Method for analyzing characteristics of sub-span of in-service multi-split conductor considering electromagnetic force action

Abstract

The application provides a method for analyzing the sub-span characteristics of a running multi-split conductor considering electromagnetic force action, and belongs to the technical field of power transmission lines.The method comprises the following steps: step 1, determining the aerodynamic force coefficient of the aerodynamic force load of the multi-split conductor; step 2, defining the electromagnetic force calculation method of each sub-conductor; step 3, establishing a finite element model of the multi-split conductor; step 4, defining the aerodynamic force load unit and the electromagnetic force load unit; step 5, obtaining the real-time rotation angle of the conductor, combining the aerodynamic force coefficient to obtain the time-varying aerodynamic force load, and applying the aerodynamic force load on the conductor unit node; step 6, obtaining the real-time spatial displacement of the conductor, combining the electromagnetic force calculation method to obtain the time-varying electromagnetic force load, and applying the electromagnetic force load on the conductor unit node; and step 7, completing the finite element numerical simulation of the galloping of the multi-split conductor based on the finite element software, calculating and obtaining the sub-span vibration characteristic parameters of the conductor, and analyzing the influence of the electromagnetic force on the sub-span characteristics.

Description

Technical Field

[0001] This invention belongs to the field of power transmission line technology, specifically relating to a method for analyzing the characteristics of spans of multi-span conductors in operation, taking into account the effect of electromagnetic forces. Background Technology

[0002] Ice accumulation on transmission lines creates an asymmetrical circular cross-section, generating a low-frequency (0.1–3 Hz), large-amplitude (5–300 times the conductor diameter) self-excited vibration under wind load. This vibration pattern resembles a dragon dance, hence the term "dancing," and can occur across the entire span or within a single span. This secondary span vibration easily leads to conductor adhesion and wear between conductors and fittings. When ice-covered multi-segmented conductors experience contact and adhesion, the electromagnetic force between the sub-conductors becomes significant, and its magnitude changes with the conductor's movement, thus altering the line's dancing characteristics.

[0003] In order to accurately reproduce the galloping and secondary span characteristics of UHV multi-span conductors, this patent proposes a vibration analysis method for secondary spans of UHV transmission lines that considers the effect of electromagnetic force. Summary of the Invention

[0004] In view of the above, this invention addresses the shortcomings of existing technologies by providing a method for analyzing the characteristics of sub-spans of multi-split conductors in operation, considering the effects of electromagnetic forces. To solve the aforementioned technical problems, the technical solution adopted by this invention includes: Step 1: Determining the aerodynamic coefficients of the aerodynamic loads of the multi-split conductor; Step 2: Defining the electromagnetic force calculation method for each sub-conductor in the multi-split conductor; Step 3: Establishing a finite element model of the multi-split conductor using finite element software; Step 4: Defining two types of attribute-free custom elements, including aerodynamic load elements and electromagnetic force load elements. These custom elements share nodes with the beam elements used for discrete conductors and have no mass, stiffness, or damping; Step 5: Dynamically calculating and applying the aerodynamic loads, utilizing... Step 4: The aerodynamic load element defined in step 4 obtains the real-time rotation angle of the conductor. Combined with the aerodynamic coefficients obtained in step 1, the time-varying aerodynamic load is obtained. The aerodynamic load is applied to the conductor element nodes through a custom element. Step 6: Dynamically calculate and apply electromagnetic force load. The real-time spatial displacement of the conductor is obtained using the electromagnetic force load element defined in step 4. Combined with the electromagnetic force calculation method in step 2, the time-varying electromagnetic force load is obtained. The electromagnetic force load is applied to the conductor element nodes through a custom element. Step 7: Coupled simulation and feature analysis. Based on finite element software, a finite element numerical simulation of the galloping of multi-span conductors is completed. The vibration characteristic parameters of the conductor's secondary span are calculated and obtained. The influence of electromagnetic force on the secondary span characteristics is analyzed.

