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Wind wake influence estimation on energy production of wind farm by adaptive neuro-fuzzy methodology
Energy 80 (2015) 361e372
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Wind wake influence estimation on energy production of wind farm by adaptive neuro-fuzzy methodology Vlastimir Nikoli c a, Shahaboddin Shamshirband b, e, *, Dalibor Petkovi c a, si Cojba c a, Torki A. Altameem d, Abdullah Gani b Kasra Mohammadi c, Zarko University of Nis, Faculty of Mechanical Engineering, Deparment for Mechatronics and Control, Aleksandra Medvedeva 14, 18000 Nis, Serbia Department of Computer System and Technology, Faculty of Computer Science and Information Technology, University of Malaya, 50603 Kuala Lumpur, Malaysia c Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran d College of Computing & Information Science, King Saud University, Salah ElDin St., 28095, 11437 Riyadh, Saudi Arabia e Department of Computer Science, Chalous Branch, Islamic Azad University (IAU), 46615-397 Chalous, Iran a
b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 5 May 2014 Received in revised form 27 November 2014 Accepted 29 November 2014 Available online 6 January 2015
Dissection of the power output in a row of working turbines and the reliance on wind course in respect to the column heading is examined. The point is to portray the extent of the wake impacts and give a sign of the indication of wind bearing. The target is to delineate whether the uniting of wakes inside extensive wind homesteads can be depicted by basic direct models or whether the consideration of the two-route collaboration between the wind turbines and the limit layer is a fundamental essential for precise models of wakes to be utilized within future wind farm plan. Soft computing methodologies may be utilized as substitute for analytical approach since they provides some benefits such as no need to information of internal system parameters, compact solution for multi-variable problems. This investigation dealt with application of ANFIS (adaptive neuro-fuzzy inference system) for predicting the wake power and wind speed deficit. To provide statistical analysis, RMSE (root mean square error), coefficient of determination (R2) and Pearson coefficient (r) were utilized. The study results suggested that ANFIS would be an efficient soft computing methodology to offer precise predictions of wake wind speed deficit and power deficit ratio in wind farms. According to the achieved results, the best prediction was observed for free wind speed of 8 m/s. The RMSE, R2 and r were computed as 0.0763, 0.9893 and 0.9946 for ANFIS prediction of wake wind speed deficit and as 0.0128, 0.9967 and 0.9984 for ANFIS prediction of power deficit ratio. © 2014 Elsevier Ltd. All rights reserved.
Keywords: Wind energy Wake wind speed Wake model Wake effect ANFIS (adaptive neuro-fuzzy system)
1. Introduction Wind turbines extract energy from the wind to generate electricity. Hence, the wind behind the wind turbine will have lesser energy compared to the wind in front of the wind turbine. In other words, the wind downstream of wind turbines has reduced speed. This downstream wind is the wake of the turbine. In case, a wind turbine positioned in the wake of another turbine, it will generate lower electricity compared to undisturbed wind turbines. Formation of a wake has some negative consequences such as reducing the wind speed which subsequently decline the level of energy generated by the wind farm as well as amplifying the turbulence intensity which increase the dynamic mechanical loading * Corresponding author. Department of Computer System and Technology, Faculty of Computer Science and Information Technology, University of Malaya, 50603 Kuala Lumpur, Malaysia. Tel.: þ60 146266763. E-mail address: [email protected] (S. Shamshirband). http://dx.doi.org/10.1016/j.energy.2014.11.078 0360-5442/© 2014 Elsevier Ltd. All rights reserved.
on downwind turbines. In order to explain a wake, a substantial number of numerical methods have been suggested so far. lez-Longatt et al. [1] developed a simplified model to appraise Gonza the influence of wake on steady-state and dynamic behaviors of two wind farms. Song et al. [2] suggested a particle model to consider the wake flow as virtual particles produced by the wind turbine blades. It was found that the proposed model shows further accuracy on flat terrain compared to the previous linear model. Vermeer et al. [3] studied the aerodynamics of horizontal axis wind turbine wakes for two near and far wake regions. Makridis and JohnChick [4] by means of Fluent software developed a CFD model to investigate the wind turbine wakes and the neutral atmospheric wind flow over complex terrain. Crasto et al. [5] utilized the concept of actuator disc for modeling the wakes of wind turbines. Mo et al. [6] performed Large eddy simulation to identify the wake characteristics. They compared the results experimental results of wind turbines. Precise prediction of power losses from wind turbine wakes in large wind farms has not conducted conclusively. Even though,
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there exist several approaches for modeling the power losses raised by wind turbine wakes in large wind farms, further appraisal and enhancement is still requisite. Absence of reliable and proper data for assessment, limited application of evaluation metrics to measure the models' capability as well as imperfect efforts made at attribution of models error are the most notable issues which have provided limitation on models enhancement. It is evident that wake of wind farm models have not been evaluated for very large wind farms. Since the combination of single wakes is the current approach to modeling wakes within offshore wind farms, there is major uncertainty in these predictions of wake interactions. This paper introduces an examination focused around a lot of information from an extensive wind farm in operation. Investigation of the power yield consecutively of working turbines and the reliance on wind course in respect to the column bearing is examined. The point is to depict the greatness of the wake impacts and give a sign of the indication of wind heading. A piece of the paper includes improvement of a model focused around the systematic arrangements of wake advancement portrayed by a few routines. The destination is to show whether the combining of wakes inside huge wind ranches can be portrayed by straightforward direct models or whether the incorporation of the two-route cooperation between the wind turbines and the limit layer is a fundamental essential to precise modeling of wakes for utilization as a part of future wind homestead plan. Physical modeling of wake effects in large wind farm demands high costs to model the prototype and requires extensive work in the laboratory [7]. For the first time, this paper presents and compares the results of wake wind speed deficit and power deficit ratio prediction in large wind farm using soft computing methodology; to date, no such work has been carried out in this area. Recently, soft computing techniques such as SVR (support vector regression) with mimetic algorithm has gained importance in electrically load forecasting issue [8]. An application of soft computing by combining different approaches including wavelet and firefly algorithms as well as fuzzy ARTMAP to predict dayahead electricity price was presented in Ref. [9]. Prediction of short-term load of power systems was conducted in Ref. [10] by developing a hybrid wavelet transform with neuro-evolutionary model. In study [11], a novel modeling framework integrating BEMD (bivariate empirical mode decomposition) and SVR (support vector regression), extended from the well-established EMD (empirical mode decomposition) based time series modeling framework in the energy demand forecasting literature, was proposed for interval forecasting of electricity demand. The correctness of a soft computing model is to a great extent relies on determination of its model parameters. Although organized strategies for selecting parameters are important, model parameter alignment also need to be made. Computational complexity is a major drawback of wake modeling approaches in large wind farm. In this paper, a soft-computing methodology (adaptive neurofuzzy inference system - ANFIS (application of adaptive neurofuzzy inference system)) [12] has been proposed for wake wind speed deficit and power deficit ratio prediction in wind farm according to wind turbine row number in wind farm and wind direction and for three free wind speeds: 6 m/s, 8 m/s and 10 m/s. The proposed ANFIS model is obtained with the combination of the two methods, neural network and fuzzy logic. The neural network searches the optimal parameters for fuzzy logic membership functions thus giving more reliable and accurate forecasts. The suggested combination of methodologies is new and unique which boost the capability of the suggested model compared to those models previously presented in the literature. The ANFIS models are designed based on experimental data and three analytical
methods of calculating the wake effect: N.O. Jensen [12], Eddy Viscosity Model [13e16] and G.C. Larsen [17,18]. In other words the ANFIS model should estimates average wake power deficit in wind farm based on the established analytical models. 2. Materials and methods Power losses because of turbine wakes in extensive offshore wind farms are anticipated by condition of-the-craftsmanship models to be of the request 10e20% and thus is a critical segment of the general money making concerns of these wind ranches. To build the understanding of the wake impacts from substantial wind farms various undertakings are currently being completed with the reason for depicting and evaluating wakes. Owing to the fact that economical aspect is a crucial driver in this venture, an improved capacity to anticipate wake losses would certainly augment the viability of expansive wind farms. Power losses raised by wakes were examined on the basis of observations from wind farm depicted schematically in Fig. 1. The wind farm data were utilized to appraise all models to the parameterization of wake addition/expansion as the wake develops directly down a row of wind turbines. The adapted databases are utilized to determine the downstream influence of several wind farms, and screen the in-park wake impacts. In parallel to the information examination, wind farm models are certainly created and assessed. The wake models include many variables such as the turbine introduction and separating, wind atmosphere as well as turbine sort. 2.1. Wake effect models Whenever, the turbine concentrates power from the wind, a wake is developed downstream of the turbine. Provided that an alternate adjacent turbine is working inside this wake, the power generated from this downstream turbine is declined in comparison to the turbine working in the free wind. The obtained loss of power which is typically in the range 2%e20% is contingent upon a series of factors including the wind dispersion, the wind turbine attributes and the wind ranch geometry. The turbines operating in the wake flow of others are confronted with a diminished wind speed as well as expanded element stacking emerging from the expanded turbulence incited by the upstream turbines. This expanded turbulence should be considered, when selecting a suitable class of turbine. In case of having different turbines, the achieved results by the single wake simulation are amassed into a consolidated come about by utilizing exact consolidation standards. 2.2. Parameters required for modeling the wake The wake models require distinctive inward wake model parameters as info and a shifting number of extra parameters depicting the landscape and wind atmosphere conditions. Info parameters for a wake model may usually be turbulence force and harshness length. Commonly, such parameters are dependent upon the harshness class (or roughness length). Table 1 suggests corresponding estimated wake model parameters [19e21]. 2.3. N.O. Jensen wake model The N.O. Jensen wake model, which is based upon the assumption of a linearly expanding wake diameter, is a simple single wake model [12]. Fig. 2 schematically illustrates the overview of N.O. Jensen wake model which it is seen that the wake is expand linearly with downstream distance, X. There is a
V. Nikolic et al. / Energy 80 (2015) 361e372
363
Fig. 1. Segment of the wind farm layout.
