A fan arrangement optimization method

Abstract

The application provides a fan arrangement optimization method, and belongs to the field of wind power generation, and comprises the following steps: obtaining three-dimensional point cloud data and wind data of a geographic information system of a target wind farm; establishing a CFD model according to the three-dimensional point cloud data of the geographic information system, simulating the spatial distribution of the wind field; combining the wind field simulation result with single-point wind speed and wind direction data in the wind data to obtain wind speed and wind direction time history information of the spatial distribution of the wind farm; and optimizing the fan arrangement by using an improved genetic algorithm according to the wind speed and wind direction time history information of the spatial distribution of the wind farm to obtain an optimized fan arrangement result. The application proposes a unique population processing method to increase the calculation efficiency in view of the problems of low calculation efficiency and easy falling into local optimization of the fan arrangement optimization, simultaneously proposes a time-varying mutation rate to avoid falling into local optimization as much as possible during the optimization process, and the proposed efficient optimization algorithm can greatly obtain a better fan arrangement scheme than the traditional algorithm.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of wind power generation, and particularly relates to a wind turbine arrangement optimization method. BACKGROUND

[0002] The demand for wind energy development is increasing, and the core is to reasonably optimize the arrangement scheme of wind turbines before the construction of a wind farm, so as to ensure the control cost and make the wind energy utilization rate as high as possible. However, due to the wake effect between the wind turbine groups, the wind turbine arrangement scheme optimization process is very complex, and it is difficult to obtain a globally optimal arrangement scheme.

[0003] The genetic algorithm is the most commonly used optimization algorithm and has been widely used for solving the wind turbine arrangement scheme optimization. The existing genetic algorithm calculates all individuals in the population, which is very time-consuming, and the mutation rate is fixed, which leads to the algorithm being easily trapped in a local optimum, and the wind turbine arrangement scheme obtained is not optimal, so there is still a great improvement space for the optimization of the wind turbine arrangement scheme. Therefore, how to reduce the time consumption of the genetic algorithm as much as possible and obtain a globally optimal solution is very important for improving the effect of the wind turbine arrangement scheme.

[0004] Therefore, the application provides a wind turbine arrangement optimization method. SUMMARY

[0005] In order to overcome the deficiencies of the prior art, the application provides a wind turbine arrangement optimization method.

[0006] In order to achieve the above purpose, the application provides the following technical scheme:

[0007] A wind turbine arrangement optimization method comprises the following steps:

[0008] Obtain three-dimensional point cloud data of a geographic information system and wind data of a target wind farm;

[0009] Establish a CFD model according to the three-dimensional point cloud data of the geographic information system, and simulate the spatial distribution of the wind field;

[0010] Combine the wind field simulation result with single-point wind speed and wind direction data in the wind data to obtain wind speed and wind direction time history information of the spatial distribution of the wind farm;

[0011] According to the wind speed and wind direction time history information of the spatial distribution of the wind farm, an improved genetic algorithm is used to optimize the arrangement of the wind turbines, and an optimized wind turbine arrangement result is obtained.

[0012] Preferably, the CFD model is established according to the three-dimensional point cloud data of the geographic information system, and the spatial distribution of the wind field is simulated, which specifically comprises the following steps:

[0013] A CFD model is established according to three-dimensional point cloud data of a geographic information system, and a grid is divided in a calculation region;

[0014] Based on the grid division result, a wind field is simulated by using a Reynolds time-averaged method RANS, a Realizable k-ε is selected as a turbulence model in the simulation, and spatial distribution of the wind field under sixteen wind direction angles is simulated.

[0015] Preferably, the wind field simulation result is combined with single-point wind speed and wind direction data in the wind data to obtain wind speed and wind direction time history information of the spatial distribution of the wind farm, and the method specifically comprises the following steps:

[0016] Terrain influence on the observed single-point wind speed and wind direction data is eliminated to obtain global wind climate information U 10,open ;

[0017]

[0018] In the formula, U station is the single-point measured wind speed data, z 0,station is a ground roughness length of the observation station, z station is a height of the observation point from the ground, and z d,station is a zero-plane displacement height of the observation station.

[0019] The RANS simulation result is combined with the global wind climate information to obtain wind speed time history information of an arbitrary point in the spatial distribution of the wind farm.

