Simplified determination method for ground wire icing local water drop collision coefficient of overhead transmission line

Abstract

The invention discloses a simplified determination method for a ground wire icing local water drop collision coefficient of an overhead transmission line, and relates to the technical field of coefficient simplification. The method at least comprises the following steps that S1, a ground wire is equivalent to a two-dimensional circle structure, the equivalent two-dimensional circle boundary is equally divided into n units, and a set A of n two-dimensional coordinate points of the ground wire surface boundary is obtained; s2, taking the ground wire boundary A and the wind speed V as input, and solving airflow velocity field distribution outside the ground wire by using a boundary element method; and S3, taking the wire surface potential value and the relative position relationship between the ground wire and the wire as input, and calculating the distribution of the external electric field intensity E of the ground wire by using a boundary element. The ground wire external airflow field and the direct-current electric field are calculated through the boundary element method, the water drop electrification condition is updated and calculated, the ground wire surface water drop collision point coordinates and the collision speed are rapidly obtained, and convenience is provided for calculation of the ground wire surface local water drop collision coefficient.

Description

Technical Field

[0001] This invention relates to the field of coefficient simplification technology, specifically a simplified method for determining the collision coefficient of local water droplets in the icing of ground wires of overhead transmission lines. Background Technology

[0002] Previous studies on icing in DC transmission lines are limited and mainly focus on the icing characteristics of conductors under laboratory conditions, lacking research on the icing morphology and characteristics of ground wires. To understand the icing growth mechanism of DC transmission line ground wires and obtain the influence of DC electric fields on icing growth, it is urgent to conduct research on the icing growth characteristics of DC transmission line ground wires considering the action of DC electric fields. The local water droplet collision coefficient on the ground wire surface is a key parameter for numerical simulation of icing.

[0003] Regarding mathematical models for the icing growth process of conductors and ground wires, numerous scholars both domestically and internationally have established numerical calculation models for icing based on environmental parameters such as the liquid water content in the air, ambient temperature, wind speed, and median volume diameter of water droplets. However, most of these models do not consider the influence of the electric field around the line on icing growth. Research on icing related to DC transmission line conductors is limited and lacks in-depth analysis. Research on icing growth of DC transmission line ground wires is even scarcer, with most studies focusing on ground wire melting. The icing characteristics and mechanisms of ground wires under the influence of DC electric fields remain unclear. Since supercooled water droplets around the DC line ground wire become charged as they pass over the wire, their trajectories inevitably change under the influence of the electric field, thus affecting the icing growth process. Current research on this phenomenon primarily employs a finite element method to establish a coupled flow and electric field calculation model, then calculates the local water droplet collision coefficient on the ground wire surface. However, the model establishment process is complex and computationally intensive, hindering the rapid assessment of water droplet capture during the DC ground wire icing process.

[0004] Therefore, a fast, simple and accurate method for calculating the collision coefficient of local water droplets on the surface of DC ground wire needs to be proposed, so as to provide technical support for the simulation of DC ground wire icing. Summary of the Invention

[0005] The purpose of this invention is to provide a simplified method for determining the collision coefficient of local water droplets in the ground wire of overhead transmission lines covered with ice, so as to solve the technical problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a simplified method for determining the collision coefficient of local water droplets accreting on the ground wire of an overhead transmission line, comprising at least the following steps:

[0007] S1: The ground wire is equivalent to a two-dimensional circular structure. The boundary of the equivalent two-dimensional circle is divided into n units to obtain a set A of n two-dimensional coordinate points on the surface boundary of the ground wire.

