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Offshore wind farm layout optimization regarding wake effects and electrical losses
Engineering Applications of Artificial Intelligence 60 (2017) 26–34
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Engineering Applications of Artificial Intelligence journal homepage: www.elsevier.com/locate/engappai
Offshore wind farm layout optimization regarding wake effects and electrical losses Luís Amarala, Rui Castrob, a b
MARK
⁎
Instituto Superior Técnico, University of Lisbon, Lisbon, Portugal INESC-ID/IST, University of Lisbon, Lisbon, Portugal
A R T I C L E I N F O
A BS T RAC T
Keywords: Offshore wind energy Electrical losses Wake effect Genetic Algorithm Particle Swarm Optimization
A major development of the offshore wind energy market is being witnessed. Since the implicated costs are considerably high, it is extremely important to ensure that the energy production is maximum, so that the costs per energy unit are minimized. Thus, the turbines should be strategically positioned to extract as much energy as possible from the wind, considering wake effect losses, as well as internal grid electrical losses. In order to avoid turbines to be placed in unrealistic positions, they should be distributed according to a grid of rectangular shaped cells; each of these is divided in multiple sub-cells. The problem of finding the turbines optimal position among the pre-defined sub-cells so that maximum annual energy is produced could be addressed using a deterministic approach. However, the problem becomes unfeasible when the number of turbines and/or the number of sub-cells increase. To overcome this difficulty, optimization techniques should be used. Genetic Algorithm and Particle Swarm Optimization are approached in this paper. This paper deals with the wind park layout optimization problem. A methodology to position the turbines inside a wind park so that the annual energy production is maximum is proposed. The results proved that the meta-heuristic method is much more CPU time efficient in providing the maximum annual year production as compared to the traditional deterministic approach.
1. Introduction Over the past years there has been a significant development of alternative energies and the global market for wind power has been expanding faster than any other renewable energy source (Bilgili et al., 2011). As the best onshore locations are already occupied, a trend towards offshore wind applications is currently being witnessed. Indeed, going offshore can tackle some disadvantages of the onshore wind energy development, such as: availability of large continuous areas, suitable for major projects; elimination of the issues of visual impact and noise, allowing the utilization of larger turbines (Henderson et al., 2003); stronger and less turbulent wind, increasing the energy produced (Appiott et al., 2014) and decreasing the fatigue loads on the turbine (Qiu et al., 2014); higher air density resulting in higher wind power output. On the other side, offshore wind power shows higher installation costs and a significant increase in operating and maintenance costs. Offshore wind farms may represent an important source of renewable energy in the future. If we look back to the past 10 years, the annual offshore wind power installed in Europe increased from about
⁎
90–1500 MW. In 2014, the total installed capacity from offshore wind farms in Europe was 8.045 GW of which 74% where installed since 2009 (Corbetta et al., 2015). Some of the previously mentioned disadvantages related to the development of wind energy offshore, namely the increase of investment costs and accessibility, can be softened if the annual energy production (AEP) is highly enough to reduce the overall levelized cost of energy (LCOE). To achieve this purpose, new techniques and designs should be introduced. Wind Farm Layout Optimization Problem (WFLOP) is an example of such research, since by optimizing the Wind Turbine Generators (WTGs) disposal, losses may be reduced and the energy production increased, thus reducing the LCOE. To optimize the turbines disposal, the assumption that they are initially placed according to a traditional layout with an offset is normally considered. A grid with cells where WTGs may be positioned is supposed and, to approach the micro-sitting positioning, it is assumed that each cell is divided into multiple sub-cells allowing the turbine position not to be restricted to the centre of the main cell. The WFLOP aiming to maximize the AEP may be solved by a deterministic approach that runs every possible combinations of
Corresponding author. E-mail address: [email protected] (R. Castro).
http://dx.doi.org/10.1016/j.engappai.2017.01.010 Received 17 February 2016; Received in revised form 24 November 2016; Accepted 12 January 2017 0952-1976/ © 2017 Elsevier Ltd. All rights reserved.
Engineering Applications of Artificial Intelligence 60 (2017) 26–34
L. Amaral, R. Castro
position. Rodrigues et al. (2015) proposed an optimization technique based on covariance matrix adaptation where the turbines move according to the wind direction in order to minimize the wake effect. In this paper, the WFLOP is assessed by determining the optimal position of the WTGs inside a wind farm. The objective function that is to be optimized (maximized, in this case) is the AEP, by minimizing both the wake losses and the electrical losses inside the wind farm internal grid. Losses minimization, namely those associated with wake effect and Joule losses in the internal collection system, is not trivial, as the former decrease with the separation distance of the wind turbines while the latter increase with the separation distance. The assessed optimization techniques are GA and PSO, these two being used to validate the developed algorithms in a test wind farm; following the conclusion that GA is more effective, meaning that it finds a good result approximation more often, this technique was used to determine the optimal position (maximum AEP) of the WTGs inside a realistic wind farm. Other optimization criteria could be used, for instance, to minimize the production cost of electricity produced. In this case, data concerning the investment and operation and maintenance costs should be considered, which is outside the scope of this paper. The paper is organized as follows. In Section 2, the wake model implemented is presented and the reasons for using it are discussed. In Section 3, items concerning energy conversion and power flow analysis are tackled. Also, in that Section, the internal grid electrical losses model and how they are computed is introduced. The optimization algorithms developed for the WFLOP are exposed and validated in Section 4. In Section 5, the results obtained for a wind farm application case-study are presented and discussed. Lastly, the main conclusions of this research are drawn.
turbines layout and chooses the one that leads to the maximum AEP. Happens that, the micro-sitting approach considered is a highly complex problem, e.g. for a wind park with 80 turbines and cells divided in 9 sub-cells there are more than 2.185×1076 possible combinations, resulting in decades of simulation time. To overcome this issue, optimization techniques, such as, Genetic Algorithm (GA) and Particle Swarm Optimization (PSO), are applied in order to reduce the computation time. The algorithms calculate the AEP considering the turbines characteristics, wake losses, electrical losses and wind site conditions. Most of the optimization techniques applied to the WFLOP found in literature are based on evolutionary algorithms (EAs). In 1994, Mosetti et al. (1994) and later, in 2005, Grady et al. (2005) optimized the wind turbines position throughout the use of a GA. The main goal of this study was to minimize the total cost (the cost function assumed was very simple and only depended on the number of turbines and the energy produced) of the wind farm by maximizing the energy produced. The study presented in (Grady et al., 2005) is an improvement to the one proposed in (Mosetti et al., 1994). Since 2005, many studies about the best wind turbines positioning have been made (e.g. Mora et al. (2007) and Kusiak and Song (2010)) but, more recently, in 2009, Sisbot et al. (2010) implemented a multiobjective GA to optimize the placement of wind turbines by maximizing the power production capacity, while constraining the budget of installed turbines. Although the algorithm presented good results, the main issue of the study was that the authors considered a single wind scenario. In 2010, Wan et al. (2010) proposed a PSO based on Gaussian mutation algorithm. The algorithm proved to be more accurate than the standard PSO and with a computation time substantially reduced. It was considered a standard PSO but, if the algorithm does not improve for a predefined number of iterations, each particle suffers a mutation that improves its position. The method results are more reliable once they have a lower standard deviation than the traditional PSO. With the development of offshore wind energy, other design optimization approaches are being witnessed. Besides the WTG positioning (e.g. Wu et al. (2014) and Hou et al. (2015)), researchers have studied both the internal connections and transport systems (e.g. Wu et al. (2014), Zhao et al. (2009) and González-Longatt et al. (2012)), as going offshore, these two components gain relevance compared with onshore installation costs and electrical losses. Zhao et al. (2009) use a GA with many variables, as such the cross sections of the various cables, offshore substation rated power and the different systems rated voltages. On the other hand, González-Longatt et al. (2012) focus their study on the optimization of the internal connections by using a modified GA. The study showed that if the proposed method is applied, then a reduction of about 11% of the total cable length compared with a traditional manual design can be achieved. More recently Wu et al. (2014) and Hou et al. (2015), in 2014 and 2015 respectively, considered not only the wake losses but also the energy loss in the electrical system. Hou et al. (2015) used a standard PSO with inertia weight and considered two approaches: constant distance between turbines from different rows and a sparse layout. Wu et al. (2014) apply two optimization algorithms; first, GA is used to find the turbines optimal position and once they are defined, the Ant Colony System (ACS) is applied to study the optimal internal network system, considering the connections between turbines and substation and submarine cables characteristics. The main issue of the proposed ACS it that the connections are made directly simply regarding the distance between turbines/substation. A more realistic procedure would have to take under consideration the philosophy of not crossing cables. Although the concept is in a primary stage, some characteristics of floating turbines are already being considered as advantages, such as the fact that a floating turbine does not have to stay always in the same
