A method for optimizing offshore wind farm layout based on wake constraint random reconstruction

Abstract

The application provides a sea wind farm layout optimization method based on tail flow constraint random reconstruction, aiming at the problems that the tail flow effect and electrical fault control are separated in the prior art, and the aerodynamic interference is ignored in fault reconstruction. The application first establishes an initial layout model with tail flow awareness, maximizes wind energy capture efficiency through nonlinear space optimization, then constructs a probability scenario of fault and wind speed, and quantifies the influence of cable random fault on tail flow propagation. Specifically, the application designs a dynamic reconstruction optimization layer, embeds aerodynamic power constraints and tail flow sequence into electrical topology decision, has aerodynamic and electrical regulation and control capability in fault state, realizes investment planning and reconstruction optimization through progressive solution, and introduces a tail flow feasibility cutting mechanism to improve robustness. The application effectively solves the limitations of traditional layout design, improves power generation efficiency, reduces tail flow loss, shortens fault recovery period, and provides a high-precision scheme for sea wind farm layout optimization.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of offshore wind farm layout optimization, and proposes a layout optimization method based on wake constraint random reconstruction, which solves the problems of separation of wake effect and electrical fault control in the prior art, and improves the power generation efficiency and fault recovery capability of offshore wind farms. BACKGROUND

[0002] With the increasing global energy demand and the growing emphasis on environmental protection, offshore wind power as a clean and renewable energy form has received widespread attention. The layout optimization of offshore wind farms is a complex and multi-dimensional engineering problem, involving efficient utilization of wind energy resources, wake effect between wind turbines, reliability of electrical systems, and fault recovery capability, and many other aspects.

[0003] In the prior art, the layout design of offshore wind farms usually focuses on maximizing wind energy capture efficiency, but often ignores the mutual influence between wake effect and electrical faults. Wake effect refers to the wake of an upstream wind turbine, which will attenuate the effective wind speed of a downstream wind turbine, thereby reducing the power generation efficiency of the downstream wind turbine. Electrical faults such as cable faults not only affect the normal operation of the wind turbine, but also interfere with the aerodynamic characteristics of the entire wind farm through wake propagation. Wake effect and electrical fault control are usually handled separately, without fully considering the interaction between the two. In the wind turbine layout design phase, although factors such as wind direction and wind speed are considered, the impact of cable faults on wake propagation is often ignored, and in the fault reconstruction process, aerodynamic interference is often ignored, resulting in prolonged fault recovery period and reduced power generation efficiency.

[0004] In addition, the traditional layout design method has limitations and cannot effectively quantify the joint probability distribution of cable failure rate and wind speed fluctuation. In actual operation, cable failure and wind speed fluctuation are random events, and their joint probability distribution is crucial for optimizing wind farm layout. However, the existing technology lacks effective modeling and quantification methods for this joint probability distribution, making it difficult to achieve coordinated regulation of aerodynamics and electricity in fault state. These problems not only affect the overall performance of offshore wind farms, but also increase the operation and maintenance costs and risks. SUMMARY

[0005] The application aims at the problems of tail flow effect and electrical fault control separation in the prior art, and proposes a sea wind farm layout optimization method based on tail flow constraint random reconstruction, which firstly establishes a tail flow aware initial layout model, and maximizes wind energy capture efficiency through nonlinear space optimization, and then constructs a probability scenario of fault and wind speed, and quantifies the influence of cable random fault on tail flow propagation.

[0006] The sea wind farm layout optimization method based on tail flow constraint random reconstruction comprises the following steps:

[0007] S1: a mapping relationship between a wind turbine space coordinate set and a wind resource parameter is established, and a nonlinear layout optimization model is constructed to maximize annual power generation under tail flow interference as an objective, while satisfying dynamic spacing constraints and sea area boundary restrictions, specifically, first, define the wind turbine position decision variable as a two-dimensional Cartesian coordinate set The set completely describes the spatial distribution of all wind turbines in the planning sea area:

[0008]

[0009] Wherein, N represents the total number of wind turbines in the wind farm, each coordinate pair (x i ,y i ) uniquely identifies the center position of the i-th wind turbine, the horizontal coordinate x i and the vertical coordinate y i are positive real numbers, ensuring that the wind turbine is located in the actual physical space, on the basis of position coordinate definition, combined with wind resource space-time characteristics and wind turbine aerodynamic parameters, the wind resource parameter matrix W is represented by a three-dimensional parameter matrix:

[0010] W=[w d,s ] D×S

[0011] w d,s =(v d ,f s ,ρ s )

[0012] Wherein, v d represents the average wind speed of the wind direction sector d, with the unit of m / s, f s is the annual occurrence frequency of the wind speed interval s, with the unit of %, and wd,s For wind resource parameters, the matrix includes D wind direction sectors and S wind speed intervals, p s is the air density corresponding to the operating condition, with the unit of kg / m 3 , the power curve P i (v) describes the variation of output power with wind speed v, the thrust coefficient C T,j (v) quantifies the disturbance intensity of the wind turbine to the airflow, both of which are piecewise differentiable functions of wind speed;

[0013] The optimization objective is to maximize the annual power generation under the wake interference, since the upstream wind turbine wake will attenuate the effective wind speed of the downstream wind turbine, the actual power output of a single wind turbine i under a specific wind direction d and wind speed v needs to calculate the cumulative wake effect

[0014]

[0015] wherein, denotes the set of wind turbine units located upstream of wind turbine i in wind direction d, P i (v) denotes the power curve, and the wake attenuation factor η j→i is calculated by the improved Jensen wake model:

[0016]

[0017] wherein, R represents the wind turbine rotor radius, with the unit of m, δ ji denotes the longitudinal distance between wind turbine j and i in wind direction projection, with the unit of m, C T,j (v) denotes the thrust coefficient, d ji denotes the Euclidean distance between the two wind turbines, with the unit of m, and h represents the wake attenuation empirical constant, the annual power generation objective function finally integrates all wind direction and wind speed operating conditions:

[0018]

[0019] wherein, T op represents the annual standard operating hours, S represents the number of wind speed intervals, v d represents the average wind speed of wind direction sector d, the spatial constraints include two types of dynamic spacing constraints and sea area boundary constraints, the dynamic spacing constraints prevent aerodynamic interference between wind turbines, any two wind turbines satisfy the minimum safety distance, the dynamic spacing constraints ensure that the distance between wind turbine i and j is not less than the product of the safety factor γ and the rotor diameter D rotor :

[0020]

[0021] wherein, D rotor= 2R, gamma is 3 times the rotor diameter to avoid the risk of turbulence interference, and the sea area boundary constraint ensures that all wind turbines are located within the planned sea area. The rectangular boundary box determined by geographic data is realized:

[0022] x i ∈[X min ,X max ]

[0023] y i ∈[Y min ,Y max ]

[0024] where (X min ,X max ,Y min ,Y max ) represents the boundary coordinates determined by sea survey data, and the constructed nonlinear optimization model integrates the target and constraints:

[0025]

[0026] x i ∈[X min ,X max ],y i ∈[Y min ,Y max ]

