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Fuzzy modeling techniques and artificial neural networks to estimate annual energy output of a wind turbine
Renewable Energy 35 (2010) 2008–2014
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Renewable Energy journal homepage: www.elsevier.com/locate/renene
Fuzzy modeling techniques and artificial neural networks to estimate annual energy output of a wind turbine M. Jafarian*, A.M. Ranjbar Department of Electrical Engineering, Sharif University of Technology, Tehran, Iran
a r t i c l e i n f o
a b s t r a c t
Article history: Received 3 March 2009 Accepted 1 February 2010 Available online 26 February 2010
The purpose of this article is to develop a new method to estimate annual energy output for a given wind turbine in any region which should be easy to use and has satisfactory accuracy. To do this, hourly wind speeds of 25 different stations in Netherlands, output power curve of S47 wind turbine and fuzzy modeling techniques and artificial neural networks were used and a model is developed to estimate annual energy output for S47 wind turbine in different regions. Since this model has three inputs (average wind speed, standard deviation of wind speed, and air density of that region), this model is easy to use. The accuracy of this method is compared with the accuracy of conventional methods and it is shown that this new method performs better. Thereafter, we have shown that by making some small changes to this proposed model, other pitch control wind turbines could be modeled too. As an example, we have modeled E82 wind turbine based on the model developed for S47 and it is shown that this model has still satisfactory accuracy. Ó 2010 Elsevier Ltd. All rights reserved.
Keywords: Annual energy output Artificial neural network Fuzzy modeling technique Wind turbine
1. Introduction The wind has been used as an energy source for a very long time. The first windmills were used by the Persians in approximately 900 AD [1,2]. Wind energy became a significant topic in the 1970’s during the energy crisis in the U.S. [3] and now it continues to be the fastest growing power generating technology in the world [4] due to its availability, low cost and environment friendly operation of this technology [5]. Development of techniques for accurately assessing the wind energy potential of a site is gaining increased importance [6], since expected power output has to be estimated in advance so as to make possible the assessment of the economic viability of any wind farm project [7]. Energy output estimation for wind turbines of different power ranges has been the subject of a number of papers. Most of these studies have used the wind speed pattern of a region to estimate the wind speed distribution of that region and then, by knowing the wind turbine specifications, the energy output of that turbine is estimated. We will give a brief review of these methods in section 3 of this article. In this paper, a new method is developed to estimate the annual energy output of a known wind turbine in any region, using fuzzy
* Corresponding author. Tel./fax: þ98 2166164037. E-mail address: [email protected] (M. Jafarian). 0960-1481/$ – see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2010.02.001
modeling techniques and artificial neural networks. To develop such a model, the output power curve of the wind turbine and the hourly wind speed records of one year of at least 25 different regions are required. This new method has two advantages than the conventional ones that it requires only 3 inputs (annual average wind speed, standard deviation of wind speed and average air density of the region in which the wind turbine is installed) so it is easy to use and also it provides better accuracy in estimation as will be proved in this paper. One of the disadvantages of this model is that for any wind turbine, a new model should be built, but we will show later that the model built for an arbitrary pitch control wind turbine, can be used with other pitch control ones by means of making some small changes to the former model. To make these changes, the rated power, the hub height and the rated wind speed of the former and the later wind turbine should be known. 2. Basic principles of wind turbine power production Wind turbine power production is a function of two quantities: wind speed and air density. The dependency of wind turbine power production on wind speed can be shown by a curve such as Fig. 1. This curve is expressed in 1.225 kg/m3 air density (1.225 kg/m3 is the air density in standard conditionals of 288.16 Kelvin air temperature and 101 325 Pascal air pressure). On the other hand, the output of a wind turbine has linear relation with air density [1]. Therefore wind turbine power production can be calculated using equation (1):
M. Jafarian, A.M. Ranjbar / Renewable Energy 35 (2010) 2008–2014
Nomenclature
h r r0 sy A C Cp Cpr COD D Eann f(v) h0
pðvÞ ¼
hi IEann K pave p(v) pw(v)
overall power efficiency of wind turbine air density (kg/m3) air density in standard conditions (kg/m3) standard deviation of the measured data y swept area of wind turbine (m2) Weibull scale parameter (m/s) power coefficient of wind turbine nominal power coefficient coefficient of determination wind turbine blade diameter (m) annual energy output, kJ Wind speed probability density function surface roughness length, m
r p ðvÞ r0 w
Pr RMSE s v vave vc vf vr
(1)
where pw(v) is the wind turbine output power in standard air density which is obtained from wind turbine power curve and r0 is air density in standard conditions. If the wind turbine hub height is not the same as the anemometer height, the wind speed should be estimated at the wind turbine hub height. The Logarithmic profile is often used to estimate wind speed from a reference height, h1, to another level, h2, using the following relationship [1,8]:
lnðh2 Þ=lnðh0 Þ vðh2 Þ ¼ vðh1 Þ lnðh1 Þ=lnðh0 Þ
(2)
where v(h1) and v(h2) are the values of wind speed at altitude h1 and h2 and h0 is the surface roughness length of the region. The surface roughness length is a parameter that characterizes the roughness of the surrounding terrain. The values of surface roughness lengths for various types of terrain are cited in Manwell et al. [1]. 3. Review of conventional methods used to estimate wind energy potential As it was mentioned before, in most of the methods used to estimate wind energy potential of a certain region, it has been tried to find a suitable wind speed distribution model to approximate the real wind speed pattern of that region such as the Weibull, the Rayleigh and the Lognormal distributions. The two-parameter
2009
altitude above ground level, m five year average of Eann, kJ Weibull shape parameter the average output power of wind turbine, kW wind turbine produced power in wind speed v, kW wind turbine produced power in wind speed v in standard conditions, kW wind turbine rated power, kW root mean square error operating range of wind speed, m/s wind speed, m/s average wind speed, m/s cut-in speed of the wind turbine, m/s cut-out speed of the wind turbine, m/s rated speed of the wind turbine, m/s
Weibull function is accepted as the best among these distributions [1,6,9–11]. Weibull probability density function can be expressed by the following equation:
f ðvÞ ¼
k1 k k v v exp c c c
(3)
in this equation, c is Weibull scale parameter and k is Weibull shape parameter. Different methods have been used to estimate k and c parameters for different regions. Some of these well known methods are: maximum likelihood method [11,12], mean wind speed_standard deviation method (MWS_SD) [13,14] and least square error method [3]. Next we review the conventional methods used to estimate energy potential of a region. 3.1. One-two-three equation Carlin [15] used the Rayleigh distribution to model wind speed pattern of a given region and suggested the following equation to calculate the average output power of a wind turbine in a site in which average wind speed equals vave.
pave ¼
r 2 D r0 3
2
v3ave
(4)
In this equation, D is the wind turbine blade diameter. If Eann is the annual energy output of the wind turbine, it can be calculated using the following equation which he called the one-two-three equation.
