Method, device and equipment for analyzing out-of-plane motion of thin-film floating photovoltaic platform

Abstract

The application discloses a thin-film type floating photovoltaic platform out-of-plane motion analysis method, device and equipment. The method comprises the following steps: constructing an overall dynamic equation of the out-of-plane motion of the photovoltaic platform based on a dynamic equation and a displacement equation of the out-of-plane motion of the thin film and the floating ring; determining a time-domain wave load of the out-of-plane motion of the photovoltaic platform; determining a time-domain mooring force in the vertical direction of each mooring cable for constraining the photovoltaic platform, and determining a vertical component of a mooring point reaction force based on the time-domain mooring force; constructing a compatibility matrix based on the displacement equation of the out-of-plane motion of the thin film and the floating ring, and constructing a coupled dynamic equation of the out-of-plane motion of the photovoltaic platform based on the overall dynamic equation, the time-domain wave load, the vertical component and the compatibility matrix by using a Lagrange multiplier method, and performing time-domain solving on the coupled dynamic equation to obtain a time-domain response of the out-of-plane motion of the photovoltaic platform. Therefore, the out-of-plane motion response of the photovoltaic platform can be accurately described.

Description

Technical Field

[0001] This application relates to the field of offshore floating photovoltaic system analysis technology, and in particular to a method, apparatus and equipment for analyzing the out-of-plane motion of a thin-film floating photovoltaic platform. Background Technology

[0002] With the transformation of the global energy structure and the proposal of "dual carbon targets," offshore photovoltaic (PV) power generation, as an important component of clean and renewable energy, is becoming a new direction for marine energy development. Traditional land-based PV systems are limited by land resources in coastal and densely populated areas, while offshore floating PV platforms can make full use of ocean space and natural cooling effects, improving power generation efficiency and reducing maintenance costs. Currently, most floating PV platforms widely used in engineering are raft structures. These rigid or semi-rigid systems are suitable for calm waters, but in open seas, they are prone to excessive structural stress and mooring loads under the combined effects of waves and wind, making it difficult to meet the stability requirements for long-term service.

[0003] In recent years, thin-film floating photovoltaic platforms, composed of a float and a thin film, have gradually become a research hotspot. Characterized by high flexibility, low freeboard, and lightweight materials, they can undergo out-of-plane deformation in response to wave undulations, effectively reducing wave-added mass and environmental loads, making them a potential solution for adapting to mid-to-far-sea environments. However, since the main load-bearing structure of this photovoltaic platform is a flexible thin film, its out-of-plane motion exhibits strong fluid-structure interaction and nonlinear characteristics, making it difficult for existing methods to accurately describe the out-of-plane motion response of this photovoltaic platform. Summary of the Invention

[0004] This application provides a method, apparatus, and device for analyzing the out-of-plane motion of a thin-film floating photovoltaic platform, which can accurately describe the out-of-plane motion response of the photovoltaic platform.

[0005] In a first aspect, embodiments of this application provide a method for analyzing the out-of-plane motion of a thin-film floating photovoltaic platform, including:

[0006] The dynamic equations for the out-of-plane motion of the thin film and the floating ring in the photovoltaic platform are determined respectively, and the displacement equations for the out-of-plane motion of the thin film and the floating ring are determined respectively based on the modal superposition method;

[0007] Based on the dynamic equations of the out-of-plane motion of the thin film and the floating ring, and the displacement equation, the overall dynamic equations of the out-of-plane motion of the photovoltaic platform are constructed.

[0008] The frequency domain wave load of the out-of-plane motion of the photovoltaic platform is determined, and the frequency domain wave load is converted into the time domain wave load of the out-of-plane motion of the photovoltaic platform.

[0009] Determine the time-domain mooring force in the vertical direction of each mooring cable constraining the photovoltaic platform, and determine the vertical component of the reaction force at the mooring point connecting the mooring cable and the photovoltaic platform based on the time-domain mooring force;

[0010] A compatibility matrix is ​​constructed based on the displacement equations of the out-of-plane motion of the thin film and the floating ring. The Lagrange multiplier method is used to construct the coupled dynamic equations of the out-of-plane motion of the photovoltaic platform based on the overall dynamic equations, the time-domain wave load, the vertical component, and the compatibility matrix. The coupled dynamic equations are then solved in the time domain to obtain the time-domain response of the out-of-plane motion of the photovoltaic platform.

[0011] Secondly, embodiments of this application provide an out-of-plane motion analysis device for a thin-film floating photovoltaic platform, comprising:

[0012] The first processing module is used to determine the dynamic equations of the out-of-plane motion of the thin film and the floating ring in the photovoltaic platform, and to determine the displacement equations of the out-of-plane motion of the thin film and the floating ring based on the modal superposition method.

[0013] The second processing module is used to construct the overall dynamic equation of the out-of-plane motion of the photovoltaic platform based on the dynamic equation of the out-of-plane motion of the thin film and the floating ring and the displacement equation;

[0014] The third processing module is used to determine the frequency domain wave load of the out-of-plane motion of the photovoltaic platform and convert the frequency domain wave load into the time domain wave load of the out-of-plane motion of the photovoltaic platform.

[0015] The fourth processing module is used to determine the time-domain mooring force in the vertical direction of each mooring cable constraining the photovoltaic platform, and to determine the vertical component of the reaction force at the mooring point where the mooring cable connects to the photovoltaic platform based on the time-domain mooring force.

[0016] The fifth processing module is used to construct a compatibility matrix based on the displacement equations of the out-of-plane motion of the thin film and the floating ring, and to construct the coupled dynamic equations of the out-of-plane motion of the photovoltaic platform based on the overall dynamic equations, the time-domain wave load, the vertical component, and the compatibility matrix using the Lagrange multiplier method, and to solve the coupled dynamic equations in the time domain to obtain the time-domain response of the out-of-plane motion of the photovoltaic platform.

[0017] Thirdly, embodiments of this application provide an electronic device, including a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, it implements the method provided in embodiments of this application.

