- Email: [email protected]
A neural network based approach for wind resource and wind generators production assessment
Applied Energy 87 (2010) 1744–1748
Contents lists available at ScienceDirect
Applied Energy journal homepage: www.elsevier.com/locate/apenergy
A neural network based approach for wind resource and wind generators production assessment L. Thiaw *, G. Sow *, S.S. Fall, M. Kasse, E. Sylla, S. Thioye Laboratoire d’Energies Renouvelables, École Supérieure Polytechnique de Dakar, BP: 5085, Dakar, Senegal
a r t i c l e
i n f o
Article history: Received 13 July 2009 Received in revised form 9 September 2009 Accepted 5 October 2009 Available online 30 October 2009 Keywords: Wind energy Wind generator Artificial neural network Multi Layer Perceptron Weibull model
a b s t r a c t The statistical study of wind speed measurements on a site makes it possible to determine a distribution law, needed to assess the available or recoverable wind energy potential. The classical approach consists in assimilating the distribution law to standard models, for example Weibull or Rayleigh, and in determining the parameters of the model so that it gets closest to the discrete law obtained by statistically treating the wind speed measurements. The Weibull model is the most used one and provides good results. However, the accurate determination of the wind speed distribution law constitutes a major problem. Multi Layer Perceptron type artificial neural networks, highly effective in function approximation problems, are used here for the approximation of the wind speed distribution law. The site energy characteristics have been determined by means of the neural approach and compared with those obtained by the classical method. The results show that the distribution law achieved by the neural model provides assessments closer to the discrete distribution than the Weibull model. This approach has enabled the wind energy potential on the Dakar site to be determined in a more accurate way. The models are also used to assess the amount of energy the wind generator WES18 of 80 kW power, set up at 10 m and 40 m above the ground, would produce annually. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction Energy is a development vector essential for all countries. Although fossil energies are still to be exploited for a long time to come, the whole humankind is facing an energy crisis with serious repercussions on the cost of life, more particularly in poor countries. This energy crisis is aggravated by a deteriorating environment in the world due to a greenhouse effect gas emission originating from the exploitation and the use of polluting fossil energies. We have thus been for the past few years witnessing a renewed interest for renewable energies generally speaking and wind energy in particular [17,6,14,10,3]. More and more wind farms are being set up with increasing powers. In Senegal, there is no wind farms installed yet. But the interest towards renewable energies implies a good assessment of the available wind energy potential. Accurate and reliable wind potential analysis tools are necessary for a good assessment of the available and recoverable potential. The wind potential assessment of a site requires the knowledge of the distribution law of the wind speed measured on the site. The statistical treatment of these measurements makes it possible to
* Corresponding authors. Tel.: +221 77 658 59 97; fax: +221 33 825 55 94. E-mail addresses: [email protected] (L. Thiaw), [email protected] (G. Sow). 0306-2619/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2009.10.001
have a discrete distribution law. However, a more accurate analysis of the wind potential needs obtaining a continuous distribution law. The Weibull or Rayleigh models are often used. The approach consists in assimilating the distribution law to one of these models and to determine the model parameters so that it gets closest to the discrete law achieved by the statistical treatment of the wind speed measurements. Several studies have shown that the Weibull and Rayleigh models provide good results. In [1], these models have been compared in an analysis study of the wind energy potential. The results achieved for the two models are similar and satisfactory. In [8], the Weibull model parameters have been estimated by using different methods. The results have shown that the assessment method of these parameters, based on a linear regression method, provide better results than that based on empirical formulas. The Weibull model is also used in [16] to determine the monthly and yearly distribution laws of the wind speeds, as well as the available power and the amount of energy produced by different wind generators. Determining a distribution law for the speeds can be considered as a non linear regression problem, in which the distribution law chosen (Weibull or Rayleigh) is identified so as to get nearer the discrete law. As regards function approximation, however, the techniques based on the artificial neural networks approach have shown that very good performances can be obtained [4,7].
