Real-time feedback control method for arrayed wave energy conversion device

Abstract

The invention provides a real-time feedback control method for an arrayed wave energy conversion device, which comprises the following steps of: carrying out numerical modeling and hydrodynamic analysis on the arrayed wave energy conversion device, establishing a time domain motion equation and a space state equation of the arrayed wave energy conversion device, replacing a convolution term of the time domain motion equation with the state-space equation to obtain a motion state of the arrayed wave energy conversion device, and carrying out real-time feedback control on the arrayed wave energy conversion device. According to the method, wave spectrum characteristics and hydrodynamic response characteristics of floaters are combined, hydrodynamic interference among the floaters in an array system is comprehensively considered, a causal mapping relation between floater speed and wave exciting force is constructed, expected floater response speed is calculated, control force is applied to the PTO through a feedback control means, and the wave excitation force is calculated. The device is kept in an approximately optimal resonance state under the action of random waves, so that the speed of each floater is close to the optimal function extraction condition of each wave frequency, and efficient real-time extraction of wave energy is realized.

Description

Technical Field

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

[0002] Amidst the accelerating global energy transition, the development of marine renewable energy has become a strategic priority for energy technology innovation. Wave energy, due to its wide distribution, high energy density, and ability to synergize with offshore infrastructure for power generation, is recognized as one of the most promising blue energy sources. Its core device, the Wave Energy Converter (WEC), uses energy-harvesting elements such as floats and a pendulum mechanism to convert wave kinetic energy into mechanical energy, ultimately outputting electrical energy through the power system. It has demonstrated potential in areas such as powering remote islands and providing energy for marine ranches.

[0003] Although a variety of energy capture configurations have emerged in the field of wave energy conversion devices, their average energy conversion efficiency is still relatively low. After wave energy is captured, how to achieve high-efficiency wave energy absorption remains a key technology for wave power generation. Summary of the Invention

[0004] The purpose of the present invention is to propose a real-time feedback control method for an arrayed wave energy conversion device, construct a causal mapping relationship between the float speed and the wave excitation force, solve the causal transfer function of the wave excitation force and the float speed, calculate the expected float response speed through the causal transfer function of the wave excitation force and the float speed and the current wave excitation force, and apply a control force to the PTO through feedback control means, so that the device maintains a near-optimal resonance state under the action of random waves, thereby realizing efficient real-time extraction of wave energy.

[0005] The present invention is achieved by adopting the following technical solutions: A real-time feedback control method for an arrayed wave energy conversion device is proposed, comprising: S1, numerical modeling and hydrodynamic analysis of arrayed wave energy conversion devices; S2: Establish the time domain motion equation of the wave energy conversion device based on impulse response theory; S3: Establish the state space equation of the array 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 array wave energy conversion device; S4, constructing a transfer function between wave excitation force and float velocity, calculating a target float velocity response based on the current wave excitation force, extracting an actual float velocity from the calculated motion state, and controlling the arrayed wave energy conversion device to extract wave energy based on a deviation between the actual velocity and the target float velocity, including: Extracting power from arrayed wave energy converters: , ;in, is the wave excitation force-buoy velocity transfer function, is the desired float velocity response; is the wave excitation force; is the wave force transfer function, For the spectrum; ; Z represents the inherent impedance of the system; Define the second item in P as the Loss loss function, and we get , transforming the power conversion problem into the problem of solving the minimum value of the loss function; make , the loss function Loss is used to transfer the function The first-order partial derivative is zero to obtain the optimal value ;in, , ; based on The optimal value and the wave excitation force at the current moment are used to obtain the target speed response. In addition, the actual speed of the float is extracted from the calculated motion state, and the deviation between the actual speed and the target speed is transmitted to the PID control module so that the PID control module controls the arrayed wave energy conversion device to extract wave energy.

