A method, device, equipment and medium for calculating internal force of a wind turbine tower

Abstract

This invention discloses a method, device, equipment, and medium for calculating the internal forces of a wind turbine tower, relating to the field of engineering structural mechanics. This invention extracts the dominant vibration modes through modal analysis or modal identification, decoupling the complex multi-degree-of-freedom time-history analysis into solving a few single-degree-of-freedom modal vibration equations. This integrates complex aerodynamic damping, modal coupling, and rigid vibration dynamic characteristics into the modal vibration equations through tower top load projection, directly describing the vibration response of each mode under load excitation. Furthermore, by reconstructing the dynamic response at different tower heights through modal superposition, the dynamic coupling problem between tower vibration, blades, and the control system is simplified to an analysis of the dynamic response of the tower structure itself with equivalent damping characteristics under known load excitation. This improves the accuracy of tower internal force estimation and ultimately achieves safe design and operation of wind turbine towers.

Description

Technical Field

[0001] This invention relates to the field of engineering structural mechanics, and in particular to a method, apparatus, equipment and medium for calculating the internal forces of a wind turbine tower. Background Technology

[0002] The tower is one of the key components of a wind turbine. Its function is to support the wind power generation system located in the air. The tower is connected to the foundation and bears various loads caused by the operation of the wind power generation system. At the same time, it transmits these loads to the foundation, so that the entire wind turbine can operate stably and reliably.

[0003] Wind turbine towers undergo significant dynamic responses under the aerodynamic load at the tower top. The tower spends most of its time in a coupled tower-blade vibration state under wind load. When the wind turbine is running or shut down but encounters strong winds, the internal forces of the tower are likely to reach their maximum value. Determining the tower's internal forces requires considering both the total aerodynamic load at the tower's top and the wind load it experiences. Only by determining the distribution of internal forces under different operating conditions can the tower's cross-section be designed, ensuring structural safety. Therefore, a comprehensive dynamic response analysis of the wind turbine structure system is typically required to determine the time-varying nature of the tower's internal forces, ultimately determining the tower's design internal forces.

[0004] Currently, the determination of internal forces in wind turbine towers typically relies on overall coupled dynamic analysis. This involves using specialized wind turbine simulation software such as Bladed and FAST to establish a complete model that includes the blades, nacelle, tower, and control system. After inputting environmental loads such as wind conditions, time-domain simulation is performed to extract the time history of the tower's internal forces. However, wind turbine towers often contain complex dynamic characteristics such as aerodynamic damping, modal coupling, and rigid vibration. This approach generally only collects the tower top load based on static or quasi-static methods and obtains the internal forces based on the tower top load. It is difficult to accurately consider the dynamic coupling effect between tower vibration, blades, and the control system, resulting in low accuracy in internal force estimation and ultimately making it difficult to achieve safe design of wind turbine towers. Summary of the Invention

[0005] This invention provides a method, apparatus, equipment, and medium for calculating the internal forces of a wind turbine tower, which can solve the problems existing in the prior art.

[0006] This invention provides a method for calculating the internal forces of a wind turbine tower, comprising the following steps: Acquire aerodynamic load data at the top of the wind turbine tower under operating or shutdown conditions, as well as structural parameters at different heights of the wind turbine tower; Based on the structural parameters at different heights of the tower, a finite element model of the tower was established using the finite element method, and the vibration equation of the tower finite element model was constructed. Based on aerodynamic load data, modal analysis was performed on the finite element model to extract the modal parameters corresponding to each mode shape under the dominance of the tower's dynamic response. Based on the modal parameters corresponding to each mode shape, the vibration equation of the tower finite element model was decoupled into modal vibration equations corresponding to single-degree-of-freedom mode shapes through modal decomposition. The modal parameters corresponding to each mode shape were then substituted into the modal vibration equations to obtain the generalized coordinates corresponding to each mode shape. Based on the generalized coordinates corresponding to each mode shape, the contribution of each mode shape to the displacement is superimposed along the tower height using the modal superposition method to obtain the displacement time history at different tower heights; based on the displacement time history at different tower heights, the internal forces at different tower heights are obtained from the structural mechanics relationship of the tower.

