Method and system for power optimization of floating wind farm based on agent model assistance

Abstract

The embodiment of the present disclosure provides a kind of based on agent model auxiliary floating wind farm power optimization method and system, belong to computing technical field, specifically include: obtain target function;Using Latin hypercube sampling method initializes the position of each particle in population;Global agent model is constructed and local agent model is constructed;Based on local agent model and its determined subspace, with PI filling criterion as agent model target function, the decision value of population particle is updated;Based on global agent model, the target function value of population particle generated by algorithm is predicted, and the mark value of population particle is updated;The speed and position of particle are updated by the mark value and decision value of population particle;The real target function value of the particle with mark value 1 in population is calculated, and the repeated sampling point is removed;The optimal solution of optimization problem is output.The scheme of the present disclosure improves the calculation efficiency and accuracy of floating wind farm output power optimization.

Description

Technical Field

[0001] This disclosure relates to the field of computing technology, and in particular to a method and system for optimizing the power of floating wind farms based on a surrogate model. Background Technology

[0002] Currently, for deep-sea areas with more favorable wind conditions and wider construction areas, using floating foundations to construct floating wind farms makes it easier to ensure the economic viability of the wind farm. Unlike stationary wind turbines, floating wind turbines have mobility within a certain range. In a floating wind farm, the movement of the turbines is mainly affected by their own aerodynamic thrust, mooring cable tension, and fluid viscous drag. When only these three main factors are considered, the stable position of each turbine is uniquely determined by its own aerodynamic thrust and mooring cable tension. Due to the wake effect, when the turbine's position changes, the aerodynamic thrust and mooring cable tension it experiences also change, thus affecting the turbine's output power; correspondingly, the power output of a floating wind farm is closely related to the steady-state position of each turbine in the floating wind farm. To calculate the power output of floating wind farms, Kheirabad et al. designed a simplified model, FOWFsim, combining engineering wake models and mooring cable models. This model can calculate the stable position and stable power of wind turbines in a floating wind farm under given wind conditions. Based on this model, using the axial induction factor and yaw angle of each turbine as optimization variables, they employed a sequential quadratic programming (SQP) algorithm to optimize the overall output power of a floating wind farm with up to 49 turbines arranged in a 7x7 grid. This research pioneered the solution to the problem of optimizing the output power of floating wind farms.

[0003] Nevertheless, the power optimization problem of floating wind farms is a non-convex optimization problem. For non-convex optimization problems, swarm intelligence algorithms are more likely to obtain the global optimum than numerical optimization methods. However, in the process of obtaining the objective function of the optimization problem through the FOWFsim model, it is necessary to iteratively solve the stable position of the wind turbine, which will consume a lot of time and significantly increase the time cost of swarm intelligence algorithms.

[0004] It is evident that there is an urgent need for an efficient and accurate method for power optimization of floating wind farms based on surrogate models. Summary of the Invention

[0005] In view of this, the present disclosure provides a method and system for optimizing the power of floating wind farms based on a proxy model, which at least partially solves the problems of poor computational efficiency and accuracy in the prior art.

[0006] In a first aspect, embodiments of this disclosure provide a method for optimizing the power of floating wind farms based on a surrogate model, including:

[0007] Step 1: Determine the optimization variables and their range of values ​​for the optimization problem of the floating wind farm, and obtain the objective function;

[0008] Step 2: Initialize the position of each particle in the population using the Latin hypercube sampling method, calculate the objective function value corresponding to each particle, and add the position and objective function value of each particle to the sampled database;

[0009] Step 3: Based on the Gaussian process regression model, extract the latest p sampled points from the historical database to construct a global proxy model, and extract the q sampled points that are closest to the optimal sampled point in Euclidean distance from the historical database to construct a local proxy model.

[0010] Step 4: Based on the local surrogate model and its determined subspace, the PI filling criterion is used as the objective function of the surrogate model. A nonlinear optimization algorithm is used to generate the optimal sampling point and update the decision value of the population particles.

[0011] Step 5: Based on the global proxy model, predict the objective function value of the population particles generated by the algorithm, pre-select particles that move to a better position by using the predicted objective function value, and update the label value of the population particles.

[0012] Step 6: Update the particle's velocity and position using the population particle's label value and decision value;

[0013] Step 7: Calculate the true objective function value of particles with a marked value of 1 in the population, remove duplicate sampling points, and add the deduplicated sampled point information to the historical database;

[0014] Step 8: Repeat steps 3 to 7 until the termination condition of the algorithm is met, and output the optimal solution to the optimization problem.

[0015] According to a specific implementation of an embodiment of this disclosure, step 1 specifically includes:

[0016] Construct a lookup function that includes the mapping relationship between mooring cable tension and wind turbine coordinates;

[0017] The steady-state position of each wind turbine is obtained by using the lookup function, and the steady-state equivalent wind speed at the hub of each wind turbine is combined to obtain the steady-state output power of the floating wind farm.

[0018] The axial sensing factor and yaw angle of each wind turbine in the floating wind farm are selected as optimization variables, and the constraints on the axial sensing factor and yaw angle are determined.

[0019] The steady-state output power of a floating wind farm under given wind conditions and given optimization variables is used as the objective function.

