CN116341226A - Multi-objective optimization method for layout and wiring of offshore wind farm in consideration of noise - Google Patents
Multi-objective optimization method for layout and wiring of offshore wind farm in consideration of noise Download PDFInfo
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Abstract
With the expansion of offshore wind farms, most wind turbines do not consider noise. When solving the high-dimensional multi-objective problem of the wind power plant, the traditional optimization algorithm has limited effect. The double-layer high-dimensional multi-objective optimization method is provided, and in the method, the position and the cable topological structure of the wind turbine can be optimized simultaneously, and noise is reduced additionally. The outer layer is expressed as a constrained high-dimensional multi-objective optimization problem to obtain an optimal wind farm layout, wherein the four optimization objectives are annual energy production, electrical energy quality, total investment cost and noise, respectively; then, a plurality of non-dominant sorting genetic algorithms-III under different environments are proposed to optimize the outer layer model. The inner layer is a multi-constraint optimization problem, and the optimization aim is to minimize the cable cost and solve the problem by using a dynamic spanning tree algorithm. Experimental results show that the method not only can consider the long-term economic benefit of the wind farm, but also can reduce noise. The experimental results show that annual energy production increases by about 10105MW and noise is also reduced by 37.94dB.
Description
Technical Field
The invention relates to the technical field of wind farm layout optimization, in particular to a multi-objective optimization method for the layout and wiring of an offshore wind farm, which is more in line with the actual requirements of the offshore wind farm and considers noise.
Background
Since offshore wind energy reserves are more abundant, developing offshore wind power is one of the key technologies to achieve low carbon economy, wake effects are a major factor affecting wind farm productivity, and upstream wind turbines extract energy from the wind resulting in insufficient wind speed behind their swept area, which compromises energy capture by downstream wind turbines; it is therefore important to determine the position of the wind turbines to maximize the power output of the wind farm. In addition, the current collecting system is the core of the offshore wind farm, and the operation efficiency, performance and economic benefit of the offshore wind farm are related to the optimal design relationship of the current collecting system of the wind farm, and the cable connection structure, the transformer station position and the type selection of the cable are close. Even minor improvements in blower arrangements or electrical system topology design can save significant budgets due to the much higher costs of establishing an offshore wind farm. In recent years, students have considered joint optimization between fan micro-addressing and cabling. The prior art provides a fan micro-site selection and two-layer combined optimization method of an electrical system by combining a genetic algorithm and an ant colony algorithm. Still further studies have proposed a two-layer multi-objective optimization framework that first considers power quality, using a third generation non-dominant ordered genetic algorithm (NSGA-iii) and a binary particle swarm optimization algorithm to obtain fan position and cable layout, respectively.
The current research on the problem of optimizing the layout of a wind farm is mostly focused on investment cost and power output, and the environmental influence of the wind farm is paid more and more attention. Noise is no longer a limiting factor but an optimization objective. In recent years, researchers have also considered the interaction between wind farm microscopic site selection and joint optimization of cable layout. However, the amount of output power of a wind farm is typically set as a target to be maximized, but its power quality is rarely considered. The influence of noise of an offshore wind farm on the ecological environment is not negligible, and when considering the economic benefit of the wind farm, it is necessary to reduce the influence of noise on the environment. Although the combined optimization of the micro-addressing and the wiring of the fan has made some important progress at present, a plurality of factors are comprehensively considered in actual construction. Currently, further research is required for joint optimization consideration of microscopic site selection and current collection systems of wind farms. Because of the complexity of wind farm layout optimization problems, it has become a consensus to use heuristic algorithms to solve these problems, where evolutionary algorithms are a good way to solve such problems. Because there are many infeasible areas in the search space of the multi-constraint multi-objective wind farm layout optimization problem, it is often difficult to find a truly viable, uniformly distributed non-poor solution. When the target dimension is increased, the traditional multi-target optimization method is difficult to achieve ideal effect, and the convergence and diversity of the population are difficult to balance
Therefore, in order to overcome the defects in the prior art, the invention provides a multi-objective optimization method for the layout and wiring of the offshore wind farm, which takes noise into consideration.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a high-dimensional multi-objective joint optimization model which meets the actual needs. Annual energy production, electric energy quality, total investment cost and wind farm noise are comprehensively considered, and meanwhile, wind farm micro-site selection and cable design are optimized. According to the high-dimensional multi-objective wind farm layout optimization problem, NSGA-III algorithms (Differential Environments Multiple Populations NSGA-III, DEMP NSGA-III) based on multiple groups under different environments are provided to balance diversity and convergence of the groups, better individuals are reserved, and better fan placement positions can be found.
