A centralized clutch control method for arrayed wave energy conversion devices

Abstract

The present invention discloses a centralized clutch control method for an arrayed wave energy conversion device, comprising: numerical modeling and hydrodynamic analysis of the arrayed wave energy conversion device; establishing a time-domain motion equation for the arrayed wave energy conversion device; establishing a state-space equation for the arrayed wave energy conversion device, using it to replace the convolution term of the time-domain motion equation, calculating the motion state of the arrayed wave energy conversion device, and finally implementing centralized clutch control on the arrayed wave energy conversion device to maximize the capture of wave energy. The present invention fully considers the hydrodynamic interference effect between the wave energy conversion units in the array, takes the overall energy capture efficiency of the arrayed wave energy conversion device as the optimization goal, solves the optimal global control command, and coordinately adjusts the motion of each wave energy conversion unit, showing significant advantages in energy capture efficiency and effectively improving the overall energy absorption capacity of the wave energy conversion device.

Description

Technical Field

[0001] The present invention belongs to the technical field of wave energy power generation, and in particular relates to a centralized clutch control method for an arrayed wave energy conversion device. Background Art

[0002] To cope with the rapid growth of global energy demand, the development of various energy systems is being actively promoted, including solutions for obtaining electricity from ocean energy (such as sea waves, temperature differences, tides, etc.).

[0003] In the field of marine energy, wave energy offers advantages such as wide distribution, 24 / 7 availability, and high energy density. Furthermore, it can be applied to remote islands to power offshore industries such as fish farms and oil and gas platforms. Therefore, wave energy has long been considered a high-quality renewable energy source. Devices that directly or indirectly harvest wave energy using energy harvesters (such as floats or blades) and then convert the mechanical energy of these harvesters into electrical energy using generators are called wave energy converters.

[0004] Although various energy harvesting concepts have been proposed, the capture efficiency of wave energy converters remains low, hindering the large-scale application of wave energy technology. To improve the capture efficiency of wave energy converters, regulating the motion characteristics of wave energy converters through controllers is considered an effective approach. Control algorithms for single wave energy converters have been extensively studied, but the control of multiple wave energy converters in an array is less fully understood. Summary of the Invention

[0005] The purpose of the present invention is to overcome the deficiencies of the above-mentioned prior art and provide a centralized clutch control algorithm for arrayed wave energy conversion devices. The algorithm introduces the influence of the additional inertial force between the devices and the delay function of the radiation effect into the time domain motion equation to fully consider the complex hydrodynamic effects between the two wave energy conversion units, and collects all information of the arrayed wave energy conversion devices (including the motion state of each wave energy conversion device and the wave excitation force it receives) into the central controller for processing. The overall energy capture efficiency is used as the optimization objective function to solve the optimal global control command, which is then used to adjust the motion of each wave energy conversion device to maximize the energy capture efficiency of the entire arrayed wave energy conversion device.

[0006] The present invention is achieved by adopting the following technical solutions:

[0007] A centralized clutch control method for an arrayed wave energy conversion device is proposed, comprising:

[0008] S1, performing numerical modeling and hydrodynamic analysis on an arrayed wave energy conversion device, wherein the arrayed wave energy conversion device comprises a first wave energy conversion unit and a second wave energy conversion unit;

[0009] S2, establishing a time-domain motion equation for the arrayed wave energy conversion device; the time-domain motion equation includes a delay term for the additional mass generated between the wave energy conversion units and the radiation effect of the movement of a single wave energy conversion unit on its adjacent units;

[0010] S3, establishing a state space equation for the arrayed wave energy conversion device, replacing the convolution term of the time domain motion equation with the state space equation, and calculating the motion state of the arrayed wave energy conversion device;

[0011] S4, implementing centralized clutch control on arrayed wave energy conversion devices to maximize energy extraction from waves, including:

[0012] Define the Hamiltonian function ,in, is the motion equation of the array wave energy conversion device, Represents functional capture of wave energy arrays; It is the motion state of the arrayed wave energy conversion device; and is a control command for controlling a single wave energy conversion device, and is the PTO damping coefficient of a single wave energy conversion device; are the movement speeds of the two wave energy conversion units respectively; is the Lagrange multiplier;

[0013] According to the state space equation of the array wave energy conversion device, the Hamiltonian function is expanded and the Lagrange multiplier is obtained by solving the Hamiltonian function.