2. Wake effect Wind turbines extract energy from the wind, therefore the downstream wind must have less energy content than the upstream. Wake effect is a consequence of the wind impact on turbine's blades where the wind becomes slower and more turbulent, resulting on a wake behind the wind turbine. As the wind flow proceeds further downstream this wake will begin to spread and gradually return to surrounding wind characteristics. In a wind farm where there are multiple wind turbines, it is most likely that the swept area of a turbine is influenced by one or more upstream turbines. This event is called shadowing effect. Slower and turbulent wind means less energy available, but turbulence has another prejudicial factor, it increases fatigue damage, lowering turbine's reliability (Qiu et al., 2014). Both of these consequences contribute to decrease the energy produced by a WTG resulting in less energy produced by the wind farm. Nowadays, there are many available models to study the wake diameter and the wind speed variations over the distance (e.g. Jensen model (Jensen, 1983), Frandsen model (Frandsen et al., 2006) and EWTS-II model (Dekker and Pierik, 1998)). Some of these models are simpler and, consequently, with lower precision, but they present faster computation times. N.O. Jensen proposed his model in 1983 (Otto Jensen, 1983) and it was further developed in 1986 by Katic et al. (1986). It assumes that the initial wake diameter is the same as the turbine diameter and it will expand linearly as a function of downwind distance. Similar to wake diameter, downstream wind deficit decays linearly with the turbine distance. On one hand, the main advantage of Jensen model is that it is much more computational efficient than other complex but more precise models. As so, it is useful to provide a quick insight to eliminate some options before going into a more detailed and time heavily model; for that reason, it is used in many publications about WFLOP. On the disadvantages side, because it is a simple model, it does not take into account factors such as wind turbulence. 27
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L. Amaral, R. Castro
where Aturb = πrr2 and (zw is hub height of the turbine that causes the wake and dhorz is perpendicular to x axis and it is the horizontal distance between the two turbines):
2.1. Single wake effect In this paper, Jensen model further improved in 1994, Mosetti et al. (1994) was used. This model consists of a linear expansion of the wake diameter and a linear decay of the velocity deficit inside the wake. This wake analysis supposes that the momentum is conserved inside the wake neglecting the near field behind the upstream turbine. After performing a momentum balance and using Betz theory to determine the wind speed immediately behind the rotor, the wind speed downstream of the turbine is:
2a vd = ⎛x⎞ 1 + α⎜ r ⎟ ⎝ 1⎠
⎛ r2 + d2 − r2 ⎞ ⎛ r2 + d2 − r2 ⎞ 1 r ⎟⎟rr2 + arccos⎜⎜ 1 ⎟⎟r12 Ashadow = arccos⎜⎜ r 2r2d 2r1d ⎝ ⎠ ⎝ ⎠ 2 2 2 ⎡ ⎤ ⎛r + d − r ⎞ 1 ⎥ ⎟⎟ rrd − sin⎢arccos⎜⎜ r ⎢⎣ 2rrd ⎝ ⎠⎥⎦
d=
1−
1 − CT 2
(1)
; α=
1 1−a and r1 = rr ⎛z⎞ 1 − 2a 2 ln⎜ z ⎟ ⎝ 0⎠
(2)
u = u 0(1 − vd )Aratio
In these equations, it is: vd is the velocity deficit at distance x, a is the axial induction factor, CT is the thrust coefficient determined by the turbine manufacturer, r1 is the wake radius, rr is the turbine's rotor radius, z is the hub height and z0 is the surface roughness length, its value depending on the sea water characteristics. The roughness length value for water surface is usually taken as 0.0002 m. Finally, the wind velocity, u, in the shadow of the turbine is given by:
u = u 0(1 − vd )
(7)
2.2. Multiple wake effect In a wind farm where there are many turbines installed it is likely that wakes can intersect and affect turbines downwind at the same time (Samorani, 2013). This problem can be solved by assuming the kinetic energy deficit of a mixed wake to be equal to the sum of the energy deficits for each wake at the calculated downwind position (Katic et al., 1986). Therefore, the following equations can be obtained by generalization:
(3)
where u0 is the upstream wind speed. The wake area is also known as shadowed area, hence a turbine that is aerodynamically affected by another is said to be under the shadow area of an upstream turbine. To go further in the wake model precision, it must be taken into account that the wake effect may not be total, i.e. the downstream turbine may be only partially affected by the upstream one, resulting on a lower velocity deficit. Fig. 1 represents a partial shadowing where the white circle represents the affected turbine swept area and the grey circle represents the wake area. The real distance between turbines is not relevant for the case. The fraction of area that is affected by the wake is:
Aratio =
(6)
If Ashadow is not a real number, for instance, if the argument of arccos function is greater than 1 or less than −1, it means that either there is no wake effect or the turbine is completely shadowed. If rr + r1 < d there is no wake effect and Aratio=0, if rr+r1≥ d the wake is total and Aratio=1. Finally, the wind velocity of a turbine that suffers a single aerodynamic effect is:
with:
a=
2 z − zw 2 + dhorz
(5)
vdij =
2a ⎛ xij ⎞ 1 + α ⎜ r (x ) ⎟ ⎝ 1 ij ⎠
vdef (j ) =
∑
(8)
[vdijAratio (i , j )]2
i ∈ upwind
u(j ) = u 0(1 − vdef (j ))
(9) (10)
where vdef (j) is the total velocity deficit at turbine j and vdij is the velocity deficit caused by turbine i in turbine j. 2.3. Wind direction variation
Ashadow Aturb
(4) Modern wind generators are equipped with a yaw system drive that allows turbine blades to face the wind in order to maximize the energy extracted. Therefore, a deficit analysis must be made for each possible wind direction. 3. Electrical system model Wind parks electrical connections are responsible for collecting the energy from WTGs and transporting it to shore. As any electrical system, it has losses that have impact on the energy delivered to the main grid. Two distinct electrical systems are considered: the internal grid network that is responsible for collecting the power from WTGs and delivering it to the substation; the transmission system that transfers the energy from the substation to shore. The latter was not considered once it does not influence the wind farm layout output. 3.1. Turbine power curve Turbines are designed to work within a certain range of wind speeds, known as the cut-in, u0, and cut-out, umax, wind speeds. For wind velocities lower than u0 the operation costs are too high for what
Fig. 1. Example of a partial shadowing.
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assumption, since the WTGs power electronics interface is able to regulate the power factor. Each branch (array cables) described by its length, its longitudinal impedance and shunt capacitance per length unit and its rated power. The power flow is described by a complex non-linear equation system given by:
the turbine yields, as so the WTG is disconnected. When wind speeds are higher than umax, the generator is shut down so as to avoid damaging the equipment. Between rated wind speed, uR, and cut-out wind speed, the wind turbine is regulated to operate at rated power, PR. The power curve, i.e. the electrical power output as a function of the wind speed, can be analytically represented using a sigmoid function:
⎧ 0 u < u0 ⎪ P R u 0 ≤ u < uR ⎪ c1− u Pg(u ) = ⎨ 1 + e c2 ⎪ P uR ≤ u < umax R ⎪ u > umax ⎩ 0
⎡⎛ S ⎞*⎤ ⎢⎜ ⎟ ⎥ = [Y][V] ⎢⎣⎝ V ⎠ ⎥⎦
(12)
where the first member is the injected currents vector (S being the injected complex power), Y is the nodal admittances matrix and V is the complex voltage vector. When the iterative process converges, all the voltages and the injected complex power in the slack bus are known. Once the complex voltages in each bus are established, it is possible to calculate the branch losses. Cables are represented by the equivalent π-model. First of all, the current in each cable is computed from the voltages at the sending and receiving buses and from the electrical parameters of the cable (resistance, reactance and capacitance). Then, the total Joule losses are calculated through (B is the number of cables and In is the current in each cable):
(11)
where c1 and c2 are constants that need to be determined, in order that the sigmoid function fits as good as possible when compared with real samples supplied by the manufacturer. It should be noted that the wind speed considered in (11) is the wind speed that passes through the turbine, i.e. after being affected by the deficit introduced by the wake model. 3.2. Collection system design Most of offshore wind farms are connected in a string arrangement, i.e. each row of turbines is series connected between them and then to the substation. For internal connections, a medium voltage submarine grid between 25 kV and 40 kV is typically buried 1–2 m deep in the seabed (Henderson et al., 2003). A group of independent turbines is called a cluster. In this paper, a string configuration with redundancy for the internal grid is considered. Redundancy is achieved because, for instance, in case of a failure in any cable connecting two turbines, an alternative path to drain the energy is provided (Fig. 2). Some authors (e.g. Appiott et al. (2014)) state that clusters with redundancy, in spite of having higher internal grid electrical losses, may be an advantageous option, once they increment reliability.
B
Plosses =
∑ 3RIn2
(13)
n =1
3.4. Annual energy production (AEP) The power generated by WTGs depends both on wind speed and direction and the electrical losses depend on the generated power. So, for a certain sample of wind speed and direction, we will have a certain average power and power losses. Let us consider a wind farm with T WTGs and that we have W wind samples, in one year. The AEP of the wind park is therefore:
AEP =
3.3. Power flow and electrical losses To determine the electrical losses in the collection system, the power flow for the entire wind farm internal network must be solved. For that, MATPOWER software is used (Zimmerman et al., 2011). MATPOWER is a package of Matlab M-files for solving power flow problems. There must be a generator representing the onshore grid and the transmission system with the purpose of balancing the power flow and a transformer representing the substation transformer. In all buses the injected active and reactive power are specified (PQ bus) except for one special bus called the slack bus. At this bus, the voltage magnitude is fixed in 1 pu and an angle of 0°. The generated active power from WTGs is the active power that the particular WTG addressed is producing in a specific moment, depending on the wind speed and direction. Moreover, a unity power factor was assumed, meaning that the injected reactive power by each WTG is zero. This is a valid
8760 W
W
⎛
T
⎞
⎝ t =1
⎠
∑ ⎜⎜∑ (Pgt (uw )) − Plosses(uw )⎟⎟ w =1
(14)
4. Wind farm layout optimization 4.1. Traditional layout In most cases, the layout of an offshore wind park can be represented by a grid or a group of smaller grids attached to each other (e.g. Kentish Flats, Barrow and London Array wind parks in United Kingdom). This imaginary grid is composed by rectangular cells that may or may not have a turbine as represented in Fig. 3. Initially, in case it exists, the turbine is placed in the centre of the cell. The first optimization approach aims to determine the optimal distance between lines and rows of turbines, i.e. what the best distance in the prevailing wind direction and in the crosswind direction is. According to Hou et al. (2015), the first should be between 8D and 12D while the second is expected to be from 3D to 5D (D is the rotor diameter of the concerned turbine). To avoid wake losses, an offset perpendicular to prevailing wind direction should be applied to the grid from the start (Wu et al., 2014) as shown in Fig. 3. 4.2. Micro-sitting approach Going further in the WFLOP, each turbine position cannot be restricted to the centre of a cell, turbines must be placed in a more accurate manner. In past years, some authors stated that a grid similar to the one presented before should be created and that the optimization
Fig. 2. String cluster with redundancy configuration.
