A multi-machine wind farm layout optimization method

Abstract

The present invention discloses a method for optimizing the layout of a multi-machine wind farm, comprising the following steps: 1) gridding the wind farm area to form a plurality of grids, arranging a wind turbine in all grids or randomly in some grids, wherein the types of wind turbines arranged in each grid are randomly arranged to form an initial layout; after repeatedly arranging the wind turbines, several initial layouts are formed; 2) establishing a wind speed model for the wind farm, then inputting the incoming wind speed and wind direction, and then calculating the levelized cost of energy of each initial layout according to the incoming wind speed and wind direction; 3) optimizing the initial layout using a genetic algorithm, wherein the optimization goal is to minimize the levelized cost of energy, and when the layout results converge, the optimal multi-machine layout is obtained. By estimating the wake effect between multiple types of wind turbines, fatigue damage is converted into maintenance cost, thereby effectively optimizing the layout of the wind farm and reducing the maintenance cost.

Description

Technical Field

[0001] The present invention relates to the technical field of wind power generation, and in particular to a method for optimizing the layout of a multi-machine wind farm for minimizing the levelized cost of energy. Background Art

[0002] In recent years, people have begun to consider installing multiple types of wind turbines in a wind farm to improve the space utilization of the wind farm and increase the economic benefits of the wind farm. In the wind farm layout optimization of multiple types of wind turbines, the wake interaction between different types of wind turbines determines the power generation of the wind farm, but this problem is much more complicated than the wind farm layout optimization of a single type of wind turbine and is difficult to estimate.

[0003] In previous studies on wind farm layout optimization, in order to estimate the wind turbine wake effect, scholars have used one-dimensional wake models that assume uniform distribution of wind turbine wakes and two-dimensional models that assume Gaussian or sinusoidal distribution of wind turbine wakes. However, when optimizing the design of multi-type wind farms, due to the differences in wind turbine sizes, wake interaction is actually a three-dimensional phenomenon and one-dimensional or two-dimensional wake models cannot be used. Recently, some three-dimensional wake models have been developed, but they have rarely been used for wind farm layout optimization or multi-type wind turbine problems. The application of these three-dimensional wake models in multi-type wind farm layout optimization should be cautious, especially when dealing with the problem of multiple wake superposition.

[0004] Another issue in multi-type wind farm layout optimization is the estimation of wind farm cost. For single-type wind farm layout optimization, its cost depends roughly on the number of wind turbines, which does not need to be accurately modeled during the optimization process. When multiple types of wind turbines are included, the cost is nonlinear with the number of wind turbines, and it is important to estimate its cost in detail.

[0005] In addition to construction costs, maintenance costs should also be considered in wind farm costs. Some researchers have linked maintenance costs to fatigue damage to wind turbines caused by wake effects and proposed fatigue coefficients to evaluate fatigue loads on wind turbine units, but such detailed models have not yet been used to optimize the layout of multi-machine wind farms. The uncertain proportion of maintenance costs for different wind turbines makes this issue more complicated and requires further consideration. Summary of the invention

[0006] In view of the above-mentioned deficiencies in the prior art, the purpose of the present invention is to solve the problems of poor optimization and high cost of wind farm layout of multiple types of wind turbines, and to provide a method for optimizing the layout of wind farms with multiple types of wind turbines. By estimating the wake effect between multiple types of wind turbines, fatigue damage is converted into maintenance cost, thereby effectively optimizing the wind farm layout and reducing maintenance costs.

[0007] In order to solve the above technical problems, the technical solution adopted by the present invention is as follows: a method for optimizing the layout of a multi-machine wind farm, characterized in that it comprises the following steps:

[0008] 1) The wind farm area is divided into several grids, and a wind turbine is arranged in all grids or randomly in some grids, wherein the types of wind turbines arranged in each grid are arranged randomly to form an initial layout; after repeatedly arranging the wind turbines for several times, several initial layouts are formed;

[0009] 2) Establish a wind speed model for the wind farm, then input the incoming wind speed and wind direction, and then calculate the levelized cost of energy for each initial layout based on the incoming wind speed and wind direction;

[0010] 3) Genetic algorithm is used to optimize the initial layout. The optimization goal is to minimize the levelized energy cost. When the layout results converge, the optimal multi-machine layout is obtained.

