Wind wave coupling dynamic indirect approximation method for Spar type floating offshore wind turbine

Abstract

The invention discloses a storm coupling dynamic indirect approximation method for a Spar type floating offshore wind turbine. The storm coupling dynamic indirect approximation method comprises the steps that a system equation of a Spar type floating offshore wind turbine platform is constructed; the system equation of the Spar type floating offshore wind turbine platform is converted into a second-order system; expanding the second-order system to obtain an expanded system; designing an auxiliary system according to the extended system, and obtaining a state estimation value of the auxiliary system; defining an error vector; designing an intermediate virtual control law according to the error vector; according to the error vector and the intermediate virtual control law, designing a change law of an auxiliary system control law; obtaining an auxiliary system control law according to the change law of the auxiliary system control law; and designing an indirect approximator of an unknown nonlinear function according to the state estimation value of the auxiliary system and the control law of the auxiliary system. According to the method, the dynamic influence of the wind wave coupling effect on the Spar type floating offshore wind turbine platform can be effectively approximated, and a new technical approach is provided for coupling dynamic response approximation of the Spar type floating offshore wind turbine platform.

Description

Technical Field

[0001] This invention relates to a wind-wave coupled dynamic indirect approximation method for Spar-type floating offshore wind turbines, belonging to the field of offshore wind turbine platform stability control technology. Background Technology

[0002] With the increasing depletion of fossil fuels, wind energy has received widespread attention as a viable alternative renewable energy source, and wind power, as its primary development form, has naturally become a research hotspot. Compared to onshore turbines, offshore floating wind turbines are located further from residential areas, have better wind resources, and offer higher equivalent utilization hours, thus attracting substantial research attention. In recent years, the rapid development of nearshore wind power has led to market saturation, and research focus has gradually shifted to the more resource-rich deep sea. However, the deep-sea environment is more complex and demanding. Spar-type floating offshore wind turbine platforms must simultaneously withstand the hydrodynamic loads generated by wind and waves, resulting in significant coupling responses among the main structural components, leading to greater challenges to foundation stability. Therefore, to ensure the long-term, safe, and reliable operation of the wind turbine installation, it is essential to systematically assess and effectively mitigate the impact of wind and wave loads on the stability of the Spar-type floating offshore wind turbine platform.

[0003] In the stability control of offshore Spar-type floating wind turbine platforms, effectively handling the wind-wave coupling effect is a key aspect of improving control performance. The unknown function problem introduced by this effect has attracted considerable attention and research from scholars. However, the wind-wave coupling effect involves multiple factors such as wave height, wind speed, and frequency spectrum, and its complexity poses a significant challenge to accurate modeling.

[0004] To address the stability control problem of Spar-type floating offshore wind turbine platforms, existing research has attempted to approximate the unknown function of wind-wave coupling effects. For example, some works have adopted a phased modeling approach to handle wind-wave coupling effects by combining physical equations with empirical parameterization. However, in practical applications, the dynamic behavior of Spar-type floating offshore wind turbine platforms under wind-wave coupling is extremely complex, often presenting a contradiction between empirical parameterization and physical simplification, while also requiring a trade-off between computational resources and multi-scale resolution. This not only makes it difficult to establish accurate mathematical models but also exposes them to the influence of other unknown external disturbances. Therefore, traditional modeling methods struggle to accurately describe wind-wave coupling effects, thus constraining the stability assurance of Spar-type floating offshore wind turbine platforms.

[0005] In Spar-type floating offshore wind turbine platform systems, the approximation of wind-wave coupling effects is crucial because it directly impacts system performance and adaptability. Wind-wave coupling typically introduces complex dynamic disturbances, affecting platform stability and the effectiveness of control strategies; therefore, accurately approximating these disturbances is essential. The accuracy of the approximation is closely related to system stability. If the system fails to effectively characterize the disturbances caused by wind-wave coupling on the Spar-type floating offshore wind turbine platform, it may lead to decreased control performance or even the risk of instability or capsizing. Therefore, for Spar-type floating offshore wind turbine platform systems, research on the approximation of wind-wave coupling effects is not only necessary but also critical.