[0018] Fourthly, embodiments of this application provide a computer-readable storage medium, characterized in that it stores a computer program thereon, which, when executed in a computer, causes the computer to perform the method provided in embodiments of this application.

[0019] The technical solution provided in this application determines the time-domain mooring force in the vertical direction of each mooring cable, and uses this time-domain mooring force to determine the vertical component of the reaction force at the mooring point connecting the mooring cable and the photovoltaic platform. A compatibility matrix is ​​constructed using the displacement equations of the out-of-plane motion of the thin film and the float. Based on this vertical component and the compatibility matrix, a coupled dynamic equation for the out-of-plane motion of the photovoltaic platform is constructed, and this coupled dynamic equation is solved to obtain the time-domain response of the out-of-plane motion of the photovoltaic platform. In other words, the time-domain mooring force in the vertical direction of the mooring cable is used as an influencing factor for the out-of-plane motion of the photovoltaic platform. Compared to the prior art where the mooring cable is simplified to a static spring or catenary and only the horizontal mooring force is considered, this approach achieves true dynamic coordination between the photovoltaic platform and the mooring system, and can accurately describe the out-of-plane motion response of the photovoltaic platform. This application embodiment uses the modal superposition method to determine the displacement equations of the out-of-plane motion of the thin film and the float, and constructs the photovoltaic platform's out-of-plane response using these displacement equations and the dynamic equations of the out-of-plane motion of the thin film and the float. The overall dynamic equation of the out-of-plane motion can transform the dynamic equation of the out-of-plane motion of the membrane and the float into a finite-dimensional modal coordinate form, realizing the representation in the time domain. The vertical component of the reaction force at the mooring point is determined by the time-domain mooring force in the vertical direction of each mooring cable, which is also a representation in the time domain. Since the compatibility matrix is ​​determined by the displacement equation determined by the modal iteration method, the compatibility matrix is ​​also a representation in the time domain. By constructing the coupled dynamic equation of the out-of-plane motion of the photovoltaic platform using the time-domain wave load, the vertical component, the compatibility matrix, and the overall dynamic equation of the out-of-plane motion of the photovoltaic platform, the time-domain solution can be realized to obtain the time-domain response of the out-of-plane motion of the photovoltaic platform, which can reflect the instantaneous deformation and nonlinear behavior of the photovoltaic platform under the combined action of waves, the mooring system, etc. In the embodiment of this application, the coupling effect of the membrane, the float and the mooring system is considered when constructing the coupled dynamic equation, so as to accurately reflect the out-of-plane motion response of the photovoltaic platform under complex sea conditions. Attached Figure Description

[0020] Figure 1 One method provided for implementation of this application is a flowchart of an out-of-plane motion analysis method for a thin-film floating photovoltaic platform, as provided in an embodiment of this application.

[0021] Figure 2 This is a schematic diagram of the splicing method;

[0022] Figure 3 Schematic diagrams of the modal responses;

[0023] Figure 4The flowchart shows the main calculation process for the out-of-plane motion response of the photovoltaic platform.

[0024] Figure 5 This application provides a structural block diagram of a thin-film floating photovoltaic platform out-of-plane motion analysis device according to an embodiment of the present application;

[0025] Figure 6 This is a schematic diagram of an electronic device structure provided in an embodiment of this application. Detailed Implementation

[0026] The present application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0027] like Figure 1 As shown, Figure 1 This is a flowchart of an out-of-plane motion analysis method for a thin-film floating photovoltaic platform provided in an embodiment of this application. The method can be executed by an out-of-plane motion analysis device for a thin-film floating photovoltaic platform. The device can be implemented by software and / or hardware, and the method can be configured in an electronic device such as a computer.

[0028] The technical solution provided in this application mainly treats the flexible membrane, the annular float, and the mooring system as a coupled dynamic system. Based on potential flow theory, structural mode decomposition, and time-domain analysis techniques, a unified computational framework for the floating body-water-mooring system is established, specifically as follows: Figure 1 As shown, the technical solution provided in this application includes:

[0029] S110: Determine the dynamic equations of the out-of-plane motion of the thin film and the floating ring in the photovoltaic platform, and determine the displacement equations of the out-of-plane motion of the thin film and the floating ring based on the modal superposition method.

[0030] In this embodiment, the photovoltaic platform can be a thin-film floating photovoltaic platform, and the dynamic equation of the thin film in the photovoltaic platform can be:

[0031] (1);

[0032] in, This indicates the mass of the film per unit area. This represents the tension per unit length in a thin film; express Time, and radial coordinate and circumferential coordinates are The acceleration of the out-of-plane motion of the thin film at that time; express Time, and radial coordinate and circumferential coordinates are The displacement of the thin film surface during motion; This indicates the vertically distributed load acting on the thin film; and These represent the radial and circumferential coordinates of any point on the thin film, respectively. Where is the thin film radius; This represents the dimensionless radial coordinate in the polar coordinate system.

[0033] The dynamic equation of the float can be:

[0034] (2);

[0035] in, This refers to the mass per unit length of the float. The azimuth angle represents the angle between the line connecting any point on the float to the center of the film and the axis (X-axis). express At what moment, the acceleration of the out-of-plane motion of the float? This represents the displacement due to the out-of-plane motion of the float. This indicates the Poisson's ratio of the float material; Indicates the out-of-plane bending stiffness of the float. The radius of the float is This is the out-of-plane load per unit length of the float.