relationship between R1 and X such that, as it is clear from Fig. 2, R1 increases linearly with increasing X. Fig. 3 shows a possible layout of three wind turbines in a wind farm. The two upper turbines affect the bottom wind turbine by two wakes. The multiple partial interference of the wake effects from the two upstream turbines occurred, as it shown in Fig. 3. The calculation of the overall wind speed at the downstream turbine is done using Eq. (1).
To calculate the wind speed after the two wind turbine rotor, as it illustrated in Fig. 3, following equation is utilized: where: u0 is the free stream wind speed considered in this equal to 12 m/s, a is the axial induction factor computed from the thrust coefficient, CT via the following expression:
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 u0 12 0 12 u u C B uB B B C C C uB C B B C C uB B B C C C uB B B C C C uB C B B C C uB B B C C C uB C B B C C 2a 2a uB B B C C C ¼ ui *B1 uB C þB C C 1 1 0 0 2 2 u B B C C C uB B B C C C uB B B C C C C C B B uB B B B C C C C C B B X X u B B1 þ aB C C C 1 þ aB rffiffiffiffiffiffiffiffiffiffiffiffiffiffi!C rffiffiffiffiffiffiffiffiffiffiffiffiffiffi!C uB B B B C C C C C B B u@ B @ @ @ 1a A A 1a A A C t A @ Rr Rr 1 2a 1 2a 0
uiþ1
i ¼ 0; 1…:N
(1)
V. Nikolic et al. / Energy 80 (2015) 361e372
364 Table 1 Wake model parameters [19,20]. Terrain classification
Roughness class
Roughness length
Wake decay constant
Ambient turbulence at 50 m
Additional detailed description
Offshore. Water areas Mixed water and land Very open farmland Open farmland Mixed farmland. Trees and farmland Forests and villages Large towns and cities Large build up cities
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
0.0002 0.0024 0.03 0.055 0.10 0.20 0.40 0.80 1.60
0.040 0.052 0.063 0.075 0.083 0.092 0.100 0.108 0.117
0.06 0.07 0.10 0.11 0.12 0.13 0.15 0.17 0.21
Water areas, oceans and large lakes. General water bodies. Mixed water and land. Also applies to the very smooth terrain No crossing hedges. Scattered buildings. Smooth hills. Some buildings. Crossing hedges with 8 m height with distance 1250 m apart. Some buildings. Crossing hedges 8 m high with distance 800 m apart Closed appearance. Dense vegetation. 8 m hedges 250 m apart. Villages, small towns and much closed farmland. Many high hedges. Forests. Large towns, cities with extended build up areas. Large cities with build up areas and high buildings.
a¼
0:5 ln zz0
(4)
z and z0 are hub height and surface roughness, respectively. The value of surface roughness is variable according to the terrains. For plain terrains, the surface roughness is considered equal to 0.3. 2.4. Eddy viscosity model In Ref. [13], for the first time, an axi-symmetric formulation of the time averaged NS (Navier Stokes) equations with an eddy viscosity closure was applied to model the wind turbine wake. For this application, the cylindrical coordinates under assumption of incompressible fluid is utilized. The continuity equation in cylindrical coordinates can be written as [14]:
1 vrv vu þ ¼0 r vr vx
In the thin layer approximation and using cylindrical coordinates, the NS equation is presented by:
Fig. 2. Schematic of N.O. Jensen wake model.
CT ¼ 4að1 aÞ
(2) u
X is the downstream distance of the turbine. The relationship between R1 and Rr can be presented by:
R1 ¼ Rr
(5)
rffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1a 1 2a
vu vu 1 vðruvÞ þv ¼ vx vr r vr
The near wake length is represented by combination of ambient turbulence, rotor generated turbulence and shear generated turbulence [16] and is divided into two regions which the first xh may formulated by:
(3)
" xh ¼ r0
a is the entertainment obtained by the following equation:
(6)
2 2 #0:5 dr 2 dr dr þ þ dx a dx l dx m
r0 is ‘effective’ radius of expanded rotor disc obtained by:
Fig. 3. Interferences of the wake effects.
(7)
V. Nikolic et al. / Energy 80 (2015) 361e372
r0 ¼ ½D=2
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðm þ 1Þ=2
(8)
Rw ¼
and m is aerodynamic coefficient:
.pffiffiffiffiffiffiffiffiffiffiffiffiffi m¼1 1 Ct
(9)
2
¼
a
(10)
where
The c1 parameter partly separates the rotor drag dependence [9]. Therefore, c1 is expected to be relative insensitive to the design and size of the rotor:
D is the rotor diameter. The components of Eq. (7) are computed as:
dr dx
1=5 h i1=5 2c21 ½CT Ax1=3
c1 is a non-dimensional mixing length, defined by c1 ¼ l[CTAx]1/3 l is Prandtl's mixing length
where
35 2p
365
c1 ¼
2:5I þ 0:05 for I 0:02 5I for I < 0:02
ambient turbulence
1=2 D ½CT Ax0 5=6 2
(11)
where
2
dr dx
l
¼ 0:012Bl
rotor generated turbulence
h pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffii dr 2 ¼ ð1 mÞ 1:49 þ m dx m . ð9:76ð1 þ mÞÞ shear generated turbulence
where
A is the rotor area D is the diameter of the upstream rotor x0 is an approximation parameter, determined by the Equation (12) below
x0 ¼ 9:5D
2R9:5 3 1 D
(12)
The mean wind deficit is determined from the expression (13),
( i1=3
1=2 ua h CT Ax2 Du ¼ r 3=2 3c21 CT Ax 9 ) 3=10
1=5 2 35 2 3c1 2p
I is the ambient turbulence intensity B is the number of rotor blades l is the tip speed ratio
2.5. G.C. Larsen model
(13)
where
G.C. Larsen model [17], as another suggested wake model, is a semi analytical model derived on the basis of Prandtl's rotational symmetric turbulent boundary layer equations. Due to the asymptotic expressions, the model may be sort of conservative for close spacing. Considering similarity between deficits at different downstream positions and only moderate velocity deficits, the wake radius may then be represented using the following relation:
ua is the ambient mean wind velocity at hub height. 2.6. Validation of the wake effect models As can be seen in Fig. 4, the mixed farmland terrain seems to have the largest wake power speed deficit for the three presented wake models. It seems the class of N.O. Jensen wake models has the
Wake models calculation in comparison to measured energy 8
Eddy Viscosity
Wake power deficit [%]
7 6 G.C. Larsen
5
N.O. Jensen
Mixed water/land
4
Very open farmland
3
Open farmland
2
Mixed farmland
1 0 0.5
1
1.5
2 2.5 Wake models
3
3.5
Fig. 4. Wake models for different wind farm terrains.