[0027]

[0028] where, represents a two-dimensional Cartesian coordinate set, T op represents the annual standard operating hours, N represents the total number of wind turbines in the wind farm, and the model is solved by a sequential quadratic programming algorithm, and the optimal wind turbine coordinate set is output

[0029] S2: Quantify the joint probability distribution of cable failure rate and wind speed fluctuation; based on the wake conduction dynamics model, calculate the spatial gradient of wind speed disturbance field caused by failure, and represent the chain transmission effect of electrical failure to aerodynamic interference;

[0030] S3: Dynamic reconstruction optimization layer, simultaneously optimizing power generation loss and topology change cost; embedding aerodynamic power limiting constraint and wake safety sequence into electrical decision, output optimal cable topology;

[0031] S4: Construct a two-level framework of main problem and subproblem, the main problem decides the cable investment planning, and the subproblem solves the real-time strategy of failure scenario; introduce the wake feasibility cutting mechanism, when the wind speed disturbance exceeds the threshold, trigger the layout re-optimization;

[0032] S5: define the correlation matrix of wind turbine spatial position and wake propagation timing; construct 0-1 integer constraint group based on safe sequence, and re-optimize the process to avoid the risk of continuous shutdown of wind turbines in high turbulence intensity area.

[0033] According to a specific implementation manner of the embodiment of the application, the specific steps of S2 are as follows:

[0034] On the basis of the initial layout optimization, the effects of cable fault and wind speed fluctuation are quantified accurately; the fault event set is defined as Wherein f m represents the mth cable fault mode, M represents the total number of cable fault modes, and the wind speed fluctuation characteristics are modeled through historical meteorological data:

[0035]

[0036] Wherein, represents the long-term average wind speed, and the unit is m / s, σ v is the standard deviation of wind speed fluctuation, the unit is m / s, ε(t) is a random disturbance term subject to standard normal distribution, t represents time, and the unit is s; the statistical correlation between the cable fault rate and the wind speed fluctuation is modeled through a Copula function, and it is assumed that the cable fault rate p f has a strong correlation with the wind speed fluctuation amplitude |Δv|, and the joint cumulative distribution function is:

[0037] P(F≤f,V≤v)=C θ (Φ f (f),Φ v (v))

[0038]

[0039] Wherein, Φ f (·) represents the marginal cumulative distribution function of the fault rate, subject to a Weibull distribution with a shape parameter α and a scale parameter β, Φ v (·) is the marginal cumulative distribution function of the wind speed fluctuation, subject to a Rayleigh distribution with a scale parameter σ, C θ represents a Clayton Copula function, and the parameter θ controls the tail correlation, wherein u1=Φ f (f) and u2=Φ v (v) are the probability integral transformation values of the fault rate and the wind speed fluctuation respectively, and a wake conduction dynamics model is used to calculate the propagation of the wind speed disturbance caused by the fault. When the cable fault causes the wind turbine i to be unplanned shutdown, the sudden disappearance of the wake will cause the downstream flow field to be reconstructed. Based on the law of conservation of mass and momentum, the change of the disturbance wind speed Δv i (x,t) at the position x=(x,y) and the time t satisfies:

[0040]

[0041] where u = (u x ,u y ) is the background wind speed field vector, v represents the air dynamic viscosity coefficient, and β is the disturbance decay coefficient. The disturbance gradient tensor under the fault scenario s = (f m ,v(t)) is:

[0042]

[0043] wherein represents a set of fault wind turbine indexes, and represent the change rates of the wind speed disturbance in the east-west direction and the north-south direction, respectively, represents the spatial sharpness of the fault influence, and the maximum position thereof identifies a high-risk area. The chain transmission effect is fully characterized by the disturbance propagation matrix:

[0044]

[0045] wherein represents the wind speed disturbance gradient amplitude caused by the fault of the wind turbine i at the position of the wind turbine j, is the initial disturbance gradient amplitude at the position of the fault source, represents the fault propagation coefficient of the fault wind turbine i to the wind turbine j, and when j is located downstream of the wake of i otherwise 0, the matrix maps the electrical fault to the aerodynamic disturbance, and the output is a set of fault and wind speed scenarios wherein K represents the total number of scenarios, and each scenario s k includes a fault mode f m , a wind speed fluctuation sequence v(t), a disturbance gradient field and a transmission matrix

[0046] According to a specific implementation manner of an embodiment of the present application, the specific steps of the S3 are as follows:

[0047] based on the optimal wind turbine coordinate set of the step S1 and the set of fault and wind speed scenarios of the step S2 A collaborative optimization model of the cable topology structure and the wind turbine control strategy is established, the target of which is to realize the minimization of the cost and the maximization of the power generation stability under the premise of ensuring the system reliability by jointly optimizing the electrical connection mode and the wind turbine operation parameters. The cable topology structure adopts a binary adjacency matrix Z to represent:

[0048] Z = [z ij ] N×N

[0049] where z ij represents the direct cable connection status between wind turbine i and wind turbine j, N represents the total number of wind turbines in the wind farm, z ij = 1 indicates the existence of a physical cable connection, and z ij = 0 indicates no direct connection, and the matrix satisfies the tree topology constraint condition:

[0050]

[0051] where z ij represents the direct cable connection status between wind turbine i and wind turbine j, N represents the total number of wind turbines in the wind farm, this constraint ensures that the entire wind farm forms a loop-free connected network, avoiding the occurrence of electrical islands or redundant connections, and the diagonal elements of the matrix are always zero z ij = 0 and satisfy the symmetry z ij = z ji , and the wind farm control strategy is a scenario-dependent dynamic parameter set:

[0052]

[0053] where U( k) represents the set of full-farm control strategies under scenario s k , and the control vector of each wind turbine contains two key operating variables:

[0054]

[0055] where represents the pitch angle adjustment of wind turbine i under fault scenario s k , in degrees, which is allowed to be continuously adjusted within the range of (0°, 90°), represents the rotor speed under the corresponding scenario, in radians per second, which needs to satisfy the safe operating range [ω min , ω max ], and the control parameters directly affect the aerodynamic characteristics and power output characteristics of the wind turbine;

[0056] Fault loss minimization objective quantifies the power generation loss caused by cable faults

[0057]

[0058] where P nom is the rated power of the wind turbine, in megawatts, represents the rotor speed under the corresponding scenario, is the actual output power of wind turbine i in scenario s k , in megawatts, represents the equivalent wind speed after the wake effect correction, in m / s, τk is the duration of scenario s k , in hours, is the failure propagation coefficient of wind turbine i, reflecting the influence strength of local failure on the global system, and the infrastructure investment corresponding to the target calculation topology of cable construction cost:

[0059]

[0060] where C cable represents the total cable construction cost, including material cost, laying cost and insurance cost, c unit represents the comprehensive cost per unit length of cable, is the optimal wind turbine coordinate of step S1, in meters, ||·|| is the Euclidean distance operator, which calculates the actual cable laying path length, and the robustness of power generation evaluates the adaptability of the control strategy to wind speed fluctuations:

[0061]

[0062] where K represents the total number of scenarios, represents the rotor speed under the corresponding scenario, and Δv (k) is the wind speed disturbance amplitude of step S2, in m / s, which quantifies the stability of power output by ratio, and the value closer to 1 indicates stronger anti-interference ability, and the comprehensive objective function integrates the three sub-objectives by weighted summation:

[0063]

[0064] where, represents the failure loss of scenario s k , C cable represents the total cable construction cost, and r represents the robustness of power generation, and the weight coefficients w1, w2, w3 satisfy the normalization constraint:

[0065] w1+w2+w3=1

[0066] w m ≥0(m=1,2,3)

[0067] where w2 represents the economic weight coefficient, w1 represents the reliability weight coefficient, and w3 represents the stability weight coefficient, which is determined by the analytic hierarchy process;

[0068] The electrical connectivity constraint ensures the integrity of the network by graph theory method:

[0069] rank(L)=N-1

[0070] L=diag(Z1)-Z

[0071] where L is the Laplacian matrix with a connected tree topology, Z is the full-field cable topology matrix, and 1 is a column vector of all ones, and the power balance equation takes into account cable transmission losses:

[0072]

[0073] where, denotes the electrical neighborhood of fan i, the output power of fan i, denotes the transmission power from i to j in megawatts, is the cable current in kiloamperes, and R ij is the resistance per unit length in ohms per kilometer, is the cable length, and the aerodynamic and electrical constraints jointly govern the energy conversion process:

[0074]

[0075] where p is the air density in kg / m 3 , C P is the power coefficient, which is a function of the pitch angle and the tip speed ratio , and R is the fan rotor radius in meters, and η conv denotes the electromechanical conversion efficiency; a decomposition optimization framework is used, with branch and bound method used to solve the variable Z in the outer layer, and sequential quadratic programming used to optimize the continuous variable U in the inner layer (K) ; the iterative convergence condition is:

[0076]

[0077] where, denotes the total cable construction cost at the tth time, denotes the total cable construction cost at the (t-1)th time, and the optimal cable topology matrix Z* and the set of scenario control strategies are output

[0078] According to a specific implementation manner of the embodiment of the application, the specific steps of the S4 are:

[0079] A double-layer optimization framework of the main problem and the sub-problem is constructed, and the collaborative solution of the cable investment planning and the real-time strategy of the fault scenario is realized; the main problem decides the cable investment portfolio scheme, and the objective function is to minimize the total investment cost

[0080]

[0081] where l ij denotes the cable investment decision variable, and c unit is the unit length cost of the cable, is a set of critical fault scenarios generated by Monte Carlo sampling, is the fault response cost returned by the subproblem, ε denotes the candidate cable edge set, and the main problem outputs the optimal cable portfolio is the input boundary condition of the subproblem; the subproblem is for a specific fault scenario and Reconstruction optimization is performed, and the objective function is to minimize the power generation loss and topology change cost:

[0082]

[0083] where δ ω represents the occurrence probability of the wind speed scenario ω, σ 0 represents the initial switch state, σ ωu represents the scenario-dependent switch state matrix, where 0 represents open and 1 represents closed, ΔE ωu is the power generation loss, with a unit of MWh, is the electricity price coefficient, with a unit of ten thousand yuan / MWh, and b is the topology change penalty coefficient; the subproblem solves the output optimal switch action sequence Σ u* = {σ ωu*} ω∈Ω When the amplitude of the wind speed disturbance gradient exceeds the safety threshold, a spatial cutting constraint is automatically generated:

[0084]

[0085] wherein, is the amplitude of the wind speed disturbance gradient at the fan i in step S2, τ thresh is the turbulence intensity threshold, is the set of critical cables affecting fan i, and this constraint forces the optimization process to avoid high-risk layout schemes. The layout amount is realized through the following trigger logic:

[0086]

[0087] wherein, represents the layout adjustment amount, represents the area of the Delaunay triangulation unit, which satisfies the aerodynamic gradient constraint:

[0088]

[0089] wherein, Δx j , Δy j is the coordinate adjustment amount of the fan j, ∈ is the gradient change tolerance, and the adjusted layout is fed back to step S1 to restart the optimization cycle; the execution engine performs adaptive scenario reduction, retaining only scenarios with a probability greater than 10 -3The key scene is converged when the investment cost change of two consecutive iterations is less than a threshold value:

[0090]

[0091] wherein, denotes the total investment cost at time t, denotes the total investment cost at time t-1, and outputs the globally optimal cable investment portfolio and a failure response strategy library

[0092] According to a specific implementation manner of an embodiment of the present application, the specific steps of S5 are as follows:

[0093] define a space-time correlation tensor wherein N denotes the total number of wind turbines in the wind farm, T denotes the total number of time periods in the operation cycle, and the tensor a i,j,t denotes whether the wind turbine j is located in the influence cone area of the wind turbine i in the main direction of the wake at time period t, and the calculation is based on the geometric position relationship and the dynamic characteristics of the wind farm:

[0094]

[0095] wherein, is the optimal wind turbine coordinate of step S1, d t is the dominant wind direction unit vector at time period t, I(·) is an indicator function, and ensures that the correlation flag is 1 when the wind turbine j is located within the ±15 cone angle range of the main direction of the wake of the wind turbine i, and is 0 otherwise; the turbulence intensity prediction model describes the downstream turbulence enhancement effect caused by the shutdown of a single wind turbine; when the wind turbine i is shut down at time period t, the wake disappearance of the wind turbine i leads to the turbulence intensity increment at the downstream wind turbine i:

[0096]

[0097] wherein κ is the turbulence transfer coefficient, R is the wind turbine rotor radius, and the exponential term represents the spatial decay law of the turbulence intensity; a binary shutdown decision variable δ i,t is introduced, wherein 1 represents shutdown and 0 represents operation, and a threefold safety constraint system is constructed; the single-time-period turbulence intensity constraint ensures that the turbulence accumulation at any position in any time period does not exceed the safety threshold value:

[0098]

[0099] wherein, denotes the turbulence intensity increment, δ i,t denotes the wind turbine shutdown decision, ζ safe is the turbulence safety threshold value, covering all wind turbines j and time periods t, and the continuous-time-period shutdown constraint prevents the flow field from being unstable due to the long-time shutdown of the same wind turbine:

[0100] δ i,t +δ i,t+1 +δ i,t+2 ≤2

[0101] wherein, δ i,t represents binary shutdown decision variable at t time, δ i,t+1 represents binary shutdown decision variable at t+1 time, δ i,t+2 represents binary shutdown decision variable at t+2 time, this constraint forces any wind turbine to shutdown at most twice in consecutive three time periods, avoiding the continuous accumulation of turbulence intensity, and the spatial correlation shutdown constraint limits the concentrated shutdown in the local area:

[0102]

[0103] wherein, is the adjacent unit set within 5 times rotor radius of wind turbine j as the center, is the number of correlation set elements, ensuring that more than half of the adjacent wind turbines remain running, forming an extended objective function:

[0104]

[0105] wherein, λ∑δ i,t is the shutdown penalty term, λ is the cost coefficient, T represents the total number of time periods of wind farm operation period, Z is the cable topology matrix, U is the wind turbine control strategy, the solving process uses branch and price algorithm to handle mixed integer programming problem, and the spatial correlation constraint is dynamically added through row generation technology, improving the calculation efficiency. BRIEF DESCRIPTION OF DRAWINGS

[0106] Figure 1 is a flowchart of the method;

[0107] Figure 2 is an architectural diagram of the method. DETAILED DESCRIPTION

[0108] In order to facilitate those skilled in the art to understand and implement the present application, the present application will be further described in detail below in conjunction with examples and drawings.

