Modeling Solar Energy Potential in a Tehran Province Using Artificial Neural Networks

International Journal of Green Energy, 10: 177–191, 2013 Copyright © Taylor & Francis Group, LLC ISSN: 1543-5075 print / 1543-5083 online DOI: 10.1080/15435075.2011.647172

MODELING SOLAR ENERGY POTENTIAL IN A TEHRAN PROVINCE USING ARTIFICIAL NEURAL NETWORKS Zeynab Ramedani, Mahmoud Omid, and Alireza Keyhani Department of Agricultural Machinery Engineering, Faculty of Agricultural Engineering and Technology, University of Tehran, Karaj, Iran Prediction of daily global solar radiation (GSR) plays an important role in design of renewable energy systems. Artificial Neural Networks (ANNs) are powerful tools for modeling and estimating GSR even though using few inputs. In order to train the networks, a dataset of meteorological daily time series for 15 years (1993–2008) collected in Tehran by Iran Meteorological Office were used. The meteorological parameters used to estimate GSR were daily values of maximum, minimum, and mean temperatures; relative humidity; sunshine duration; and precipitation as inputs and the daily GSR in MJ m−2 day−1 as output. Various ANN models were designed and implemented by combining different meteorological data. The optimum model for estimating GSR had one hidden layer multilayer perceptron (MLP) with 37 neurons in it when the inputs were number of the maximum and minimum temperature, sunshine duration, daylight hours, extraterrestrial radiation, and number of day in the year. The empirical Hargreaves and Samani equation (HS) was also considered for the comparison. To estimate the difference between measured and estimated values of ANN and empirical models, mean absolute error (MAE), root mean square error (RMSE), and correlation coefficient (r) were determined. For 6-37-1 topology, r, RMSE, and MAE values were found to be 0.968, 3.09, and 2.57, respectively. Obtained results showed that ANN model outperformed HS model and can be successfully used for estimating the daily GSR for Tehran province and any other location. Keywords: Global solar radiation; Solar energy; Artificial neural networks; Modeling; Hargreaves and Samani equation; Estimation

INTRODUCTION Solar radiation is a perpetual source of natural energy that, along with other forms of renewable energy, has a great potential for a wide variety of applications due to its abundance and accessibility (Acra et al. 1989). We can capture and convert solar radiation into useful forms of energy, such as heat and electricity using various technologies. By measuring global horizontal irradiation (GHI) in meteorological stations, diffuse horizontal irradiation (DHI) is detected. Subsequently, direct normal irradiation (DNI) is calculated by the data logger using GHI, DHI, and the actual sun height angle by known time and coordinates of the location. For solar collectors that are flat in nature, solar radiation data in the form of GHI is useful, whereas for solar collectors that are concentrating in nature Address correspondence to Dr. Mahmoud Omid, Department of Agricultural Machinery Engineering, Faculty of Agricultural Engineering and Technology, University of Tehran, Karaj, Iran. E-mail: [email protected]