[0011] Furthermore, in step 2), the calculation process of the levelized energy cost is as follows:

[0012] S1) Decompose the incoming wind speed into average wind speed and turbulence intensity, and calculate the wake effect of a single wind turbine according to the wake model;

[0013] Assuming the hub height of the wind turbine is H, the rotor diameter is D, and the bottom of the wind turbine tower is taken as the origin, the wake generated by any wind turbine is:

[0014] ΔU / U h =F(C T ,I a ,x / D)φ(r / σ);

[0015] In the formula, ΔU / U h is the ratio of the wind speed deficit at the downstream coordinate (x, y, z) to the average wind speed at the hub of the wind turbine; F(C T ,I a ,x / D) and φ(r / σ) are the “stream function” and “span function” respectively;

[0016] At the same time, the additional turbulence generated by the wind turbine is:

[0017]

[0018] In the formula, Δσ u / U h is the ratio of the standard deviation of the additional turbulence at the downstream coordinate (x, y, z) to the average wind speed at the hub of the wind turbine; G(C T ,I a ,x / D) and Also known as “stream function” and “span function”; ΔIa It indicates the reduction of turbulence intensity under the wind turbine;

[0019] S2) superimposing the wake effects of a single wind turbine according to a set rule to obtain the average wind speed and turbulence intensity in the multi-wake area;

[0020] The wind speed loss superposition formula in multiple wake areas is:

[0021]

[0022] Where U i represents the average wind speed at the hub of the i-th wind turbine, ΔU j represents the wind speed deficit caused by the jth wind turbine, U0 represents the average wind speed of the wind farm, and n represents the number of upstream wind turbines;

[0023] The additional turbulence superposition formula in multiple wake regions is:

[0024]

[0025] In the formula, σ u,i represents the standard deviation of turbulence at the hub height of the i-th wind turbine, σ u,0 represents the standard deviation of turbulence in the wind farm flow, Δσ u,j represents the standard deviation of the additional turbulence generated by the jth wind turbine, Δσ u,jk represents the correction caused by the wake shear of the jth wind turbine and its upstream wind turbine, n j represents the number of wind turbines upstream of the i-th wind turbine, n k represents the number of wind turbines upstream of the j-th wind turbine;

[0026] S3) calculating the power generation of each wind turbine according to the average wind speed at the hub of each wind turbine obtained above, and accumulating the total power generation of the wind farm;

[0027]

[0028] In the formula, C P =4a(1-a) 2 is the axial induction factor is the wind turbine efficiency; ρ is the gas density; u h,i represents the average wind speed at the hub of the i-th wind turbine; N wt represents the total number of wind turbines;

[0029] S4) estimating the cumulative fatigue factor of each wind turbine during its life cycle based on the generated power of each wind turbine and the turbulence intensity at the hub obtained above;

[0030]

[0031] Where P rate is the rated power of the wind turbine; D dis is the wind farm turbulence fatigue equivalent coefficient, which is 0.7; I a is the turbulence intensity around the wind turbine;

[0032] S5) Calculate the construction cost of the wind farm; Assume that two different types of wind turbines are to be built in the wind farm, and the unit price of one of the wind turbines is set to unit 1, and the unit price of the other wind turbine is k; then:

[0033]

[0034] In the formula, N1 and N2 are the number of two types of wind turbines respectively;

[0035] S6) Calculate the maintenance cost of the wind farm:

[0036]

[0037] Where: c f =C PM N PM +C CM N CM ; C PM and C CM are the costs of one-time preventive maintenance and corrective replacement, respectively;

[0038] S7) Calculate the levelized energy cost based on the total power generation, maintenance cost and construction cost obtained above:

[0039]

[0040] In the formula, C main The value should be converted based on the price of a single wind turbine as unit 1.