[0005] Furthermore, determining the aerodynamic coefficients for the aerodynamic load of multi-split conductors includes: using wind tunnel experiments and FLUENT fluid dynamics software to determine the aerodynamic coefficients for UHV six-split and eight-split conductors.

[0006] Furthermore, the electromagnetic force calculation method described in step 2 is as follows: For two finite-length, arbitrarily curved wires C1 and C2, carrying currents of magnitudes I1 and I2 respectively, each wire is divided into N units. The electromagnetic force exerted on unit q of wire C2 by unit p of wire C1 is expressed as: ; Where dl2 and dl1 represent the length vectors of elements p and q, respectively, R represents the splitting distance between the midpoints of the two elements at the previous time step, and a r The unit vector representing this distance.

[0007] Furthermore, the establishment of the finite element model of the multi-split conductor using finite element software includes: establishing the finite element model of the multi-split conductor using ABAQUS finite element software, where the conductor and sub-spacers are equivalently represented by beam elements.

[0008] Furthermore, in step 4, the custom elements are defined according to the standard element definition format of the finite element software. The defined aerodynamic and electromagnetic loads are set to have no mass, no stiffness, and no damping, with the AMATRX matrix being zero. A corresponding subroutine is created for each element. The basic equation used in the custom element program is the dynamic equilibrium equation RHS, expressed as: ; Among them: G t+Δt Let G be the internal state variable at the current moment. For aerodynamic load elements, it represents aerodynamic forces; for electromagnetic load elements, it represents electromagnetic forces. t Let ü be the internal state variable of the previous time step. t+Δt v is the acceleration at the current moment, and v is the numerical damping.

[0009] Furthermore, step 5, which involves dynamically calculating and applying aerodynamic loads, includes: Using the aerodynamic load unit defined in step 4, read the rotation angles of each sub-conductor of the multi-split conductor at the current time and the previous time. The aerodynamic loads of the sub-conductor at the current and previous moments are obtained using the aerodynamic coefficients from step 1, as shown in the following equation: (4) In the formula F L F D M and M represent aerodynamic lift, aerodynamic drag, and aerodynamic torque loads, respectively. , d and d represent air density, wind speed, and diameter of the bare conductor, respectively. (i=L, D, M) are the aerodynamic coefficients as a function of angle of attack, as measured by wind tunnel tests and simulations; The load margin is calculated using the dynamic equilibrium equation RHS of the aerodynamic load custom element, and the aerodynamic load is applied to the conductor element nodes through the common node element.

[0010] Furthermore, step 6, which involves dynamically calculating and applying electromagnetic force loads, includes: using the electromagnetic force load unit defined in step 4, iteratively solving for the spatial displacement values ​​of each node of the conductor during the actual calculation process; the program automatically reads the actual displacements of each sub-conductor of the multi-split conductor at the current and previous moments; using the electromagnetic force calculation method in step 2 to obtain the electromagnetic forces of each sub-conductor of the multi-split conductor at the current and previous moments; calculating the load margin through the dynamic equilibrium equation RHS of the electromagnetic force load custom unit; and applying the aerodynamic load to the conductor unit nodes through the common node unit.

[0011] Furthermore, step 7, coupled simulation and feature analysis, includes: using ABAQUS finite element software, completing the finite element numerical simulation of the galloping of UHV multi-span conductors, calculating and obtaining characteristic parameters such as the vibration amplitude, frequency, and modes of the secondary span of the conductor, comparing the characteristics of the secondary span without electromagnetic force, and clarifying the influence of electromagnetic force on the secondary span characteristics.

[0012] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the program, implements the method described in any of the above descriptions.

[0013] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method described in any of the above.

[0014] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. Significantly improves the accuracy of analysis on galloping and secondary span vibration of multi-span conductors: Existing analysis methods usually ignore the electromagnetic force between sub-conductors, while this method is the first to dynamically couple aerodynamic and electromagnetic forces in numerical simulation. This application calculates and applies the electromagnetic force generated by conductor current and relative motion in real time through custom elements, thereby more realistically reflecting the complex mechanical state when conductors are "adhering" or close together, making the prediction of secondary span vibration amplitude, frequency and other characteristics more accurate and reliable.