Eann ¼ 8760
2
r 2 D r0 3
v3ave
(5)
This method is easy to use because it has only three inputs, but it does not have an acceptable accuracy. 3.2. Kiranoudis method In this method, two assumptions are reclaimed: Weibull distribution is used to model wind speed pattern and the power coefficient of a wind turbine, Cp is assumed to have the following relationship with wind speed [5]:
Cp ¼ Cpr exp Fig. 1. S47 output power curve.
ðln v ln vr Þ2 2ðln sÞ2
! (6)
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M. Jafarian, A.M. Ranjbar / Renewable Energy 35 (2010) 2008–2014
In this expression, the turbine characteristics are: the nominal power coefficient, Cpr, the rated wind speed, vr, and a parameter expressing the operating range of wind speed, s. Therefore Eann can be expressed as follow:
Eann
r pr ¼ 8760 r0 v3r
Z
vf
exp
ðln v ln vr Þ2
0
2ðln sÞ2
3.4. Random number generation
! 3
v f ðvÞdv
(7)
where in this equation, f(v) is Weibull distribution. This model has six input parameters: pr, vr, s that can be obtained from wind turbine specifications, k and c the parameters of Weibull distribution that can be calculated by means of any methods that was mentioned before, and air density. This model has two disadvantages; it needs many inputs and also it does not have satisfactory accuracy, but it should be noticed that its accuracy is much better than the one-two-three equation one. 3.3. Polynomial modeling of wind turbine power curve In this method, wind turbine power curve is approximated by a polynomial like the following equation [16–18]:
8 <0 pr pðvÞ ¼ m : m v vm vr vm c c
v < vc or v > vf vr < v < vf vc v vr
(8)
In this relationship, vc is the cut-in speed (the minimal wind speed that wind turbine can produce power), vr is the rated speed, vf is the cut-out speed (the maximum wind speed that wind turbine can produce power) and m usually is considered to be equal to 1 or 2. Therefore to estimate Eann in this method, equation (9) can be suggested:
0
Eann
r ¼ 8760pr @ r0
Zvr vc
vm vm c f ðvÞdv þ m vm r vc
Zvf
modern wind turbines. In this type of wind turbine, wind turbine output power is constant in a certain wind speed range, say [vr vf]. This constant value is referred to as wind turbine rated power (pr).
1 f ðvÞdvA
(9)
vr
where in this relationship, f(v) is Weibull distribution. One of the main disadvantages of this model is that the simple model used to approximate the wind turbine output power curve in this method, has adequate accuracy, only for pitch-controlled wind turbines [17]. This method has several inputs and it is another disadvantage of this method. Its accuracy is acceptable but this method is not as accurate as the new method which will be introduced in this article. It should be said that three strategies are used to control the speed of a wind turbine to prevent the high values of wind speed to damage the wind turbine. These methods are named pitch control, yaw control and stall control. Based on the method used to control the speed of the wind turbine, the wind turbine output power curve may be one of the three different curves depicted in Fig. 2 [18]. Nowadays mostly the pitch control method is used in
Fig. 2. Output power curves of three different types of wind turbine.
In this method, hourly wind speed values during a period of one year are synthesized by means of generation of 8760 random numbers. The Weibull distribution is used to generate these random numbers. Then, using the output power curve of the wind turbine, these pseudo wind speed values can be converted to 8760 pseudo hourly power values. Therefore, Eann can be estimated using the following equation:
Eann ¼
X r 8760 pðv Þ r0 i ¼ 1 i
(10)
This method requires k and c parameter of Weibull distribution (because the pseudo values of wind speed (vi) will be generated using Weibull distribution and to do that, the parameters of Weibull distribution should be known), air density of the region in which wind turbine is installed, and output power curve of the wind turbine. This method has not been used up to now and is introduced in this article for the first time, but because this method uses probabilistic distributions to describe the wind speed pattern, it is introduced as a conventional method. This method is not user friendly; it needs the output power curve of the wind turbine and a method to generate random number generation. Also this method is not as accurate as the new method which will be introduced in next section. 4. Fuzzy modeling techniques and neural networks to estimate wind turbine energy output Use of neural networks for prediction of wind speed and wind turbine power production has been the subject of some articles. Kalogirou [19] uses neural network to predict the mean monthly wind speed in regions of Cyprus. He developed two networks, one with 5 inputs for prediction of mean monthly wind speed in a determined region and another with 11 inputs for prediction of mean monthly wind speed in nearby locations and he found that the proposed neural networks perform successfully. Mabel and Fernandez [20] use artificial neural networks for prediction of mean monthly energy production of a wind farm in Muppandal, Tamil Nadu (India), and they claimed that the proposed network gives acceptable results.
Fig. 3. Normalized standard deviations of Eann average values for s210, s225, and s380 stations.