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An artificial neural network (ANN) is a complex network made up of interconnected elementary computing units named formal neurons. The neurons are organized in clusters or layers and can be interconnected in different ways. In function of the network architecture, there are several types of neural networks. The neural networks are used in applications as various as varied: in [2], a neural network has been used to predict energy consumption in a residential sector; in [9] a in [9] a neural network has been used to predict storms in the short term; in [11], the rain assessment network starting from radar measurements. The ANN of the Multi Layer Perceptron (MLP) type are those most used, notably in non linear regression problems. In this research work, an MLP network is used to more accurately determine the wind speed distribution law. This approach makes it possible to better assess the wind energy potential and the wind generator performances. This paper is structured as follows: Section 2 introduces the wind potential analysis classical method; Section 3 introduces the MLP-type artificial neural networks; Section 4 describes the method for using an MLP to analyse the wind potential; the last part presents the results on the site of Dakar, Senegal. 2. Classical method for wind resource and wind generators production assessment The wind speed can be considered as a random variable. Simply measuring it is not enough to characterize a site wind potential. Knowing the frequencies of the speeds or better the distribution function (probability density) of wind speeds is essential. This speed distribution law enables the energy amounts available, recoverable or produced by a wind generator to be assessed. It becomes necessary to carry out a statical study to characterize the site wind potential completely. 2.1. The Weibull distribution To study the distribution of wind speeds, the two-parameter Weibull model is used very often. The more complete for the modelling of the wind potential but more complex three-parameter Weibull model is rarely used. The two-parameter Weibull distribution law or probability density is defined by:
k k v k1 v f ðv Þ ¼ exp c c c
ð1Þ
where f ðÞ is distribution law or probability density; v is the wind speed ðm=sÞ; c is the scale factor ðm=sÞ; and k is the shape factor (characterizes the distribution dissymmetry). The distribution function of wind speeds FðÞ defined as the likelihood that the wind speed will be lower than a value v is expressed by:
k v Fðv Þ ¼ 1 exp c
ð2Þ
Rewriting Eq. (2) in the form of:
ln½ lnð1 Fðv ÞÞ ¼ k lnðv Þ k lnðcÞ
ð3Þ
and setting y ¼ ln½ lnð1 Fðv ÞÞ and x ¼ lnðv Þ a regression straight line is obtained:
y ¼ mx þ b
ð4Þ
Determining parameters m and b by the least squares method makes it possible to assess Weibull model parameters c and k :
k¼m
b c ¼ exp k
ð5Þ ð6Þ
2.2. Wind energy assessment The wind instantaneous power across a unit surface, perpendicular to the wind speed direction, is expressed by the relation:
P¼
1 q v3 2
ð7Þ
where q is the air density. The average power available in the wind can be assessed by the relation:
Pm ¼
1 q 2
Z
1
f ðv Þ v 3 dv
ð8Þ
0
For a discrete distribution law the relation (8) is written:
Pm ¼
N 1 X q f ðv i Þ v 3i 2 i¼1
ð9Þ
N designating the number of measurements. The average energy available for a duration period of T hours (in kWh=m2 ) is assessed, for a continuous distribution law by the relation:
T 1 q 1000 2
EmT ¼
Z
1
f ðv Þ v 3 dv
ð10Þ
0
and for a discrete law, by the relation: N T 1 X f ðv i Þ v 3i q 1000 2 i¼1
EmT ¼
ð11Þ
A wind generator is generally characterized by its power curve function of the speed P ¼ Pðv Þ, its rated power P r , its starting V s , rated V r , maximum V c as well as the diameter of its blades D sweeping a surface S. These characteristics make it possible to assess the available energy amount the wind generator can recover on a given site. For a continuous distribution law, this energy amount is assessed for a T duration period by the relation:
EgT ¼
T 1 qS 1000 2
Z
Vr
Vs
f ðv Þ v 3 dv þ V 3r
Z
Vc
f ðv Þ dv
ð12Þ
Vr
For a discrete distribution law, the relation (12) is written:
EgT ¼
r c X X T 1 f ðV i Þ V 3i þ V 3r f ðV i Þ qS 1000 2 i¼s i¼r
! ð13Þ
where n the indexes s; r and c correspond to the speeds V s ; V r and V c respectively. The amount of energy a wind generator would produce on a given site during the period T can be assessed from the characteristics P ¼ Pðv Þ and the wind speed distribution law on the site: relation (14) for a continuous distribution law and relation (15) for a discrete distribution law.
EgpT ¼ EgpT ¼
T 1000
Z
Vc
Vs
f ðv Þ Pðv Þ dv !
c X T f ðV i Þ PðV i Þ 1000 i¼s
ð14Þ ð15Þ
Relations (10)–(15) enable the amounts of energy available, recoverable or produced monthly ðT ¼ 30 24 hÞ or yearly ðT ¼ 365 24 hÞ. If the wind speed measurements have been made from a height of H1 above the ground, it is possible to assess the wind speeds at a height H2 by the relation:
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L. Thiaw et al. / Applied Energy 87 (2010) 1744–1748
a H2 V2 ¼ V1 H1
ð16Þ
3
where a is a parameter depending on the soil roughness [1,15].
1 3. Feed forward neural networks
4 An ANN can be defined as a complex network made up of interconnected elementary computing units (formal neurons). The neurons are organized in clusters or layers and can be connected in different ways. This connection topology between the neurons defines the network architecture, linked to the task it has to perform. This task is often specified in the form of examples1 including a set of input values and a set of corresponding output values the network has ‘‘to learn” in order to be able to supply correct answers for other unknown inputs. The learning is the network parameter assessment procedure which allows it to meet a performance criteria minimizing the error between the network output and the actual output. The learning is carried out according to an algorithm peculiar to the network architecture. There are several types of ANN. The MLP-type ANN are the most used ones, notably in non linear regression problems [4,7]. An MLP network includes one or several hidden layers with sigmoid type activation function as well as an output layer. Fig. 1 represents an example of a two-input MLP network including a three-neuron hidden layer and a one-neuron output layer. The L hidden layer neurons receive information from L 1 layer neurons (or units) and are connected to the L þ 1 layer neurons. There are no connections between neurons of the same layer. Each output layer neuron achieves a non linear function of the network inputs. For more information about the MLP, see [7,13,5]. The potential si of a neuron i and its activation Oi are given by relations (17) and (18) respectively.