[0008] S2: Using the boundary element method with the ground wire boundary A and wind speed V as input, solve for the airflow velocity field distribution outside the ground wire;

[0009] S3: Using the surface potential of the conductor and the relative positional relationship between the ground wire and the conductor as input, the boundary element method is used to calculate the distribution of the external electric field intensity E of the ground wire;

[0010] S4: Calculate the ideal spacing ds between supercooled water droplets in the air during ground wire icing using two parameters: the liquid water content in the air and the median volume diameter of the water droplets;

[0011] S5: Calculate the charge Q of the supercooled water droplets outside the ground wire based on the field charge principle, and update the charge of the water droplets in real time according to the size of the water droplets and the electric field strength at their location;

[0012] S6: Track the trajectory of water droplets as they approach the ground line from far to near based on the distance between the water droplets, and calculate the resultant force F when the water droplets collide with the ground line;

[0013] S7: Calculate the local water droplet collision coefficient on the ground wire surface for water droplets that collide with the ground wire surface.

[0014] Furthermore, in S2, for an inviscid, incompressible, and irrotational external potential flow, the velocity potential Φ within the flow field domain Ω satisfies the following solution:

[0015] (1).

[0016] Furthermore, in S3, for the passive free space, i.e., outside the ground wire, the scalar potential φ satisfies the Laplace equation, and the electric field intensity E is the negative gradient of the potential φ:

[0017] (2)

[0018] (3).

[0019] Furthermore, the ideal distance ds between the water droplets is calculated as follows:

[0020] (4)

[0021] The number of water droplet trajectories N is represented as:

[0022] (5)

[0023] Let w be the liquid water content in the air, g / m 3 The median volume diameter of the water droplet is D. w , μm; water droplet density is ρ w kg / m 3 The diameter of the icing ground line is D.

[0024] Furthermore, the charge Q of the water droplet is calculated using the following formula:

[0025] (6)

[0026] Where R d ε0 and ε0 are the radius of the water droplet in meters (m); p These are the vacuum permittivity and the relative permittivity of water, respectively.

[0027] Furthermore, when calculating the resultant force F on the water droplet in S6, it is necessary to consider the combined effects of gravity G, air viscous resistance Fd, electric field force Fe, and polarization force Fp on the water droplet. The calculation of the resultant force F is expressed as follows:

[0028] (7)

[0029] Where, ρ a S w and C a These represent air density, water droplet cross-sectional area, and air drag coefficient, respectively; u and v are the airflow velocity and water droplet velocity, respectively.

[0030] Furthermore, the calculation of the local water droplet collision coefficient on the ground wire surface includes at least the following steps:

[0031] It is assumed that the local collision coefficient β1 of water droplets is not zero at locations on the ground wire surface where water droplets collide, and is zero at locations where there are no water droplet collisions.

[0032] Let the coordinates of two adjacent water droplets colliding with the ground wire surface be P1(x1, y1) and P2(x2, y2), and their collision velocities be v1 and v2, respectively. Let the center coordinate point be P0. Then, the local collision coefficient of the water droplets at point P0 on the ground wire surface is:

[0033] (8).

[0034] Compared with the prior art, the beneficial effects of the present invention are:

[0035] This invention calculates the external airflow field and DC electric field of the ground wire using the boundary element method, updates the calculation of the water droplet charge, and quickly obtains the coordinates and collision velocity of the water droplet collision point on the ground wire surface, thus facilitating the calculation of the local water droplet collision coefficient on the ground wire surface. Attached Figure Description

[0036] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0037] Figure 1 This is a flowchart of the present invention;

[0038] Figure 2 This is a schematic diagram of the ground wire surface unit division involved in the present invention;

[0039] Figure 3 This invention relates to a comparison diagram of the trajectories of charged and uncharged water droplets outside the ground wire;

[0040] Figure 4 Distribution of water droplet collision coefficients on the surface of the ground wire;

[0041] Figure 5 The icy state of the ground line under natural conditions after water droplets collide and freeze. Detailed Implementation

[0042] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0043] like Figure 1 As shown, the simplified method for determining the local water droplet collision coefficient during the icing process of the ground wire of an overhead transmission line is specifically a simplified calculation method for the local water droplet collision coefficient during the icing process of the ground wire of a DC overhead transmission line. The implementation process includes the following steps:

[0044] S1: As Figure 2 As shown, the ground wire is equivalent to a two-dimensional circular structure. The boundary of the equivalent two-dimensional circle is divided into n units, resulting in a set A of n two-dimensional coordinate points on the ground wire surface boundary. The minimum length of the ground wire surface segmentation unit must not be greater than the ideal spacing ds of the water droplets (see S4 for specific calculations).