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L. Amaral, R. Castro
Fig. 3. Grid traditional turbine disposal with offset layout.
Fig. 5. Implemented GA flowchart.
4.3.1. Genetic algorithm GAs are Evolutionary Algorithms (EAs) and were designed to mimic the natural selection of species and the reproduction of the best fitted individuals from a population. They consist of a population transformed by three genetic operators: selection, crossover and mutation (Sisbot et al., 2010). The GA flowchart is depicted in Fig. 5. In each generation, individuals are ordered according their fitness and then the best fitted is selected to integrate the next population. A percentage of the remaining individuals will be selected for the breeding process and the others are discarded. A high crossover percentage is considered because crossover operation is the main responsible for the “local evolution” of the population. After the selection process is complete, the breeding individuals will cross genetic information between them. A scattered crossover (Sisbot et al., 2010) with 50% from each parent is applied, i.e. each child receives half of its genes from one parent and the other half from another. Scattered crossover operation is displayed in Fig. 6. According to Safari et al. (2010), a Darwinian interpretation on selection for crossover generates positive results, i.e. the most fitted individuals are more likely to transmit genetic information. In this paper, a slightly different approach was taken: probabilities are neglected and it is assured that the most fitted individual (after the elite one) will mate with all the other individuals, generating one offspring in each operation. The selection and crossover operations are represented in Fig. 7. A mutation is a simple modification in the genetic code, when a mutation occurs, only one gene is changed. Before the next generation is ready, it is submitted to the mutation operation. Mutation may or may not occur, its occurrence probability is called mutation probability, and it should be kept low (Mora et al., 2007), since a high value would make the algorithm tend to a random search (Mosetti et al., 1994). Nevertheless, mutation operation is substantial as it allows the creation of individuals which are different from the individuals in the previous population (Mora et al., 2007) thus introducing new zones of possible good solutions and preventing the algorithm to fall into a local optimum value (Wu et al., 2014). In the WFLOP, layouts represent individuals, genes represent turbines position and a mutated gene represents a turbine changing position.
Fig. 4. Example of a grid with cells divided into 9 sub-cells.
algorithm should be able to arrange the grid placing a predefined number of wind generators inside the cells which, theoretically, can perform good results (e.g. Sisbot et al. (2010), Pérez et al. (2013) and Emami and Noghreh (2010)). In reality, it is not convenient that an offshore wind park has turbines displaced in cells with no pre-defined guidelines (for several reasons, such as more expensive cable laying, expensive installation and maintenance and operation costs, for example). Therefore, this paper proposes that each turbine should be contained in a relatively large cell divided into multiple sub-cells. Then, the wind generator is to be placed in the centre of one of the sub-cells. This will make possible to achieve optimum results while maintaining the traditional disposal with its inherent installation advantages. Fig. 4 exemplifies this procedure.
4.3. Optimization algorithms Optimization algorithms can be divided in two categories: deterministic and probabilistic (Valverde et al., 2013). The former will search for every possible solutions and select the optimal one, while the latter is an iterative method that only computes a small number of solutions in each iteration, but trends to a maximum or a minimum with time. Once the WFLOP includes several design variables, the deterministic algorithm becomes unfeasible due to higher CPU times needed to search all possible solutions. The complexity and consequent CPU time of probabilistic algorithms are also dependent of the number of variables but they can perform significant better CPU times presenting results very close (or identical) to the deterministic value. The probabilistic optimization algorithms considered and implemented in this paper are Genetic Algorithm (GA) and Particle Swarm Optimization (PSO).
4.3.2. Particle Swarm Optimization Particle Swarm Optimization (PSO) was inspired in some of these species behaviour such as fish schooling and bird flocking (Hou et al., 2015). The algorithms consist in randomly displaying particles inside a 30
Engineering Applications of Artificial Intelligence 60 (2017) 26–34
L. Amaral, R. Castro
Fig. 6. Scattered crossover for a general case with a genome length of N (in the WFLOP, for a wind park with N turbines).
Fig. 7. Selection and crossover operations scheme for implemented GA considering a population with 6 individuals.
hyperspace (possible solutions) and then assigning them velocities. Once it is an iterative process, in every iteration each particle adjusts its “flying” according to its own flying experience (self-awareness) and its companions’ (swarm) flying experience (social awareness). The PSO implemented in this study is an improved version proposed by Clerc and Kennedy (2002). As stated in Dor et al. (2012), particles move are influenced by three components: (i) physical component: the particle tends to keep its current direction of displacement (also known as inertia); (ii) cognitive component: the particle tends to move towards the best site that it has explored until now; (iii) social component: the particle tends to rely on the experience of its congeners, then moves towards the best site already explored by its neighbours. Let the best known position of each particle i be pBesti (personal best) and the best known position of all particles be the gBest (global best). Each particle's velocity and position in the next iteration is given by (15) and (16), respectively.
vik +1 = Ψ [Cphy + ψ1rand 1Ccog + ψ2 rand 2Csoc]
(15)
xik +1 = xik + vik +1
(16)
Fig. 8. Implemented PSO flowchart.
Cognitive and social components are responsible for intensification, i.e. they explore known”regions”, whereas the physical component is responsible for diversification, once it forces the particle to search new ”regions”. Ψ is the constriction factor and is given by:
2 − (ψ1 + ψ2 ) −
(ψ1 + ψ2 )2 − 4(ψ1 + ψ2 )
(18)
The implemented PSO flowchart is displayed in Fig. 8. Initially particles are disposed randomly and given random velocities. In every iteration, each particle pBest is evaluated. If the current particle position fits better than the its pBest, this value is replaced for the current position. A similar logic is applied to gBest. After every particles pBest is evaluated, the algorithm checks if any of them is better fitted than the gBest value and updates it if necessary. When the swarm obeys to a pre-defined criterion, the algorithm stops. Due to randomness, sometimes the algorithm computes positions and velocities that throw particles out from the search space. To avoid that, a technique adopted in (Pookpunt and Ongsakul, 2013) is applied here, positions and velocities are restrained in a range [pmin,pmax] and [vmin,vmax], respectively.
where Cphy is the physical component, Ccog is the cognitive component and Csoc is the social component, given by:
Cphy = vik Ccog = (pBestik − xik ) Csoc = (gBest k − xik )
2
Ψ=
(17) 31
Engineering Applications of Artificial Intelligence 60 (2017) 26–34
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Table 2 Genetic algorithm statistics of the 100 runs. GA parameters
GA statistics
Population size Crossover percentage Mutation probability
20 80% 10%
AEP best result AEP worst result AEP average result Standard deviation Deterministic layout matches Average n° of iterations Total CPU time
58.107 GWh 58.034 GWh 58.091 GWh 0.023 GWh 54/100 44.050 2.053 h
Table 3 Particle Swarm Optimization statistics of the 100 runs. PSO parameters
PSO statistics
Population size Cognitive learning factor Social learning factor
Fig. 9. Optimal layout as determined by the deterministic algorithm; 4 sub-cells (light blue lines inside the rectangles) and 8 WTGs (solid dark points). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
20 2.5 1.6
AEP best result AEP worst result AEP average result Standard deviation Deterministic layout matches Average n° of iterations Total CPU time
58.107 GWh 57.894 GWh 58.056 GWh 0.052 GWh 12/100 37.870 1.765 h
5. Results and discussion study are from the last year of measurements (2012), as so 2920 samples were picked up. The average wind speed for that year was 7.0804 m/s. The Weibull shape and scale parameters were estimated as k=1.6898 and c=7.9265 m/s. In the case study, only GA optimization technique was considered. For the same wind farm specifications and wind samples, different number of sub-cells are considered and the results are displayed. Table 4 displays the obtained AEP as a function of the considered number of sub-cells and in Fig. 10 the layouts for 0, 4, 9 and 16 subcells are presented. It can be seen that the optimal layout is the one corresponding to 25 sub-cells, as so it is presented in a separate figure (Fig. 11). One may consider the base case as the one with 0 sub-cells, the WTGs being positioned in the centre of the cells in this layout. From Table 4, it can be concluded that the optimal positioning in the 25 subcells layout leads to an increase of 1.24% of the AEP, with respect to the base case. The influence of the number of sub-cells is apparent, the higher the number of sub-cells is, the higher AEP obtained. On the other hand, the AEP incremental increase reduces with the number of sub-cells. This means that, at some point, extend the problem complexity (i.e. adding more sub-cells) will not pay the results obtained, because the AEP will not increase significantly. Finally, it is important to state that neither the layout that targets less electrical losses, nor the layout that targets maximum wind energy captured by WTGs is the optimal solution. In Table 5 a comparison between these three different targets is presented, for the case study conditions stated before.
5.1. GA and PSO implemented algorithms validation To validate the proposed resolution method for a problem, it is needed to know the solution. Hence, the deterministic algorithm was run to determine the best turbine disposal of a wind farm with 8 turbines (Vestas V90-3.0 MW) and 4 sub-cells in each cell. The wind data was kindly supplied by WavEC and consists of one sample per day (average wind speed and direction), for one year, therefore a total of 365 samples were used for this validation purpose. The results are shown in Fig. 9 (optimal layout) and Table 1 (numerical output). To validate GA and PSO, each algorithm was run 100 times with the parameters presented in Tables 2 and 3. The obtained results are also presented in the afore mentioned tables. It is possible to conclude that both optimization techniques are able to reach the deterministic results. Also, standard deviation of the 100 runs performed is very low. Moreover, it should be mentioned that GA reaches the deterministic exact result in 54% of the runs, while PSO hits 12%. It also can be inferred that PSO is faster once it founds the optimal value after an average of 38 iterations (CPU time near 1.8 h), while GA takes an average of 44 iterations to find the optimal value (CPU time near 2.1 h). Therefore, one can conclude that PSO is more efficient, meaning that it is faster to reach a good result approximation, while GA is more effective, meaning that it finds a good result approximation more often. 5.2. Case-study In order to apply the developed optimization methodologies to a more realistic wind park, a 18 WTGs wind park was considered. Vestas V90-3.0 MW WTG and submarine cables of 400 mm2, 590 A rated current were used. The wind data was kindly provided by WavEC – Offshore Renewables and was collected 10 km offshore from a location in the Northern part of Portugal. 3 h average samples were obtained at 10 m high and for that reason Prandtl law was applied to calculate the wind speed at rotor's height (95 m). The samples considered in this
Table 4 AEP and electrical losses as function of the number of sub-cells.