si ¼
p X
xij xj bi
ð17Þ
j¼1
Oi ¼ g i ðsi Þ
ð18Þ
where p designates the number of units of the upstream layer, connected to neuron i; xj represents the input j of the network if neuron i belongs to the first hidden layer, or in the opposite case, the neuron j output Oj of the hidden layer coming before that of neuron i; xij is a scalar constant representing the weight of the connection between neuron i and neuron (or input) j; bi is a scalar constant called bias; and g i ðÞ is the activation function of neuron i. It can be different depending on whether the neuron is a hidden neuron or an output neuron. In general, all the hidden neurons have the same activation function which is often a sigmoid function (for example gðsÞ ¼ 1=ð1 þ expðsÞÞ). The output neurons also have the same activation function, in general linear (for example gðsÞ ¼ s). The determination of the MLP network parameters is made according to a supervised learning mode: the learning database is presented to the network which has to adapt its parameters according to an algorithm so that the difference between the system output and that of the model is low enough. The most used learning technique in MLP networks is the back propagation algorithm [12]. 4. Assessing wind resource by neural network In this research work, an MLP neural network is used to determine the wind speed distribution law. The statistical study of wind 1
These examples constitute the network learning database.
6
2 5 output layer inputs hidden layer Fig. 1. Example of an MLP network.
speed measurements makes it possible to determine the frequencies of the speed contained in each speed interval Ii ¼ V i1 ; V i ; i ¼ 1; . . . ; M, M being the index corresponding to the maximum speed recorded. For each interval Ii , frequency fi is calculated by the expression:
fi ¼
Ni N
ð19Þ
in which Ni is the number of speed values contained in Ii . An MLP neural networks is then worked out to determine the speed distribution law f ðv Þ. The learning database consists of the couples of points ðV i ; f i Þ, where the V i are the inputs and the fi , the outputs. Determining the relation f ðv Þ enables the amounts of energy available, recoverable or produced (cf Eqs. (11), (13) and (15)) to be determined. The assessment of a wind generator production is made starting from the machine power curve, provided by the constructor in the form of couples of points ðv i ; Pi Þ. A more accurate calculation would necessitate to have a continuous relation P ¼ Pðv Þ. There are empirical models allowing the characteristics P ¼ Pðv Þ of a wind generator to be represented. The Gauss theoretical model described by relation (20) is often used:
Pðv Þ ¼ P0 þ
A v V0 pffiffiffiffiffiffiffiffiffi exp 2 2 w w p=2
ð20Þ
in which P0 ; V 0 ; A and w are parameters to be identified. In [1], these parameters are identified by using the Origin 5.0 software. In the present work, the relation P ¼ Pðv Þ is determined by using a neural network. The learning database consists of the points ðv i ; Pi Þ provided by the constructor. 5. Results and discussion The wind energy assessment methodology proposed was applied on the site of Dakar, Senegal (latitude: 14 370 N, longitude: 17 270 W, altitude: 0 m). The available wind speed measurements, obtained at the Dakar Airport site, are instantaneous values recorded every 3 h and cover a period of 10 years, from 1995 to 2005. These data are used here only for the purpose of the proposed method validation. More accurate wind energy assessment require more complete wind speed measurements. Fig. 2 gives the monthly average of the wind speeds at a height of 10 m above the ground. The results show that the most important winds are recorded in December with an average of 5:5 m=s and the least windy month is July with an average of 3:9 m=s. The annual average of the wind speed is 4:4 m=s. The speed variation slot has been divided into
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L. Thiaw et al. / Applied Energy 87 (2010) 1744–1748
5.5
0.3 discret MLP Weibull
0.2
5
Probability
Mean wind speed (m/s)
0.25
4.5
0.15 0.1 0.05 0
4 2
4
6
8
10
−0.05
12
0
2
4
6
Month
18 intervals and in each interval, the frequencies have been determined by relation (19). On the basis of the Weibull model determination method presented in the paragraph Section 2.1, the following parameters values have been found: c ¼ 4:9 m=s and k ¼ 2:19. On the other hand, an MLP neural network with one input, two hidden layers including three neurons each and 1 output has been identified. Wind potential characteristics assessed by the use of these two models are then compared with those assessed using the discrete method. The discrete distribution law obtained by treating the measurements statistically as well as the continuous distribution laws corresponding to the Weibull model and to the identified MLP neural network are represented in Fig. 3. To verify that the relation obtained with the MLP network is a distribution law, the integral Iv defined by relation (21) has been calculated. The results gives Iv ¼ 0:997, showing that the relation obtained can be considered as a distribution law (f must verify R1 the condition 0 f ðv Þ dv ¼ 1).
f ðv Þ dv
12
14
16
18
150 discret MLP Weibull
100
50
0 0
2
4
6
8
10
12
14
16
18
Wind speed (m/s) Fig. 4. Yearly available energies assessed with different methods.