[0020] A calculation formula of the wind speed time history information of the spatial distribution of the wind farm is as follows:

[0021]

[0022] In the formula, U(x, i) is an i-th value of the wind speed time history, U 10,in is a 10m height wind speed of a CFD simulation inlet, U 10,open (i) is a 10m height wind speed after local terrain is eliminated, U CFD (x, θ i ) is a CFD simulation wind speed under a wind direction angle θ i corresponding to the i-th wind speed.

[0023] Preferably, the wind speed and wind direction time history information of the spatial distribution of the wind farm is used to optimize a wind turbine arrangement by using an improved genetic algorithm to obtain an optimized wind turbine arrangement result, and the method comprises the following steps:

[0024] Related parameters involved in the wind turbine arrangement optimization are determined, the genetic algorithm divides a region into equidistant grids, and assumes that there are two possibilities at a center of each grid, i.e., installing a wind turbine and not installing a wind turbine, which correspond to 1 and 0, i.e., a "gene". Each individual corresponds to a wind turbine arrangement scheme, and is composed of a string of "genes".

[0025] The population initialization is given in a random manner, each "gene" is randomly assigned as 0 or 1;

[0026] The individual fitness is calculated based on the unique processing, and the population individuals are completely non-repeated;

[0027] The random individual selection is performed by using the roulette selection method;

[0028] The random crossover is performed on each two individuals, that is, the "genes" corresponding to the positions of the two individuals are exchanged; a certain time-varying mutation rate is given to each individual after the random crossover, and the formula is as follows;

[0029]

[0030] In the formula, P mut is the time-varying mutation rate, iteration is the number of current iterations, N iter is the total number of iterations, r1 is the initial mutation rate, and r2 is the final mutation rate;

[0031] When the number of calculations reaches the set value, the fan arrangement optimization scheme is obtained.

[0032] Preferably, the individual fitness is calculated based on the unique processing, including the following steps:

[0033] The reduced wind speed of each fan after being affected by the tail flow of the upstream fan is calculated considering the fan tail flow effect, and the calculation formula of the reduced wind speed is as follows:

[0034]

[0035]

[0036] In the formula, V is the reduced wind speed time history considering the fan tail flow effect, U is the wind speed time history data, C t is the thrust coefficient of the fan, k G is the tail flow diffusion rate related to the ground roughness length, ε G is a parameter related to the thrust coefficient of the fan, s is the horizontal distance of the downstream fan from the upstream fan, D is the blade diameter, and r is the radial distance of the center of the tail flow fan from the influence area of the upstream fan;

[0037] The annual power generation of each fan is calculated according to the fan reduced wind speed of the hub height of each fan, and the sum is the annual power generation of the entire wind farm;

[0038]

[0039] In the formula, AEP is the annual power generation of the wind farm, N turN is the number of wind turbines, N is the length of the sample, P is the wind turbine power curve given by the manufacturer, V j is the reduced wind speed of the wind turbine, P rated is the rated power generation of the wind turbine, N h is the number of hours corresponding to the sample, X turbine is the horizontal coordinate of the wind turbine;

[0040] According to the wind turbine arrangement scheme, the construction cost of the wind farm is calculated, and combined with the annual power generation, the individual fitness is determined;

[0041] Fitness=1 / objective=AEP / cost

[0042] cost=FCR×ICC+AOE

[0043]

[0044] In the formula, Fitness represents the individual fitness, expressed in unit cost power generation, the larger the value, the better the result; objective represents the target value, which is the reciprocal of the fitness; cost represents the construction cost of the wind farm, which needs to consider the initial investment cost ICC and annual cost AOE; FCR represents the conversion rate, which means the conversion coefficient of the initial investment cost to the annual cost, which is related to the interest rate and the service life of the wind turbine; A represents the conversion of all expenses to the equivalent annual premium value, P represents the conversion of all expenses to the present value at the beginning of the first year, i represents the annual interest rate, and n represents the service life of the wind turbine.