[0109] As shown in the accompanying Figure 1 and the accompanying Figure 2 , a layout optimization method for offshore wind farms based on wake constraint random reconstruction comprises the following steps:

[0110] Step 1: establish the mapping relationship between the wind turbine spatial coordinate set and the wind resource parameters; construct a nonlinear layout optimization model to maximize the annual power generation under the wake interference as the target, while meeting the dynamic spacing constraint and the sea area boundary restriction. Specifically, first, define the wind turbine position decision variable as a two-dimensional Cartesian coordinate set The set completely describes the spatial distribution of all wind turbines in the planning sea area:

[0111]

[0112] wherein N represents the total number of wind turbines in the wind farm, each coordinate pair (x i ,y i ) uniquely identifies the center position of the i-th wind turbine, the horizontal coordinate x i and the vertical coordinate y i are positive real numbers, ensuring that the wind turbine is located in the actual physical space, on the basis of the definition of the position coordinates, combined with the temporal and spatial characteristics of wind resources and the aerodynamic parameters of wind turbines, the wind resource parameter matrix W is represented by a three-dimensional parameter matrix:

[0113] W = [w d,s ] D×S

[0114] w d,s = (v d ,f s ,ρ s )

[0115] wherein v d represents the average wind speed of the wind direction sector d, with the unit of m / s, f s is the annual occurrence frequency of the wind speed interval s, with the unit of %, w d,s is the wind resource parameter, the matrix includes D wind direction sectors and S wind speed intervals, ρ s is the air density corresponding to the working condition, with the unit of kg / m 3 , the power curve P i (v) describes the variation law of the output power with the wind speed v, the thrust coefficient C T,j (v) quantifies the disturbance intensity of the wind turbine to the airflow, both of which are piecewise differentiable functions of the wind speed;

[0116] The optimization objective is to maximize the annual power generation under the wake interference, since the effective wind speed of the downstream wind turbine will be attenuated by the wake of the upstream wind turbine, the actual power output of a single wind turbine i under a specific wind direction d and wind speed v needs to calculate the cumulative wake effect

[0117]

[0118] wherein represents the set of wind turbines located upstream of the wind turbine i under the wind direction d, P i (v) represents the power curve, the wake attenuation factor η j→i is calculated by the improved Jensen wake model:

[0119]

[0120] Where R represents the radius of the fan rotor, in meters, and δ ji This represents the longitudinal distance between wind turbines j and i projected in the wind direction, in meters (m) and denoted by C. T,j (v) represents the thrust coefficient, d ji The distance between the two wind turbines is represented by Euclidean distance in meters (m), and h represents the empirical constant for wake attenuation. The annual power generation objective function ultimately integrates all wind direction and wind speed conditions.

[0121]

[0122] Among them, T op This represents the annual standard operating hours, S represents the number of wind speed ranges, and v d The average wind speed in sector d represents the wind direction. Spatial constraints include two types: dynamic spacing constraints and sea boundary constraints. Dynamic spacing constraints prevent aerodynamic interference between wind turbines, ensuring that any two wind turbines meet the minimum safe distance. Dynamic spacing constraints use the Euclidean distance formula to ensure that the distance between wind turbines i and j is not less than the safety factor γ and the rotor diameter D. rotor The product of:

[0123]

[0124] Among them, D rotor =2R, where γ is 3 times the rotor diameter to avoid the risk of turbulence interference. The marine boundary constraint ensures that all wind turbines are located within the planned marine area, which is achieved by a rectangular boundary box determined by geographic data.

[0125] x i ∈[X min ,X max ]

[0126] y i ∈[Y min ,Y max ]

[0127] Among them, (X) min ,X max ,Y min ,Y max The boundary coordinates () are determined by marine survey data. The constructed nonlinear optimization model integrates the objective and constraints.

[0128]

[0129]

[0130] x i ∈[X min ,X max ],y i ∈[Y min ,Y max ]

[0131]

[0132] in, Let T represent the set of two-dimensional Cartesian coordinates. op The model represents the annual standard operating hours, and N represents the total number of wind turbines in the wind farm. The model is solved using a sequential quadratic programming algorithm, and the output is the optimal set of wind turbine coordinates.

[0133] Step 2: Quantify the joint probability distribution of cable failure rate and wind speed fluctuation; based on the wake conduction dynamics model, calculate the spatial gradient of the wind speed disturbance field caused by the fault, and characterize the chain transmission effect of electrical fault to aerodynamic disturbance.

[0134] Based on the initial layout optimization, the effects of cable faults and wind speed fluctuations are precisely quantified; the set of fault events is defined as follows: Where f m This represents the m-th type of cable fault mode, where M represents the total number of cable fault modes. Wind speed fluctuation characteristics are modeled using historical meteorological data.

[0135]

[0136] in, This represents the long-term average wind speed, in m / s, σ v Let be the standard deviation of wind speed fluctuation in m / s, ε(t) be a random disturbance term following a standard normal distribution, and t represent time in seconds. The statistical correlation between cable failure rate and wind speed fluctuation is modeled using a Copula function, where p is the cable failure rate. f There is a strong correlation between the wind speed fluctuation amplitude |Δv| and the joint cumulative distribution function:

[0137] P(F≤f,V≤v)=C θ (Φ f (f),Φ v (v))

[0138]

[0139] Where, Φ f (·) represents the marginal cumulative distribution function of the failure rate, which follows a Weibull distribution with shape parameter α and scale parameter β, Φ v (·) is the marginal cumulative distribution function of wind speed fluctuations, which follows a Rayleigh distribution with a scale parameter σ, C θ This represents the Clayton Copula function, where the parameter θ controls the tail correlation, and u1 = Φ f (f) and u2=Φ v(v) represent the probability integral transformation values ​​of the failure rate and wind speed fluctuation, respectively. The wake propagation dynamics model is used to calculate the propagation of wind speed disturbances caused by the fault. When a cable fault causes an unplanned shutdown of wind turbine i, the sudden disappearance of the wake will trigger a downstream flow field reconstruction. Based on the laws of conservation of mass and momentum, the disturbance wind speed Δv i The changes of (x,t) at position x = (x,y) and time t satisfy:

[0140]

[0141] Among them, u=(u x ,u y ) is the background wind speed field vector, ν represents the aerodynamic viscosity coefficient, β is the disturbance attenuation coefficient, and the fault scenario s = (f m The perturbation gradient tensor under v(t) is:

[0142]

[0143]

[0144] in, Represents the set of indices for faulty wind turbines. and These represent the rates of change of wind speed disturbance in the east-west and north-south directions, respectively. The spatial sharpness of the fault's impact is indicated, with the location of its maximum value identifying high-risk areas. The chain reaction effect is fully characterized by the perturbation propagation matrix.

