Method for calculating dynamic stiffness of polyester cable of deepwater floating photovoltaic platform

Abstract

This invention provides a method for calculating the dynamic stiffness of polyester cables for deep-water floating photovoltaic platforms, including: Step S1: Defining the initial stiffness value of the polyester cable and calculating the average tension value at the top of each polyester cable. L m1 Step S2: Calculate the... L m1 Substituting the expression for cable stiffness, the average tension at the tip of each polyester cable can be calculated. L m2 Step S3: Calculate the converged average tension using iteration, and substitute the calculated average tension into the dynamic stiffness expression; Step S4: Perform dynamic analysis to obtain the platform displacement and cable tension. This invention fully considers the influence of the structural changes in the polyester cable, uses an iterative method to calculate and update the static stiffness of the polyester cable, and then obtains the dynamic stiffness of the polyester cable; the lumped mass method is used to better simulate the dynamic characteristics of the polyester cable at various times, making the calculation and analysis more accurate and reliable.

Description

Technical Field

[0001] This invention belongs to the field of marine photovoltaic clean and renewable energy development technology, specifically relating to a method for calculating the dynamic stiffness of polyester cables for deep-water floating photovoltaic platforms. Background Technology

[0002] Solar photovoltaic (PV) power generation is rapidly developing as a green, clean, and renewable energy source. However, the scarcity of land resources has limited the development of onshore PV power plants, making floating PV power plants a new option. Floating PV power projects are mainly built in inland waterways and have higher power generation efficiency than onshore PV.

[0003] Floating photovoltaic (PV) systems in deep water are more complex than those on inland waterways and are affected by the complex marine environment. Floating PV platforms and mooring structures are subjected to the effects of ocean winds, waves, and currents, making them prone to displacement and mooring loads. Polyester cables are a commonly used mooring material; their length varies with tension, time, and load rate. Their elastic modulus is related to the average value of the load within the polyester cable and the magnitude and period of load variation, exhibiting dynamic stiffness characteristics. Currently, polyester cables are mainly used in floating production storage and offloading (PSA) vessels or oil drilling platforms in deep and ultra-deep waters, while their application in offshore renewable energy PV development is still in its early stages.

[0004] Accurately predicting the motion response of a platform and the tension response of polyester cables under complex marine environmental conditions is a crucial aspect of mooring system design. The main factor affecting the maximum displacement of the platform and the maximum tension of the polyester cables is the stiffness of the polyester cables. Among the material properties of polyester cables, determining the dynamic stiffness is particularly important, as the stiffness of the polyester cable is not constant throughout the loading and unloading process but changes over time. This complex material nonlinearity significantly increases the design difficulty. Although existing research has proposed some empirical formulas to determine the dynamic stiffness of polyester cables, these methods are insufficient to accurately reflect the stiffness changes and stress-strain mechanical properties of deep-water floating photovoltaic polyester cables under complex sea conditions. Summary of the Invention

[0005] In view of this, and in response to the gaps in existing technologies and the practical needs of new technology applications, the purpose of this invention is to propose a simple, accurate and efficient method for calculating the dynamic stiffness of polyester cables for deep-water floating photovoltaic platforms, which can provide a new analytical tool for the preliminary design of offshore photovoltaic systems.

[0006] This invention fully considers the influence of structural changes in polyester cables, uses an iterative method to calculate and update the static stiffness of polyester cables, and then obtains the dynamic stiffness of polyester cables; it also uses the lumped mass method to better simulate the dynamic characteristics of polyester cables at various times, making the calculation and analysis more accurate and reliable.

[0007] This invention relates to a floating photovoltaic platform designed for offshore photovoltaic fields. It establishes a coupled numerical model of the polyester cable mooring system for the floating photovoltaic platform and proposes a method for calculating and analyzing the dynamic stiffness of the polyester cables, comprising the following steps:

[0008] 1) Define the initial stiffness value of the synthetic polyester cable and calculate the average tension T at the top of each polyester cable. m1 ;

[0009] 2) Calculate T m1 Substituting the expression for the stiffness of the polyester cable, the average tension T at the tip of each polyester cable is calculated. m2 ;

[0010] 3) Use iteration to find the converged average tension, and substitute the obtained average tension into the dynamic stiffness expression;

[0011] 4) Perform dynamic analysis to obtain the platform displacement and polyester cable tension.