[0006] In some embodiments of the present invention, the time domain motion equation established in S2 is: , ; Among them, M1 and M2 are the masses of the two wave energy conversion devices respectively; 11 and 22 are the additional masses of the two wave energy conversion devices, 12 and 21 They are the effects of the additional inertial force generated by the movement of one wave energy conversion device on the other wave energy conversion device in the heave direction; are the displacement, velocity and acceleration of the two wave energy conversion devices 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 devices, indicating the historical impact of the radiation waves generated by the device's own motion on its own velocity; They represent the delay function of the radiation effect of the movement of one wave conversion device on another wave conversion device; K is the still water restoring stiffness. e,1 and F e,2 They are the wave excitation force of the first wave energy conversion device and the wave excitation force of the second wave energy conversion device, and the calculation formula is , Re represents the real part of the complex function, is the transfer function of the wave excitation force, For the spectrum, is the wave frequency, is the random phase of the wave; The force provided by the wave energy conversion device from the PTO system.

[0007] In some embodiments of the present invention, the state space equation established by S3 is: , , ; in, represents the n×1-dimensional state variable, , , are used to approximate the convolution terms, representing n×n-dimensional, n×1-dimensional, and 1×n-dimensional state space matrices, respectively, and are calculated using the system identification method.

[0008] In some embodiments of the present invention, in S3, a new state variable is defined , bring the established state space equation into the time domain motion equation and transform it into a linear differential equation: ; The fourth Runge-Kutta method is used to solve the linear differential equation to obtain the motion state of the array wave energy conversion device. in, , , , ; , .

[0009] In some embodiments of the present invention, S4 extracting the power of the arrayed wave energy conversion device includes: Power extraction from arrayed wave energy conversion devices: ;in, Indicates the load force provided by the PTO device. Indicates the velocity response of the float; According to the inherent impedance of the arrayed wave energy conversion device Performing a mathematical transformation on the power extraction formula: ; The mathematical equivalent transformation is simplified to: .

[0010] In some embodiments of the present invention, in S4, according to the minimum principle, the first-order partial derivative of the function is zero, which is a necessary condition for the minimum value. The loss function LOSS is used to calculate the transfer function Find the partial derivative: , According to the basic derivation rule, the original formula is decomposed , Integration , According to the minimum principle, let the first-order partial derivative of the loss function with respect to the transfer function be zero , get .

[0011] Compared with the prior art, the advantages and positive effects of the present invention are as follows: In the real-time feedback control method for arrayed wave energy conversion devices proposed by the present invention, the wave spectrum characteristics and the hydrodynamic response characteristics of the float are combined, the hydrodynamic interference between the floats in the array system is comprehensively considered, and a causal mapping relationship between the float speed and the wave excitation force is constructed. The desired float response speed is thereby calculated, and a control force is applied to the PTO through feedback control means, so that the device maintains a near-optimal resonant state under the action of random waves, so that the speed of each float is close to the optimal functional extraction condition for each wave frequency, thereby achieving efficient real-time extraction of wave energy. The method of the present invention shows significant advantages in power absorption, not only effectively improving the overall energy absorption capacity of the arrayed wave energy conversion device, but also providing counting support for the operation of large-scale wave energy arrays. The method has a simple structure, clear physics, and is easy to implement in engineering, making it particularly suitable for the design of control systems for wave energy arrays. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] 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.

[0013] Figure 1 The steps of the real-time feedback control method of the arrayed wave energy conversion device proposed by the present invention; Figure 2 This is a schematic diagram of the structure of an arrayed wave energy conversion device; Figure 3 The control principle of the arrayed wave energy conversion device proposed in the present invention; Figure 4 A comparison diagram of the transfer function wave energy capture efficiency of the method of the present invention and the existing method without control and taking into account the mutual hydrodynamic interference effect; Figure 5 This is an example of a specific implementation diagram for working condition design. The random wave environment is a random wave spectrum generated based on jonswap. DETAILED DESCRIPTION

[0014] 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.

[0015] When a wave energy converter (hereinafter referred to as a wave energy converter or device) is in resonance, the wave force acting on the device and the device's velocity are completely in phase. The waves then continuously perform positive work on the device, maximizing the wave energy captured. Therefore, resonance is an effective method for improving the energy capture efficiency of wave energy converters.