M. Jafarian, A.M. Ranjbar / Renewable Energy 35 (2010) 2008–2014 Table 1 Average wind speed, Standard deviation of wind speed and IEann for 50 different regions in Netherlands. Station Average wind speed (m/s) Standard deviation of wind speed (m/s) IEann (kW)
S210 7.5444 4.3926
S225 8.1420 4.1150
– – –
S380 4.7632 2.7889
1.8367e þ 6
2.1661 e þ 6
–
7.9403 e þ 6
The main point about these articles is that these predictions are valid only for one region, but in this article some networks and techniques are introduced to predict annual energy output of a wind turbine in any region. In this method, hourly wind speed values from 50 stations in different locations of Netherlands collected over a period of several years in Hydra project (which are collected by Royal Netherlands Meteorological Institute and Koninklijk Netherlands Meteorological Institute) are used to build a model to estimate wind energy potential. The first step to build this model is to use equation (1) to convert the values of wind speed for all stations to new values so that all values would correspond to the same altitude (40 m), because wind speed values are recorded in different altitudes. The wind turbine used in this study is S47 with a rated power of 660 kW, a pitch control system with hub height of 40 m. The output power curve for this wind turbine is depicted in Fig. 1 [21]. The wind speed annual average of a given region varies from year to year, resulting in various annual energy outputs for a given wind turbine. Therefore, to be able to estimate wind energy potential of a region, wind speed variations in that region should be studied over several years. In this article, three stations of S210, S225, and S380 are studied for their annual wind speed variations. For each of these stations, Eann is calculated for several years and is averaged over periods of n years (n ¼ 1, 2, ., 12). Then for all values of n, the normalized standard deviations (standard deviation divided by average) of these average values are calculated. Fig. 3 depicts these normalized standard deviations for three stations s210, s225, and s380 with respect to n. If we suppose the normalized value of standard deviation to be the uncertainty (due to variations of Eann over different years) of estimating Eann for a wind turbine, it can be seen that for the case n ¼ 5, this uncertainty in estimation is less than 15% for all three stations. Therefore, to achieve an acceptable estimation uncertainty, the index of annual energy output of a wind turbine in
2011
a given region (IEann) is equal to the average of annual energy output values of that wind turbine over five successive years. Therefore, IEann is calculated as follows:
IEann ¼
5 X 1 r X 1 r 8760*5 Eann ðiÞ ¼ pðvi Þ 5 r0 i ¼ 1 5 r0 i ¼ 1
(11)
For all 50 stations, based on the values of hourly wind speed values of five successive years and output power curve of S47, IEann values are calculated using equation (11) for standard air density. Then, for each station, average and standard deviation values of wind speed are calculated for this period, the results of which is presented in Table 1. It should be said that not all values are given in this table, just a sample is presented. The values of average wind speed and standard deviation of wind speed form the inputs for the model which gives the estimated value of IEann in standard air density. Having chosen the model’s inputs and output, we then use common types of fuzzy modeling techniques and artificial neural networks, and train them using the data available in Table 1 to develop the model. In the former case we utilized Takagi-Sugeno model [22] and Sugeno-Yasukawa model [23], and in the latter, Feed Forward and Cascade Forward Backpropagation Networks [24], Radial Basis Network [25], Generalized Regression Network [26] and ANFIS network [27] are used. To start, the data points of Table 1 are divided into two random groups A and B, each of which includes 25 data points. In each stage, one group is used to build a model, and the other to test its performance. That is to say, the model built using data group B is tested with data group A, and similarly, the model built with data group A is tested with data group B. Therefore, 50 estimated values of IEann are obtained and are compared with true values using the Coefficient of Determination (COD) and Root Mean Square Error (RMSE) tests. The definition of the COD is [4]:
COD ¼ 1
s2y;x s2y
(12)
where sy is the standard deviation of the measured data y from its own mean value ym, which is conventionally defined as:
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u n uX sy ¼ t ðyi ym Þ2 =ðn 1Þ
(13)
i¼1
Table 2 COD and RMSE values for different methods used to estimate IEann. Methods
Takagi-Sugeno model Radial Basis network Generalized Regression Network One-two-three equation Polynomial modeling of wind turbine power curve Random number generation Kiranoudis method
Inputs COD and RMSE
Mean wind speed – standard deviation of wind speed
k and c using maximum likelihood method
k and c using modified maximum likelihood method
k and c using Least Square Error
k and c using mean wind speed-standard deviation method
Wind turbine blade diameter
COD RMSE COD RMSE COD RMSE COD RMSE COD RMSE COD RMSE COD RMSE
0.9239 1.48e þ 5 0.9351 1.37e þ 5 0.9266 1.45e þ 5 – – – – – – – –
– – – – – – – – 0.9071 1.64e þ 5 0.9108 1.60e þ 5 0.7503 2.68e þ 5
– – – – – – – – 0.9018 1.68e þ 5 0.9157 1.56e þ 5 0.7757 2.54e þ 5
– – – – – – – – 0.9047 1.66e þ 5 0.9011 1.69e þ 5 0.7616 2.62e þ 5
– – – – – – – – 0.8984 1.71e þ 5 0.9159 1.55e þ 5 0.7735 2.56e þ 5
– – – – – – 12.1452 1.95e þ 6 – – – – – –
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Table 3 COD and RMSE values of 35-sampled models.
COD RMSE
Takagi-Sugeno model
Radial Basis network
Generalized Regression Network
0.9334 1.31e þ 5
0.9330 1.32e þ 5
0.8992 1.62e þ 5
where n is the total number of measurements (here n equals 50). Similarly,
sy;x
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u n uX ¼ t ðyi yic Þ2 =ðn 2Þ
(14)
i¼1
where the yi are the actual values of y, and yic are the values computed from the correlation equation for the same value of x. A higher COD represents a better fit using the theoretical or empirical function. Normally, a value higher than 70% of COD is acceptable [4]. RMSE can be calculated using equation (15):
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u n uX RMSE ¼ t ðyi yic Þ2 =n
(15)
i¼1
The smaller the value of this parameter, the better the function approximates the measured data. Our simulations suggest that among these proposed models, Sugeno-Yasukawa model, Feed Forward Back-propagation, Cascade Forward Back-propagation, and ANFIS Networks couldn’t meet the desired accuracy for they give COD values less than 0.7, while others could. The values of accuracy of these methods are compared with four conventional models mentioned in section 3. For the conventional models which require k and c parameter of Weibull distribution, every four possible methods mentioned to calculate k and c is examined. Table 2 represents the results of this comparison, which clearly states that the Takagi-Sugeno, Radial Basis network and Generalized Regression Network models perform better as compared to other conventional methods for they have greater COD and less RMSE values. The model which is build by Takagi-Sugeno method consists of 4 fuzzy rules. In this model, two fuzzy sets are determined for mean wind speed and two for wind speed standard deviation. It should be mentioned that Takagi-Sugeno method chooses the proper fuzzy sets and rules by itself. For the Radial Basis Network, a network with one hidden layer that consists of 25 neurons is used. By choosing different values for the spread parameter of this network, it was recognized that the best value for this parameter is 0.26. For Generalized Regression a network with one 25 neurons hidden layer is used and the best value for spread parameter is recognized equal to 500. With the results reported in Table 2, these new models excel conventional ones in terms of the ease with which they can be used, the fact that they require only three inputs and the much better accuracy they would provide. The only drawback of these proposed models is the high volume of data required for their development.