[0014] ,

[0015] When the Hamiltonian reaches its maximum value, there exists an optimal control sequence ; Where 1 represents loading of a single wave energy conversion unit, and 0 represents unloading of a single wave energy conversion unit; m1 and m2 are the masses of the two wave energy conversion units respectively; and are the additional masses of the two wave energy conversion units, and They are the additional masses generated by the movement of one wave energy conversion unit on the other wave energy conversion unit in the heave direction; are the speeds of the two wave energy conversion units respectively; n is the order of the system.

[0016] In some embodiments of the present invention, the time domain motion equation established by S2 is:

[0017] ,

[0018] ;

[0019] Among them, m1 and m2 are the masses of the two wave energy conversion units; x1, x2, are the displacement, velocity and acceleration of the two wave energy conversion units respectively; is the delay function representing the radiation interaction, is the radiation damping, They represent the self-radiation delay functions of the two wave energy conversion units, indicating the historical impact of the radiation waves generated by the unit's own motion on its own velocity; They represent the delay functions of the radiation effect of the motion of one wave energy conversion unit on another wave energy conversion unit; K is the still water restoring stiffness; is the wave excitation force on the first wave conversion unit, is the wave excitation force on the second wave conversion unit, where represents the real part of the complex function. represents the transfer function of the wave excitation force, represents the amplitude of the regular wave component j, represents the frequency of the regular wave component j, represents the random phase of the regular wave component j; They represent the reaction forces provided by the two wave energy conversion devices from the PTO system, and c represents the damping coefficient of the PTO system.

[0020] In some embodiments of the present invention, the state space equation established in S3 is:

[0021] ;

[0022] in, represents the n×1-dimensional state variable, Represent n×n dimensional, n×1 dimensional, and 1×n dimensional state space matrices respectively.

[0023] In some embodiments of the present invention, the established state space equation is substituted into the time domain motion equation to obtain:

[0024] ;

[0025] Defining new state variables , the time domain motion equation is transformed into a linear differential equation:

[0026] , and the Runge-Kutta method is used to solve the motion state X of the array wave energy conversion device; where,

[0027] ;

[0028] ;

[0029] ;

[0030] ; and are the hydrostatic recovery stiffness of the wave energy conversion unit;

[0031] ,

[0032] .

[0033] In some embodiments of the present invention, during the Hamiltonian solution process, the motion equation is integrated forward from 0 to T, and the control equation is integrated backward from T to 0, including:

[0034] 1. In Simulate the time and obtain the motion state X of the wave energy conversion device by integrating the motion equation from t=0 to t=T;

[0035] 2. Determine the Lagrange multiplier by reversely integrating the governing equation from t=T to t=0 ;

[0036] 3. Given the state vector X and the Lagrange multiplier To determine the control sequence , to maximize the Hamiltonian;

[0037] 4. Iterate the process using the updated control sequence until the control sequence convergence.

[0038] In some embodiments of the present invention, the damping coefficient of the PTO in step S2 is optimized using the following formula:

[0039] ;in, is the radiation damping, Indicates the angular frequency.

[0040] Compared with the existing technology, the advantages and positive effects of the present invention are: in the centralized clutch method for arrayed wave energy conversion devices proposed in the present invention, the complex hydrodynamic interactions between the wave energy conversion devices in the array are fully considered in the designed time domain motion equations, and at the same time it has high practicality and is easy to implement in actual physical equipment. The central controller uses the overall energy capture efficiency as the optimization objective function to solve the optimal global control command. Compared with the control scheme of the array wave energy device without control and the traditional single wave energy conversion device, the algorithm has been verified to show significant advantages in energy capture efficiency. It not only effectively improves the overall energy absorption capacity of the wave energy conversion device, but also provides technical support for the optimized operation of large-scale wave energy arrays.