[0045] The wind turbine arrangement optimization method provided by the application has the following beneficial effects:

[0046] The method is aimed at the problems of low calculation efficiency and easy to fall into local optimum in wind turbine arrangement optimization, proposes a way of unique processing of the population to increase the calculation efficiency, and proposes a mutation rate that changes with time to avoid the optimization process from falling into local optimum as much as possible. The proposed efficient optimization algorithm can greatly obtain a better wind turbine arrangement scheme than the traditional algorithm. The method greatly improves the calculation efficiency of the genetic algorithm, and at the same time, the global optimal wind turbine arrangement result is obtained as much as possible. BRIEF DESCRIPTION OF DRAWINGS

[0047] In order to more clearly illustrate the embodiments of the application and the design scheme, the drawings required by the embodiments will be briefly introduced below. The drawings in the following description are only part of the embodiments of the application, and those skilled in the art can obtain other drawings according to these drawings without creating labor.

[0048] Figure 1 is the flowchart of the wind turbine arrangement optimization method disclosed by the application;

[0049] Figure 2 Improved genetic algorithm optimization flow chart

[0050] Figure 3 Target wind farm terrain elevation height cloud chart for example 1

[0051] Figure 4 Comparison chart of wind turbine arrangement scheme for example 1 DETAILED DESCRIPTION

[0052] In order for those skilled in the art to better understand the technical solutions of the present application and can be implemented, the present application is described in detail below in conjunction with the drawings and specific examples. The following examples are only used to more clearly illustrate the technical solutions of the present application, and cannot be used to limit the protection scope of the present application.

[0053] The present application provides a wind turbine arrangement optimization method, as shown in Figure 1 The method comprises the following steps:

[0054] Step A. Obtain the geographic information system three-dimensional point cloud data and wind data of the target wind farm, and the geographic information system three-dimensional point cloud data is referred to as GIS three-dimensional point cloud data.

[0055] Specifically, the geographic information system (Geographic Information System, GIS) generally includes terrain elevation information, which can be used for numerical modeling of the target wind farm, combined with the observed single-point wind speed and wind direction data, which can be used to reproduce the spatial distribution of wind speed and wind direction time history information of the entire wind farm.

[0056] Step B. Establish a CFD model according to the geographic information system three-dimensional point cloud data to simulate the spatial distribution of the wind field.

[0057] Specifically, how to model the target wind farm by CFD and accurately simulate the spatial wind speed distribution of the entire wind farm is very important for calculating the wind power generation under a specified wind turbine arrangement scheme, and the simulation process includes:

[0058] According to the GIS three-dimensional point cloud data, a CFD model is established, and the grid division of the calculation region is carried out.

[0059] Based on the grid division result, the wind field is simulated by using the Reynolds averaged Navier-Stokes (Reynold Averaged Navier-Stokes, RANS) method, the Realizable k-ε turbulence model is selected, and the spatial distribution of the wind field under sixteen wind direction angles is simulated.

[0060] Step C. Obtain the spatial distribution of wind speed and wind direction time history information of the wind farm.

[0061] Specifically, the RANS simulation results are combined with single-point wind speed and wind direction data in observed wind data to obtain wind speed and wind direction time history information of the spatial distribution of the wind farm. Since the terrain significantly affects the observed wind data, the effect of the terrain on the observed data needs to be removed before the corresponding transformation is performed, as follows.

[0062]

[0063]

[0064] In the formula, U(x, i) is the i-th value of the wind speed time history, U 10,in is the 10m height wind speed at the CFD simulation inlet, U 10,open (i) is the 10m height wind speed after removing the local terrain, U CFD (x, θ i ) is the CFD simulation wind speed at the i-th wind speed and wind direction angle θ i , U station is the single-point measured wind speed data, z 0,station is the ground roughness length of the observation station, z station is the height of the observation point from the ground, and z d,station is the zero plane displacement height of the observation station.

[0065] According to the above formula, the single-point measured wind speed data U station can be removed from the local terrain to obtain global wind climate (GWC) information U 10,open , which is combined with the CFD simulation results U CFD to calculate the wind speed time history information U(x, i) of any point in space. U 10,open in formula (2) is the global wind climate information, which is the data after removing the local terrain effect.

[0066] Step D. According to the wind speed and wind direction time history information of the spatial distribution of the wind farm, the improved genetic algorithm is used to optimize the wind turbine arrangement, and the optimized wind turbine arrangement result is obtained.