[0020] According to a specific implementation of this disclosure, the step of obtaining the steady-state output power of the floating wind farm by obtaining the stable position of each wind turbine according to the lookup function and combining it with the steady-state equivalent wind speed at the hub of each wind turbine includes:

[0021] Establish a set of nonlinear equations in which the vector sum of aerodynamic thrust and mooring cable tension is zero:

[0022]

[0023] Where [xs,i, ys,i] represents the stable position of the i-th floating wind turbine;

[0024] A lookup function Tf was constructed that includes the mapping relationship between mooring cable tension and wind turbine coordinates:

[0025]

[0026] The new position of the i-th floating wind turbine is calculated using the lookup function Tf:

[0027]

[0028] The iteration ends when the position change of the i-th floating wind turbine is less than a set threshold during the iteration, and the stable position of the i-th floating wind turbine is obtained.

[0029] when

[0030] Where ε is the threshold set for judging the convergence of the iteration;

[0031] After determining the stable position of the i-th floating wind turbine, the stable positions of its downstream turbines are calculated sequentially to obtain the stable positions of all floating wind turbines in the floating wind farm. The steady-state equivalent wind speed V at the hub of each floating wind turbine is then calculated. s,i Thus, the steady-state output power of the floating wind farm is obtained:

[0032]

[0033] Among them, P P To fit the parameters of the wind tunnel experiment; C P,i Let the wind energy utilization coefficient of the i-th wind turbine be:

[0034] C P,i =4a i (1-a i ) 2 η

[0035] Where η is a constant that limits the upper limit of the wind energy utilization coefficient.

[0036] According to a specific implementation of this disclosure, the objective function is:

[0037] Φ=P s (a,γ,V∞,θ), where P s For steady-state output power, α is the axial induction factor, γ is the yaw angle, V∞ is the wind speed, and θ is the dominant wind direction of the floating wind farm. The angle between the positive axis and the positive axis.

[0038] According to a specific implementation of an embodiment of this disclosure, step 4 specifically includes:

[0039] Using the PI function as the objective function of the surrogate model, a nonlinear optimization algorithm is used to search for the optimal sampling point in the subspace, and the position and velocity of the worst-performing particle in the historical objective function of the population generated by the swarm intelligence algorithm are modified.

[0040] Secondly, embodiments of this disclosure provide a floating wind farm power optimization system based on a surrogate model, comprising:

[0041] The objective function determination module is used to determine the optimization variables and their range of values ​​corresponding to the optimization problem of floating wind farms, and to obtain the objective function.

[0042] The initialization module is used to initialize the position of each particle in the population using the Latin hypercube sampling method, calculate the objective function value corresponding to each particle, and add the position and objective function value of each particle to the sampled database.

[0043] The module is used to construct a global proxy model based on a Gaussian process regression model by extracting the latest p sampled points from the historical database, and to construct a local proxy model by extracting the q sampled points that are closest to the optimal sampled point in Euclidean distance from the historical database.

[0044] The first update module is used to generate the optimal sampling point based on the local surrogate model and its determined subspace, using the PI filling criterion as the objective function of the surrogate model, and employing a nonlinear optimization algorithm to update the decision values ​​of the population particles.

[0045] The second update module is used to predict the objective function value of the population particles generated by the algorithm based on the global proxy model, pre-select particles that move to a better position by using the predicted objective function value, and update the label value of the population particles.

[0046] The third update module is used to update the velocity and position of particles based on the label and decision values ​​of the population particles;

[0047] The calculation module is used to calculate the true objective function value of particles with a marked value of 1 in the population, remove duplicate sampling points, and add the deduplicated sampled point information to the historical database.

[0048] The iteration module is used to repeat steps 3 to 7 until the termination condition of the algorithm is met, and output the optimal solution to the optimization problem.

[0049] The floating wind farm power optimization scheme based on a surrogate model in this embodiment includes: Step 1, determining the optimization variables and their ranges corresponding to the optimization problem of the floating wind farm, and obtaining the objective function; Step 2, initializing the position of each particle in the population using the Latin hypercube sampling method, calculating the objective function value corresponding to each particle, and adding the position and objective function value of each particle to the sampled database; Step 3, based on the Gaussian process regression model, extracting the latest p sampled points from the historical database to construct a global surrogate model, and extracting the q sampled points closest to the optimal sampled point in Euclidean distance from the historical database to construct a local surrogate model; Step 4, based on the local surrogate model and its determination... In the subspace of the population, the PI filling criterion is used as the objective function of the surrogate model. A nonlinear optimization algorithm is used to generate the optimal sampling point and update the decision value of the population particles. Step 5: Based on the global surrogate model, the objective function value of the population particles generated by the algorithm is predicted. Particles that move to a better position are pre-selected by the predicted objective function value and the label value of the population particles is updated. Step 6: The velocity and position of the particles are updated by the label value and decision value of the population particles. Step 7: The true objective function value of the particles with a label value of 1 in the population is calculated, duplicate sampling points are removed, and the deduplicated sampled point information is added to the historical database. Step 8: Steps 3 to 7 are repeated until the termination condition of the algorithm is met, and the optimal solution of the optimization problem is output.