[0006] Traditional control methods based on fuzzy logic systems directly use the fuzzy logic system as an approximator to approximate unknown nonlinear functions. However, this method has an inherent limitation: the approximation error depends on the selection of empirical parameters in the basis functions. Specifically, how to choose appropriate basis function parameters to minimize the approximation error directly affects the accuracy and stability of the control system. Due to the existence of this approximation error, traditional methods struggle to accurately characterize complex wind-wave coupling effects, thus limiting their approximation and tracking control performance in practical applications.

[0007] In view of this, the present invention is hereby proposed. Summary of the Invention

[0008] To more effectively handle the nonlinear function of wind-wave coupling effect, this invention provides a dynamic indirect approximation method for wind-wave coupling in Spar-type floating offshore wind turbines. On one hand, this invention designs an auxiliary system control law for the Spar-type floating offshore wind turbine platform; on the other hand, it extends the original system equations after transforming them into a second-order system, and obtains the state estimate of the auxiliary system based on the extended system design auxiliary system. Then, by subtracting the auxiliary system control law from the state estimate of the auxiliary system, a nonlinear function approximation value for the wind-wave coupling effect is obtained.

[0009] The technical solution of this invention is:

[0010] According to a first aspect of the present invention, a wind-wave coupled dynamic indirect approximation method for a Spar-type floating offshore wind turbine is provided, comprising:

[0011] The system equations for constructing the Spar-type floating offshore wind turbine platform are established.

[0012] The system equations of the Spar type floating offshore wind turbine platform are transformed into a second-order system.

[0013] The second-order system is extended to obtain an extended system; an auxiliary system is designed based on the extended system, and the state estimate of the auxiliary system is obtained.

[0014] Define the error vector; design the intermediate virtual control law based on the error vector; design the change law of the auxiliary system control law based on the error vector and the intermediate virtual control law; obtain the auxiliary system control law based on the change law of the auxiliary system control law; wherein, the intermediate virtual control law is solved using a first-order filter.

[0015] Based on the state estimate of the auxiliary system and the control law of the auxiliary system, an indirect approximator for the unknown nonlinear function is designed.

[0016] Furthermore, let The second-order system is as follows:

[0017] ;

[0018] in, The deflection angle of the Spar type floating offshore wind turbine platform; = , This represents the torque control input in the Spar-type floating offshore wind turbine platform. This represents the moment of inertia of the Spar type floating offshore wind turbine platform; = , Represents the unknown wind-wave coupling force function; X =  [ x 1 , x 2 ] T ; This indicates transpose.

[0019] Furthermore, let The extended system is as follows:

[0020] ;

[0021] in, For auxiliary system control law The law of change; It is an unknown nonlinear function.

[0022] Furthermore, the auxiliary system is designed as follows:

[0023] ;

[0024] in, express The estimated value, express The estimated value; , Indicates the auxiliary system gain; for The estimated value; For fuzzy basis functions; This represents the ideal weight vector for a fuzzy logic system.

[0025] Furthermore, based on the error variable, the intermediate virtual control law is designed as follows:

[0026] ;

[0027] in, , These represent the first and second intermediate virtual control laws, respectively. , These are the design constants; the error of the second-order system. Represented as: , It is the given expected deflection angle; , The deflection angle of the Spar type floating offshore wind turbine platform; It is the second error variable; It is a positive number.

[0028] Furthermore, based on the error vector and the intermediate virtual control law, the variation law of the auxiliary system control law is designed as follows:

[0029] ;

[0030] in, For auxiliary system control law The law of change; It is a positive constant in the design; As the second error variable, It is the third error variable; Indicates the auxiliary system gain; It is a positive number; express The estimated value, = , , This refers to the deflection angle of the Spar type floating offshore wind turbine platform.