[0067] The above wind speed time history data does not consider the wake effect between wind turbines. Since the wake effect of different wind turbine arrangement schemes is very different, the genetic algorithm needs to be used to consider the wake effect of each wind turbine arrangement scheme to calculate the annual power generation of the wind farm. However, the traditional genetic algorithm calculates each individual in the population when calculating the power generation, and the mutation rate of the individual is a constant value, which is not conducive to the global optimization of the wind turbine arrangement scheme. Therefore, an improved genetic algorithm is proposed to optimize the wind turbine arrangement scheme, and the detailed process is as follows Figure 2 .

[0068] (D1) Parameter setting

[0069] The related parameters involved in the determination of the fan arrangement optimization, such as fan parameters and algorithm parameters, etc. It should be noted that the genetic algorithm divides the area into equidistant grids and assumes that there are two possibilities at the center of each grid, installing a fan and not installing a fan, which correspond to 1 and 0 respectively, i.e. "genes". Therefore, each individual corresponds to a fan arrangement scheme, which is composed of a string of "genes".

[0070] (D2) Population initialization

[0071] The population initialization is given in a random manner, and each "gene" is randomly assigned a value of 0 or 1.

[0072] (D3) Calculate individual fitness based on unique processing

[0073] Firstly, the fan wake effect needs to be considered to obtain the reduced wind speed time history, and the annual power generation of each individual is calculated, combined with the construction and operation cost of the wind farm, to calculate the fitness of the individual. The related calculation formula of the reduced wind speed is as follows:

[0074]

[0075]

[0076] In the formula, V is the reduced wind speed time history considering the fan wake effect, U is the wind speed time history data, C t is the fan thrust coefficient, k G is the wake diffusion rate related to the ground roughness length, ε G is a parameter related to the fan thrust coefficient, s is the horizontal distance of the downstream fan from the upstream, D is the blade diameter, and r is the radial distance from the center of the wake fan to the influence area of the upstream fan. According to this formula, the reduced wind speed of each fan affected by the wake of the upstream fan can be calculated. Since a fan may be affected by multiple upstream fans, the reduced wind speed of each fan affected by the wake of the upstream fan group needs to be calculated according to the law of conservation of energy loss.

[0077] Secondly, the annual power generation of each fan can be calculated according to the fan reduced wind speed at the hub height, and the sum is the annual power generation of the entire wind farm.

[0078]

[0079] In the formula, AEP is the annual power generation of the wind farm, N tur is the number of fans, N is the sample length, P is the fan power curve given by the manufacturer, V j is the fan reduced wind speed, P rated is the rated power of the fan, N h is the number of hours corresponding to the sample, and X turbineX is the horizontal coordinate of the wind turbine turbine And the same as the previous x meaning, plus turbine means for the wind turbine position.

[0080] Then, according to the wind turbine arrangement scheme, the construction cost of the wind farm is calculated, and combined with the annual power generation, the individual fitness is determined.

[0081] Fitness = 1 / objective = AEP / cost (6)

[0082] cost = FCR x ICC + AOE (7)

[0083]

[0084] In the formula, Fitness represents the individual fitness, expressed in unit cost power generation, the greater the value, the better the result; objective represents the target value, which is the inverse of the fitness; cost represents the construction cost of the wind farm, which needs to consider the initial investment cost ICC and annual cost AOE; FCR represents the conversion rate, which means the coefficient of converting the initial investment cost to annual cost, which is related to the interest rate and the service life of the wind turbine.

[0085] According to the above calculation, the fitness of each individual in the population can be obtained, however, the traditional algorithm calculates each individual in the population, which is extremely time-consuming. Since part of the individuals in the population will be repeated after a period of iteration, it is difficult to waste the calculation of each individual. The present application proposes that the population is first processed uniquely to obtain completely non-repeated population individuals, and then the fitness is calculated, which can greatly increase the calculation efficiency.

[0086] (D4) Individual selection

[0087] The higher the fitness of the individual, the higher the probability of being selected, and the random selection is performed by the roulette selection method.

[0088] (D5) Individual crossover

[0089] In order to ensure that the excellent "gene" (i.e. each grid point) is inherited, biological simulation is performed on each two individuals to randomly cross, which means that the "genes" corresponding to the positions of the two individuals are exchanged.

[0090] (D6) Considering individual mutation based on time-varying mutation rate

[0091] A certain mutation rate is adopted for each individual to avoid falling into local optimum as much as possible. Individual mutation usually assumes that only 1 "gene" is mutated at a small probability, such as "installing a fan" to "not installing a fan", or vice versa. Traditional algorithms adopt a constant mutation rate, usually between 0.5% and 2%, which is not conducive to global optimization of the algorithm. The present application proposes a time-varying mutation rate, as follows.