[0012] The specific technical solution adopted by this invention to solve its technical problem is as follows:

[0013] A method for calculating the dynamic stiffness of polyester cables for deep-water floating photovoltaic platforms includes the following steps:

[0014] Step S1: Considering that during operation, the floating photovoltaic platform is simultaneously subjected to the direct effects of sea wind, random waves, and ocean currents, resulting in six degrees of freedom motion. The lower polyester cable structure undergoes tensile deformation as the platform moves, generating mooring tension that acts on the platform, constraining it. The platform, constrained by the polyester cable structure, moves again, creating a scenario where the two are mutually coupled and mutually restrictive. Define the initial stiffness value of the polyester cable and calculate the average tension T at the top of each polyester cable. m1 ;

[0015] Step S2: Calculate T m1 Substituting the expression for the stiffness of the polyester cable, the average tension T at the tip of each polyester cable is calculated. m2 ;

[0016] Step S3: Use iteration to calculate the converged average tension, and substitute the calculated average tension into the dynamic stiffness expression.

[0017] Step S4: Perform dynamic analysis to obtain the platform displacement and polyester cable tension.

[0018] Furthermore, step S1 specifically includes:

[0019] The lumped mass method was used to perform dynamic analysis on the polyester cable mooring system. The polyester cable was considered to be composed of a series of mass nodes and massless springs. Each spring and the two end nodes constituted a unit. The tension and contraction of the polyester cable were simulated by the spring units, while the mass nodes represented the dynamic response of the polyester cable, including its mass, forces, and displacement. Each polyester cable unit was divided into two parts. Half of the mass of two adjacent units was concentrated at the mass nodes, while the nodes at the head and tail only contained part of the mass of the polyester cable units. The nodes constituted the overall mass of the polyester cable. The marine environmental loads applied to the polyester cable acted directly on the nodes. For the polyester cable at the guide hole, the buoyancy and hydrodynamic loads of the polyester cable changed when it floated up and down on the sea surface under the action of the floating platform. The lumped mass method was used to better simulate the dynamic characteristics of the polyester cable at various times.

[0020] Define the initial stiffness value of the polyester cable, and calculate the equilibrium position of the floating platform under stable wind, current, and second-order wave forces in static analysis. Determine the average tension T at the tip of each polyester cable. m1 :

[0021] T m1 =T w (ε t )+(1-2ν)·P o A o +EA nom ·ξ·(dL / dt) / L0 (1)

[0022] Among them, T w (ε t ) represents the relationship between the tension and strain of the polyester cable; ν is Poisson's ratio; P o For hydrostatic external pressure of polyester cable; A o Equivalent area of ​​polyester cable cross-section; EA nom ε is the standard axial stiffness of the polyester cable when the average axial tensile strain is zero; L0 is the initial length of the element; L is the length of the element at any time t; ε t For axial tensile strain, ε t = (L-λL0) / λL0; λ is the amplification factor caused by the thermal expansion and contraction of the polyester cable; ξ is the axial numerical damping coefficient of the polyester cable;

[0023] ξ=(2·m s ·L0 / EA nom ) 1 / 2 ·ξ t , where m s For the unit mass of the polyester cable, ξ t is the target axial damping coefficient of the polyester cable.

[0024] Furthermore, step S2 specifically includes:

[0025] T obtained in step S1 m1 Substitute the static stiffness expression of the polyester cable, update the stiffness of the polyester cable, recalculate the equilibrium position of the floating platform, and obtain the average tension T on the top of each polyester cable. m2 ;

[0026] The expression for the static stiffness of a polyester cable, which is linearly related only to the average tension, is:

[0027]

[0028] Where MBS is the minimum breaking load of the polyester cable, T m1 denoted as , where is the percentage of the average tension on the polyester cable relative to the minimum breaking load, and a and b are the material parameters of the polyester cable during the static analysis phase.