[0036] In this embodiment, from a structural mechanics perspective, the float can be considered as a ring-shaped curved beam with constant cross-sectional properties, its geometric centerline being a closed circle. Treating the float as a curved beam not only preserves its circumferential geometric characteristics and bending stiffness distribution but also conveniently describes its out-of-plane dynamic characteristics. Therefore, the out-of-plane motion of the float can be considered as the bending vibration of a curved beam, and the displacement equation for the out-of-plane motion of the float, determined by the modal superposition method, can be:

[0037] (3);

[0038] Among them, the above formula (3) is the displacement equation for the out-of-plane motion of the floating ring in the time domain; express At time, the azimuth angle is The displacement of the float in out-of-plane motion; for Circumferential modal amplitude at time t; and All indicate The amplitudes of the cosine and sinusoidal modes in the circumferential mode of the out-of-plane motion of the floating ring at a given moment; Indicates the circumferential modal truncation order;

[0039] The displacement equation for the out-of-plane motion of the thin film can be expressed by the separation of variables method using Bessel function expansion, that is, the displacement equation for the out-of-plane motion of the thin film can be obtained by the modal superposition method:

[0040] (4);

[0041] Among them, the above formula (4) is the displacement equation for the out-of-plane motion of the float in the time domain; and They represent out-of-plane motion of the thin film at time 1 The amplitudes of the cosine and sinusoidal modes; Indicates the first Eigenvalues ​​of the first mode, These represent the cutoff orders of the circumferential and radial modes, respectively. To indicate out-of-plane motion of the thin film at time 1 The amplitude of the first mode; For the first Eigenvalues ​​of the first mode; For the eigenvalues And the radial coordinate is The 0th order Bessel function; Eigenvalues And the radial coordinate is time The order Bessel function.

[0042] S120: Construct the overall dynamic equation of the out-of-plane motion of the photovoltaic platform based on the dynamic equation of the out-of-plane motion of the thin film and the floating ring and the displacement equation.

[0043] In this embodiment, specifically, the displacement expansions based on the out-of-plane motion equations of the membrane and the float can be substituted into the respective out-of-plane motion dynamic equations for matrix concatenation to obtain the overall dynamic equations of the membrane and the float. The method for concatenating the overall dynamic equations can refer to... Figure 2 , Figure 2 The specific forms of each matrix in the overall dynamic equation are reflected in this. Therefore, in this embodiment, the thin film and the floating ring are taken as the main components of the photovoltaic platform, and the study mainly focuses on the thin film and the floating ring in the photovoltaic platform. Therefore, the overall dynamic equation of the thin film and the floating ring is taken as the overall dynamic equation of the out-of-plane motion of the photovoltaic platform, wherein the overall dynamic equation is specifically as follows:

[0044] (5);

[0045] in, , and These are the generalized displacement matrix, generalized velocity matrix, and generalized acceleration matrix, respectively, composed of the modal amplitudes of the thin film and the floating ring in the time domain. This represents the overall modal mass matrix, which consists of the modal masses of the film and the out-of-plane motion of the float. Represents the modal mass matrix of the thin film; Modal mass matrix of the float ring; The modal loads are those generated during the out-of-plane motion of the photovoltaic platform in the time domain. Here is the damping matrix; ,in, This is the damping matrix corresponding to the thin film; Here is the damping matrix corresponding to the float ring;

[0046] This represents the overall modal stiffness matrix, which consists of the out-of-plane motion modal stiffness of the thin film and the float. This represents the modal stiffness matrix of the thin film. This represents the modal stiffness matrix of the floating ring.

[0047] In this embodiment, by constructing the dynamic equations of the out-of-plane motion of the thin film and the float, and by using the modal superposition method and Fourier series expansion, the complex displacement (in this embodiment, the vertical displacement) is decomposed into a linear combination of multiple modes. Furthermore, the optimal mode cutoff order can be determined through modal convergence analysis. By comparing the modal amplitudes under different orders, the minimum effective mode set can be determined, satisfying the dual requirements of accuracy and efficiency in engineering design.

[0048] S130: Determine the frequency domain wave load of the out-of-plane motion of the photovoltaic platform, and convert the frequency domain wave load into the time domain wave load of the out-of-plane motion of the photovoltaic platform.

[0049] In this embodiment, based on the linear potential flow theory to decompose the velocity potential of the flow field, the frequency domain wave load of the out-of-plane motion of the photovoltaic platform can be expressed as:

[0050] (6);

[0051] in, Indicates wave frequency. It is the symbol for imaginary numbers; This represents the additional quality coefficient matrix in the frequency domain. This represents the damping coefficient matrix in the frequency domain. This represents the wave excitation force matrix in the frequency domain. This represents the still water restoring force coefficient matrix. This represents the generalized displacement matrix composed of the mode amplitudes of the thin film and the floating ring in the frequency domain; where, With the still water restoring force coefficient matrix It can be obtained by solving the potential flow software WAMIT. The frequency domain wave load of the out-of-plane motion of the photovoltaic platform can be calculated using the Cummins equations. Converted to time-domain wave load :

[0052] (7);

[0053] in, For the photovoltaic platform in Time-domain wave load at time; and They are respectively The generalized acceleration matrix and generalized displacement matrix are composed of the modal amplitudes of the thin film and the floating ring at time t. yes The modal amplitudes of the thin film and the floating ring at any given time form a generalized velocity matrix; This represents the additional mass matrix at infinite frequency; For the out-of-plane motion of the photovoltaic platform in The wave excitation force matrix at any given time, i.e., the wave excitation force matrix in the time domain of the out-of-plane motion of the photovoltaic platform; It is a time delay function related to radiation damping; for The time delay function at time step.

[0054] in, (8);

[0055] In this embodiment, the frequency-domain wave load of the out-of-plane motion of the photovoltaic platform is converted into a time-domain wave load using the Cummins equation, taking into account the radiation wave time delay effect and preserving the time-domain characteristics of fluid-structure interaction. Figure 3 As shown, this illustrates a photovoltaic platform with a diameter of 1m operating at a modal order of [missing value]. The modal responses calculated in both the time and frequency domains verified the accuracy of the time-domain wave load calculation results; among them, Figure 3 In this context, FD represents the frequency domain calculation result of the modal response; TD represents the time domain calculation result of the modal response.

[0056] S140: Determine the time-domain mooring force in the vertical direction of each mooring cable constraining the photovoltaic platform, and determine the vertical component of the reaction force at the mooring point where the mooring cable connects to the photovoltaic platform based on the time-domain mooring force.