[0045] S2: Using the ground boundary A and wind speed V as inputs, the boundary element method is used to solve for the airflow velocity field distribution outside the ground boundary; for inviscid, incompressible, and irrotational external potential flow, the velocity potential Φ within the flow field domain Ω satisfies the following solution:

[0046] (1).

[0047] S3: Using the surface potential of the conductor and the relative position of the ground wire and the conductor as input, the boundary element method is used to calculate the electric field intensity E distribution outside the ground wire; for the source-free free space, i.e., outside the ground wire, the scalar potential φ satisfies the Laplace equation, and the electric field intensity E is the negative gradient of the potential φ:

[0048] (2)

[0049] (3).

[0050] S4: Calculate the ideal spacing ds between supercooled water droplets in the air during ground wire icing using two parameters: the liquid water content in the air and the median volume diameter of the water droplets;

[0051] The ideal distance ds between water droplets is calculated as follows:

[0052] (4)

[0053] The number of water droplet trajectories N is represented as:

[0054] (5)

[0055] Let w be the liquid water content in the air, g / m 3 The median volume diameter of the water droplet is D. w , μm; water droplet density is ρ w kg / m 3 The diameter of the icing ground line is D.

[0056] S5: Calculate the charge Q of the supercooled water droplets outside the ground wire based on the field charge principle, and update the charge of the water droplets in real time according to the size of the water droplets and the electric field strength at their location;

[0057] The charge Q of a water droplet is calculated using the following formula:

[0058] (6)

[0059] Where R d ε0 and ε0 are the radius of the water droplet in meters (m); p These are the vacuum permittivity and the relative permittivity of water, respectively.

[0060] S6: Track the trajectory of the water droplets as they approach the ground line from a distance based on the distance between the droplets, and calculate the net force F when the droplets collide with the ground line. The calculation of the net force F requires consideration of the combined effects of gravity G, air viscous drag Fd, electric field force Fe, and polarization force Fp on the droplets. The net force F is expressed as follows:

[0061] (7)

[0062] Where, ρ a S w and C a These represent air density, water droplet cross-sectional area, and air drag coefficient, respectively; u and v are the airflow velocity and water droplet velocity, respectively.

[0063] S7: Calculating the local water droplet collision coefficient on the ground wire surface for water droplets colliding with the ground wire surface includes at least the following steps:

[0064] It is assumed that the local collision coefficient β1 of water droplets is not zero at locations on the ground wire surface where water droplets collide, and is zero at locations where there are no water droplet collisions.

[0065] Let the coordinates of two adjacent water droplets colliding with the ground wire surface be P1(x1, y1) and P2(x2, y2), and their collision velocities be v1 and v2, respectively. Let the center coordinate point be P0. Then, the local collision coefficient of the water droplets at point P0 on the ground wire surface is:

[0066] (8).

[0067] Figure 4 The local droplet collision coefficient β1 distributions on the ground wire surface under charged and uncharged conditions, corresponding to two droplet sizes Dd = 50 μm and 30 μm respectively (where wind speed V = 3 m / s), are calculated using the above method. It can be seen that, compared to uncharged conditions, the β1 distribution calculated by the method proposed in this invention clearly reflects the phenomenon of increased collision range and collision dispersion of charged water droplets on the ground wire surface under the influence of electric field attraction (e.g., ...). Figure 5 As shown, water droplets collide and freeze on both the windward and leeward sides of the ground wire (and are relatively dispersed), which also lays the foundation for accurate calculation of ground wire icing under the action of an electric field.