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DNI data is required. Solar thermal power plants are essentially Concentrating Solar Power (CSP) units. For designing solar thermal power plants, DNI data is therefore a prerequisite. In this study, we use GSR instead of GHI. Almost 34% of greenhouse crops are produced in Tehran province, Iran, and making it the main greenhouse production area in the country. Based on a study in Tehran province greenhouses, among input energy sources, diesel fuel consumption was found to be the highest with 49.02%–54.17% share (Heidari and Omid 2010). The high amount use of fossil energy is not economically and environmentally appropriate. The yearly average solar radiation in Tehran province is 4.92 kWh m−2 day−1 (SSE 2011). Considering this great potential in the region, by installing solar energy systems in greenhouses and other agricultural building, one can achieve economic efficiency and reduction in greenhouse gas emissions. Schnitzer, Brunner, Gwehenberger (2007) investigated the potential for, and the economic viability of, using solar energy heat processes in industry by applying an Austrian dairy plant model. The success of applying these technologies is highly related to the amount of available solar radiation. An efficient conversion and utilization of solar energy systems require an accurate detailed long-term knowledge of available global solar radiation (GSR) data in various forms, depending on the related application (Sozen, Arcaklioglu, and Ozalp 2004). Cost, difficulty in measurement, and lack of accuracy of measurement devices are major items that cause solar radiation data not to be as readily available as air temperature, wind speed, and precipitation data. Because of this, developing alternative ways of generating required data are essential. In this study, artificial neural network (ANN) that is a numerical modeling technique is used for estimating daily GSR. ANNs can accommodate multiple input variables to predict multiple output variables. They differ from statistical modeling approaches in their ability to learn about the system that can be modeled without prior knowledge of the process relationships (Barma et al. 2011). The prediction by a well-trained ANN is normally much faster than the conventional simulation programs or mathematical models as no lengthy iterative calculations are needed to solve differential equations using numerical methods. By the way, the selection of an appropriate neural network topology is important in terms of model accuracy and model simplicity. In addition, it is possible to add or remove input and output variables in the ANN algorithm if it is needed. Several researches have used ANNs to estimate GSR as a function of meteorological data. In 17 stations of Turkey, estimation of solar potential was carried out by ANN and best learning algorithms were investigated (Sozen, Arcaklioglu, and Ozalp 2004). Mellit, Benghanem, and Kalogirou (2006) used wavelet network that is a combination of neural network and wavelet theory to find a suitable forecasting model for predicting the daily solar radiation. In China, an ANN model was developed for estimating mean daily GSR of eight typical cities; then, the result of this modeling was compared with some empirical regression models (Jiang 2009). Moghaddamnia and others (2009) developed several nonlinear including multilayer perceptron (MLP), Elman neural network, neural network auto-regressive models with exogenous inputs (NNARX), and adaptive neurofuzzy inference system (ANFIS) models with the aid of Gamma test. Azadeh, Maghsoudi, and Sohrabkhani (2009) introduced an integrated ANN model for prediction of solar global by using monthly data in six nominal cities in Iran. Behrang and others (2010) used six different combinations of meteorological data as inputs of ANN and compared them with one another. Tymvios and others (2005) in Cyprus, Benghanem, Mellit, and Alamri (2009) in Algeria, Senkal (2010) in Turkey, and Rahimikhoob (2010) in Iran are other researchers who estimated solar radiation with the help of neural networks.

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For stations with poor meteorological data, some empirical models can be a great help in GSR prediction. One of them is Hargreaves and Samani (HS) model (Hargreaves and Samani 1982). The HS model uses only the maximum and minimum temperatures that are available in most weather stations. Some researchers also have studied the linear models to predict solar radiation. Sabziparvar and Shetaee (2007) used different radiation models and various input parameters (e.g., cloud cover, sunshine duration, relative humidity, temperature, and altitude) to develop a general altitude-dependent formula for the prediction of the direct and diffuse monthly average daily solar radiation for 64 mountainous arid and semi-arid locations in West and East of Iran. In Egypt, Robaa (2009) used different meteorological data at nine stations during the period 1983–2006 to calculate the monthly mean values of GSR over these stations using 10 conventional linear models and then compared them on the basis of many statistical error tests. Li et al. (2010) proposed a new empirical model for estimating GSR on horizontal surfaces by day of the year. The performance of this model was validated by comparing with three trigonometric correlations at nine representative stations of China using statistical error test. Cucumo and others (2007) in Italy, Liu and others (2009) in China, and Ruiz-Arias and others (2010) in Spain are some other researchers who also studied solar radiation estimating models not based on neural networks. The motivation behind this study is two-fold: (1) Solar radiation affects crop growth and numerical models are used to estimate soil humidity, photosynthesis, and potential evapotranspiration (Ball, Purcell, and Carey 2004). However, solar radiation is an infrequently measured meteorological variable, compared to temperature, relative humidity, sunshine duration, rainfall, etc. There are many agricultural regions in Tehran and Alborz provinces (in Iran) for which radiation data are not available and they have to be predicted. (2) Analysis of the output of solar thermal systems needs condensed input data set of meteorological data mainly GSR for achieving a reliable estimate of the long term average annual performance of a wide range of such systems. Moreover, availability of this data or estimations based on specific sites or mechanistic prediction models, improves the usefulness of climate data set and is an important variable used in agricultural applications, meteorology, hydrology, and soil physics. The objectives of this study are: (1) to develop the ANN models with the aid of different combinations of time-series meteorological data as the inputs and solar radiation as the output; (2) investigate the effect of changing the number of processing elements that exist in the hidden layer of the ANN on the forecasted parameters; (3) to choose the best structure of each model; (4) to compare the results obtained from each ANN-models with statistical indicators; and (5) to exploit empirical relationships between the ratio of GSR and temperature by using HS model for evaluation with ANN models.