V. Nikolic et al. / Energy 80 (2015) 361e372
366
Wake wind speed deficit 11 2°
10°
20°
30°
Wind speed deficit [m/s]
10 9
Experiment-1
8
Experiment-2 Experiment-3
7 6
5 0
5
10 15 20 Experimental samples
25
30
Fig. 5. Wake wind speed deficit for different wind input angles and wind turbine position.
best match of the measured wake data i.e. the smallest wake wind power deficit was for the N.O. Jensen wake models. However, the G.C. Larsen model and especially the Eddy Viscosity wake model seem to overestimate the wake losses quite a bit. The reason for this over-estimation could be that neither of the wake models do include a model for wake meandering. 2.6.1. Experimental validation of wake effect The rows 1 through 8 in the wind farm are analyzed using a 0e30 input wind sector. In Fig. 1 is depicted wind farm with input wind direction of 0 . The wind speed was considered between 6 and 10 m/s since this is the wind speed interval which generates relatively high power. The multiple partial interference of the wake effects from the two upstream turbines occurred as it shown in Fig. 3. The calculation of the overall wind speed at the downstream turbine was conducted via Eq. (1).
The measured wake effect is plotted for relative power drop of each turbine in the row as it shown in Figs. 5 and 6 for three experiments which amount of wind speeds are: Experiment-1: 6 m/s, Experiment-2: 8 m/s, Experiment-3: 10 m/s. Clearly, the biggest relative power drop is seen from column 1 to line 2, though the force drop from line 2 to column 8 is lower compared to the initial 2 columns. Other than watching the mean esteem down the line of turbines it is truly intriguing that the standard deviation of the results is expansive for all cases. This demonstrates that the results cover altogether various circumstances. There exists a few conceivable purposes behind the vast deviations and these ought to be checked separately (turbulence,
Wake rower deficit ratio 1.1 2°
10°
20°
30°
Power deficit ratio
1 0.9 Experiment-1
0.8
Experiment-2 Experiment-3
0.7 0.6 0.5 0
5
10 15 20 25 Experimental samples
30
Fig. 6. Wake power deficit ratio for different wind input angles and for different wind turbine position.
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367
Fig. 7. ANFIS structure.
wind shear and wind bearing reliance). This may be due to the fact that the results cover more than one wonder or physical state of the wake.
2.7. Adaptive neuro-fuzzy inference system ANFIS models are developed in this research work for estimation of the reduced wind speed and power deficit ratio of the wind turbines in wind farm in relation to the turbine position in the wind farm and wind input angle. For the present study the experimental data was used for training and checking of the ANFIS networks. Fig. 7 shows an ANFIS structure with two inputs: wind turbine row and wind input angle. For this research, the first-order Sugeno model with two inputs and fuzzy IF-THEN rules of Takagi and Sugeno's type is utilized:
if x is A and y is C and z is E then f1 ¼ p1 x þ q1 y þ r1 z þ t
(14)
The 1st layer is comprised of two input variables MFs (membership functions), named as input 1 and input 2. Its function is providing the input values for the next layer. In this study, the inputs are wind turbine position in wind farm (row number) and wind input angle. In the first layer every node is an adaptive node with a node function
O ¼ mðxÞ; where m(x)i are MFs. In this paper, bell-shaped MFs (3) with maximum equal to 1 and minimum equal to 0 is chosen
1 2b
f ðx; a; b; cÞ ¼ 1þ
wi ¼ mðxÞi *mðxÞiþ1
In the 3rd layer, named as the rule layer, every node (neuron) function is conducting the pre-condition matching of the fuzzy rules, Every node in the 3rd layers computes the weights which are normalized. Nodes in the 3rd layer, similar to the 2nd layer, are non-adaptive and they computes the ratio of the rule's firing strength to the sum of all rules' firing strengths like
w*i ¼
wi w1 þ w2
(17)
i ¼ 1; 2: The 3rd layer's outputs are named normalized firing strengths or normalized weights. The next or 4th layer (defuzzification layer), which its nodes are adaptive node with node function, offers the output values resulting from the inference of rules.
O4i ¼ w*i xf ¼ w*i ðpi x þ qi y þ ri Þ
(18)
where {pi, qi,r} is the parameter set and in this layer is referred to as consequent parameters. Here {pi, qi,r} represents the parameter set which in the 4th is referred as consequent parameters. The 5th layer (output layer) sums up all the inputs coming from the 4th layer and transforms the results of fuzzy classification to a crisp (binary). Here the nodes same as the 2nd and 3rd layers are
(15)
xc a
The bell-shaped function depends on three parameters a, b and c. The parameter b is usually positive. As it is illustrated in Fig. 8, c is located at the center of the curve. In the 2nd layer, which is also called membership layer, the weights of each MFs is checked. The 1st layer provides the input values for this layer so that it can performs as MFs for representing the fuzzy sets of the respective input variables. Unlike the 1st layer, the nodes are non-adaptive in this layer. The 2nd layer's functions is multiplying the incoming signals and sending the product out like
(16)
Fig. 8. Bell-shaped membership function (a ¼ 2, b ¼ 4, c ¼ 6).
V. Nikolic et al. / Energy 80 (2015) 361e372
368 Table 2 Statistical parameters for data sets. Variable
Statistical parameters
Wind row number Wind direction
Min
Max
Mean
1 2
8 30
4.5 16
not-adaptive and their function is calculating the overall output as the sum of all incoming signals
O4i
¼
X i
w*i xf
P wf ¼ Pi i i wi
(19)
2.8. Model performance evaluation
Fig. 10. Simulink block diagram for estimation of the wind speed deficit and power deficit ratio.
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn 2 i¼1 ðPi Oi Þ ; RMSE ¼ n
(20)
To assess the proficiency of the ANFIS model some statistical indicators were examined as follows: 1) RMSE (root-mean-square error)
2) Pearson correlation coefficient (r)
Pn Pn Pn $ n O $P O P i i i i i¼1 i¼1 i¼1 r ¼ vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u 2 2 u P Pn t n Pn O2 Pn O $ n ni¼1 P 2i i¼1 i i¼1 i i¼1 Pi (21) 3) coefficient of determination (R2)
"
Pn i¼1 Oi Oi $ Pi Pi
R2 ¼ P n i¼1
#2
P
Oi Oi $ ni¼1 Pi Pi
(22)
where Pi and Oi are known as the experimental and forecast values, respectively, while Pi and Oi are the mean value of Pi and Oi, respectively and n is the total number of test data. 3. Results 3.1. Input parameters Experimental work was conducted to study the effects of the wake in order to study wind speed deficit and power deficit ration in wind farm. The capability of the ANFIS to provide favorable estimations is reliant upon input parameter selection. In this study, 2 input parameters (wind turbine row number in wind farm and wind direction) were used for generating ANFIS model. The data were collected for three free wind speeds: 6 m/s, 8 m/s and 10 m/s. Some statistical parameters consisting minimum, maximum and mean values obtained for the 2 input parameters are presented in Table 2. 3.2. ANFIS models Fig. 9. ANFIS predicted relationships between wind turbine row number in wind farm, wind input angle and wind speed deficit (a) and power deficit ratio (b).