[0145]

[0146] in, This represents the magnitude of the wind speed disturbance gradient at the location of fan j caused by the failure of fan i. It is the initial disturbance gradient magnitude at the location of the fault source. This represents the fault propagation coefficient from faulty fan i to fan j, when j is downstream of the wake of fan i. Otherwise, the value is 0. This matrix maps electrical faults to aerodynamic disturbances, and the output is a set of fault and wind speed scenarios. Where K represents the total number of scenes, and each scene s k Including failure mode f m Wind speed fluctuation sequence v(t), disturbance gradient field and transfer matrix

[0147] Step 3: Dynamically reconstruct the optimization layer, simultaneously optimizing power generation losses and topology change costs; embed aerodynamic power limiting constraints and wake safety sequences into electrical decisions to output the optimal cable topology;

[0148] Based on the optimal wind turbine coordinate set in step S1 And the fault and wind speed scenario set in step S2 A collaborative optimization model for cable topology and wind turbine control strategy is established. The goal is to minimize costs and maximize power generation stability while ensuring system reliability by jointly optimizing electrical connection methods and wind turbine operating parameters. The cable topology is represented by a binary adjacency matrix Z.

[0149] Z = [z ij ] N×N

[0150] Among them, z ij This indicates the direct cable connection status between wind turbine i and wind turbine j, where N represents the total number of wind turbines in the wind farm. ij =1 indicates the presence of a physical cable connection, z ij =0 indicates no direct connection, and the matrix satisfies the tree topology constraints:

[0151]

[0152] Among them, z ij This represents the direct cable connection between wind turbine i and wind turbine j, and N represents the total number of wind turbines in the wind farm. This constraint ensures that the entire wind farm forms a loop-free connected network, avoiding electrical islands or redundant connections. The diagonal elements of the matrix are always zero. ij =0 and satisfies symmetry z ij =z ji The overall control strategy for wind turbines is a set of dynamic parameters related to the specific scenario:

[0153]

[0154] Among them, U (k) Representing scenario s k The overall control strategy set includes two key operational variables in the control vector of each wind turbine:

[0155]

[0156] in, Indicating in fault scenario s k The pitch angle adjustment of downwind fan i, in degrees, is allowed to be continuously adjusted within the range of (0°, 90°). This indicates the rotor speed in the corresponding scenario, expressed in radians per second, and must meet the safe operating range [ω]. min ,ω max The control parameters directly affect the aerodynamic characteristics and power output characteristics of the fan;

[0157] Minimize Fault Losses: Quantify the power generation loss caused by cable faults.

[0158]

[0159] Among them, P nom The rated power of the wind turbine is expressed in megawatts (MW). This indicates the rotor speed in the corresponding scenario. For scene s k The actual output power of the medium-sized wind turbine i, in megawatts. τ represents the equivalent wind speed after wake effect correction, in m / s. k For scene s k Duration, in hours This is the fault propagation coefficient of wind turbine i, reflecting the intensity of the impact of a local fault on the global system. The target cost of cable construction is calculated based on the infrastructure investment corresponding to the topology.

[0160]

[0161] Among them, C cable This represents the total construction cost of the cable, including material costs, laying fees, and insurance costs. unit This indicates the total cost per unit length of cable. The optimal wind turbine coordinates are given in step S1, in meters. ||·|| is the Euclidean distance operator. The actual cable laying path length is calculated. The power generation robustness target evaluates the control strategy's adaptability to wind speed fluctuations.

[0162]

[0163] Where K represents the total number of scenes, This represents the rotor speed in the corresponding scenario, Δv (k) This is the wind speed disturbance amplitude in step S2, in m / s. The stability of the power output is quantified by calculating the ratio. The closer the value is to 1, the stronger the anti-interference ability. The comprehensive objective function integrates the three sub-objectives by weighted summation:

[0164]

[0165] in, Representing scenario s k The amount of failure loss, C cable This indicates the total construction cost of the cable. This represents the robustness index of the entire power generation system, with weighting coefficients w1, w2, and w3 satisfying normalization constraints.

[0166] w1 + w2 + w3 = 1

[0167] wm ≥0 (m=1,2,3)

[0168] Where w2 represents the economic weight coefficient, w1 represents the reliability weight coefficient, and w3 represents the stability weight coefficient, which are determined by the analytic hierarchy process.

[0169] Electrical connectivity constraints ensure network integrity using graph theory methods:

[0170] rank(L) = N-1

[0171] L = diag(Z1) - Z

[0172] The Laplace matrix L has a connected tree structure, Z represents the overall cable topology matrix, where 1 represents a column vector with all elements equal to 1, and the power balance equation considers cable transmission loss.

[0173]

[0174] in, Denotes the set of electrical neighbors of fan i. The output power of fan i This represents the transmission power from i to j, in megawatts. This is the cable current, measured in kiloamperes (kA). R ij Resistance per unit length, expressed in ohms per kilometer. For the cable length, the energy conversion process is constrained by both pneumatic and electrical systems:

[0175]

[0176] Where ρ is the air density, with units of kg / m³. 3 C P The power coefficient is the pitch angle. Speed ​​ratio of leaf tip A bivariate function, where R is the radius of the fan rotor in meters, and η is the variable. conv The electromechanical conversion efficiency is represented; a decomposition optimization framework is adopted, with the outer layer using the branch and bound method to solve for variable Z, and the inner layer optimizing the continuous variable U through sequential quadratic programming. K) The iterative convergence condition is:

[0177]

[0178] in, This represents the total construction cost of the cable at time t. This represents the total cable construction cost at time t-1. Output the optimal cable topology matrix Z* and the scenario control strategy set.

[0179] Step 4: Construct a two-layer framework of main problem and sub-problems. The main problem determines cable investment planning, while the sub-problems solve real-time strategies for fault scenarios. Introduce a wake feasibility cutting mechanism to trigger layout re-optimization when wind speed disturbance exceeds the threshold.

[0180] A two-tier optimization framework consisting of a main problem and subproblems is constructed to achieve collaborative solving of cable investment planning and real-time strategies for fault scenarios. The main problem determines the cable investment portfolio scheme, with the objective function being to minimize the total investment cost.

[0181]

[0182] Among them, l ij c represents the variable for cable investment decisions. unit Cost per unit length of cable It is a set of critical fault scenarios generated through Monte Carlo sampling. The subproblem returns the failure handling cost, ε represents the candidate cable edge set, and the main problem outputs the optimal cable portfolio. As input boundary conditions for the subproblem; the subproblem is specific to a particular fault scenario. and The reconfiguration optimization is performed with the objective function of minimizing power generation losses and topology change costs.