[0016] To achieve efficient absorption of wave energy, the applicant proposed a latching control strategy in a previous application based on the principle of optimal resonant phase. This strategy uses an external mechanism to periodically lock or release the wave energy device to adjust its motion state, slowing the system's oscillation frequency and thereby aligning the float's velocity phase with the wave excitation force. This strategy is suitable for wave energy devices with a natural frequency higher than the wave frequency. In contrast, a declutching control strategy was developed for devices with a natural frequency lower than the wave frequency. Although both strategies can enable the system to meet the optimal phase condition, they are not optimal control strategies because their control force is discontinuous and amplitude matching is not considered.

[0017] In contrast, complex conjugate control (CCC), also known as reactive control (RCC), continuously applies control force to the device through the PTO (power take-off) system, so that the float and the wave excitation force maintain an optimal resonant state, thereby theoretically achieving maximum power capture. It is the representative of the current optimal control strategy. However, this strategy uses the complex conjugate of the system's inherent impedance as the basis for the optimal load impedance. While the inherent impedance is defined as a complex function in the frequency domain, the control process must be implemented in the time domain. When mapping the frequency domain impedance to the time domain, an integral control term in the form of a convolution kernel must be introduced. This convolution kernel inevitably depends on future float velocity information, causing the complex conjugate control strategy to behave as non-causal control in the time domain. Specifically, the integral control component in complex conjugate control is completely non-causal, and its implementation requires predicting the future state of the wave energy device, which limits its real-time nature and engineering feasibility.

[0018] Therefore, how to maintain high energy absorption efficiency while avoiding dependence on future states and construct a causal optimal or suboptimal control method has become a key issue in current wave energy control research.

[0019] This invention aims to overcome these technical bottlenecks by proposing a wave force-buoy velocity control strategy based on a causal transfer function. This method combines the local wave spectrum characteristics with the hydrodynamic response characteristics of the floats, comprehensively considering the hydrodynamic interference effects between floats in the array system, and constructs a causal mapping relationship between float velocity and wave excitation force. The desired float response speed is then calculated, and a control force is applied to the PTO through feedback control methods (such as PID control) to maintain a near-optimal resonant state under random wave conditions, achieving efficient, real-time wave energy extraction. This method has a simple structure, clear physics, and is easy to implement in engineering, making it particularly suitable for control system design for wave energy arrays.

[0020] The following is an example of an array wave energy conversion device including two wave energy conversion devices (the case of more than two wave energy conversion devices can be expanded according to the concept of this embodiment). Figure 3 The control principle is used to illustrate the real-time feedback control method proposed in the present invention.

[0021] like Figure 1 As shown, the method includes the following steps: S1: Numerical modeling and hydrodynamic analysis of arrayed wave energy conversion devices.

[0022] The arrayed wave energy conversion device consists of two completely identical and coordinated oscillating float wave energy conversion devices. The oscillating float wave energy conversion device is a device that captures the kinetic energy of waves based on the reciprocating motion of the float with the waves, and then drives the generator to generate electricity through the power output system PTO. The float, connecting rod and PTO system are its main components. Among them, the float is connected to the PTO system through a connecting rod. The PTO system mainly includes hydraulic, mechanical transmission, hydraulic, pneumatic, linear motor and hybrid hydraulic types. The present invention selects 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 to work, and the hydraulic motor drives the generator to generate electricity.

[0023] Furthermore, the operating principle of the oscillating float wave energy conversion device 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 inside 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.

[0024] The present invention combines Figure 2As shown, the arrayed wave energy conversion device consists of two oscillating float wave energy conversion devices (wave energy conversion device 1 and wave energy conversion device 2) with exactly the same size and shape; the wave energy conversion devices 1 and 2 are mainly composed of a float 11, a connecting rod 12 and a PTO 13. The float 11 adopts a cylindrical floating body with a radius of 2.5m and a draft of 5m. The PTO 13 adopts a hydraulic PTO system, which is mainly composed 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 operate, and the hydraulic motor drives the generator to generate electricity. The float 11 is moved by the waves. Under the action of the hydraulic cylinder, it reciprocates in the heaving 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 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 liquid pressure energy in the pipeline into the mechanical energy (torque and speed) of the output shaft, and then drives the rear-end generator to generate electricity. The generator adopts existing equipment: a three-phase permanent magnet synchronous motor; the wave energy conversion device 2 is mainly composed of a float 21, a connecting rod 22 and a hydraulic PTO 23, and its working principle is consistent with that of the wave energy conversion device 1.