[0015] 2. Achieved dynamic coupling simulation of multiphysics fields: This application creatively solved the challenge of synchronously and dynamically applying time-varying aerodynamic forces (related to torsional angle) and time-varying electromagnetic forces (related to relative displacement) within the framework of general-purpose finite element software (such as ABAQUS) by developing two dedicated custom load elements (aerodynamic element and electromagnetic force element). This enables real-time coupled calculation of multiphysics fields involving fluid (wind load), structure (conductor vibration), and electromagnetic fields, demonstrating a high degree of technical integration.

[0016] 3. This application provides a more reliable basis for the anti-galling design and safety assessment of UHV transmission lines: It allows for the quantitative analysis of the enhancement or suppression effect of electromagnetic force on sub-span oscillations, clarifying its influencing mechanism. This enables engineers to more accurately assess the risk of sub-conductor collisions and wear under different operating conditions during the design phase, thereby optimizing key parameters such as spacer bar arrangement and sub-conductor spacing, and improving the anti-galling capability and operational safety of UHV transmission lines.

[0017] 4. This application establishes a complete analytical framework, from aerodynamic parameter acquisition, electromagnetic force calculation, finite element modeling to dynamic load coupling. This framework is applicable to common UHV conductor types such as six-split and eight-split conductors, and can analyze various operating conditions such as crescent-shaped icing. It has important practical guiding significance for the operation and maintenance, anti-galling technology research, and standard formulation of UHV transmission lines. Attached Figure Description

[0018] The present invention will now be described in further detail with reference to the accompanying drawings.

[0019] Figure 1 : A schematic diagram of the lift coefficient, drag coefficient, and torque coefficient in the aerodynamic coefficients of the conductor in this invention; Figure 2 : A schematic diagram of the electromagnetic force between parallel conductors in this invention; Figure 3 : A schematic diagram of the electromagnetic force of two arbitrarily bent wires in this invention; Figure 4 : A schematic diagram of the structure of the eight-split wire finite element model in this invention. Detailed Implementation

[0020] To better understand the present invention, the content of the invention is further clearly illustrated below with reference to embodiments and accompanying drawings. However, the scope of protection of the present invention is not limited to the embodiments described below. Numerous specific details are set forth in the following description to provide a more thorough understanding of the invention. However, it will be apparent to those skilled in the art that the present invention can be practiced without one or more of these details.

[0021] Example 1: See Figure 1-4This embodiment provides a method for analyzing the characteristics of the span of a multi-span conductor in operation, considering the effect of electromagnetic forces. The method includes: Step 1: Determine the aerodynamic coefficients of multi-split conductors. Wind tunnel experiments and FLUENT fluid dynamics software were used to study and determine the aerodynamic coefficients of UHV six-split and eight-split conductors, including lift, drag, and torque coefficients. The aerodynamic coefficients of a typical crescent-shaped eight-split conductor are shown below. Figure 1 As shown, the aerodynamic load on the conductor can be obtained from the aerodynamic coefficient. Figure 1 In this context, Lift coefficients represent the lift coefficient, Drag coefficients represent the drag coefficient, and moment coefficients represent the torque coefficient.

[0022] Step 2: Define the method for calculating the electromagnetic force on each sub-conductor in a multi-split conductor.

[0023] ① Method for calculating the electromagnetic force between any two conductors: Assume two parallel, infinitely long straight conductors C1 and C2 with a distance d between them, carrying currents of the same direction and magnitudes I1 and I2 respectively. For example... Figure 2 As shown, if the length Q of conductor C1 is considered as an infinite number of units q... i The sum of the lengths of the two elements means that the element p on C2 experiences an electromagnetic force from the conductor C1. This can be expressed as: (1) Where μ0 is the free permeability, taken as 4π × 10⁻⁶. -7 H / m.