To develop such models, one must have hourly wind speed data collected in at least 25 different regions during a period of at least one year. Next, the effect of the number of samples used to train the proposed models on their accuracy is examined. To do this, we regroup the data in Table 1 and divide it into three groups E, F, and G each having fifteen data samples (leaving 5 data samples not involved in this grouping process). Using 35 data samples which are not included in E, a model is built. Then, this model is evaluated using the remained data samples, which are members of E. The same procedure is repeated for the other groups of F and G. Therefore, 45 estimated values for IEann are obtained and compared with the real ones using COD and RMSE indexes the result of which is explained in Table 3. In this situation, the number of fuzzy rules and sets in the model build by Takagi-Sugeno method is similar to previous one, but for Radial Basis Network, the number of neurons in hidden layer equals to 35 and the best value for the spread parameter equals to 0.45 and for Generalized Regression Network, the number of neurons in hidden layer equals to 35 and the best value for the spread parameter equals to 500. According to the data available in Table 3, as the number of samples used to train the models increases, the accuracy of Generalized Regression Network decreases, but the accuracy of Radial Basis network and Takagi-Sugeno model changes a bit, suggesting that the Takagi-Sugeno model and Radial Basis network are not overfit as the number of samples increases and hence are appropriate for our purpose. 5. Applying the proposed model to other pitch control wind turbines As stated before, pitch control wind turbines have similar output power curves. They have a common characteristic that their output power is constant in a certain wind speed range, say [vr vf]. This similarity in output power curves makes possible for the developed model for S47 turbine to be used for other pitch control wind turbines. However, since other properties such as the hub height, the rated power, cut-in speed, cut-out speed, and the rated wind speed have different values for other turbines, for the model to be precise for the new turbines, it should be changed a little bit. But, it should be noticed that, the value of cut-in speed does not have a considerable effect on the Eann due to very low produced power around cut-in speed, therefore, different cut-in speeds for different turbines does not necessitate any change in the model. Also, no change in the model is made due to different cut-out speeds, since wind speeds near cut-out speed rarely happen and hence the effect of cut-out speed on Eann is negligible (less than 1%) [16]. Therefore, to use the model developed for S47 for other pitch control wind turbines, three different properties between S47 and the new turbine should be taken into account: hub height, rated power, and rated wind speed. 5.1. Taking into account different hub heights Equation (2), explains the altitude’s influence on wind speed. Using this equation, the relationship between mean wind speed
Fig. 4. Process of modification of the S47 model to be used with other pitch control wind turbines.
M. Jafarian, A.M. Ranjbar / Renewable Energy 35 (2010) 2008–2014
and standard deviation of wind speed in different hub heights can be written as:
Mean wind speed ðh2 Þ ¼ Mean wind speed ðh1 Þ
lnðh2 =h0 Þ lnðh1 =h0 Þ
lnðh2 =h0 Þ SD of wind speed ðh2 Þ ¼ SD of wind speed ðh1 Þ lnðh1 =h0 Þ
(16)
(17)
where in equation (17), SD stands for Standard Deviation. Equations (16) and(17) suggest that to modify the model for a new hub height, model inputs must be multiplied by the term ln(h2/h0)/ln(h1/h0). 5.2. Taking into account different rated powers To take into account different rated powers, the developed model’s outputs should be multiplied by the term pr2/pr1, where pr1 is the rated power of S47 and pr2 is the rated power of the new turbine for which the model is to be modified. 5.3. Taking into account different rated wind speeds To consider the effect of different rated wind speeds, we use the same idea which is used in polynomial modeling of wind turbine power curve method to estimate the difference between Eann values of these two turbines. To do this, the unit difference of annual output energies (Eann divided by rated power of wind turbine) for these two turbines is estimated using equation (18).
0 DE ¼ 8760@
Zvr2 vc
v2 v2c f ðvÞdv þ v2r2 v2c
Zvr2 vc
1 v2 v2c f ðvÞdvA v2r1 v2c
(18)
where f(v) is the Weibull distribution for which k and c can be calculated using mean wind speed-standard deviation method. Also in the above equation, cut-in speed values are supposed to be the same for both turbines. It should be noticed that here, we have used the polynomial modeling of wind turbine power curve method, just to make necessary modifications which validate our model for the new turbine, and not to directly estimate its annual energy output because as was shown before, this technique is not so accurate in the direct estimation of Eann. To combine all these 3 changes required to be done on S47 model to modify it to be usable for a new pitch control wind turbine; a scheme like what is depicted in Fig. 4, can be suggested. To evaluate this proposed process, the model which was developed for S47 wind turbine using Takagi-Sugeno and Radial Basis network techniques is modified using the above described process to model ENERCON E82 wind turbine. This turbine’s characteristics are as follows: rated power of 2000 kW, rated wind
2013
Table 4 COD and RMSE values to use S-47 modified model for E82 wind turbine.
COD RMSE
Takagi-Sugeno model
Radial Basis Network
0.9667 3.52e þ 5
0.9659 3.56e þ 5
speed of 12 m/s, hub height of 80 m, and its output power curve is depicted in Fig. 5 [28]. Therefore to change the model of S47 for E82, values of h1, h2, vr1, vr2, pr1 and pr2 are set as: 40 m, 80 m, 13 m/s, 12 m/s, 660 kW and 2000 kW respectively. Using hourly wind speeds of 50 stations (collected in Hydra project) and output power curve of E82, the true values of IEann is derived for all 50 stations. Then, using the proposed models this time, IEann is estimated and compared to true values. Results of this comparison are presented in Table 4 stating that the proposed process has satisfactory accuracy. 6. Conclusions In this article a new method to estimate annual energy output for a wind turbine in a site of known wind topology was introduced. In this new method, hourly wind speeds of 25 different stations in Netherlands, output power curve of S47 wind turbine, fuzzy modeling techniques and artificial neural networks are used to develop a model to estimate annual energy output for S47 wind turbine in different regions. These models have only three inputs: average wind speed, standard deviation of wind speed, and air density of the region in which the wind turbine is installed. These models were tested using the data extracted from 50 stations. The results of this test demonstrated that models that are built using Takagi-Sugeno modeling technique, radial basis network and Generalized Regression Network, have better accuracy in their estimations than the conventional methods. Then, the effect of the number of samples used to train the models on their accuracy was studied. It was shown that as the number of samples increases, the accuracy of Generalized Regression Network decreases, but the accuracy of Radial Basis network and Takagi-Sugeno model changes a bit, suggesting that the TakagiSugeno model and Radial Basis network are not overfit as the number of samples increases and hence are appropriate for our purpose. Finally, some modifications were made to the model built for S47 wind turbine, to develop a new model to estimate Eann of any arbitrary pitch control wind turbine in any region. As an example, the model that was built for S47 wind turbine was modified so as to develop a model for E82 wind turbine that estimates its annual energy output. It was shown that the accuracy of this modified model was satisfactory for all 50 Hydra stations. References
Fig. 5. Output power curve of E82 wind turbine.