ð21Þ
0
The amount of energy available assessed with the relations (10) and (11) for a 1-year period have been determined. Fig. 4 shows the contribution of each speed to the amount of energy available annually. The assessments made with the MLP network are nearer the assessments obtained with the discrete law than those obtained with the Weibull law. The speed–duration curves have also been determined. Fig. 5 shows that the results obtained with the MLP neural network are closer to the results obtained by means of the discrete law. The wind generator WES18 has been simulated with the site data. The characteristics of this wind generator2 are: Rated power 80 kW. Starting speed V s ¼ 2:7 m=s. Rated speed V r ¼ 13 m=s. Cut-off speed V c ¼ 25 m=s. Surface swept by the blades S ¼ 254 m2 .
100 discret MLP Weibull
90 80 70
Duration (%)
Iv ¼
V max
10
Fig. 3. Wind speed distribution laws obtained by different methods.
Available energy (kWh/m2)
Fig. 2. Monthly mean wind speed on the site of Dakar at 10 m above the ground.
Z
8
Wind speed (m/s)
60 50 40 30 20 10 0 0
2
4
6
8
10
12
14
16
18
Wind speed (m/s) Fig. 5. Speed–duration curves obtained with different methods.
The power–speed characteristics of the wind generator supplied by the constructor has been modelled by an MLP neural network with one input, two hidden layers containing two and three neurons respectively, and a one-neuron output layer. The characteris2
Source: http://www.windenergysolutions.nl.
tic supplied by the constructor and that obtained by the MLP model are presented in Fig. 6. Tables 1 and 2 give the total amounts of energies available as well as those recoverable and produced by the aerogenerator WES18 at heights 10 m and 40 m respectively.
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L. Thiaw et al. / Applied Energy 87 (2010) 1744–1748
90 Constructor MLP
80
Electrical power (kW)
70 60 50 40 30 20 10 0 −10
0
5
10
15
20
Wind speed (m/s)
References
Fig. 6. The power–speed characteristic of the wind generator WES18.
Table 1 Annual energies available, recoverable and produced by the wind generator WES18 at 10 m above the ground. Energies
Discrete law
Weibull
MLP
Available ðkWh=m2 Þ Recoverable ðMWhÞ Produced ðMWhÞ
895.6 223.1 69.1
770.5 191.7 60.9
879.2 218.0 68.0
Table 2 Annual energies available, recoverable and produced by the wind generator WES18 at 40 m above the ground. Energies 2
Available ðkWh=m Þ Recoverable ðMWhÞ Produced ðMWhÞ
wind speed frequencies, wind speed–duration curves, energies available, recoverable and produced. A comparative study with the method using the Weibull model shows that the results achieved with the help of the neural method proposed are closer to the results achieved with the discrete method obtained by the statistical treatment of measured wind speeds. The assessment of the amount of energies available annually at a height of 10 m above the ground obtained by the discrete, the Weibull and the neural models gives 895:6 kWh=m2 ; 770:5 kWh=m2 and 879:2 kWh=m2 respectively. For a 40 m height, the estimated available energies are 1896:8 kWh=m2 ; 1842:4 kWh=m2 and 2102:4 kWh=m2 respectively for the discrete, the Weibull and the neural models. The models have also enabled the annual production of the wind generator WES18 of 80 kW power set up at 10 m and 40 m above the ground to be assessed.
Discrete law
Weibull
MLP
1896.8 439.3 134.4
1842.4 454.7 144.1
2102.4 466.3 143.0
6. Conclusion A new neural technique-based approach designed to assess the wind energy potential has been proposed in this paper. An MLP neural network with one input, two hidden layers including three neurons each and 1 output is identified and satisfactorily represents the wind speed distribution law of the Dakar site. The Weibull parameters of the wind speed distribution law are also determined: the scale factor is 4:9 m=s and the shape factor is 2.19. The proposed neural approach has made it possible to more accurately determine the Dakar site wind energy characteristics:
[1] Amar FB, Elamouri M, Dhifaoui R. Energy assessment of the first wind farm section of Sidi Daoud, Tunisia. Renew Energy 2008;33:2311–21. [2] Aydinalp M, Ugursal V, Fung A. Modeling of the appliance, lighting, and space cooling energy consumption in the residential sector using neural networks. Appl Energy 2002;71(2):87–110. [3] Blanco MI. The economics of wind energy. Renew Sustain Energy Rev 2009;13:1372–82. [4] Cybenko G. Approximation by superposition of a sigmoidal function. Math Control Signals Syst 1989;2:303–14. [5] Eberhart R, Dobbins R. Neural network PC tools: a practical guide. Academic Press; 1990. [6] Himri Y, Malik AS, Stambouli AB, Himri S, Draoui B. Review and use of the algerian renewable energy for sustainable development. Renew Sustain Energy Rev 2009;13:1584–91. [7] Hornik K, Stinchcombe M, White H. Multilayer feedforward networks are universal approximators. Neural Networks 1989;2(5):359–66. [8] Jowder FAL. Wind power analysis and site matching of wind turbine generators in kingdom of Bahrain. Appl Energy 2009;86:538–45. [9] Lee T-L. Back-propagation neural network for the prediction of the short-term storm surge in Taichung harbor, Taiwan. Eng Appl Artif Intell 2008;21:63–72. [10] Lin C-J, Yu OS, Chang C-L, Liu Y-H, Chuang Y-F, Lin Y-L. Challenges of wind farms connection to future power systems in Taiwan. Renew Energy 2009;34:1926–30. [11] Liu H, Chandrasekar V, Xu G. An adaptive neural network scheme for radar rainfall estimation from WSR-88D observations. J Appl Meteorol 2001;40:2038–50. [12] Rumelhart D, Hinton G, Williams R. Learning representations by backpropagating errors. Nature (London) 1986;323:533–6. [13] Haykin S. Neural networks: a comprehensive foundation. 2nd ed. Prentice Hall; 1998. [14] Snyder B, Kaiser MJ. A comparison of offshore wind power development in europe and us: patterns and drivers of development. Appl Energy 2009;86:1845–56. [15] Thiaw L. Contribution to setting up rational tools and methodologies for sizing electrical power systems in isolated sites, PhD thesis, Cheikh Anta DIOP University of Dakar; 2002. [16] Ucar A, Balo F. Evaluation of wind energy potential and electricity generation at six locations in Turkey. Appl Energy 2009;86:1864–72. [17] Weigt H. Germany’s wind energy: the potential for fossil capacity replacement and cost saving. Appl Energy 2009;86:1857–63.