[0024] When secondary span vibrations occur during the galloping of a multi-segmented conductor, the individual sub-conductors may no longer remain parallel during their motion. Assume two finite-length, arbitrarily curved conductors C1 and C2, carrying currents I1 and I2 respectively. Each conductor is divided into N units, such as... Figure 3 As shown.

[0025] The electromagnetic force exerted on element q on conductor C2 by element p on conductor C1 is as follows: (2) In the formula, dl2 and dl1 represent the length vectors of elements p and q, respectively, R represents the distance between the midpoints of the two elements, and a r Let df be the unit vector representing this distance. Then C2 experiences an electromagnetic force (df) from element p on C1. 21 ) p C1 is subjected to the electromagnetic force (df) of unit q on C2. 12 ) q These can be expressed as: ; (3) ② Calculation method for electromagnetic force of multi-split sub-conductors: Taking a six-split conductor as an example, repeat the calculation method for the electromagnetic force between any two conductors in ①. This allows us to obtain the calculation methods for sub-conductors 2, 3, 4, 5, and 6 on sub-conductor 1 respectively. Summing the electromagnetic forces yields the electromagnetic force on sub-conductor 1. The solution method for an eight-split conductor is similar.

[0026] Step 3: Establish the finite element analysis model of the UHV multi-split conductor. The finite element model of the multi-split conductor is established using ABAQUS finite element software. The conductor and sub-spacers are represented by equivalent beam elements, such as... Figure 4 As shown, Wind represents the aerodynamic force applied by the wind, Sub-conductor represents the sub-conductor, and Spacer represents the spacer bar.

[0027] Step 4: Define aerodynamic and electromagnetic load elements. Since the aerodynamic load is related to the torsional angle of the conductor and the electromagnetic force is closely related to the relative displacement during the conductor's motion, the existing ABAQUS general-purpose finite element software lacks loading functionality. Therefore, two custom elements are needed to apply the loads: an aerodynamic load element and an electromagnetic load element. The custom elements share nodes with a beam element used for discrete conductors and have no mass, stiffness, or damping. Referring to the standard element definition format of the ABAQUS finite element software, a corresponding subroutine is developed for each element. The basic equations used in the user-defined element program are the dynamic equilibrium equation and the residual equation, where M is the mass matrix, C and K are the damping matrix and stiffness matrix, respectively, and G... t+Δt For the current internal state variable (aerodynamic force for "aerodynamic load element", electromagnetic force for "electromagnetic force load element"), G t Let ü be the internal state variable of the previous time step. t+Δt v is the acceleration at the current moment, and v is the numerical damping.

[0028] Since the defined aerodynamic load element and electromagnetic load element are massless, stiffnessless, and damped, and the matrix AMATRX is a zero matrix, RHS can be expressed as... (3) Step 5: Apply aerodynamic load. Using the aerodynamic load unit defined in Step 4, read the rotation angle of each sub-conductor of the multi-split conductor at the current time and the previous time. Using the aerodynamic coefficient in Step 1, obtain the aerodynamic load (time-varying aerodynamic load) of the sub-conductor at the current time and the previous time through formula (4). Complete the calculation of the load margin through formula (3) in Step 4, and apply the aerodynamic load to the conductor unit node through the common node unit.

[0029] (4) In the formula F L F D M and M represent aerodynamic lift, aerodynamic drag, and aerodynamic torque loads, respectively. , d and d represent air density, wind speed, and diameter of the bare conductor, respectively. (i=L, D, M) are the aerodynamic coefficients that vary with angle of attack, as measured by wind tunnel tests and simulations.

[0030] Step 6: Apply electromagnetic force load. Using the electromagnetic force load element defined in Step 4, the element will iteratively solve the problem during the actual calculation process and give the spatial displacement value of each node of the conductor. The program will automatically read the actual displacement of each sub-conductor of the multi-split conductor at the current time and the previous time. The electromagnetic force load (time-varying electromagnetic force load) of each sub-conductor of the multi-split conductor at the current time and the previous time is obtained by using the electromagnetic force calculation method in Step 2. The load margin is calculated by formula (3) in Step 4, and the aerodynamic load is applied to the conductor element node through the common node element.