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[9] Celik AN. Energy output estimation for small-scale wind power generators using Weibull-representative wind data. J Wind Eng Ind Aerodyn 2003;91: 693–707. [10] Carta JA, Mentado D. A continuous bivariate model for wind power density and wind turbine energy output estimations. Energy Conver Manage 2007;48:420–32. [11] Seguro JV, Lambert TW. Modern estimation of the parameters of the Weibull wind speed distribution for wind energy analysis. J Wind Eng Ind Aerodyn 2000;85:75–84. [12] Stevens MJ, Smulders PT. The estimation of the parameters of the Weibull wind speed distribution for wind energy utilization purposes. Wind Eng 1979; 3:132–45. [13] Lu L, Yang H, Burnett J. Investigation on wind power potential on Hong Kong islandsdan analysis of wind power and wind turbine characteristics. Renew Energy 2002;27:1–12. [14] Zhou W, Yang H, Fang Z. Wind power potential and characteristic analysis of the Pearl River Delta region China. Renew Energy 2006;31:739–53. [15] Carlin PW. Analytic expressions for maximum wind turbine, average power in a Rayleigh wind regime, Proc. 1997 ASME/AIAA wind Symposium, pp. 255–263. [16] Pallabazzer R. Previsional estimation of the energy output of windgenerators. Renew Energy 2004;29:413–20. [17] Torres JL, Prieto E, Garcia A, De Blas M, Ramirez F, De Francisco A. Effects of the model selected for the power curve on the site effectiveness and the capacity factor of a pitch regulated wind turbine. Solar Energy 2003;74:93–102.
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Contents lists available at ScienceDirect
Renewable Energy journal homepage: www.elsevier.com/locate/renene
Fuzzy modeling techniques and artificial neural networks to estimate annual energy output of a wind turbine M. Jafarian*, A.M. Ranjbar Department of Electrical Engineering, Sharif University of Technology, Tehran, Iran
a r t i c l e i n f o
a b s t r a c t
Article history: Received 3 March 2009 Accepted 1 February 2010 Available online 26 February 2010
The purpose of this article is to develop a new method to estimate annual energy output for a given wind turbine in any region which should be easy to use and has satisfactory accuracy. To do this, hourly wind speeds of 25 different stations in Netherlands, output power curve of S47 wind turbine and fuzzy modeling techniques and artificial neural networks were used and a model is developed to estimate annual energy output for S47 wind turbine in different regions. Since this model has three inputs (average wind speed, standard deviation of wind speed, and air density of that region), this model is easy to use. The accuracy of this method is compared with the accuracy of conventional methods and it is shown that this new method performs better. Thereafter, we have shown that by making some small changes to this proposed model, other pitch control wind turbines could be modeled too. As an example, we have modeled E82 wind turbine based on the model developed for S47 and it is shown that this model has still satisfactory accuracy. Ó 2010 Elsevier Ltd. All rights reserved.
Keywords: Annual energy output Artificial neural network Fuzzy modeling technique Wind turbine
1. Introduction The wind has been used as an energy source for a very long time. The first windmills were used by the Persians in approximately 900 AD [1,2]. Wind energy became a significant topic in the 1970’s during the energy crisis in the U.S. [3] and now it continues to be the fastest growing power generating technology in the world [4] due to its availability, low cost and environment friendly operation of this technology [5]. Development of techniques for accurately assessing the wind energy potential of a site is gaining increased importance [6], since expected power output has to be estimated in advance so as to make possible the assessment of the economic viability of any wind farm project [7]. Energy output estimation for wind turbines of different power ranges has been the subject of a number of papers. Most of these studies have used the wind speed pattern of a region to estimate the wind speed distribution of that region and then, by knowing the wind turbine specifications, the energy output of that turbine is estimated. We will give a brief review of these methods in section 3 of this article. In this paper, a new method is developed to estimate the annual energy output of a known wind turbine in any region, using fuzzy
* Corresponding author. Tel./fax: þ98 2166164037. E-mail address: [email protected] (M. Jafarian). 0960-1481/$ – see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2010.02.001
modeling techniques and artificial neural networks. To develop such a model, the output power curve of the wind turbine and the hourly wind speed records of one year of at least 25 different regions are required. This new method has two advantages than the conventional ones that it requires only 3 inputs (annual average wind speed, standard deviation of wind speed and average air density of the region in which the wind turbine is installed) so it is easy to use and also it provides better accuracy in estimation as will be proved in this paper. One of the disadvantages of this model is that for any wind turbine, a new model should be built, but we will show later that the model built for an arbitrary pitch control wind turbine, can be used with other pitch control ones by means of making some small changes to the former model. To make these changes, the rated power, the hub height and the rated wind speed of the former and the later wind turbine should be known. 2. Basic principles of wind turbine power production Wind turbine power production is a function of two quantities: wind speed and air density. The dependency of wind turbine power production on wind speed can be shown by a curve such as Fig. 1. This curve is expressed in 1.225 kg/m3 air density (1.225 kg/m3 is the air density in standard conditionals of 288.16 Kelvin air temperature and 101 325 Pascal air pressure). On the other hand, the output of a wind turbine has linear relation with air density [1]. Therefore wind turbine power production can be calculated using equation (1):
M. Jafarian, A.M. Ranjbar / Renewable Energy 35 (2010) 2008–2014
Nomenclature
h r r0 sy A C Cp Cpr COD D Eann f(v) h0
pðvÞ ¼
hi IEann K pave p(v) pw(v)
overall power efficiency of wind turbine air density (kg/m3) air density in standard conditions (kg/m3) standard deviation of the measured data y swept area of wind turbine (m2) Weibull scale parameter (m/s) power coefficient of wind turbine nominal power coefficient coefficient of determination wind turbine blade diameter (m) annual energy output, kJ Wind speed probability density function surface roughness length, m
r p ðvÞ r0 w
Pr RMSE s v vave vc vf vr
(1)
where pw(v) is the wind turbine output power in standard air density which is obtained from wind turbine power curve and r0 is air density in standard conditions. If the wind turbine hub height is not the same as the anemometer height, the wind speed should be estimated at the wind turbine hub height. The Logarithmic profile is often used to estimate wind speed from a reference height, h1, to another level, h2, using the following relationship [1,8]:
lnðh2 Þ=lnðh0 Þ vðh2 Þ ¼ vðh1 Þ lnðh1 Þ=lnðh0 Þ
(2)
where v(h1) and v(h2) are the values of wind speed at altitude h1 and h2 and h0 is the surface roughness length of the region. The surface roughness length is a parameter that characterizes the roughness of the surrounding terrain. The values of surface roughness lengths for various types of terrain are cited in Manwell et al. [1]. 3. Review of conventional methods used to estimate wind energy potential As it was mentioned before, in most of the methods used to estimate wind energy potential of a certain region, it has been tried to find a suitable wind speed distribution model to approximate the real wind speed pattern of that region such as the Weibull, the Rayleigh and the Lognormal distributions. The two-parameter
2009
altitude above ground level, m five year average of Eann, kJ Weibull shape parameter the average output power of wind turbine, kW wind turbine produced power in wind speed v, kW wind turbine produced power in wind speed v in standard conditions, kW wind turbine rated power, kW root mean square error operating range of wind speed, m/s wind speed, m/s average wind speed, m/s cut-in speed of the wind turbine, m/s cut-out speed of the wind turbine, m/s rated speed of the wind turbine, m/s
Weibull function is accepted as the best among these distributions [1,6,9–11]. Weibull probability density function can be expressed by the following equation:
f ðvÞ ¼
k1 k k v v exp c c c
(3)
in this equation, c is Weibull scale parameter and k is Weibull shape parameter. Different methods have been used to estimate k and c parameters for different regions. Some of these well known methods are: maximum likelihood method [11,12], mean wind speed_standard deviation method (MWS_SD) [13,14] and least square error method [3]. Next we review the conventional methods used to estimate energy potential of a region. 3.1. One-two-three equation Carlin [15] used the Rayleigh distribution to model wind speed pattern of a given region and suggested the following equation to calculate the average output power of a wind turbine in a site in which average wind speed equals vave.
pave ¼
r 2 D r0 3
2
v3ave
(4)
In this equation, D is the wind turbine blade diameter. If Eann is the annual energy output of the wind turbine, it can be calculated using the following equation which he called the one-two-three equation.