[0050] The beneficial effects of the embodiments of this disclosure are as follows: Through the scheme of this disclosure, (1) a general surrogate model-assisted algorithm framework is proposed, which is applicable to general heuristic algorithms and can improve the search efficiency of the algorithm while ensuring the search capability of the algorithm. The data-driven surrogate model can learn from the historical data generated during the optimization process of the swarm intelligence algorithm and continuously improve the approximation ability of the solution space of the optimization problem as the iteration progresses, thereby guiding the swarm intelligence algorithm to find the best solution and reducing the number of searches in the solution space with poor objective function values, thereby reducing the time cost caused by calculating expensive objective functions; (2) a surrogate model-assisted mechanism is proposed, including assisted sampling based on the global surrogate model (GSM) and population pre-screening based on the local surrogate model (LSM). In the assisted sampling stage, considering the improvement magnitude and improvement probability of the optional solutions in the optimization space compared with the known optimal solutions, a nonlinear optimization algorithm is used to generate recommended solutions to guide the swarm intelligence algorithm to find the best solution. In the pre-screening stage of the population, the local proxy model is used to approximate the solution space of the optimization problem near the known optimal solution. The candidate solutions obtained by the swarm intelligence algorithm are directly evaluated in advance with low computational cost. The screening pass rate of the candidate solutions is adaptively adjusted according to the iteration stage, saving the computational resources consumed by the swarm intelligence algorithm and accelerating the convergence of the algorithm to the global optimal solution. (3) A mapping lookup table is constructed using the floating wind turbine position and the corresponding mooring cable tension data. Based on this mapping lookup table, the stable position of each wind turbine in the floating wind farm is quickly determined through iteration, thereby obtaining the stable output power of the floating wind farm. Attached Figure Description

[0051] To more clearly illustrate the technical solutions of the embodiments of this disclosure, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this disclosure. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0052] Figure 1 A flowchart illustrating a power optimization method for floating wind farms based on a proxy model, provided in this embodiment of the disclosure;

[0053] Figure 2 A top view schematic diagram of a floating wind farm provided for an embodiment of this disclosure;

[0054] Figure 3 A schematic diagram illustrating the specific process of a floating wind farm power optimization method based on a proxy model provided in this embodiment of the disclosure;

[0055] Figure 4 This is a schematic diagram of a floating wind farm power optimization system based on a proxy model, provided in an embodiment of this disclosure. Detailed Implementation

[0056] The embodiments of this disclosure will now be described in detail with reference to the accompanying drawings.

[0057] The following specific examples illustrate the implementation of this disclosure. Those skilled in the art can easily understand other advantages and effects of this disclosure from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of this disclosure, and not all of them. This disclosure can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this disclosure. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. Based on the embodiments in this disclosure, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this disclosure.

[0058] It should be noted that various aspects of embodiments within the scope of the appended claims are described below. It will be apparent that the aspects described herein can be embodied in a wide variety of forms, and any particular structure and / or function described herein is merely illustrative. Based on this disclosure, those skilled in the art will understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects set forth herein can be used to implement the device and / or practice the method. Additionally, this device and / or method can be implemented using structures and / or functionalities other than one or more of the aspects set forth herein.

[0059] It should also be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of this disclosure. The drawings only show the components related to this disclosure and are not drawn according to the number, shape and size of the components in actual implementation. In actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0060] Furthermore, specific details are provided in the following description to facilitate a thorough understanding of the examples. However, those skilled in the art will understand that the described aspects can be practiced without these specific details.

[0061] This disclosure provides a method for optimizing the power of floating wind farms based on a surrogate model, which can be applied to the power optimization process of floating wind farms in offshore wind power scenarios.

[0062] See Figure 1 This is a flowchart illustrating a surrogate model-assisted power optimization method for floating wind farms provided in an embodiment of this disclosure. Figure 1As shown, the method mainly includes the following steps:

[0063] Step 1: Determine the optimization variables and their range of values ​​for the optimization problem of the floating wind farm, and obtain the objective function;

[0064] Furthermore, step 1 specifically includes:

[0065] Construct a lookup function that includes the mapping relationship between mooring cable tension and wind turbine coordinates;

[0066] The steady-state position of each wind turbine is obtained by using the lookup function, and the steady-state equivalent wind speed at the hub of each wind turbine is combined to obtain the steady-state output power of the floating wind farm.

[0067] The axial sensing factor and yaw angle of each wind turbine in the floating wind farm are selected as optimization variables, and the constraints on the axial sensing factor and yaw angle are determined.

[0068] The steady-state output power of a floating wind farm under given wind conditions and given optimization variables is used as the objective function.

[0069] Furthermore, the step of obtaining the stable position of each wind turbine according to the lookup function and combining it with the steady-state equivalent wind speed at the hub of each wind turbine to obtain the steady-state output power of the floating wind farm includes:

[0070] Establish a set of nonlinear equations in which the vector sum of aerodynamic thrust and mooring cable tension is zero:

[0071]

[0072] Where [xs,i, ys,i] represents the stable position of the i-th floating wind turbine;

[0073] A lookup function Tf was constructed that includes the mapping relationship between mooring cable tension and wind turbine coordinates:

[0074]

[0075] The new position of the i-th floating wind turbine is calculated using the lookup function Tf:

[0076]

[0077] The iteration ends when the position change of the i-th floating wind turbine is less than a set threshold during the iteration, and the stable position of the i-th floating wind turbine is obtained.

[0078] when

[0079] Where ε is the threshold set for judging the convergence of the iteration;

[0080] After determining the stable position of the i-th floating wind turbine, the stable positions of its downstream turbines are calculated sequentially to obtain the stable positions of all floating wind turbines in the floating wind farm. The steady-state equivalent wind speed V at the hub of each floating wind turbine is then calculated. s,i Thus, the steady-state output power of the floating wind farm is obtained:

[0081]

[0082] Among them, P P To fit the parameters of the wind tunnel experiment; C P,i Let the wind energy utilization coefficient of the i-th wind turbine be:

[0083] C P,i =4a i (1-a i ) 2 η

[0084] Where η is a constant that limits the upper limit of the wind energy utilization coefficient.