[0041] Further, in step S1),

[0042]

[0043]

[0044]

[0045]

[0046]

[0047] Further, in step S2), for different overlapping situations A F,1,2 and A P,1,2, correction value Δσ u,jk The value of

[0048]

[0049] In the formula, r j is the crosswind distance from the wake center of the jth wind turbine to the hub of the ith wind turbine; Δσ u,j,tip represents the standard deviation of the additional turbulence on the blade tip side of the jth wind turbine; D w is the wake width; L w,jk is the vertical length of the intersecting wake region between the jth and kth wind turbines, which is calculated as follows:

[0050]

[0051]

[0052] The label in the upper right corner of the coordinate represents the coordinate rotation transformation, which rotates the hubs of the two wind turbines to the same horizontal plane and is calculated as follows:

[0053]

[0054] θ=arctan[(H j -H k ) / (y k -y j )];

[0055] In the formula, y j , H j ,y k , H k are the cross-wind coordinates of the hubs of the two wind turbines;

[0056] Complete Overlap A F,1,2 The conditions are:

[0057]

[0058]

[0059] Partial Overlap A P,1,2 The conditions are:

[0060]

[0061]

[0062] In the formula, x j 、x k Respectively represent the downwind coordinates of the two wind turbines; D w,k (x j) represents the wake width of the k-th wind turbine when its wake reaches the j-th wind turbine.

[0063] Further, in step S6), the number of preventive maintenance is first calculated:

[0064]

[0065] Where, T ser is the design life of the wind turbine, T PM It is the maintenance period of the wind farm, usually half a year;

[0066] The number of corrective replacements is then calculated:

[0067]

[0068] In the formula, λ means that the fatigue coefficient of the wind turbine is reduced to λ times of the original value after each preventive maintenance; F fault Indicates the set fatigue factor threshold. When the threshold is reached, corrective replacement is performed.

[0069] Compared with the prior art, the present invention has the following advantages: a three-dimensional Gaussian model is used to estimate the wake effects of multiple types of wind turbines, and the wake superposition effect of multiple wake areas is taken into account, thereby improving the accuracy of power generation assessment; the wind farm layout optimization goal is to minimize the levelized energy cost, and the maintenance cost is taken into account in the cost estimation, thereby more accurately evaluating the economic efficiency of the wind farm. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 is the simulated incoming wind profile in the embodiment of the present invention;

[0071] Figure 2 A schematic diagram of partial superposition of wake effects of different types of wind turbines in an embodiment of the present invention;

[0072] Figure 3 A schematic diagram of complete superposition of wake effects of different types of wind turbines in an embodiment of the present invention;

[0073] Figure 4 It is a schematic diagram of the change of fatigue coefficient after preventive maintenance and corrective replacement in an embodiment of the present invention;

[0074] Figure 5 A flow chart of a genetic algorithm in an embodiment of the present invention;

[0075] Figure 6 is a flow chart for calculating the individual fitness (1 / LCOE) of the genetic algorithm in an embodiment of the present invention;

[0076] Figure 7It is a curve diagram of the changes in LCOE and total power generation during the iterative process of the genetic algorithm in an embodiment of the present invention. DETAILED DESCRIPTION

[0077] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0078] Example: See Figure 1-Figure 7 , a multi-machine wind farm layout optimization method, comprising the following steps:

[0079] 1) The wind farm area is divided into several grids, and a wind turbine is arranged in all grids or randomly in some grids, wherein the types of wind turbines arranged in each grid are randomly arranged to form an initial layout; after repeatedly arranging the wind turbines for several times, several initial layouts are formed.

