Centralized clutch control method for arrayed wave energy conversion device

Abstract

The invention discloses a centralized clutch control method for an arrayed wave energy conversion device. The centralized clutch control method comprises the steps that numerical modeling and hydrodynamic analysis are conducted on the arrayed wave energy conversion device; establishing a time domain motion equation of the array wave energy conversion device; a state-space equation of the arrayed wave energy conversion device is established, the state-space equation is used for replacing a convolution term of a time domain motion equation, the motion state of the arrayed wave energy conversion device is obtained through calculation, and finally centralized clutch control is carried out on the arrayed wave energy conversion device to capture wave energy to the maximum extent. According to the method, the hydrodynamic interference effect between the wave energy conversion units in the array is fully considered, the overall energy capture efficiency of the array type wave energy conversion device is taken as an optimization target, the optimal global control command is solved, the movement of each wave energy conversion unit is cooperatively adjusted, and the method has a remarkable advantage in the aspect of energy capture efficiency and is suitable for large-scale popularization and application. And the overall energy absorption capacity of the wave energy conversion device is effectively improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of wave energy power generation, and specifically 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 marine energy sources such as ocean waves, temperature differences, and tides.

[0003] In the field of marine energy, wave energy has the advantages of wide distribution, availability all day long, and relatively high energy density. In addition, it can be applied to remote islands to supply power to offshore industries such as fish farms and oil and gas platforms. Therefore, wave energy has always been regarded as a high-quality renewable energy source. A device that directly or indirectly collects the energy of ocean waves through an energy capture body (such as a float or a blade) and then converts the mechanical energy of these capture bodies into electrical energy through a generator is called a wave energy conversion device.

[0004] Although various concepts for energy collection have been proposed at present, the capture efficiency of wave energy conversion devices is still relatively low, which is one of the obstacles hindering the large-scale application of wave energy technology. To improve the capture efficiency of wave energy conversion devices, adjusting the motion characteristics of wave energy conversion devices through a controller is considered an effective approach. Control algorithms for individual wave energy conversion devices in the prior art have been widely studied, but the control of multiple wave energy conversion devices in an array is not 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 an arrayed wave energy conversion device. An additional inertial force influence between devices and a delay function of radiation effects are introduced into the time-domain motion equation to fully consider the complex hydrodynamic interactions between two wave energy conversion units. All information of the arrayed wave energy conversion device (including the motion state of each wave energy conversion device and the wave excitation force received) is collected in a central controller for processing. The overall energy capture efficiency is used as an optimization objective function to solve for 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 implemented by adopting the following technical solutions: A centralized clutch control method for an arrayed wave energy conversion device is proposed, including: S1, numerically modeling and performing hydrodynamic analysis on the arrayed wave energy conversion device; the arrayed wave energy conversion device is composed of a first wave energy conversion unit and a second wave energy conversion unit; S2. Establish the time-domain motion equation of the arrayed wave energy conversion device; introduce the added mass generated between wave energy conversion units and the delay term of the radiation effect of the motion of a single wave energy conversion unit on its adjacent units into the time-domain motion equation; 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; S4. Implement centralized clutch control on the arrayed wave energy conversion device to maximize the extraction of energy from waves, including: Define the Hamiltonian function , where, is the motion equation of the arrayed wave energy conversion device, represents the functional capture of the wave energy array; is the motion state of the arrayed wave energy conversion device; and are control commands for controlling a single wave energy conversion device, and are the PTO damping coefficients of a single wave energy conversion device; are the motion speeds of two wave energy conversion units respectively; is the Lagrange multiplier; Expand the Hamiltonian function according to the state-space equation of the arrayed wave energy conversion device, solve the Hamiltonian function to obtain the Lagrange multiplier. When satisfying , , the Hamiltonian reaches the maximum value, and there exists an optimal control sequence ; where, 1 represents loading a single wave energy conversion unit, 0 represents unloading a single wave energy conversion unit; m1 and m2 are the masses of two wave energy conversion units respectively; and are the added masses of two wave energy conversion units respectively, and are the added masses generated by the motion of a wave energy conversion unit in the heaving direction on another wave energy conversion unit respectively; are the speeds of two wave energy conversion units respectively; n is the order of the system.