[0029] The linearized dynamic stiffness expression is:

[0030]

[0031] Among them, T m2 represents the percentage determined during the static analysis phase, while c and d are the material parameters for the polyester cable during the dynamic analysis phase.

[0032] Furthermore, step S3 specifically includes:

[0033] Determine T m1 With T m2 Are they equal? ​​If they are equal, then set T. m2 Substitute the values ​​into the dynamic stiffness expression to obtain the dynamic stiffness value; if they are not equal, use T. m2 Substituting the static stiffness expression of the polyester cable, the stiffness of the polyester cable is updated, and the average tension T of the polyester cable is calculated. m3 Then determine T m2 With T m3 Check if they are equal; repeat this step until the calculated average tension of the polyester cable is equal to the value of the previous iteration, indicating that the result has converged.

[0034] Furthermore, step S4 specifically involves: converting the converged T... mn Substitute the dynamic stiffness expression, perform dynamic analysis, and output the dynamic analysis results.

[0035] Compared with the prior art, the present invention and its preferred embodiments have the following advantages:

[0036] 1. Taking full account of the viscoelastic variation characteristics of polyester cables, a dynamic stiffness calculation method is proposed, which can more accurately describe the length and tension response of polyester cables.

[0037] 2. An iterative method is used to calculate and update the static stiffness of the polyester cable, thereby obtaining the dynamic stiffness of the polyester cable, making the calculation more accurate and reliable.

[0038] 3. The lumped mass method was adopted, which can better simulate the dynamic characteristics of the polyester cable at various times. Attached Figure Description

[0039] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0040] Figure 1 This is a schematic diagram of the arrangement of a polyester cable mooring system for a floating photovoltaic platform in one embodiment of the present invention;

[0041] Figure 2 This is a schematic diagram of a polyester cable model in one embodiment of the present invention;

[0042] Figure 3 This is a flowchart simulating a program in one embodiment of the present invention. Detailed Implementation

[0043] To make the features and advantages of this patent more apparent and understandable, specific embodiments are provided below for detailed explanation:

[0044] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used in this specification have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0045] Please refer to Figure 3 This invention provides a method for calculating the dynamic stiffness of polyester cables for deep-water floating photovoltaic platforms, comprising the following four steps:

[0046] Step 1: Define the initial stiffness value of the polyester cable and calculate the average tension T at the top of each polyester cable. m1

[0047] In this embodiment, specifically, such as Figure 1 As shown, during operation, the floating photovoltaic platform is simultaneously subjected to the direct effects of sea wind, random waves, and ocean currents, resulting in six degrees of freedom motion. The lower polyester cable structure undergoes tensile deformation as the platform moves, generating mooring tension that acts on the platform and constrains it. The platform, constrained by the polyester cable structure, moves again, and the two are mutually coupled and mutually restrictive.

[0048] The lumped mass method is used to perform dynamic analysis on the polyester cable mooring system. The polyester cable is considered to consist of a series of mass nodes and massless springs. Each spring and its two end nodes form a unit, such as... Figure 2As shown, the tension and contraction of the polyester cable can be simulated by spring elements, while the mass nodes characterize the dynamic response of the polyester cable, including its mass, stress, and displacement. Each polyester cable element is divided into two parts: half of the mass of two adjacent elements is concentrated at the mass nodes, while the nodes at the beginning and end contain only a portion of the mass of the polyester cable elements. The nodes constitute the overall mass of the polyester cable. The marine environmental loads applied to the polyester cable act directly on the nodes. For the polyester cable at the guide hole, the movement of the floating platform may cause it to float up and down on the sea surface, changing the buoyancy and hydrodynamic loads of the polyester cable. The lumped mass method can better simulate the dynamic characteristics of the polyester cable at various times.