Table 1 Deterministic solution (numerical results). Deterministic
Solution
AEP Total CPU time
58.107 GWh 149.73 h
32
N° of subcells
AEP (GWh)
AEP increase (%)
Electrical losses (MWh)
N° of iterations
CPU time (h)
0 4 9 16 25
141.294 142.361 142.574 142.932 143.041
– 0.76% 0.91% 1.16% 1.24%
327.726 334.594 331.651 332.927 335.827
– 41 148 157 210
– 17.063 92.390 130.678 218.490
Engineering Applications of Artificial Intelligence 60 (2017) 26–34
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Fig. 10. Layout for the case study with 0 (a), 4 (b), 9 (c) and 16 (d) sub-cells (light blue lines inside the rectangles) and 18 WTGs (solid dark points). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
6. Conclusions The wind farm layout optimization problem applied to offshore wind power output maximization has been addressed in this research. This is an important issue, since offshore wind power is still expensive and maximizing annual energy production (AEP) is a major contribution to reduce the levelized cost of energy. AEP maximization is obtained by reducing all kinds of losses inside the park. In this research, only wake and internal network electrical losses have been considered, because these are among the most significant ones. The problem can be addressed using a deterministic technique. This methodology evaluates all possible combinations of WTG locations inside a pre-defined wind park topology. When the number of WTGs and/or the number of sub-cells increase, the computational burden involved may render the problem virtually unfeasible. To overcome this limitation, optimization algorithms are commonly applied. These algorithms try to select the best element (with regard to some criteria) from a defined set of available alternatives. An objective function is maximized or minimized by systematically choosing input values from within an allowed set and computing the value of the function. In this work, GA and PSO were the used optimization techniques. The deterministic algorithm has been implemented and the results obtained served as a benchmark to assess the performance of GA and PSO. An 8 WTGs wind park with 4 sub-cells has been considered for validation purposes. The comparison resulted favourable, because both optimization algorithms reached very good approximations of the AEP exact result as calculated by the deterministic technique. In fact, in average terms (after 100 runs), the error associated to GA output is – 0.03% and –0.09% in the case of PSO, with respect to the deterministic solution. This shows how effective both methods are, because they
Fig. 11. Optimal layout for the case study with 18 WTGs (solid dark points) 25 sub-cells (light blue lines inside the rectangles). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Table 5 Comparison between three different targets: minimum electrical losses, maximum wind capture and optimal solution.
Electrical losses (MWh) Turbines production (GWh) AEP (GWh)
Minimum electrical losses
Maximum wind captured
Optimal
160.338
342.223
335.827
120.722
143.381
143.377
120.561
143.039
143.041
33
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Emami, Alireza, Noghreh, Pirooz, 2010. New approach on optimization in placement of wind turbines within wind farm by genetic algorithms. Renew. Energy 35 (7), 1559–1564. http://dx.doi.org/10.1016/j.renene.2009.11.026. Frandsen, Sten, Barthelmie, Rebecca, Pryor, Sara, Rathmann, Ole, Larsen, Søren, Højstrup, Jørgen, Thøgersen, Morten, 2006. Analytical modelling of wind speed deficit in large offshore wind farms. Wind Energy 9 (1–2), 39–53. http://dx.doi.org/ 10.1002/we.189. González-Longatt, Francisco M., Wall, Peter, Regulski, Pawel, Terzija, Vladimir, 2012. Optimal electric network design for a large offshore wind farm based on a modified genetic algorithm approach. IEEE Syst. J. 6 (1), 164–172. http://dx.doi.org/ 10.1109/JSYST.2011.2163027. Grady, S.A., Hussaini, M.Y., Abdullah, Makola M., 2005. Placement of wind turbines using genetic algorithms. Renew. Energy 30 (2), 259–270. http://dx.doi.org/ 10.1016/j.renene.2004.05.007. Henderson, Andrew R., Morgan, Colin, Smith, Bernie, Sørensen, Hans C., Barthelmie, Rebecca J., Boesmans, Bart, 2003. Offshore wind energy in Europe – a review of the state-of-the-art. Wind Energy 6 (1), 35–52. http://dx.doi.org/10.1002/we.82. Hou, Peng, Hu, Weihao, Soltani, Mohsen, Chen, Zhe, 2015. Optimized placement of wind turbines in large-scale offshore wind farm using particle swarm optimization algorithm. IEEE Trans. Sustain. Energy, 1–11. http://dx.doi.org/10.1109/ TSTE.2015.2429912. Jensen, Niels Otto, 1983. A Note on Wind Generator Interaction. Risø National Laboratory, Roskilde, Denmark, (November, UDC: 621.548:533.69.048.3). Katic, I., Højstrup, J., Jensen, N.O., 1986. A simple model for cluster efficiency. In: Proceedings of the European Wind Energy Association Conference and Exhibition, pp. 407–410. Kusiak, Andrew, Song, Zhe, 2010. Design of wind farm layout for maximum wind energy capture. Renew. Energy 35 (3), 685–694. http://dx.doi.org/10.1016/ j.renene.2009.08.019. Mora, José Castro, Barón, José M. Calero, Santos, Jesús M. Riquelme, Burgos Payán, Manuel, 2007. An evolutive algorithm for wind farm optimal design. Neurocomputing 70 (16), 2651–2658. Mosetti, G., Poloni, Carlo, Diviacco, B., 1994. Optimization of wind turbine positioning in large windfarms by means of a genetic algorithm. J. Wind Eng. Ind. Aerodyn. 51 (1), 105–116. http://dx.doi.org/10.1016/0167-6105(94)90080-9. Pérez, Beatriz, Mínguez, Roberto, Guanche, Raúl, 2013. Offshore wind farm layout optimization using mathematical programming techniques. Renew. Energy 53, 389–399. http://dx.doi.org/10.1016/j.renene.2012.12.007. Pookpunt, Sittichoke, Ongsakul, Weerakorn, 2013. Optimal placement of wind turbines within wind farm using binary particle swarm optimization with time-varying acceleration coefficients. Renew. Energy 55, 266–276. http://dx.doi.org/10.1016/ j.renene.2012.12.005. Qiu, Yingning, Xu, Yili, Li, Jiawei, Feng, Yanhui, Yang, Wenxian, Infield, David, 2014. Wind turbulence impacts to onshore and offshore wind turbines gearbox fatigue life. In: Proceedings of the 3rd Renewable Power Generation Conference (RPG 2014). September, pp. 1–5. http://dx.doi.org/10.1049/cp.2014.0903. Rodrigues, S.F., Teixeira Pinto, R., Soleimanzadeh, M., Bosman, Peter A.N., Bauer, P., 2015. Wake losses optimization of offshore wind farms with moveable floating wind turbines. Energy Convers. Manag. 89, 933–941. http://dx.doi.org/10.1016/ j.enconman.2014.11.005. Samorani, Michele, 2013. The wind farm layout optimization problem. In: Handbook of Wind Power Systems. Springer, pp. 21–38. http://dx.doi.org/10.1007/978-3-64241080-22. Safari, A., Jahani, R., Shayanfar, H.A., Olamaei, J., 2010. Optimal DG allocation in distribution network. Int. J. Electr., Comput., Energ., Electron. Commun. Eng. 4 (3), 617–620. Sisbot, Sedat, Turgut, Ozgu, Tunc, Murat, Camdali, Unal, 2010. Optimal positioning of wind turbines on Gokceada using multi-objective genetic algorithm. Wind Energy 13 (4), 297–306. http://dx.doi.org/10.1002/we.339. Valverde, Pedro Santos, Sarmento, António J.N.A., Alves, Marco, 2013. Offshore Wind farm layout optimization – state of the art. In: Proceedings of the The Twenty-third International Offshore and Polar Engineering Conference. International Society of Offshore and Polar Engineers, Anchorage, Alaska, June. Wan, Chunqiu, Wang, Jun, Yang, Geng, Zhang, Xing, 2010. Particle Swarm Optimization based on Gaussian mutation and its application to wind farm micro-siting. In: Proceedings of the 2010 49th IEEE Conference on Decision and Control (CDC). December, pp. 2227–2232. http://dx.doi.org/10.1109/CDC.2010.5716941. Wu, Yuan-Kang, Lee, Ching-Yin, Chen, Chao-Rong, Hsu, Kun-Wei, Tseng, Huang-Tien, 2014. Optimization of the wind turbine layout and transmission system planning for a large-scale offshore wind farm by AI technology. IEEE Trans. Ind. Appl. 50 (3), 2071–2080. http://dx.doi.org/10.1109/TIA.2013.2283219. Zhao, M., Chen, Zhe, Blaabjerg, Frede, 2009. Optimisation of electrical system for offshore wind farms via genetic algorithm. IET Renew. Power Gener. 3 (2), 205–216. http://dx.doi.org/10.1049/iet-rpg:20070112. Zimmerman, Ray Daniel, Murillo-Sánchez, Carlos Edmundo, Thomas, Robert John, 2011. MATPOWER: steady-state operations, planning, and analysis tools for power systems research and education. IEEE Trans. Power Syst. 26 (1), 12–19. http:// dx.doi.org/10.1109/TPWRS.2010.2051168.