[0080] Specifically, two types of wind turbines with rated power of 2MW and 5MW are arranged in a 2km×2km wind farm, and the wind farm is divided into 10×10 grids. Accordingly, a 10×10 matrix can be established to represent this layout. The following is a random layout example:

[0081]

[0082] Among them, 0 means that there is no wind turbine in the grid, 1 means that a 2MW wind turbine is arranged, and 2 means that a 5MW wind turbine is arranged. The specific numbers of the two types of wind turbines are shown in the following table:

[0083]

[0084] 2) Establish a wind farm wind speed model, then input the incoming wind speed and wind direction, and then calculate the levelized cost of energy (LCOE) of each initial layout based on the incoming wind speed and wind direction; the details are as follows:

[0085] S1) Decompose the future wind speed into average wind speed and turbulence intensity; Figure 1 As shown in the figure, in order to obtain the wind profile including the average wind speed and turbulence intensity at the inlet, it is assumed that the average wind speed of the wind farm inflow at a height of 90m is U0(z0)=12m / s, and the wind direction is due east. Applying the Hellman exponential law, the average wind speed at different heights can be calculated as follows:

[0086]

[0087] Where α is the roughness index; assuming that the wind farm is located near the offshore sea surface, α is taken as 0.12.

[0088] According to IEC61400-1 standard, average wind speed U0(z) and turbulence intensity I a,0 The relationship between (z) can be expressed as follows:

[0089]

[0090] Among them, I ref It is a reference value of turbulence intensity. In this embodiment, it is assumed that the wind field is a low turbulence field and the value is 0.12.

[0091] Then the wake effect of a single wind turbine is calculated based on the wake model;

[0092] Assuming the hub height of the wind turbine is H, the rotor diameter is D, and the bottom of the wind turbine tower is taken as the origin, the wake generated by any wind turbine is:

[0093] ΔU / U h =F(C T ,I a ,x / D)φ(r / σ);

[0094] In the formula, ΔU / U h is the ratio of the wind speed deficit at the downstream coordinate (x, y, z) to the average wind speed at the hub of the wind turbine; F(C T ,I a ,x / D) and φ(r / σ) are the “stream function” and “span function” respectively;

[0095]

[0096]

[0097] At the same time, the additional turbulence generated by the wind turbine is:

[0098]

[0099] In the formula, Δσ u / U h is the ratio of the standard deviation of the additional turbulence at the downstream coordinate (x, y, z) to the average wind speed at the hub of the wind turbine; G(C T ,I a ,x / D) and Also known as “stream function” and “span function”; ΔI a It indicates the reduction of turbulence intensity under the wind turbine;

[0100]

[0101]

[0102]

[0103] The unknown coefficients of the above formula can be determined by the following formula, where C T is the thrust coefficient of the wind turbine, Ia is the turbulence intensity around the wind turbine:

[0104]

[0105] S2) superimposing the wake effects of a single wind turbine according to a set rule to obtain the average wind speed and turbulence intensity in the multi-wake area;

[0106] The wind speed loss superposition formula in multiple wake areas is:

[0107]

[0108] Where U i represents the average wind speed at the hub of the i-th wind turbine, ΔU j represents the wind speed deficit caused by the jth wind turbine, U0 represents the average wind speed of the wind farm, and n represents the number of upstream wind turbines;

[0109] The additional turbulence superposition formula in multiple wake regions is:

[0110]

[0111] In the formula, σ u,i represents the standard deviation of turbulence at the hub height of the i-th wind turbine, σ u,0 represents the standard deviation of turbulence in the wind farm flow, Δσ u,j represents the standard deviation of the additional turbulence generated by the jth wind turbine, Δσ u,jk represents the correction caused by the wake shear of the jth wind turbine and its upstream wind turbine, n j represents the number of wind turbines upstream of the i-th wind turbine, n k represents the number of wind turbines upstream of the j-th wind turbine.