[0031] Furthermore, the indirect approximator of the unknown nonlinear function as follows:

[0032] ;

[0033] in, express The estimated value, , For an unknown nonlinear function, = , This represents the torque control input in the Spar-type floating offshore wind turbine platform. This represents the moment of inertia of the Spar type floating offshore wind turbine platform; This is an auxiliary system control law.

[0034] According to a second aspect of the present invention, a terminal device is provided, comprising a memory, a processor, and a program stored in the memory and executable by the processor, wherein the processor, when executing the program, implements the wind-wave coupled dynamic indirect approximation method for a Spar-type floating offshore wind turbine as described in any of the preceding claims.

[0035] The beneficial effects of this invention are:

[0036] Compared to traditional fuzzy approximators that directly approximate unknown nonlinear functions using fuzzy logic systems, the approximation error is difficult to characterize due to a lack of experience in parameter selection. In contrast, the approximation error of the indirect approximator designed in this invention can be characterized by the state error of the auxiliary system; that is, increasing the gain of the auxiliary system reduces the approximation error. Simulation results show that, under the same control parameters, the output curve of the proposed indirect approximation method has a smaller approximation error compared to the traditional model output curve obtained using fuzzy logic systems. Furthermore, magnified details reveal that the approximation error obtained using traditional fuzzy logic systems is within the range of (-20, 20), while the approximation error of the proposed indirect approximator for unknown nonlinear functions is smaller than that of the traditional FLS approximator. This indicates that the proposed method can effectively approximate the dynamic impact of wind-wave coupling on the Spar-type floating offshore wind turbine platform, providing a new technical approach for approximating the coupled dynamic response of the Spar-type floating offshore wind turbine platform. Attached Figure Description

[0037] Figure 1 This is a diagram of the Spar type floating offshore wind turbine platform provided according to an embodiment of the present invention.

[0038] Figure 2 This is a schematic diagram of the approximation error between the FLS approximation method and the approximation method proposed in this invention.

[0039] Figure 3 The diagram shows the approximation results of the FLS approximation method and the approximation method proposed in this invention.

[0040] Figure 4 This is a flowchart of the indirect approximation method proposed in this invention. Detailed Implementation

[0041] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of this application can be arbitrarily combined with each other.

[0042] To address the requirement for high stability and adaptability of Spar-type floating offshore wind turbine platforms under wind and wave interference, it is necessary to overcome the difficulties and low accuracy of existing methods in modeling the nonlinear function of wind-wave coupling effects. Therefore, an indirect approximation method is proposed to approximate the unknown nonlinear function introduced by the wind-wave coupling effect on the Spar-type floating offshore wind turbine platform system. A specific implementation example is given below:

[0043] Example 1: As Figures 1-4 As shown, according to a first aspect of the present invention, a wind-wave coupled dynamic indirect approximation method for a Spar-type floating offshore wind turbine is provided, comprising: constructing the system equations of the Spar-type floating offshore wind turbine platform; transforming the system equations of the Spar-type floating offshore wind turbine platform into a second-order system; extending the second-order system to obtain an extended system; designing an auxiliary system based on the extended system and obtaining the state estimate of the auxiliary system; defining an error vector; designing an intermediate virtual control law based on the error vector; designing a variation law of the auxiliary system control law based on the error vector and the intermediate virtual control law; obtaining the auxiliary system control law based on the variation law of the auxiliary system control law; wherein, the intermediate virtual control law is solved using a first-order filter; and designing an indirect approximator of an unknown nonlinear function based on the state estimate of the auxiliary system and the auxiliary system control law.

[0044] The construction of the present invention is further described below:

[0045] 1. Problem statement.

[0046] In this invention, the structure of the Spar-type floating offshore wind turbine platform can be considered as a swinging model, wherein the physical model of the Spar-type floating offshore wind turbine platform is as follows: Figure 1 As shown.

[0047] According to the Newton-Euler formula, the system equations for the Spar type floating offshore wind turbine platform are:

[0048] (1).