The method has the advantages that: compared with the traditional combined optimization method for micro-site selection and wiring of the wind turbines of the offshore wind farm, the double-layer optimization method provided by the invention can reduce noise and improve comprehensive economic benefit of the wind farm. Comprises the following specific steps:
step 1: acquiring power of a wind turbine generator in a wind power plant;
step 2: setting a wake flow model of the wind turbine generator;
step 3: calculating the output power of the wind power plant;
step 4: calculating the electric energy quality of the wind power plant;
step 5: calculating the wind turbine generator cost, the cable cost and the transformer cost of the wind power plant;
step 6: calculating noise of the wind farm;
step 7: constructing a double-layer structure optimization model of the wind power plant;
step 8: optimizing the outer layer of the double-layer structure optimization model based on a proposed DEMP NSGA-III algorithm, and optimizing the inner layer of the double-layer structure optimization model based on a Dynamic Minimum Spanning Tree (DMST) algorithm;
drawings
FIG. 1 is a flow diagram of a multi-objective optimization method for noise-considered offshore wind farm placement and routing in accordance with an embodiment of the present invention;
FIG. 2 is a double-layer optimization framework diagram of a wind farm according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a Gaussian wake model in accordance with an embodiment of the invention;
FIG. 4 is a two-layer high-dimensional multi-objective optimization flow chart of an embodiment of the invention;
FIG. 5 is a diagram of a result of a hierarchical optimization model of wind turbine layout and wiring of an offshore wind farm in an embodiment of the invention;
FIG. 6 is a diagram of a layout and wiring double-layer optimization model of a wind turbine generator in an offshore wind farm according to an embodiment of the invention;
FIG. 7 is a diagram of an optimization result of a NSGA-III algorithm for layout and wiring of wind turbines in an offshore wind farm according to an embodiment of the invention;
FIG. 8 is a diagram of the optimization result of an NSGA-III algorithm for improving the layout and wiring of wind turbines in an offshore wind farm according to an embodiment of the invention;
Detailed Description
The present invention will be described in further detail below with reference to the drawings and detailed description for the purpose of better understanding of the technical solution of the present invention to those skilled in the art.
As shown in FIG. 1, the invention provides a double-layer combined multi-objective optimization method for a wind farm, which comprises the following specific steps:
step 1: acquiring power of a wind turbine generator in a wind power plant;
the logistic function with two parameters alpha and beta is used for representing the power curve of the wind turbine, and the method is as follows
Wherein v is in ，v r And v out The cut-in wind speed, the rated wind speed and the cut-out wind speed of the fan are respectively, P wt，r Is the rated power of the fan.
Step 2: setting a wake flow model of the wind turbine generator;
the wind speed of the downstream fans is lower than upstream due to a phenomenon known as wake effect, resulting in a reduction of the total output power of the wind farm. Calculating wind speed v at distance x and radius r from wind turbine generator by using Gaussian wake model x，r 。
Wherein v is 0 For ambient wind speed, A (x) is an undetermined coefficient of x, sigma is wake characteristic width, r r For the radius of the rotor of the wind turbine, C t For fan thrust coefficient, α is the entrainment constant, and the formula is as follows:
wherein z is 0 Indicating the surface roughness length, z h And the hub height of the wind turbine generator is represented.
In this model, the radius of the wake is infinitely extended due to the nature of the exponential function. Thus, with respect to a given wind turbine, all wind turbines located downstream are in the wake, and no wind turbine will be partially in the wake of another wind turbine, regardless of the distance between them.
Step 3: calculating the output power of the wind power plant;
for a given wind direction, the wind farm is rotated to the positive X-axis direction so that the wind direction is consistent, and the coordinates of the wind farm should be converted from the original layout [ X, Y ] to the new layout [ X, Y ] according to the following equation.
When determining the relative distance between wind turbines in the new coordinates, the i-th wind turbine (i= {1,2, …, N) wt ) The received actual wind speed calculation formula is as follows:
wherein b i.j Is a binary variable, 1 when the ith fan is behind the jth fan, or 0, deltav i，j Wake loss for the ith fan caused by the jth fan.
Thus, the total power P of the wind farm total The calculation is as follows:
wherein P is wt (v i ) Representing the output power of the ith wind turbine generator system, N wt Representing the total number of wind turbines in a wind farm, wherein h is the total number of equally-wide intervals with discrete wind directions, and f j (θ) is the frequency of occurrence of the jth wind direction.
Step 4: calculating the electric energy quality of the wind power plant;
the formula for giving the band energy quality of the wind power plant is as follows:
wherein the daily average capacity coefficient mu wf Representing the quantity of output power of wind farm, sigma wf Representing the quality of electrical energy produced by a wind farm during the day, σ wf The smaller the value, the smaller the power fluctuation, and the better the quality of the obtained electric energy.
Step 5: calculating the wind turbine generator cost, the cable cost and the transformer cost of the wind power plant;
total cost C of wind turbine generator system wt From daily investment cost C wt，invest And daily operation maintenance cost C wt，o&m The composition is as follows:
C wt ＝C wt，invest +C wt，o&m (8)
C wt，invest the calculation can be made according to the following formula:
where d is the rate of discount, l wt Is the service life of the fan, c 1 The unit cost of the wind turbine generator is calculated by the following formula:
c 1 ＝α wt +β wt P wt，r (10)
wherein alpha is wt Is the offset constant, beta wt Is the slope constant.
C wt，o&m Obtained from equation (11):
C wt，o&m ＝e wt C wt，invest (11)
wherein e wt And the method is cost-effective for operation and maintenance of the wind turbine generator.