There are two ANFIS networks, one for wake wind speed deficit estimation and on for wake power deficit estimation. At the
V. Nikolic et al. / Energy 80 (2015) 361e372
Fig. 11. Scatter plots of measured and predicted values of wind speed deficit using ANFIS model for wind speed of (a) 6 m/s, (b) 8 m/s and (c) 10 m/s.
beginning the ANFIS networks were trained with the experimental data presented in Figs. 5 and 6 and in Table 2. The ANFIS networks determine wake wind speed and power deficit based on the experimental measurements for different number of turbines row and for different input wind angle. Three bell-shaped membership functions were used to fuzzily the ANFIS inputs. The final decision surfaces after ANFIS training are shown in Fig. 9 (a) and (b). The wind speed deficit after the rotor or wake wind speed as function of the wind turbine row number in wind farm and wind input angle is implemented in MATLAB Simulink block diagram as it shown in Fig. 10. At the same time, the power deficit ration as function of the wind turbine row number in wind farm and wind
369
Fig. 12. Scatter plots of measured and predicted values of power deficit ratio using ANFIS model for wind speed of (a) 6 m/s, (b) 8 m/s and (c) 10 m/s.
input angle is also implemented in the Simulink block diagram. For example, for wind turbine row number 5 in wind farm and for wind input angle 10 , ANFIS estimates the wind speed after the rotor or wake wind speed 7.031 m/s and power deficit ratio is 0.678. Since mean wind speed or free stream wind speed in front of wind farm is 8 m/s it means the percentage of the wind speed deficit is 12%. This approach is very useful for quick prediction of the wake wind speed and power deficit ratio for every wind input angle and row in the wind farm. 3.3. ANFIS models analysis At the beginning, the ANFIS networks were trained with measured data by above presented experimental procedure. After
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370
Wake power deficit ratio 1.1 2°
Power deficit ratio
1
10°
20°
30°
0.9 Experiment-1
0.8
Experiment-2 Experiment-3
0.7
ANFIS
0.6 0.5 0
5
10 15 20 Experimental samples
25
30
(b) Fig. 13. ANFIS predictions for: (a) wind speed deficit and (b) power deficit ratio.
training process the ANFIS networks were tested to determine the wake wind speed deficit and power deficit ratio for different effective wind speed. Based on the experiments, the input parameters (wind turbine row number in wind farm and wind direction) and outputs (wake wind speed deficit and power deficit ratio) are collected and defined for the learning technique. The prediction results of the wake wind speed deficit and power deficit ration is represented in Figs. 11 and 12 for three experiments according to the free wind speed. According to Figs. 11 and 12, it is observed that the most of the points fall along the diagonal line. Consequently, it is clear that the predicted wake wind speed deficit and power deficit ratio enjoy very good agreement with the measured values for ANFIS method. Wake wind speed deficit predictions are not as good as power deficit ratio predictions according to the coefficient of determination R2. Also the best correlation
occurs for free wind speed of 8 m/s for wake wind speed and power deficit ration prediction. It is crystal clear that there is a favorable level of agreement between measured and estimated values by the proposed ANFIS model. ANFIS expectations against the test information are indicated in Fig. 13 for wind speed deficit and power deficit ratio respectively. The results demonstrate that there is a critical change in the wake impact when the wind is restricted to being parallel to the line bearing. The force drop from line 1 to column 2 has expanded from a normal estimation of pretty nearly 0.2 to around 0.3. This demonstrates that the expansive force drops between the initial two turbines just happens in an extremely limited part around the line bearing. At other wind bearings the force drop is essentially more modest from line 1 to column 2. For the remaining turbines the example is just about the same for the two investigates: the force
V. Nikolic et al. / Energy 80 (2015) 361e372 Table 3 Performance statistics of the ANFIS model for wake wind speed deficit estimation based upon different statistical indicators.
Wind speed 6 m/s Wind speed 8 m/s Wind speed 10 m/s
RMSE
R2
r
1.7279 0.0763 1.7908
0.9867 0.9893 0.9863
0.9933 0.9946 0.9931
371
large wind farms. Since the used training data for the ANFIS network for the wake deficit and power deficit ratio prediction is not time-series data, the obtained results are one step-ahead prediction. Furthermore, for future research the prediction can be expanded with time-series data and to include multi step-ahead prediction like in articles [24e28]. Acknowledgment
Table 4 Performance statistics of the ANFIS model for power deficit ratio estimation based upon different statistical indicators.
Wind speed 6 m/s Wind speed 8 m/s Wind speed 10 m/s
RMSE
R2
r
0.0141 0.0128 0.0113
0.9938 0.9967 0.9909
0.9969 0.9984 0.9954
drop from column 2 to line 8 is somewhere around 0.15 and 0.2, which happens in a very nearly straight line. The conclusion to this distinction between wake impacts for stream parallel to the column and wind course being marginally off the line bearing is that a wake model must have the capacity to give altogether diverse results for even little alters in wind course. At the point when making another wake model it must be chosen whether it ought to have the capacity to foresee all circumstances or basically can display the mean comes about effectively. This obviously is inquiry of the motivation behind the model. 3.4. Performance analysis In order to demonstrate the merit of the proposed ANFIS model, on a more definite and tangible basis, to estimate the wake wind speed deficit and power deficit ratio, three statistical indicators of RMSE (root-mean-square error), r and R2 were calculated and the achieved results presented in Tables 3 and 4, respectively. This verifies the achieved and discussed aforementioned results from the presented figures, especially in terms of precise estimation. The results convincingly confirm that the proposed ANFIS model can be utilized for estimation of wake wind speed deficit and power deficit ratio with favorable level of reliability and preciseness. 4. Conclusion In this research work, a soft-computing methodology (adaptive neuro-fuzzy inference system-ANFIS [22,23]) has been proposed for prediction of wake wind speed deficit and power deficit ratio in wind farm according to wind turbine row number in wind farm and wind direction and for three free wind speeds: 6 m/s, 8 m/s and 10 m/s. The proposed ANFIS model is the combination of neural network and fuzzy logic. The neural network searches the optimal parameters for fuzzy logic membership functions thus giving more reliable and accurate forecasts. This proposed combination of methodologies is unique and thus has enhanced the performance of the proposed model compared with the other earlier developed models. The achieved results clarified that the best prediction is observed for free wind speed of 8 m/s based upon RMSE, R2 and r, which are 0.0763, 0.9893 and 0.9946, respectively for ANFIS prediction of wake wind speed deficit and are 0.0128, 0.9967 and 0.9984, respectively for ANFIS prediction of power deficit ratio. As a consequence, ANFIS can be considered as an efficient soft computing methodology to offer precise results in wake wind speed deficit and power deficit ratio prediction in wind farm. The analyses in this paper showed that the wind direction is very important for the wake effect and wind energy decreasing in