[0007] Preferably, the aerodynamic load data at the top of the wind turbine tower under operating conditions includes the moment vector at the top of the wind turbine tower. and force vector ; The structural parameters of the wind turbine tower at different heights include the cross-sectional parameters and material parameters of the wind turbine tower.

[0008] Preferably, the vibration equation of the finite element model of the tower is expressed as: ; in: Represents the mass matrix; Represents the damping matrix; Represents the stiffness matrix; This represents the external load vector.

[0009] Preferably, the modal parameters corresponding to each vibration mode include the circumferential frequency. Damping ratio Modal quality Mode shape coefficient , ; Wherein, the damping ratio The total damping of the wind turbine system includes aerodynamic damping of the wind turbine due to the interaction between air and wind turbine, aerodynamic damping due to the interaction between wind and tower, structural damping, soil damping due to the interaction between soil and wind turbine foundation structure, and other forms of damping.

[0010] Preferably, obtaining the generalized coordinates corresponding to each mode shape includes: The displacement vector is obtained using the modal decomposition method. With mode matrix The relationship is represented as: ; Using the transpose of the mode matrix Multiplying the above equation on the left, we obtain the modal vibration equation of the tower as follows: ; in: Represents a generalized coordinate vector; If the system damping matrix is ​​a diagonal matrix, then for the th The modal vibration equation of the tower is expressed as follows: ; Substituting the modal parameters corresponding to each mode shape into the modal vibration equation of the tower, the generalized coordinates corresponding to each mode shape are obtained. ; If the system damping matrix is ​​a non-diagonal matrix, then the system's modal vibration equations are not a series of single-degree-of-freedom motion equations, but a damped coupled set of modal vibration equations, expressed as follows; ; in: ; ; ; ; By solving the damped coupled modal vibration equations, the generalized coordinates corresponding to each mode shape are obtained. .

[0011] Preferably, obtaining the internal forces at different heights of the tower includes: Based on the modal superposition method, considering only the dominant modal... The displacement time history at different heights of the tower when considering the contribution of the mode shape. Represented as: ; Based on the relationship between displacement, rotation angle, and internal bending moment, the bending moment at different heights of the tower is obtained. The relationship between displacement, rotation angle, and internal bending moment is expressed as follows: ; in: Indicates the bending moment of inertia of the tower section; It represents the second derivative of the shape function vector between two nodes in a finite element model; This represents the element displacement vector formed by the displacements of the nodes at both ends of a finite element; When obtaining other components of internal force, the relationship between displacement, rotation angle and internal force components is used.

[0012] This invention also provides an internal force calculation device for wind turbine towers, comprising: The data module is used to acquire aerodynamic load data at the top of the wind turbine tower under operating conditions, as well as structural parameters at different heights of the wind turbine tower. The modal analysis module is used to establish a finite element model of the tower using the finite element method based on the structural parameters at different heights of the tower, and to construct the vibration equation of the tower finite element model. Based on aerodynamic load data, modal analysis is performed on the finite element model to extract the modal parameters corresponding to each mode under the dominance of the tower's dynamic response. Based on the modal parameters corresponding to each mode, the vibration equation of the tower finite element model is decoupled into modal vibration equations corresponding to single-degree-of-freedom modes through modal decomposition. The modal parameters corresponding to each mode are then substituted into the modal vibration equations to obtain the generalized coordinates corresponding to each mode. The internal force calculation module is used to superimpose the contribution of each vibration mode to the displacement along the tower height distribution using the modal superposition method based on the generalized coordinates corresponding to each vibration mode, and obtain the displacement time history at different tower heights; based on the displacement time history at different tower heights, the internal forces at different tower heights are obtained from the structural mechanics relationship of the tower.

[0013] This invention also provides an electronic device, including a memory and a processor; The memory is used to store computer programs; When the processor executes the computer program stored in the memory, it implements the steps of the method for calculating the internal forces of a wind turbine tower as described above.