Total cost of cable C cable Is based on the daily investment cost C cb，invest Daily operation maintenance cost C cb，o&m And daily electric energy loss cost C cb，loss Composition, expressed as
C cable ＝C cb，invest +C cb，o&m +C cb，loss (12)
C cb，invest The calculation can be made according to the following formula:
where T is the set of wind turbines and substations, i.e. t= {1,2, …, N wt +1, where 1 represents the substation and the other numbers in T represent windA motor group; w is a set of cable types, i.e. w= {1,2, …, W cb W, where W cb Is the total number of cable types. c 0 Is the cable installation cost; d, d i，j Is the distance between the ith fan and the jth fan; l (L) cb Is the life of the cable, z i，j，l Is a binary decision variable, and represents the connection state and the cable type between two wind turbines. If the ith and jth fans are directly connected to each other using the first cable, z i，j，l Equal to 1, otherwise 0.c p The purchase price of the p-th cable is expressed as follows:
wherein alpha is cb ，β cb And gamma eb Is three cost coefficients of the cable, U cb，r，l And I cd，r，l The rated voltage and current of the type i cable, respectively.
C cb，o&m Obtained by the following formula:
C cb，o&m ＝e cb C cb，in (15)
e cb is cost-effective in operation and maintenance of an electrical power system
C cb，loss The calculation formula is as follows:
I wt，r is the rated current of the fan, c u Is the unit cost of the power-on loss of the cable, R cb，l Is the resistance of the first cable type, p i，j Is the power flow on the cable between the i-th and j-th fans.
Cost C of transformer trans Consists of the following parts of daily investment cost C trans，in Day operation and maintenance costs C trans，o&m The following is shown:
wherein N is trans For the total number of transformers, l trans Is the service life of the transformer c 2 Is the cost of purchasing a transformer c 2 The calculation formula of (2) is as follows:
wherein alpha is trans ，β trans And gamma trans Respectively an offset constant, a slope constant and an index, P trans，r Is the capacity of the transformer.
Step 6: calculating noise of the wind farm;
hubbard et al propose a wind turbine noise model based on an aerodynamic noise model. The model consists of three parts: noise generated when inflow turbulence meets the blade, noise generated when a turbulent boundary layer meets the trailing edge of the blade, and noise caused. By a flow of air separated from the trailing edge of the blade. Since the trailing edge of a modern wind turbine blade is mostly sharp, the noise of the third part is smaller than that of the first two parts and can be ignored. Thus, the first two parts of the Hubbard model are used to evaluate the noise generated by the wind turbines.
Where f is the band center frequency, B is the number of blades,
is the angle between the rotor hub to the predicted dotted line and its perpendicular projection onto the rotor plane. ρ is the air density, C 0.7 Rotor blade chord at 0.7 radius, R is rotor radius, σ 2 Is the average turbulence intensity, U 0.7 Is the blade advancing speed at 0.7 radius, r 0 C is the linear distance from the wheel grain center to the predicted point 0 Is the sound velocity, K a (f) Is the factor of frequency correlationSon, U is free flow velocity, delta is boundary layer thickness, l is spanwise length of the blade segment, S is Stlahaar number, S max ＝0.1，K b Is a constant scale factor, K b =5.5 db, d is the directivity factor, θ is the angle between the source to the predicted dotted line and its projection onto the rotor plane, M is the mach number, M c Is the convection mach number. M is M c ＝0.8M。
The noise observation points are affected by a plurality of noise sources generated by a plurality of wind turbines in the wind power plant, and are not just a wind turbine sound source. Therefore, the noise generated by a single wind turbine and all wind turbines at a single observation point can be respectively determined as follows:
a plurality of noise observation points can be arranged in one wind power plant, and the noise evaluation of the whole wind power plant can be obtained by accumulating the noise of the plurality of noise observation points, wherein the expression is as follows:
step 7: constructing a double-layer structure optimization model of the wind power plant;
the wind farm model can be converted into a two-layer optimization problem. The outer layer model determines the position (x, y) of the wind turbine generator, and the inner layer model is used for designing the cable type and layout. The relationship of the two layers is shown in fig. 2 and can be explained as follows:
the optimized cable topology in the inner layer model is affected by the WT position obtained in the outer layer model; on the other hand, the optimization result of the outer layer model is influenced by the total cost of the cable obtained by the inner layer model; in summary, the results of the outer layer model depend to some extent on the results of the inner model.
In the outer layer model, the decision variable X is the coordinates of the wind turbine, and can be as described in (23):
X＝[x i ，y i ]i＝1，2，...，N wt (23)
the outer layer model is a high-dimensional multi-objective optimization problem, and has four objectives of maximizing annual energy production and electric energy quality of the wind farm and minimizing total investment cost and noise.
Obj1：maxf 1 (X)＝P AEP ＝H*P total (24)
Obj2：minf 2 (X)＝σ quality ＝σ wf (25)
Obj3：minf 3 (X)＝C total ＝C wt +(H/24)*C cabl e+C trans (26)
Obj4：minf 4 (X)＝L noise ＝L farm (27)
Where H is the total hours in a year, x min ，x max ，y min And y max The lower and upper limits of the wind farm planning area are respectively. Consider the area limitations of a wind farm and the layout limitations of wind turbines.
