Method for optimizing wind farm layout with forbidden area constraint based on monarch butterfly optimization algorithm

Abstract

The method for wind farm layout optimization with forbidden area constraint based on monarch butterfly optimization algorithm comprises the following steps: step 1: the forbidden area in the wind farm is described by a convex polygon, and a lookup table of the relative position of the wind turbine and the forbidden area is formed to determine the relative position of the wind turbine and the forbidden area; step 2: the incoming flow speed of each wind turbine is predicted, and the expected output power of the wind farm is calculated according to the wind speed and direction probability of the wind condition of the wind farm; step 3: a wind farm layout optimization model considering the forbidden area constraint is established by combining step 1 and step 2, and the improved monarch butterfly optimization algorithm is used to optimize the wind farm layout optimization model. The method can use a convex polygon to describe the forbidden area in the wind farm and convert it into a constraint condition, and use the improved monarch butterfly optimization algorithm to optimize the wind farm layout, so as to further improve the output power of the wind farm while avoiding the forbidden area.

Description

Technical Field

[0001] This invention relates to the field of wind farm layout optimization technology, specifically to a wind farm layout optimization method with restricted area constraints based on the Monarch Butterfly optimization algorithm. Background Technology

[0002] Wind energy is clean and renewable, and as an excellent green energy source, global wind power capacity is growing rapidly, with wind power accounting for an increasingly larger proportion of the power structure. Wind energy is harvested and converted into electricity by wind turbines, but the wake effect can affect the power generation of wind farms. Studies have shown that the wake effect can lead to a loss of 10% to 20% in the total power generation of wind farms. At the same time, the limited area in wind farm planning and the existence of restricted areas such as wetlands, farmland, or lakes that do not allow or are unfavorable for the installation of wind turbines will further increase the complexity of wind farm layout.

[0003] Currently, many scholars have focused on the non-convex, multivariable, and highly complex characteristics of wind farm layout optimization, and have extensively applied heuristic algorithms to this problem. However, not all heuristic algorithms can effectively optimize wind farm layouts. Commonly used algorithms include Genetic Algorithms (GA), Greedy Algorithms, and Particle Swarm Optimization (PSO). Existing research continuously updates heuristic algorithms for layout optimization, and improved or new algorithms can achieve better optimization results. On the other hand, many scholars consider the existence of restricted areas in wind farm layout optimization, but two situations exist. One is to use circles and rectangles to represent the shape and extent of restricted areas, which is relatively simple but not easily consistent with reality. The other is to use complex methods to classify and process wind farm elevation data, which can well represent the actual shape of restricted areas, but the computational burden is large, and when considering reality, the criteria for data classification are not easy to determine. Summary of the Invention

[0004] To address the shortcomings of existing wind farm layout optimization methods in considering the impact of restricted areas and improving optimization performance, this invention provides a wind farm layout optimization method with restricted area constraints based on the Monarch Butterfly optimization algorithm. This method uses convex polygons to characterize the restricted areas in the wind farm and transforms them into constraints. An improved Monarch Butterfly optimization algorithm is then used to optimize the wind farm layout, further improving the wind farm's output power while ensuring that wind turbines are placed away from restricted areas.

[0005] The technical solution adopted in this invention is as follows:

[0006] The wind farm layout optimization method with restricted area constraints based on the Monarch Butterfly optimization algorithm includes the following steps:

[0007] Step 1: Delineate the restricted areas within the wind farm using convex polygons and create a lookup table of the relative positions of the wind turbines and the restricted areas to determine their relative positions.

[0008] Step 2: Using the BP wake model and the upstream and downstream relationship of the wind turbines, predict the incoming wind speed of each wind turbine, and calculate the expected output power of the wind farm based on the wind speed and direction probabilities of the wind farm conditions.

[0009] Step 3: Combine Step 1 and Step 2 to establish a wind farm layout optimization model that considers restricted area constraints, and apply the improved Monarch Butterfly optimization algorithm to optimize the wind farm layout optimization model.

[0010] In step 1, the restricted area within the wind farm is determined, the outline of the restricted area is delineated using convex polygons, and a lookup table of the relative positions of the wind turbines and the restricted area is formed based on the vertices of the convex polygons.

[0011] Step 1 includes the following steps:

[0012] S1.1: Based on the vertices of the convex polygon depicting the restricted area, the formulas for determining each edge line are obtained by using the coordinates of two vertices respectively;

[0013] S1.2: Determine the adjustment amount: Take a point within the restricted area and substitute it into the formulas for each edge line in S1.1. If the result is greater than 0, the adjustment amount is -1; otherwise, it is 1.

[0014] S1.3: Multiply the straight line formula in S1.1 with the adjustment amount in S1.2 to obtain the final judgment formula for each edge line. The calculation formula is as follows:

[0015] S lij (x i ,y i ) = w lij l ij (x i ,y i )

[0016] In the formula: (x i ,y i ) represents the x-axis and y-axis coordinates of the i-th wind turbine.

[0017] edge line l ij () can be derived from its two endpoints (x) li ,y li ) and (x lj ,y lj It is determined to be:

[0018] straight line (y li -y lj )x+(x lj -x li )y+(x liy lj -y li x lj = 0, a straight line is formed by connecting the two endpoints, where: the coordinates of the two endpoints of the line are represented as (x, y, y) = 0. li ,y li ), (x lj ,y lj ), where (x,y) represents the coordinates of any point.

[0019] w lij The adjustment quantity serves as: for the determination formula S of a certain edge line constituting the restricted area lij (), if the wind turbine is located on the restricted area side, the condition is determined to be less than 0; if it is located on the non-restricted area side, the condition is determined to be greater than 0. Furthermore, if the wind turbine relates to all S constituting the restricted area... lij If all () are less than 0, it can be determined that the wind turbine is located in a restricted area.