[0007] In some embodiments of the present invention, the time-domain motion equation established in S2 is: , ; where, m1 and m2 are the masses of two wave energy conversion units respectively; x1, x2, They are respectively the displacements, velocities, and accelerations of two wave energy conversion units; is the delay function representing the radiation interaction, is the radiation damping, respectively represent the self-radiation delay functions of two wave energy conversion units, indicating the historical influence of the radiation waves generated by the unit's own motion on its own velocity; respectively represent the delay functions of the motion of one wave energy conversion unit on the radiation effect of another wave energy conversion unit; K is the hydrostatic restoring stiffness; is the wave excitation force received by the first wave conversion unit, is the wave excitation force received by the second wave conversion unit, where, represents taking 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; respectively represent the reaction forces provided by the PTO system to two wave energy conversion devices, and c represents the damping coefficient of the PTO system.

[0008] In some embodiments of the present invention, the state space equation established in S3 is: ; Wherein, represents the n×1 dimensional state variable, respectively represent the n×n dimensional, n×1 dimensional, and 1×n dimensional state space matrices.

[0009] In some embodiments of the present invention, substituting the established state space equation into the time-domain motion equation gives: ; Define a new state variable , and the time-domain motion equation is transformed into a linear differential equation: , and the Runge-Kutta method is used to solve for the motion state X of the arrayed wave energy conversion device; wherein, ; ; ; ; and are respectively the hydrostatic restoring stiffnesses of the wave energy conversion units; , .

[0010] In some embodiments of the present invention, during the Hamiltonian solving process, the motion equation is integrated forward from 0 to T, and the control equation is integrated backward from T to 0, including: 1. At carry out simulation, and by integrating the motion equation forward from t = 0 to t = T, obtain the motion state X of the wave energy conversion device; 2. Determine the Lagrange multiplier by integrating the control equation backward from t = T to t = 0 ; 3. Given the state vector X and the Lagrange multiplier to determine the control sequence to maximize the Hamiltonian; 4. Use the updated control sequence iterative process until the control sequence converges.

[0011] In some embodiments of the present invention, the damping coefficient of the PTO in step S2 is optimized by the following formula: ; where is the radiation damping, represents the angular frequency.

[0012] Compared with the prior art, the advantages and positive effects of the present invention are as follows: In the centralized clutch method for the arrayed wave energy conversion device proposed by the present invention, the complex hydrodynamic interaction between the wave energy conversion devices in the array is fully considered in the designed time-domain motion equation, and it has high practicability and is convenient to be implemented in actual physical devices. The central controller solves the optimal global control command with the overall energy capture efficiency as the optimization objective function. Compared with the control schemes of the array wave energy device without control and the traditional single wave energy conversion device, this algorithm has been verified to show significant advantages in terms of energy capture efficiency, not only effectively improving the overall energy absorption capacity of the wave energy conversion device, but also providing technical support for the optimized operation of large-scale wave energy arrays.

[0013] After reading the detailed description of the embodiments of the present invention in conjunction with the drawings, other features and advantages of the present invention will become clearer. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0015] Figure 1Schematic diagram of the steps of the centralized clutch control method for the arrayed wave energy conversion device proposed by the present invention; Figure 2 Schematic diagram of the structure of the arrayed wave energy conversion device in the present invention; Figure 3 Schematic diagram of the numerical simulation model of the arrayed wave energy conversion device in the present invention; Figure 4 Schematic diagram of the centralized clutch control process in the present invention; Figure 5 Schematic diagram of the centralized clutch control principle in the present invention; Figure 6 Comparison chart of the wave energy capture efficiency between the centralized clutch control method shown in the present invention and the existing non-control and independent control algorithms; Specific embodiments

[0016] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0017] The present invention aims at an arrayed wave energy conversion device including multiple wave energy conversion units. In the development of the optimized control algorithm, the interaction of radiation forces is considered, that is, the radiation forces generated by the movement of the wave energy conversion units themselves will affect the movement states of the adjacent wave energy conversion units in the array, and at the same time, it is also affected by the radiation forces generated by the movement of other wave energy conversion units.