In the inner layer model, Z is used to represent the connection status and cable type between two wind turbines.
Z＝[Z i，j，w ] (29)
i，j＝1，2，...，N wt +1 i≠j w＝1，2，...，W cb
The formula of the inner layer model is as follows:
Obj：g(Z)＝minC cable (30)
consider each cable capacity constraint and the topological connection of the cable.
W＝{1，2，…，W cb }T＝{1，2，…，N wt +1}
Step 8: optimizing the outer layer of the double-layer structure optimization model based on a proposed DEMP NSGA-III algorithm, and optimizing the inner layer of the double-layer structure optimization model based on a Dynamic Minimum Spanning Tree (DMST) algorithm;
(1).DEMP NSGA-III
deb et al propose a Reference Point-based non-dominant sequential evolutionary algorithm (Reference Point-Based Many Objective NSGA-II, NSGA-IIII) to solve the high-dimensional multi-objective problem, which has better convergence and diversity in the face of multiple objectives.
However, considering the complexity of the proposed wind farm model, higher demands are placed on the diversity of solutions and the uniformity of distribution. NSGA-III algorithm is a fixed or single evolutionary mechanism, and a single population is adopted, and when the single population faces the proposed model, the searching capability of the algorithm is insufficient, the single population is easy to converge prematurely, and some better solutions may be missed, which will lead to that pareto solution sets do not necessarily contain the best solutions, and finally the diversity and consistency of the solution sets cannot be guaranteed, and the better solution sets cannot be searched. In the model, the optimized individuals represent the locations of the wind turbines, and the population represents the wind turbine micro-sites. Small changes in wind turbine position will severely affect the output power of the entire wind farm, cable layout, power quality, and the amount of noise produced by the wind farm.
The present invention therefore proposes an improved NSGA-III algorithm, designated DEMPNSGA-IIII. The mixed propagation strategies of different environments are provided, and three environments are classified according to different crossover operators and variation probabilities, namely a severe environment, a stable environment and a high-quality environment. For severe environments, the searching step length is required to be increased because the adaptability value of the population is low; for high quality environments, due to the high fitness of the population, accurate searches are needed to develop better solutions; for stable environments, the search step is medium and exploration and exploitation can be balanced. The three populations are respectively evolved in three different environments, then the populations are exchanged across the environments, high-quality individuals enter a high-quality environment after each round of iteration, and the pareto optimal set is obtained through vigorous competition and continuous variation screening. The improved NSGA-III algorithm can expand the search range, enhance the search capability of the solution, is not easy to fall into local optimum, and can improve the convergence and diversity of the solution set more than the NSGA-IIII algorithm.
The specific steps of the algorithm are as follows:
(2).DMST
peng et al propose a DMST algorithm that optimizes the cabling layout of the offshore wind farm collection system based on a Minimum Spanning Tree (MST) algorithm, in which dynamic changes in cable cost can be taken into account.
Four sets and a matrix are built in the DMST algorithm. Set I: including vertices added to the MST. Set II: not yet added to the vertices of the MST. Set III: including the weights of the branches connecting the vertices in the MST. Set IV: containing the total number of wind turbines connected to each branch in the MST. All weights between two adjacent vertices are contained in the adjacency matrix. The cable cost of the branch in this embodiment is determined by the weight. Then can pass through C cable Updating cost.
According to the positions of the wind turbine generator set and the offshore substation, which are given by the outer layer, an adjacent matrix containing all weights between two adjacent vertexes is calculated first. The cable connection layout will then be formulated as described above. Initially, the offshore substation locations in set II will be selected and the weights of the branches that can be connected to this vertex are determined. If the current of a certain branch (cable) exceeds its operational limit. During the cable selection phase, the cable types and costs will be updated using equations (12) - (16). Thereafter, the top point that may introduce the lowest cost will be selected and removed from set II. This process does not end as long as set II is not empty. Finally, an optimized layout that calculates the minimum cost and its match can be determined. ThenC to be obtained cable To the outer layer.
(3) Solution process
The outer layer model is solved by DEMPNSGA-III, and the inner layer model is solved by DMST.
All candidate combinations are ranked by a non-dominant ranking process to generate a Pareto optimal solution set, as described below.
(a) Finding a candidate combination set x= { X satisfying the constraint in (28) 1 ，X 2 ，X 3 ,...}. Each X is n E X contains WT coordinates (X, y).