[0085] Based on the above embodiments, the objective function is:

[0086] Φ=P s (a,γ,V∞,θ), where P s For steady-state output power, α is the axial induction factor, γ is the yaw angle, V∞ is the wind speed, and θ is the dominant wind direction of the floating wind farm. The angle between the positive axis and the positive axis.

[0087] In specific implementation, the embodiments of this disclosure use semi-submersible floating wind turbines as the constituent units of floating wind farms. The selected wind turbine model is the NREL 5MW model, and its corresponding platform model is the NREL semi-submersible floating platform. Figure 2 This is a top-down schematic diagram of a typical floating wind farm. The floating wind turbines are distributed in a two-dimensional Cartesian coordinate plane defined by the x and y axes. Each turbine has three buoys, and each buoy is connected to three anchor points on the seabed by mooring cables to limit the movement range and speed of the floating turbine. A set A = {1, 2, ..., N} is defined to represent the index of the N turbines in the floating wind farm, and the identifier i is used to refer to a single turbine. The upstream and downstream relationships of each turbine are determined according to the direction of the free wind flowing into the floating wind farm. Each turbine is numbered sequentially from upstream to downstream, with the upstreammost turbine numbered i = 1.

[0088] Assuming a floating wind farm has a prevailing wind direction, which is related to... The angle between the positive axis and the wind speed is V. ∞ And let the included angle in the first quadrant be positive. After obtaining the included angle θ, perform a coordinate transformation on the original Cartesian coordinate system of the floating wind farm according to equation (1) so that the wind direction coincides with the positive x-axis direction.

[0089]

[0090] In the formula: X o and Y o X and Y are the x and y coordinates of the platform center and three anchor points of each of the N floating wind turbines in the original Cartesian coordinate system, respectively; X and Y are the coordinate values ​​of the platform center and three anchor points of each floating wind turbine after coordinate transformation.

[0091] This embodiment employs the Gaussian single wake model proposed by T. Ishihara et al. and introduces multiple wake superposition to construct an aerodynamic module for a floating wind farm. This wake model uses a Gaussian distribution offset relative to the turbine rotor center to describe the wind speed loss downstream of the yaw turbine, and a double Gaussian distribution to describe the turbulence intensity increment downstream of the turbine. Since atmospheric turbulence can restore the wind direction downstream of the yaw turbine to the original incoming flow direction, the influence of the upstream turbine's yaw on the wind direction downstream is ignored. The wind speed loss caused by the yaw of the upstream turbine j on the downstream turbine i can be described as follows:

[0092]

[0093] In the formula: F is the flow direction function; C' T,j and I s,j Δx, Δy, and Δz represent the thrust coefficient of the upstream turbine j and the atmospheric turbulence intensity at its location under yaw conditions, respectively; Δx, Δy, and Δz represent the axial distance, vertical distance, and spanwise distance between the upstream and downstream turbines, respectively; d0 is the turbine impeller diameter; φ is the Gaussian distribution function; yd is the wake offset; and σ is the standard deviation.

[0094] To improve the accuracy of the calculation results, the cube root of the cubic mean of the wind speed losses at multiple points on the downstream turbine impeller surface is selected as the equivalent wind speed loss at the center of the downstream turbine hub. In a floating wind farm with N turbines, considering the superposition effect of multiple wake regions, the wind speed loss of the i-th turbine due to the wake effect of the upstream turbine is as follows:

[0095]

[0096] In the formula: Δv j,i Let be the wind speed loss generated by the j-th wind turbine at the i-th wind turbine. Combining equations (2) and (5), the equivalent wind speed at the hub of the i-th wind turbine is obtained:

[0097] V i =V ∞ (1-Δv i (4)

[0098] In the formula, V ∞Let represent the free-inflow wind speed in a floating wind farm. The aerodynamic thrust acting on the impeller surface of the i-th wind turbine is calculated from the equivalent wind speed at the hub of the i-th turbine.

[0099]

[0100] In the formula: F a,i,x and F a,i,y Let ρ be the x-component and y-component of the aerodynamic thrust acting on the i-th wind turbine, respectively; a air density; γ i C is the yaw angle of the i-th wind turbine; T,i Let be the thrust coefficient of the i-th wind turbine, which can be calculated according to the actuation disk theory using the following formula:

[0101] C T,i =4a i (1-a i (6)

[0102] In the formula: a i Let be the axial induction factor of the i-th fan.

[0103] Since the floating wind farm model established in this embodiment is a two-dimensional planar model, only the horizontal component of the mooring cable tension is considered. The magnitude and direction of the resultant force of the three mooring cables are only related to the location of the floating platform, and there is a unique mapping relationship. This paper obtains a dataset consisting of the coordinate positions of the semi-submersible floating wind turbine and the horizontal tension vector of the mooring cables from the OpenFAST software. The mapping relationship between the horizontal tension vector of the mooring cables and the coordinate positions of the floating wind turbine can be established through a lookup table function:

[0104]

[0105] In the formula: F m,i,x and F m,i,y These are the x-component and y-component of the resultant force of the three mooring cables of the i-th wind turbine, respectively; Tmoor is a lookup table function.