[0020] S1.4: Summarize all the results of the judgment formulas in S1.3 and form a lookup table as shown in Table 1. If substituting the coordinates of a wind turbine unit will make all the straight line judgment formulas less than 0, then it is determined that it is located inside the restricted area; otherwise, it is located outside the restricted area or on the boundary of the restricted area.

[0021] Table 1. Relative Locations of Wind Turbine Units and Restricted Areas

[0022]

[0023] in: It means any one of them. It indicates existence, meaning at least one.

[0024] In step 2, the Bastankhah and Porte-Agel (BP) wake model is used to predict the wake velocity of the wind turbine. A sum-of-squares model is applied to calculate the superposition of the wind turbine wake. The ratio of the wake's influence area to the wind turbine's rotor area represents the degree of impact of the wake on the downstream turbine. The expected output power E(P) of the wind farm is then calculated. total And optimize the target energy cost (COE).

[0025] Step 2 includes the following steps:

[0026] S2.1: Define the wind farm as a square area and apply it to a two-dimensional Cartesian coordinate system, with the lower left vertex as the origin of the coordinate axes. The wind farm has N... t The coordinates of each wind turbine are (x... i ,y i ), i = 1, 2, ..., N tThe incoming wind direction is set along the positive x-axis, and this is taken as the initial angle, which is 0°. If the negative y-axis is taken as 0°, 90° can be added to the initial angle beforehand.

[0027] S2.2: Adjust the wind turbine coordinates according to the incoming wind direction angle, and set the wind turbine coordinates (x... i ,y i ) becomes (x′ i ,y′ i The wind turbines are then sorted according to their new coordinates in ascending order of x-axis values ​​to determine the upstream and downstream relationships between them when facing the incoming wind direction. The coordinate transformation formula for each wind turbine is as follows:

[0028]

[0029] In the formula, (x i ,y i (x′) represents the x-axis and y-axis coordinates of the i-th wind turbine. i ,y′ i ) represents the new coordinates of the wind turbine after Cartesian coordinate transformation, and θ represents the angle between the incoming wind direction and the wind turbine.

[0030] S2.3: Based on the wind turbine sequence determined in S2.2, the BP wake model is used to predict the wake velocity of the wind turbines, obtain the incoming wind speed of each wind turbine, and calculate the output power of each wind turbine based on the wind power conversion function.

[0031] S2.4: Calculate the expected output power of the wind farm, establish a discrete joint probability distribution of wind speed and direction using measured wind direction and direction data, and calculate the wind speed v using S2.2 and S2.3. q and wind direction θ j The wind turbine output power at that time is used to obtain the expected output power E(P) of the wind farm. total The specific calculation is as follows:

[0032]

[0033] In the formula, N t Indicates the number of wind turbines in the wind farm; i (i = 1, 2, ..., N) t ) represents the serial number of the wind turbine unit; N θ This represents the number of wind directions divided, j (j = 1, 2, ..., N). θ ) represents the j-th wind direction interval; N v Indicates the number of wind speeds divided; q (q = 1, 2, ..., N) v ) represents the q-th wind speed; P i () represents the i-th unit at wind speed v q The power below; p() represents the wind speed v qand wind direction θ j Joint probability at time; v q θ represents the value of the q-th wind speed. j This represents the value of the j-th wind direction.

[0034] In step 3, the wind farm layout optimization model considering restricted area constraints is established, including the method for determining wind turbines and restricted areas, the wake model, and the total output power of the wind farm. The specific optimization model objectives and constraints are as follows:

[0035]

[0036] Where: N t This indicates the number of wind turbines in a wind farm, o i g represents the penalty value calculated for wind turbine i due to restricted area constraints. i This represents the penalty value calculated for wind turbine unit i under the unit spacing constraint; x min ,x max ,y min ,y max The upper and lower boundaries of the xy coordinate axes of the wind farm are defined by Λ; Λ represents the restricted area; (x i ,y i ), (x j ,y j ) represent the coordinates of wind turbine units i and j, respectively; d min This is the minimum distance between generator units.

[0037] In step 3, the improved Monarch Butterfly optimization algorithm is applied to optimize the wind farm layout model considering the restricted area constraints. The constraints consider the wind farm boundary, the restricted area, and the minimum allowable spacing of the wind turbines, and include the following steps:

[0038] S3.1: Combining the wind farm layout optimization model with the improved Monarch Butterfly algorithm:

[0039] Let the layout of a wind farm be analogous to individual butterflies in a population, and let 2N be the number of butterflies. t dimensional vector h = [x1, x2, x3, x4, ..., x 2Nt-1 ,x 2Nt x1, x2, x3, x4 represent the magnitudes of the 1st, 2nd, 3rd, and 4th dimension positional variables in the individual butterfly h of the algorithm, respectively; x 2Nt-1 ,x 2Nt Let represent the magnitudes of the positional variables in the 2Nt-1 and 2Nt dimensions of the butterfly individual h, respectively.

[0040] Among them, (x 2i-1 ,x 2i ) indicates that the wind turbine unit T in this individual i coordinates (x) i ,y iUsing M×2N t The order matrix H = [h1, h2, ..., h M [] represents a population of size M, where: h1, h2, ..., h M These represent the 1st, 2nd, ..., Mth butterfly individuals in population H, respectively.

[0041] By treating the restricted area and wind turbine spacing constraints as penalty terms, f is transformed into an unconstrained optimization problem to be solved, and then respectively through N t dimensional vector O = [o1, o2, ..., o Nt ] and G = [g1, g2, ..., g Nt Record constraint violation information, o1, o2, ..., o Nt These represent wind turbine units 1, 2, ..., N. t Regarding the penalty values ​​for calculating forbidden zone constraints; g1, g2, ..., g Nt These represent wind turbine units 1, 2, ..., N. t Penalty values ​​for calculating spacing constraints of wind turbine units.