[0041] Other features and advantages of the present invention will become more apparent after reading the detailed description of the embodiments of the present invention in conjunction with the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0043] Figure 1 This is a schematic diagram of the steps of the centralized clutch control method for the arrayed wave energy conversion device proposed by the present invention;

[0044] Figure 2 Schematic diagram of the structure of the arrayed wave energy conversion device in the present invention;

[0045] Figure 3 Schematic diagram of the numerical simulation model of the arrayed wave energy conversion device in the present invention;

[0046] Figure 4 This is a schematic diagram of the centralized clutch control process in the present invention;

[0047] Figure 5 Schematic diagram of the centralized clutch control principle of the present invention;

[0048] Figure 6 This is a comparison chart of the wave energy capture efficiency of the centralized clutch control method shown in the present invention and the existing uncontrolled and independent control algorithms. DETAILED DESCRIPTION

[0049] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0050] The present invention is directed to an arrayed wave energy conversion device comprising a plurality of wave energy conversion units. In the development of an optimized control algorithm, the interaction of radiation forces is taken into account. That is, the radiation force generated by the movement of the wave energy conversion unit itself affects the motion state of adjacent wave energy conversion units in the array, and the unit itself is also affected by the radiation force generated by the movement of other wave energy conversion units.

[0051] like Figure 1 As shown, taking a wave energy conversion device including two wave energy conversion units as an example (the case of more than two wave energy conversion units can be expanded based on the concept of this embodiment), the centralized clutch control method for an arrayed wave energy conversion device proposed by the present invention comprises the following steps:

[0052] S1: Numerical modeling and hydrodynamic analysis of arrayed wave energy conversion devices.

[0053] The arrayed wave energy conversion device consists of two identical, coordinated oscillating float wave energy conversion devices. The oscillating float wave energy conversion device captures the kinetic energy of waves based on the reciprocating motion of the float, which then drives a generator to generate electricity through a power take-off (PTO) system. The float, connecting rod, and PTO system are its main components. The float is connected to the PTO system via a connecting rod. PTO systems mainly include hydraulic, mechanical transmission, hydraulic, pneumatic, linear motor, and hybrid hydraulic types. The present invention uses a hydraulic PTO system, which mainly includes a hydraulic cylinder, a hydraulic motor, and a generator. The piston rod of the hydraulic cylinder is connected to the connecting rod. The hydraulic cylinder drives the hydraulic motor, which in turn drives the generator to generate electricity.

[0054] Furthermore, the operating principle of the oscillating float wave energy converter is as follows: Under the influence of the periodic motion of waves, the float drives the piston in the hydraulic cylinder to reciprocate vertically via a connecting rod. This reciprocating motion compresses and releases the hydraulic oil in the cylinder, increasing the oil pressure, thereby converting the mechanical energy of the waves into hydraulic energy. The high-pressure hydraulic oil then flows through the pipeline, driving the hydraulic motor, which further converts the hydraulic energy into rotational mechanical energy (i.e., torque and speed of the output shaft). The rotational motion of the output shaft in turn drives a three-phase permanent magnet synchronous generator, which operates based on the law of electromagnetic induction. When the mechanical energy rotates the rotor within the generator, the permanent magnets mounted on the rotor rotate accordingly, disrupting the magnetic field in the stator coils. Since the stator coils consist of three-phase coils, the rotor's rotating magnetic field generates three-phase alternating current with a phase difference of 120° in each coil group. A characteristic of this power generation method is that the rotor speed is synchronized with the frequency of the output current, ensuring stable current output. Furthermore, because permanent magnets do not require an external excitation source, three-phase permanent magnet synchronous generators offer high efficiency, simple structure, and low maintenance costs, making them ideal for the long-term operation of wave energy conversion devices. This entire process achieves efficient conversion of wave mechanical energy into electrical energy.