(b) For each X n E, X, obtaining the best { Z from the inner layer model by DMST i，j，w }, and represent it as Z n 。
(c) Evaluate each X n E outer layer model of X { P AEP σ quality C total L noise Four targets in }
(d) According to { P AEP σ quality C total L noise X is mapped to Pareto preamble. In the DEMP NSGA-III, a Pareto optimal solution set is generated through a non-dominant ranking method
In the high-dimensional multi-target model proposed by the outer layer, each target { P } AEP σ quality C total L noise There is a trade-off between. If { X } 1 ，Z 1 Is better than { X } 2 ，Z 2 Then we call solution { X } 1 ，Z 1 ) Dominant solution { X 2 ，Z 2 }. { X is only when the following two conditions are satisfied simultaneously 1 ，Z 1 ) Can control { X } 2 ，Z 2 }：1){X 1 ，Z 1 ) Not inferior to { X } in all targets 2 ，Z 2 }；2){X 1 ，Z 1 ) Strictly better than { X over at least one target 2 ，Z 2 }. When none of the objectives can be improved, one solution is called pareto optimal solution ω. All pareto optimal solutions form a pareto optimal solution set
Where each solution ω is considered equally good.
The purpose of the non-dominant ranking is to rank the candidate combination set X and annotate it according to different non-dominant ranks. Given a parameter n m Representing dominant { X n ，Z n The number of solutions to the following steps explain the acquisition
Is a process of (2).
(a) For each solution { X } in X n ，Z n Initializing m n ＝0。
(b) Will { X ] n ，Z n Solution of { X } with all other solutions m ，Z m M, n=1, 2, 3..m.noteq.n. If { X } n ，Z n Is { X } is m ，Z m Is governed by, m n ＝m n +1。
(c) Find all m n Solution of =0. Forming an optimal set of paretos
The detailed solution process of the two-layer model is shown in fig. 4.
A multi-objective optimization method for the layout and wiring of an offshore wind farm, which takes noise into account, will be described in the following with specific embodiments:
1. data source and parameter settings
The area occupied by the offshore wind farm to be optimized is rectangular, and the basic information of the wind farm is shown in table 1. The area is 6km multiplied by 6km square, and is divided into 12 multiplied by 12 grids, the offshore transformer substation is positioned at the center of the grid, and noise observation points are arranged at four corners of a rectangular area. The actual wind speed characteristics of the large gabion wind farm offshore are adopted.
TABLE 1 basic information of WF
The parameters of the wind turbines installed in the wind farm are given in table 2.
TABLE 2 parameters of E-82WT
The parameters of the cables installed in the wind farm are given in table 3.
TABLE 3 parameters of 33kV candidate cables
Tables 4 and 5 give the parameter settings, where p c And p m Is the percentage of crossover and mutation, μ is the mutation rate of NSGA-III.
Table 4. Parameter settings of nsga-III algorithm
TABLE 5 parameter settings for DEMP NSGA-III Algorithm
2. Comparative experiments
Firstly, the invention establishes a double-layer optimization model for the layout and wiring of the offshore wind farm in consideration of noise, and the model is specifically expressed as follows:
1) Outer layer model
In order to maximize annual energy production and electrical energy quality of a wind farm, minimize the total investment cost and noise of the wind farm, the outer layer problem is expressed as follows:
X＝[x i ，y i ]i＝1，2，...，N wt (32)
Obj1：maxf 1 (X)＝P AEP ＝H*P total (33)
Obj2：minf 2 (X)＝σ quality ＝σ wf (34)
Obj3：minf 3 (X)＝C total ＝C wt +(H/24)*C cable +C trans (35)
Obj4：minf 4 (X)＝L noise ＝L farm (36)
the decision variable X is the coordinate of the wind turbine generator, P AEP Is annual energy generation capacity of the wind power plant, and the total power generation amount P per hour of the wind power plant total Multiplying the total hours of one year by H to obtain; sigma (sigma) quality For the electric energy quality sigma of the wind farm wf ；C total By the total cost C of the wind turbine wt Total daily cable cost C cable Multiplying the total number of days of the year by the total cost C of the transformer substation trans Constructing; l (L) noise For wind farm noise L farm ；x min ，x max ，y min And y max Respectively the lower limit and the upper limit of a wind power plant planning area, r r The radius of the wind turbine generator system.
The constraints in the outer layer model consist of two parts;
the boundary of the wind farm planning area and the minimum allowable distance between wind turbines.
Total power P of wind farm total The calculation is as follows:
wherein P is wt (v i ) Representing the output power of the ith wind turbine generator system, N wt Representing the total number of wind turbines in a wind farm, wherein h is the total number of equally-wide intervals with discrete wind directions, and f j (θ) is the frequency of occurrence of the jth wind direction.
The formula of the electric energy quality of the wind power plant is as follows:
wherein the daily average capacity coefficient mu wf Representing the quantity of output power of wind farm, sigma wf Representing the quality of electrical energy produced by a wind farm during the day, σ wf The smaller the value, the smaller the power fluctuation, and the better the quality of the obtained electric energy.
Total cost C of wind turbine generator system wt From daily investment cost C wt，invest And daily operation maintenance cost C wt，o&m The composition is as follows:
C wt ＝C wt，invest +C wt，o&m (40)
C wt，invest the calculation can be made according to the following formula:
where d is the rate of discount, l wt Is the service life of the fan, c 1 The unit cost of the wind turbine generator is calculated by the following formula:
c 1 ＝α wt +β wt P wt，r (42)
wherein alpha is wt Is the offset constant, beta wt Is the slope constant.