Contents lists available at ScienceDirect
Applied Energy journal homepage: www.elsevier.com/locate/apenergy
A neural network based approach for wind resource and wind generators production assessment L. Thiaw *, G. Sow *, S.S. Fall, M. Kasse, E. Sylla, S. Thioye Laboratoire d’Energies Renouvelables, École Supérieure Polytechnique de Dakar, BP: 5085, Dakar, Senegal
a r t i c l e
i n f o
Article history: Received 13 July 2009 Received in revised form 9 September 2009 Accepted 5 October 2009 Available online 30 October 2009 Keywords: Wind energy Wind generator Artificial neural network Multi Layer Perceptron Weibull model
a b s t r a c t The statistical study of wind speed measurements on a site makes it possible to determine a distribution law, needed to assess the available or recoverable wind energy potential. The classical approach consists in assimilating the distribution law to standard models, for example Weibull or Rayleigh, and in determining the parameters of the model so that it gets closest to the discrete law obtained by statistically treating the wind speed measurements. The Weibull model is the most used one and provides good results. However, the accurate determination of the wind speed distribution law constitutes a major problem. Multi Layer Perceptron type artificial neural networks, highly effective in function approximation problems, are used here for the approximation of the wind speed distribution law. The site energy characteristics have been determined by means of the neural approach and compared with those obtained by the classical method. The results show that the distribution law achieved by the neural model provides assessments closer to the discrete distribution than the Weibull model. This approach has enabled the wind energy potential on the Dakar site to be determined in a more accurate way. The models are also used to assess the amount of energy the wind generator WES18 of 80 kW power, set up at 10 m and 40 m above the ground, would produce annually. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction Energy is a development vector essential for all countries. Although fossil energies are still to be exploited for a long time to come, the whole humankind is facing an energy crisis with serious repercussions on the cost of life, more particularly in poor countries. This energy crisis is aggravated by a deteriorating environment in the world due to a greenhouse effect gas emission originating from the exploitation and the use of polluting fossil energies. We have thus been for the past few years witnessing a renewed interest for renewable energies generally speaking and wind energy in particular [17,6,14,10,3]. More and more wind farms are being set up with increasing powers. In Senegal, there is no wind farms installed yet. But the interest towards renewable energies implies a good assessment of the available wind energy potential. Accurate and reliable wind potential analysis tools are necessary for a good assessment of the available and recoverable potential. The wind potential assessment of a site requires the knowledge of the distribution law of the wind speed measured on the site. The statistical treatment of these measurements makes it possible to
* Corresponding authors. Tel.: +221 77 658 59 97; fax: +221 33 825 55 94. E-mail addresses: [email protected] (L. Thiaw), [email protected] (G. Sow). 0306-2619/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2009.10.001
have a discrete distribution law. However, a more accurate analysis of the wind potential needs obtaining a continuous distribution law. The Weibull or Rayleigh models are often used. The approach consists in assimilating the distribution law to one of these models and to determine the model parameters so that it gets closest to the discrete law achieved by the statistical treatment of the wind speed measurements. Several studies have shown that the Weibull and Rayleigh models provide good results. In [1], these models have been compared in an analysis study of the wind energy potential. The results achieved for the two models are similar and satisfactory. In [8], the Weibull model parameters have been estimated by using different methods. The results have shown that the assessment method of these parameters, based on a linear regression method, provide better results than that based on empirical formulas. The Weibull model is also used in [16] to determine the monthly and yearly distribution laws of the wind speeds, as well as the available power and the amount of energy produced by different wind generators. Determining a distribution law for the speeds can be considered as a non linear regression problem, in which the distribution law chosen (Weibull or Rayleigh) is identified so as to get nearer the discrete law. As regards function approximation, however, the techniques based on the artificial neural networks approach have shown that very good performances can be obtained [4,7].