[0183]

[0184] Where, δ ω σ represents the probability of wind speed scenario ω occurring. 0 Indicates the initial switching state, σ ωu This represents a scene-related switch state matrix, where 0 indicates open, 1 indicates closed, and Δε ωu This represents power generation losses, expressed in MWh. This is the electricity price coefficient, in units of 10,000 yuan / MWh; b is the topology change penalty coefficient; the subproblem solution outputs the optimal switching action sequence Σ. u* ={σ ωu*} ω∈Ω When the magnitude of wind speed disturbance gradient exceeds the safety threshold, spatial cutting constraints are automatically generated.

[0185]

[0186] in, τ is the magnitude of the wind speed disturbance gradient at fan i in step S2. thresh The threshold for turbulence intensity. This is the set of key cables affecting wind turbine i. The constraint-driven optimization process avoids high-risk layout schemes. The re-optimization trigger logic is implemented through layout parameters:

[0187]

[0188] in, Indicates the amount of layout adjustment. This represents the area of ​​a Delaunay triangulation element, while also satisfying aerodynamic gradient constraints:

[0189]

[0190] Where, Δx j Δy j This represents the coordinate adjustment amount of wind turbine j, where ∈ represents the gradient change tolerance, and the adjusted layout. The feedback will be sent to step S1 to restart the optimization loop; the execution engine will perform adaptive scene reduction, retaining only those with a probability greater than 10. -3 In key scenarios, the convergence criterion is that the change in investment cost between two consecutive iterations is less than a threshold.

[0191]

[0192] in, This represents the total investment cost at time t. Represents the total investment cost at time t-1, and outputs the globally optimal cable investment portfolio. and fault response strategy library

[0193] Step 5: Define the correlation matrix between the spatial location of the wind turbine and the wake propagation time sequence; construct a set of 0-1 integer constraints based on the safety sequence, and re-optimize the process to avoid the risk of continuous wind turbine shutdown in high turbulence regions;

[0194] Define the spatiotemporal correlation tensor Where N represents the total number of wind turbines in the wind farm, T is the total number of operating cycles, and tensor a i,j,t This indicates whether wind turbine j is located within the influence cone region of the main wake direction of wind turbine i during time period t. The calculation is based on geometric positional relationships and wind field dynamic characteristics.

[0195]

[0196] in, The optimal wind turbine coordinates for step S1 are d. t Let I(·) be the unit vector of the prevailing wind direction during time period t, and let I(·) be the indicator function. The associated flag is set to 1 when turbine j is within ±15 cone angles of the main wake direction of turbine i, and 0 otherwise. The turbulence intensity prediction model describes the downstream turbulence enhancement effect caused by the shutdown of a single turbine. When turbine i shuts down during time period t, the disappearance of its wake leads to an increase in turbulence intensity at downstream turbine i. for:

[0197]

[0198] Where κ is the turbulence transfer coefficient, R is the fan rotor radius, the exponential term characterizes the spatial attenuation of turbulence intensity, and a binary shutdown decision variable δ is introduced. i,t Where 1 represents shutdown and 0 represents operation, a triple safety constraint system is constructed; the single-time turbulence intensity constraint ensures that the cumulative turbulence at any location at any time does not exceed the safety threshold:

[0199]

[0200] in, δ represents the increment of turbulence intensity. i,t Indicates the decision to shut down the wind turbine, ζ safe To establish a turbulence safety threshold, covering all fans j and time period t, continuous time period shutdown constraints are implemented to prevent flow field instability caused by prolonged shutdown of the same fan:

[0201] δ i,t +δ i,t+1 +δ i,t+2 ≤2

[0202] Where, δ i,t Let δ represent the binary shutdown decision variable at time t. i,t+1 Let δ represent the binary shutdown decision variable at time t+1. i,t+2 This represents the binary shutdown decision variable at time t+2. This constraint forces any wind turbine to shut down a maximum of twice within three consecutive time periods to avoid the continuous accumulation of turbulence intensity. The spatially correlated shutdown constraint restricts concentrated shutdowns within a local area.

[0203]

[0204] in, It is a collection of neighboring units with a radius of 5 times the rotor radius, centered on wind turbine j. To determine the number of elements in the association set, and to ensure that more than half of the neighboring wind turbines remain operational, an extended objective function is formed:

[0205]

[0206] Where, λ∑δ i,t λ is the downtime penalty term, T represents the total number of time periods in the wind farm's operating cycle, Z is the cable topology matrix, and U is the wind turbine control strategy. The solution process uses a branch-pricing algorithm to handle mixed integer programming problems, and spatial correlation constraints are dynamically added through row generation technology to improve computational efficiency.

Claims

1. A method for offshore wind farm layout optimization based on wake-constrained random reconstruction, characterized in that Comprising the following steps: S1: Establish the mapping relationship between the wind turbine spatial coordinate set and the wind resource parameters; construct a nonlinear layout optimization model to maximize the annual power generation under the wake interference, while meeting the dynamic spacing constraints and sea area boundary restrictions. Specifically, first define the wind turbine position decision variable as a two-dimensional Cartesian coordinate set This set completely describes the spatial distribution of all wind turbines in the planning sea area: wherein N represents the total number of wind turbines in the wind farm, each coordinate pair (x i ,y i ) uniquely identifies the center position of the ith wind turbine, the horizontal coordinate x i and the vertical coordinate y i are positive real numbers, ensuring that the wind turbine is located in the actual physical space, on the basis of the position coordinate definition, in combination with the wind resource space-time characteristics and the wind turbine aerodynamic parameters, the wind resource parameter matrix W is represented by a three-dimensional parameter matrix: W = [w d,s ] D×S w d,s = (v d ,f s ,ρ s ) where v d denotes the average wind speed in wind direction sector d, in m / s, f s is the annual occurrence frequency of wind speed interval s, in %, w d,s is the wind resource parameter, which includes D wind direction sectors and S wind speed intervals, p s is the air density corresponding to the operating condition, in kg / m 3 , the power curve P i (v) describes the variation of output power with wind speed v, the thrust coefficient C T,j (v) quantifies the disturbance intensity of the fan to the airflow, both of which are piecewise differentiable functions of wind speed. The optimization objective is to maximize the annual energy production under wake interference, since the wake of an upstream turbine will attenuate the effective wind speed for a downstream turbine, the actual power output of a single turbine i at a specific wind direction d and wind speed v needs to be calculated with cumulative wake effects where, denotes the set of turbines upstream of turbine i in wind direction d, P i (v) denotes the power curve, the wake decay factor η j→i calculated by the improved Jensen wake model: where R represents the fan rotor radius in m, δ ji represents the longitudinal distance between fan j and i in the wind direction projection in m, C T,j (v) represents the thrust coefficient, d ji represents the Euclidean distance between two fans in m, h represents the wake decay empirical constant, the annual energy production target function finally integrates all wind direction and wind speed conditions: where T op represents the annual standard operating hours, S represents the number of wind speed intervals, v d represents the average wind speed of wind direction sector d, the spatial constraints include two types of dynamic spacing constraints and sea area boundary constraints, the dynamic spacing constraints prevent aerodynamic interference between wind turbines, and any two wind turbines satisfy a minimum safety distance, the dynamic spacing constraints ensure that the distance between wind turbines i and j is not less than the product of a safety factor γ and the rotor diameter D rotor : where D rotor = 2R, γ is 3 times the rotor diameter to avoid the risk of turbulence interference, and the sea area boundary constraint ensures that all wind turbines are located within the planned sea area. The rectangular boundary box determined by geographic data is implemented: x i ∈[X min ,X max ] y i ∈[Y min ,Y max ] where (X min ,X max ,Y min ,Y max ) represents the boundary coordinates determined by the sea area survey data, and a nonlinear optimization model is constructed to integrate the target and constraints: x i ∈[X min ,X max ],y i ∈[Y min ,Y max ] wherein, represents a set of two-dimensional Cartesian coordinates, T op represents the annual standard operating hours, N represents the total number of wind turbines in the wind farm, the model is solved by a sequential quadratic programming algorithm, and an optimal set of wind turbine coordinates is output S2: Quantify the joint probability distribution of cable failure rate and wind speed fluctuation; Based on the wake conduction dynamics model, calculate the spatial gradient of wind speed disturbance field caused by failure, representing the chain transmission effect of electrical failure to aerodynamic interference; S3: Dynamically reconstruct the optimization layer, simultaneously optimizing power generation loss and topology change cost; Embed the aerodynamic power amplitude constraint and wake safety sequence into the electrical decision, output the optimal cable topology; S4: Build a double-layer framework of main problem and sub-problem, the main problem decides the cable investment planning, and the sub-problem solves the real-time strategy of failure scenario; Introduce the wake feasibility cutting mechanism, when the wind speed disturbance exceeds the threshold, trigger the layout re-optimization; S5: Define the correlation matrix of wind turbine spatial position and wake propagation time sequence; Build a 0-1 integer constraint group based on safety sequence, and avoid the risk of continuous shutdown of wind turbines in high turbulence intensity areas in the re-optimization process.