[0042] The unit spacing constraint is to satisfy a minimum permissible unit spacing, as specifically stated below:

[0043]

[0044] In the formula: (x i ,y i Let (x) be the coordinate of wind turbine i, and (x) be the coordinate of wind turbine i. j ,y j Let d be the coordinate of wind turbine j. min This is the minimum distance between wind turbine units. Where, when wind turbine T... i When the unit spacing constraint is satisfied, g i The fitness function is denoted as 0 if it is positive and 1 otherwise. Therefore, the fitness function is expressed as follows:

[0045]

[0046] N t This indicates the number of wind turbines in a wind farm, o i g represents the penalty value calculated for wind turbine i due to restricted area constraints. i This represents the penalty value calculated for wind turbine unit i under the unit spacing constraint.

[0047] The above formula is an empirical formula for energy cost. Reference [1]: Optimization of wind turbine positioning in large windfarms by means of a genetic algorithm [J]. Journal of Wind Engineering and Industrial Aerodynamics, 1994, 51(1). This paper assumes that the dimensionless cost per year of a single wind turbine is 1. When a large number of units are installed, the maximum cost of each turbine can be reduced by 1 / 3.

[0048] S3.2: The initial population is generated randomly, and the fitness of each individual in the population is calculated using the tail flow model and the lookup table method of the restricted area.

[0049] S3.3: Divide the population H into two populations H1 and H2, where H1 has a proportion of p in H2 and its behavior is migration. The update method is as follows:

[0050]

[0051] In the formula, x new,n Let r1 be a random individual from H1, r2 be a random individual from H2, and u be a random number uniformly distributed in the interval [0,1]. This method selects different positions from the two populations to form a new individual.

[0052] The adaptive behavior of group r2 differs from the migration behavior described above, and the specific update method is as follows:

[0053]

[0054] In the formula, x best,n for h best The nth dimension; u1 and u2 are uniformly distributed random numbers in the interval [0,1]; Levy is the Levy flight, t is the current iteration number; S t S is the current step size. t Through S max It is obtained by decreasing it generation by generation using an exponential decay function, and the specific calculation is as follows:

[0055]

[0056] In the formula, b is the attenuation coefficient, with a value of 0.5, and ε is the attenuation coefficient, with a value of 1.5. The two populations combine through their respective behaviors to form a new population H. new At the same time, it determines the location of the wind turbine and performs boundary checks; if it exceeds the boundary of the wind farm, it stays on the boundary.

[0057] S3.4: Calculate the new population H new The constraint value, and for H new Individuals that violate constraints are replaced. If H new individual h m The i-th wind turbine in the middle violates the restricted area or spacing constraints, i.e. (o m,n +g m,n If )>0, then a single position replacement is performed, and the unit coordinates after replacement are as follows:

[0058]

[0059] x m,2i-1 x represents the position value of individual m in the (2i-1)th dimension. m,2i The position value of the (2i-1)th dimension of individual m is represented by (x m,2i-1 ,x m,2i The coordinates are the coordinates of the i-th wind turbine in individual m, rand(x) min ,x max ) indicates that in [x min ,x max Randomly generate values ​​within the range, rand(y) min ,y max ) indicates that in [y min ,y max A random value is generated within the interval, x. min ,x max ,y min ,y max These are the upper and lower boundaries of the xy coordinate axes of the wind farm.

[0060] For this individual, based on the fitness comparison after replacement, if h s Its fitness is better than h m Then h will be replaced. m If no replacement is made, then select the three best individuals h from population H. b1 h b2 h b3 Find the position of the centroid enclosed by the three groups of individuals as the new h. m The calculation formula is as follows:

[0061]

[0062] This operation selects the three best individuals from population H, which allows individuals with poor fitness to move closer to the better individuals in population H in advance, thus improving the search speed of the algorithm.

[0063] S3.5: Calculate the new population H new The fitness of all individuals in the population is evaluated, and based on the feasibility criterion, it is determined whether individuals should be replaced, thus completing the update of the population H.

[0064] S3.6: Convergence check, determine if t has reached t_0. max If the target is reached, the iteration stops and h is output. best and f best The optimal layout and fitness are determined by the population size; otherwise, the process returns to S3.2. Through population updates and iterations, the optimal individual is obtained, which represents the optimal layout of wind turbines to avoid restricted areas.

[0065] This invention discloses a wind farm layout optimization method with restricted area constraints based on the Monarch Butterfly optimization algorithm, with the following technical effects:

[0066] 1) In step 1 of this invention, the restricted areas in the wind farm are characterized using convex polygons. The more sides of the polygon, the more accurate the outline of the restricted area. Furthermore, since the restricted areas are represented by polygons, the vertices and side expressions of the polygons can be determined. Therefore, the coordinates of the wind turbines can be substituted into the side expressions to determine whether the wind turbines are located inside the restricted area. Summarizing the method for determining the relative position of the wind turbines and the restricted area into a lookup table simplifies the calculation process and facilitates the conversion of the judgment results into numerical values, which can then be applied to the wind farm layout optimization process.

[0067] 2) In step 2 of this invention, the wind farm considers the wake effect when calculating the wind speed before each wind turbine. A BP wake model is used, whose wind speed loss profile approximates a Gaussian curve. The closer to the wake center, the more severe the wind speed loss, which closely matches the actual wind speed loss. Furthermore, when calculating the output power under a certain layout scheme, the wind speed across all wind directions is considered, resulting in a more realistic assessment than a layout based on a single wind direction.

[0068] 3) In step 3 of the present invention, a maximum update step size decay mechanism and a constraint violation replacement mechanism are added in the algorithm update stage. The former can facilitate global search and improve the accuracy of the optimal solution; the latter, as a supplement to the original algorithm population update method, solves the problem that the optimization process is prone to getting trapped in local solutions due to the penalty term.

