0125] f * (y) = k·α(y);

[0126] The initial electron avalanche generates photons, which move across the gap, with some reaching the other electrode and some disappearing into the air.

[0127] Δn p□ =f*(y)·N1·Δy·g(y)·exp -μy ;

[0128] μ is the air photon absorption coefficient, and g(y) is the geometric coefficient of the electrode surface. The geometric coefficient is the path that the outwardly radiated photons generated by the initial electron avalanche propagate to the cathode surface and requires analysis based on specific circumstances. The following uses the rod-plate model as an example:

[0129] The geometry factor in the rod-plate model is calculated by multiplying the radial component of the geometry factor by the axial component.

[0130] g(y)=g rad (y) g ax (y);

[0131] Because of the particularity of the rod-plate model, the geometric factor is equal to the square of the radial component, that is,

[0132] g(y)=g rad (y) 2 ;

[0133] The formula for the geometric factor is:

[0134]

[0135] μ is the photon absorption coefficient. Studies have shown that the photon absorption coefficient is related to the relative density of air and is directly proportional to the relative density of air. The formula for the photon absorption coefficient and the relative density of air is:

[0136] μ=δμ0;

[0137] When we select the total number of free photoelectrons reaching the cathode surface, we only need the number of free photoelectrons generated by the initial electron avalanche in the ionization region. The distance between the boundary of the ionization region and the cathode surface is yi, which is the coordinate position of the initial electron avalanche head in the gap. When that part of the free photoelectrons reaches the cathode surface and ionizes to produce a free photoelectron, the secondary electron avalanche can be generated, resulting in the direct formation of a negative polarity corona. The specific calculation formula is

[0138]

[0139] According to the above formula, the voltage will be gradually changed. The change of voltage will change the electron impact ionization coefficient and the adhesion coefficient, thereby affecting the change of the boundary of the ionization region, that is, it will change the gap electric field, and therefore affect the number of electrons in the initial electron avalanche and the number of photoelectrons radiated outward. When the above formula is equal, it is the onset voltage of the photoionization model.

[0140] The parameters for the collision ionization coefficient α and the adhesion coefficient η are set within a range determined based on existing research. E is the electric field strength, and N is the total number of molecules in the air at a given pressure, Ptotal.

[0141] The following are the parameters of α

[0142]

[0143] The following are the parameters of η

[0144]

[0145]

[0146] Where Pw is the water vapor partial pressure in the air, unit is torr, Pd is the dry vapor partial pressure in the air, unit is torr, and Ptotal is the total air pressure, unit is torr.

[0147] S3: Calculation results display

[0148] According to the flowchart of the wire-board model above, MATLAB was used for programming. The wire radius selected this time was 0.01m, and the distance from the wire to the ground was 4m.

[0149] The electric field strength on a smooth conductor is 15 kV / m. When a critical raindrop is added, the electric field strength increases to 28.97 kV / m, a 93.13% increase. The presence of raindrops distorts the electric field, transforming it from a slightly circular shape to a more curvy semi-ellipse. Simultaneously, the starting coordinates for calculating the electric field shift closer to the Earth, further increasing the magnitude of the change.

[0150] After comparing the calculated data with the actual experimental data, it was found that as the volume of attached raindrops increased, the corona onset voltage from saturated raindrops to extreme raindrops decreased by 50.47%, which is basically consistent with the 52.61% in the experimental data, thus verifying the correctness of the calculation model.

[0151] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A method for calculating the corona onset voltage of a UHVDC transmission line with dirt or water droplets, characterized in that: The following steps are involved: Step 1: Determine the overall shape of the dirt or water droplets attached to the conductor by establishing coordinates, and select points along the edge of the shape; Step 2: Use the combination of the cylindrical mirror method and the electric axis method, combined with the simulated charge method to calculate the position and charge of the equivalent line charge; Step 3: Finally, the field strength around the conductor is obtained, and the corona inception voltage is obtained through field strength calculation; The specific contents of the mirror method and electric axis method in the second step are as follows: The calculation formula of the electric axis position is: R 2 +b 2 =h 2 ; Then the coordinates of the equivalent line charge are: The distance parameter is: According to the distance formula, the distance between the point P to be determined and the electric axis is obtained, where one is the original charge point and the other is its mirror charge point; The electric potential at point P is obtained as: The potential coefficient is: The specific steps for calculating the linear charge using the simulated charge method in the second step are: Assume that there are n line charges, and the coordinates of each line charge are (x i ,y i ), set n matching points at the boundary of the wire with dirt attached, and set the coordinates of each matching point to (x j ,y j ), the potential at each matching point Equal, the value is equal to the voltage U on the wire, based on the combination of the cylindrical mirror method and the electric axis method, the coordinates of each line charge (x i ,y i ), and ε is the dielectric constant, ε0=8.85×10 -12 F / m; It represents the electric potential generated by the i-th line charge at the j-th matching point: P ij for The corresponding potential coefficient: Then we have: Substituting into the solution, we can find the charge Q of each line charge i , and thus find the field strength in the space around the wire; The calculation method of the surrounding field strength in the third step is as follows: Let any point outside the wire be A(x,y), then the distance from a single line charge to point A and the distance from its image charge to point A are: The electric field strength generated by a single line charge at point A is: So the electric field strength at point A in the x direction is: The electric field strength at point A in the y direction is: The electric field strength at point A is 2. The method for calculating the corona onset voltage of a UHVDC transmission line with dirt or water droplets according to claim 1, characterized in that: The calculation steps of the corona onset voltage are as follows: S1: Calculate the spatial electric field distribution based on the initial voltage value; S2: Calculate the collision ionization coefficient α and adhesion coefficient η parameters; S3: Calculate N eph ; S4: When N eph When ≥1, the corona inception voltage is obtained. When the above conditions are not met, the calculation of the spatial electric field distribution is restarted.

3. The method for calculating the corona onset voltage of a UHVDC transmission line with dirt or water droplets according to claim 2, characterized in that: Parameters of α: Parameters of η: Where Pw is the water vapor partial pressure in the air, Pd is the dry vapor partial pressure in the air, and Ptotal is the total air pressure.

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