2. The offshore wind farm layout optimization method based on tail flow constraint random reconstruction according to claim 1, characterized in that The specific method of step S2 is: On the basis of the initial layout optimization, the effects of cable fault and wind speed fluctuation are quantified accurately; the fault event set is defined as where f m represents the mth cable fault mode, M represents the total number of cable fault modes, and the wind speed fluctuation characteristics are modeled by historical meteorological data: wherein, represents the long-term average wind speed, in m / s, σ v is the standard deviation of wind speed fluctuation, in m / s, ε(t) is a random disturbance term following the standard normal distribution, t represents time, in s; the statistical correlation between the cable failure rate and the wind speed fluctuation is modeled by a Copula function, and it is assumed that the cable failure rate p f has a strong correlation with the wind speed fluctuation amplitude |Δv|, and the joint cumulative distribution function is: P(F≤f, V≤v) = C θ (Φ f (f),Φ v (v)) where Φ f (·) denotes the marginal cumulative distribution function of failure rate, following a Weibull distribution with shape parameter a and scale parameter b, Φ v (·) is the marginal cumulative distribution function of wind speed fluctuation, following a Rayleigh distribution with scale parameter s, C θ denotes the Clayton Copula function, with parameter q controlling the tail dependence, where u1= Φ f (f) and u2= Φ v (v) are the probability integral transform values of failure rate and wind speed fluctuation, respectively, and the wake conduction dynamics model is used to calculate the propagation of wind speed disturbance caused by failure, when the cable failure leads to unplanned shutdown of wind turbine i, the sudden disappearance of wake will trigger the reconstruction of downstream flow field, based on the law of conservation of mass and momentum, the disturbed wind speed Av i (x, t) satisfies: where u = (u x , u y ) is the background wind velocity field vector, v denotes the aerodynamic viscosity coefficient, and β is the perturbation decay coefficient, and the perturbation gradient tensor under the fault scenario s = (f m , v(t)) : where, denotes the set of faulty wind turbine indices, and denote the rate of change of wind speed perturbation in east-west and north-south directions, respectively, denotes the spatial sharpness of the fault impact, whose maximum position identifies the high-risk area, and the chain transmission effect is fully characterized by the perturbation propagation matrix: wherein, represents the wind speed disturbance gradient amplitude at the location of the fan j caused by the failure of the fan i, is the initial disturbance gradient amplitude at the location of the failure source, represents the failure propagation coefficient of the failed fan i to the fan j when j is downstream of i’s wake 0 otherwise, this matrix maps electrical faults to aerodynamic disturbances, the output is a set of fault and wind speed scenarios where K represents the total number of scenarios, each scenario s k includes the failure mode f m , the wind speed fluctuation sequence v(t), the disturbance gradient field and the transfer matrix 3. The offshore wind farm layout optimization method based on tail flow constraint random reconstruction according to claim 1, characterized in that The specific method in step S3 is: optimal wind turbine coordinate set based on step s1 and step s2 fault and wind speed scenario set A collaborative optimization model of cable topology and wind turbine control strategy is established, and the goal is to minimize the cost and maximize the power generation stability under the premise of ensuring system reliability by jointly optimizing the electrical connection mode and the wind turbine operation parameters. The cable topology is represented by a binary adjacency matrix Z: Z = [z ij ] N×N where z ij represents the direct cable connection state between wind turbine i and wind turbine j, N represents the total number of wind turbines in the wind farm, when z ij = 1 represents the existence of a physical cable connection, z ij = 0 represents no direct connection, and the matrix satisfies the tree topology constraint condition: where z ij represents the direct cable connection state between wind turbine i and wind turbine j, N represents the total number of wind turbines in the wind farm, this constraint ensures that the entire wind farm forms a loop-free connected network, avoiding the occurrence of electrical islands or redundant connections, the matrix diagonal elements are always zero z ij = 0 and satisfy the symmetry z ij = z ji , and the wind farm control strategy is a scenario-dependent dynamic parameter set: where U (k) represents the scene s k The control vector of each fan contains two key operating variables: wherein, represents the rotor speed under the fault scenario s k represents the pitch angle adjustment amount of the downwind fan i, units are degrees, which is allowed to be continuously adjusted in the range of (0°, 90°), represents the rotor speed under the corresponding scenario, units are arc seconds, which needs to meet the safe operation range [ω min ,ω max ]; the control parameter directly affects the aerodynamic characteristics and power output characteristics of the fan; Minimizing loss of generation due to cable fault quantifies loss of generation due to cable fault where P nom is the rated power of the wind turbine, in megawatt, represents the rotor speed under the corresponding scenario, is the actual output power of the wind turbine i in scenario s k , in megawatt, represents the equivalent wind speed after the wake effect correction, in meters per second, τ k is the duration of scenario s k , in hours, is the fault propagation coefficient of the wind turbine i, reflecting the influence intensity of the local fault on the global system, and the infrastructure investment corresponding to the target calculation topology of the cable construction cost: where C cable represents the total construction cost of the cable, including material cost, laying cost and insurance cost, c unit represents the comprehensive cost of the cable per unit length, is the optimal wind turbine coordinate of step S1, with the unit of m, ||·|| is the Euclidean distance operator, and the actual cable laying path length is calculated. The adaptability of the power generation robustness objective evaluation control strategy to wind speed fluctuations: where K represents the total number of scenarios, represents the rotor speed under the corresponding scenario, and Δv k is the wind speed disturbance amplitude of step S2, in m / s, and is used to quantify the stability of the power output through the ratio, with a value closer to 1 indicating stronger anti-interference ability, and the comprehensive objective function is obtained by weighted summation of the three sub-objectives: wherein, represents the fault loss amount of the scene s k C cable represents the total construction cost of the cable, represents the full-field power generation robustness index, and the weight coefficients w1, w2, and w3 satisfy the normalization constraint: w1+w2+w3=1 w m ≥0 (m = 1,2,3) Wherein, w2 represents the economic weight coefficient, w1 represents the reliability weight coefficient, and w3 represents the stability weight coefficient, which is