produce very good AEP approximations, while reducing CPU time from 150 h to 2 h. Furthermore, the results obtained demonstrated that GA is able to reach reliable solutions more often than PSO. This ability is shown by the number of times GA reaches the very exact solution, which is higher than in the PSO case (54% against 12%). Still, the errors associated with runs in which an exact match has not been achieved are low: GA worst error in one run is –0.12% and PSO's worst error is –0.37%. This explains why the average AEP output results of both techniques are so similar. It is true that PSO converges to the optimum value in fewer iterations (reduced CPU times), but sometimes it gets “trapped” in local optimum being more ineffective in searching new optimal zones. On the other hand, once GA reaches a local optimum, the genetic operator mutation helps the algorithm to find solutions away from the current search zone, therefore enabling to find new best solutions. Then, a more realistic case-study (18 WTGs wind park) was implemented and assessed. An AEP increase of 1.24% with respect to the case in which the WTGs were placed at the centre of the cells was obtained when using the micro-siting approach proposed (25 sub-cells inside major cells). This increment may be even more significant if the micro-siting approach is used after an optimization of the cells dimensions. The proposed optimization concept and turbines positioning is very realistic and project friendly, as the WGTs are restrained to a small area (when compared to the entire wind park area) favouring the wind farm construction, not only the turbines and foundations, but mainly the submarine cable laying. In this work, the criteria against which optimization takes place is the wind farm's annual electricity production, or, in other terms, the capacity factor, which we want to maximize. Other criteria could be used, for instance, to minimize seasonal variations, that is, to keep the production as constant as possible, independently of the wind fluctuations. This can be achieved using a coupled BESS (Battery Energy Storage System), whose design could be approached using optimization techniques similar to the ones used in this paper. Acknowledgments This work was supported by national funds through Fundação para a Ciência e a Tecnologia (FCT) with reference UID/CEC/50021/2013. WavEC – Offshore Renewables is deeply acknowledged for providing the wind database. References Appiott, Joseph, Dhanju, Amardeep, Cicin-Sain, Biliana, 2014. Encouraging renewable energy in the offshore environment. Ocean Coast. Manag. 90, 58–64. http:// dx.doi.org/10.1016/j.ocecoaman.2013.11.001. Bilgili, Mehmet, Yasar, Abdulkadir, Simsek, Erdogan, 2011. Offshore wind power development in Europe and its comparison with onshore counterpart. Renew. Sustain. Energy Rev. 15 (2), 905–915. http://dx.doi.org/10.1016/ j.rser.2010.11.006. Clerc, Maurice, Kennedy, James, 2002. The particle swarm - explosion, stability, and convergence in a multidimensional complex space. IEEE Trans. Evolut. Comput. 6 (1), 58–73. http://dx.doi.org/10.1109/4235.985692. Corbetta, Giorgio, Mbistrova, Ariola, Ho, Andrew, Guillet, Jérôme, Pineda, Iván, 2015. The European offshore wind industry - key trends and statistics 2014. In: Proceedings of the Technical report, European Wind Energy Association. January. Dekker, Jos W.M., Pierik, J.T.G., 1998. European Wind Turbine Standards II: Executive Summary. Netherlands Energy Research Foundation ECN, (December). Dor, Abbas El, Clerc, Maurice, Siarry, Patrick, 2012. A multi-swarm PSO using charged particles in a partitioned search space for continuous optimization. Comput. Optim. Appl. 53 (1), 271–295. http://dx.doi.org/10.1007/s10589-011-9449-4.
34
Contents lists available at ScienceDirect
Engineering Applications of Artificial Intelligence journal homepage: www.elsevier.com/locate/engappai
Offshore wind farm layout optimization regarding wake effects and electrical losses Luís Amarala, Rui Castrob, a b
MARK
⁎
Instituto Superior Técnico, University of Lisbon, Lisbon, Portugal INESC-ID/IST, University of Lisbon, Lisbon, Portugal
A R T I C L E I N F O
A BS T RAC T
Keywords: Offshore wind energy Electrical losses Wake effect Genetic Algorithm Particle Swarm Optimization
A major development of the offshore wind energy market is being witnessed. Since the implicated costs are considerably high, it is extremely important to ensure that the energy production is maximum, so that the costs per energy unit are minimized. Thus, the turbines should be strategically positioned to extract as much energy as possible from the wind, considering wake effect losses, as well as internal grid electrical losses. In order to avoid turbines to be placed in unrealistic positions, they should be distributed according to a grid of rectangular shaped cells; each of these is divided in multiple sub-cells. The problem of finding the turbines optimal position among the pre-defined sub-cells so that maximum annual energy is produced could be addressed using a deterministic approach. However, the problem becomes unfeasible when the number of turbines and/or the number of sub-cells increase. To overcome this difficulty, optimization techniques should be used. Genetic Algorithm and Particle Swarm Optimization are approached in this paper. This paper deals with the wind park layout optimization problem. A methodology to position the turbines inside a wind park so that the annual energy production is maximum is proposed. The results proved that the meta-heuristic method is much more CPU time efficient in providing the maximum annual year production as compared to the traditional deterministic approach.
1. Introduction Over the past years there has been a significant development of alternative energies and the global market for wind power has been expanding faster than any other renewable energy source (Bilgili et al., 2011). As the best onshore locations are already occupied, a trend towards offshore wind applications is currently being witnessed. Indeed, going offshore can tackle some disadvantages of the onshore wind energy development, such as: availability of large continuous areas, suitable for major projects; elimination of the issues of visual impact and noise, allowing the utilization of larger turbines (Henderson et al., 2003); stronger and less turbulent wind, increasing the energy produced (Appiott et al., 2014) and decreasing the fatigue loads on the turbine (Qiu et al., 2014); higher air density resulting in higher wind power output. On the other side, offshore wind power shows higher installation costs and a significant increase in operating and maintenance costs. Offshore wind farms may represent an important source of renewable energy in the future. If we look back to the past 10 years, the annual offshore wind power installed in Europe increased from about
⁎
90–1500 MW. In 2014, the total installed capacity from offshore wind farms in Europe was 8.045 GW of which 74% where installed since 2009 (Corbetta et al., 2015). Some of the previously mentioned disadvantages related to the development of wind energy offshore, namely the increase of investment costs and accessibility, can be softened if the annual energy production (AEP) is highly enough to reduce the overall levelized cost of energy (LCOE). To achieve this purpose, new techniques and designs should be introduced. Wind Farm Layout Optimization Problem (WFLOP) is an example of such research, since by optimizing the Wind Turbine Generators (WTGs) disposal, losses may be reduced and the energy production increased, thus reducing the LCOE. To optimize the turbines disposal, the assumption that they are initially placed according to a traditional layout with an offset is normally considered. A grid with cells where WTGs may be positioned is supposed and, to approach the micro-sitting positioning, it is assumed that each cell is divided into multiple sub-cells allowing the turbine position not to be restricted to the centre of the main cell. The WFLOP aiming to maximize the AEP may be solved by a deterministic approach that runs every possible combinations of
Corresponding author. E-mail address: [email protected] (R. Castro).
http://dx.doi.org/10.1016/j.engappai.2017.01.010 Received 17 February 2016; Received in revised form 24 November 2016; Accepted 12 January 2017 0952-1976/ © 2017 Elsevier Ltd. All rights reserved.
Engineering Applications of Artificial Intelligence 60 (2017) 26–34
L. Amaral, R. Castro
position. Rodrigues et al. (2015) proposed an optimization technique based on covariance matrix adaptation where the turbines move according to the wind direction in order to minimize the wake effect. In this paper, the WFLOP is assessed by determining the optimal position of the WTGs inside a wind farm. The objective function that is to be optimized (maximized, in this case) is the AEP, by minimizing both the wake losses and the electrical losses inside the wind farm internal grid. Losses minimization, namely those associated with wake effect and Joule losses in the internal collection system, is not trivial, as the former decrease with the separation distance of the wind turbines while the latter increase with the separation distance. The assessed optimization techniques are GA and PSO, these two being used to validate the developed algorithms in a test wind farm; following the conclusion that GA is more effective, meaning that it finds a good result approximation more often, this technique was used to determine the optimal position (maximum AEP) of the WTGs inside a realistic wind farm. Other optimization criteria could be used, for instance, to minimize the production cost of electricity produced. In this case, data concerning the investment and operation and maintenance costs should be considered, which is outside the scope of this paper. The paper is organized as follows. In Section 2, the wake model implemented is presented and the reasons for using it are discussed. In Section 3, items concerning energy conversion and power flow analysis are tackled. Also, in that Section, the internal grid electrical losses model and how they are computed is introduced. The optimization algorithms developed for the WFLOP are exposed and validated in Section 4. In Section 5, the results obtained for a wind farm application case-study are presented and discussed. Lastly, the main conclusions of this research are drawn.