[0069] Maximum update step size decay mechanism: When updating the individual position, the original algorithm can move to a new position based on the maximum step size. However, setting the maximum step size too large will affect the accuracy, while setting it too small will reduce the movement range and cause premature convergence. Therefore, the maximum step size is dynamically adjusted. The adjusted step size is obtained by applying an exponential decay function based on the maximum step size. In the early stage of iteration, the algorithm explores a wider range of individuals, which is beneficial for global search. In the later stage of iteration, it gradually approaches the optimal solution, improving the accuracy of the optimal solution and the stability of the results.

[0070] Constraint violation replacement mechanism: To address the problem that the original algorithm has a single update method and is prone to getting stuck in local solutions, an update operation for replacing individual positions is added to the original MBO algorithm. For individual positions that do not meet the constraints, this replacement mechanism makes it easier for them to enter the range of feasible solutions that satisfy all constraints in the early stages of algorithm optimization, thereby speeding up the optimization process.

[0071] 4) This invention proposes a wind farm layout optimization model that takes into account the influence of restricted areas. This model delineates restricted areas in the wind farm using polygons, which can determine the relative positions of wind turbines and restricted areas. This method is summarized as a lookup table and applied to the constraint determination in the wind farm layout optimization model. Based on this model, the improved Monarch Butterfly optimization algorithm provides a feasible method for wind farm layout optimization, which can obtain better layout schemes and improve optimization efficiency. Attached Figure Description

[0072] Figure 1 This is a flowchart of the wind farm layout optimization model that takes into account the influence of restricted areas in this invention.

[0073] Figure 2 A diagram showing the location of the restricted area of ​​a wind farm and its vertex coordinates as set up in an embodiment of the present invention.

[0074] Figure 3 This is a diagram of the BP wake model.

[0075] Figure 4 Flowchart of the improved Monarch Butterfly algorithm for applying the optimization model of this invention.

[0076] Figure 5 This is a wind direction probability rose diagram for wind conditions at a wind farm.

[0077] Figure 6 Schematic diagrams of optimized wind farm layout schemes for three restricted areas. Detailed Implementation

[0078] The specific embodiments and working principles of the present invention will be further described in detail below with reference to the accompanying drawings.

[0079] like Figure 1 As shown, the wind farm layout optimization method taking into account the impact of restricted areas includes the following steps:

[0080] S1: Determine the restricted area within the wind farm, and use a convex polygon to depict the outline of the restricted area, such as... Figure 2 As shown, the shaded area is the restricted area. A lookup table of the relative positions of the wind turbines and the restricted area is formed based on the vertices of the polygon.

[0081] S11: Based on the geometric method of determining a straight line by two points from each vertex of the polygon depicting the restricted area, the formula for determining each edge line from the coordinates of two vertices is as follows: (y li -ylj )x+(x lj -x li )y+(x li y lj -y li x lj ) = 0.

[0082] S12: Determine the adjustment amount: Take a point within the restricted area and substitute it into the formulas for each edge line in S11. If the result is greater than 0, the adjustment amount is -1; otherwise, it is 1.

[0083] S13: Multiply the straight line formula in S11 by the adjustment amount in S12 to obtain the final judgment formula for each edge line. The calculation formula is as follows:

[0084] S lij (x i ,y i ) = w lij l ij (x i ,y i )

[0085] In the formula, the edge line l ij () can be derived from its two endpoints (x) li ,y li ) and (x lj ,y lj ) is determined to be a straight line (y li -y lj )x+(x lj -x li )y+(x li y lj -y li x lj ) = 0, w lij The adjustment quantity serves as: for the determination formula S of a certain edge line constituting the restricted area lij (), if the wind turbine is located on the restricted area side, the condition is determined to be less than 0; if it is located on the non-restricted area side, the condition is determined to be greater than 0. Furthermore, if the wind turbine relates to all S constituting the restricted area... lij If all () are less than 0, it can be determined that the wind turbine is located in a restricted area.

[0086] S1.4: Summarize all the results of the judgment formulas in S1.3 and form a lookup table as shown in Table 1. If substituting the coordinates of a wind turbine unit will make all the straight line judgment formulas less than 0, then it is determined that it is located in the restricted area; otherwise, it is located outside the restricted area or on the boundary of the restricted area.

[0087] S2: Using the Bastankhah and Porte-Agel (BP) wake model, such as Figure 2As shown, the wake velocity of the wind turbine is predicted, and the sum-of-squares model is used to calculate the superposition result of the wind turbine wake. The ratio of the wake influence area to the wind turbine rotor area is used to represent the degree of influence of the wake on the downstream unit, and the expected output power E(P) of the wind farm is calculated. total And optimize the target energy cost (COE);

[0088] S2.1: Set the wind farm to a square area and apply it to a two-dimensional Cartesian coordinate system, with the lower left vertex as the origin of the coordinate axis. For example... Figure 2 As shown, the x-axis coordinate range of the wind farm is [0, 2000], and the y-axis coordinate range is [0, 2000], with the unit being meters (m).

[0089] Wind farms with N t The coordinates of each wind turbine are (x... i ,y i ), i = 1, 2, ..., N t The incoming wind direction is set along the positive x-axis, and this is taken as the initial angle, which is 0°. If the negative y-axis is taken as 0°, 90° can be added to the initial angle beforehand.

[0090] S2.2: Adjust the wind turbine coordinates according to the incoming wind direction angle, and set the wind turbine coordinates (x... i ,y i ) becomes (x′ i ,y′ i The wind turbines are then sorted according to their new coordinates, with the x-axis values ​​ascending, to determine the upstream and downstream relationships between them when facing the incoming wind direction. The coordinate transformation formula for each wind turbine is as follows:

[0091]

[0092] S2.3: Based on the wind turbine sequence determined in S2.2, the BP wake model is used to predict the wake velocity of the wind turbines, obtain the incoming wind speed of each wind turbine, and calculate the output power of each wind turbine based on the wind power conversion function.