1745
L. Thiaw et al. / Applied Energy 87 (2010) 1744–1748
An artificial neural network (ANN) is a complex network made up of interconnected elementary computing units named formal neurons. The neurons are organized in clusters or layers and can be interconnected in different ways. In function of the network architecture, there are several types of neural networks. The neural networks are used in applications as various as varied: in [2], a neural network has been used to predict energy consumption in a residential sector; in [9] a in [9] a neural network has been used to predict storms in the short term; in [11], the rain assessment network starting from radar measurements. The ANN of the Multi Layer Perceptron (MLP) type are those most used, notably in non linear regression problems. In this research work, an MLP network is used to more accurately determine the wind speed distribution law. This approach makes it possible to better assess the wind energy potential and the wind generator performances. This paper is structured as follows: Section 2 introduces the wind potential analysis classical method; Section 3 introduces the MLP-type artificial neural networks; Section 4 describes the method for using an MLP to analyse the wind potential; the last part presents the results on the site of Dakar, Senegal. 2. Classical method for wind resource and wind generators production assessment The wind speed can be considered as a random variable. Simply measuring it is not enough to characterize a site wind potential. Knowing the frequencies of the speeds or better the distribution function (probability density) of wind speeds is essential. This speed distribution law enables the energy amounts available, recoverable or produced by a wind generator to be assessed. It becomes necessary to carry out a statical study to characterize the site wind potential completely. 2.1. The Weibull distribution To study the distribution of wind speeds, the two-parameter Weibull model is used very often. The more complete for the modelling of the wind potential but more complex three-parameter Weibull model is rarely used. The two-parameter Weibull distribution law or probability density is defined by:
k k v k1 v f ðv Þ ¼ exp c c c
ð1Þ
where f ðÞ is distribution law or probability density; v is the wind speed ðm=sÞ; c is the scale factor ðm=sÞ; and k is the shape factor (characterizes the distribution dissymmetry). The distribution function of wind speeds FðÞ defined as the likelihood that the wind speed will be lower than a value v is expressed by:
k v Fðv Þ ¼ 1 exp c
ð2Þ
Rewriting Eq. (2) in the form of:
ln½ lnð1 Fðv ÞÞ ¼ k lnðv Þ k lnðcÞ
ð3Þ
and setting y ¼ ln½ lnð1 Fðv ÞÞ and x ¼ lnðv Þ a regression straight line is obtained:
y ¼ mx þ b
ð4Þ
Determining parameters m and b by the least squares method makes it possible to assess Weibull model parameters c and k :
k¼m
b c ¼ exp k
ð5Þ ð6Þ
2.2. Wind energy assessment The wind instantaneous power across a unit surface, perpendicular to the wind speed direction, is expressed by the relation:
P¼
1 q v3 2
ð7Þ
where q is the air density. The average power available in the wind can be assessed by the relation:
Pm ¼
1 q 2
Z
1
f ðv Þ v 3 dv
ð8Þ
0
For a discrete distribution law the relation (8) is written:
Pm ¼
N 1 X q f ðv i Þ v 3i 2 i¼1
ð9Þ
N designating the number of measurements. The average energy available for a duration period of T hours (in kWh=m2 ) is assessed, for a continuous distribution law by the relation:
T 1 q 1000 2
EmT ¼
Z
1
f ðv Þ v 3 dv
ð10Þ
0
and for a discrete law, by the relation: N T 1 X f ðv i Þ v 3i q 1000 2 i¼1
EmT ¼
ð11Þ
A wind generator is generally characterized by its power curve function of the speed P ¼ Pðv Þ, its rated power P r , its starting V s , rated V r , maximum V c as well as the diameter of its blades D sweeping a surface S. These characteristics make it possible to assess the available energy amount the wind generator can recover on a given site. For a continuous distribution law, this energy amount is assessed for a T duration period by the relation:
EgT ¼
T 1 qS 1000 2
Z
Vr
Vs
f ðv Þ v 3 dv þ V 3r
Z
Vc
f ðv Þ dv
ð12Þ
Vr
For a discrete distribution law, the relation (12) is written:
EgT ¼
r c X X T 1 f ðV i Þ V 3i þ V 3r f ðV i Þ qS 1000 2 i¼s i¼r
! ð13Þ
where n the indexes s; r and c correspond to the speeds V s ; V r and V c respectively. The amount of energy a wind generator would produce on a given site during the period T can be assessed from the characteristics P ¼ Pðv Þ and the wind speed distribution law on the site: relation (14) for a continuous distribution law and relation (15) for a discrete distribution law.
EgpT ¼ EgpT ¼
T 1000
Z
Vc
Vs
f ðv Þ Pðv Þ dv !
c X T f ðV i Þ PðV i Þ 1000 i¼s
ð14Þ ð15Þ
Relations (10)–(15) enable the amounts of energy available, recoverable or produced monthly ðT ¼ 30 24 hÞ or yearly ðT ¼ 365 24 hÞ. If the wind speed measurements have been made from a height of H1 above the ground, it is possible to assess the wind speeds at a height H2 by the relation:
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a H2 V2 ¼ V1 H1
ð16Þ
3
where a is a parameter depending on the soil roughness [1,15].