[0106] The aerodynamic thrust on the i-th floating wind turbine in a floating wind farm is related to its position [x]. i y i and the location of the upstream wind turbine [x] j y j The mooring cable tension on the i-th floating wind turbine is related to its own position, while the stable position of all upstream wind turbines of the i-th floating wind turbine is determined. s,i y s,i Afterwards, the aerodynamic thrust and mooring cable tension acting on the i-th floating wind turbine are only related to its own position. Solving the nonlinear equations where the vector sum of the aerodynamic thrust and mooring cable tension is zero will determine the stable position of the i-th floating wind turbine.

[0107]

[0108] In the formula: [x s,i y s,i Let ] represent the stable position of the i-th floating wind turbine. The general method for solving nonlinear equations is the iterative method, which involves continuously iterating using a pre-constructed iterative function until the variables approximate and converge to the solution. To accelerate the solution of the above equations, a lookup function T, which includes the mapping relationship between the mooring cable tension and the wind turbine coordinates, is first constructed. f :

[0109]

[0110] Suppose that in the t-th iteration, the position of the i-th floating wind turbine is [x]. i t y i t The aerodynamic thrust of the fan at this position can be calculated using equation (5). By balancing the mooring cable tension and aerodynamic thrust on the wind turbine, the new position of the i-th floating wind turbine can be calculated using equation (9):

[0111]

[0112] The iteration ends when the position change of the i-th floating wind turbine is less than a set threshold during the iteration, and the stable position of the i-th floating wind turbine is obtained.

[0113] when

[0114] In the formula: ε is the threshold set for judging the convergence of the iteration. After determining the stable position of the i-th floating wind turbine, the stable positions of its downstream wind turbines are calculated in turn to obtain the stable positions of all floating wind turbines in the floating wind farm. The steady-state equivalent wind speed V at the hub of each floating wind turbine is calculated by formula (4). s,i Thus, the steady-state output power of the floating wind farm is obtained:

[0115]

[0116] In the formula: P P To fit the parameters of the wind tunnel experiment; C P,i Let i be the wind energy utilization coefficient of the i-th wind turbine

[11] :

[0117] C P,i =4a i (1-a i ) 2 η (13)

[0118] In the formula: η is a constant that limits the upper limit of the wind energy utilization coefficient.

[0119] Considering that the operation of wind turbines affects the steady-state output power of floating wind farms, the axial induction factor 'a' for each wind turbine in a floating wind farm is selected. i and yaw angle γ i These are the optimization variables. The constraints on these variables are as follows:

[0120] 0.1≤a i ≤0.333 (14)

[0121] -30°≤γ i ≤30° (15)

[0122] The objective function is the steady-state output power of the floating wind farm under given wind conditions and given optimization variables:

[0123] Φ=P s (a,γ,V ∞ ,θ) (16)

[0124] Step 2: Initialize the position of each particle in the population using the Latin hypercube sampling method, calculate the objective function value corresponding to each particle, and add the position and objective function value of each particle to the sampled database;

[0125] In practice, the standard particle swarm optimization (SPSO) algorithm introduces an adaptive random topology and rotation invariance on the basis of the original particle swarm optimization algorithm. It performs well in unimodal and separable test function families, but still has the defect of being unable to escape local optima

[12] . Therefore, this paper improves the SPSO algorithm to enhance its global search capability and proposes an improved standard particle swarm optimization (ISPSO) algorithm.

[0126] Assuming the dimension of the optimization variable is n and the number of particles in the population is N, when the number of iterations is k, the position and velocity information of the i-th particle are as follows:

[0127]

[0128]

[0129] In the formula: j represents the dimension of the optimization variable; This represents the position component of the i-th particle in the j-th dimension when the number of iterations is k; This represents the velocity component of the i-th particle in the j-th dimension when the number of iterations is k.

[0130] Furthermore, the historical best position P of each particle in the population i k and the historical best position of the population It can be represented as:

[0131]

[0132]

[0133] In the formula: and Let J represent the j-th dimension component of the historical best position of the i-th particle and the j-th dimension component of the historical best position of the population, respectively, when the number of iterations is k.

[0134] The SPSO algorithm utilizes the concept of rotation invariance, treating each particle in the k-th iteration around its current position X. i k Point L, slightly deviating from the current best position in the particle's history. i k And point L, which is slightly off from the current population's historical best position. g k The center of gravity G is defined. i k :

[0135]

[0136]

[0137]

[0138] In the formula: c1 and c2 are parameters that control the deviation. and It is a matrix composed of random numbers in the interval [0,1].

[0139] Update the position and velocity of the i-th particle:

[0140]

[0141]

[0142] In the formula: H i (G i k ,||G i k -X i k ||) represents the target position obtained by the random hyperspherical function; ω is the inertial weight that controls the jump amplitude of the particle position.

[0143] To improve the optimization capability of the SPSO algorithm throughout the entire iteration process, the particle velocity update formula in equation (22) was modified:

[0144]

[0145] In the formula: The adaptive inertia weight, unique to each particle at the current iteration number, is calculated as follows:

[0146]

[0147]

[0148] In the formula: ω max and ω min These are the maximum and minimum values ​​of the inertia weight, T. m The maximum number of iterations is given by d, where Q is the control parameter for the decay rate of the inertial weight, and d is the maximum number of iterations. i Let d be the Euclidean distance between the position of the i-th particle and the target position. U and d L For all d i The minimum value of the maximum value.

[0149] The inertial weight update formula proposed in equation (25) enables the inertial weight ω to be adaptively adjusted with the distance between the particle position and the target position and the number of iterations, thereby enhancing the local search capability and the ability to escape local optima of the SPSO algorithm.