[0055] The present invention combines Figure 2 As shown, the arrayed wave energy conversion device consists of two oscillating float-type wave energy conversion devices (a first wave energy conversion unit and a second wave energy conversion unit) of identical size and shape. The wave energy conversion unit mainly consists of a float 11, a connecting rod 12, and a PTO 13. The float 11 is a cylindrical floating body with a radius of 2.5m and a draft of 5m. The PTO 13 adopts a hydraulic PTO system, which mainly consists of a piston rod, a hydraulic cylinder, a hydraulic motor, and a generator. The piston rod of the hydraulic cylinder is connected to the connecting rod 12. The hydraulic cylinder drives the hydraulic motor, which drives the generator to generate electricity. Under the action of waves, the float 11 reciprocates in the heave direction and is connected to the PTO 13 through the connecting rod 12. The connecting rod 12 drives the hydraulic cylinder piston to rise and fall in the heave direction, increasing the pressure of the hydraulic oil in the hydraulic cylinder cavity. This process converts mechanical energy into hydraulic energy. The hydraulic oil then drives the hydraulic motor, converting the pressure energy of the liquid in the pipeline into mechanical energy (torque and speed) of the output shaft, which then drives the rear-end generator to generate electricity. The generator uses an existing device: a three-phase permanent magnet synchronous motor.

[0056] Combine Figure 3 and Figure 4 As shown, the present invention uses the GeniE module in DNV-GL's SESAM software to establish a numerical model of a wave energy conversion device that only includes the portion below the waterplane. This is because only the hydrodynamic forces acting on the portion below the waterplane of the float are considered. The specific modeling process is as follows:

[0057] (1) Construct the geometric model of the float through points, lines, and surfaces;

[0058] (2) define the wetted surface of the float;

[0059] (3) Applying a load to the wetted surface of the float;

[0060] (4) Divide the grid and set the grid size to 0.1m;

[0061] (5) Run the analysis and generate a .fem file.

[0062] After obtaining the .fem file, perform frequency domain hydrodynamic analysis on the float. The specific analysis process is as follows:

[0063] (1) Define environmental parameters, i.e., wave direction, frequency range, etc., as well as the draft, center of buoyancy, and center of gravity of the floating body;

[0064] (2) Create a hydrodynamic model;

[0065] (3) Import the .fem panel model file;

[0066] (4) Create a quality model;

[0067] (5) Operational analysis;

[0068] (6) Review and post-process the results to obtain the hydrodynamic parameters of the wave energy conversion device.

[0069] S2: Establishing a time-domain motion equation for the wave energy conversion device; introducing into the time-domain motion equation an additional inertial force term generated between the wave energy conversion units and a delay term of the radiation effect of the movement of a single wave energy conversion unit on its adjacent devices.

[0070] A right-handed coordinate system is used, fixed on the Earth, with the center of the coordinate system fixed on the mean sea surface. The Z axis is positive upward, and the X axis is the direction of propagation of the coastal waves.

[0071] The time domain motion equation of the arrayed wave energy conversion device is shown in formula (1):

[0072] ,

[0073] (1)

[0074] Where m1 and m2 are the masses of the two wave energy conversion units respectively; and are the additional masses of the two wave energy conversion units, and are the additional masses generated by the movement of a wave energy conversion unit on another wave energy conversion unit in the heave direction; x1, x2, are the displacement, velocity and acceleration of the two wave energy conversion units respectively; is the delay function representing the radiation interaction, is the radiation damping, They represent the self-radiation delay functions of the two wave energy conversion units, indicating the historical impact of the radiation waves generated by the unit's own motion on its own velocity; They represent the delay functions of the radiation effect of the motion of one wave conversion unit on another wave conversion unit; K is the still water restoring stiffness. and are the wave excitation force of the first wave energy conversion unit and the wave excitation force of the second wave energy conversion unit, respectively. The calculation formulas are as follows:

[0075] (2)

[0076] (3)

[0077] in, represents the real part of the complex function. represents the transfer function of the wave excitation force, represents the amplitude of the regular wave component j, represents the frequency of the regular wave component j, represents the random phase of the regular wave component j; They represent the reaction forces provided by the two wave energy conversion units from the PTO system, and c represents the damping coefficient of the PTO system.