[0057] In this embodiment, a dynamic model of the mooring system can be constructed. The time-domain system force in the vertical direction of each mooring cable can be calculated using this model, thereby determining the vertical component of the reaction force at the mooring point, i.e., the mooring load in the time domain. The mooring system includes mooring cables; the number of mooring cables can be one or more.

[0058] In this embodiment, optionally, determining the vertical component of the mooring point reaction force connecting the mooring cable and the photovoltaic platform based on the time-domain mooring force includes: determining the resultant force of the time-domain mooring forces in the vertical direction of all mooring cables based on the time-domain mooring forces of each mooring cable; determining the modal force when the circumferential modal order is zero based on the resultant force of the time-domain mooring forces, and using it as the vertical component of the mooring point reaction force when the circumferential modal order is zero; determining the sinusoidal modal force and cosine modal force when the circumferential modal order is not zero based on the resultant force of the time-domain mooring forces, and determining the vertical component of the mooring point reaction force when the circumferential modal order is not zero based on the sinusoidal modal force and the cosine modal force.

[0059] Specifically, the dynamic model of the mooring system adopts a lumped mass model to consider structural characteristics and uses the Morrison model to calculate hydrodynamic loads. After selecting an appropriate element length, the mooring cable is divided into finite element units, resulting in individual tiny elements. Each element of the mooring cable is simplified to a lumped mass located at the center of gravity. By introducing springs to connect all the lumped masses, the mooring cable is simplified to a system of mass points connected by springs. It is assumed that the entire photovoltaic platform is connected... mooring cable, first The mooring cable is divided into K tiny units, each connected to two nodes, meaning there are K+1 nodes on the entire mooring cable. The dynamic equation for the k-th node is:

[0060] (9):

[0061] Wherein, a node can be the center of each tiny unit; the above formula (9) is the dynamic model of the mooring system; subscript Indicates the node number. For the first The centralized quality of each node, For the first Additional mass at each node For the first The acceleration vector of each node. , The first , Tension of each unit , The first , Internal damping of each unit; For the first One gravity term, , They represent the first Normal resistance and tangential resistance at each node Indicates when the first Damping when the height of a node is lower than the height of the seabed.

[0062] In this embodiment, by solving the above formula (9) through time-domain integration (such as the Newmark-β method), the first time step at each time step can be obtained sequentially. Each node The acceleration, velocity, and displacement at time t are respectively Then the first The node and the first Elongation of the unit between +1 nodes ;in The symbol represents the magnitude of the vector; for +1 node at Displacement at any given moment. Root mooring cable The total length of a time interval is the sum of the lengths of the K units: , No. Root mooring cable Total elongation at time According to Hooke's Law, the first... Root mooring cable Total tension at any moment , here Values ​​can be taken from 1 to In this embodiment, only the vertical component is considered, so it needs to be multiplied by the corresponding direction vector. This allows us to obtain the time-domain mooring force in the vertical direction for each mooring cable. :

[0063] (10);

[0064] in, Indicates the first Root mooring cable The length of time; Original length; Indicates the equivalent axial stiffness; Represents the direction vector; Indicates the number of mooring cables.

[0065] In this embodiment, the vertical component can be determined based on the following formula:

[0066] (11);

[0067] in, (12);

[0068] in, (13);

[0069] in, (14);

[0070] in, The vertical component; The resultant force of the time-domain mooring forces in the vertical direction of all mooring cables; For the first Root mooring cable in vertical direction Mooring force at all times; For the first Root mooring cable The length of time; Indicates the number of mooring cables; For Dirac functions; The radius of the float is [missing information]. The azimuth angle represents the angle between the line connecting any point on the float to the center of the film and the axis. Indicates the location of the mooring point; Indicates the circumferential modal order; The modal force when the circumferential modal order is zero; The cosine modal force when the circumferential modal order is not zero; It is the sinusoidal modal force when the circumferential modal order is not zero.

[0071] S150: Construct a compatibility matrix based on the displacement equations of the out-of-plane motion of the thin film and the floating ring, and use the Lagrange multiplier method to construct the coupled dynamic equations of the out-of-plane motion of the photovoltaic platform based on the overall dynamic equations, the time-domain wave load, the vertical component, and the compatibility matrix. Solve the coupled dynamic equations in the time domain to obtain the time-domain response of the out-of-plane motion of the photovoltaic platform.

[0072] In this embodiment, optionally, constructing a compatibility matrix based on the displacement equations of the out-of-plane motion of the thin film and the float includes: constructing a modal amplitude relationship equation between the thin film and the float based on the consistency of the vertical displacements of the out-of-plane motion of the thin film and the float; constructing a compatibility matrix based on the modal amplitude relationship equation; wherein the product of the compatibility matrix and the generalized displacement matrix is ​​a zero matrix; wherein the generalized displacement matrix is ​​a generalized displacement matrix composed of the modal amplitudes of the thin film and the float in the time domain.

[0073] Specifically, based on the consistency of the vertical displacement between the film and the out-of-plane movement of the float, that is, in... hour Combining formulas (3) and (4), we can obtain:

[0074] (15);

[0075] Formula (15) can be understood as the modal amplitude relationship equation between the thin film and the floating ring. Based on formula (15), a compatibility matrix can be constructed, wherein the compatibility matrix is:

[0076] (16);

[0077] in, (17);

[0078] in, (18);

[0079] in, (19); where formula (19) is the geometric compatibility condition.

[0080] in, The compatibility matrix is ​​the matrix described above. The circumferential modal order is Thin film correlation matrix at time; The circumferential modal order is The floating ring correlation matrix at that time; These represent the cutoff orders of the circumferential and radial modes, respectively. They are the first Eigenvalues ​​of the first mode; for The eigenvalues ​​are 0, and the eigenvalues ​​are respectively The 0th order Bessel function; They are the first Eigenvalues ​​of the first mode; They are respectively Non-zero, and the eigenvalues ​​are respectively time Bessel function of order 1; The circumferential modal orders are 0 to 1000 respectively. Thin film correlation matrix at time; The circumferential modal orders are 0 to 1000 respectively. The floating ring correlation matrix is ​​obtained by constructing the compatibility matrix using the above formula (15), which reflects the interaction between the thin film and the floating ring.