Eann ¼ 8760
2
r 2 D r0 3
v3ave
(5)
This method is easy to use because it has only three inputs, but it does not have an acceptable accuracy. 3.2. Kiranoudis method In this method, two assumptions are reclaimed: Weibull distribution is used to model wind speed pattern and the power coefficient of a wind turbine, Cp is assumed to have the following relationship with wind speed [5]:
Cp ¼ Cpr exp Fig. 1. S47 output power curve.
ðln v ln vr Þ2 2ðln sÞ2
! (6)
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M. Jafarian, A.M. Ranjbar / Renewable Energy 35 (2010) 2008–2014
In this expression, the turbine characteristics are: the nominal power coefficient, Cpr, the rated wind speed, vr, and a parameter expressing the operating range of wind speed, s. Therefore Eann can be expressed as follow:
Eann
r pr ¼ 8760 r0 v3r
Z
vf
exp
ðln v ln vr Þ2
0
2ðln sÞ2
3.4. Random number generation
! 3
v f ðvÞdv
(7)
where in this equation, f(v) is Weibull distribution. This model has six input parameters: pr, vr, s that can be obtained from wind turbine specifications, k and c the parameters of Weibull distribution that can be calculated by means of any methods that was mentioned before, and air density. This model has two disadvantages; it needs many inputs and also it does not have satisfactory accuracy, but it should be noticed that its accuracy is much better than the one-two-three equation one. 3.3. Polynomial modeling of wind turbine power curve In this method, wind turbine power curve is approximated by a polynomial like the following equation [16–18]:
8 <0 pr pðvÞ ¼ m : m v vm vr vm c c
v < vc or v > vf vr < v < vf vc v vr
(8)
In this relationship, vc is the cut-in speed (the minimal wind speed that wind turbine can produce power), vr is the rated speed, vf is the cut-out speed (the maximum wind speed that wind turbine can produce power) and m usually is considered to be equal to 1 or 2. Therefore to estimate Eann in this method, equation (9) can be suggested:
0
Eann
r ¼ 8760pr @ r0
Zvr vc
vm vm c f ðvÞdv þ m vm r vc
Zvf
modern wind turbines. In this type of wind turbine, wind turbine output power is constant in a certain wind speed range, say [vr vf]. This constant value is referred to as wind turbine rated power (pr).
1 f ðvÞdvA
(9)
vr
where in this relationship, f(v) is Weibull distribution. One of the main disadvantages of this model is that the simple model used to approximate the wind turbine output power curve in this method, has adequate accuracy, only for pitch-controlled wind turbines [17]. This method has several inputs and it is another disadvantage of this method. Its accuracy is acceptable but this method is not as accurate as the new method which will be introduced in this article. It should be said that three strategies are used to control the speed of a wind turbine to prevent the high values of wind speed to damage the wind turbine. These methods are named pitch control, yaw control and stall control. Based on the method used to control the speed of the wind turbine, the wind turbine output power curve may be one of the three different curves depicted in Fig. 2 [18]. Nowadays mostly the pitch control method is used in
Fig. 2. Output power curves of three different types of wind turbine.
In this method, hourly wind speed values during a period of one year are synthesized by means of generation of 8760 random numbers. The Weibull distribution is used to generate these random numbers. Then, using the output power curve of the wind turbine, these pseudo wind speed values can be converted to 8760 pseudo hourly power values. Therefore, Eann can be estimated using the following equation:
Eann ¼
X r 8760 pðv Þ r0 i ¼ 1 i
(10)
This method requires k and c parameter of Weibull distribution (because the pseudo values of wind speed (vi) will be generated using Weibull distribution and to do that, the parameters of Weibull distribution should be known), air density of the region in which wind turbine is installed, and output power curve of the wind turbine. This method has not been used up to now and is introduced in this article for the first time, but because this method uses probabilistic distributions to describe the wind speed pattern, it is introduced as a conventional method. This method is not user friendly; it needs the output power curve of the wind turbine and a method to generate random number generation. Also this method is not as accurate as the new method which will be introduced in next section. 4. Fuzzy modeling techniques and neural networks to estimate wind turbine energy output Use of neural networks for prediction of wind speed and wind turbine power production has been the subject of some articles. Kalogirou [19] uses neural network to predict the mean monthly wind speed in regions of Cyprus. He developed two networks, one with 5 inputs for prediction of mean monthly wind speed in a determined region and another with 11 inputs for prediction of mean monthly wind speed in nearby locations and he found that the proposed neural networks perform successfully. Mabel and Fernandez [20] use artificial neural networks for prediction of mean monthly energy production of a wind farm in Muppandal, Tamil Nadu (India), and they claimed that the proposed network gives acceptable results.
Fig. 3. Normalized standard deviations of Eann average values for s210, s225, and s380 stations.