[0049] in, , , These represent the states of the Spar type floating offshore wind turbine platform, namely, deflection angle, angular velocity, and angular acceleration. , , These represent the inertia, damping coefficient, and elastic modulus of the Spar-type floating offshore wind turbine platform, respectively; in addition, The unknown wind-wave coupling force function represents the wind-wave coupling force experienced by the Spar type floating offshore wind turbine platform, which is treated as an external disturbance. This represents the torque control input in the Spar type floating offshore wind turbine platform.

[0050] For the unknown wind-wave coupling force function This can be simplified as follows:

[0051] (2).

[0052] in, and These represent the wind force coefficient and real-time wind speed, respectively. and These represent the wave force coefficient and the real-time wave height, respectively. , and These represent the coupling coefficient, wave frequency, and phase difference between the wind and wave interactions, respectively. Due to the complexity of wind-wave coupling effects, accurate modeling of the wind-wave coupling force is a significant challenge, posing a substantial obstacle to the stability control of the Spar-type floating offshore wind turbine platform. To address the difficulty in modeling the wind-wave coupling force on the Spar-type floating offshore wind turbine platform system, this invention employs an approximation method to approximate this unknown wind-wave coupling force function. Therefore, the research objective of this invention is to obtain an approximation value of the unknown wind-wave coupling function by designing a virtual control law and an auxiliary system.

[0053] 2. The approximator of this invention is designed as follows:

[0054] First, regarding the approximation problem of the wind-wave coupling force function experienced by the Spar-type floating offshore wind turbine platform, we first let... The system equations of the Spar type floating offshore wind turbine platform corresponding to equation (1) are transformed into a second-order system, as follows:

[0055] (3).

[0056] Among them, control law = , = ; X =  [ x 1 , x 2 ] T Based on this, the error of the second-order system It can be represented as , It is a given expected deflection angle; note that... It is a smooth and bounded reference signal, making and its derivative It is continuous and bounded.

[0057] Based on the dynamic surface control method, the following first-order filter is introduced:

[0058] , ;(4)。

[0059] in, For the first One auxiliary variable; for When =0, the first The auxiliary variable, i.e. the first auxiliary variable. Initial values ​​for each auxiliary variable; for When =0, the first An intermediate virtual control law; For the first There are two intermediate virtual control laws, namely the first and second intermediate virtual control laws. For the first There are n positive numbers, and they satisfy:

[0060] (5).

[0061] make Let the output error of the first-order filter be represented by:

[0062] (6).

[0063] in It is a continuous and bounded function, and satisfies ,in It is a constant.

[0064] The above , , , It is a function of time, that is , , ,

[0065] To design the unknown nonlinear function in the second-order system of equation (3) The indirect approach made Therefore, the second-order system of equation (3) is extended to obtain the extended system as follows:

[0066] (7).

[0067] in, For auxiliary system control law The law of change; It is an unknown nonlinear function.

[0068] Unknown nonlinear function Fuzzy logic system can be used Approximation, that is:

[0069] (8).

[0070] in, for The estimated value; for The estimated value; For fuzzy basis functions; Indicates transpose; The ideal weight vector for the fuzzy logic system; It is the fuzzy approximation error.

[0071] According to (8) Mode, and Minimum approximation error of fuzzy logic system It is given by the following formula:

[0072] (9).

[0073] because Then there is .

[0074] For the extended system of equation (7), its auxiliary system can be designed as follows:

[0075] (10).

[0076] in, , Indicates the auxiliary system gain; , They are respectively , The first derivative; express The estimated value, express The estimated value.

[0077] The state error of the auxiliary system is given by the following formula:

[0078] (11).

[0079] in, express and The difference; express and The difference; express and The difference;

[0080] make x ̃  = [ x ̃ 2 , x ̃ 3 ] T Then (11) can be represented in the following vector form:

[0081] (12).

[0082] in, x  = [ x 2 , x 3 ] T , A= 0 1 0 0 ,B=[0,1 ] T , C=[0,1 ] T , L=[ L 1 , L 2 ] T , It is the auxiliary system gain vector, the vector selection. Make It is a strict Hurwitz matrix.