[0078] The linear damping coefficient of PTO can be optimized using formula (4):

[0079] (4)

[0080] in, is the radiation damping, Indicates the angular frequency.

[0081] The above hydrodynamic parameters, such as added mass at infinite frequency, radiation damping, and transfer function of wave force, are calculated in the hydrodynamic analysis software SESAM-WADAM.

[0082] S3: Establish the state space equation of the arrayed wave energy conversion device, replace the convolution term of the time domain motion equation with the state space equation, and calculate the motion state of the arrayed wave energy conversion device.

[0083] The convolution term in the time-domain motion equation of the arrayed wave energy conversion device in step S2 is replaced by the state-space equation to facilitate the implementation of the control algorithm.

[0084] The state space equation is shown in formula (5):

[0085] (5)

[0086] in, represents the n×1-dimensional state variable, are used to approximate the convolution terms, representing n×n, n×1, and 1×n dimensional state space matrices, respectively. Their expansion formula (6) is shown below:

[0087] , ,

[0088] (6)

[0089] The present invention fully considers the hydrodynamic interaction between adjacent wave energy conversion units and adopts , , The state space matrix is used to approximate the time domain motion equation of the array wave energy conversion device, which involves a delay function representing the radiation effect. In the following control method, the state space matrix is changed , , To simulate the hydrodynamic interaction between adjacent wave energy conversion units.

[0090] The above vectors p and q can be calculated by the least squares method, and the calculation formula (7) is as follows:

[0091] (7)

[0092] Furthermore, by substituting formula (5) into the convolution term of formula (1), the time domain motion equation can be rewritten as:

[0093] (8)

[0094] Furthermore, a new state variable X is defined as shown in formula (9):

[0095] (9)

[0096] 、 These are the motion states of the two wave energy conversion units.

[0097] Then, the time domain motion equation of the float can be rewritten as a linear differential equation:

[0098] (10)

[0099] Specifically:

[0100] ;in,

[0101] ;

[0102] ;

[0103] ;

[0104] ; and are the hydrostatic recovery stiffness of the wave energy conversion unit;

[0105] ;

[0106] .

[0107] The initial condition X(0)=0 is defined, and the state space equation of the arrayed wave energy conversion device is solved using the fourth-order Runge-Kutta method in MATLAB to obtain the motion state of the arrayed wave energy conversion device.

[0108] S4: Implement centralized clutch control on arrayed wave energy conversion devices to maximize energy extraction from waves.

[0109] like Figure 5 As shown in the figure, centralized clutch control optimizes the overall power capture of the array by collecting information from all wave energy conversion devices in the array and performing coordinated control. Specifically, the information of all wave energy conversion devices (referring to the motion state of the wave energy conversion devices and the wave excitation forces they are subjected to) is collected and transmitted to a central controller, which integrates the developed centralized clutch control method and obtains centralized control commands through iterative updates of the algorithm. .

[0110] Clutch control is essentially phase control, which is achieved by controlling the command Alternating loading ( =1) and uninstall ( =0) PTO system to keep the velocity phase of the float consistent with the phase of the wave excitation force, thereby improving the wave energy capture efficiency. The goal of controlling the arrayed wave energy conversion device is to maximize the total energy capture of the arrayed wave energy conversion device. The constraint criterion is to maximize the motion equation (10) of the arrayed wave energy conversion device. This is a constrained optimization problem and is not easy to solve.

[0111] Therefore, in the present invention, a Hamiltonian function H is defined to transform the complex constrained optimization problem into an unconstrained optimization problem. The Hamiltonian function H is shown in formula (12). The Hamiltonian function is a linear function of the control command β and reaches its maximum value when it satisfies formula (18):

[0112] (12)

[0113] in, is the motion equation of the arrayed wave energy conversion device; J is the objective function, which represents the functional capture of the wave energy array, and its expression (13) is as follows:

[0114] (13)

[0115] represents a control command for controlling the first wave energy conversion unit, represents a control command for controlling the second wave energy conversion unit, represents the PTO damping coefficient of the first wave energy conversion unit, represents the PTO damping coefficient of wave energy conversion unit 2, represents the movement speed of the first wave energy conversion unit, Indicates the movement speed of the second wave energy conversion unit.