[0014] This invention also provides a computer-readable storage medium for storing a computer program, which, when executed by a processor, implements the steps of the internal force calculation method for a wind turbine tower as described above.

[0015] This invention provides a method, apparatus, equipment, and medium for calculating the internal forces of wind turbine towers. Compared with the prior art, its advantages are as follows: This invention first constructs a finite element model of the tower and its vibration equations. Modal analysis is then performed on the finite element model to extract the modal parameters corresponding to each mode shape under the dominant dynamic response of the tower. Based on these modal parameters, the vibration equations of the tower's finite element model are decoupled into modal vibration equations corresponding to single-degree-of-freedom modes through modal decomposition. This process extracts the dominant mode shape through modal analysis, decoupling the originally complex multi-degree-of-freedom time history analysis into solving a few single-degree-of-freedom modal vibration equations. This allows the complex dynamic characteristics such as aerodynamic damping, modal coupling, and rigid vibration to be directly integrated into the modal vibration equations through the projection of each mode shape from the tower top load. This directly describes the resonance response of each mode under load excitation. Furthermore, the dynamic response at different heights of the tower is reconstructed through modal superposition. This simplifies the dynamic coupling problem between tower vibration, blades, and the control system into a dynamic response analysis of the tower structure itself with equivalent damping characteristics under known load excitation, thereby improving the accuracy of tower internal force estimation and ultimately achieving safe design and application of wind turbine towers. Attached Figure Description

[0016] Figure 1 A schematic diagram of the overall process for calculating the internal forces of a wind turbine tower, provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of the finite element model construction of a wind turbine tower, which is provided as an embodiment of the present invention for a method of calculating the internal forces of a wind turbine tower. Detailed Implementation

[0017] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of the present invention. However, the present invention can be practiced in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0018] Wind turbine towers undergo significant dynamic responses under aerodynamic loads at the tower top. The tower spends most of its time in a coupled tower-blade vibration state under wind loads. When the wind turbine is running or shut down but encounters strong winds, the internal forces of the tower are likely to reach their maximum values. Determining these internal forces requires considering both the total aerodynamic load at the tower's top and the wind load it experiences. Only by determining the distribution of internal forces under different operating conditions can the tower's cross-section be designed, ensuring structural safety. Therefore, a comprehensive dynamic response analysis of the wind turbine structure is typically required to determine the time-varying nature of the tower's internal forces, ultimately determining the tower's design internal forces. The current methods for analyzing the internal forces of wind turbine towers follow these steps: (1) Using wind turbine modeling software such as Bladed, the overall structural system of the wind turbine, including blades, nacelle, tower, etc., is modeled.

[0019] (2) Input environmental loads and perform overall dynamic response analysis on the wind turbine.

[0020] (3) Extract the time history of internal forces in the tower.

[0021] Due to limitations in the scope and responsibility of design work, the design of wind turbine towers typically involves the main equipment manufacturer (OEM) creating an overall structural model of the wind turbine and determining the internal forces of the tower. The tower design unit then designs the tower structure based on these internal forces provided by the OEM. This design process is extremely complex, requiring multiple data exchanges between the OEM and the tower design unit to ensure consistency in the tower's calculation parameters. OEMs generally only provide the total aerodynamic load transmitted to the top of the tower under various operating conditions and the tower's internal forces calculated using wind turbine modeling software; they do not provide the geometric and aerodynamic parameters of the wind turbine blades. Furthermore, due to the dynamic effects of the tower, the total aerodynamic load at the top provided by the OEM cannot be directly used for the tower's cross-section design. This prevents the tower design unit from establishing a fully coupled model that simultaneously considers blade and tower vibrations to verify the internal force calculation results.