[0150] Furthermore, a larger population size facilitates global optimization but reduces convergence speed and increases computational resource consumption. Conversely, a smaller population size accelerates convergence but makes the algorithm more prone to getting trapped in local optima. To balance convergence speed and optimization accuracy, a linear population reduction strategy is introduced to adaptively adjust the population size. The calculation formula is as follows:

[0151]

[0152] Where: N init N represents the initial number of particles in the population. min This represents the minimum number of particles in the population. In the early stages of optimization, a larger population size helps the algorithm explore the optimization space. As optimization progresses, a gradually decreasing population size can accelerate the convergence speed of the algorithm and save computational resources.

[0153] Step 3: Based on the Gaussian process regression model, extract the latest p sampled points from the historical database to construct a global proxy model, and extract the q sampled points that are closest to the optimal sampled point in Euclidean distance from the historical database to construct a local proxy model.

[0154] In practice, surrogate models are used to replace the original, expensive optimization model to reduce optimization time. Commonly used surrogate modeling methods include: RBF Neural Network (RBFNN), Generalized Regression Neural Network (GRNN), Random Forest (RF), and Gaussian Process Regression (GPR). Considering both the accuracy and time cost of surrogate modeling, GPR is chosen as the surrogate model construction method for the floating wind farm optimization problem. GPR is a supervised machine learning method based on statistical theory and has been widely used in the construction of surrogate models. GPR first establishes a prior function in the given dataset D = {X, Y}, generates the posterior distribution of the input data under the test input data X*, and, based on the assumption that there is a joint Gaussian distribution between the test output data Y* and the given output data Y, establishes the Gaussian process model through maximum likelihood estimation, obtaining the posterior distribution of the output data Y* of the test input data X*.

[0155] M = f gpr (X,Y) (33)

[0156] (μ,s 2 )=M(X * (34)

[0157] Y*~N(μ,s 2 (35)

[0158] In the formula: M is the GPR surrogate model, μ and s 2 These are the mean and variance of the output data Y* corresponding to the test input data X*, respectively.

[0159] Considering both modeling accuracy and time cost, GPR was chosen as the surrogate model construction method for the floating wind farm optimization problem. First, to ensure high prediction accuracy of GSM within the current search region of the algorithm, p sampled points S from D that are closest to the sum of Euclidean distances of all particles in the algorithm population were selected. g ={(X1,Y1),(X2,Y2),…,(X p ,Y p GSM is constructed using Gaussian process regression.

[0160] M gsm =f gpr (X g ,Y g (36)

[0161] In the formula: X g With Y g S g The sample location and the sample objective function value.

[0162] Then, to ensure that the LSM lies within the promising search space of the optimization problem, select q sampled points S from D that are closest to the known optimal solution in Euclidean distance. l ={(X1,Y1),(X2,Y2),…,(X q ,Y q LSM is constructed using Gaussian process regression:

[0163] M lsm =f gpr (X l ,Y l (37)

[0164] In the formula: X l and Y l S l The sample location and the sample objective function value.

[0165] Step 4: Based on the local surrogate model and its determined subspace, the PI filling criterion is used as the objective function of the surrogate model. A nonlinear optimization algorithm is used to generate the optimal sampling point and update the decision value of the population particles.

[0166] Based on the above embodiments, step 4 specifically includes:

[0167] Using the PI function as the objective function of the surrogate model, a nonlinear optimization algorithm is used to search for the optimal sampling point in the subspace, and the position and velocity of the worst-performing particle in the historical objective function of the population generated by the swarm intelligence algorithm are modified.

[0168] In practical implementation, LSM lies within a promising search region of the optimization problem and has low computational cost. To address the low optimization efficiency of the ISPSO algorithm, firstly, the sampled point set S... l Determine the boundary of the sub-optimization space:

[0169]

[0170]

[0171] In the formula: U b and L b These are the upper and lower bounds of the sub-optimization space, respectively.

[0172] Considering that surrogate models inevitably contain errors in approximate optimization problems, if the predicted mean of the LSM is used as the objective function of the surrogate optimization problem, it will be difficult to find more valuable sampling points in the sub-optimization space. Therefore, the improved lifting (PI) function is adopted as the objective function of the surrogate optimization problem.

[20] :

[0173]

[0174] In the formula: F is the cumulative distribution function of the standard normal distribution, Φ * and s l Sampling point X * Predicted mean and standard deviation:

[0175]

[0176] Then, after determining the objective function of the surrogate optimization problem, L-BFGS is used.

[21] The algorithm searches for the optimal sampling point X in the sub-optimization space. sas :

[0177]

[0178] Finally, the value of the search region where the particle is located is evaluated using the objective function value corresponding to the historical best position of the particle in the population. The decision value of the particle located in the worst search region in the population is set to 1, while the decision value of other particles is 0.

[0179]

[0180] To reasonably select the parameter q required for constructing the LSM, the gain value S of the auxiliary sampling in each iteration is defined. sas :

[0181] S sas =Φ(X sas )-Φ(X pd,t )

[0182]

[0183] By modifying the position of the individual with the worst objective function value in the population generated by the swarm intelligence algorithm to the position of the optimal sampling point, the development and exploration capabilities of the population can be improved, guiding the swarm intelligence algorithm to find the best.