C wt，o&m Obtained from equation (43):
C wt，o&m ＝e wt C wt，invest (43)
wherein e wt And the method is cost-effective for operation and maintenance of the wind turbine generator.
Total cost of cable C cable Is based on the daily investment cost C cb，invest Daily operation maintenance cost C cb，o&m And daily electric energy loss cost C cb，loss Composition, expressed as
C cable ＝C cb，invest +C cb，o&m +C cb，loss (44)
C cb，invest The calculation can be made according to the following formula:
where T is the set of wind turbines and substations, i.e. t= {1,2, …, N wt +1, where 1 represents a substation, and the other numbers in T represent wind turbines; w is a set of cable types, i.e. w= {1,2, …, W cb W, where W cb Is the total number of cable types. c 0 Is the cable installation cost; d, d i，j Is the distance between the ith fan and the jth fan; l (L) cb Is the life of the cable, z i，j，l Is a binary decision variable, and represents the connection state and the cable type between two wind turbines. If the ith and jth fans are directly connected to each other using the first cable, z i，j，l Equal to 1, otherwise 0.c p The purchase price of the p-th cable is expressed as follows:
wherein alpha is cb ，β cb And beta cb Is three cost coefficients of the cable, U cb，r，l And I cb，r，l The rated voltage and current of the type i cable, respectively.
C cb，o&m Obtained by the following formula:
C cb，o&m ＝e cb C cb，in (47)
e cb is cost-effective in operation and maintenance of an electrical power system
C cb，loss The calculation formula is as follows:
I wt，r is the rated current of the fan, c u Is the unit cost of the power-on loss of the cable, R cb，l Is of the first cable typeResistance, p i，j Is the power flow on the cable between the i-th and j-th fans.
Cost C of transformer trans Consists of the following parts of daily investment cost C trans，in Day operation and maintenance costs C trans，o&m The following is shown:
wherein N is trans For the total number of transformers, l trans Is the service life of the transformer c 2 Is the cost of purchasing a transformer c 2 The calculation formula of (2) is as follows:
wherein alpha is trans ，β trans And gamma trans Respectively an offset constant, a slope constant and an index, P trans，r Is the capacity of the transformer.
The first two parts of the Hubbard model are used for evaluating noise generated by the wind turbine.
Where f is the band center frequency, B is the number of blades,
is the angle between the rotor hub to the predicted dotted line and its perpendicular projection onto the rotor plane. p is air density, C 0.7 Rotor blade chord at 0.7 radius, R is rotor radius, σ 2 Is the average turbulence intensity, U 0.7 Is the blade advancing speed at 0.7 radius, r 0 C is the linear distance from the wheel grain center to the predicted point 0 Is the sound velocity, K a (f) Is a frequency dependent scaling factor, U is free flow velocity, delta is boundary layer thickness, l is spanwise length of the blade segment, S is Stlahaar number, S max ＝0.1，K b Is a constant scale factor, K b =5.5 db, d is the directivity factor, θ is the angle between the source to the predicted dotted line and its projection onto the rotor plane, M is the mach number, M c Is the convection mach number. M is M c ＝0.8M。/>
The noise observation points are affected by a plurality of noise sources generated by a plurality of wind turbines in the wind power plant, and are not just a wind turbine sound source. Therefore, the noise generated by a single wind turbine and all wind turbines at a single observation point can be respectively determined as follows:
a plurality of noise observation points can be arranged in one wind power plant, and the noise evaluation of the whole wind power plant can be obtained by accumulating the noise of the plurality of noise observation points, wherein the expression is as follows:
2) Inner layer model
Obj：g(Z)＝minC cable (55)
W＝{1，2，…，W cb }T＝{1，2，…，N wt +1}
z i，j，w Is a binary decision variable, and represents the connection state and the cable type between two wind turbines. If the ith and jth wind turbines are directly connected to each other using the first cable, z i，j，w Equal to 1, otherwise 0. Where T is the set of wind turbines and substations, i.e. t= {1,2, …, N wt +1, where 1 represents the substation, which is among THe numbers represent wind turbines; w is a set of cable types, i.e. w= {1,2, …, W cb W, where W cb Is the total number of cable types, p i，j Is the power flow on the cable between the i-th and j-th fans.
The constraints in the inner layer model consist of two parts.
The capacity of each cable in a wind farm limits the topological connections to different cable types.
(a) Comparison of different planning models of wind power plant
Double-layer planning and single-layer planning are studied in the wind farm optimization problem. In this experimental section, we used NSGA-III algorithm and DMST algorithm for optimization.
TABLE 6 optimization results under different optimization models
The layout result of the wind farm optimized by the model 1 is shown in fig. 5; model 2 optimized wind farm layout results are shown in fig. 6. The investment costs of wind turbines and transformers are fixed in the total investment costs, only the different cable layouts will affect the final total investment costs. Thus we list C alone cable Is provided. First, in model 1, the wind turbine layout and wiring are optimized separately. The optimal configuration of wind turbines does not produce the minimum C cable As separating as many wind turbines as possible reduces wake effects while increasing the overall length of the cable. Second, it can be seen that model 2 achieves better annual energy production than model 1, with a 5.3% increase in maximum annual energy production. The overall optimized cable layout cost of model 2 is lower than model 1. In addition, the fluctuation of the power quality is small. Finally, noise optimization hasThe obvious effect is achieved. In model 1, the difference between the maximum and minimum exceeds 100dB, and in model 2, the difference is also close to 70dB. The best optimization result for model 2 is even 10.45dB lower than model 1.