This paper is supported by Project Grant ТР35005 “Research and development of new generation wind turbines of high-energy efficiency” (2011e2015) financed by Ministry of Education, Science and Technological Development, Republic of Serbia. References lez-Longatt F, Wall P, Terzija V. Wake effect in wind farm performance: [1] Gonza steady-state and dynamic behavior. Renew Energy 2012;39:329e38. [2] Song MX, Chen K, He ZY, Zhang X. Wake flow model of wind turbine using particle simulation. Renew Energy 2012;41:185e90. [3] Vermeer LJ, Sorensen JN, Crespo A. Wind turbine wake aerodynamics. Prog Aerosp Sci 2003;39:467e510. [4] Makridis A, Chick J. Validation of a CFD model of wind turbine wakes with terrain effects. J Wind Eng Ind Aerodyn 2013;123:12e29. [5] Crasto G, Gravdahl AR, Castellani F, Piccioni E. Wake modeling with the actuator disc concept. Energy Procedia 2012;24:385e92. [6] Mo J-O, Choudhry A, Arjomandi M, Lee Y-H. Large eddy simulation of the wind turbine wake characteristics in the numerical wind tunnel model. J Wind Eng Ind Aerodyn 2013;112:11e24. [7] Sanderse B, Van Der Pijl SP, Koren B. Review of computational fluid dynamics for wind turbine wake aerodynamics. Wind Energy 2011;14:799e819. http:// dx.doi.org/10.1002/we.458. [8] Hu Zhongyi, Bao Yukun, Xiong Tao. Electricity load forecasting using support vector regression with memetic algorithms. Sci World J 2013;2013:10. Article ID 292575. [9] Haque AU, Meng Julian, Srivastava AK, Martinez R. A novel hybrid approach using wavelet, firefly algorithm, and fuzzy ARTMAP for day-ahead electricity price forecasting. Power Systems IEEE Trans 2013;28(2):1041e51. http:// dx.doi.org/10.1109/TPWRS.2012.2222452. [10] Amjady N, Keynia F. Short-term load forecasting of power systems by combination of wavelet transform and neuro-evolutionary algorithm. Energy 2009;34:46e57. http://dx.doi.org/10.1016/j.energy.2008.09.020. [11] Xiong T, Bao Y, Hu Z. Interval forecasting of electricity demand: a novel bivariate EMD-based support vector regression modeling framework. Int J Electr Power Energy Syst 2014;63:353e62. http://dx.doi.org/10.1016/ j.ijepes.2014.06.010. Nikoli si [12] Petkovi c D, Cojba c Z, c V. Adaptive neuro-fuzzy approach for wind turbine power coefficient estimation. Renew Sustain Energy Rev 2013;28: 191e5. http://dx.doi.org/10.1016/j.rser.2013.07.049. [13] Kati c I, Højstrup J, Jensen NO. A simple model for cluster efficiency, European Wind Energy Association, Conference and Exhibition, 7e9 October 1986, Rome, Italy. [14] Ainslie JF. Calculating the flowfield in the wake of wind turbines. J Wind Eng Ind Aerodyn 1988;27:213e24. [15] Shames Irving H. Mechanics of fluids. McGraw-Hil International Editions; 1992. [16] Tennekes H, Lumley JL. A first course in turbulence. The MIT Press; 1972. [17] Vermeulen PEJ. An experimental analysis of wind turbine wakes. In: Proceedings of the International Symposium on Wind Energy Systems, Lyngby; 1980. [18] Larsen GC, Højstrup J, Madsen HA. Wind fields in wakes. In: EUWEC ’96, Gothenburg; 1996. [19] ECN-C-99e073 European wind turbine standards II. 1999. [20] Guidelines for design of wind turbines, DNV/Risø, 2nd ed.: Risø National Laboratory. [21] Morten Lybech Thøgersen. Introduction to wind turbine wake modelling and wake generated turbulence, DNV/Risø, 2nd ed.: Risø National Laboratory, EMD International A/S. [22] Shamshirband S, Petkovic D, Hashim R, Motamedi S, Anuar NB. An appraisal of wind turbine wake models by adaptive neuro-fuzzy methodology. Int J Electr Power Energy Syst 2014;63:618e24. [23] Shamshirband S, Petkovic D, Hashim R, Motamedi S. Adaptive neuro-fuzzy methodology for noise assessment of wind turbine. PloS One 2014;9(7): e103414. [24] Bao Yukun, Xiong Tao, Hu Zhongyi. Multi-step-ahead time series prediction using multiple-output support vector regression. Neurocomputing 10 April 2014;129:482e93. [25] Ben Taieb Souhaib, Bontempi Gianluca, Atiya Amir F, Sorjamaa Antti. A review and comparison of strategies for multi-step ahead time series forecasting
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based on the NN5 forecasting competition. Expert Syst Appl 15 June 2012;39(8):7067e83. [26] Xiong Tao, Bao Yukun, Hu Zhongyi. Beyond one-step-ahead forecasting: evaluation of alternative multi-step-ahead forecasting models for crude oil prices. Energy Econ November 2013;40:405e15.
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Energy journal homepage: www.elsevier.com/locate/energy
Wind wake influence estimation on energy production of wind farm by adaptive neuro-fuzzy methodology Vlastimir Nikoli c a, Shahaboddin Shamshirband b, e, *, Dalibor Petkovi c a, si Cojba c a, Torki A. Altameem d, Abdullah Gani b Kasra Mohammadi c, Zarko University of Nis, Faculty of Mechanical Engineering, Deparment for Mechatronics and Control, Aleksandra Medvedeva 14, 18000 Nis, Serbia Department of Computer System and Technology, Faculty of Computer Science and Information Technology, University of Malaya, 50603 Kuala Lumpur, Malaysia c Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran d College of Computing & Information Science, King Saud University, Salah ElDin St., 28095, 11437 Riyadh, Saudi Arabia e Department of Computer Science, Chalous Branch, Islamic Azad University (IAU), 46615-397 Chalous, Iran a
b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 5 May 2014 Received in revised form 27 November 2014 Accepted 29 November 2014 Available online 6 January 2015
Dissection of the power output in a row of working turbines and the reliance on wind course in respect to the column heading is examined. The point is to portray the extent of the wake impacts and give a sign of the indication of wind bearing. The target is to delineate whether the uniting of wakes inside extensive wind homesteads can be depicted by basic direct models or whether the consideration of the two-route collaboration between the wind turbines and the limit layer is a fundamental essential for precise models of wakes to be utilized within future wind farm plan. Soft computing methodologies may be utilized as substitute for analytical approach since they provides some benefits such as no need to information of internal system parameters, compact solution for multi-variable problems. This investigation dealt with application of ANFIS (adaptive neuro-fuzzy inference system) for predicting the wake power and wind speed deficit. To provide statistical analysis, RMSE (root mean square error), coefficient of determination (R2) and Pearson coefficient (r) were utilized. The study results suggested that ANFIS would be an efficient soft computing methodology to offer precise predictions of wake wind speed deficit and power deficit ratio in wind farms. According to the achieved results, the best prediction was observed for free wind speed of 8 m/s. The RMSE, R2 and r were computed as 0.0763, 0.9893 and 0.9946 for ANFIS prediction of wake wind speed deficit and as 0.0128, 0.9967 and 0.9984 for ANFIS prediction of power deficit ratio. © 2014 Elsevier Ltd. All rights reserved.
Keywords: Wind energy Wake wind speed Wake model Wake effect ANFIS (adaptive neuro-fuzzy system)
1. Introduction Wind turbines extract energy from the wind to generate electricity. Hence, the wind behind the wind turbine will have lesser energy compared to the wind in front of the wind turbine. In other words, the wind downstream of wind turbines has reduced speed. This downstream wind is the wake of the turbine. In case, a wind turbine positioned in the wake of another turbine, it will generate lower electricity compared to undisturbed wind turbines. Formation of a wake has some negative consequences such as reducing the wind speed which subsequently decline the level of energy generated by the wind farm as well as amplifying the turbulence intensity which increase the dynamic mechanical loading * Corresponding author. Department of Computer System and Technology, Faculty of Computer Science and Information Technology, University of Malaya, 50603 Kuala Lumpur, Malaysia. Tel.: þ60 146266763. E-mail address: [email protected] (S. Shamshirband). http://dx.doi.org/10.1016/j.energy.2014.11.078 0360-5442/© 2014 Elsevier Ltd. All rights reserved.