[0031] Step 7: Complete the vibration characteristic calculation of the secondary span. Based on ABAQUS finite element software, complete the finite element numerical simulation of the galloping of the multi-span conductor, calculate and obtain characteristic parameters such as the vibration amplitude, frequency, and modes of the secondary span of the conductor, and compare the characteristics of the secondary span without electromagnetic force to clarify the influence of electromagnetic force on the secondary span characteristics.

[0032] Technical effects of this embodiment: 1. Significantly improves the accuracy of analysis on galloping and secondary span vibration of UHV split conductors: Existing analysis methods usually ignore the electromagnetic force between sub-conductors, while this method is the first to dynamically couple aerodynamic and electromagnetic forces in numerical simulation. This application calculates and applies the electromagnetic force generated by conductor current and relative motion in real time through custom elements, thereby more realistically reflecting the complex mechanical state when conductors are "adhering" or close together, making the prediction of secondary span vibration amplitude, frequency and other characteristics more accurate and reliable.

[0033] 2. Achieved dynamic coupling simulation of multiphysics fields: This application successfully solved the challenge of synchronously and dynamically applying time-varying aerodynamic forces (related to torsional angle) and time-varying electromagnetic forces (related to relative displacement) within the framework of general-purpose finite element software (such as ABAQUS) by developing two dedicated custom load elements (aerodynamic element and electromagnetic force element). This enables real-time coupled calculation of multiphysics fields involving fluid (wind load), structure (conductor vibration), and electromagnetic fields, demonstrating a high degree of technical integration.

[0034] Example 2: An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor executes the program to implement the method described in Example 1.

[0035] Example 3: A computer-readable storage medium having a computer program stored thereon, characterized in that the program, when executed by a processor, implements the method described in Example 1.

[0036] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Any other modifications or equivalent substitutions made by those skilled in the art to the technical solutions of the present invention, as long as they do not depart from the spirit and scope of the technical solutions of the present invention, should be covered within the scope of the claims of the present invention.

Claims

1. A method for analyzing the characteristics of the span of a multi-span conductor in operation, considering the effect of electromagnetic force, characterized in that, include: Step 1: Determine the aerodynamic coefficients of the aerodynamic load on the multi-split conductor; Step 2: Define the method for calculating the electromagnetic force of each sub-conductor in a multi-split conductor; Step 3: Use finite element software to establish a finite element model of the multi-split conductor; Step 4: Define two types of attribute-free custom elements, including aerodynamic load elements and electromagnetic load elements. The custom elements share nodes with the beam elements used for discrete conductors and have no mass, no stiffness, and no damping. Step 5: Dynamically calculate and apply aerodynamic loads. Use the aerodynamic load unit defined in Step 4 to obtain the real-time rotation angle of the conductor. Combine the aerodynamic coefficients obtained in Step 1 to obtain the time-varying aerodynamic loads. Apply the aerodynamic loads to the conductor unit nodes through custom units. Step 6: Dynamically calculate and apply electromagnetic force load. Use the electromagnetic force load unit defined in Step 4 to obtain the real-time spatial displacement of the conductor. Combine the electromagnetic force calculation method in Step 2 to obtain the time-varying electromagnetic force load. Apply the electromagnetic force load to the conductor unit node through a custom unit. Step 7: Coupled simulation and feature analysis. Based on finite element software, complete the finite element numerical simulation of the galloping of multi-span conductors, calculate and obtain the vibration characteristic parameters of the secondary span of the conductor, and analyze the influence of electromagnetic force on the secondary span characteristics.

2. The method for analyzing the characteristics of the span of a multi-span conductor in operation, considering the effect of electromagnetic force, as described in claim 1, is characterized in that... The determination of the aerodynamic coefficients for the aerodynamic load of multi-split conductors includes: using wind tunnel experiments and FLUENT fluid dynamics software to determine the aerodynamic coefficients of UHV six-split and eight-split conductors.