Overall, the results obtained from model 2 are superior to those obtained from model 1 on all four targets. This demonstrates that double-layer joint optimization of wind turbine micro-positioning and routing is necessary and efficient in wind farm planning.
(b) Comparison of different algorithms
In this experiment we used different algorithms to solve the two-layer optimization model proposed by the present invention.
Method 1.Nsga-III algorithm is combined with DMST algorithm.
The optimization method provided by the invention; i.e. the DEMP NSGA-III algorithm is combined with the DMST algorithm.
TABLE 7 optimization results of different optimization algorithms
The layout result of the wind farm optimized by the method 1 is shown in fig. 7; the optimized wind farm layout result of method 2 is shown in fig. 8.
Clearly we can consider that method 1 gives poorer optimization results than method 2. In methods 1 and 2, the DMST algorithm is used to optimize the inner layer model and the NSGA-III algorithm and the DEMP NSGA-III algorithm are used to optimize the outer layer model, respectively. It can be seen that the best results of method 2 are superior to method 1 on every objective, with an annual energy production increase of about 10105MW, a power quality fluctuation reduction of 0.38%, a total cost per day savings of cable of about 209 Euro, and a noise reduction of 37.94dB. Experimental results prove that when the optimization algorithm of the internal model is a DMST algorithm, the optimization effect of the NSGA-III algorithm is not ideal due to the characteristics of the high-dimensional multi-objective model, and the solution of the model can be prevented from falling into a local extremum too early by adopting a mixed propagation strategy under different environments by the DEMP NSGA-III algorithm, and the search range is enlarged to search for a globally optimal solution, so that better fan layout positions meeting a plurality of objective functions can be found under complex constraint. Therefore, the double-layer optimization method provided by the invention is effective, and can simultaneously find better micro-addressing and wiring of the wind turbine generator and reduce noise. The method can provide a new method for constructing the offshore wind farm which is more economical and environment-friendly.
Experiments prove that the double-layer optimization framework provided by the invention is feasible, and the combined optimization of the position and the wiring of the wind turbine is superior to the independent optimization, so that the double-layer optimization framework has more comprehensive economic benefit. The invention provides a double-layer optimization method meeting the actual engineering requirements of an offshore wind farm, and the economic benefit of the wind farm is considered in the optimization target, and the electric energy quality and the noise are also considered. According to the characteristics of the wind farm problem, an improved method for combining an NSGA-III algorithm and a DMST algorithm is provided for solving. When the DEMP NSGA-III algorithm is used for solving the outer layer problem, the mixed propagation strategies in different environments can be used for searching feasible areas more widely, so that diversity and distribution uniformity of the knowledge set are enhanced, convergence and diversity of the knowledge set are improved, and local optimization is not easy to fall into. This may search for a better solution set than the original NSGA-III algorithm, thereby improving the overall economic benefit of wind farm construction. Finally, it is important to incorporate noise into the joint optimization model, which will be beneficial to marine life and the surrounding environment. The combined optimization model provided by the invention can simultaneously consider the economic benefits of wind power plants and environmental protection. It is to be understood that the above embodiments are merely illustrative of the application of the principles of the present invention, but not in limitation thereof. Various modifications and improvements may be made by those skilled in the art without departing from the spirit and substance of the invention, and are also considered to be within the scope of the invention.
Claims (13)
1. The multi-objective optimization method for the layout and the wiring of the offshore wind farm taking noise into consideration is characterized by comprising the following specific steps of:
step 1: acquiring power of a wind turbine generator in a wind power plant;
step 2: setting a wake flow model of the wind turbine generator;
step 3: calculating the output power of the wind power plant;
step 4: calculating the electric energy quality of the wind power plant;
step 5: calculating the wind turbine generator cost, the cable cost and the transformer cost of the wind power plant;
step 6: calculating noise of the wind farm;
step 7: constructing a double-layer structure optimization model of the wind power plant;
step 8: and optimizing the outer layer of the double-layer structure optimization model based on the proposed DEMP NSGA-III algorithm, and optimizing the inner layer of the double-layer structure optimization model based on a Dynamic Minimum Spanning Tree (DMST) algorithm.
2. The method of claim 1, wherein the obtaining the power of the wind turbines in the wind farm comprises:
the logistic function with two parameters alpha and beta is used for representing the power curve of the wind turbine, and the method is as follows:
wherein v is in ,v r And v out The cut-in wind speed, the rated wind speed and the cut-out wind speed of the fan are respectively, P wt，r Is the rated power of the fan.