[0184] Step 5: Based on the global proxy model, predict the objective function value of the population particles generated by the algorithm, pre-select particles that move to a better position by using the predicted objective function value, and update the label value of the population particles.

[0185] In practical implementation, GSM exhibits high prediction accuracy and low computational cost within the current search region of the SA-ISPSO algorithm. To address the high time cost of the ISPSO algorithm during optimization, this paper first utilizes GSM to predict approximate objective function values ​​for the new positions of population particles.

[0186]

[0187] In the formula: Xpd,i The new position obtained by the particle based on its own velocity:

[0188]

[0189] Then, using the obtained approximate objective function value Filter and label particles in the population that move toward more promising regions:

[0190]

[0191] In the formula: C(k) is an adaptive coefficient that controls the pre-screening rate. In the early stage of iteration, particles with poor objective function values ​​are allowed to pass through the screening to enhance population diversity. As the iteration progresses, the threshold for population particles to pass through the screening is gradually increased to remove redundancy. The calculation formula is as follows:

[0192]

[0193] In the formula: C l and C u These are the initial and final values ​​of C(k), respectively.

[0194] To rationally select the parameter p required for constructing the GSM, the success rate S of the pre-screening strategy in each iteration is defined. pd :

[0195]

[0196]

[0197] By pre-screening the offspring generated by the swarm intelligence algorithm, the number of times the swarm intelligence algorithm searches in regions where the probability of improving the objective function value is low can be reduced, thereby reducing the time cost of computing expensive objective functions.

[0198] Step 6: Update the velocity and position of the particles using the label and decision values ​​of the population particles.

[0199] In practice, after obtaining the label value and decision value of the population particles, the velocity and position of the particles can be further updated based on the label value and decision value of the population particles.

[0200] Step 7: Calculate the true objective function value corresponding to the new location of an individual in the population, and add the information of the sampled points to the historical database;

[0201] In practice, after obtaining the new location of an individual in the population, the true objective function value corresponding to the new location of the individual is calculated, and the information of the sampled points is added to the historical database.

[0202] Step 8: Repeat steps 3 to 6 until the termination condition of the algorithm is met, and output the optimal solution to the optimization problem.

[0203] In practice, steps 3 through 6 need to be repeated iteratively until the termination condition of the algorithm is met, outputting the optimal solution to the optimization problem and achieving power optimization. The specific process of this embodiment is as follows: Figure 3 As shown.

[0204] The floating wind farm power optimization method based on surrogate model assistance provided in this embodiment proposes the following: (1) a surrogate model-assisted intelligent optimization framework for floating wind farm power optimization. This framework includes four parts: an improved standard particle swarm optimization (ISPSO) algorithm, a floating wind farm steady-state power model, a historical database, and a surrogate model assistance mechanism. The SA-ISPSO algorithm proposed based on this framework performs well in terms of solution effect and computational efficiency when solving the floating wind farm power optimization problem; (2) an ISPSO algorithm combining adaptive inertia weight and adaptive population size reduction is proposed. The adaptive mechanism adjusts the algorithm's inertia weight and population size according to the iteration information, thereby improving the algorithm's global search capability and convergence speed; (3) a new surrogate model assistance mechanism is proposed. This assistance mechanism includes an auxiliary sampling strategy based on a local surrogate model and a pre-screening strategy based on a global surrogate model. Both strategies guide the particles to update their own velocity and position by generating the label value and decision value of the population particles, thereby improving the algorithm's optimization efficiency.

[0205] For a corresponding method embodiment, see [link to relevant documentation]. Figure 4 This disclosure also provides a surrogate model-assisted floating wind farm power optimization system 40, comprising:

[0206] The objective function determination module 401 is used to determine the optimization variables and their range of values ​​corresponding to the optimization problem of the floating wind farm, and to obtain the objective function.

[0207] Initialization module 402 is used to initialize the position of each particle in the population using the Latin hypercube sampling method, calculate the objective function value corresponding to each particle, and add the position and objective function value of each particle to the sampled database.

[0208] Module 403 is used to construct a global proxy model based on a Gaussian process regression model by extracting the latest p sampled points from the historical database, and to construct a local proxy model by extracting the q sampled points that are closest to the optimal sampled point in Euclidean distance from the historical database.

[0209] The first update module 404 is used to generate the optimal sampling point based on the local surrogate model and its determined subspace, using the PI filling criterion as the objective function of the surrogate model, and to update the decision value of the population particles using a nonlinear optimization algorithm.

[0210] The second update module 405 is used to predict the objective function value of the population particles generated by the algorithm based on the global proxy model, pre-select particles that move to a better position through the predicted objective function value, and update the label value of the population particles.

[0211] The third update module 406 is used to update the velocity and position of particles based on the label value and decision value of the population particles.

[0212] The calculation module 407 is used to calculate the true objective function value of particles with a marked value of 1 in the population, remove duplicate sampling points, and add the deduplicated sampled point information to the historical database.

[0213] The iteration module 408 is used to repeat steps 3 to 7 until the termination condition of the algorithm is met, and output the optimal solution to the optimization problem.

[0214] Figure 4 The system shown can execute the contents of the above method embodiments. For the parts not described in detail in this embodiment, please refer to the contents recorded in the above method embodiments, and they will not be repeated here.

[0215] The units described in the embodiments of this disclosure can be implemented in software or in hardware.

[0216] It should be understood that the various parts of this disclosure can be implemented in hardware, software, firmware, or a combination thereof.