[0083] Define error variables as follows:

[0084] , (13).

[0085] Based on the error variable, the intermediate virtual control law is designed as follows:

[0086] (14).

[0087] Based on the error variable and the intermediate virtual control law, the variation law of the auxiliary system control law is designed as follows:

[0088] (15).

[0089] in, , and It is a positive constant in the design.

[0090] The adaptive law is designed as follows:

[0091] (16).

[0092] in, and It is a positive constant in the design.

[0093] Indirect approximator for unknown nonlinear functions as follows:

[0094] (17).

[0095] Next, consider the following Lyapunov function. :

[0096] (18).

[0097] Where P is a positive definite matrix, it satisfies the following equation:

[0098] (19).

[0099] in, Given a positive constant, Let represent the second-order identity matrix. In equation (18) Differentiation yields:

[0100] (20).

[0101] in, = -2, and select >2.

[0102] Substituting (14), (15), and (16) into (20), we get:

[0103] (twenty one).

[0104] in: express The smallest eigenvalue;

[0105] (twenty two).

[0106] (twenty three).

[0107] From equation (21), we can conclude that Bounded, meaning the extended system is stable.

[0108] It should be noted that, regarding the wind-wave coupling effect interference problem in the Spar-type floating offshore wind turbine platform system, some scholars have designed a fuzzy logic system based on fuzzy logic to handle the influence of external disturbances and have proven its effectiveness. This allows the unknown function of the wind-wave coupling effect on the Spar-type floating offshore wind turbine platform to be approximated. However, traditional approximators rely on the selection of empirical parameters. Compared with existing technical solutions based on traditional fuzzy logic systems, this invention proposes a method to approximate the Spar-type floating offshore wind turbine platform under the influence of external wind-wave coupling effects, which has the following advantages:

[0109] (1) To address the difficulty in modeling the wind-wave coupling effect, considering the external wind-wave interference in the Spar type floating offshore wind turbine platform system, this invention utilizes an auxiliary system to transform the problem of modeling the wind-wave coupling effect into a problem of approximating a nonlinear function and thus solves the problem.

[0110] (2) The approximation error of the indirect fuzzy approximator proposed in this invention can be characterized by the auxiliary system state error, that is, the expression of the approximation error is equivalent to the auxiliary system state error, which is different from the traditional direct approximator whose approximation error depends on the selection of empirical parameters.

[0111] As can be seen from the above technical solutions, a Spar-type floating offshore wind turbine platform system is mainly affected by the external wind-wave coupling effect, causing it to be in an unstable state. The accuracy of modeling this external wind-wave coupling effect determines the effectiveness of the system's control. If the modeling accuracy is low, the Spar-type floating offshore wind turbine platform system may be at risk of capsizing when subjected to wind and wave interference. Therefore, addressing the wind-wave coupling effect is urgent and of great importance. Thus, this invention proposes an unknown function approximation method for the wind-wave coupling effect to solve the problem of external wind-wave coupling effect interference, avoiding the complex modeling process of traditional methods.

[0112] like Figure 2The figure shows the error curves for approximating the wind-wave coupling effect function using the method proposed in this invention compared to the traditional fuzzy logic system (FLS). Visual analysis of the simulation shows that the nonlinear function approximation model constructed based on this invention exhibits superior fitting performance. Under the same control parameters, the approximation value obtained by the method proposed in this invention (…) NEW) and the traditional approximation value obtained by using fuzzy logic systems for unknown functions ( Compared to FLS, the indirect approximation method proposed in this invention has a smaller approximation error in its output curve compared to the traditional model output curve obtained using a fuzzy logic system. In the magnified details, it can also be seen that the approximation error obtained using a fuzzy logic system is in the range of (-20, 20), while the indirect approximation error of the proposed in this invention for unknown nonlinear functions is smaller than that of the traditional FLS approximator.