[0018] As Figure 1 shown, taking a wave energy conversion device including two wave energy conversion units as an example (the case of more than two can be extended according to the idea of this embodiment), the centralized clutch control method for the arrayed wave energy conversion device proposed by the present invention has the following steps: S1: Perform numerical modeling and hydrodynamic analysis on the arrayed wave energy conversion device.

[0019] The arrayed wave energy conversion device is composed of two identical and coordinated oscillating buoy type wave energy conversion devices. The oscillating buoy type wave energy conversion device is a device that captures the kinetic energy of waves based on the reciprocating motion of the buoy with the waves, and then drives a generator to generate electricity through a power take-off (PTO) system. The buoy, connecting rod, and PTO system are its main components. Among them, the buoy is connected to the PTO system through a connecting rod. The PTO system mainly includes hydraulic type, mechanical transmission type, hydraulic type, pneumatic type, linear motor type, and hybrid hydraulic type, etc. In this invention, a hydraulic PTO system is selected, and this system mainly includes a hydraulic cylinder, a hydraulic motor, and a generator. The piston rod of the hydraulic cylinder is connected to the connecting rod, and the hydraulic cylinder drives the hydraulic motor to work, and the hydraulic motor drives the generator to generate electricity.

[0020] Furthermore, the working principle of the oscillating buoy type wave energy conversion device is as follows: Under the action of the periodic motion of the waves, the buoy drives the piston in the hydraulic cylinder to reciprocate vertically through the connected connecting rod. This reciprocating motion increases the oil pressure by compressing and releasing the hydraulic oil in the hydraulic cylinder, thereby converting the mechanical energy of the waves into hydraulic energy. Subsequently, the high-pressure hydraulic oil flows through the pipeline to drive the hydraulic motor, and the hydraulic motor further converts the hydraulic energy into rotational mechanical energy (i.e., the torque and rotational speed of the output shaft). The rotational motion of the output shaft then drives a three-phase permanent magnet synchronous generator, and its working principle is based on the law of electromagnetic induction. When mechanical energy causes the rotor inside the generator to rotate, the permanent magnets installed on the rotor rotate accordingly, cutting the magnetic field in the stator coil. Since the stator coil is composed of three-phase coils, the rotating magnetic field of the rotor generates three-phase alternating current with a phase difference of 120° in each coil. The characteristic of this power generation method is that the rotational speed of the rotor is synchronized with the frequency of the output current, ensuring a stable output of the current. At the same time, since the permanent magnet does not require an external excitation source, the three-phase permanent magnet synchronous generator has high efficiency, simple structure, and low maintenance cost, and is very suitable for the long-term operation of the wave energy conversion device. This entire process realizes the efficient conversion from wave mechanical energy to electrical energy.

[0021] In this invention, combined with Figure 2As shown in the figure, the arrayed wave energy conversion device consists of two oscillating buoy type wave energy conversion devices (the first wave energy conversion unit and the second wave energy conversion unit) with exactly the same size and shape; the wave energy conversion unit mainly consists of a buoy 11, a connecting rod 12, and a PTO 13. The buoy 11 is a cylindrical floating body with a radius of 2.5 m and a draft of 5 m. The PTO 13 uses 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 to act, and the hydraulic motor drives the generator to generate electricity. The buoy 11 makes a reciprocating motion in the heaving direction under the action of waves and is connected to the PTO 13 through the connecting rod 12. The connecting rod 12 drives the piston of the hydraulic cylinder to make a heaving motion in the heaving 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 the mechanical energy (torque and speed) of the output shaft, and then driving the generator at the rear end to generate electricity. The generator uses existing equipment: a three-phase permanent magnet synchronous motor.