MATERIALS AND METHODS Data Despite the large spectrum of applications demanding solar radiation data, such direct measurements of solar energy are not widely available, rendering the use of numerical techniques an essential alternative. With such indirect techniques, other observed meteorological data are mathematically exploited in order to estimate the amounts of GSR reaching the earth. Except GSR, other meteorological data are parameters that are routinely recorded at a large number of climatological stations (manned and automatic),

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due to the low cost of the respective recording instrumentation and the easiness of data acquisition. Measured daily, data for 15 years for the period of 1993–2008 were collected from the Islamic Republic of Iran Meteorological Office data center (IRIMO) in Tehran station. Some of geographical parameters in this station are shown in Table 1. The yearly average solar radiation in the region is 4.92 kWh m−2 day−1 . The monthly mean daily temperature ranged from a minimum of −1.5◦ C in January and a maximum of 33.9◦ C in July (IRIMO). The meteorological parameters used to estimate solar radiation were daily values of maximum, minimum, and mean temperatures (◦ C); relative humidity (%); sunshine duration (h); precipitation (mm); and solar radiation (MJ m−2 day−1 ). Figure 1 shows the average monthly GSR between years 1993 to 2008. The maximum and minimum solar radiation occurs in June and December, respectively. Daylight hours (h), extraterrestrial radiation (MJ m−2 day−1 ), and the number of days between 1 (January 1st) and 365 or 366 (December 31st) are three other daily parameters that affect solar radiation. The extraterrestrial solar radiation that is the solar radiation received at the top of the earth’s atmosphere on a horizontal surface, for each day of the year and for different latitudes, can be estimated by (FAO 2008): Ra =

24 × 60 [ωs sin(ϕ) sin(δ) + cos(ϕ) cos(δ) sin(ωs )]Gsc dr , π

(1)

where Ra is extraterrestrial radiation (MJ m−2 day−1 ), Gsc is solar constant that is equal to 0.0820 MJ m−2 min−1 , dr is inverse relative distance of earth-sun (dimensionless), ωs is Table 1 Geographical Parameters in Tehran Province Parameters Location Altitude Latitude Longitude Average precipitation Average radiation

Symbol

Value

Northern Tehran z φ λ p GSR

1548.2 m 35◦ 47 N 51◦ 37 E 429 mm 4.92 kWh m−2 day−1

Radiation (MJ m–2 day–1)

35 30 25 20 15 10 5 0

1

2

3

4

5

6 7 Month

8

9

10 11 12

Figure 1 Distribution of solar radiation in different month of year (color figure available online).

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sunset hour angle (rad), ϕ is latitude (rad) that is positive for the northern hemisphere and negative for the southern hemisphere, and δ is solar declination angle (rad). The expressions for dr , δ, ωs , and N (daylight hours) are given by Equations (A.1)–(A.4) in Appendix A, respectively. In this study, by using three indicators extraterrestrial radiation (Ra ), clear-sky (Rso ), and relative sunshine duration, quality control of data was carried out. The expression for Rso is given as (FAO 2008): Rso = (0.75 + 2 × 10−5 z)Ra ,

(2)

where z is the site altitude. In the studied area for z = 1548.2 m, Rso = 0.781Ra . The relative sunshine duration is a ratio that expresses the cloudiness of the atmosphere. It is the ratio of actual sunshine duration (n) to the daylight hours or maximum sunshine duration (N). Relative sunshine duration is in the range of 0–1. This ratio is equal to 1 when the whole sky is sunny, e.g., n = N. Figure 2 illustrates the evolution of daily irradiation for the year 1994, it also shows the values of Ra and Rso . The data for the day for which any of the following occurs, were excluded from the training and cross validation and testing data sets whenever: (1) (2) (3) (4) (5)

there was missing data; solar radiation was greater than Ra ; solar radiation was greater than Rso ; sunshine duration was higher than daylight hours; and sunshine duration to daylight hours ratio was lower than 0.3 (Tymvios et al. 2005). Therefore, only correctly measured (properly and logical) data were used in this

study.