[0112] For different overlapping situations A F,1,2 and A P,1,2 ,like Figure 2 , Figure 3 As shown, the correction value Δσ u,jk The value of is:

[0113]

[0114] In the formula, r j is the crosswind distance from the wake center of the jth wind turbine to the hub of the ith wind turbine; Δσ u,j,tip represents the standard deviation of the additional turbulence on the blade tip side of the jth wind turbine; D w is the wake width; L w,jk is the vertical length of the intersecting wake region between the jth and kth wind turbines, which is calculated as follows:

[0115]

[0116]

[0117] The label in the upper right corner of the coordinate represents the coordinate rotation transformation, which rotates the hubs of the two wind turbines to the same horizontal plane and is calculated as follows:

[0118]

[0119] θ=arctan[(H j -H k ) / (y k -y j )];

[0120] In the formula, y j , H j ,t k , H k are the cross-wind coordinates of the hubs of the two wind turbines;

[0121] Complete Overlap A F,1,2 The conditions are:

[0122]

[0123]

[0124] Partial Overlap A P,1,2 The conditions are:

[0125]

[0126]

[0127] In the formula, x j 、x k Respectively represent the downwind coordinates of the two wind turbines; D w,k (x j ) represents the wake width of the k-th wind turbine when its wake reaches the j-th wind turbine.

[0128] S3) Calculate the power generation of each wind turbine according to the average wind speed at the hub of each wind turbine obtained above, and add up the total power generation of the wind farm:

[0129]

[0130] In the formula, C P =4a(1-a) 2 is the axial induction factor is the wind turbine efficiency; ρ is the gas density; U h,irepresents the average wind speed at the hub of the i-th wind turbine; N wt represents the total number of wind turbines;

[0131] S4) estimating the cumulative fatigue factor of each wind turbine during its life cycle based on the generated power of each wind turbine and the turbulence intensity at the hub obtained above;

[0132]

[0133] Where P rate is the rated power of the wind turbine; D dis is the wind farm turbulence fatigue equivalent coefficient, which is 0.7;

[0134] S5) Calculate the construction cost of the wind farm; Assume that two different types of wind turbines are to be built in the wind farm, and the unit price of one wind turbine (5MW wind turbine) is set to unit 1, and the unit price of the other wind turbine is k; then:

[0135]

[0136] Wherein, N1 and N2 are the numbers of two types of wind turbines respectively; in this embodiment, k is 0.427.

[0137] S6) Calculate the maintenance cost of the wind farm:

[0138] First calculate the number of preventive maintenance visits:

[0139]

[0140] Where, T ser is the design life of the wind turbine; T MP is the maintenance period of the wind farm. In this embodiment, T PM Take half a year;

[0141] The number of corrective replacements is then calculated:

[0142]

[0143] In the formula, λ means that the fatigue coefficient of the wind turbine is reduced to λ times of the original value after each preventive maintenance; F fault Indicates the set fatigue coefficient threshold. When the threshold is reached, corrective replacement is performed. The change of fatigue coefficient during maintenance is as follows: Figure 4 As shown; in this embodiment, λ is taken as 80%, F fault Take 0.1.

[0144] The maintenance cost of each wind turbine includes the cost of preventive maintenance and the cost of corrective replacement:

[0145]

[0146] Where: c f =C PM N PM +C CM N CM ; C PM and C CM are the cost of one-time preventive maintenance and corrective replacement respectively. PM Both are 0.0002672, and the C of a 5MW wind turbine CM The C of a 2MW wind turbine is 0.05344. CM is k×0.05344.

[0147] S7) Based on the total power generation, maintenance cost and construction cost obtained above:

[0148]

[0149] In the formula, C main The value should be converted based on the price of a single wind turbine as unit 1.