[0092]

[0093] In the formula, P mut is the time-varying mutation rate, iteration is the number of current iterations, N iter is the total number of iterations, r1 is the initial mutation rate, and r2 is the final mutation rate. It is recommended to take r1 = 0.5% and r2 = 2%, which can ensure that better "genes" are saved as much as possible in the early optimization stage, and a higher mutation rate is used in the later optimization stage to avoid falling into local optimum too early.

[0094] (D7) Convergence

[0095] When the number of calculations reaches the set value, stop iteration; otherwise, repeat steps (4) to (7).

[0096] (D8) Output fan arrangement scheme

[0097] Step E. Output the obtained fan arrangement optimization scheme.

[0098] Based on the obtained fan arrangement optimization scheme, the relevant parameters of the wind farm can be calculated, including the annual power generation of the wind farm.

[0099] The optimization process is only to find the optimal solution of fan arrangement, and the calculated parameters are few, only the annual power generation is calculated; but after the optimal fan arrangement scheme is determined, the wake loss, fan number, time consumption, etc. can be calculated.

[0100] Example 1

[0101] A certain wind farm in Hunan Province is taken as the research object, and the fan arrangement optimization method proposed in the present application is used for micro-siting of the wind farm. The terrain elevation height cloud map is as shown in Figure 3 .

[0102] The target wind farm is simulated in all wind directions, and the long-term observation wind speed data is combined to obtain the spatial distribution wind speed and wind direction time history information of the wind farm. Then, the original genetic algorithm and the improved genetic algorithm are used to optimize the fan arrangement scheme, and the arrangement schemes obtained by the two algorithms are as shown in Figure 4 . Figure 4 (a) is the fan arrangement diagram of the original genetic algorithm, Figure 4(b) the fan arrangement of the improved genetic algorithm.

[0103] The parameters of the two fan arrangement schemes are compared, as shown in Table 1. As shown in Table 1, compared with the original genetic algorithm, the proposed improved genetic algorithm can reduce the time consumption by 79% and improve the arrangement effect by about 13%. Overall, the proposed fan arrangement scheme high-efficiency algorithm can greatly reduce the calculation time consumption, and better improve the optimization effect of the fan arrangement.

[0104] Table 1 Comparison of fan arrangement scheme parameters

[0105]

[0106] From the implementation, it can be seen that by using the proposed improved genetic algorithm, while considering the power generation and cost of the wind farm, the arrangement effect of the wind farm can be improved by about 13%, and the calculation time consumption can be saved by about 79%.

[0107] When the genetic algorithm is used to optimize the fan arrangement scheme, the calculation efficiency is usually very low. The present application proposes to uniquely process all individuals in the population, which can greatly save the calculation time consumption. At the same time, the mutation rate changing with time is proposed, which can avoid the optimization process from falling into local optimum as much as possible. The method proposed in the present application is very efficient, and is suitable for the optimization of the fan arrangement scheme.

[0108] The above-described embodiments are only the preferred specific embodiments of the present application, and the protection scope of the present application is not limited thereto. Any simple change or equivalent replacement of the technical solutions within the technical range disclosed in the present application, which can be obviously obtained by those skilled in the art, shall belong to the protection scope of the present application.