[0022] For tower design units, relying solely on the total aerodynamic load at the top provided by the turbine manufacturer allows for simplified consideration of the vibration coupling effect between the blades and the tower, and the calculation of the internal forces of the wind turbine tower, significantly improving the efficiency of tower optimization design. Based on this, this invention provides a simplified calculation method for solving the internal forces at various heights and locations of the wind turbine tower under the condition of top load, specifically including: Given the total load time history at the top of the wind turbine tower, i.e., the moment vector at the top of the wind turbine tower. Force vector The forces acting in other directions are known; for a given tower, the cross-sectional geometry and material properties at different heights are known. A finite element model of the tower is established using the finite element method, where the wind turbine and nacelle can be simplified and simulated as concentrated masses located at the top of the tower (e.g., Figure 1 Modal analysis of the finite element model yields the modal parameters of the tower, which can also be obtained by analyzing measured tower vibration data using modal identification methods. Assuming the tower vibration originates from the previous... If the mode shape dominates, then we can assume that the modal parameters corresponding to these modes are known, i.e., the circular frequencies. Damping ratio Modal quality Mode shape coefficient It is known that .

[0023] The simplified method for calculating internal forces is derived as follows: Assume the vibration equation of the tower finite element model is expressed as: .

[0024] in: For the quality matrix, Here is the damping matrix. Here is the stiffness matrix. Let be the external load vector. According to the modal decomposition method, the displacement vector can be determined. With mode matrix The relationship is ;use Multiplying the above expression on the left yields:

[0025] .

[0026] in: Let be a generalized coordinate vector. For the ... For the mode shape, the above equation can be written in the following form:

[0027] This equation represents the modal vibration equation of the tower; by substituting the known modal parameters, the generalized coordinates corresponding to each mode shape can be obtained. According to the modal superposition method, considering only the dominant mode... The displacement time history at different heights of the tower when considering the contribution of the mode shape. The following formula can be used as an approximation: .

[0028] This allows us to obtain the displacement time history at different heights of the tower; for example, when calculating the bending moment at a certain location on the tower, we can use the relationship between displacement, rotation angle, and bending moment: .

[0029] The bending moments at different heights of the tower can be obtained, where: Indicates the bending moment of inertia of the tower section. The second derivative of the shape function vector between two nodes in a finite element model is represented by the second derivative. It represents the element displacement vector formed by the displacements of the nodes at both ends of a finite element.

[0030] Based on the above description, such as Figure 2 As shown, the simplified process of the present invention includes: Wind turbine manufacturers provide aerodynamic load data for the tower top under operating conditions, i.e., along the wind direction ( (Directional) Thrust Load Time History and bending moment time history Moreover, the cross-section and material parameters of the wind turbine tower are known.

[0031] (1) Solving for mode shape and frequency.

[0032] Step 1: Simplify the wind turbine and nacelle into a concentrated mass located at the top of the tower, and the load is the concentrated force and bending moment acting on the concentrated mass.

[0033] Step 2: Establish a finite element model, using a two-degree-of-freedom modal model.

[0034] Step 3: Based on the model solution results, read the first and second order frequencies, damping ratios, modal masses, and mode shape coefficients.

[0035] (2) Calculate the generalized coordinates.

[0036] Calculate the generalized coordinates based on the modal vibration equations of the tower.

[0037] (3) Calculate the internal forces of the tower at different heights. Step 1: Calculate the displacement and rotation at various positions of the tower using the modal superposition method.

[0038] Step 2: Calculate the internal forces of the tower at different heights based on the relationship between bending moment, displacement, and rotation angle.

[0039] Specific experiment: Assume the wind turbine manufacturer provides aerodynamic load data for the tower top under operating conditions. This load is obtained under the assumption that the tower is stationary or does not consider the tower at all. Among these, the downwind direction ( (Direction) Load time history is The average wind speed was 10 m / s, and the turbulence type was normal turbulence.

[0040] Considering only the two bending moment modes along the windward direction of the tower, that is, only the modal parameters of the first and second modes of the tower are known, i.e., the frequencies. and Damping ratio and Modal quality and Mode shape coefficient and Given the above parameters, a two-degree-of-freedom modal model can be established. Through modeling, the total damping ratio of the first-order mode is 6.575%, the circular frequency is 1.4016, and the modal mass is... The total damping ratio of the second-order mode is 5.63%, the circular frequency is 7.8420, and the modal mass is... Based on the relationship between stiffness and mass: .