[0150] 3) Genetic algorithm is used to optimize the initial layout. The optimization goal is to minimize the levelized energy cost. When the layout results converge, the optimal multi-machine layout is obtained. In this solution, genetic algorithm is a mature existing technology. The specific algorithm process is as follows: Figure 5 and 6 Specifically, this solution uses genetic algorithm to optimize the initial layout, which includes the following steps:

[0151] 31) Using the several layout matrices in step 1) as the initial population of the genetic algorithm, the LCOE of each wind farm layout is calculated according to step 2).

[0152] 32) Taking 1 / LCOE as individual fitness, a roulette wheel selection method is used to create a new population based on the initial population.

[0153] 33) The new population in step 32) is subjected to gene recombination and gene mutation. For individuals with N-bit codes, the current code contains N1 1s and N2 2s. If the total mutation rate is p, let p0, p1 and p2 be the mutation rates of 0, 1 and 2 respectively. The relationship between p, p0, p1 and p2 can be written as:

[0154]

[0155]

[0156] Wherein, M is the number of individuals in the population, that is, the number of random layouts generated. In this embodiment, M is taken as 100, N is 100, the crossover rate is 0.08, and the total mutation rate is 0.01.

[0157] 34) Recalculate the individual fitness of the population that has undergone gene recombination and gene mutation, and return to step 32), and iterate until the highest individual fitness in the population converges; Figure 7 As shown, the layout matrix of the individual with the highest individual fitness in the population represents the optimal multi-machine layout.

[0158] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit the technical solution. Those skilled in the art should understand that those modifications or equivalent substitutions of the technical solution of the present invention that do not depart from the purpose and scope of the technical solution should be included in the scope of the claims of the present invention.