3. The method for analyzing the characteristics of the span of a multi-span conductor in operation, considering the effect of electromagnetic force, as described in claim 1, is characterized in that... The electromagnetic force calculation method described in step 2 is as follows: For two finite-length, arbitrarily curved wires C1 and C2, carrying currents of magnitudes I1 and I2 respectively, each wire is divided into N units. The electromagnetic force exerted on unit q of wire C2 by unit p of wire C1 is expressed as: ; Where dl2 and dl1 represent the length vectors of elements p and q, respectively, R represents the splitting distance between the midpoints of the two elements at the previous time step, and a r The unit vector representing this distance.

4. The method for analyzing the characteristics of the span of a multi-span conductor in operation, considering the effect of electromagnetic force, as described in claim 1, is characterized in that... The establishment of the finite element model of the multi-split conductor using finite element software includes: establishing the finite element model of the multi-split conductor using ABAQUS finite element software, with the conductor and sub-spacers being equivalently represented by beam elements.

5. The method for analyzing the characteristics of the span of a multi-span conductor in operation, considering the effect of electromagnetic force, as described in claim 1, is characterized in that... In step 4, the custom elements are defined according to the standard element definition format of the finite element software. The defined aerodynamic and electromagnetic loads are set to have no mass, no stiffness, and no damping, with the AMATRX matrix being zero. A corresponding subroutine is created for each element. The basic equation used in the custom element program is the dynamic equilibrium equation RHS, expressed as: ; Among them: G t+Δt Let G be the internal state variable at the current moment. For aerodynamic load elements, it represents aerodynamic forces; for electromagnetic load elements, it represents electromagnetic forces. t Let ü be the internal state variable of the previous time step. t+Δt v is the acceleration at the current moment, and v is the numerical damping.

6. The method for analyzing the characteristics of the span of a multi-span conductor in operation, considering the effect of electromagnetic force, as described in claim 1, is characterized in that... Step 5, which involves dynamically calculating and applying aerodynamic loads, includes: Using the aerodynamic load unit defined in step 4, read the rotation angles of each sub-conductor of the multi-split conductor at the current time and the previous time. The aerodynamic loads of the sub-conductor at the current and previous moments are obtained using the aerodynamic coefficients from step 1, as shown in the following equation: （4） In the formula F L F D M and M represent aerodynamic lift, aerodynamic drag, and aerodynamic torque loads, respectively. , d and d represent air density, wind speed, and diameter of the bare conductor, respectively. (i=L, D, M) are the aerodynamic coefficients as a function of angle of attack, as measured by wind tunnel tests and simulations; The load margin is calculated using the dynamic equilibrium equation RHS of the aerodynamic load custom element, and the aerodynamic load is applied to the conductor element nodes through the common node element.

7. The method for analyzing the characteristics of the span of a multi-span conductor in operation, considering the effect of electromagnetic force, as described in claim 1, is characterized in that... Step 6, which involves dynamically calculating and applying electromagnetic force loads, includes: using the electromagnetic force load unit defined in step 4, iteratively solving for the spatial displacement values ​​of each node of the conductor during the actual calculation process; the program automatically reads the actual displacements of each sub-conductor of the multi-split conductor at the current and previous moments; using the electromagnetic force calculation method in step 2 to obtain the electromagnetic force of each sub-conductor of the multi-split conductor at the current and previous moments; calculating the load margin through the dynamic equilibrium equation RHS of the electromagnetic force load custom unit; and applying the aerodynamic load to the conductor unit nodes through the common node unit.

8. The method for analyzing the characteristics of the span of a multi-span conductor in operation, considering the effect of electromagnetic force, as described in claim 1, is characterized in that... Step 7, coupled simulation and feature analysis, includes: using ABAQUS finite element software, completing the finite element numerical simulation of the galloping of UHV multi-span conductors, calculating and obtaining characteristic parameters such as the vibration amplitude, frequency, and modes of the conductor's secondary span, comparing the characteristics of the secondary span without electromagnetic force, and clarifying the influence of electromagnetic force on the secondary span characteristics.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the method as described in any one of claims 1-8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the method as described in any one of claims 1-8.

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