[0041] Then the stiffness matrix for: .

[0042] Based on the relationship between damping, mass, and damping ratio: .

[0043] Then the damping matrix for: .

[0044] Substitute into the following formula: .

[0045] available: .

[0046] .

[0047] Since the first and second vibration modes of the model are known and and load Substitute the values ​​to find the answer. and .

[0048] At time 67 seconds, the modal loads corresponding to the first and second vibration modes are... and The values ​​are 0.8311 and 0.4424 respectively. Substituting these values ​​into the equation, we can solve for the corresponding generalized coordinates. and ,use The displacement and rotation time history at each section of the entire tower can then be calculated. Based on the relationship between displacement and bending moment:

[0049] .

[0050] The internal forces at each section of the tower can then be calculated. Table 1 shows the tower's array coefficients, and Table 2 shows the bending moments distributed along the tower height calculated by the two-degree-of-freedom model. The results were compared with those calculated by the fully coupled model, and the results show that the internal forces calculated by the two-degree-of-freedom model and the fully coupled model are very close.

[0051] Table 1. Vibration mode coefficients of 140m tower Table 2 Dynamic response and bending moment of 140m tower at various height sections This invention integrates the dominant aerodynamic damping in operation into the modal damping ratio and incorporates the dynamic influence of the wind turbine on the tower into the tower top load time history. This simplifies the complex fluid-structure interaction and system coupling problems into a dynamic response analysis problem of the tower structure itself with equivalent damping characteristics under known load excitation. At the same time, by extracting the dominant vibration mode through modal analysis, the original complex time history analysis with multiple degrees of freedom is decoupled into the solution and superposition of a few single-degree-of-freedom modal equations, which greatly reduces the computational scale and time consumption. This allows tower design units to quickly complete the internal force analysis of a large number of working conditions or parameter variations with conventional computing resources.

[0052] This invention introduces a modal damping ratio that includes aerodynamic damping and load distribution based on vibration modes. Essentially, it constructs an "equivalent filter" that can reflect the key dynamic characteristics of the system. The modal vibration equation directly describes the resonance response of each mode under load excitation, and projects the tower top load onto each vibration mode. This means that the load will be "intelligently" distributed according to the dynamic deformation of the tower, rather than simply applied statically. This more realistically simulates the dynamic process of the interaction between tower vibration and aerodynamic load in a real coupled system.

[0053] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.

Claims

1. A method for calculating the internal forces of a wind turbine tower, characterized in that, Includes the following steps: Acquire aerodynamic load data at the top of the wind turbine tower under operating or shutdown conditions, as well as structural parameters at different heights of the wind turbine tower; Based on the structural parameters at different heights of the tower, a finite element model of the tower was established using the finite element method, and the vibration equation of the finite element model of the tower was constructed. Based on aerodynamic load data, modal analysis is performed on the finite element model to extract the modal parameters corresponding to each mode shape under the dominance of the tower's dynamic response. Based on the modal parameters corresponding to each mode shape, the vibration equation of the tower finite element model is decoupled into modal vibration equations corresponding to single-degree-of-freedom mode shapes through modal decomposition. The modal parameters corresponding to each mode shape are then substituted into the modal vibration equations to obtain the generalized coordinates corresponding to each mode shape. Based on the generalized coordinates corresponding to each mode shape, the contribution of each mode shape to the displacement is superimposed along the tower height using the modal superposition method to obtain the displacement time history at different tower heights; based on the displacement time history at different tower heights, the internal forces at different tower heights are obtained from the structural mechanics relationship of the tower.

2. The method for calculating the internal forces of a wind turbine tower according to claim 1, characterized in that, The aerodynamic load data at the top of the wind turbine tower under operating conditions includes the moment vector at the top of the wind turbine tower. and force vector ; The structural parameters of the wind turbine tower at different heights include the cross-sectional parameters and material parameters of the wind turbine tower.