[0113] like Figure 3 The figure shows the approximation effect of the FLS approximation method and the approximation method proposed in this invention. As can be seen from the figure, the approximation value of the unknown nonlinear function obtained by the indirect approximator proposed in this invention is closer to the true value than the approximation value obtained by the traditional FLS. This indicates that the method of this invention can effectively approximate the dynamic influence of wind and wave coupling effect on the Spar type floating offshore wind turbine platform, and provides a new technical approach for approximating the coupled dynamic response of the Spar type floating offshore wind turbine platform.

[0114] According to a second aspect of the present invention, a terminal device is provided, including a memory, a processor, and a program stored in the memory and executable by the processor, wherein the processor executes the program to implement the wind-wave coupled dynamic indirect approximation method for a Spar-type floating offshore wind turbine as described in any of the above embodiments.

[0115] The specific embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A wind-wave coupled dynamic indirect approximation method for a Spar type floating offshore wind turbine, characterized in that, The method comprises the following steps: constructing system equations of a Spar type floating offshore wind turbine platform; transforming the system equations of the Spar type floating offshore wind turbine platform into a second-order system; extending the second-order system to obtain an extended system; designing an auxiliary system according to the extended system, and obtaining state estimation values of the auxiliary system; defining an error vector; designing an intermediate virtual control law according to the error vector; designing a change law of an auxiliary system control law according to the error vector and the intermediate virtual control law; and obtaining the auxiliary system control law according to the change law of the auxiliary system control law; designing an indirect approximator of an unknown nonlinear function according to the state estimation values of the auxiliary system and the auxiliary system control law.

2. The wave coupled dynamic indirect approximation method for Spar type floating offshore wind turbines according to claim 1, characterized in that, Let The second order system is then as follows: ； wherein, is the yaw angle of the Spar type floating offshore wind turbine platform; , represents the control input of the moment in the Spar type floating offshore wind turbine platform, represents the inertia of the Spar type floating offshore wind turbine platform; , represents the unknown wind-wave coupling force function; ; represents the transpose.​​ 3. The wave coupled dynamic indirect approximation method for Spar type floating offshore wind turbines according to claim 2, characterized in that, Let , the extended system is as follows: ； wherein is the auxiliary system control law is the variation law; is an unknown nonlinear function.

4. The wave coupled dynamic indirect approximation method for Spar type floating offshore wind turbines according to claim 3, characterized in that, The auxiliary system is designed as follows: ； wherein represents an estimate of , represents an estimate of ; , represents an auxiliary system gain; is an estimate of ; is a fuzzy basis function; is a fuzzy logic system ideal weight vector.

5. The wave coupled dynamic indirect approximation method for Spar type floating offshore wind turbines according to claim 1, characterized in that, The intermediate virtual control law is designed according to the error variable as follows: ； wherein, , respectively denote the first and second intermediate virtual control laws; , is a design normal number; the error of the second-order system is expressed as: , is a given desired deflection angle; , is the deflection angle of the Spar type floating offshore wind turbine platform; is a second error variable; is a normal number.

6. The wave coupled dynamic indirect approximation method for Spar type floating offshore wind turbines according to claim 1, characterized in that, The change law of the auxiliary system control law is designed according to the error vector and the intermediate virtual control law as follows: ； wherein is a change law for the auxiliary system control law ; is a design normal number; is a second error variable, is a third error variable; denotes an auxiliary system gain; is a normal number; denotes an estimated value of , = , , is a deflection angle of a Spar type floating offshore wind turbine platform.

7. The wave coupled dynamic indirect approximation method for Spar type floating offshore wind turbines according to claim 1, characterized in that, Indirect approximators of unknown nonlinear functions As follows: ； wherein represents an estimate of , is an unknown nonlinear function, = , denotes the control input of the moment in a Spar type floating offshore wind turbine platform, denotes the inertia of the Spar type floating offshore wind turbine platform; is the auxiliary system control law.

8. A terminal device, comprising: The method comprises a memory, a processor, and a program stored in the memory and executable by the processor, and the processor executes the program to implement the method for indirect approximation of wind-wave coupling dynamics of a Spar type floating offshore wind turbine according to any one of claims 1-7.

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