on downwind turbines. In order to explain a wake, a substantial number of numerical methods have been suggested so far. lez-Longatt et al. [1] developed a simplified model to appraise Gonza the influence of wake on steady-state and dynamic behaviors of two wind farms. Song et al. [2] suggested a particle model to consider the wake flow as virtual particles produced by the wind turbine blades. It was found that the proposed model shows further accuracy on flat terrain compared to the previous linear model. Vermeer et al. [3] studied the aerodynamics of horizontal axis wind turbine wakes for two near and far wake regions. Makridis and JohnChick [4] by means of Fluent software developed a CFD model to investigate the wind turbine wakes and the neutral atmospheric wind flow over complex terrain. Crasto et al. [5] utilized the concept of actuator disc for modeling the wakes of wind turbines. Mo et al. [6] performed Large eddy simulation to identify the wake characteristics. They compared the results experimental results of wind turbines. Precise prediction of power losses from wind turbine wakes in large wind farms has not conducted conclusively. Even though,
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there exist several approaches for modeling the power losses raised by wind turbine wakes in large wind farms, further appraisal and enhancement is still requisite. Absence of reliable and proper data for assessment, limited application of evaluation metrics to measure the models' capability as well as imperfect efforts made at attribution of models error are the most notable issues which have provided limitation on models enhancement. It is evident that wake of wind farm models have not been evaluated for very large wind farms. Since the combination of single wakes is the current approach to modeling wakes within offshore wind farms, there is major uncertainty in these predictions of wake interactions. This paper introduces an examination focused around a lot of information from an extensive wind farm in operation. Investigation of the power yield consecutively of working turbines and the reliance on wind course in respect to the column bearing is examined. The point is to depict the greatness of the wake impacts and give a sign of the indication of wind heading. A piece of the paper includes improvement of a model focused around the systematic arrangements of wake advancement portrayed by a few routines. The destination is to show whether the combining of wakes inside huge wind ranches can be portrayed by straightforward direct models or whether the incorporation of the two-route cooperation between the wind turbines and the limit layer is a fundamental essential to precise modeling of wakes for utilization as a part of future wind homestead plan. Physical modeling of wake effects in large wind farm demands high costs to model the prototype and requires extensive work in the laboratory [7]. For the first time, this paper presents and compares the results of wake wind speed deficit and power deficit ratio prediction in large wind farm using soft computing methodology; to date, no such work has been carried out in this area. Recently, soft computing techniques such as SVR (support vector regression) with mimetic algorithm has gained importance in electrically load forecasting issue [8]. An application of soft computing by combining different approaches including wavelet and firefly algorithms as well as fuzzy ARTMAP to predict dayahead electricity price was presented in Ref. [9]. Prediction of short-term load of power systems was conducted in Ref. [10] by developing a hybrid wavelet transform with neuro-evolutionary model. In study [11], a novel modeling framework integrating BEMD (bivariate empirical mode decomposition) and SVR (support vector regression), extended from the well-established EMD (empirical mode decomposition) based time series modeling framework in the energy demand forecasting literature, was proposed for interval forecasting of electricity demand. The correctness of a soft computing model is to a great extent relies on determination of its model parameters. Although organized strategies for selecting parameters are important, model parameter alignment also need to be made. Computational complexity is a major drawback of wake modeling approaches in large wind farm. In this paper, a soft-computing methodology (adaptive neurofuzzy inference system - ANFIS (application of adaptive neurofuzzy inference system)) [12] has been proposed for wake wind speed deficit and power deficit ratio prediction in wind farm according to wind turbine row number in wind farm and wind direction and for three free wind speeds: 6 m/s, 8 m/s and 10 m/s. The proposed ANFIS model is obtained with the combination of the two methods, neural network and fuzzy logic. The neural network searches the optimal parameters for fuzzy logic membership functions thus giving more reliable and accurate forecasts. The suggested combination of methodologies is new and unique which boost the capability of the suggested model compared to those models previously presented in the literature. The ANFIS models are designed based on experimental data and three analytical
methods of calculating the wake effect: N.O. Jensen [12], Eddy Viscosity Model [13e16] and G.C. Larsen [17,18]. In other words the ANFIS model should estimates average wake power deficit in wind farm based on the established analytical models. 2. Materials and methods Power losses because of turbine wakes in extensive offshore wind farms are anticipated by condition of-the-craftsmanship models to be of the request 10e20% and thus is a critical segment of the general money making concerns of these wind ranches. To build the understanding of the wake impacts from substantial wind farms various undertakings are currently being completed with the reason for depicting and evaluating wakes. Owing to the fact that economical aspect is a crucial driver in this venture, an improved capacity to anticipate wake losses would certainly augment the viability of expansive wind farms. Power losses raised by wakes were examined on the basis of observations from wind farm depicted schematically in Fig. 1. The wind farm data were utilized to appraise all models to the parameterization of wake addition/expansion as the wake develops directly down a row of wind turbines. The adapted databases are utilized to determine the downstream influence of several wind farms, and screen the in-park wake impacts. In parallel to the information examination, wind farm models are certainly created and assessed. The wake models include many variables such as the turbine introduction and separating, wind atmosphere as well as turbine sort. 2.1. Wake effect models Whenever, the turbine concentrates power from the wind, a wake is developed downstream of the turbine. Provided that an alternate adjacent turbine is working inside this wake, the power generated from this downstream turbine is declined in comparison to the turbine working in the free wind. The obtained loss of power which is typically in the range 2%e20% is contingent upon a series of factors including the wind dispersion, the wind turbine attributes and the wind ranch geometry. The turbines operating in the wake flow of others are confronted with a diminished wind speed as well as expanded element stacking emerging from the expanded turbulence incited by the upstream turbines. This expanded turbulence should be considered, when selecting a suitable class of turbine. In case of having different turbines, the achieved results by the single wake simulation are amassed into a consolidated come about by utilizing exact consolidation standards. 2.2. Parameters required for modeling the wake The wake models require distinctive inward wake model parameters as info and a shifting number of extra parameters depicting the landscape and wind atmosphere conditions. Info parameters for a wake model may usually be turbulence force and harshness length. Commonly, such parameters are dependent upon the harshness class (or roughness length). Table 1 suggests corresponding estimated wake model parameters [19e21]. 2.3. N.O. Jensen wake model The N.O. Jensen wake model, which is based upon the assumption of a linearly expanding wake diameter, is a simple single wake model [12]. Fig. 2 schematically illustrates the overview of N.O. Jensen wake model which it is seen that the wake is expand linearly with downstream distance, X. There is a
V. Nikolic et al. / Energy 80 (2015) 361e372
363
Fig. 1. Segment of the wind farm layout.
relationship between R1 and X such that, as it is clear from Fig. 2, R1 increases linearly with increasing X. Fig. 3 shows a possible layout of three wind turbines in a wind farm. The two upper turbines affect the bottom wind turbine by two wakes. The multiple partial interference of the wake effects from the two upstream turbines occurred, as it shown in Fig. 3. The calculation of the overall wind speed at the downstream turbine is done using Eq. (1).
To calculate the wind speed after the two wind turbine rotor, as it illustrated in Fig. 3, following equation is utilized: where: u0 is the free stream wind speed considered in this equal to 12 m/s, a is the axial induction factor computed from the thrust coefficient, CT via the following expression:
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 u0 12 0 12 u u C B uB B B C C C uB C B B C C uB B B C C C uB B B C C C uB C B B C C uB B B C C C uB C B B C C 2a 2a uB B B C C C ¼ ui *B1 uB C þB C C 1 1 0 0 2 2 u B B C C C uB B B C C C uB B B C C C C C B B uB B B B C C C C C B B X X u B B1 þ aB C C C 1 þ aB rffiffiffiffiffiffiffiffiffiffiffiffiffiffi!C rffiffiffiffiffiffiffiffiffiffiffiffiffiffi!C uB B B B C C C C C B B u@ B @ @ @ 1a A A 1a A A C t A @ Rr Rr 1 2a 1 2a 0
uiþ1
i ¼ 0; 1…:N
(1)
V. Nikolic et al. / Energy 80 (2015) 361e372
364 Table 1 Wake model parameters [19,20]. Terrain classification
Roughness class
Roughness length
Wake decay constant
Ambient turbulence at 50 m
Additional detailed description
Offshore. Water areas Mixed water and land Very open farmland Open farmland Mixed farmland. Trees and farmland Forests and villages Large towns and cities Large build up cities
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
0.0002 0.0024 0.03 0.055 0.10 0.20 0.40 0.80 1.60
0.040 0.052 0.063 0.075 0.083 0.092 0.100 0.108 0.117
0.06 0.07 0.10 0.11 0.12 0.13 0.15 0.17 0.21
Water areas, oceans and large lakes. General water bodies. Mixed water and land. Also applies to the very smooth terrain No crossing hedges. Scattered buildings. Smooth hills. Some buildings. Crossing hedges with 8 m height with distance 1250 m apart. Some buildings. Crossing hedges 8 m high with distance 800 m apart Closed appearance. Dense vegetation. 8 m hedges 250 m apart. Villages, small towns and much closed farmland. Many high hedges. Forests. Large towns, cities with extended build up areas. Large cities with build up areas and high buildings.
a¼
0:5 ln zz0
(4)
z and z0 are hub height and surface roughness, respectively. The value of surface roughness is variable according to the terrains. For plain terrains, the surface roughness is considered equal to 0.3. 2.4. Eddy viscosity model In Ref. [13], for the first time, an axi-symmetric formulation of the time averaged NS (Navier Stokes) equations with an eddy viscosity closure was applied to model the wind turbine wake. For this application, the cylindrical coordinates under assumption of incompressible fluid is utilized. The continuity equation in cylindrical coordinates can be written as [14]:
1 vrv vu þ ¼0 r vr vx
In the thin layer approximation and using cylindrical coordinates, the NS equation is presented by:
Fig. 2. Schematic of N.O. Jensen wake model.
CT ¼ 4að1 aÞ
(2) u
X is the downstream distance of the turbine. The relationship between R1 and Rr can be presented by:
R1 ¼ Rr
(5)
rffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1a 1 2a
vu vu 1 vðruvÞ þv ¼ vx vr r vr
The near wake length is represented by combination of ambient turbulence, rotor generated turbulence and shear generated turbulence [16] and is divided into two regions which the first xh may formulated by:
(3)
" xh ¼ r0
a is the entertainment obtained by the following equation:
(6)
2 2 #0:5 dr 2 dr dr þ þ dx a dx l dx m
r0 is ‘effective’ radius of expanded rotor disc obtained by:
Fig. 3. Interferences of the wake effects.