[0025] The present invention utilizes the GeniE module in the DNV-GL SESAM software to establish a numerical model of the wave energy conversion device that only includes the portion below the water plane, because only the hydrodynamic effects on the portion below the water plane of the float are considered.

[0026] The specific modeling process is as follows: (1) Construct a geometric model of the float using points, lines, and surfaces, and build a numerical model of the wave energy array with a radius of 2.5 m and a draft of 5 m; (2) Define the wetted surface of the double unit wave energy array; (3) Applying load to the wet surface of the dual-unit wave energy array; (4) Divide the grid and set the grid size to 0.1m; (5) Run the analysis and generate a .fem file.

[0027] After obtaining the .fem file, import it into the hydroD module for frequency domain hydrodynamic analysis. The specific analysis process is as follows: (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; (2) Create a hydrodynamic model; (3) Import the .fem panel model file; (4) Create a quality model; (5) Operational analysis; (6) Review and post-process the results to obtain the hydrodynamic parameters of the wave energy conversion device.

[0028] S2: Establish the time domain motion equation of the wave energy conversion device based on impulse response theory.

[0029] A right-handed coordinate system fixed on the earth is used, with the center of the coordinate system fixed on the mean sea surface. The Z axis is upward and the X axis is along the direction of wave propagation. The time domain motion equation of the array wave energy conversion device is: ; Expand it into the multi-degree-of-freedom float motion equation: ; , ; in, and are the masses of the two wave energy conversion devices respectively; 11 and 22 are the additional masses of the two wave energy conversion devices, 12 and 21 They are the effects of the additional inertial force generated by the movement of one wave energy conversion device on the other wave energy conversion device in the heave direction; are the displacement, velocity and acceleration of the two wave energy conversion devices 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 devices, indicating the historical impact of the radiation waves generated by the device's own motion on its own velocity; They represent the delay functions of the radiation effect of the motion of one wave conversion device on another wave conversion device; K is the hydrostatic restoring stiffness; The force provided by the wave energy conversion device from the PTO system; and They are the wave excitation force of the first wave energy conversion device and the wave excitation force of the second wave energy conversion device, and the calculation formula is as follows: ; Re represents the real part of the complex function. is the transfer function of the wave excitation force, For the spectrum, is the wave frequency, is the random phase of the wave.

[0030] The above hydrodynamic parameters, such as the added mass at infinite frequency , the transfer function of wave force All of them were calculated using the hydrodynamic analysis software SESAM-WADAM.

[0031] 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.

[0032] The state space equation is shown in formula (5): , , ; Using linear differential equation approximation formula in , the linear differential equation is as follows As shown: ; Combining formula (5) and (6) we can get formula (7) , , ; in, represents the n×1-dimensional state variable, 、 、 is used to approximate the convolution term, representing n×n-dimensional, n×1-dimensional, and 1×n-dimensional state space matrices, respectively. Its expansion is Calculated by system identification method.

[0033] Specifically, first solve the linear differential equation Performing Laplace transformation yields: ; The delay function for the radiation interaction Performing Fourier transform yields: ; Again Performing Fourier transform yields: ; Combined formula and ,get: ; calculate get: , ; in, are radiation damping and additional mass, respectively, which are calculated by the hydrodynamic software Hydrod. Then p and q are calculated according to formula (12), and then we get 、 、 .

[0034] Above, the numerator coefficient group and the denominator coefficient group The target frequency response function is obtained by the least squares fitting method. It is extracted and used to construct a class of rational transfer functions, which aims to approximate the dynamic characteristics of the original radiation memory kernel function in the complex frequency domain (that is, as shown in formula (12), the original radiation memory kernel function The real part represents the radiation damping, and the imaginary part is divided by represents added mass).

[0035] The state space equation of the wave energy array Substitute the float's time-domain motion equation into the equation and define new state variables: ; Then the time domain motion equation of the wave energy array can be rewritten as a linear differential equation: ; Define the initial condition X(0) = 0 and use the fourth Runge-Kutta method to solve the formula By calculation, the motion state X of the arrayed wave energy conversion device can be obtained.