3. The method for calculating the internal forces of a wind turbine tower according to claim 2, characterized in that, The vibration equation of the finite element model of the tower is expressed as: ； in: Represents the mass matrix; Represents the damping matrix; Represents the stiffness matrix; This represents the external load vector.

4. The method for calculating the internal forces of a wind turbine tower according to claim 3, characterized in that, The modal parameters corresponding to each vibration mode include the circumferential frequency. Damping ratio Modal quality Mode shape coefficient , ; Wherein, the damping ratio The total damping of the wind turbine system includes aerodynamic damping of the wind turbine due to the interaction between air and wind turbine, aerodynamic damping due to the interaction between wind and tower, structural damping, soil damping due to the interaction between soil and wind turbine foundation structure, and other forms of damping.

5. The method for calculating the internal forces of a wind turbine tower according to claim 4, characterized in that, Obtaining the generalized coordinates corresponding to each mode shape includes: The displacement vector is obtained using the modal decomposition method. With mode matrix The relationship is represented as: ； Using the transpose of the mode matrix Multiplying the above equation on the left, we obtain the modal vibration equation of the tower as follows: ； in: Represents a generalized coordinate vector; If the system damping matrix is ​​a diagonal matrix, then for the th The modal vibration equation of the tower is expressed as follows: ； Substituting the modal parameters corresponding to each mode shape into the modal vibration equation of the tower, the generalized coordinates corresponding to each mode shape are obtained. ; If the system damping matrix is ​​a non-diagonal matrix, then the system's modal vibration equations are not a series of single-degree-of-freedom motion equations, but a damped coupled set of modal vibration equations, expressed as follows; ； in: ; ; ; ; By solving the damped coupled modal vibration equations, the generalized coordinates corresponding to each mode shape are obtained. .

6. The method for calculating the internal forces of a wind turbine tower according to claim 5, characterized in that, The acquisition of internal forces at different heights of the tower includes: Based on the modal superposition method, considering only the dominant modal... The displacement time history at different heights of the tower when considering the contribution of the mode shape. Represented as: ； Based on the relationship between displacement, rotation angle, and internal bending moment, the bending moment at different heights of the tower is obtained. The relationship between displacement, rotation angle, and internal bending moment is expressed as follows: ； in: Indicates the bending moment of inertia of the tower section; It represents the second derivative of the shape function vector between two nodes in a finite element model; This represents the element displacement vector formed by the displacements of the nodes at both ends of a finite element; When obtaining other components of internal force, the relationship between displacement, rotation angle and internal force components is used.

7. A device for calculating the internal forces of a wind turbine tower, characterized in that, include: The data module is used to acquire aerodynamic load data at the top of the wind turbine tower under operating conditions, as well as structural parameters at different heights of the wind turbine tower. The modal analysis module is used to establish a finite element model of the tower based on the structural parameters at different heights of the tower, and to construct the vibration equation of the tower finite element model. Based on aerodynamic load data, modal analysis is performed on the finite element model to extract the modal parameters corresponding to each mode shape under the dominance of the tower's dynamic response. Based on the modal parameters corresponding to each mode shape, the vibration equation of the tower finite element model is decoupled into modal vibration equations corresponding to single-degree-of-freedom mode shapes through modal decomposition. The modal parameters corresponding to each mode shape are then substituted into the modal vibration equations to obtain the generalized coordinates corresponding to each mode shape. The internal force calculation module is used to superimpose the contribution of each vibration mode to the displacement along the tower height distribution using the modal superposition method based on the generalized coordinates corresponding to each vibration mode, and obtain the displacement time history at different tower heights; based on the displacement time history at different tower heights, the internal forces at different tower heights are obtained from the structural mechanics relationship of the tower.

8. An electronic device, characterized in that, include: Memory and processor; The memory is used to store computer programs; When the processor executes the computer program stored in the memory, it implements the steps of the method for calculating the internal forces of a wind turbine tower as described in any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that, Used to store a computer program, which, when executed by a processor, implements the steps of a method for calculating the internal forces of a wind turbine tower as described in any one of claims 1 to 6.

Images