[0022] Combined with Figure 3 and Figure 4 As shown, the present invention uses the GeniE module in the DNV-GL SESAM software to establish a numerical model of the wave energy conversion device that only includes the part below the waterline surface because only the hydrodynamic forces acting on the part of the buoy below the waterline surface are considered. The specific modeling process is as follows: (1) Construct the geometric model of the buoy through points, lines, and surfaces; (2) Define the wet surface of the buoy; (3) Apply loads to the wet surface of the buoy; (4) Divide the mesh, and set the mesh size to 0.1 m; (5) Run the analysis to generate a.fem file.

[0023] After obtaining the.fem file, perform a frequency-domain hydrodynamic analysis on the buoy. The specific analysis process is as follows: (1) Define the environmental parameters, that is, parameters such as the direction and frequency range of the waves, as well as parameters such as the draft, buoyancy center, and center of gravity position of the floating body; (2) Create a hydrodynamic model; (3) Import the.fem panel model file; (4) Create a mass model; (5) Run the analysis; (6) View and post-process the results to obtain the hydrodynamic parameters of the wave energy conversion device.

[0024] S2: Establish the time-domain motion equation of the wave energy conversion device; an additional inertial force term generated between wave energy conversion units and a delay term of the radiation effect of the motion of a single wave energy conversion unit on its adjacent device are introduced into the time-domain motion equation.

[0025] Adopt a right-handed coordinate system fixed on the earth, with the coordinate system center fixed on the mean sea surface. The Z-axis is positive upward, and the X-axis is along the wave propagation direction.

[0026] The time-domain motion equation of the arrayed wave energy conversion device is shown in formula (1): , (1) Among them, m1 and m2 are the masses of two wave energy conversion units respectively; and are the added masses of two wave energy conversion units respectively, and are the added masses generated by the motion of one wave energy conversion unit in the heaving direction on the other wave energy conversion unit; x1, x2, are the displacements, velocities and accelerations of two wave energy conversion units respectively; is a delay function representing the radiation interaction, is the radiation damping, represent the self-radiation delay functions of two wave energy conversion units respectively, indicating the historical influence of the radiation wave generated by the unit's own motion on its own velocity; represent the delay functions of the radiation effect of the motion of one wave conversion unit on the other wave conversion unit respectively; K is the hydrostatic restoring stiffness. and are the wave excitation forces of the first wave energy conversion unit and the second wave energy conversion unit respectively, and the calculation formulas are as follows: (2) (3) Among them, represents taking 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; represent the reaction forces provided by the PTO system for two wave energy conversion units respectively, and c represents the damping coefficient of the PTO system.

[0027] The linear damping coefficient of the PTO can be optimized using formula (4): (4) Among them, is the radiation damping, represents the angular frequency.

[0028] The above hydrodynamic parameters, such as the added mass at infinite frequency, radiation damping, and transfer function of wave force, are all calculated in the hydrodynamic analysis software SESAM-WADAM.

[0029] S3: Establish the state-space equation of the arrayed wave energy conversion device, replace the convolution term in the time-domain motion equation with the state-space equation, and calculate the motion state of the arrayed wave energy conversion device.

[0030] Replace the convolution term in the time-domain motion equation of the arrayed wave energy conversion device in step S2 with the state-space equation to facilitate the implementation of the control algorithm.

[0031] The state-space equation is as shown in formula (5): (5) Among them, represents the n×1 dimensional state variable, is used to approximate the convolution term, and respectively represent the n×n dimensional, n×1 dimensional, and 1×n dimensional state-space matrices. Their expansion formula (6) is as follows: , , (6) The present invention fully considers the hydrodynamic interaction between adjacent wave energy conversion units, and adopts , , The state-space matrix to approximate the delay function representing the radiation effect involved in the time-domain motion equation of the arrayed wave energy conversion device. In the following control method, the hydrodynamic interaction between adjacent wave energy conversion units is simulated by changing the state-space matrix , , .