determined by the analytic hierarchy process; The electrical connectivity constraint guarantees the network integrity through graph theory method: rank(L)=N-1 L=diag(Z1)-Z Wherein, the topology of Laplace matrix L is connected tree structure, Z represents the full field cable topology matrix, wherein 1 is an element full of 1 column vector, and the power balance equation considers the cable transmission loss: wherein, represents the electrical neighborhood of fan i, output power of fan i, represents the transmission power from i to j in megawatts, is the cable current in kiloamperes, R ij is the resistance per unit length in ohms per kilometer, is the cable length, where p is the air density in kg / m 3 , C P is the power coefficient, which is a bi-variate function of the pitch angle and the tip speed ratio , R is the wind turbine rotor radius in m, and η conv represents the electromechanical conversion efficiency; the decomposition optimization framework is adopted, in which the branch and bound method is used to solve the variable Z in the outer layer, and the sequential quadratic programming is used to optimize the continuous variable U in the inner layer (K) ; the iterative convergence condition is: wherein, represents the total cable construction cost at the tth time, represents the total cable construction cost at the (t-1)th time, outputs the optimal cable topology matrix Z* and the set of scenario control strategies 4. The offshore wind farm layout optimization method based on tail flow constraint random reconstruction according to claim 1, characterized in that The specific steps in step S4 are: A bi-level optimization framework of master problem and sub-problem is constructed to realize the collaborative solution of cable investment planning and real-time strategy of fault scenarios; the master problem decides the cable investment portfolio scheme, and the objective function is to minimize the total investment cost where l ij denotes the cable investment decision variable, c unit is the cable unit length cost, is the set of key fault scenarios generated by Monte Carlo sampling, is the fault response cost returned by the subproblem, ε denotes the candidate cable edge set, and the main problem outputs the optimal cable investment portfolio as the input boundary condition of the subproblem; the subproblem is targeted at a specific fault scenario and performs the reconstruction optimization, with the objective function being to minimize the generation loss and topology change cost: where δ ω is the probability of wind speed scenario ω, σ 0 is the initial switching state, σ ωu is the scenario-dependent switching state matrix, where 0 represents open and 1 represents closed, Δε ωu is the generation loss, with the unit of MWh, is the electricity price coefficient, with the unit of ten thousand yuan / MWh, and b is the topology change penalty coefficient; the sub-problem is solved to output the optimal switching action sequence ∑ u* = {σ ωu*} ω∈Ω When the amplitude of the wind speed disturbance gradient exceeds the safety threshold, a spatial cutting constraint is automatically generated: wherein, is the wind speed disturbance gradient amplitude at the fan i of step S2, τ thresh is the turbulence intensity threshold, is the set of critical cables impacting the fan i, this constraint forces the optimization process to avoid high risk layout scenario re-optimization trigger logic pass through the layout quantity: wherein, denotes the layout adjustment amount, denotes the Delaunay triangulation cell area, while satisfying the aerodynamic gradient constraint: wherein Δx j , Δy j is the coordinate adjustment amount of the fan j, ∈ is the gradient change tolerance, the adjusted layout feedback to step S1 restart optimization cycle; the execution engine performs adaptive scene reduction, only retaining key scenes with a probability greater than 10 -3 of the investment cost change amount of the continuous two iterations is less than the threshold value: wherein, represents the total investment cost at time t, represents the total investment cost at time t-1, outputs the globally optimal cable investment portfolio and a failure response strategy library 5. The offshore wind farm layout optimization method based on tail flow constraint random reconstruction according to claim 1, characterized in that The specific steps in step S5 are: Defining spatiotemporal correlation tensor where N denotes the total number of wind turbines in the wind farm, T is the total number of time periods in the operation cycle, and tensor a i,j,t represents whether the wind turbine j is located within the influence cone of the wind turbine i in the main direction of the wake at time period t, and the calculation is based on the geometric position relationship and the dynamic characteristics of the wind farm: wherein, is the optimal wind turbine coordinate of step S1, d t is the dominant wind direction unit vector at time period t, I(·) is an indicator function that ensures the associated flag bit is 1 when wind turbine j is within the ±15 cone angle range of the wake direction of wind turbine i, and 0 otherwise; the turbulence intensity prediction model describes the downstream turbulence enhancement effect induced by the shutdown of a single wind turbine; when wind turbine i is shut down at time period t, the disappearance of its wake leads to an increase in the turbulence intensity at downstream wind turbine i is: where k is the turbulent transfer coefficient, R is the fan rotor radius, and the exponential term represents the spatial decay law of the turbulence intensity, and a binary shutdown decision variable d is introduced i,t where 1 represents shutdown and 0 represents operation, and a triple safety constraint system is constructed; the single-time-period turbulence intensity constraint ensures that the turbulence accumulation at any location in any time period does not exceed the safety threshold: wherein, denotes the turbulence intensity increment, δ i,t denotes the fan shutdown decision, ζ safe is the turbulence safety threshold, covering all fans j and time periods t, the consecutive time period shutdown constraint prevents long time shutdown of the same fan leading to flow field instability: δ i,t +δ i,t+1 +δ i,t+2 ≤2 where δ i,t represents the binary shutdown decision variable at time t, δ i,t+1 represents the binary shutdown decision variable at time t+1, δ i,t+2 represents the binary shutdown decision variable at time t+2, this constraint forces any wind turbine to shut down at most twice in a row of three time periods, avoiding the continuous accumulation of turbulence intensity, the spatially related shutdown constraint limits the concentration of shutdowns in a local area: wherein, is the adjacent unit set within 5 times the rotor radius centered on the fan j, is the number of associated set elements, ensuring that more than half of the adjacent fans remain in operation, forming an extended objective function: where λ∑δ i,t is the shutdown penalty term, λ is the cost coefficient, T represents the total number of time periods in the wind farm operating cycle, Z is the cable topology matrix, and U is the wind turbine control strategy. The solution process uses a branch-and-price algorithm to handle the mixed integer programming problem, and the spatial correlation constraints are dynamically added through row generation techniques to improve computational efficiency.

Images