[0036] The specific solution steps are as follows: ; in, represents the viscous damping of the system (critical damping is 1%), is the density of water, is the acceleration due to gravity, M is the mass of the float, μ is the additional mass at infinite frequency, Restore stiffness for still water.

[0037] Perform matrix operations on the above formula and convert it into : ; , , , , , .

[0038] The fourth Runge-Kutta method is used to solve the state space equation of the array wave energy conversion device and obtain the motion state of the array wave energy conversion device.

[0039] S4: Constructing a transfer function between wave excitation force and float velocity, calculating a target float velocity response based on the current wave excitation force, extracting the actual float velocity from the calculated motion state, and controlling the arrayed wave energy conversion device to extract wave energy based on the deviation between the actual velocity and the target float velocity.

[0040] The wave force-buoy velocity coupling control strategy described in this invention belongs to complex conjugate control. Its core concept is to ensure that the speed of the energy capture device (i.e., the wave energy conversion device) is in phase with the wave excitation force. Through feedback control, a continuous control force is applied to the PTO to achieve the purpose of eliminating the system force (referring to the reaction force naturally generated by the wave energy conversion device itself in the waves, including radiation damping force, added mass force, and restoring force, which together hinder the free movement of the float) to achieve the purpose of resonance. The optimal load impedance is equal to the complex conjugate of the system's inherent impedance. At this time, the device capture power can reach the theoretical maximum value. Therefore, complex conjugate control is the optimal control method.

[0041] Since the optimal load impedance is equal to the complex conjugate of the system's natural impedance, which is essentially a complex function defined in the frequency domain, it must be mapped from the frequency domain to the time domain when used in control strategies. This mapping process corresponds to the introduction of a time-domain convolution kernel, which typically includes dependencies on future system states (such as float velocity).

[0042] In other words, while complex conjugate control establishes optimal energy absorption conditions in the frequency domain, its control command in the time domain—the force exerted by the PTO—is based on a convolution response derived from the frequency-domain impedance. Because this convolution kernel involves a weighted integral of future velocities, the controller must know the system's future motion state at the current moment, and thus, must predict future wave excitations.

[0043] Therefore, the complex conjugate control strategy is essentially non-causal, and its non-causality mainly stems from its dependence on future states. This characteristic constitutes an obstacle to the promotion and application of complex conjugate control in practical engineering. In order to overcome this problem, the present invention proposes a wave force-buoy velocity dynamic coupling control strategy based on a causal transfer function. The method of the present invention does not require prediction of future wave excitations, but instead constructs a causal transfer function through rigorous theoretical derivation to achieve a direct mapping relationship between the current wave excitation force and the expected float velocity response, thereby effectively avoiding the non-causal problem in traditional optimal control strategies and providing a practical solution for the real-time control and engineering implementation of wave energy arrays.

[0044] The power extraction of the arrayed wave energy conversion device is calculated according to the following formula: ; in, Indicates the load force provided by the PTO device. represents the velocity response of the float, and * represents the complex conjugate.

[0045] According to the inherent impedance of the arrayed wave energy conversion device: ; Formula Perform mathematical transformations: ; Where Z represents the inherent impedance of the system, Represents the wave excitation force.

[0046] Combined formula and , perform mathematical equivalent transformation on the power extraction of wave energy conversion device: , , ; make , the power extraction of the wave energy conversion device can be simplified to: ; ; is the wave excitation force-buoy velocity transfer function, is the desired float velocity response.

[0047] If it complies with formula (22), that is, the speed of the wave energy conversion device is consistent with the phase of the wave excitation force, resonance is achieved, and the optimal load impedance is equal to the complex conjugate of the inherent impedance of the system. At this time, the power captured by the device can reach the theoretical maximum value.

[0048] For given wave conditions, the formula The first term is a constant, and the second term is positioned as the Loss loss function. When Loss takes a minimum value, the energy capture power of the wave energy conversion device is the maximum. Combining formulas (21) and (22), the loss function is mathematically expressed as: ; The wave excitation force is expressed as: ; is the wave force transfer function, For the spectrum, is the wave energy-buoy velocity transfer function.

[0049] By formula 、 right The loss function is transformed: ; ; The power conversion problem of the wave energy conversion device is transformed into the problem of solving the minimum value of the loss function.