[0081] In this embodiment, optionally, the step of constructing the coupled dynamic equations of the out-of-plane motion of the photovoltaic platform based on the overall dynamic equations, the time-domain wave loads, the vertical components, and the compatibility matrix using the Lagrange multiplier method includes: determining the modal loads in the time domain of the out-of-plane motion of the photovoltaic platform based on the vertical components and the time-domain wave loads; and determining the coupled dynamic equations based on the modal loads in the time domain of the out-of-plane motion of the photovoltaic platform and the compatibility matrix using the Lagrange multiplier method.

[0082] Specifically, the vertical components, namely the mooring load and the time-domain wave load, are added together to obtain the modal load in the time domain of the out-of-plane motion of the photovoltaic platform. The Lagrange multiplier method is used to obtain the corresponding equilibrium equation based on formulas (5) and (19). Specifically, the geometric compatibility condition formula (19) is introduced into formula (5) to obtain the corresponding equilibrium equation. The equilibrium equation is then rewritten to obtain the coupled dynamic equation of the out-of-plane motion of the photovoltaic platform:

[0083] (20);

[0084] in, (twenty one);

[0085] The specific derivation process is as follows: From formula (5), we can see that:

[0086]

[0087] Among them, the right side of equation (5) ;

[0088] in, The calculation can be seen in formula (7):

[0089]

[0090] Therefore, the right side of equation (5) Substituting this formula into formula (5) yields the following result:

[0091] make

[0092] make ;

[0093] make ;

[0094] but By using the Lagrange multiplier method and introducing the geometric compatibility condition, i.e., formula (19), we can obtain formula (20).

[0095] in, , and These are the generalized displacement matrix, generalized velocity matrix, and generalized acceleration matrix, respectively, composed of the modal amplitudes of the thin film and the floating ring in the time domain. It is the generalized displacement matrix composed of the modal amplitudes of the thin film in the time domain; The generalized displacement matrix is ​​composed of the modal amplitudes of the floating ring in the time domain; for The generalized velocity matrix composed of the modal amplitudes of the thin film and the floating ring at time t;

[0096] in, , and These are the Lagrange multiplier, the first derivative of the Lagrange multiplier, and the second derivative of the Lagrange multiplier, respectively. This is the transpose of the compatibility matrix; Here is the damping matrix; This is the still water restoring force coefficient matrix; These represent the corresponding damping coefficients; This represents the partial modal loads under the out-of-plane motion of the photovoltaic platform in the time domain. The solution to the above formula (21) can be obtained using the Newmark-beta method in the time domain, which inversely yields the out-of-plane motion response of the photovoltaic platform. The known quantities in the above formula (21) are: , , , The solution is... , , can be It is obtained by integration within the time step.

[0097] Among them, the coupled dynamic equations of the out-of-plane motion of the photovoltaic platform comprehensively consider the interaction and coupling effect between the thin film, the float and the mooring system, establish the dynamic relationship of the photovoltaic platform structure under external excitation, and ensure the displacement coordination of the thin film and the float through the geometric compatibility conditions at the connection, thereby realizing the solution of the out-of-plane motion response of the photovoltaic platform.

[0098] The main calculation process for the out-of-plane motion response of the photovoltaic platform can be found by referring to... Figure 4 ,like Figure 4 As shown, the structural parameters mainly include geometric parameters and material parameters. Specifically, the overall modal mass matrix composed of the modal masses of the out-of-plane motion of the membrane and the float, and the overall modal stiffness matrix composed of the modal stiffness are constructed through the structural parameters. Among them, the structural parameters include the membrane diameter and thickness, the float diameter, the float cross-sectional radius and the float tube thickness, the elastic modulus, Poisson's ratio, pretension, etc. The generalized hydrodynamic force is calculated through the wave parameters at time t-1 and the velocity of the membrane and the float, which includes the parameters in formula (6). , and Among them, wave parameters include wave frequency, etc.; the generalized mooring force is calculated using the mooring parameters at time t-1 and the coordinates of the mooring point, that is, it is calculated using formula (11). It can be understood as generalized mooring force; mooring parameters are used to describe the mooring cable itself and its arrangement characteristics, including but not limited to the initial length, linear density, axial stiffness, diameter, hydrodynamic resistance coefficient, end connection position and anchoring method of the mooring cable; based on generalized hydrodynamics, generalized mooring force, the aforementioned overall modal stiffness matrix and overall modal mass matrix, input the coupled dynamic equation of the photovoltaic platform out-of-plane motion based on generalized displacement, i.e., formula (20), thereby calculating the generalized displacement of the photovoltaic platform out-of-plane motion, which can be understood as modal amplitude; calculate the displacement of the float and the film out-of-plane motion based on the above formula (3) and formula (4) through generalized displacement, and differentiate to obtain the velocity of the float and the film at time t; and determine the coordinates of the mooring point at time t through generalized displacement and based on the preset coordinate system; determine whether the time has ended, if yes, end the process, if no, at the next time t+1, return to the steps of calculating generalized hydrodynamics, generalized mooring force, etc., until the process ends. At the initial moment, the coordinates of the mooring point can be considered as the original coordinates, and the velocities of the float and the membrane can be 0.