[0116] Furthermore, the Hamiltonian function H can be written as formula (14):

[0117] (14)

[0118] in, is the Lagrange multiplier, following the governing equation (15):

[0119] (15)

[0120] Through the control equation (16), the Lagrange multiplier can be solved, and then the control command β is updated through the Lagrange multiplier. The solution process is as follows:

[0121] (1) Based on the state space equation of the array wave energy conversion device, expand the Hamiltonian function:

[0122] (16)

[0123] (2) Solve the above Hamiltonian function and calculate the Lagrange multiplier as shown in the following formula (17):

[0124] (17)

[0126] Here, the Hamiltonian is about the binary control sequence When the linear function of satisfies formula (18), the Hamiltonian reaches its maximum value:

[0127] ,

[0128] (18)

[0129] like Figure 5 As shown, according to the Pontryagin maximum principle, when the Hamiltonian is maximized, there exists an optimal control sequence β. It is worth noting that although the motion equation and the control equation of the wave energy array are both first-order partial differential equations, they cannot be solved in parallel because the two formulas are at different times when the initial conditions are. and is the mass of a single wave energy conversion unit, represents the added mass of a wave energy conversion unit, represents the additional mass of another wave energy conversion unit, and Both represent the additional mass generated by the movement of one wave energy conversion unit on another wave energy conversion unit in the heave direction; 1 represents loading a single wave energy conversion unit, and 0 represents unloading a single wave energy conversion unit.

[0130] Specifically, the equations of motion are integrated forward from 0 to T, and the control equations are integrated backward from T to 0. An interactive optimization algorithm is used to solve this problem. First, The simulation is performed at t = 0 and the motion without control is obtained by integrating the equation of motion forward from t = 0 to t = T. The Lagrange multiplier is then determined by integrating the governing equation backward from t = T to t = 0. Finally, given the state vector X and the Lagrange multiplier To determine the control sequence , to maximize the Hamiltonian. The process is iterated using the updated control sequence until the control sequence convergence.

[0131] In a specific embodiment of the present invention, numerical simulations were conducted for an array system consisting of two wave energy converters under three control methods (no control, independent control, and centralized control) to compare their energy capture performance. The incident wave was described using the JONSWAP spectrum, and a wave condition with a significant wave height of 1.4 m and a spectral peak period of 5.5 s was selected. The total simulation duration was 3600 s, with a sampling interval of 0.01 s.

[0132] The wave energy capture efficiency under no control, independent control, and centralized clutch control algorithms is as follows: Figure 6 As shown. In the case of no control, the energy capture efficiency of the arrayed wave energy conversion device is about 12kW in 1 hour; in the independent control mode (i.e., the clutch control algorithm is implemented separately for each of the two wave energy conversion devices, Figure 5 ), its energy capture efficiency increased to approximately 31kW; when the centralized control algorithm was used, the energy capture efficiency was further increased to approximately 43kW. Compared with the uncontrolled case, the centralized control algorithm increased energy capture efficiency by 258.33%; compared with independent control, the increase was 38.7%. This demonstrates that the centralized control algorithm developed in this invention can significantly improve wave energy capture efficiency, demonstrating superior performance advantages.

[0133] It should be pointed out that the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by ordinary technicians in this technical field within the essential scope of the present invention should also fall within the scope of protection of the present invention.