1 3. Feed forward neural networks
4 An ANN can be defined as a complex network made up of interconnected elementary computing units (formal neurons). The neurons are organized in clusters or layers and can be connected in different ways. This connection topology between the neurons defines the network architecture, linked to the task it has to perform. This task is often specified in the form of examples1 including a set of input values and a set of corresponding output values the network has ‘‘to learn” in order to be able to supply correct answers for other unknown inputs. The learning is the network parameter assessment procedure which allows it to meet a performance criteria minimizing the error between the network output and the actual output. The learning is carried out according to an algorithm peculiar to the network architecture. There are several types of ANN. The MLP-type ANN are the most used ones, notably in non linear regression problems [4,7]. An MLP network includes one or several hidden layers with sigmoid type activation function as well as an output layer. Fig. 1 represents an example of a two-input MLP network including a three-neuron hidden layer and a one-neuron output layer. The L hidden layer neurons receive information from L 1 layer neurons (or units) and are connected to the L þ 1 layer neurons. There are no connections between neurons of the same layer. Each output layer neuron achieves a non linear function of the network inputs. For more information about the MLP, see [7,13,5]. The potential si of a neuron i and its activation Oi are given by relations (17) and (18) respectively.
si ¼
p X
xij xj bi
ð17Þ
j¼1
Oi ¼ g i ðsi Þ
ð18Þ
where p designates the number of units of the upstream layer, connected to neuron i; xj represents the input j of the network if neuron i belongs to the first hidden layer, or in the opposite case, the neuron j output Oj of the hidden layer coming before that of neuron i; xij is a scalar constant representing the weight of the connection between neuron i and neuron (or input) j; bi is a scalar constant called bias; and g i ðÞ is the activation function of neuron i. It can be different depending on whether the neuron is a hidden neuron or an output neuron. In general, all the hidden neurons have the same activation function which is often a sigmoid function (for example gðsÞ ¼ 1=ð1 þ expðsÞÞ). The output neurons also have the same activation function, in general linear (for example gðsÞ ¼ s). The determination of the MLP network parameters is made according to a supervised learning mode: the learning database is presented to the network which has to adapt its parameters according to an algorithm so that the difference between the system output and that of the model is low enough. The most used learning technique in MLP networks is the back propagation algorithm [12]. 4. Assessing wind resource by neural network In this research work, an MLP neural network is used to determine the wind speed distribution law. The statistical study of wind 1
These examples constitute the network learning database.
6
2 5 output layer inputs hidden layer Fig. 1. Example of an MLP network.
speed measurements makes it possible to determine the frequencies of the speed contained in each speed interval Ii ¼ V i1 ; V i ; i ¼ 1; . . . ; M, M being the index corresponding to the maximum speed recorded. For each interval Ii , frequency fi is calculated by the expression:
fi ¼
Ni N
ð19Þ
in which Ni is the number of speed values contained in Ii . An MLP neural networks is then worked out to determine the speed distribution law f ðv Þ. The learning database consists of the couples of points ðV i ; f i Þ, where the V i are the inputs and the fi , the outputs. Determining the relation f ðv Þ enables the amounts of energy available, recoverable or produced (cf Eqs. (11), (13) and (15)) to be determined. The assessment of a wind generator production is made starting from the machine power curve, provided by the constructor in the form of couples of points ðv i ; Pi Þ. A more accurate calculation would necessitate to have a continuous relation P ¼ Pðv Þ. There are empirical models allowing the characteristics P ¼ Pðv Þ of a wind generator to be represented. The Gauss theoretical model described by relation (20) is often used:
Pðv Þ ¼ P0 þ
A v V0 pffiffiffiffiffiffiffiffiffi exp 2 2 w w p=2
ð20Þ
in which P0 ; V 0 ; A and w are parameters to be identified. In [1], these parameters are identified by using the Origin 5.0 software. In the present work, the relation P ¼ Pðv Þ is determined by using a neural network. The learning database consists of the points ðv i ; Pi Þ provided by the constructor. 5. Results and discussion The wind energy assessment methodology proposed was applied on the site of Dakar, Senegal (latitude: 14 370 N, longitude: 17 270 W, altitude: 0 m). The available wind speed measurements, obtained at the Dakar Airport site, are instantaneous values recorded every 3 h and cover a period of 10 years, from 1995 to 2005. These data are used here only for the purpose of the proposed method validation. More accurate wind energy assessment require more complete wind speed measurements. Fig. 2 gives the monthly average of the wind speeds at a height of 10 m above the ground. The results show that the most important winds are recorded in December with an average of 5:5 m=s and the least windy month is July with an average of 3:9 m=s. The annual average of the wind speed is 4:4 m=s. The speed variation slot has been divided into
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5.5
0.3 discret MLP Weibull
0.2
5
Probability
Mean wind speed (m/s)
0.25
4.5
0.15 0.1 0.05 0
4 2
4
6
8
10
−0.05
12
0
2
4
6
Month
18 intervals and in each interval, the frequencies have been determined by relation (19). On the basis of the Weibull model determination method presented in the paragraph Section 2.1, the following parameters values have been found: c ¼ 4:9 m=s and k ¼ 2:19. On the other hand, an MLP neural network with one input, two hidden layers including three neurons each and 1 output has been identified. Wind potential characteristics assessed by the use of these two models are then compared with those assessed using the discrete method. The discrete distribution law obtained by treating the measurements statistically as well as the continuous distribution laws corresponding to the Weibull model and to the identified MLP neural network are represented in Fig. 3. To verify that the relation obtained with the MLP network is a distribution law, the integral Iv defined by relation (21) has been calculated. The results gives Iv ¼ 0:997, showing that the relation obtained can be considered as a distribution law (f must verify R1 the condition 0 f ðv Þ dv ¼ 1).