3. The method according to claim 1, wherein the setting of the wake model of the wind turbine generator is performed according to the following relation:
wherein v is 0 For ambient wind speed, A (x) is an undetermined coefficient of x, sigma is wake characteristic width, r r For the radius of the rotor of the wind turbine, C t For fan thrust coefficient, α is the entrainment constant, and the formula is as follows:
wherein z is 0 Indicating the surface roughness length, z h And the hub height of the wind turbine generator is represented.
4. The method of claim 1, wherein the calculating the output power of the wind farm is represented as follows:
wherein P is wt (v i ) Representing the output power of the ith wind turbine generator system, N wt Representing the total number of wind turbines in a wind farm, wherein h is the total number of equally-wide intervals with discrete wind directions, and f j (θ) is the frequency of occurrence of the jth wind direction.
5. The method according to claim 1, wherein the calculating the power quality of the wind farm is specifically related as follows:
wherein the daily average capacity coefficient mu wf Representing the quantity of output power of wind farm, sigma wf Representing the quality of electrical energy produced by a wind farm during the day, σ wf The smaller the value, the smaller the power fluctuation, and the better the quality of the obtained electric energy.
6. The method according to claim 1, wherein the calculating of wind turbine costs, cable costs and transformer costs of the wind farm is specifically as follows:
C wt ＝C wt，invest +C wt，o&m
C cable ＝C cb，invest +C cb，o&m +C cb，loss
C trans ＝C trnns，in +C trans，o&m
wherein the total cost C of the wind turbine generator system wt From daily investment cost C wt，invest And daily operation maintenance cost C wt，o&m Composition; total cost of cable C cable Is based on the daily investment cost C cb，invest Daily operation maintenance cost C cb，o&m And daily electric energy loss cost C cb，loss Composition; cost C of transformer trans Cost of daily investment C trans，in Day operation and maintenance costs C trans，o&m Composition is prepared.
7. The method according to claim 1, characterized in that said calculating the noise of said wind farm is in particular as follows:
wherein L is j For a single wind turbine generator set,
noise generated by all wind turbines at single observation point, L farm Is a noise evaluation value of the whole wind power plant.
8. The method according to any one of claims 1 to 7, wherein said constructing a bilayer structure optimization model of the wind farm comprises:
setting an outer layer model to maximize annual energy production and electric energy quality of the wind farm and minimize total investment cost and noise of the wind farm;
and setting an inner layer model to plan the cable layout of the wind power plant and optimize the cable cost.
9. The method of claim 8, wherein the outer layer model expression is as follows:
X＝[x i ，y i ] i＝1，2，...，N wt
Obj1：maxf 1 (X)＝P AEP ＝H*P total
Obj2：minf 2 (X)＝σ quality ＝σ wf
Obj3：minf 3 (X)＝C total ＝C wt +(H/24)*C cable +C trans
Obj4：minf 4 (X)＝L noise ＝L farm
the decision variable X is the coordinates of the wind turbine, where H is the total hours in a year, X min ，x max ，y min And y max Respectively the lower limit and the upper limit of a wind power plant planning area, r r The radius of the wind turbine generator system.
10. The method according to claim 9, characterized in that the constraints in the outer layer model consist of two parts, in particular comprising:
the boundary of the wind farm planning area and the minimum allowable distance between wind turbines.
11. The method of claim 8, wherein the interior model expression is as follows:
Obj：g(Z)＝minC cable
W＝{1，2，…，W cb }T＝{1，2，…，N wt +1}
z i,j，w the system is a binary decision variable, and represents the connection state and the cable type between two wind turbines; if the ith and jth wind turbines are directly connected to each other using the first cable, z i,j，w Equal to 1, otherwise 0; where T is the set of wind turbines and substations, i.e. t= {1,2, …, N wt +1, where 1 represents a substation, and the other numbers in T represent wind turbines; w is a set of cable types, i.e. w= {1,2, …, W cb W, where W cb Is the total number of cable types, p i，j Is the power flow on the cable between the i-th and j-th fans.
12. The method according to claim 11, wherein the constraints in the inner layer model consist of two parts, in particular comprising: the capacity of each cable in a wind farm limits the topological connections to different cable types.
13. The method according to any one of claims 1 to 7, wherein the optimizing the outer layer of the two-layer structure optimization model based on the proposed DEMP NSGA-III algorithm, optimizing the inner layer of the two-layer structure optimization model based on a Dynamic Minimum Spanning Tree (DMST) algorithm, comprises:
three populations of DEMP NSGA-III are randomly generated;
initializing a severe environment, a stable environment and a high-quality environment based on NSGA-III of various groups under different environments;
setting the iteration times t=1;
calculating daily electricity production quantity, electric energy quality, total daily cost and wind power plant noise of the wind power plant;
DMST solves the inner layer model, and obtains cable layout and cable cost to the outer layer model;
evaluating an objective function in the outer layer model;
performing a non-dominant solution ordering process in each environment to generate pareto optimal solutions;
performing selection, crossover and mutation processes in different environments to update the population across the environments;
the individuals in each environment are subject to non-dominant ordering and individual exchange;
t reaches the maximum iteration times, if so, a final result is obtained, and if not, iteration optimization is continued.
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