(7)
V. Nikolic et al. / Energy 80 (2015) 361e372
r0 ¼ ½D=2
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðm þ 1Þ=2
(8)
Rw ¼
and m is aerodynamic coefficient:
.pffiffiffiffiffiffiffiffiffiffiffiffiffi m¼1 1 Ct
(9)
2
¼
a
(10)
where
The c1 parameter partly separates the rotor drag dependence [9]. Therefore, c1 is expected to be relative insensitive to the design and size of the rotor:
D is the rotor diameter. The components of Eq. (7) are computed as:
dr dx
1=5 h i1=5 2c21 ½CT Ax1=3
c1 is a non-dimensional mixing length, defined by c1 ¼ l[CTAx]1/3 l is Prandtl's mixing length
where
35 2p
365
c1 ¼
2:5I þ 0:05 for I 0:02 5I for I < 0:02
ambient turbulence
1=2 D ½CT Ax0 5=6 2
(11)
where
2
dr dx
l
¼ 0:012Bl
rotor generated turbulence
h pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffii dr 2 ¼ ð1 mÞ 1:49 þ m dx m . ð9:76ð1 þ mÞÞ shear generated turbulence
where
A is the rotor area D is the diameter of the upstream rotor x0 is an approximation parameter, determined by the Equation (12) below
x0 ¼ 9:5D
2R9:5 3 1 D
(12)
The mean wind deficit is determined from the expression (13),
( i1=3
1=2 ua h CT Ax2 Du ¼ r 3=2 3c21 CT Ax 9 ) 3=10
1=5 2 35 2 3c1 2p
I is the ambient turbulence intensity B is the number of rotor blades l is the tip speed ratio
2.5. G.C. Larsen model
(13)
where
G.C. Larsen model [17], as another suggested wake model, is a semi analytical model derived on the basis of Prandtl's rotational symmetric turbulent boundary layer equations. Due to the asymptotic expressions, the model may be sort of conservative for close spacing. Considering similarity between deficits at different downstream positions and only moderate velocity deficits, the wake radius may then be represented using the following relation:
ua is the ambient mean wind velocity at hub height. 2.6. Validation of the wake effect models As can be seen in Fig. 4, the mixed farmland terrain seems to have the largest wake power speed deficit for the three presented wake models. It seems the class of N.O. Jensen wake models has the
Wake models calculation in comparison to measured energy 8
Eddy Viscosity
Wake power deficit [%]
7 6 G.C. Larsen
5
N.O. Jensen
Mixed water/land
4
Very open farmland
3
Open farmland
2
Mixed farmland
1 0 0.5
1
1.5
2 2.5 Wake models
3
3.5
Fig. 4. Wake models for different wind farm terrains.
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366
Wake wind speed deficit 11 2°
10°
20°
30°
Wind speed deficit [m/s]
10 9
Experiment-1
8
Experiment-2 Experiment-3
7 6
5 0
5
10 15 20 Experimental samples
25
30
Fig. 5. Wake wind speed deficit for different wind input angles and wind turbine position.
best match of the measured wake data i.e. the smallest wake wind power deficit was for the N.O. Jensen wake models. However, the G.C. Larsen model and especially the Eddy Viscosity wake model seem to overestimate the wake losses quite a bit. The reason for this over-estimation could be that neither of the wake models do include a model for wake meandering. 2.6.1. Experimental validation of wake effect The rows 1 through 8 in the wind farm are analyzed using a 0e30 input wind sector. In Fig. 1 is depicted wind farm with input wind direction of 0 . The wind speed was considered between 6 and 10 m/s since this is the wind speed interval which generates relatively high power. The multiple partial interference of the wake effects from the two upstream turbines occurred as it shown in Fig. 3. The calculation of the overall wind speed at the downstream turbine was conducted via Eq. (1).
The measured wake effect is plotted for relative power drop of each turbine in the row as it shown in Figs. 5 and 6 for three experiments which amount of wind speeds are: Experiment-1: 6 m/s, Experiment-2: 8 m/s, Experiment-3: 10 m/s. Clearly, the biggest relative power drop is seen from column 1 to line 2, though the force drop from line 2 to column 8 is lower compared to the initial 2 columns. Other than watching the mean esteem down the line of turbines it is truly intriguing that the standard deviation of the results is expansive for all cases. This demonstrates that the results cover altogether various circumstances. There exists a few conceivable purposes behind the vast deviations and these ought to be checked separately (turbulence,
Wake rower deficit ratio 1.1 2°
10°
20°
30°
Power deficit ratio
1 0.9 Experiment-1
0.8
Experiment-2 Experiment-3
0.7 0.6 0.5 0
5
10 15 20 25 Experimental samples
30
Fig. 6. Wake power deficit ratio for different wind input angles and for different wind turbine position.
V. Nikolic et al. / Energy 80 (2015) 361e372
367
Fig. 7. ANFIS structure.
wind shear and wind bearing reliance). This may be due to the fact that the results cover more than one wonder or physical state of the wake.
2.7. Adaptive neuro-fuzzy inference system ANFIS models are developed in this research work for estimation of the reduced wind speed and power deficit ratio of the wind turbines in wind farm in relation to the turbine position in the wind farm and wind input angle. For the present study the experimental data was used for training and checking of the ANFIS networks. Fig. 7 shows an ANFIS structure with two inputs: wind turbine row and wind input angle. For this research, the first-order Sugeno model with two inputs and fuzzy IF-THEN rules of Takagi and Sugeno's type is utilized:
if x is A and y is C and z is E then f1 ¼ p1 x þ q1 y þ r1 z þ t
(14)
The 1st layer is comprised of two input variables MFs (membership functions), named as input 1 and input 2. Its function is providing the input values for the next layer. In this study, the inputs are wind turbine position in wind farm (row number) and wind input angle. In the first layer every node is an adaptive node with a node function
O ¼ mðxÞ; where m(x)i are MFs. In this paper, bell-shaped MFs (3) with maximum equal to 1 and minimum equal to 0 is chosen
1 2b
f ðx; a; b; cÞ ¼ 1þ
wi ¼ mðxÞi *mðxÞiþ1
In the 3rd layer, named as the rule layer, every node (neuron) function is conducting the pre-condition matching of the fuzzy rules, Every node in the 3rd layers computes the weights which are normalized. Nodes in the 3rd layer, similar to the 2nd layer, are non-adaptive and they computes the ratio of the rule's firing strength to the sum of all rules' firing strengths like
w*i ¼
wi w1 þ w2
(17)
i ¼ 1; 2: The 3rd layer's outputs are named normalized firing strengths or normalized weights. The next or 4th layer (defuzzification layer), which its nodes are adaptive node with node function, offers the output values resulting from the inference of rules.
O4i ¼ w*i xf ¼ w*i ðpi x þ qi y þ ri Þ
(18)
where {pi, qi,r} is the parameter set and in this layer is referred to as consequent parameters. Here {pi, qi,r} represents the parameter set which in the 4th is referred as consequent parameters. The 5th layer (output layer) sums up all the inputs coming from the 4th layer and transforms the results of fuzzy classification to a crisp (binary). Here the nodes same as the 2nd and 3rd layers are
(15)
xc a
The bell-shaped function depends on three parameters a, b and c. The parameter b is usually positive. As it is illustrated in Fig. 8, c is located at the center of the curve. In the 2nd layer, which is also called membership layer, the weights of each MFs is checked. The 1st layer provides the input values for this layer so that it can performs as MFs for representing the fuzzy sets of the respective input variables. Unlike the 1st layer, the nodes are non-adaptive in this layer. The 2nd layer's functions is multiplying the incoming signals and sending the product out like
(16)
Fig. 8. Bell-shaped membership function (a ¼ 2, b ¼ 4, c ¼ 6).
V. Nikolic et al. / Energy 80 (2015) 361e372
368 Table 2 Statistical parameters for data sets. Variable
Statistical parameters
Wind row number Wind direction
Min
Max
Mean
1 2
8 30
4.5 16
not-adaptive and their function is calculating the overall output as the sum of all incoming signals
O4i
¼
X i
w*i xf
P wf ¼ Pi i i wi
(19)
2.8. Model performance evaluation
Fig. 10. Simulink block diagram for estimation of the wind speed deficit and power deficit ratio.