[0068] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

Claims

1. A simplified method for determining the collision coefficient of local water droplets accreting on the ground wire of an overhead transmission line, characterized in that: At least the following steps are included: S1: The ground wire is equivalent to a two-dimensional circular structure. The boundary of the equivalent two-dimensional circle is divided into n units to obtain a set A of n two-dimensional coordinate points on the surface boundary of the ground wire. S2: Using the boundary element method with the ground wire boundary A and wind speed V as input, solve for the airflow velocity field distribution outside the ground wire; S3: Using the surface potential of the conductor and the relative positional relationship between the ground wire and the conductor as input, the boundary element method is used to calculate the distribution of the external electric field intensity E of the ground wire; S4: Calculate the ideal spacing ds between supercooled water droplets in the air during ground wire icing using two parameters: the liquid water content in the air and the median volume diameter of the water droplets; S5: Calculate the charge Q of the supercooled water droplets outside the ground wire based on the field charge principle, and update the charge of the water droplets in real time according to the size of the water droplets and the electric field strength at their location; S6: Track the trajectory of water droplets as they approach the ground line from far to near based on the distance between the water droplets, and calculate the resultant force F when the water droplets collide with the ground line; S7: Calculate the local water droplet collision coefficient on the ground wire surface for water droplets that collide with the ground wire surface.

2. The simplified method for determining the collision coefficient of local water droplets accreting on the ground wire of an overhead transmission line according to claim 1, characterized in that: For the inviscid, incompressible, and irrotational external potential flow in S2, the velocity potential Φ within the flow field domain Ω satisfies the following solution: (1)。 3. The simplified method for determining the collision coefficient of local water droplets accreting on the ground wire of an overhead transmission line according to claim 2, characterized in that: In S3, for the source-free free space, i.e., outside the ground wire, the scalar potential φ satisfies the Laplace equation, and the electric field intensity E is the negative gradient of the potential φ: (2)； (3)。 4. The simplified method for determining the collision coefficient of local water droplets accreting on the ground wire of an overhead transmission line according to claim 3, characterized in that: The ideal distance ds between the water droplets is calculated as follows: (4)； The number of water droplet trajectories N is represented as: (5)； Let w be the liquid water content in the air, g / m 3 The median volume diameter of the water droplet is D. w , μm; water droplet density is ρ w kg / m 3 The diameter of the icing ground line is D.

5. The simplified method for determining the collision coefficient of local water droplets accreting on the ground wire of an overhead transmission line according to claim 4, characterized in that: The charge Q of the water droplet is calculated using the following formula: (6)； Where R d ε0 and ε0 are the radius of the water droplet in meters (m); p These are the vacuum permittivity and the relative permittivity of water, respectively.

6. The simplified method for determining the collision coefficient of local water droplets accreting on the ground wire of an overhead transmission line according to claim 5, characterized in that: The resultant force F acting on the water droplet in S6 needs to be calculated considering the combined effects of gravity G, air viscous drag Fd, electric field force Fe, and polarization force Fp. The resultant force F is expressed as follows: (7)； Where, ρ a S w and C a These represent air density, water droplet cross-sectional area, and air drag coefficient, respectively; u and v are the airflow velocity and water droplet velocity, respectively.

7. The simplified method for determining the collision coefficient of local water droplets accreting on the ground wire of an overhead transmission line according to claim 6, characterized in that: The calculation of the local water droplet collision coefficient on the ground wire surface includes at least the following steps: It is assumed that the local collision coefficient β1 of water droplets is not zero at locations on the ground wire surface where water droplets collide, and is zero at locations where there are no water droplet collisions. Let the coordinates of two adjacent water droplets colliding with the ground wire surface be P1(x1, y1) and P2(x2, y2), and their collision velocities be v1 and v2, respectively. Let the center coordinate point be P0. Then, the local collision coefficient of the water droplets at point P0 on the ground wire surface is: (8)。

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