[0049] Select any segment of polyester cable for dynamic analysis, such as... Figure 2 As shown, when external ocean current pressure acts on the polyester cable, the effective tension of the polyester cable can be calculated based on the force balance of the unit:

[0050] T m1 =T w (ε t )+(1-2ν)·P o A o +EA nom ·ξ·(dL / dt) / L0 (1)

[0051] Among them, T w (ε t ) represents the relationship between the tension and strain of the polyester cable; ν is Poisson's ratio; P o For hydrostatic external pressure of polyester cable; A o Equivalent area of ​​polyester cable cross-section; EA nom ε is the standard axial stiffness of the polyester cable when the average axial tensile strain is zero; L0 is the initial length of the element; L is the length of the element at any time t; ε t For axial tensile strain, ε t = (L-λL0) / λL0; λ is the amplification factor caused by the thermal expansion and contraction of the polyester cable; ξ is the axial numerical damping coefficient of the polyester cable, ξ = (2·m s ·L0 / EA nom ) 1 / 2 ·ξ t , where m s For the unit mass of the polyester cable, ξ t is the target axial damping coefficient of the polyester cable.

[0052] Step 2: Calculate T m1 Substituting the expression for the stiffness of the polyester cable, the average tension T at the tip of each polyester cable is calculated. m2 .

[0053] In this embodiment, specifically, the calculated T m1Substitute the static stiffness expression for the polyester cable, update the polyester cable stiffness, recalculate the equilibrium position of the floating platform, and determine the average tension T on each polyester cable. m2 .

[0054] The expression for the static stiffness of a polyester cable that is linearly related only to the average tension is:

[0055]

[0056] Where MBS is the minimum breaking load of the polyester cable, T m1 denoted as the percentage of the average tension on the polyester cable relative to the minimum breaking load, and denoted as a and b as the material parameters of the polyester cable in the static analysis stage, respectively, which are taken as 15 and 0.25.

[0057] The linearized dynamic stiffness expression is further derived as follows:

[0058]

[0059] Among them, T m2 is the percentage determined in the static analysis stage, and c and d are the material parameters of the polyester cable in the dynamic analysis stage, which are taken as 18.5 and 0.33, respectively.

[0060] Step 3: Use iteration to calculate the converged average tension, and substitute the calculated average tension into the dynamic stiffness expression.

[0061] In this embodiment, specifically, T is determined. m1 With T m2 Are they equal? ​​If they are equal, then set T. m2 Substitute the values ​​into the dynamic stiffness expression to obtain the dynamic stiffness value; if they are not equal, use T. m2 Substituting the static stiffness expression of the polyester cable, the stiffness of the polyester cable is updated, and the average tension T of the polyester cable is calculated. m3 Determine T m2 With T m3 The process of checking for equality continues until the average tension of the polyester cable equals the value of the previous iteration, indicating that the result has converged.

[0062] Step 4: Perform dynamic analysis to determine the platform displacement and polyester cable tension.

[0063] In this embodiment, specifically, the converged T mn Substitute the dynamic stiffness expression, perform dynamic analysis, and output the dynamic analysis results.

[0064] This patent is not limited to the above-described preferred embodiment. Anyone can derive other methods for calculating the dynamic stiffness of polyester cables for deep-water floating photovoltaic platforms based on the inspiration of this patent. All equivalent changes and modifications made within the scope of this patent application shall fall within the scope of this patent.