turbines layout and chooses the one that leads to the maximum AEP. Happens that, the micro-sitting approach considered is a highly complex problem, e.g. for a wind park with 80 turbines and cells divided in 9 sub-cells there are more than 2.185×1076 possible combinations, resulting in decades of simulation time. To overcome this issue, optimization techniques, such as, Genetic Algorithm (GA) and Particle Swarm Optimization (PSO), are applied in order to reduce the computation time. The algorithms calculate the AEP considering the turbines characteristics, wake losses, electrical losses and wind site conditions. Most of the optimization techniques applied to the WFLOP found in literature are based on evolutionary algorithms (EAs). In 1994, Mosetti et al. (1994) and later, in 2005, Grady et al. (2005) optimized the wind turbines position throughout the use of a GA. The main goal of this study was to minimize the total cost (the cost function assumed was very simple and only depended on the number of turbines and the energy produced) of the wind farm by maximizing the energy produced. The study presented in (Grady et al., 2005) is an improvement to the one proposed in (Mosetti et al., 1994). Since 2005, many studies about the best wind turbines positioning have been made (e.g. Mora et al. (2007) and Kusiak and Song (2010)) but, more recently, in 2009, Sisbot et al. (2010) implemented a multiobjective GA to optimize the placement of wind turbines by maximizing the power production capacity, while constraining the budget of installed turbines. Although the algorithm presented good results, the main issue of the study was that the authors considered a single wind scenario. In 2010, Wan et al. (2010) proposed a PSO based on Gaussian mutation algorithm. The algorithm proved to be more accurate than the standard PSO and with a computation time substantially reduced. It was considered a standard PSO but, if the algorithm does not improve for a predefined number of iterations, each particle suffers a mutation that improves its position. The method results are more reliable once they have a lower standard deviation than the traditional PSO. With the development of offshore wind energy, other design optimization approaches are being witnessed. Besides the WTG positioning (e.g. Wu et al. (2014) and Hou et al. (2015)), researchers have studied both the internal connections and transport systems (e.g. Wu et al. (2014), Zhao et al. (2009) and González-Longatt et al. (2012)), as going offshore, these two components gain relevance compared with onshore installation costs and electrical losses. Zhao et al. (2009) use a GA with many variables, as such the cross sections of the various cables, offshore substation rated power and the different systems rated voltages. On the other hand, González-Longatt et al. (2012) focus their study on the optimization of the internal connections by using a modified GA. The study showed that if the proposed method is applied, then a reduction of about 11% of the total cable length compared with a traditional manual design can be achieved. More recently Wu et al. (2014) and Hou et al. (2015), in 2014 and 2015 respectively, considered not only the wake losses but also the energy loss in the electrical system. Hou et al. (2015) used a standard PSO with inertia weight and considered two approaches: constant distance between turbines from different rows and a sparse layout. Wu et al. (2014) apply two optimization algorithms; first, GA is used to find the turbines optimal position and once they are defined, the Ant Colony System (ACS) is applied to study the optimal internal network system, considering the connections between turbines and substation and submarine cables characteristics. The main issue of the proposed ACS it that the connections are made directly simply regarding the distance between turbines/substation. A more realistic procedure would have to take under consideration the philosophy of not crossing cables. Although the concept is in a primary stage, some characteristics of floating turbines are already being considered as advantages, such as the fact that a floating turbine does not have to stay always in the same
2. Wake effect Wind turbines extract energy from the wind, therefore the downstream wind must have less energy content than the upstream. Wake effect is a consequence of the wind impact on turbine's blades where the wind becomes slower and more turbulent, resulting on a wake behind the wind turbine. As the wind flow proceeds further downstream this wake will begin to spread and gradually return to surrounding wind characteristics. In a wind farm where there are multiple wind turbines, it is most likely that the swept area of a turbine is influenced by one or more upstream turbines. This event is called shadowing effect. Slower and turbulent wind means less energy available, but turbulence has another prejudicial factor, it increases fatigue damage, lowering turbine's reliability (Qiu et al., 2014). Both of these consequences contribute to decrease the energy produced by a WTG resulting in less energy produced by the wind farm. Nowadays, there are many available models to study the wake diameter and the wind speed variations over the distance (e.g. Jensen model (Jensen, 1983), Frandsen model (Frandsen et al., 2006) and EWTS-II model (Dekker and Pierik, 1998)). Some of these models are simpler and, consequently, with lower precision, but they present faster computation times. N.O. Jensen proposed his model in 1983 (Otto Jensen, 1983) and it was further developed in 1986 by Katic et al. (1986). It assumes that the initial wake diameter is the same as the turbine diameter and it will expand linearly as a function of downwind distance. Similar to wake diameter, downstream wind deficit decays linearly with the turbine distance. On one hand, the main advantage of Jensen model is that it is much more computational efficient than other complex but more precise models. As so, it is useful to provide a quick insight to eliminate some options before going into a more detailed and time heavily model; for that reason, it is used in many publications about WFLOP. On the disadvantages side, because it is a simple model, it does not take into account factors such as wind turbulence. 27
Engineering Applications of Artificial Intelligence 60 (2017) 26–34
L. Amaral, R. Castro
where Aturb = πrr2 and (zw is hub height of the turbine that causes the wake and dhorz is perpendicular to x axis and it is the horizontal distance between the two turbines):
2.1. Single wake effect In this paper, Jensen model further improved in 1994, Mosetti et al. (1994) was used. This model consists of a linear expansion of the wake diameter and a linear decay of the velocity deficit inside the wake. This wake analysis supposes that the momentum is conserved inside the wake neglecting the near field behind the upstream turbine. After performing a momentum balance and using Betz theory to determine the wind speed immediately behind the rotor, the wind speed downstream of the turbine is:
2a vd = ⎛x⎞ 1 + α⎜ r ⎟ ⎝ 1⎠
⎛ r2 + d2 − r2 ⎞ ⎛ r2 + d2 − r2 ⎞ 1 r ⎟⎟rr2 + arccos⎜⎜ 1 ⎟⎟r12 Ashadow = arccos⎜⎜ r 2r2d 2r1d ⎝ ⎠ ⎝ ⎠ 2 2 2 ⎡ ⎤ ⎛r + d − r ⎞ 1 ⎥ ⎟⎟ rrd − sin⎢arccos⎜⎜ r ⎢⎣ 2rrd ⎝ ⎠⎥⎦
d=
1−
1 − CT 2
(1)
; α=
1 1−a and r1 = rr ⎛z⎞ 1 − 2a 2 ln⎜ z ⎟ ⎝ 0⎠
(2)
u = u 0(1 − vd )Aratio
In these equations, it is: vd is the velocity deficit at distance x, a is the axial induction factor, CT is the thrust coefficient determined by the turbine manufacturer, r1 is the wake radius, rr is the turbine's rotor radius, z is the hub height and z0 is the surface roughness length, its value depending on the sea water characteristics. The roughness length value for water surface is usually taken as 0.0002 m. Finally, the wind velocity, u, in the shadow of the turbine is given by:
u = u 0(1 − vd )
(7)
2.2. Multiple wake effect In a wind farm where there are many turbines installed it is likely that wakes can intersect and affect turbines downwind at the same time (Samorani, 2013). This problem can be solved by assuming the kinetic energy deficit of a mixed wake to be equal to the sum of the energy deficits for each wake at the calculated downwind position (Katic et al., 1986). Therefore, the following equations can be obtained by generalization:
(3)
where u0 is the upstream wind speed. The wake area is also known as shadowed area, hence a turbine that is aerodynamically affected by another is said to be under the shadow area of an upstream turbine. To go further in the wake model precision, it must be taken into account that the wake effect may not be total, i.e. the downstream turbine may be only partially affected by the upstream one, resulting on a lower velocity deficit. Fig. 1 represents a partial shadowing where the white circle represents the affected turbine swept area and the grey circle represents the wake area. The real distance between turbines is not relevant for the case. The fraction of area that is affected by the wake is:
Aratio =
(6)
If Ashadow is not a real number, for instance, if the argument of arccos function is greater than 1 or less than −1, it means that either there is no wake effect or the turbine is completely shadowed. If rr + r1 < d there is no wake effect and Aratio=0, if rr+r1≥ d the wake is total and Aratio=1. Finally, the wind velocity of a turbine that suffers a single aerodynamic effect is:
with:
a=
2 z − zw 2 + dhorz
(5)
vdij =
2a ⎛ xij ⎞ 1 + α ⎜ r (x ) ⎟ ⎝ 1 ij ⎠
vdef (j ) =
∑
(8)
[vdijAratio (i , j )]2
i ∈ upwind
u(j ) = u 0(1 − vdef (j ))
(9) (10)
where vdef (j) is the total velocity deficit at turbine j and vdij is the velocity deficit caused by turbine i in turbine j. 2.3. Wind direction variation
Ashadow Aturb
(4) Modern wind generators are equipped with a yaw system drive that allows turbine blades to face the wind in order to maximize the energy extracted. Therefore, a deficit analysis must be made for each possible wind direction. 3. Electrical system model Wind parks electrical connections are responsible for collecting the energy from WTGs and transporting it to shore. As any electrical system, it has losses that have impact on the energy delivered to the main grid. Two distinct electrical systems are considered: the internal grid network that is responsible for collecting the power from WTGs and delivering it to the substation; the transmission system that transfers the energy from the substation to shore. The latter was not considered once it does not influence the wind farm layout output. 3.1. Turbine power curve Turbines are designed to work within a certain range of wind speeds, known as the cut-in, u0, and cut-out, umax, wind speeds. For wind velocities lower than u0 the operation costs are too high for what
Fig. 1. Example of a partial shadowing.
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assumption, since the WTGs power electronics interface is able to regulate the power factor. Each branch (array cables) described by its length, its longitudinal impedance and shunt capacitance per length unit and its rated power. The power flow is described by a complex non-linear equation system given by:
the turbine yields, as so the WTG is disconnected. When wind speeds are higher than umax, the generator is shut down so as to avoid damaging the equipment. Between rated wind speed, uR, and cut-out wind speed, the wind turbine is regulated to operate at rated power, PR. The power curve, i.e. the electrical power output as a function of the wind speed, can be analytically represented using a sigmoid function:
⎧ 0 u < u0 ⎪ P R u 0 ≤ u < uR ⎪ c1− u Pg(u ) = ⎨ 1 + e c2 ⎪ P uR ≤ u < umax R ⎪ u > umax ⎩ 0
⎡⎛ S ⎞*⎤ ⎢⎜ ⎟ ⎥ = [Y][V] ⎢⎣⎝ V ⎠ ⎥⎦
(12)
where the first member is the injected currents vector (S being the injected complex power), Y is the nodal admittances matrix and V is the complex voltage vector. When the iterative process converges, all the voltages and the injected complex power in the slack bus are known. Once the complex voltages in each bus are established, it is possible to calculate the branch losses. Cables are represented by the equivalent π-model. First of all, the current in each cable is computed from the voltages at the sending and receiving buses and from the electrical parameters of the cable (resistance, reactance and capacitance). Then, the total Joule losses are calculated through (B is the number of cables and In is the current in each cable):
(11)
where c1 and c2 are constants that need to be determined, in order that the sigmoid function fits as good as possible when compared with real samples supplied by the manufacturer. It should be noted that the wind speed considered in (11) is the wind speed that passes through the turbine, i.e. after being affected by the deficit introduced by the wake model. 3.2. Collection system design Most of offshore wind farms are connected in a string arrangement, i.e. each row of turbines is series connected between them and then to the substation. For internal connections, a medium voltage submarine grid between 25 kV and 40 kV is typically buried 1–2 m deep in the seabed (Henderson et al., 2003). A group of independent turbines is called a cluster. In this paper, a string configuration with redundancy for the internal grid is considered. Redundancy is achieved because, for instance, in case of a failure in any cable connecting two turbines, an alternative path to drain the energy is provided (Fig. 2). Some authors (e.g. Appiott et al. (2014)) state that clusters with redundancy, in spite of having higher internal grid electrical losses, may be an advantageous option, once they increment reliability.