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn 2 i¼1 ðPi Oi Þ ; RMSE ¼ n
(20)
To assess the proficiency of the ANFIS model some statistical indicators were examined as follows: 1) RMSE (root-mean-square error)
2) Pearson correlation coefficient (r)
Pn Pn Pn $ n O $P O P i i i i i¼1 i¼1 i¼1 r ¼ vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u 2 2 u P Pn t n Pn O2 Pn O $ n ni¼1 P 2i i¼1 i i¼1 i i¼1 Pi (21) 3) coefficient of determination (R2)
"
Pn i¼1 Oi Oi $ Pi Pi
R2 ¼ P n i¼1
#2
P
Oi Oi $ ni¼1 Pi Pi
(22)
where Pi and Oi are known as the experimental and forecast values, respectively, while Pi and Oi are the mean value of Pi and Oi, respectively and n is the total number of test data. 3. Results 3.1. Input parameters Experimental work was conducted to study the effects of the wake in order to study wind speed deficit and power deficit ration in wind farm. The capability of the ANFIS to provide favorable estimations is reliant upon input parameter selection. In this study, 2 input parameters (wind turbine row number in wind farm and wind direction) were used for generating ANFIS model. The data were collected for three free wind speeds: 6 m/s, 8 m/s and 10 m/s. Some statistical parameters consisting minimum, maximum and mean values obtained for the 2 input parameters are presented in Table 2. 3.2. ANFIS models Fig. 9. ANFIS predicted relationships between wind turbine row number in wind farm, wind input angle and wind speed deficit (a) and power deficit ratio (b).
There are two ANFIS networks, one for wake wind speed deficit estimation and on for wake power deficit estimation. At the
V. Nikolic et al. / Energy 80 (2015) 361e372
Fig. 11. Scatter plots of measured and predicted values of wind speed deficit using ANFIS model for wind speed of (a) 6 m/s, (b) 8 m/s and (c) 10 m/s.
beginning the ANFIS networks were trained with the experimental data presented in Figs. 5 and 6 and in Table 2. The ANFIS networks determine wake wind speed and power deficit based on the experimental measurements for different number of turbines row and for different input wind angle. Three bell-shaped membership functions were used to fuzzily the ANFIS inputs. The final decision surfaces after ANFIS training are shown in Fig. 9 (a) and (b). The wind speed deficit after the rotor or wake wind speed as function of the wind turbine row number in wind farm and wind input angle is implemented in MATLAB Simulink block diagram as it shown in Fig. 10. At the same time, the power deficit ration as function of the wind turbine row number in wind farm and wind
369
Fig. 12. Scatter plots of measured and predicted values of power deficit ratio using ANFIS model for wind speed of (a) 6 m/s, (b) 8 m/s and (c) 10 m/s.
input angle is also implemented in the Simulink block diagram. For example, for wind turbine row number 5 in wind farm and for wind input angle 10 , ANFIS estimates the wind speed after the rotor or wake wind speed 7.031 m/s and power deficit ratio is 0.678. Since mean wind speed or free stream wind speed in front of wind farm is 8 m/s it means the percentage of the wind speed deficit is 12%. This approach is very useful for quick prediction of the wake wind speed and power deficit ratio for every wind input angle and row in the wind farm. 3.3. ANFIS models analysis At the beginning, the ANFIS networks were trained with measured data by above presented experimental procedure. After
V. Nikolic et al. / Energy 80 (2015) 361e372
370
Wake power deficit ratio 1.1 2°
Power deficit ratio
1
10°
20°
30°
0.9 Experiment-1
0.8
Experiment-2 Experiment-3
0.7
ANFIS
0.6 0.5 0
5
10 15 20 Experimental samples
25
30
(b) Fig. 13. ANFIS predictions for: (a) wind speed deficit and (b) power deficit ratio.
training process the ANFIS networks were tested to determine the wake wind speed deficit and power deficit ratio for different effective wind speed. Based on the experiments, the input parameters (wind turbine row number in wind farm and wind direction) and outputs (wake wind speed deficit and power deficit ratio) are collected and defined for the learning technique. The prediction results of the wake wind speed deficit and power deficit ration is represented in Figs. 11 and 12 for three experiments according to the free wind speed. According to Figs. 11 and 12, it is observed that the most of the points fall along the diagonal line. Consequently, it is clear that the predicted wake wind speed deficit and power deficit ratio enjoy very good agreement with the measured values for ANFIS method. Wake wind speed deficit predictions are not as good as power deficit ratio predictions according to the coefficient of determination R2. Also the best correlation
occurs for free wind speed of 8 m/s for wake wind speed and power deficit ration prediction. It is crystal clear that there is a favorable level of agreement between measured and estimated values by the proposed ANFIS model. ANFIS expectations against the test information are indicated in Fig. 13 for wind speed deficit and power deficit ratio respectively. The results demonstrate that there is a critical change in the wake impact when the wind is restricted to being parallel to the line bearing. The force drop from line 1 to column 2 has expanded from a normal estimation of pretty nearly 0.2 to around 0.3. This demonstrates that the expansive force drops between the initial two turbines just happens in an extremely limited part around the line bearing. At other wind bearings the force drop is essentially more modest from line 1 to column 2. For the remaining turbines the example is just about the same for the two investigates: the force
V. Nikolic et al. / Energy 80 (2015) 361e372 Table 3 Performance statistics of the ANFIS model for wake wind speed deficit estimation based upon different statistical indicators.
Wind speed 6 m/s Wind speed 8 m/s Wind speed 10 m/s
RMSE
R2
r
1.7279 0.0763 1.7908
0.9867 0.9893 0.9863
0.9933 0.9946 0.9931
371
large wind farms. Since the used training data for the ANFIS network for the wake deficit and power deficit ratio prediction is not time-series data, the obtained results are one step-ahead prediction. Furthermore, for future research the prediction can be expanded with time-series data and to include multi step-ahead prediction like in articles [24e28]. Acknowledgment
Table 4 Performance statistics of the ANFIS model for power deficit ratio estimation based upon different statistical indicators.
Wind speed 6 m/s Wind speed 8 m/s Wind speed 10 m/s
RMSE
R2
r
0.0141 0.0128 0.0113
0.9938 0.9967 0.9909
0.9969 0.9984 0.9954
drop from column 2 to line 8 is somewhere around 0.15 and 0.2, which happens in a very nearly straight line. The conclusion to this distinction between wake impacts for stream parallel to the column and wind course being marginally off the line bearing is that a wake model must have the capacity to give altogether diverse results for even little alters in wind course. At the point when making another wake model it must be chosen whether it ought to have the capacity to foresee all circumstances or basically can display the mean comes about effectively. This obviously is inquiry of the motivation behind the model. 3.4. Performance analysis In order to demonstrate the merit of the proposed ANFIS model, on a more definite and tangible basis, to estimate the wake wind speed deficit and power deficit ratio, three statistical indicators of RMSE (root-mean-square error), r and R2 were calculated and the achieved results presented in Tables 3 and 4, respectively. This verifies the achieved and discussed aforementioned results from the presented figures, especially in terms of precise estimation. The results convincingly confirm that the proposed ANFIS model can be utilized for estimation of wake wind speed deficit and power deficit ratio with favorable level of reliability and preciseness. 4. Conclusion In this research work, a soft-computing methodology (adaptive neuro-fuzzy inference system-ANFIS [22,23]) has been proposed for prediction of wake wind speed deficit and power deficit ratio in wind farm according to wind turbine row number in wind farm and wind direction and for three free wind speeds: 6 m/s, 8 m/s and 10 m/s. The proposed ANFIS model is the combination of neural network and fuzzy logic. The neural network searches the optimal parameters for fuzzy logic membership functions thus giving more reliable and accurate forecasts. This proposed combination of methodologies is unique and thus has enhanced the performance of the proposed model compared with the other earlier developed models. The achieved results clarified that the best prediction is observed for free wind speed of 8 m/s based upon RMSE, R2 and r, which are 0.0763, 0.9893 and 0.9946, respectively for ANFIS prediction of wake wind speed deficit and are 0.0128, 0.9967 and 0.9984, respectively for ANFIS prediction of power deficit ratio. As a consequence, ANFIS can be considered as an efficient soft computing methodology to offer precise results in wake wind speed deficit and power deficit ratio prediction in wind farm. The analyses in this paper showed that the wind direction is very important for the wake effect and wind energy decreasing in
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