Claims

1. A centralized clutch control method for an arrayed wave energy conversion device, characterized in that: include: S1, performing numerical modeling and hydrodynamic analysis on an arrayed wave energy conversion device, wherein the arrayed wave energy conversion device comprises a first wave energy conversion unit and a second wave energy conversion unit; S2, establishing a time-domain motion equation for the arrayed wave energy conversion device; the time-domain motion equation includes an additional mass generated by the interaction between the wave energy conversion units and a delay term for the radiation effect of the motion of a single wave energy conversion unit on its adjacent units; S3, establishing a state space equation for the arrayed wave energy conversion device, replacing the convolution term of the time domain motion equation with the state space equation, and calculating the motion state of the arrayed wave energy conversion device; S4, implementing centralized clutch control on arrayed wave energy conversion devices to maximize energy extraction from waves, including: Define the Hamiltonian function ;in, is the motion equation of the array wave energy conversion device, Represents functional capture of wave energy arrays; It is the motion state of the arrayed wave energy conversion device; For control sequence; and is a control command for controlling a single wave energy conversion device, and is the PTO damping coefficient of a single wave energy conversion device; are the movement speeds of the two wave energy conversion units respectively; is the Lagrange multiplier; Expand and solve the Hamiltonian function to obtain the Lagrange multiplier, and satisfy ， When the Hamiltonian reaches its maximum value, there exists an optimal control sequence ; Where 1 represents loading of a single wave energy conversion unit, and 0 represents unloading of a single wave energy conversion unit; m1 and m2 are the masses of the two wave energy conversion units respectively; 11 and 22 are the additional masses of the two wave energy conversion units, 12 and 21 are the additional masses generated by the movement of one wave energy conversion unit on the other wave energy conversion unit in the heave direction; are the speeds of the two wave energy conversion units respectively; n is the order of the system.

2. The centralized clutch control method for arrayed wave energy conversion devices according to claim 1, characterized in that: The time domain motion equation established by S2 is: ， ； Among them, x1, x2, are the displacement and acceleration of the two wave energy conversion units, respectively; is the delay function representing the radiation interaction, is the radiation damping, They represent the self-radiation delay functions of the two wave energy conversion units, indicating the historical impact of the radiation waves generated by the unit's own motion on its own velocity; They represent the delay functions of the radiation effect of the motion of one wave energy conversion unit on another wave energy conversion unit; K is the still water restoring stiffness; is the wave excitation force on the first wave conversion unit, is the wave excitation force on the second wave conversion unit, where represents the real part of the complex function. represents the transfer function of the wave excitation force, represents the amplitude of the regular wave component j, represents the frequency of the regular wave component j, represents the random phase of the regular wave component j; They represent the reaction forces provided by the two wave energy conversion units from the PTO system, and c represents the damping coefficient of the PTO system.

3. The centralized clutch control method for arrayed wave energy conversion devices according to claim 1, characterized in that: The state space equation established in S3 is: ； in, represents the n×1-dimensional state variable, Represent n×n dimensional, n×1 dimensional, and 1×n dimensional state space matrices respectively.

4. The centralized clutch control method for arrayed wave energy conversion devices according to claim 3, characterized in that: Substituting the established state space equation into the time domain motion equation, we can obtain: Substitute the established state space equation into the time domain motion equation and define new state variables , transform the time domain motion equation into a linear differential equation: ;in, ； ； ； ; and are the hydrostatic recovery stiffness of the wave energy conversion unit; ； ； The Runge-Kutta method is used to solve the motion state X of the array wave energy conversion device.

5. The centralized clutch control method for arrayed wave energy conversion devices according to claim 1, characterized in that: During the Hamiltonian solution, the equations of motion are integrated forward from 0 to T, and the control equations are integrated backward from T to 0, including: exist Simulate the time and obtain the motion state X of the wave energy conversion device by integrating the motion equation from t=0 to t=T; Determine the Lagrange multiplier by inversely integrating the governing equations from t = T to t = 0 ; Given the state vector X and the Lagrange multiplier To determine the control sequence , to maximize the Hamiltonian; The process is iterated using the updated control sequence until the control sequence convergence.

6. The centralized clutch control method for arrayed wave energy conversion devices according to claim 1, characterized in that: In step S2, the damping coefficient of the PTO is optimized using the following formula: 。

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