[0032] The above vectors p and q can be calculated by the least squares method, and the calculation formula (7) is as follows: (7) Furthermore, substituting formula (5) into the convolution term of formula (1), the time-domain motion equation can be rewritten as: (8) Furthermore, define a new state variable X as shown in formula (9): (9) , They are the motion states of the two wave energy conversion units respectively.

[0033] Then, the time domain motion equation of the float can be rewritten as a linear differential equation: (10) Specific: ;in, ; ; ; ; and are the hydrostatic recovery stiffness of the wave energy conversion unit, respectively; ; .

[0034] The initial condition X(0)=0 is defined, and the state space equation of the arrayed wave energy conversion device is solved by the fourth-order Runge-Kutta method in MATLAB to obtain the motion state of the arrayed wave energy conversion device.

[0035] S4: Implement centralized clutch control on arrayed wave energy conversion devices to maximize the energy extraction from waves.

[0036] like Figure 5 As shown in the figure, the 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 the centralized control command through iterative updates of the algorithm. .

[0037] Clutch control is essentially phase control. Alternating loading ( =1) and uninstall ( =0) PTO system to make 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.

[0038] 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), and this Hamiltonian function is a linear function of the control command β and reaches its maximum value when it satisfies formula (18): (12) where, is the motion equation of the arrayed wave energy conversion device; J is the objective function representing the functional capture of the wave energy array, and its expression (13) is as follows: (13) represents the control command for controlling the first wave energy conversion unit, represents the 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 the wave energy conversion unit 2, represents the motion speed of the first wave energy conversion unit, represents the motion speed of the second wave energy conversion unit.

[0039] Furthermore, the Hamiltonian function H can be written as formula (14): (14) where, is the Lagrange multiplier, which follows the control equation (15): (15) 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: (1) Expand the Hamiltonian function according to the state - space equation of the arrayed wave energy conversion device: (16) (2) Solve the above - mentioned Hamiltonian function, and calculate the Lagrange multiplier as shown in the following formula (17): (17) where the Hamiltonian is a linear function of the binary control sequence and reaches its maximum value when it satisfies formula (18): , (18) such as Figure 5As shown, according to the Pontryagin maximum principle, when the Hamiltonian is at its maximum, there exists an optimal control sequence β. It should be noted that although the motion equation and the control equation of the wave energy array are both first-order partial differential equations, since the two formulas have initial conditions at different times, they cannot be solved in parallel. As mentioned above, and is the mass of a single wave energy conversion unit, represents the added mass of one wave energy conversion unit, represents the added mass of another wave energy conversion unit, and both represent the added mass generated by the motion of one wave energy conversion unit in the heaving direction on another wave energy conversion unit; 1 represents loading a single wave energy conversion unit, and 0 represents unloading a single wave energy conversion unit.

[0041] Specifically, the motion equation is integrated forward from 0 to T, and the control equation is integrated backward from T to 0. An interactive optimization algorithm is used to solve this problem. First, at , a simulation is carried out. By integrating the motion equation forward from t = 0 to t = T, the motion without control action is obtained. Subsequently, the Lagrange multiplier is determined by integrating the control equation backward from t = T to t = 0. Finally, given the state vector X and the Lagrange multiplier , the control sequence is determined to maximize the Hamiltonian. The iterative process of using the updated control sequence is carried out until the control sequence converges.

[0042] In a specific embodiment of the present invention, for an array system composed of two wave energy conversion devices, numerical simulations of the wave energy conversion devices under three control methods (no control, independent control, and centralized control) are carried out to compare their energy capture performances. The incident wave is described by the JONSWAP spectrum, and a wave condition is selected, with an effective wave height of 1.4 m and a spectral peak period of 5.5 s. The total duration of the simulation is 3600 s, and the sampling time interval is 0.01 s.