[0217] The above description is merely a specific embodiment of this disclosure, but the scope of protection of this disclosure is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this disclosure should be included within the scope of protection of this disclosure. Therefore, the scope of protection of this disclosure should be determined by the scope of the claims.

Claims

1. A method for proxy model assisted optimization of power for floating wind farms, characterized in that, include: Step 1: Determine the optimization variables and their range of values ​​for the optimization problem of the floating wind farm, and obtain the objective function; Step 2: Initialize the position of each particle in the population using the Latin hypercube sampling method, calculate the objective function value corresponding to each particle, and add the position and objective function value of each particle to the sampled database; Step 3: Based on the Gaussian process regression model, extract the latest p sampled points from the historical database to construct a global proxy model, and extract the q sampled points that are closest to the optimal sampled point in Euclidean distance from the historical database to construct a local proxy model. Step 4: Based on the local surrogate model and its determined subspace, the PI filling criterion is used as the objective function of the surrogate model. A nonlinear optimization algorithm is used to generate the optimal sampling point and update the decision value of the population particles. Step 5: Based on the global proxy model, predict the objective function value of the population particles generated by the algorithm, pre-select particles that move to a better position by using the predicted objective function value, and update the label value of the population particles. Step 6: Update the particle's velocity and position using the population particle's label value and decision value; Step 7: Calculate the true objective function value of particles with a marked value of 1 in the population, remove duplicate sampling points, and add the deduplicated sampled point information to the historical database; Step 8: Repeat steps 3 to 7 until the termination condition of the algorithm is met, and output the optimal solution to the optimization problem.

2. The method of claim 1, wherein Step 1 specifically includes: Construct a lookup function that includes the mapping relationship between mooring cable tension and wind turbine coordinates; The steady-state position of each wind turbine is obtained by using the lookup function, and the steady-state equivalent wind speed at the hub of each wind turbine is combined to obtain the steady-state output power of the floating wind farm. The axial sensing factor and yaw angle of each wind turbine in the floating wind farm are selected as optimization variables, and the constraints on the axial sensing factor and yaw angle are determined. The steady-state output power of a floating wind farm under given wind conditions and given optimization variables is used as the objective function.

3. The method of claim 2, wherein The step of obtaining the stable position of each wind turbine according to the lookup function and combining it with the steady-state equivalent wind speed at the hub of each wind turbine to obtain the steady-state output power of the floating wind farm includes: Establish a set of nonlinear equations in which the vector sum of aerodynamic thrust and mooring cable tension is zero: Where [xs,i, ys,i] represents the stable position of the i-th floating wind turbine; A lookup function Tf was constructed that includes the mapping relationship between mooring cable tension and wind turbine coordinates: The new position of the i-th floating wind turbine is calculated using the lookup function Tf: The iteration ends when the position change of the i-th floating wind turbine is less than a set threshold during the iteration, and the stable position of the i-th floating wind turbine is obtained. When Where ε is the threshold set for judging the convergence of the iteration; After determining the stable position of the i-th floating wind turbine, the stable positions of its downstream turbines are calculated sequentially to obtain the stable positions of all floating wind turbines in the floating wind farm. The steady-state equivalent wind speed Vs,i at the hub of each floating wind turbine is calculated, and then the steady-state output power of the floating wind farm is obtained. where P P is the parameter of the fitting wind tunnel experiment; C P,i is the wind energy utilization coefficient of the ith wind turbine; CP,i=4ai(1-ai)2η Where η is a constant that limits the upper limit of the wind energy utilization coefficient.

4. The method of claim 3, wherein The objective function is Φ = Ps(a,γ,V∞,θ), where Ps is the steady-state output power, a is the axial induction factor, γ is the yaw angle, V∞ is the wind speed, and θ is the dominant wind direction of the floating wind farm. The angle between the positive axis and the positive axis.

5. The method of claim 4, wherein Step 4 specifically includes: Using the PI function as the objective function of the surrogate model, a nonlinear optimization algorithm is used to search for the optimal sampling point in the subspace, and the position and velocity of the worst-performing particle in the historical objective function of the population generated by the swarm intelligence algorithm are modified.

6. A proxy model assisted based floating wind farm power optimization system, characterized in that, include: The objective function determination module is used to determine the optimization variables and their range of values ​​corresponding to the optimization problem of floating wind farms, and to obtain the objective function. The initialization module is used to initialize the position of each particle in the population using the Latin hypercube sampling method, calculate the objective function value corresponding to each particle, and add the position and objective function value of each particle to the sampled database. The module is used to construct a global proxy model based on a Gaussian process regression model by extracting the latest p sampled points from the historical database, and to construct a local proxy model by extracting the q sampled points that are closest to the optimal sampled point in Euclidean distance from the historical database. The first update module is used to generate the optimal sampling point based on the local surrogate model and its determined subspace, using the PI filling criterion as the objective function of the surrogate model, and employing a nonlinear optimization algorithm to update the decision values ​​of the population particles. The second update module is used to predict the objective function value of the population particles generated by the algorithm based on the global proxy model, pre-select particles that move to a better position by using the predicted objective function value, and update the label value of the population particles. The third update module is used to update the velocity and position of particles based on the label and decision values ​​of the population particles; The calculation module is used to calculate the true objective function value of particles with a marked value of 1 in the population, remove duplicate sampling points, and add the deduplicated sampled point information to the historical database. The iterative module is used to repeat steps 3 to 7 until the termination condition of the algorithm is met, and output the optimal solution to the optimization problem.

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