Claims

1. A method for optimizing the layout of a multi-machine wind farm, characterized in that: The steps include: 1) The wind farm area is divided into several grids, and a wind turbine is arranged in all grids or randomly in some grids, wherein the types of wind turbines arranged in each grid are arranged randomly to form an initial layout; after repeatedly arranging the wind turbines for several times, several initial layouts are formed; 2) Establish a wind speed model for the wind farm, then input the incoming wind speed and wind direction, and then calculate the levelized cost of energy for each initial layout based on the incoming wind speed and wind direction; The calculation process of the levelized energy cost is as follows: S1) Decompose the incoming wind speed into average wind speed and turbulence intensity, and calculate the wake effect of a single wind turbine according to the wake model; Assuming the hub height of the wind turbine is H, the rotor diameter is D, and the bottom of the wind turbine tower is taken as the origin, the wake generated by any wind turbine is: ΔU / U h =F(C T ,I a ,x / D)φ(r / σ); In the formula, ΔU / U h is the ratio of the wind speed deficit at the downstream coordinate (x, y, z) to the average wind speed at the wind turbine hub; F(C T ,I a ,x / D) and φ(r / σ) are the "stream function" and "span function" respectively; At the same time, the additional turbulence generated by the wind turbine is: In the formula, Δσ u / U h is the ratio of the standard deviation of the additional turbulence at the downstream coordinate (x, y, z) to the average wind speed at the hub of the wind turbine; G(C T ,I a ,x / D) and Also known as "stream function" and "span function" respectively; ΔI a It indicates the reduction of turbulence intensity under the wind turbine; in: Where: C T is the thrust coefficient of the wind turbine; S2) superimposing the wake effects of a single wind turbine according to a set rule to obtain the average wind speed and turbulence intensity in the multi-wake area; The wind speed loss superposition formula in multiple wake areas is: Where U i represents the average wind speed at the hub of the i-th wind turbine, ΔU j represents the wind speed deficit caused by the jth wind turbine, U0 represents the average wind speed of the wind farm, and n represents the number of upstream wind turbines; The additional turbulence superposition formula in multiple wake regions is: In the formula, σ u,i represents the standard deviation of turbulence at the hub height of the i-th wind turbine, σ u,0 represents the standard deviation of turbulence in the wind farm flow, Δσ u,j represents the standard deviation of the additional turbulence generated by the jth wind turbine, Δσ u,jk represents the correction caused by the wake shear of the jth wind turbine and its upstream wind turbine, n j represents the number of wind turbines upstream of the i-th wind turbine, n k represents the number of wind turbines upstream of the j-th wind turbine; For different overlapping situations A F,1,2 and A P,1,2 , correction value Δσ u,jk The value of is: In the formula, r j is the crosswind distance from the wake center of the jth wind turbine to the hub of the ith wind turbine; Δσ u,j,tip represents the standard deviation of the additional turbulence on the blade tip side of the jth wind turbine; D j is the rotor diameter of the jth wind turbine; y i ′、H i ′、y j ′、H j ′ respectively represent the crosswind coordinates and hub height of the i-th wind turbine and the j-th wind turbine after the coordinate rotation. The coordinate rotation transformation transforms the two wind turbines D w,j is the wake width of the jth wind turbine; L w,jk is the vertical length of the intersecting wake region between the jth and kth wind turbines, which is calculated as follows: Where D w,k is the wake width of the kth wind turbine; y j ′、y k ′ respectively represent the crosswind coordinates of the jth and kth wind turbines after the coordinate rotation. The coordinate rotation transformation rotates the hubs of the two wind turbines to the same horizontal plane and is calculated as follows: θ=arctan[(H j -H k ) / (and k -and j )]; In the formula, y j , H j ,y k , H k are the cross-wind coordinates of the hubs of the two wind turbines; Complete Overlap A F,1,2 The conditions are: Partial Overlap A P,1,2 The conditions are: In the formula, x j 、x k Respectively represent the downwind coordinates of the two wind turbines; D w,k (x j ) represents the wake width of the k-th wind turbine when the wake reaches the j-th wind turbine; S3) calculating the power generation of each wind turbine according to the average wind speed at the hub of each wind turbine obtained above, and accumulating the total power generation of the wind farm; In the formula, C P =4a(1-a) 2 is the axial induction factor is the wind turbine efficiency; ρ is the gas density; D i represents the rotor diameter of the i-th wind turbine; U h,i represents the average wind speed at the hub of the i-th wind turbine; N wt represents the total number of wind turbines; S4) estimating the cumulative fatigue factor of each wind turbine during its life cycle based on the generated power of each wind turbine and the turbulence intensity at the hub obtained above; Where P is the actual power generated by the wind turbine; P rate is the rated power of the wind turbine; D dis is the wind farm turbulence fatigue equivalent coefficient, which is 0.7; I a is the turbulence intensity around the wind turbine; S5) Calculate the construction cost of the wind farm; Assume that two different types of wind turbines are to be built in the wind farm, and the unit price of one of the wind turbines is set to unit 1, and the unit price of the other wind turbine is k; then: In the formula, N1 and N2 are the number of two types of wind turbines respectively; S6) First calculate the number of preventive maintenance: Where, T ser is the design life of the wind turbine, T PM It is the maintenance period of the wind farm, usually half a year; The number of corrective replacements is then calculated: In the formula, λ means that the fatigue coefficient of the wind turbine is reduced to λ times of the original value after each preventive maintenance; F fault Indicates the set fatigue factor threshold, when the threshold is reached, corrective replacement is performed; Then calculate the maintenance cost of the wind farm: Where: c f =C PM N PM +C CM N CM ; C PM and C CM are the cost of one preventive maintenance and corrective replacement respectively; N PM and N CM are the number of preventive maintenance and corrective replacement required for the i-th wind turbine, respectively; S7) Calculate the levelized energy cost based on the total power generation, maintenance cost and construction cost obtained above: In the formula, C main The value of should be converted based on the price of a single wind turbine as unit 1; 3) Genetic algorithm is used to optimize the initial layout. The optimization goal is to minimize the levelized energy cost. When the layout results converge, the optimal multi-machine layout is obtained.

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