[0099] The technical solution provided in this application determines the time-domain mooring force in the vertical direction of each mooring cable, and uses this time-domain mooring force to determine the vertical component of the reaction force at the mooring point connecting the mooring cable and the photovoltaic platform. A compatibility matrix is ​​constructed using the displacement equations of the out-of-plane motion of the thin film and the float. Based on this vertical component and the compatibility matrix, a coupled dynamic equation for the out-of-plane motion of the photovoltaic platform is constructed, and this coupled dynamic equation is solved to obtain the time-domain response of the out-of-plane motion of the photovoltaic platform. In other words, the time-domain mooring force in the vertical direction of the mooring cable is used as an influencing factor for the out-of-plane motion of the photovoltaic platform. Compared to the prior art where the mooring cable is simplified to a static spring or catenary and only the horizontal mooring force is considered, this approach achieves true dynamic coordination between the photovoltaic platform and the mooring system, and can accurately describe the out-of-plane motion response of the photovoltaic platform. This application embodiment uses the modal superposition method to determine the displacement equations of the out-of-plane motion of the thin film and the float, and constructs the photovoltaic platform's out-of-plane response using these displacement equations and the dynamic equations of the out-of-plane motion of the thin film and the float. The overall dynamic equation of the out-of-plane motion can transform the dynamic equation of the out-of-plane motion of the membrane and the float into a finite-dimensional modal coordinate form, realizing the representation in the time domain. The vertical component of the reaction force at the mooring point is determined by the time-domain mooring force in the vertical direction of each mooring cable, which is also a representation in the time domain. Since the compatibility matrix is ​​determined by the displacement equation determined by the modal iteration method, the compatibility matrix is ​​also a representation in the time domain. By constructing the coupled dynamic equation of the out-of-plane motion of the photovoltaic platform using the time-domain wave load, the vertical component, the compatibility matrix, and the overall dynamic equation of the out-of-plane motion of the photovoltaic platform, the time-domain solution can be realized to obtain the time-domain response of the out-of-plane motion of the photovoltaic platform, which can reflect the instantaneous deformation and nonlinear behavior of the photovoltaic platform under the combined action of waves, the mooring system, etc. In the embodiment of this application, the coupling effect of the membrane, the float and the mooring system is considered when constructing the coupled dynamic equation, so as to accurately reflect the out-of-plane motion response of the photovoltaic platform under complex sea conditions.

[0100] The technical solutions provided in this application have clear technical feasibility and industrial application potential, and can be directly applied in multiple stages such as engineering design, performance evaluation and operation safety management.

[0101] The main load-bearing structure of the photovoltaic platform is a flexible thin film, whose out-of-plane motion exhibits strong fluid-structure interaction and nonlinear characteristics. Existing frequency-domain linear potential flow models and quasi-static analysis methods cannot accurately describe the transient response and nonlinear behavior under the combined action of waves. The technical solution provided in this application, by constructing a time-domain solution method, can reflect the instantaneous response and nonlinear behavior of the photovoltaic platform under the combined action of waves, mooring systems, etc. Since there is a significant structural coupling effect between the thin film and the float, neglecting the coupling conditions at the boundary (displacement continuity and force balance) will lead to deviations in the calculation of overall dynamic characteristics. This application, by introducing Lagrange multipliers, transforms the displacement constraints of the float and the thin film into coupled dynamic equations, thereby reflecting the boundary coupling conditions. This allows the bending stiffness of the float and the pretension of the thin film to work together in the out-of-plane motion response, achieving overall coordinated deformation.

[0102] The technical solution provided in this application combines the computational accuracy of linear potential flow theory with the nonlinear adaptability of the Morrison equation, enabling simultaneous calculation of key parameters such as wave, current velocity, and mooring tension changes in practical engineering. Compared with traditional frequency domain analysis or empirical calculation models, it offers significant improvements in peak prediction of out-of-plane motion response, energy transfer analysis, and load coupling simulation. The technical solution provided in this application can also stably solve the time-domain response problem of large-scale flexible structures, exhibiting good numerical stability and computational efficiency. Furthermore, the computational process employed in the technical solution provided in this application is highly modular, easily integrated with existing hydrodynamic analysis and structural design software interfaces, and can be applied to the design and safety assessment of various types of equipment, including flexible floating photovoltaic platforms, offshore thin-film structures, flexible fishery cages, and marine ranching platforms.

[0103] The technical solutions provided in this application can also be directly applied to the hydrodynamic performance evaluation and structural optimization design of thin-film floating photovoltaic platforms. In the preliminary design phase of a project, this method can be used to quickly predict the out-of-plane response characteristics of the photovoltaic platform under different sea states; during the construction and operation and maintenance phases, it can be used to evaluate the stability and mooring safety of the photovoltaic platform under extreme loads, assisting in the formulation of protection and emergency strategies; it can also significantly improve the design efficiency and operational reliability of related equipment, possessing good potential for scientific research transformation and industrial application prospects.

[0104] Figure 5 This application provides a structural block diagram of a thin-film floating photovoltaic platform out-of-plane motion analysis device, which includes:

[0105] The first processing module 510 is used to determine the dynamic equations of the out-of-plane motion of the thin film and the floating ring in the photovoltaic platform, and to determine the displacement equations of the out-of-plane motion of the thin film and the floating ring based on the modal superposition method.

[0106] The second processing module 520 is used to construct the overall dynamic equation of the out-of-plane motion of the photovoltaic platform based on the dynamic equation of the out-of-plane motion of the thin film and the floating ring and the displacement equation;

[0107] The third processing module 530 is used to determine the frequency domain wave load of the out-of-plane motion of the photovoltaic platform and convert the frequency domain wave load into the time domain wave load of the out-of-plane motion of the photovoltaic platform.

[0108] The fourth processing module 540 is used to determine the time-domain mooring force in the vertical direction of each mooring cable constraining the photovoltaic platform, and to determine the vertical component of the reaction force at the mooring point where the mooring cable connects to the photovoltaic platform based on the time-domain mooring force.

[0109] The fifth processing module 550 is used to construct a compatibility matrix based on the displacement equations of the out-of-plane motion of the thin film and the floating ring, and to construct the coupled dynamic equations of the out-of-plane motion of the photovoltaic platform based on the overall dynamic equations, the time-domain wave load, the vertical component and the compatibility matrix using the Lagrange multiplier method, and to solve the coupled dynamic equations in the time domain to obtain the time-domain response of the out-of-plane motion of the photovoltaic platform.