M. Jafarian, A.M. Ranjbar / Renewable Energy 35 (2010) 2008–2014 Table 1 Average wind speed, Standard deviation of wind speed and IEann for 50 different regions in Netherlands. Station Average wind speed (m/s) Standard deviation of wind speed (m/s) IEann (kW)
S210 7.5444 4.3926
S225 8.1420 4.1150
– – –
S380 4.7632 2.7889
1.8367e þ 6
2.1661 e þ 6
–
7.9403 e þ 6
The main point about these articles is that these predictions are valid only for one region, but in this article some networks and techniques are introduced to predict annual energy output of a wind turbine in any region. In this method, hourly wind speed values from 50 stations in different locations of Netherlands collected over a period of several years in Hydra project (which are collected by Royal Netherlands Meteorological Institute and Koninklijk Netherlands Meteorological Institute) are used to build a model to estimate wind energy potential. The first step to build this model is to use equation (1) to convert the values of wind speed for all stations to new values so that all values would correspond to the same altitude (40 m), because wind speed values are recorded in different altitudes. The wind turbine used in this study is S47 with a rated power of 660 kW, a pitch control system with hub height of 40 m. The output power curve for this wind turbine is depicted in Fig. 1 [21]. The wind speed annual average of a given region varies from year to year, resulting in various annual energy outputs for a given wind turbine. Therefore, to be able to estimate wind energy potential of a region, wind speed variations in that region should be studied over several years. In this article, three stations of S210, S225, and S380 are studied for their annual wind speed variations. For each of these stations, Eann is calculated for several years and is averaged over periods of n years (n ¼ 1, 2, ., 12). Then for all values of n, the normalized standard deviations (standard deviation divided by average) of these average values are calculated. Fig. 3 depicts these normalized standard deviations for three stations s210, s225, and s380 with respect to n. If we suppose the normalized value of standard deviation to be the uncertainty (due to variations of Eann over different years) of estimating Eann for a wind turbine, it can be seen that for the case n ¼ 5, this uncertainty in estimation is less than 15% for all three stations. Therefore, to achieve an acceptable estimation uncertainty, the index of annual energy output of a wind turbine in
2011
a given region (IEann) is equal to the average of annual energy output values of that wind turbine over five successive years. Therefore, IEann is calculated as follows:
IEann ¼
5 X 1 r X 1 r 8760*5 Eann ðiÞ ¼ pðvi Þ 5 r0 i ¼ 1 5 r0 i ¼ 1
(11)
For all 50 stations, based on the values of hourly wind speed values of five successive years and output power curve of S47, IEann values are calculated using equation (11) for standard air density. Then, for each station, average and standard deviation values of wind speed are calculated for this period, the results of which is presented in Table 1. It should be said that not all values are given in this table, just a sample is presented. The values of average wind speed and standard deviation of wind speed form the inputs for the model which gives the estimated value of IEann in standard air density. Having chosen the model’s inputs and output, we then use common types of fuzzy modeling techniques and artificial neural networks, and train them using the data available in Table 1 to develop the model. In the former case we utilized Takagi-Sugeno model [22] and Sugeno-Yasukawa model [23], and in the latter, Feed Forward and Cascade Forward Backpropagation Networks [24], Radial Basis Network [25], Generalized Regression Network [26] and ANFIS network [27] are used. To start, the data points of Table 1 are divided into two random groups A and B, each of which includes 25 data points. In each stage, one group is used to build a model, and the other to test its performance. That is to say, the model built using data group B is tested with data group A, and similarly, the model built with data group A is tested with data group B. Therefore, 50 estimated values of IEann are obtained and are compared with true values using the Coefficient of Determination (COD) and Root Mean Square Error (RMSE) tests. The definition of the COD is [4]:
COD ¼ 1
s2y;x s2y
(12)
where sy is the standard deviation of the measured data y from its own mean value ym, which is conventionally defined as:
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u n uX sy ¼ t ðyi ym Þ2 =ðn 1Þ
(13)
i¼1
Table 2 COD and RMSE values for different methods used to estimate IEann. Methods
Takagi-Sugeno model Radial Basis network Generalized Regression Network One-two-three equation Polynomial modeling of wind turbine power curve Random number generation Kiranoudis method
Inputs COD and RMSE
Mean wind speed – standard deviation of wind speed
k and c using maximum likelihood method
k and c using modified maximum likelihood method
k and c using Least Square Error
k and c using mean wind speed-standard deviation method
Wind turbine blade diameter
COD RMSE COD RMSE COD RMSE COD RMSE COD RMSE COD RMSE COD RMSE
0.9239 1.48e þ 5 0.9351 1.37e þ 5 0.9266 1.45e þ 5 – – – – – – – –
– – – – – – – – 0.9071 1.64e þ 5 0.9108 1.60e þ 5 0.7503 2.68e þ 5
– – – – – – – – 0.9018 1.68e þ 5 0.9157 1.56e þ 5 0.7757 2.54e þ 5
– – – – – – – – 0.9047 1.66e þ 5 0.9011 1.69e þ 5 0.7616 2.62e þ 5
– – – – – – – – 0.8984 1.71e þ 5 0.9159 1.55e þ 5 0.7735 2.56e þ 5
– – – – – – 12.1452 1.95e þ 6 – – – – – –
2012
M. Jafarian, A.M. Ranjbar / Renewable Energy 35 (2010) 2008–2014
Table 3 COD and RMSE values of 35-sampled models.
COD RMSE
Takagi-Sugeno model
Radial Basis network
Generalized Regression Network
0.9334 1.31e þ 5
0.9330 1.32e þ 5
0.8992 1.62e þ 5
where n is the total number of measurements (here n equals 50). Similarly,
sy;x
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u n uX ¼ t ðyi yic Þ2 =ðn 2Þ
(14)
i¼1
where the yi are the actual values of y, and yic are the values computed from the correlation equation for the same value of x. A higher COD represents a better fit using the theoretical or empirical function. Normally, a value higher than 70% of COD is acceptable [4]. RMSE can be calculated using equation (15):
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u n uX RMSE ¼ t ðyi yic Þ2 =n
(15)
i¼1
The smaller the value of this parameter, the better the function approximates the measured data. Our simulations suggest that among these proposed models, Sugeno-Yasukawa model, Feed Forward Back-propagation, Cascade Forward Back-propagation, and ANFIS Networks couldn’t meet the desired accuracy for they give COD values less than 0.7, while others could. The values of accuracy of these methods are compared with four conventional models mentioned in section 3. For the conventional models which require k and c parameter of Weibull distribution, every four possible methods mentioned to calculate k and c is examined. Table 2 represents the results of this comparison, which clearly states that the Takagi-Sugeno, Radial Basis network and Generalized Regression Network models perform better as compared to other conventional methods for they have greater COD and less RMSE values. The model which is build by Takagi-Sugeno method consists of 4 fuzzy rules. In this model, two fuzzy sets are determined for mean wind speed and two for wind speed standard deviation. It should be mentioned that Takagi-Sugeno method chooses the proper fuzzy sets and rules by itself. For the Radial Basis Network, a network with one hidden layer that consists of 25 neurons is used. By choosing different values for the spread parameter of this network, it was recognized that the best value for this parameter is 0.26. For Generalized Regression a network with one 25 neurons hidden layer is used and the best value for spread parameter is recognized equal to 500. With the results reported in Table 2, these new models excel conventional ones in terms of the ease with which they can be used, the fact that they require only three inputs and the much better accuracy they would provide. The only drawback of these proposed models is the high volume of data required for their development.