[0093] S2.4: Calculate the expected output power of the wind farm, establish a discrete joint probability distribution of wind speed and direction using measured wind direction and direction data, and calculate the wind speed v using S2.2 and S2.3. q and wind direction θ j The wind turbine output power at that time is used to obtain the expected output power E(P) of the wind farm. total The specific calculation is as follows:

[0094]

[0095] In the formula, N tRepresents the number of wind turbines in the wind farm, i (i = 1, 2, ..., N). t ) represents the serial number of the wind turbine unit; N θ This represents the number of wind directions divided, j (j = 1, 2, ..., N). θ ) represents the j-th wind direction interval; N v The number of wind speeds is represented by q (q = 1, 2, ..., N). v P represents the q-th wind speed. i () represents the i-th unit at wind speed v q The power below; p() represents the wind speed v q and wind direction θ j The joint probability at time v. q θ represents the value of the q-th wind speed. j This represents the value of the j-th wind direction.

[0096] S3: Combines the wind farm layout optimization model that takes into account the impact of restricted areas with the improved Monarch Butterfly algorithm. The algorithm flowchart is as follows: Figure 3 As shown, the specific steps are as follows:

[0097] S3.1: Combine the wind farm layout optimization model with the improved Monarch Butterfly algorithm. Let the wind farm layout scheme be analogous to individual butterflies in a population, and denote 2N... t dimensional vector h = [x1, x2, x3, x4, ..., x 2Nt-1 ,x 2Nt ], where (x 2i-1 ,x 2i ) indicates that the wind turbine unit T in this individual i coordinates (x) i ,y i Using M×2N t The order matrix H = [h1, h2, ..., h M Let ] represent a population of size M. The constraints on restricted areas and wind turbine spacing are used as penalty terms to transform f into an unconstrained optimization problem, which is then solved using N... t dimensional vector O = [o1, o2, ..., o Nt ] and G = [g1, g2, ..., g Nt Record constraint violation information, among which, the unit spacing constraint is represented as follows:

[0098]

[0099] When the wind turbine unit T i When the unit spacing constraint is satisfied, g i The fitness function is denoted as 0 if it is positive and 1 otherwise. Therefore, the fitness function is expressed as follows:

[0100]

[0101] S3.2: The initial population is generated randomly, and the fitness of each individual in the population is calculated using the tail flow model and the lookup table method of the restricted area.

[0102] S3.3: Divide the population H into two populations H1 and H2, where H1 has a proportion of p in H2 and its behavior is migration. The update method is as follows:

[0103]

[0104] In the formula, x new,n Let r1 be a random individual from H1, r2 be a random individual from H2, and u be a random number uniformly distributed in the interval [0,1]. This method selects different positions from the two populations to form a new individual.

[0105] The adaptive behavior of group r2 differs from the migration behavior described above, and the specific update method is as follows:

[0106]

[0107] In the formula, x best,n for h best In the nth dimension, u1 and u2 are random numbers uniformly distributed in the interval [0,1], Levy is the levy flight, t is the current iteration number, and S t S is the current step size. t Through S max It is obtained by decreasing it generation by generation using an exponential decay function, and the specific calculation is as follows:

[0108]

[0109] In the formula, b is the attenuation coefficient, with a value of 0.5, and ε is the attenuation coefficient, with a value of 1.5. The two populations combine through their respective behaviors to form a new population H. new At the same time, it determines the location of the wind turbine and performs boundary checks; if it exceeds the boundary of the wind farm, it stays on the boundary.

[0110] S3.4: Calculate the new population H new The constraint value, and for H new Individuals that violate constraints are replaced. If H new individual h m The i-th wind turbine in the middle violates the restricted area or spacing constraints, i.e. (o m,n +g m,n If )>0, then a single position replacement is performed, and the unit coordinates after replacement are as follows:

[0111]

[0112] For this individual, based on the fitness comparison after replacement, if h sIts fitness is better than h m Then h will be replaced. m If no replacement is made, then select the three best individuals h from population H. b1 h b2 h b3 Find the position of the centroid enclosed by the three groups of individuals as the new h. m The calculation formula is as follows:

[0113]

[0114] This operation selects the three best individuals from population H, which allows individuals with poor fitness to move closer to the better individuals in population H in advance, thus improving the search speed of the algorithm.

[0115] S3.5: Calculate the new population H new The fitness of all individuals in the population is evaluated, and based on the feasibility criterion, it is determined whether individuals should be replaced, thus completing the update of the population H.

[0116] S3.6: Convergence check, determine if t has reached t_0. max If the target is reached, the iteration stops and h is output. best and f best The optimal layout and fitness are determined by the population size; otherwise, the process returns to S3.2. Through population updates and iterations, the optimal individual is obtained, which represents the optimal layout of wind turbines to avoid restricted areas.

[0117] Example:

[0118] For a classic 2km×2km wind farm case study, hourly measured wind speed and direction data from the Ada wind farm station in North Dakota, USA, between 2010 and 2019 were collected as the wind farm's wind conditions. The wind direction probability rose diagram is shown below. Figure 4 As shown in Table 2, the optimal layout is achieved by calculating the expected hourly power generation of the wind farm under the unit cost. The parameter information of the wind turbine and the wind farm is shown in Table 2.

[0119] Table 2 Parameters of Wind Turbine Units and Wind Farms

[0120]

[0121] In this embodiment, no restricted area, one restricted area, and two restricted areas are set as restricted area scenarios 1 to 3. Figure 5 The diagram shows the available and restricted areas for wind farm turbine installation in Scenario 3. The blank areas represent available areas, while the shaded areas represent restricted areas 1 and 2. The coordinates of the endpoints of the restricted areas are marked. Similarly, Scenario 1 has no restricted areas, while Scenario 2 only has restricted area 1. The percentage of available area to total area in the three scenarios is 100%, 87.42%, and 77.79%, respectively.