B
Plosses =
∑ 3RIn2
(13)
n =1
3.4. Annual energy production (AEP) The power generated by WTGs depends both on wind speed and direction and the electrical losses depend on the generated power. So, for a certain sample of wind speed and direction, we will have a certain average power and power losses. Let us consider a wind farm with T WTGs and that we have W wind samples, in one year. The AEP of the wind park is therefore:
AEP =
3.3. Power flow and electrical losses To determine the electrical losses in the collection system, the power flow for the entire wind farm internal network must be solved. For that, MATPOWER software is used (Zimmerman et al., 2011). MATPOWER is a package of Matlab M-files for solving power flow problems. There must be a generator representing the onshore grid and the transmission system with the purpose of balancing the power flow and a transformer representing the substation transformer. In all buses the injected active and reactive power are specified (PQ bus) except for one special bus called the slack bus. At this bus, the voltage magnitude is fixed in 1 pu and an angle of 0°. The generated active power from WTGs is the active power that the particular WTG addressed is producing in a specific moment, depending on the wind speed and direction. Moreover, a unity power factor was assumed, meaning that the injected reactive power by each WTG is zero. This is a valid
8760 W
W
⎛
T
⎞
⎝ t =1
⎠
∑ ⎜⎜∑ (Pgt (uw )) − Plosses(uw )⎟⎟ w =1
(14)
4. Wind farm layout optimization 4.1. Traditional layout In most cases, the layout of an offshore wind park can be represented by a grid or a group of smaller grids attached to each other (e.g. Kentish Flats, Barrow and London Array wind parks in United Kingdom). This imaginary grid is composed by rectangular cells that may or may not have a turbine as represented in Fig. 3. Initially, in case it exists, the turbine is placed in the centre of the cell. The first optimization approach aims to determine the optimal distance between lines and rows of turbines, i.e. what the best distance in the prevailing wind direction and in the crosswind direction is. According to Hou et al. (2015), the first should be between 8D and 12D while the second is expected to be from 3D to 5D (D is the rotor diameter of the concerned turbine). To avoid wake losses, an offset perpendicular to prevailing wind direction should be applied to the grid from the start (Wu et al., 2014) as shown in Fig. 3. 4.2. Micro-sitting approach Going further in the WFLOP, each turbine position cannot be restricted to the centre of a cell, turbines must be placed in a more accurate manner. In past years, some authors stated that a grid similar to the one presented before should be created and that the optimization
Fig. 2. String cluster with redundancy configuration.
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Fig. 3. Grid traditional turbine disposal with offset layout.
Fig. 5. Implemented GA flowchart.
4.3.1. Genetic algorithm GAs are Evolutionary Algorithms (EAs) and were designed to mimic the natural selection of species and the reproduction of the best fitted individuals from a population. They consist of a population transformed by three genetic operators: selection, crossover and mutation (Sisbot et al., 2010). The GA flowchart is depicted in Fig. 5. In each generation, individuals are ordered according their fitness and then the best fitted is selected to integrate the next population. A percentage of the remaining individuals will be selected for the breeding process and the others are discarded. A high crossover percentage is considered because crossover operation is the main responsible for the “local evolution” of the population. After the selection process is complete, the breeding individuals will cross genetic information between them. A scattered crossover (Sisbot et al., 2010) with 50% from each parent is applied, i.e. each child receives half of its genes from one parent and the other half from another. Scattered crossover operation is displayed in Fig. 6. According to Safari et al. (2010), a Darwinian interpretation on selection for crossover generates positive results, i.e. the most fitted individuals are more likely to transmit genetic information. In this paper, a slightly different approach was taken: probabilities are neglected and it is assured that the most fitted individual (after the elite one) will mate with all the other individuals, generating one offspring in each operation. The selection and crossover operations are represented in Fig. 7. A mutation is a simple modification in the genetic code, when a mutation occurs, only one gene is changed. Before the next generation is ready, it is submitted to the mutation operation. Mutation may or may not occur, its occurrence probability is called mutation probability, and it should be kept low (Mora et al., 2007), since a high value would make the algorithm tend to a random search (Mosetti et al., 1994). Nevertheless, mutation operation is substantial as it allows the creation of individuals which are different from the individuals in the previous population (Mora et al., 2007) thus introducing new zones of possible good solutions and preventing the algorithm to fall into a local optimum value (Wu et al., 2014). In the WFLOP, layouts represent individuals, genes represent turbines position and a mutated gene represents a turbine changing position.
Fig. 4. Example of a grid with cells divided into 9 sub-cells.
algorithm should be able to arrange the grid placing a predefined number of wind generators inside the cells which, theoretically, can perform good results (e.g. Sisbot et al. (2010), Pérez et al. (2013) and Emami and Noghreh (2010)). In reality, it is not convenient that an offshore wind park has turbines displaced in cells with no pre-defined guidelines (for several reasons, such as more expensive cable laying, expensive installation and maintenance and operation costs, for example). Therefore, this paper proposes that each turbine should be contained in a relatively large cell divided into multiple sub-cells. Then, the wind generator is to be placed in the centre of one of the sub-cells. This will make possible to achieve optimum results while maintaining the traditional disposal with its inherent installation advantages. Fig. 4 exemplifies this procedure.
4.3. Optimization algorithms Optimization algorithms can be divided in two categories: deterministic and probabilistic (Valverde et al., 2013). The former will search for every possible solutions and select the optimal one, while the latter is an iterative method that only computes a small number of solutions in each iteration, but trends to a maximum or a minimum with time. Once the WFLOP includes several design variables, the deterministic algorithm becomes unfeasible due to higher CPU times needed to search all possible solutions. The complexity and consequent CPU time of probabilistic algorithms are also dependent of the number of variables but they can perform significant better CPU times presenting results very close (or identical) to the deterministic value. The probabilistic optimization algorithms considered and implemented in this paper are Genetic Algorithm (GA) and Particle Swarm Optimization (PSO).
4.3.2. Particle Swarm Optimization Particle Swarm Optimization (PSO) was inspired in some of these species behaviour such as fish schooling and bird flocking (Hou et al., 2015). The algorithms consist in randomly displaying particles inside a 30
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Fig. 6. Scattered crossover for a general case with a genome length of N (in the WFLOP, for a wind park with N turbines).
Fig. 7. Selection and crossover operations scheme for implemented GA considering a population with 6 individuals.
hyperspace (possible solutions) and then assigning them velocities. Once it is an iterative process, in every iteration each particle adjusts its “flying” according to its own flying experience (self-awareness) and its companions’ (swarm) flying experience (social awareness). The PSO implemented in this study is an improved version proposed by Clerc and Kennedy (2002). As stated in Dor et al. (2012), particles move are influenced by three components: (i) physical component: the particle tends to keep its current direction of displacement (also known as inertia); (ii) cognitive component: the particle tends to move towards the best site that it has explored until now; (iii) social component: the particle tends to rely on the experience of its congeners, then moves towards the best site already explored by its neighbours. Let the best known position of each particle i be pBesti (personal best) and the best known position of all particles be the gBest (global best). Each particle's velocity and position in the next iteration is given by (15) and (16), respectively.
vik +1 = Ψ [Cphy + ψ1rand 1Ccog + ψ2 rand 2Csoc]
(15)
xik +1 = xik + vik +1
(16)
Fig. 8. Implemented PSO flowchart.