[0050] make ,but .

[0051] According to the minimum principle, the first-order partial derivative of the function is zero, which is a necessary condition for the minimum value, so the loss function is right Find the partial derivative: ; According to the basic derivation rule, the original formula is decomposed: ; According to the rules for derivation of scalar functions on matrices in The Matrix Cookbook, the original formula is integrated: ; According to the minimum principle, let the first-order partial derivative of the loss function with respect to the transfer function be zero ; ; , is an asymmetric matrix; , is a symmetric matrix.

[0052] That is, when the wave excitation force-buoy velocity transfer function For the formula When taking the value, the loss function right The partial derivatives are all 0, which is a necessary condition for finding the minimum point.

[0053] According to the minimum principle, the first-order partial derivative of each component of a multivariate function is 0, and the Hessian matrix of the function is positive definite, which is the minimum point: ; ; Transforming the rows and columns of the Hessian matrix does not change the positive definiteness of the matrix: ; Since the positive definiteness of the block diagonal matrix is ​​determined by the positive definiteness of each diagonal sub-block, the positive definiteness of the Hessian matrix depends on the positive definiteness of the A matrix: ; in: , , , , ; Therefore, formula (34) can be expanded as: ; According to the necessary and sufficient conditions for judging the positive definiteness of a matrix, when the principal minors of all orders of the matrix are greater than 0, the matrix must be positive definite. middle: ; ; By the formula 、 As shown, the A matrix must be positive definite, and the positive definiteness of the block matrix means that the Hessian matrix must also be positive definite.

[0054] Therefore The loss function is the smallest when , that is, the wave energy absorption efficiency is the largest.

[0055] Specifically, when the loss function reaches its minimum, energy loss is minimized and wave energy absorption efficiency is maximized. It's worth noting that while the absorption efficiency of the array wave energy device is maximized at this point, the absorption efficiency of a single device is not optimal, but rather the overall absorption efficiency is improved. The desired float response, derived from the wave force-buoy velocity transfer function, is not the optimal float oscillation velocity, but rather a suboptimal control approach that approximates causality as closely as possible.

[0056] In order to achieve the maximum power generation of the arrayed wave energy conversion device, the loss function LOSS is constructed and aligned to be minimized to obtain the optimal value of the transfer function between the wave excitation force and the float velocity, as shown in formula (31). This transfer function is used to characterize the optimal float velocity response and the transfer relationship between the wave excitation force that the device should achieve under a given wave excitation.

[0057] Combined with the wave excitation force on each float in the array at the current moment, the target speed response of each float is calculated based on the transfer function as shown in formula (22). Further combined with the actual motion state of the device obtained in real time in S3, the actual speed of the float is extracted, and the deviation between the actual speed and the target speed is used as input and transmitted to the PID control module. The PID module uses the speed deviation as a feedback signal and outputs a control instruction, that is, the mechanical force of the PTO device, forming a closed-loop control, realizing dynamic adjustment and optimal guidance of the device motion state, thereby improving energy capture efficiency and approaching the theoretical optimal functional absorption state.

[0058] In a specific embodiment of the present invention, a numerical simulation of a wave energy converter array system consisting of two wave energy converters was conducted under controlled and transfer function control strategies to compare their energy capture performance. The incident wave was described using the JONSWAP spectrum. Taking working condition 1 as an example, its significant wave height Hs is 2m, the spectrum peak period Tp is 6s, and the constant value λ required by the JONSWAP spectrum is 3. Working conditions 2 and 3 are only adjusted in terms of significant wave height and spectrum peak period, as shown in Figure 2. Figure 4 The total simulation time is 3600s, and the sampling time interval is 0.01s.

[0059] Figure 5The following chart compares the one-hour wave energy capture efficiency of the wave energy converter under different operating conditions, comparing uncontrolled and transfer function-based control strategies. Taking operating condition 1 as an example, without a control strategy, the wave energy converter captures an average power of 14 kW over the one-hour period. However, with the transfer function-based control strategy applied, the average power captured over the one-hour period is 142 kW. Compared to the uncontrolled case, the transfer function-based control algorithm increases energy capture efficiency by 914.28%. This demonstrates that the transfer function-based control algorithm proposed in this invention can significantly improve wave energy capture efficiency, demonstrating superior performance.