[0122] This embodiment applies the IMBO algorithm to optimize the wind farm layout model. Furthermore, to compare the optimization performance of the IMBO algorithm, the Differential Adaptive Monarch Butterfly Optimization (DAMBO), MBO algorithm, and PSO algorithm are applied sequentially to optimize the wind farm layout in the aforementioned three scenarios. The population size H of the algorithms is set to 50, and t... max The number of iterations is 350. Table 3 shows the parameter settings for the algorithm in the example.

[0123] Table 3 Algorithm Parameter Settings

[0124]

[0125] Note: In the PSO algorithm, c1 and c2 are individual and global learning factors, ω is the inertia coefficient, and V... max This represents the maximum speed at which the particle travels.

[0126] The IMBO algorithm was applied to optimize the layout of wind farms considering exclusion zone constraints under three different exclusion zone scenarios, verifying the effectiveness of the exclusion zone determination based on the lookup table method of this invention. The layout results are as follows: Figure 6 As shown in Table 4, the optimization results are as follows.

[0127] Table 4. Layout optimization adaptability results in three scenarios

[0128]

[0129] Figure 6 The layout results for scenarios 1 through 3 are shown in sequence. The dots in the images represent wind turbine generators, and the expected output power of each wind turbine generator has different color levels, corresponding to... Figure 6 The color bar on the right shows the north wind direction from top to bottom. Additionally, the dashed boxes in Scene 1 and Scene 2 correspond to the restricted areas in Scene 3. As a comparative analysis of different restricted areas, the following phenomenon can be observed:

[0130] 1) By optimizing the layout, Figure 6 Wind turbine units can be placed within the dashed box in sub-diagram a. Figure 6 The subgraph in section b constrains restricted area 1, therefore the wind turbines are placed away from this restricted area. Figure 6 The constraint of adding two restricted areas to the middle c subgraph means that no wind turbines are placed in either restricted area. This shows that the relative position determination of wind turbines and restricted areas based on the lookup table method is feasible. The IMBO algorithm can effectively avoid restricted areas when optimizing the layout.

[0131] 2) Through optimized layout, the wind turbine units are arranged in a more dispersed manner, combined with... Figure 6The expected output power of each wind turbine in the wind farm is higher for turbines located to the south and northwest of the wind farm. This is related to... Figure 4 The prevailing wind direction is the same in the wind rose diagram, indicating that the IMBO algorithm can reasonably arrange wind farms.

[0132] 3) Figure 6 The lowest output power of the wind turbine in sub-graph a is 0.96MW. Figure 6 The lowest output power of the wind turbines in the C-subgraph is 0.94MW. Since the optimized layout allows for better placement of the wind turbines while meeting constraints, it is still less than... Figure 6 In the sub-graphs a and c, the restricted areas compress the usable area of ​​the wind farm, resulting in reduced spacing between wind turbines, increased wake effects, and decreased performance of some wind turbines.

[0133] Table 4 is... Figure 6 The adaptability results of optimized layout schemes in various scenarios are presented, along with the corresponding expected output power E(P) of the wind farm. total And efficiency η. Since the number of wind turbines is fixed, scenario 1 has the minimum COE, corresponding to E(P) total ) and η are the largest, Scenario 2 results are the second largest, and Scenario 3 E(P) is the largest. total The minimum is 0.05%. This is because if there are restricted areas in a wind farm, the available area on the site will be limited, causing wind turbines to be moved away from locations with better wind energy resources. At the same time, the spacing between them will be shortened, and the wind turbines will be arranged more densely, ultimately resulting in a decline in the overall performance of the wind farm.

[0134] To analyze the superiority of the IMBO algorithm in wind farm layout optimization models considering restricted area constraints, the IMBO, DAMBO, MBO, and PSO algorithms were compared in three restricted area scenarios. Each algorithm was run 30 times individually. Based on whether the fitness satisfied the constraints, the number of feasible solutions that met the constraints was counted, along with the average and minimum fitness results. The results are shown in Table 5. The following phenomena can be observed:

[0135] 1) Scenario 1 considers only the spacing constraints of wind turbine generators and the boundary constraints of the wind farm, without considering the restricted area constraints. In this scenario, almost all four algorithms can optimize to obtain feasible layout schemes in 30 runs. Among them, the fitness of the DAMBO algorithm is 0.7610, which is better than the IMBO algorithm. However, based on the average results, the IMBO algorithm is better than the other algorithms.

[0136] 2) Scenarios 2 and 3 both consider restricted area constraints. The IMBO algorithm almost always guarantees a feasible layout solution in 30 runs, while other algorithms have fewer feasible solutions and are prone to getting trapped in local solutions during optimization. Furthermore, in both scenarios, the IMBO algorithm outperforms other algorithms in both average and minimum fitness.

[0137] The above phenomena indicate that, without considering the restricted area constraint, the DAMBO algorithm can find a better fitness result than the IMBO algorithm. However, in the two scenarios considering the restricted area, the fitness result obtained by the IMBO algorithm is superior to other algorithms. Therefore, although the IMBO algorithm does not have an absolute advantage for wind farm layout optimization models in all scenarios, it still makes a certain contribution to solving the problem of this invention.

[0138] The IMBO algorithm of this invention can find feasible solutions in almost all three scenarios, has good global search capability, and shows good optimization accuracy, thus demonstrating that the improvement to MBO is effective.

[0139] Table 5. Fitness results of different algorithms in three scenarios

[0140]

[0141] As can be seen from the above results, the present invention applies the improved Monarch Butterfly algorithm to optimize the wind farm layout considering the influence of restricted areas. It can obtain a lookup table to determine the relative position of wind turbines and restricted areas by identifying the restricted areas. Then, the method is embedded into the wind farm layout optimization model based on the improved Monarch Butterfly algorithm to solve the layout result that simultaneously satisfies the restricted area constraint and maximizes the output power.