[0110] like Figure 6 As shown in the figure, this application provides an electronic device, including a processor 111, a communication interface 112, a memory 113, and a communication bus 114, wherein the processor 111, the communication interface 112, and the memory 113 communicate with each other through the communication bus 114.

[0111] Memory 113 is used to store computer programs;

[0112] In one embodiment of this application, when the processor 111 executes a program stored in the memory 113, it implements the method provided in any of the foregoing method embodiments, including:

[0113] The dynamic equations for the out-of-plane motion of the thin film and the floating ring in the photovoltaic platform are determined respectively, and the displacement equations for the out-of-plane motion of the thin film and the floating ring are determined respectively based on the modal superposition method;

[0114] Based on the dynamic equations of the out-of-plane motion of the thin film and the floating ring, and the displacement equation, the overall dynamic equations of the out-of-plane motion of the photovoltaic platform are constructed.

[0115] Determine the frequency domain wave load of the out-of-plane motion of the photovoltaic platform, and convert the frequency domain wave load into the time domain wave load of the out-of-plane motion of the photovoltaic platform;

[0116] Determine the time-domain mooring force in the vertical direction of each mooring cable constraining the photovoltaic platform, and determine the vertical component of the reaction force at the mooring point connecting the mooring cable and the photovoltaic platform based on the time-domain mooring force;

[0117] A compatibility matrix is ​​constructed based on the displacement equations of the out-of-plane motion of the thin film and the floating ring. Then, using the Lagrange multiplier method, coupled dynamic equations for the out-of-plane motion of the photovoltaic platform are constructed based on the overall dynamic equations, the time-domain wave load, the vertical component, and the compatibility matrix. These coupled dynamic equations are then solved in the time domain to obtain the time-domain response of the out-of-plane motion of the photovoltaic platform.

[0118] This application also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the method provided in any of the foregoing method embodiments.

[0119] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.

[0120] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented using software plus a general-purpose hardware platform, or of course, using hardware. Based on this understanding, the above technical solutions, in essence or the parts that contribute to the related technology, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0121] The above embodiments are merely illustrative examples and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations. However, obvious variations or modifications derived therefrom are still within the scope of protection of this application.

Claims

1. A method for analyzing the out-of-plane motion of a thin-film floating photovoltaic platform, characterized in that, include: The dynamic equations for the out-of-plane motion of the thin film and the floating ring in the photovoltaic platform are determined respectively, and the displacement equations for the out-of-plane motion of the thin film and the floating ring are determined respectively based on the modal superposition method; Based on the dynamic equations of the out-of-plane motion of the thin film and the floating ring, and the displacement equation, the overall dynamic equations of the out-of-plane motion of the photovoltaic platform are constructed. Determine the frequency domain wave load of the out-of-plane motion of the photovoltaic platform, and convert the frequency domain wave load into the time domain wave load of the out-of-plane motion of the photovoltaic platform; The time-domain mooring force in the vertical direction of each mooring cable constraining the photovoltaic platform is determined, and the vertical component of the reaction force at the mooring point connecting the mooring cable and the photovoltaic platform is determined based on the time-domain mooring force. Specifically, an appropriate element length is selected, and the mooring cable is divided into finite element units to obtain individual tiny elements. Each element of the mooring cable is simplified to a concentrated mass located at the center of gravity. By introducing springs to connect all concentrated masses, the mooring cable is simplified to a system of mass points connected by springs. A compatibility matrix is ​​constructed based on the displacement equations of the out-of-plane motion of the thin film and the floating ring. The Lagrange multiplier method is used to construct the coupled dynamic equations of the out-of-plane motion of the photovoltaic platform based on the overall dynamic equations, the time-domain wave load, the vertical component, and the compatibility matrix. The coupled dynamic equations are then solved in the time domain to obtain the time-domain response of the out-of-plane motion of the photovoltaic platform. The determination of the vertical component of the reaction force at the mooring point connecting the mooring cable and the photovoltaic platform based on the time-domain mooring force includes: The resultant force of the time-domain mooring forces in the vertical direction of all mooring cables is determined based on the time-domain mooring force in the vertical direction of each mooring cable. The modal force when the circumferential modal order is zero is determined based on the resultant force of the mooring forces in the time domain, and is used as the vertical component of the mooring point reaction force when the circumferential modal order is zero. Based on the resultant force of the time-domain mooring forces, determine the sinusoidal modal force and cosine modal force when the circumferential modal order is not zero, and based on the sinusoidal modal force and the cosine modal force, determine the vertical component of the mooring point reaction force when the circumferential modal order is not zero; The vertical component is determined based on the following formula: ； in, ; in, ; in, ; in, The vertical component; The resultant force of the time-domain mooring forces in the vertical direction of all mooring cables; For the first Root mooring cable in vertical direction Mooring force at all times; For the first Root mooring cable The length of time; Indicates the number of mooring cables; For Dirac functions; The radius of the float is [missing information]. The azimuth angle represents the angle between the line connecting any point on the float to the center of the film and the axis. Indicates the location of the mooring point; Indicates the circumferential modal order; The modal force when the circumferential modal order is zero; The cosine modal force when the circumferential modal order is not zero; It is the sinusoidal modal force when the circumferential modal order is not zero.

2. The method according to claim 1, characterized in that, The construction of the compatibility matrix based on the displacement equations of the thin film and the out-of-plane motion of the float includes: Based on the consistency of the vertical displacement of the film and the float in out-of-plane motion, a modal amplitude relationship equation between the film and the float is constructed. A compatibility matrix is ​​constructed based on the modal amplitude relationship equation; wherein the product of the compatibility matrix and the generalized displacement matrix is ​​a zero matrix; wherein the generalized displacement matrix is ​​the generalized displacement matrix composed of the modal amplitudes of the thin film and the floating ring in the time domain.