[0060] 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 real-time feedback control method for an arrayed wave energy conversion device, characterized in that: include: S1, numerical modeling and hydrodynamic analysis of arrayed wave energy conversion devices; S2: Establish the time domain motion equation of the wave energy conversion device based on impulse response theory; S3: Establish the state space equation of the array 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 array wave energy conversion device; S4, constructing a transfer function between wave excitation force and float velocity, calculating a target float velocity response based on the current wave excitation force, extracting an actual float velocity from the calculated motion state, and controlling the arrayed wave energy conversion device to extract wave energy based on a deviation between the actual velocity and the target float velocity, including: Extracting power from arrayed wave energy converters: , ;in, is the wave excitation force-buoy velocity transfer function, is the desired float velocity response; is the wave excitation force; is the wave force transfer function, For the spectrum; ; Represents the inherent impedance of the system; Define the second item in P as the Loss loss function, and we get , transforming the power conversion problem into the problem of solving the minimum value of the loss function; make , the loss function Loss is used to transfer the function The first-order partial derivative is zero to obtain the optimal value ;in, ， ； based on The optimal value and the wave excitation force at the current moment are used to obtain the target speed response. In addition, the actual speed of the float is extracted from the calculated motion state, and the deviation between the actual speed and the target speed is transmitted to the PID control module so that the PID control module controls the arrayed wave energy conversion device to extract wave energy.

2. The real-time feedback control method for arrayed wave energy conversion devices according to claim 1, characterized in that: The time domain motion equation established in S2 is: ， ； Among them, M1 and M2 are the masses of the two wave energy conversion devices respectively; 11 and 22 are the additional masses of the two wave energy conversion devices, 12 and 21 They are the effects of the additional inertial force generated by the movement of one wave energy conversion device on the other wave energy conversion device in the heave direction; are the displacement, velocity and acceleration of the two wave energy conversion devices 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 devices, indicating the historical impact of the radiation waves generated by the device's own motion on its own velocity; They represent the delay functions of the radiation effect of the movement of one wave conversion device on another wave conversion device; K is the hydrostatic restoring stiffness; F e,1 and F e,2 They are the wave excitation force of the first wave energy conversion device and the wave excitation force of the second wave energy conversion device, and the calculation formula is , Re represents the real part of the complex function, is the transfer function of the wave excitation force, For the spectrum, is the wave frequency, is the random phase of the wave; The force provided by the wave energy conversion device from the PTO system.

3. The real-time feedback control method for arrayed wave energy conversion devices according to claim 1, characterized in that: The state space equation established by S3 is: ， ， ； in, represents the n×1-dimensional state variable, , , are used to approximate the convolution terms, representing n×n-dimensional, n×1-dimensional, and 1×n-dimensional state space matrices, respectively, and are calculated using the system identification method.

4. The real-time feedback control method for arrayed wave energy conversion devices according to claim 3, characterized in that: In S3, define new state variables , bring the established state space equation into the time domain motion equation and transform it into a linear differential equation: ； The fourth Runge-Kutta method is used to solve the linear differential equation to obtain the motion state of the array wave energy conversion device. in, ， ， ， ； ， 。 5. The real-time feedback control method for arrayed wave energy conversion devices according to claim 1, characterized in that: S4 extracts power from arrayed wave energy conversion devices, including: Power extraction from arrayed wave energy conversion devices: ;in, Indicates the load force provided by the PTO device. Indicates the velocity response of the float; According to the inherent impedance of the arrayed wave energy conversion device Performing a mathematical transformation on the power extraction formula: ； The mathematical equivalent transformation is simplified to: 。 6. The real-time feedback control method for arrayed wave energy conversion devices according to claim 5, characterized in that: In S4, according to the minimum principle, the first-order partial derivative of the function is zero, which is a necessary condition for the minimum value. Then the loss function LOSS is used to calculate the transfer function. Find the partial derivative: ， According to the basic derivation rule, the original formula is decomposed ， Integration ， According to the minimum principle, let the first-order partial derivative of the loss function with respect to the transfer function be zero ， get .

Images