Claims

1. A method for calculating the dynamic stiffness of polyester cables for deep-water floating photovoltaic platforms, characterized in that, Includes the following steps: Step S1: Considering that during operation, the floating photovoltaic platform is simultaneously subjected to the direct effects of sea wind, random waves, and ocean currents, resulting in six degrees of freedom motion. The lower polyester cable structure undergoes tensile deformation as the platform moves, generating mooring tension that acts on the platform, constraining it. The platform, constrained by the polyester cable structure, moves again, creating a scenario where the two are mutually coupled and mutually restrictive. Define the initial stiffness value of the polyester cable and calculate the average tension T at the top of each polyester cable. m1 ; Step S2: Calculate T m1 Substituting the expression for the stiffness of the polyester cable, the average tension T at the tip of each polyester cable is calculated. m2 ; Step S3: Calculate the converged average tension using iteration, and substitute the calculated average tension into the dynamic stiffness expression. Step S4: Perform dynamic analysis to obtain the platform displacement and polyester cable tension; Step S1 is as follows: The lumped mass method was used to perform dynamic analysis on the polyester cable mooring system. The polyester cable was considered to be composed of a series of mass nodes and massless springs. Each spring and the two end nodes constituted a unit. The tension and contraction of the polyester cable were simulated by the spring units, while the mass nodes represented the dynamic response of the polyester cable, including its mass, forces, and displacement. Each polyester cable unit was divided into two parts. Half of the mass of two adjacent units was concentrated at the mass nodes, while the nodes at the head and tail only contained part of the mass of the polyester cable units. The nodes constituted the overall mass of the polyester cable. The marine environmental loads applied to the polyester cable acted directly on the nodes. For the polyester cable at the guide hole, the buoyancy and hydrodynamic loads of the polyester cable changed when it floated up and down on the sea surface under the action of the floating platform. The lumped mass method was used to better simulate the dynamic characteristics of the polyester cable at various times. Define the initial stiffness value of the polyester cable, and calculate the equilibrium position of the floating platform under stable wind, current, and second-order wave forces in static analysis. Determine the average tension T at the tip of each polyester cable. m1 : （1） Among them, T w (ε t ) represents the relationship between the tension and strain of the polyester cable; ν is Poisson's ratio; P o For hydrostatic external pressure of polyester cable; A o Equivalent area of ​​polyester cable cross-section; EA nom ε is the standard axial stiffness of the polyester cable when the average axial tensile strain is zero; L0 is the initial length of the element; L is the length of the element at any time t; ε t For axial tensile strain, ε t =(L-λL0) / λL0; λ is the amplification factor caused by the thermal expansion and contraction of the polyester cable; ξ is the axial numerical damping coefficient of the polyester cable; ξ=(2·m s ·L0 / EA nom ) 1 / 2 ·ξ t , where m s For the unit mass of the polyester cable, ξ t The target axial damping coefficient of the polyester cable; Step S2 is as follows: T obtained in step S1 m1 Substitute the static stiffness expression of the polyester cable, update the stiffness of the polyester cable, recalculate the equilibrium position of the floating platform, and obtain the average tension T on the top of each polyester cable. m2 ; The expression for the static stiffness of a polyester cable, which is linearly related only to the average tension, is: （2） Where MBS is the minimum breaking load of the polyester cable, T m1 denoted as , where is the percentage of the average tension on the polyester cable relative to the minimum breaking load, and a and b are the material parameters of the polyester cable during the static analysis phase. The linearized dynamic stiffness expression is: （3） Among them, T m2 represents the percentage determined during the static analysis phase, while c and d are the material parameters for the polyester cable during the dynamic analysis phase.

2. The method for calculating the dynamic stiffness of polyester cables for deep-water floating photovoltaic platforms according to claim 1, characterized in that: Step S3 is as follows: Determine T m1 With T m2 Are they equal? ​​If they are equal, then set T. m2 Substitute the values ​​into the dynamic stiffness expression to obtain the dynamic stiffness value; if they are not equal, use T. m2 Substituting the static stiffness expression of the polyester cable, the stiffness of the polyester cable is updated, and the average tension T of the polyester cable is calculated. m3 Then determine T m2 With T m3 Check if they are equal; repeat this step until the calculated average tension of the polyester cable is equal to the value of the previous iteration, indicating that the result has converged.

3. The method for calculating the dynamic stiffness of polyester cables for deep-water floating photovoltaic platforms according to claim 2, characterized in that: Step S4 specifically involves: converting the converged T... mn Substitute the dynamic stiffness expression, perform dynamic analysis, and output the dynamic analysis results.

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