Claims

1. A method for optimizing the arrangement of fans, characterized in that, The method comprises the following steps: obtaining geographic information system three-dimensional point cloud data and wind data of a target wind farm; establishing a CFD model according to the geographic information system three-dimensional point cloud data to simulate the spatial distribution of the wind field; combining the wind field simulation result with single-point wind speed and wind direction data in the wind data to obtain wind speed and wind direction time history information of the spatial distribution of the wind farm; optimizing the wind turbine arrangement according to the wind speed and wind direction time history information of the spatial distribution of the wind farm by using an improved genetic algorithm to obtain an optimized wind turbine arrangement result; the combining of the wind field simulation result with the single-point wind speed and wind direction data in the wind data to obtain the wind speed and wind direction time history information of the spatial distribution of the wind farm specifically comprises the following steps: Eliminate the influence of terrain on the observed single-point wind speed and direction data to obtain global wind climate information U 10,open ; wherein is the single-point measured wind speed data, is the ground roughness length of the observation station, is the height of the observation point from the ground, is the zero-plane displacement height of the observation station; combining the RANS simulation result with global wind climate information to obtain wind speed time history information of any point in the spatial distribution of the wind farm; the calculation formula of the wind speed time history information of the spatial distribution of the wind farm is: wherein, is the i-th value of the wind speed time history, is the 10 m height wind speed at the CFD simulation inlet, is the 10 m height wind speed after removing local topography, is the i-th wind speed corresponding wind direction angle CFD simulated wind speed at the i-th wind speed. the optimization of the wind turbine arrangement according to the wind speed and wind direction time history information of the spatial distribution of the wind farm by using the improved genetic algorithm to obtain the optimized wind turbine arrangement result comprises the following steps: determining related parameters involved in the optimization of the wind turbine arrangement, the genetic algorithm divides the region into equidistant grids, and assumes that there are two possibilities for the center of each grid, i.e. installing a wind turbine and not installing a wind turbine, which correspond to 1 and 0 respectively, i.e. "genes", each individual corresponds to a wind turbine arrangement scheme and is composed of a string of "genes"; population initialization is given in a random manner, each "gene" is randomly assigned a value of 0 or 1; calculating the fitness of individuals based on unique processing to obtain completely non-repeated population individuals; random individual selection is performed by using the roulette selection method; random crossover is performed on each two individuals, i.e. the "genes" in the corresponding positions of the two individuals are exchanged; a certain mutation rate varying with time is given to each individual after random crossover, and the formula is as follows: wherein is the time-varying mutation rate, iteration is the step number of the current iteration, N iter is the total number of iteration steps, r 1 is the initial mutation rate, r 2 is the final mutation rate; when the number of iterations reaches a set value, the obtained wind turbine arrangement optimization scheme is obtained.

2. The fan arrangement optimization method of claim 1, wherein the establishment of the CFD model according to the geographic information system three-dimensional point cloud data to simulate the spatial distribution of the wind field specifically comprises the following steps: establishing the CFD model according to the geographic information system three-dimensional point cloud data, and dividing the calculation region into grids; Based on the grid division results, the wind field is simulated by using the Reynolds time-averaged method (RANS), and the Realizable k-ε turbulence model is selected for the simulation to simulate the spatial distribution of the wind field under sixteen wind direction angles.

3. The fan arrangement optimization method of claim 1, wherein the calculation of the fitness of individuals based on unique processing comprises the following steps: considering the wake effect of the wind turbine, the reduced wind speed of each wind turbine affected by the wake of the upstream wind turbine is calculated, and the calculation formula of the reduced wind speed is as follows: wherein, V is the time history of the reduced wind speed considering the wake effect of the wind turbine, U is the time history of the wind speed data, is the thrust coefficient of the wind turbine, is the wake diffusion rate related to the roughness length of the ground, is a parameter related to the thrust coefficient of the wind turbine, s is the horizontal distance of the downstream wind turbine from the upstream wind turbine, D is the diameter of the blade, r is the radial distance of the center of the wake wind turbine from the influence area of the upstream wind turbine. according to the wind turbine reduced wind speed at the hub height of each wind turbine, the annual power generation of each wind turbine is calculated, and the sum is the annual power generation of the entire wind farm; wherein, AEP is the annual energy production of the wind farm, N tur is the number of wind turbines, N is the sample length, P is the wind turbine power curve given by the manufacturer, is the cut-out wind speed of the wind turbine, is the rated power of the wind turbine, is the number of hours corresponding to the sample, X turbine is the horizontal coordinate of the wind turbine; according to the wind turbine arrangement scheme, the construction cost of the wind farm is calculated, and the annual power generation is combined to determine the fitness of individuals; In the formula, Fitness represents the individual fitness, expressed in unit cost of power generation, the larger the value, the better the result; objective represents the target value, which is the inverse of the fitness; cost represents the construction cost of the wind farm, which needs to consider the initial investment cost ICC and annual cost AOE ; FCR represents the conversion rate, which means the coefficient of converting the initial investment cost to the annual cost, related to the interest rate and the service life of the wind turbine; A represents the conversion of all costs to the equivalent annual value of each year, P represents the conversion of all costs to the present value at the beginning of the first year, i represents the annual interest rate, n represents the service life of the wind turbine.

Images