Figure 2 Daily evolution of global solar radiation, extraterrestrial global irradiation, and clear-sky radiation (color figure available online).

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Artificial Neural Networks Artificial neural network (ANN) is a mathematical model that performs a computational simulation of the behavior of neurons as in the human brain by replicating, on a small scale, the brain’s patterns in order to produce results from the events perceived, i.e., it is a model based on learning a set of training data (Bocco, Willington, and Arias 2010). The knowledge obtained during the training phase is not stored as equations or in a knowledge base, but is distributed throughout the network in the form of connection weights between neurons (Omid, Baharlooei, and Ahmadi 2009). The first step in developing ANN deals with the definition of the network architecture, which is defined by the basic processing elements (neurons) and by the way in which they are interconnected (layers). ANNs are trained with known data and tested with data not used in training (Mohanraj, Jayaraj, and Muraleedharan 2008). In the training process, the inputs of each neuron are multiplied by the weight of connection and obtained products and biases are summarized and passed through an activation function and the output of neuron is obtained. In other words, in the simplest case, the products and biases are simply summed, then transformed through a transfer function to generate a result, and finally an output is obtained (Sozen, Arcaklioglu, and Ozalp 2004). In this study, the activation function was hyperbolic tangent (TANH) and bias axon in the hidden and output layers, respectively. Since ANNs are constructed with layers of units, they are termed multilayer ANNs. Multilayer perceptrons (MLP) are perhaps the most common type of feed-forward networks (Behrang et al. 2010). The MLP networks are used in a variety of problems especially in forecasting because of their inherent capability of arbitrary input-output mapping (Zhang, Eddy-Patuwo, and Hu 1998; Omid, Baharlooei, and Ahmadi 2009). In the feed-forward networks, error minimization can be obtained by a number of procedures including Gradient Descent (GD), Levenberg–Marquardt (LM), and Conjugate Gradient (CG). MLPs are normally trained with error back propagation (BP) algorithm (Barma et al. 2011). BP uses a gradient descent (GD) technique, which is very stable when a small learning rate (η) is used, but has slow convergence properties (Omid, Mahmoudi, and Omid 2009). Several methods for speeding up BP have been developed including adding a momentum term or using a variable learning rate. In this article, GD with momentum (GDM) algorithm, which is an improvement to that in straight GD rule in the sense that a momentum term is used to avoiding local minima, speeding up learning, and stabilizing convergence, is used. Weights, wji , update scheme in the nth training iteration for GDM is given by (Omid, Baharlooei, and Ahmadi 2009): (n−1) w(n) + w(n) ji = wji ji ,

(3)

and the weights adjustment are given by: (n) n (n−1) w(n) , ji = ηδj oi + α wji

(4)

where wji is the weight between the jth node (neuron) of the upper layer and the ith node of the lower layer, δj error signal of the jth node, oi output value of the ith node of the previous layer, and η and α are the learning rate and the momentum term, respectively. In developing MFNN models, the values of η = 0.1 and α = 0.7 were used in Equation (4). The terms w(n) ji in Equations (3) and (4) are in fact the gradient vector associated with the

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Figure 3 A typical feedforward neural network (MLP). T: temperature, RH: relative humidity, n: daily sunshine duration, P: precipitation, N: daylight hours, Ra : daily extraterrestrial radiation, and J: number of day in the year, starting from first January.

weights. The gradient vector is the set of derivatives for all weights with respect to the output error. In this study, NeuroSolutions 5.0 software was used for design and testing of ANN models (NeuroDimension Inc., Gainesville, FL). A typical configuration that consists of input layer, hidden layer, and output layer is shown in Figure 3. The number of neurons in input and output layers depends on independent and dependent variables, respectively. Connection between all the layers is established by their neurons. The neurons are interconnected with the weighted unidirectional connection (Krishnaiah et al. 2007). Due to the generalization capabilities of the neural networks, it performs similarly on data for testing that have not been used for training (Mohandes, Rehman, and Halawani 1998). Up-to-date designing a (near) optimal network architecture is made by a human expert and requires a tedious trial and error process (Kiranyaz et al. 2009). Despite their many advantages over conventional statistical models, ANNs are particularly susceptible to over-fitting due to the complexity of the model architecture (i.e., the number of estimated parameters) relative to the number of training data (May, Maier, and Dandy 2010). To avoid “over fitting”, the MSE of the CV subset was calculated after adjusting of weights and biases. The training process continued until the minimum MSE of the validating sets was reached (early-stopping scheme). To develop a statistically sound model, the networks were trained three times and the average values were recorded for each parameter (Omid, Mahmoudi, and Omid 2009). The network weights and biases are then adapted and employed for validation in order to determine the neural network model overall performance. The root mean square error (RMSE) and correlation coefficient (r) of the MFNN model on test sets are then calculated.