[0142] By optimizing the layout under different restricted areas, wind turbines can be placed away from restricted areas while maintaining permissible spacing, and their layout can be rationally arranged according to the wind conditions of the wind farm. Furthermore, the IMBO algorithm, applied during the optimization process of the model in this invention, exhibits better convergence and optimization speed, further improving the output power of the wind farm through rational layout while ensuring layout constraints.

Claims

1. A wind farm layout optimization method with restricted area constraints based on the Monarch Butterfly optimization algorithm, characterized in that... Includes the following steps: Step 1: Delineate the restricted areas within the wind farm using convex polygons and create a lookup table of the relative positions of the wind turbines and the restricted areas to determine their relative positions. Step 2: Predict the incoming wind speed of each wind turbine and calculate the expected output power of the wind farm based on the wind speed and direction probabilities of the wind farm conditions. Step 3: Combine Step 1 and Step 2 to establish a wind farm layout optimization model that considers restricted area constraints, and apply the improved Monarch Butterfly optimization algorithm to optimize the wind farm layout optimization model; In step 1, the restricted area within the wind farm is determined, the outline of the restricted area is delineated using convex polygons, and a lookup table of the relative positions of the wind turbines and the restricted area is formed based on the vertices of the convex polygons. Step 1 includes the following steps: S1.1: Based on the vertices of the convex polygon depicting the restricted area, the formulas for determining each edge line are obtained by using the coordinates of two vertices respectively; S1.2: Determine the adjustment amount: Take a point within the restricted area and substitute it into the formulas for each edge line in S1.

1. If the result is greater than 0, the adjustment amount is -1; otherwise, it is 1. S1.3: Multiply the straight line formula in S1.1 with the adjustment amount in S1.2 to obtain the final judgment formula for each edge line. The calculation formula is as follows: ； In the formula: Indicates the first Typhoon generator x shaft and y Axis coordinates; edge line It can be obtained from its two endpoints and Determined as: straight line A straight line is formed by connecting the two endpoints. Where: the coordinates of the two endpoints of the line are respectively represented as , , Represents the coordinates of any point; The adjustment quantity serves as a determination formula for a certain edge line constituting a restricted area. If the wind turbine is located on the side of the restricted area, the result is less than 0; if it is located on the side outside the restricted area, the result is greater than 0. Furthermore, if the wind turbine relates to all elements constituting the restricted area... If all values ​​are less than 0, it can be determined that the wind turbine is located within a restricted area; S1.4: Summarize all the results of the judgment formulas in S1.

3. If substituting the coordinates of a wind turbine makes all the straight line judgment formulas less than 0, then it is determined that it is located inside the restricted area; otherwise, it is located outside the restricted area or on the boundary of the restricted area.

2. The wind farm layout optimization method with restricted area constraints based on the Monarch Butterfly optimization algorithm according to claim 1, characterized in that: In step 2, the Bastankhah and Porte-Agel (BP) wake model is used to predict the wake velocity of the wind turbine. The sum-of-squares model is applied to calculate the superposition result of the wind turbine wake. The ratio of the wake influence area to the wind turbine rotor area is used to represent the degree of influence of the wake on the downstream unit, and the expected output power of the wind farm is calculated. E ( P total And optimize the target energy cost (COE).

3. The wind farm layout optimization method with restricted area constraints based on the Monarch Butterfly optimization algorithm according to claim 2, characterized in that: Step 2 includes the following steps: S2.1: Define the wind farm as a square area and apply it to a two-dimensional Cartesian coordinate system, with the lower left vertex as the origin of the coordinate axes; the wind farm has N t The coordinates of each wind turbine are ( x i , y i ), i =1,2,…, N t ; Incoming wind direction set along x The positive direction of the axis, and taking this as the initial angle, is 0°. If along... y The negative axis is 0°, and 90° can be added to the initial angle beforehand. S2.2: Adjust the wind turbine coordinates according to the incoming wind direction angle, and set the wind turbine coordinates ( x i , y i ) becomes ( , ), and according to the new coordinates x The axis values ​​are sorted from smallest to largest to determine the upstream and downstream relationships between wind turbines when facing the incoming wind direction; the coordinate transformation formula for the wind turbines is expressed as follows: ； In the formula, ( x i , y i ) indicates the first i Typhoon generator x shaft and y Axis coordinates, ( , () represents the new coordinates of the wind turbine after Cartesian coordinate transformation. Indicates the angle between the incoming wind direction and the wind turbine unit; S2.3: Based on the wind turbine sequence determined in S2.2, the BP wake model is used to predict the wake velocity of the wind turbines, obtain the incoming wind speed of each wind turbine, and calculate the output power of each wind turbine based on the wind power conversion function. S2.4: Calculate the expected output power of the wind farm, establish a discrete joint probability distribution of wind speed and direction using measured wind direction and direction data, and calculate the wind speed using S2.2 and S2.

3. v q and wind direction θ j The wind turbine output power at that time is used to obtain the desired output power of the wind farm. E ( P total The specific calculation is as follows: ； In the formula, N t This indicates the number of wind turbines in the wind farm; i ( i = 1, 2, …, N t () represents the serial number of the wind turbine unit; N θ Indicates the number of wind directions divided. j ( j = 1, 2, …, N θ ) indicates the first j One wind direction range; N v Indicates the number of wind speeds divided; q ( q =1, 2, …, N v ) indicates the first q wind speed; P i ( ) is the first i Taiwanese units at wind speed v q The power below; p () indicates wind speed v q and wind direction θ j The joint probability at time; Indicates the first q The wind speed value. Indicates the first j The value for each wind direction.