To develop such models, one must have hourly wind speed data collected in at least 25 different regions during a period of at least one year. Next, the effect of the number of samples used to train the proposed models on their accuracy is examined. To do this, we regroup the data in Table 1 and divide it into three groups E, F, and G each having fifteen data samples (leaving 5 data samples not involved in this grouping process). Using 35 data samples which are not included in E, a model is built. Then, this model is evaluated using the remained data samples, which are members of E. The same procedure is repeated for the other groups of F and G. Therefore, 45 estimated values for IEann are obtained and compared with the real ones using COD and RMSE indexes the result of which is explained in Table 3. In this situation, the number of fuzzy rules and sets in the model build by Takagi-Sugeno method is similar to previous one, but for Radial Basis Network, the number of neurons in hidden layer equals to 35 and the best value for the spread parameter equals to 0.45 and for Generalized Regression Network, the number of neurons in hidden layer equals to 35 and the best value for the spread parameter equals to 500. According to the data available in Table 3, as the number of samples used to train the models increases, the accuracy of Generalized Regression Network decreases, but the accuracy of Radial Basis network and Takagi-Sugeno model changes a bit, suggesting that the Takagi-Sugeno model and Radial Basis network are not overfit as the number of samples increases and hence are appropriate for our purpose. 5. Applying the proposed model to other pitch control wind turbines As stated before, pitch control wind turbines have similar output power curves. They have a common characteristic that their output power is constant in a certain wind speed range, say [vr vf]. This similarity in output power curves makes possible for the developed model for S47 turbine to be used for other pitch control wind turbines. However, since other properties such as the hub height, the rated power, cut-in speed, cut-out speed, and the rated wind speed have different values for other turbines, for the model to be precise for the new turbines, it should be changed a little bit. But, it should be noticed that, the value of cut-in speed does not have a considerable effect on the Eann due to very low produced power around cut-in speed, therefore, different cut-in speeds for different turbines does not necessitate any change in the model. Also, no change in the model is made due to different cut-out speeds, since wind speeds near cut-out speed rarely happen and hence the effect of cut-out speed on Eann is negligible (less than 1%) [16]. Therefore, to use the model developed for S47 for other pitch control wind turbines, three different properties between S47 and the new turbine should be taken into account: hub height, rated power, and rated wind speed. 5.1. Taking into account different hub heights Equation (2), explains the altitude’s influence on wind speed. Using this equation, the relationship between mean wind speed
Fig. 4. Process of modification of the S47 model to be used with other pitch control wind turbines.
M. Jafarian, A.M. Ranjbar / Renewable Energy 35 (2010) 2008–2014
and standard deviation of wind speed in different hub heights can be written as:
Mean wind speed ðh2 Þ ¼ Mean wind speed ðh1 Þ
lnðh2 =h0 Þ lnðh1 =h0 Þ
lnðh2 =h0 Þ SD of wind speed ðh2 Þ ¼ SD of wind speed ðh1 Þ lnðh1 =h0 Þ
(16)
(17)
where in equation (17), SD stands for Standard Deviation. Equations (16) and(17) suggest that to modify the model for a new hub height, model inputs must be multiplied by the term ln(h2/h0)/ln(h1/h0). 5.2. Taking into account different rated powers To take into account different rated powers, the developed model’s outputs should be multiplied by the term pr2/pr1, where pr1 is the rated power of S47 and pr2 is the rated power of the new turbine for which the model is to be modified. 5.3. Taking into account different rated wind speeds To consider the effect of different rated wind speeds, we use the same idea which is used in polynomial modeling of wind turbine power curve method to estimate the difference between Eann values of these two turbines. To do this, the unit difference of annual output energies (Eann divided by rated power of wind turbine) for these two turbines is estimated using equation (18).
0 DE ¼ 8760@
Zvr2 vc
v2 v2c f ðvÞdv þ v2r2 v2c
Zvr2 vc
1 v2 v2c f ðvÞdvA v2r1 v2c
(18)
where f(v) is the Weibull distribution for which k and c can be calculated using mean wind speed-standard deviation method. Also in the above equation, cut-in speed values are supposed to be the same for both turbines. It should be noticed that here, we have used the polynomial modeling of wind turbine power curve method, just to make necessary modifications which validate our model for the new turbine, and not to directly estimate its annual energy output because as was shown before, this technique is not so accurate in the direct estimation of Eann. To combine all these 3 changes required to be done on S47 model to modify it to be usable for a new pitch control wind turbine; a scheme like what is depicted in Fig. 4, can be suggested. To evaluate this proposed process, the model which was developed for S47 wind turbine using Takagi-Sugeno and Radial Basis network techniques is modified using the above described process to model ENERCON E82 wind turbine. This turbine’s characteristics are as follows: rated power of 2000 kW, rated wind
2013
Table 4 COD and RMSE values to use S-47 modified model for E82 wind turbine.
COD RMSE
Takagi-Sugeno model
Radial Basis Network
0.9667 3.52e þ 5
0.9659 3.56e þ 5
speed of 12 m/s, hub height of 80 m, and its output power curve is depicted in Fig. 5 [28]. Therefore to change the model of S47 for E82, values of h1, h2, vr1, vr2, pr1 and pr2 are set as: 40 m, 80 m, 13 m/s, 12 m/s, 660 kW and 2000 kW respectively. Using hourly wind speeds of 50 stations (collected in Hydra project) and output power curve of E82, the true values of IEann is derived for all 50 stations. Then, using the proposed models this time, IEann is estimated and compared to true values. Results of this comparison are presented in Table 4 stating that the proposed process has satisfactory accuracy. 6. Conclusions In this article a new method to estimate annual energy output for a wind turbine in a site of known wind topology was introduced. In this new method, hourly wind speeds of 25 different stations in Netherlands, output power curve of S47 wind turbine, fuzzy modeling techniques and artificial neural networks are used to develop a model to estimate annual energy output for S47 wind turbine in different regions. These models have only three inputs: average wind speed, standard deviation of wind speed, and air density of the region in which the wind turbine is installed. These models were tested using the data extracted from 50 stations. The results of this test demonstrated that models that are built using Takagi-Sugeno modeling technique, radial basis network and Generalized Regression Network, have better accuracy in their estimations than the conventional methods. Then, the effect of the number of samples used to train the models on their accuracy was studied. It was shown that as the number of samples increases, the accuracy of Generalized Regression Network decreases, but the accuracy of Radial Basis network and Takagi-Sugeno model changes a bit, suggesting that the TakagiSugeno model and Radial Basis network are not overfit as the number of samples increases and hence are appropriate for our purpose. Finally, some modifications were made to the model built for S47 wind turbine, to develop a new model to estimate Eann of any arbitrary pitch control wind turbine in any region. As an example, the model that was built for S47 wind turbine was modified so as to develop a model for E82 wind turbine that estimates its annual energy output. It was shown that the accuracy of this modified model was satisfactory for all 50 Hydra stations. References
Fig. 5. Output power curve of E82 wind turbine.
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