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ANN-Based Implementation of GSR Models To consider the effect of each input variable on prediction of solar radiation, five models of ANN for the MLP type were designed. Each model was built with a different number of neurons in the input layer, which received as input patterns of daily timeseries values. These five models that were combinations of various input variables are from ANN1 to ANN5. The number of inputs in each case is defined as: ANN1: daily maximum temperature (T max ), daily minimum temperature (T min ), daily relative humidity (RH), daylight hours (N), and daily extraterrestrial radiation (Ra ). ANN2: daily maximum temperature (T max ), daily minimum temperature (T min ), daily sunshine duration (n), daylight hours (N), daily extraterrestrial radiation (Ra ), and number of day in the year (J). ANN3: daily sunshine duration (n), daily extraterrestrial radiation (Ra ), and number of day in the year (J). ANN4: mean temperature (T), daily sunshine duration (n), and daily precipitation (P). ANN5: daily relative humidity (RH), daily precipitation (P), daylight hours (N), and number of day in the year (J). These models are summarized in Table 2. In this study, the process of ANN for predicting daily GSR potential is divided into three sets, i.e., training, cross validation and testing sets. 70, 20, and 10% of this data were used for training, cross validation and testing the network, respectively. Since time-series metrological data were used, no randomization of data was carried out. It should also be noted that the number of hidden elements in training process is obtained by trial and error. Thus, the training process was accomplished with a minimum number of hidden layers. Therefore, each model of ANN was separated into three groups denoted by ANNi-1, ANNi-2, and ANNi-3, where i is the model number (i = 1, 2, . . . , 5) and 1, 2, and 3 are the number of hidden layers. For example, ANN3-2 means the 3rd model of ANN that has 2 hidden layers in the training process. The number of neurons in the hidden layer of each group is increased by 2 in the range from 2–60. After training of each group, the best structure of ANN was determined. Empirical Models Several empirical methods have been proposed to estimate the daily radiation from commonly observed meteorological data. The empirical model used for this comparative study is that of Hargreaves and Samani (1982). Table 2 Combination of Different Data as Inputs of Estimated ANN and HS Models Forecast model ANN1 ANN2 ANN3 ANN4 ANN5 HS

T

T max

T min

RH

x x

x x

x x x x

x x x

x

n

P

x x

N

Ra

J

x x

x x x

x x

x

x

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Having a capability to predict solar radiation for locations with no or very few data is an important need (Chineke 2008). Hargreaves and Samani (1982) recommended a simple equation to estimate GSR. This model uses temperature-based meteorological data and is a good model when daily weather data such as sunshine duration is limited or missing. As can be seen in Equation (5), GSR in a given day is proportional to the square root of the difference between T max and T min (Hargreaves and Samani 1982): GSR = a(Tmax − Tmin )0.5 Ra

(5)

where T max and T min are in ◦ C and a is an empirical coefficient and differs for interior or coastal regions. For interior locations, where land mass dominates and air masses are not strongly influenced by a large water body, a ∼ = 0.16 and for coastal locations, situated on or adjacent to the coast of a large land mass and where air masses are influenced by a nearby water body, a ∼ = 0.19 (FAO 2008). In this study, Equation (5) was calibrated for estimating GSR by the data used for the training the neural network. Thus, the calibrated HS model estimates can be compared with the GSR values produced by neural network estimates. RESULTS AND DISCUSSION Daily GSR is estimated by means of five mentioned models of MLP neural networks for Northern Tehran station of Iran. Forecasting ability of the model is evaluated by fitting graphs of the predicted and real rates versus time. This can be done by calculating mean absolute error (MAE), root mean squared error (RMSE), and correlation coefficient (r) between the trends until the optimal offset is identified. It is up to the user to interpret the resulting values as they are likely to differ for each of the above fitting methods. These three statistical criterions; r, RMSE, and MAE are defined as Equations (6), (7), and (8), respectively (NeuroDimension Inc., Gainesville, FL 2010):   M 2    (P − P )(O − O ) i i i i  i=1 , r= M M   (Pi − Pi )2 (Oi − Oi )2 i=1

i=1

M MAE =  RMSE =

(6)

i=1

|Pi − Oi | , M

M i=1

(Pi − Oi )2 , M

(7)