[0043] The wave energy capture efficiencies under no control, independent control, and the centralized clutch control algorithm are as Figure 6 shown. For the case of no control, the energy capture efficiency of the arrayed wave energy conversion device within 1 hour is approximately 12 kW; in the independent control mode (i.e., separately implementing the clutch control algorithm for the two wave energy conversion devices, Figure 5), its energy capture efficiency is increased to approximately 31 kW; when the centralized control algorithm is adopted, the energy capture efficiency is further increased to approximately 43 kW. Compared with the case without control, the centralized control algorithm increases the energy capture efficiency by 258.33%; compared with independent control, it is increased by 38.7%. Thus, it can be seen that the centralized control algorithm developed by the present invention can significantly improve the wave energy capture efficiency and demonstrate superior performance advantages.

[0044] It should be noted 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 those of ordinary skill in the art within the scope of the essence of the present invention should also fall within the protection scope of the present invention.

Claims

1. A centralized clutch control method for an arrayed wave energy conversion device, characterized in that Including: S1, numerically modeling and performing hydrodynamic analysis on the arrayed wave energy conversion device; the arrayed wave energy conversion device is composed of a first wave energy conversion unit and a second wave energy conversion unit; S2, establishing the time-domain motion equation of the arrayed wave energy conversion device; an additional mass generated by the interaction between wave energy conversion units and a delay term of the radiation effect of the motion of a single wave energy conversion unit on its adjacent unit are introduced into the time-domain motion equation; S3, establishing the state-space equation of 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 the arrayed wave energy conversion device to maximize the extraction of energy from waves, including: Define the Hamiltonian function ; where is the motion equation of the arrayed wave energy conversion device, represents the functional capture of the wave energy array; is the motion state of the arrayed wave energy conversion device; is the control sequence; and are the control commands for controlling a single wave energy conversion device, and are the PTO damping coefficients of a single wave energy conversion device; are the motion speeds of two wave energy conversion units respectively; is the Lagrange multiplier; Expanding and solving the Hamiltonian function to obtain the Lagrange multiplier, and satisfying ， At this time, the Hamiltonian reaches its maximum value and there exists an optimal control sequence ; where 1 represents loading a single wave energy conversion unit and 0 represents unloading 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 added masses of the two wave energy conversion units respectively, 12 and 21 are the added masses generated by the motion of one wave energy conversion unit in the heaving direction on the other wave energy conversion unit respectively; are the velocities of the two wave energy conversion units respectively; n is the order of the system.

2. The centralized clutch control method for the arrayed wave energy conversion device according to claim 1, wherein The time-domain motion equation established in S2 is: ， ； where x1 and x2 are the displacements and accelerations of two wave energy conversion units respectively; is a delay function representing the radiative interaction, is the radiative damping, represent the self-radiation delay functions of two wave energy conversion units respectively, indicating the historical influence of the radiative waves generated by the unit's own motion on its own velocity; represent the delay functions of the radiative action of the motion of one wave energy conversion unit on the other wave energy conversion unit respectively; K is the hydrostatic restoring stiffness; is the wave exciting force acting on the first wave conversion unit, is the wave exciting force acting on the second wave conversion unit, where represents taking the real part of the complex function, is the transfer function of the wave exciting 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; represent the reaction forces provided by the PTO system to two wave energy conversion units respectively, and c represents the damping coefficient of the PTO system.

3. The centralized clutch control method for the arrayed wave energy conversion device according to claim 1, wherein The state-space equation established in S3 is: ； Among them, represents an \(n\times1\) -dimensional state variable, respectively represent an \(n\times n\) -dimensional, an \(n\times1\) -dimensional, and a \(1\times n\) -dimensional state - space matrix.

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

5. The centralized clutch control method for the arrayed wave energy conversion device according to claim 1, characterized in that During the solution process of the Hamiltonian, the motion equation is integrated forward from 0 to T, and the control equation is integrated backward from T to 0, including: At simulation is carried out. By integrating the motion equation forward from t = 0 to t = T, the motion state X of the wave energy conversion device is obtained; The Lagrange multipliers are determined by integrating the governing equations backward from t = T to t = 0 ; Given the state vector X and the Lagrange multipliers to determine the control sequence , to maximize the Hamiltonian; Iterate the process using the updated control sequence until the control sequence converges.

6. The centralized clutch control method for the arrayed wave energy conversion device 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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