3. The method according to claim 2, characterized in that, The compatibility matrix is: ； in, ; in, ; in, , which is a geometric compatibility condition; in, The compatibility matrix is ​​the matrix described above. It is the generalized displacement matrix composed of the modal amplitudes of the thin film and the floating ring in the time domain; The circumferential modal order is Thin film correlation matrix at time; The circumferential modal order is The floating ring correlation matrix at that time; These represent the cutoff orders of the circumferential and radial modes, respectively. They are the first Eigenvalues ​​of the first mode; for The eigenvalues ​​are 0, and the eigenvalues ​​are respectively The 0th order Bessel function; They are the first Eigenvalues ​​of the first mode; They are respectively Non-zero, and the eigenvalues ​​are respectively time Bessel function of order 1; The circumferential modal orders are 0 to 1000 respectively. Thin film correlation matrix at time; The circumferential modal orders are 0 to 1000 respectively. The correlation matrix of the floating ring at that time.

4. The method according to claim 1, characterized in that, The coupled dynamic equations for the out-of-plane motion of the photovoltaic platform, constructed using the Lagrange multiplier method based on the overall dynamic equations, the time-domain wave load, the vertical component, and the compatibility matrix, include: The modal loads of the photovoltaic platform in the out-of-plane motion time domain are determined based on the vertical component and the time-domain wave load. The coupled dynamic equations are determined using the Lagrange multiplier method based on the modal loads in the time domain of the out-of-plane motion of the photovoltaic platform and the compatibility matrix.

5. The method according to claim 4, characterized in that, The coupling dynamics equation is: ； in, ; in, , and These are the generalized displacement matrix, generalized velocity matrix, and generalized acceleration matrix, respectively, composed of the modal amplitudes of the thin film and the floating ring in the time domain. It is the generalized displacement matrix composed of the modal amplitudes of the thin film in the time domain; The generalized displacement matrix is ​​composed of the modal amplitudes of the floating ring in the time domain; for The generalized velocity matrix composed of the modal amplitudes of the thin film and the floating ring at time t; in, , and These are the Lagrange multiplier, the first derivative of the Lagrange multiplier, and the second derivative of the Lagrange multiplier, respectively. The compatibility matrix is ​​the matrix described above. This is the transpose of the compatibility matrix; Here is the damping matrix; This is the still water restoring force coefficient matrix; in, This represents the overall modal mass matrix, which consists of the modal masses of the film and the out-of-plane motion of the float. Represents the modal mass matrix of the thin film; Modal mass matrix of the float ring; This represents the additional mass matrix at infinite frequency; This represents the overall modal stiffness matrix, which consists of the out-of-plane motion modal stiffness of the thin film and the float. This represents the modal stiffness matrix of the thin film. This represents the modal stiffness matrix of the floating ring; These represent the corresponding damping coefficients; The wave excitation force matrix in the time domain of the out-of-plane motion of the photovoltaic platform; In order to be in The time delay function related to radiation damping at time; The vertical component; This refers to the partial modal loads in the time domain of out-of-plane motion of the photovoltaic platform.

6. A thin-film floating photovoltaic platform out-of-plane motion analysis device, characterized in that, include: The first processing module is used to determine the dynamic equations of the out-of-plane motion of the thin film and the floating ring in the photovoltaic platform, and to determine the displacement equations of the out-of-plane motion of the thin film and the floating ring based on the modal superposition method. The second processing module is used to construct the overall dynamic equation of the out-of-plane motion of the photovoltaic platform based on the dynamic equation of the out-of-plane motion of the thin film and the floating ring and the displacement equation; The third processing module is used to determine the frequency domain wave load of the out-of-plane motion of the photovoltaic platform and convert the frequency domain wave load into the time domain wave load of the out-of-plane motion of the photovoltaic platform. The fourth processing module is used to determine the time-domain mooring force in the vertical direction of each mooring cable constraining the photovoltaic platform, and to determine the vertical component of the reaction force at the mooring point where the mooring cable connects to the photovoltaic platform based on the time-domain mooring force. The fifth processing module is used to construct a compatibility matrix based on the displacement equations of the out-of-plane motion of the thin film and the floating ring, and to construct the coupled dynamic equations of the out-of-plane motion of the photovoltaic platform based on the overall dynamic equations, the time-domain wave load, the vertical component, and the compatibility matrix using the Lagrange multiplier method, and to solve the coupled dynamic equations in the time domain to obtain the time-domain response of the out-of-plane motion of the photovoltaic platform. The determination of the vertical component of the reaction force at the mooring point connecting the mooring cable and the photovoltaic platform based on the time-domain mooring force includes: The resultant force of the time-domain mooring forces in the vertical direction of all mooring cables is determined based on the time-domain mooring force in the vertical direction of each mooring cable. The modal force when the circumferential modal order is zero is determined based on the resultant force of the mooring forces in the time domain, and is used as the vertical component of the mooring point reaction force when the circumferential modal order is zero. Based on the resultant force of the time-domain mooring forces, determine the sinusoidal modal force and cosine modal force when the circumferential modal order is not zero, and based on the sinusoidal modal force and the cosine modal force, determine the vertical component of the mooring point reaction force when the circumferential modal order is not zero; The vertical component is determined based on the following formula: ； in, ; in, ; in, ; in, The vertical component; The resultant force of the time-domain mooring forces in the vertical direction of all mooring cables; For the first Root mooring cable in vertical direction Mooring force at all times; For the first Root mooring cable The length of time; Indicates the number of mooring cables; For Dirac functions; The radius of the float is [missing information]. The azimuth angle represents the angle between the line connecting any point on the float to the center of the film and the axis. Indicates the location of the mooring point; Indicates the circumferential modal order; The modal force when the circumferential modal order is zero; The cosine modal force when the circumferential modal order is not zero; It is the sinusoidal modal force when the circumferential modal order is not zero.

7. An electronic device, characterized in that, It includes a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the method as described in any one of claims 1-5.

8. A computer-readable storage medium, characterized in that, It stores a computer program that, when executed in a computer, causes the computer to perform the method described in any one of claims 1-5.

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