4. The wind farm layout optimization method with restricted area constraints based on the Monarch Butterfly optimization algorithm according to claim 1, characterized in that: In step 3, the wind farm layout optimization model considering the restricted area constraint is established. The specific optimization model objective and constraint conditions are as follows: ； In the formula: This indicates the number of wind turbines in the wind farm. Indicates wind turbine i The penalty value calculated using restricted area constraints. Indicates wind turbine i Penalty value calculated based on unit spacing constraints; x min , x max , y min , y max These are the upper and lower boundaries of the xy coordinate axes of the wind farm; Indicates the restricted area; x i , y i ), ( x j , y j These are wind turbine units. i, j The coordinates; d min This is the minimum distance between generator units.

5. The wind farm layout optimization method with restricted area constraints based on the Monarch Butterfly optimization algorithm according to claim 4, characterized in that: In step 3, the improved Monarch Butterfly optimization algorithm is applied to optimize the wind farm layout model considering the restricted area constraints. The constraints consider the wind farm boundary, the restricted area, and the minimum allowable spacing of the wind turbines, and include the following steps: S3.1: Combining the wind farm layout optimization model with the improved Monarch Butterfly algorithm: Imagine the layout of a wind farm as an individual butterfly in a population, and denote it as 2. N t dimensional vector h =[ x 1, x 2, x 3, x 4,…, x 2Nt-1 , x 2Nt ], x 1, x 2, x 3, x 4 represent the individual butterflies in the algorithm. h The magnitude of the positional variables in the 1st, 2nd, 3rd, and 4th dimensions; x 2Nt-1 , x 2Nt Each represents an individual butterfly. h China No. 2 Nt -1, 2 Nt Size of the positional variable; in,( x 2i-1 , x 2i ) indicates that the wind turbine unit T in this individual i coordinates ( x i , y i );use M 2 N t 1-th order matrix H =[ h 1, h 2,…, h M ] indicates a size of M The population, of which: h 1, h 2,, h M Let represent the 1st, 2nd, ..., th elements in population H, respectively. M Individual butterfly; Using the distance constraints between restricted areas and wind turbine units as a penalty, f The problem is transformed into an unconstrained optimization problem and solved by... N t dimensional vector O =[ o 1, o 2,…, o Nt ]and G =[ g 1, g 2,…, g Nt Record information on violations of constraints. o 1, o 2,…, o Nt These represent wind turbine units 1, 2, …, N t Regarding the penalty value for calculating restricted area constraints; g 1, g 2,…, g Nt These represent wind turbine units 1, 2, …, N t Penalty values ​​for calculating spacing constraints of wind turbine units; The unit spacing constraint is to satisfy a minimum permissible unit spacing, as specifically stated below: ； In the formula: ( x i , y i (for wind turbine units) i coordinates, ( x j , y j (for wind turbine units) j coordinates d min The distance between the minimum number of generating units; Among them, when wind turbine T i When the unit spacing constraints are met, g i The fitness function is denoted as 0 if it is positive and 1 otherwise; therefore, the fitness function is expressed as follows: ； This indicates the number of wind turbines in the wind farm. Indicates wind turbine i The penalty value calculated using restricted area constraints. Indicates wind turbine i Penalty value calculated based on unit spacing constraints; S3.2: The initial population is generated randomly, and the fitness of each individual in the population is calculated using the tail flow model and the lookup table method of the restricted area. S3.3: Population H Divided into two groups H 1 and H 2, H 1 in H The proportion in is p Its behavior is migration, and the update method is as follows: ； In the formula, For the first individual n dimension, r 1 is H Random individuals in 1, r 2 is H The random individuals in 2, u The random numbers are uniformly distributed in the interval [0,1]; this method selects different positions from two groups to form new individuals; group r The adaptive behavior of 2 differs from the migration behavior described above, and the specific update method is as follows: ； In the formula, for h best The first in n dimension; u 1. u 2 represents a random number uniformly distributed in the interval [0,1]; Levy represents Levy flight. t This represents the current iteration number; S t The current step size, S t pass S max It is obtained by decreasing it generation by generation using an exponential decay function, and the specific calculation is as follows: ； In the formula, b The attenuation coefficient is... ε The decay coefficient refers to the combination of two populations through their respective behaviors to form a new population. H new At the same time, the location of the wind turbine is checked for boundary violations; if it exceeds the boundary of the wind farm, it stops at the boundary. S3.4: Calculate the new population H new The constraint value, and on H new Individuals that violate constraints will be replaced; if H new medium-sized individuals h m The Middle i The typhoon turbines violated restricted areas or spacing constraints, i.e. ( o m,n + g m,n If )>0, then a single position replacement is performed, and the unit coordinates after replacement are as follows: ； The second element representing individual m i -1 dimension position value, The second element representing individual m i -1 dimension position value, from ( , The coordinates of the individual m are the first... i Coordinates of the typhoon generator unit Indicates in [ x min , x max Randomly generate values ​​within the range. Indicates in [ y min , y max Randomly generate values ​​within the range. x min , x max , y min , y max These are the upper and lower boundaries of the xy coordinate axes of the wind farm; For this individual, based on the fitness comparison after replacement, if... h s Its fitness is better than h m Then it will be replaced. h m If no replacement is made, then select a population. H The three best groups of individuals h b1 , h b2 , h b3 The position of the centroid enclosed by the three groups of individuals is obtained as the new... h m The calculation formula is as follows: ； This operation involves selecting a population. H The three best individuals can be introduced into the population earlier, allowing less fit individuals to be introduced earlier. H By placing superior individuals closer together, the algorithm's search speed can be improved. S3.5: Calculate the new population H new The fitness of all individuals in the population is assessed, and based on feasibility criteria, it is determined whether individuals should be replaced, ultimately completing the population analysis. H Update; S3.6: Convergence judgment, judgment t Has it been achieved? t max If the condition is met, stop iterating and output the result. h best and f best As the optimal layout scheme and fitness, otherwise return to S3.2; through population update and iteration, obtain the optimal individual, which is the optimal layout of wind turbine units that avoids restricted areas.

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