Cognitive and social components are responsible for intensification, i.e. they explore known”regions”, whereas the physical component is responsible for diversification, once it forces the particle to search new ”regions”. Ψ is the constriction factor and is given by:
2 − (ψ1 + ψ2 ) −
(ψ1 + ψ2 )2 − 4(ψ1 + ψ2 )
(18)
The implemented PSO flowchart is displayed in Fig. 8. Initially particles are disposed randomly and given random velocities. In every iteration, each particle pBest is evaluated. If the current particle position fits better than the its pBest, this value is replaced for the current position. A similar logic is applied to gBest. After every particles pBest is evaluated, the algorithm checks if any of them is better fitted than the gBest value and updates it if necessary. When the swarm obeys to a pre-defined criterion, the algorithm stops. Due to randomness, sometimes the algorithm computes positions and velocities that throw particles out from the search space. To avoid that, a technique adopted in (Pookpunt and Ongsakul, 2013) is applied here, positions and velocities are restrained in a range [pmin,pmax] and [vmin,vmax], respectively.
where Cphy is the physical component, Ccog is the cognitive component and Csoc is the social component, given by:
Cphy = vik Ccog = (pBestik − xik ) Csoc = (gBest k − xik )
2
Ψ=
(17) 31
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Table 2 Genetic algorithm statistics of the 100 runs. GA parameters
GA statistics
Population size Crossover percentage Mutation probability
20 80% 10%
AEP best result AEP worst result AEP average result Standard deviation Deterministic layout matches Average n° of iterations Total CPU time
58.107 GWh 58.034 GWh 58.091 GWh 0.023 GWh 54/100 44.050 2.053 h
Table 3 Particle Swarm Optimization statistics of the 100 runs. PSO parameters
PSO statistics
Population size Cognitive learning factor Social learning factor
Fig. 9. Optimal layout as determined by the deterministic algorithm; 4 sub-cells (light blue lines inside the rectangles) and 8 WTGs (solid dark points). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
20 2.5 1.6
AEP best result AEP worst result AEP average result Standard deviation Deterministic layout matches Average n° of iterations Total CPU time
58.107 GWh 57.894 GWh 58.056 GWh 0.052 GWh 12/100 37.870 1.765 h
5. Results and discussion study are from the last year of measurements (2012), as so 2920 samples were picked up. The average wind speed for that year was 7.0804 m/s. The Weibull shape and scale parameters were estimated as k=1.6898 and c=7.9265 m/s. In the case study, only GA optimization technique was considered. For the same wind farm specifications and wind samples, different number of sub-cells are considered and the results are displayed. Table 4 displays the obtained AEP as a function of the considered number of sub-cells and in Fig. 10 the layouts for 0, 4, 9 and 16 subcells are presented. It can be seen that the optimal layout is the one corresponding to 25 sub-cells, as so it is presented in a separate figure (Fig. 11). One may consider the base case as the one with 0 sub-cells, the WTGs being positioned in the centre of the cells in this layout. From Table 4, it can be concluded that the optimal positioning in the 25 subcells layout leads to an increase of 1.24% of the AEP, with respect to the base case. The influence of the number of sub-cells is apparent, the higher the number of sub-cells is, the higher AEP obtained. On the other hand, the AEP incremental increase reduces with the number of sub-cells. This means that, at some point, extend the problem complexity (i.e. adding more sub-cells) will not pay the results obtained, because the AEP will not increase significantly. Finally, it is important to state that neither the layout that targets less electrical losses, nor the layout that targets maximum wind energy captured by WTGs is the optimal solution. In Table 5 a comparison between these three different targets is presented, for the case study conditions stated before.
5.1. GA and PSO implemented algorithms validation To validate the proposed resolution method for a problem, it is needed to know the solution. Hence, the deterministic algorithm was run to determine the best turbine disposal of a wind farm with 8 turbines (Vestas V90-3.0 MW) and 4 sub-cells in each cell. The wind data was kindly supplied by WavEC and consists of one sample per day (average wind speed and direction), for one year, therefore a total of 365 samples were used for this validation purpose. The results are shown in Fig. 9 (optimal layout) and Table 1 (numerical output). To validate GA and PSO, each algorithm was run 100 times with the parameters presented in Tables 2 and 3. The obtained results are also presented in the afore mentioned tables. It is possible to conclude that both optimization techniques are able to reach the deterministic results. Also, standard deviation of the 100 runs performed is very low. Moreover, it should be mentioned that GA reaches the deterministic exact result in 54% of the runs, while PSO hits 12%. It also can be inferred that PSO is faster once it founds the optimal value after an average of 38 iterations (CPU time near 1.8 h), while GA takes an average of 44 iterations to find the optimal value (CPU time near 2.1 h). Therefore, one can conclude that PSO is more efficient, meaning that it is faster to reach a good result approximation, while GA is more effective, meaning that it finds a good result approximation more often. 5.2. Case-study In order to apply the developed optimization methodologies to a more realistic wind park, a 18 WTGs wind park was considered. Vestas V90-3.0 MW WTG and submarine cables of 400 mm2, 590 A rated current were used. The wind data was kindly provided by WavEC – Offshore Renewables and was collected 10 km offshore from a location in the Northern part of Portugal. 3 h average samples were obtained at 10 m high and for that reason Prandtl law was applied to calculate the wind speed at rotor's height (95 m). The samples considered in this
Table 4 AEP and electrical losses as function of the number of sub-cells.
Table 1 Deterministic solution (numerical results). Deterministic
Solution
AEP Total CPU time
58.107 GWh 149.73 h
32
N° of subcells
AEP (GWh)
AEP increase (%)
Electrical losses (MWh)
N° of iterations
CPU time (h)
0 4 9 16 25
141.294 142.361 142.574 142.932 143.041
– 0.76% 0.91% 1.16% 1.24%
327.726 334.594 331.651 332.927 335.827
– 41 148 157 210
– 17.063 92.390 130.678 218.490
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Fig. 10. Layout for the case study with 0 (a), 4 (b), 9 (c) and 16 (d) sub-cells (light blue lines inside the rectangles) and 18 WTGs (solid dark points). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
6. Conclusions The wind farm layout optimization problem applied to offshore wind power output maximization has been addressed in this research. This is an important issue, since offshore wind power is still expensive and maximizing annual energy production (AEP) is a major contribution to reduce the levelized cost of energy. AEP maximization is obtained by reducing all kinds of losses inside the park. In this research, only wake and internal network electrical losses have been considered, because these are among the most significant ones. The problem can be addressed using a deterministic technique. This methodology evaluates all possible combinations of WTG locations inside a pre-defined wind park topology. When the number of WTGs and/or the number of sub-cells increase, the computational burden involved may render the problem virtually unfeasible. To overcome this limitation, optimization algorithms are commonly applied. These algorithms try to select the best element (with regard to some criteria) from a defined set of available alternatives. An objective function is maximized or minimized by systematically choosing input values from within an allowed set and computing the value of the function. In this work, GA and PSO were the used optimization techniques. The deterministic algorithm has been implemented and the results obtained served as a benchmark to assess the performance of GA and PSO. An 8 WTGs wind park with 4 sub-cells has been considered for validation purposes. The comparison resulted favourable, because both optimization algorithms reached very good approximations of the AEP exact result as calculated by the deterministic technique. In fact, in average terms (after 100 runs), the error associated to GA output is – 0.03% and –0.09% in the case of PSO, with respect to the deterministic solution. This shows how effective both methods are, because they
Fig. 11. Optimal layout for the case study with 18 WTGs (solid dark points) 25 sub-cells (light blue lines inside the rectangles). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Table 5 Comparison between three different targets: minimum electrical losses, maximum wind capture and optimal solution.
Electrical losses (MWh) Turbines production (GWh) AEP (GWh)
Minimum electrical losses
Maximum wind captured
Optimal
160.338
342.223
335.827
120.722
143.381
143.377
120.561
143.039
143.041
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produce very good AEP approximations, while reducing CPU time from 150 h to 2 h. Furthermore, the results obtained demonstrated that GA is able to reach reliable solutions more often than PSO. This ability is shown by the number of times GA reaches the very exact solution, which is higher than in the PSO case (54% against 12%). Still, the errors associated with runs in which an exact match has not been achieved are low: GA worst error in one run is –0.12% and PSO's worst error is –0.37%. This explains why the average AEP output results of both techniques are so similar. It is true that PSO converges to the optimum value in fewer iterations (reduced CPU times), but sometimes it gets “trapped” in local optimum being more ineffective in searching new optimal zones. On the other hand, once GA reaches a local optimum, the genetic operator mutation helps the algorithm to find solutions away from the current search zone, therefore enabling to find new best solutions. Then, a more realistic case-study (18 WTGs wind park) was implemented and assessed. An AEP increase of 1.24% with respect to the case in which the WTGs were placed at the centre of the cells was obtained when using the micro-siting approach proposed (25 sub-cells inside major cells). This increment may be even more significant if the micro-siting approach is used after an optimization of the cells dimensions. The proposed optimization concept and turbines positioning is very realistic and project friendly, as the WGTs are restrained to a small area (when compared to the entire wind park area) favouring the wind farm construction, not only the turbines and foundations, but mainly the submarine cable laying. In this work, the criteria against which optimization takes place is the wind farm's annual electricity production, or, in other terms, the capacity factor, which we want to maximize. Other criteria could be used, for instance, to minimize seasonal variations, that is, to keep the production as constant as possible, independently of the wind fluctuations. This can be achieved using a coupled BESS (Battery Energy Storage System), whose design could be approached using optimization techniques similar to the ones used in this paper. Acknowledgments This work was supported by national funds through Fundação para a Ciência e a Tecnologia (FCT) with reference UID/CEC/50021/2013. WavEC – Offshore Renewables is deeply acknowledged for providing the wind database. References Appiott, Joseph, Dhanju, Amardeep, Cicin-Sain, Biliana, 2014. Encouraging renewable energy in the offshore environment. Ocean Coast. Manag. 90, 58–64. http:// dx.doi.org/10.1016/j.ocecoaman.2013.11.001. Bilgili, Mehmet, Yasar, Abdulkadir, Simsek, Erdogan, 2011. Offshore wind power development in Europe and its comparison with onshore counterpart. Renew. Sustain. Energy Rev. 15 (2), 905–915. http://dx.doi.org/10.1016/ j.rser.2010.11.006. Clerc, Maurice, Kennedy, James, 2002. The particle swarm - explosion, stability, and convergence in a multidimensional complex space. IEEE Trans. Evolut. Comput. 6 (1), 58–73. http://dx.doi.org/10.1109/4235.985692. Corbetta, Giorgio, Mbistrova, Ariola, Ho, Andrew, Guillet, Jérôme, Pineda, Iván, 2015. The European offshore wind industry - key trends and statistics 2014. In: Proceedings of the Technical report, European Wind Energy Association. January. Dekker, Jos W.M., Pierik, J.T.G., 1998. European Wind Turbine Standards II: Executive Summary. Netherlands Energy Research Foundation ECN, (December). Dor, Abbas El, Clerc, Maurice, Siarry, Patrick, 2012. A multi-swarm PSO using charged particles in a partitioned search space for continuous optimization. Comput. Optim. Appl. 53 (1), 271–295. http://dx.doi.org/10.1007/s10589-011-9449-4.
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