f ðv Þ dv
12
14
16
18
150 discret MLP Weibull
100
50
0 0
2
4
6
8
10
12
14
16
18
Wind speed (m/s) Fig. 4. Yearly available energies assessed with different methods.
ð21Þ
0
The amount of energy available assessed with the relations (10) and (11) for a 1-year period have been determined. Fig. 4 shows the contribution of each speed to the amount of energy available annually. The assessments made with the MLP network are nearer the assessments obtained with the discrete law than those obtained with the Weibull law. The speed–duration curves have also been determined. Fig. 5 shows that the results obtained with the MLP neural network are closer to the results obtained by means of the discrete law. The wind generator WES18 has been simulated with the site data. The characteristics of this wind generator2 are: Rated power 80 kW. Starting speed V s ¼ 2:7 m=s. Rated speed V r ¼ 13 m=s. Cut-off speed V c ¼ 25 m=s. Surface swept by the blades S ¼ 254 m2 .
100 discret MLP Weibull
90 80 70
Duration (%)
Iv ¼
V max
10
Fig. 3. Wind speed distribution laws obtained by different methods.
Available energy (kWh/m2)
Fig. 2. Monthly mean wind speed on the site of Dakar at 10 m above the ground.
Z
8
Wind speed (m/s)
60 50 40 30 20 10 0 0
2
4
6
8
10
12
14
16
18
Wind speed (m/s) Fig. 5. Speed–duration curves obtained with different methods.
The power–speed characteristics of the wind generator supplied by the constructor has been modelled by an MLP neural network with one input, two hidden layers containing two and three neurons respectively, and a one-neuron output layer. The characteris2
Source: http://www.windenergysolutions.nl.
tic supplied by the constructor and that obtained by the MLP model are presented in Fig. 6. Tables 1 and 2 give the total amounts of energies available as well as those recoverable and produced by the aerogenerator WES18 at heights 10 m and 40 m respectively.
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L. Thiaw et al. / Applied Energy 87 (2010) 1744–1748
90 Constructor MLP
80
Electrical power (kW)
70 60 50 40 30 20 10 0 −10
0
5
10
15
20
Wind speed (m/s)
References
Fig. 6. The power–speed characteristic of the wind generator WES18.
Table 1 Annual energies available, recoverable and produced by the wind generator WES18 at 10 m above the ground. Energies
Discrete law
Weibull
MLP
Available ðkWh=m2 Þ Recoverable ðMWhÞ Produced ðMWhÞ
895.6 223.1 69.1
770.5 191.7 60.9
879.2 218.0 68.0
Table 2 Annual energies available, recoverable and produced by the wind generator WES18 at 40 m above the ground. Energies 2
Available ðkWh=m Þ Recoverable ðMWhÞ Produced ðMWhÞ
wind speed frequencies, wind speed–duration curves, energies available, recoverable and produced. A comparative study with the method using the Weibull model shows that the results achieved with the help of the neural method proposed are closer to the results achieved with the discrete method obtained by the statistical treatment of measured wind speeds. The assessment of the amount of energies available annually at a height of 10 m above the ground obtained by the discrete, the Weibull and the neural models gives 895:6 kWh=m2 ; 770:5 kWh=m2 and 879:2 kWh=m2 respectively. For a 40 m height, the estimated available energies are 1896:8 kWh=m2 ; 1842:4 kWh=m2 and 2102:4 kWh=m2 respectively for the discrete, the Weibull and the neural models. The models have also enabled the annual production of the wind generator WES18 of 80 kW power set up at 10 m and 40 m above the ground to be assessed.
Discrete law
Weibull
MLP
1896.8 439.3 134.4
1842.4 454.7 144.1
2102.4 466.3 143.0
6. Conclusion A new neural technique-based approach designed to assess the wind energy potential has been proposed in this paper. An MLP neural network with one input, two hidden layers including three neurons each and 1 output is identified and satisfactorily represents the wind speed distribution law of the Dakar site. The Weibull parameters of the wind speed distribution law are also determined: the scale factor is 4:9 m=s and the shape factor is 2.19. The proposed neural approach has made it possible to more accurately determine the Dakar site wind energy characteristics:
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