(8)

where M is number of observation, Pi is estimated radiation, Oi is observed radiation, Pi is average value for Pi , and Oi average value for Oi . The RMSE provides information on the short term performance of the correlations by allowing a term by term comparison of the actual deviation between the calculated and measured values. There is no absolute criterion for a “good” value of any of RMSE or MAE. These are measured in the same units as the original data and are usually similar

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Table 3 Statistical Test for Different Simulation Between Measured and Estimated ANN-Models ANN architecture (MLP)

Best structure of MLP

r

RMSE

MAE

5-43-1 5-43-21-1 5-43-21-14-1

0.924 0.913 0.896

4.89 5 4.46

4.20 4.19 3.38

6-37-1 6-37-18-1 6-37-18-12-1

0.968 0.932 0.949

3.09 4.34 4.11

2.57 3.51 3.51

3-50-1 3-50-32-1 3-50-33-21-1

0.965 0.944 0.946

3.62 3.98 3.63

3.09 3.21 2.80

3-50-1 3-50-32-1 3-50-32-21-1

0.893 0.908 0.901

6.06 5.55 5.66

5.29 4.79 4.88

4-50-1 4-50-25-1 4-50-25-17-1

0.924 0.925 0.924

4.06 4.67 4.19

3.26 3.98 3.42

ANN1 (T max , T min , RH, N, Ra ) ANN1-1 ANN1-2 ANN1-3 ANN2 (T max , T min , n, N, Ra , J) ANN2-1 ANN2-2 ANN2-3 ANN3 (n, Ra , J) ANN3-1 ANN3-2 ANN3-3 ANN4 (T, n, P) ANN4-1 ANN4-2 ANN4-3 ANN5 (RH, P, N, J) ANN5-1 ANN5-2 ANN5-3

ANN2-1 (bold face) resulted the best model estimating the daily GSR.

in magnitude, but MAE is slightly smaller than, the RMSE. The smaller values of these errors, the better are the model’s performance. Obtained results are summarized in Table 3. The values of r, RMSE, and MAE for these models ranges from 0.893 to 0.968, from 3.09 to 6.06, and from 2.57 to 5.29, respectively. Among the trained networks, ANN2-1 resulted the best model estimating the daily GSR. The ANN2-1 can be written mathematically as: GSR =

37 j=1

w(o) j

f

6

 w(h) ji Oi

+

w(h) jo

+ w(o) o ,

(9)

i=1

where GSR is the estimated value of the daily GSR in the network, and Oi = f (neti ) = tanh(neti ). Notice the use of hyperbolic tangent activation function for the hidden layer neurons and in the output layer, the outputs of the hidden layer are summed linearly to produce GSR as it is desired for forecasting problems. Similar expressions, as in Equation (9), can be given for ANN1, ANN3, ANN4, and ANN5 networks. Therefore, the (6-37-1)-MLP, namely, a network having six input variables (T min , T max , n, N, Ra , and J), 37 neurons in its hidden layer and a single output variable (GSR) is selected as the optimum network. For this topology, r, RMSE, and MAE values were found to be 0.968, 3.09, and 2.57, respectively. The estimated GSR values by the selected ANN model were compared with the calculated for the testing period that is shown in Figure 4. It can be seen that the evolution is similar and one line is practically superimposed over the other. Figure 5b presents the regression analysis of daily values calculated from the selected ANN model. It can be seen, the selected ANN model performs very well compared to GSR measurements. ANN3-1 is another model that gives good estimation but its performance

MODELING SOLAR ENERGY POTENTIAL IN TEHRAN PROVINCE

Radiation (Mj m–2 day–1)

35

Measured data

187

ANN2-1 stimated

30 25 20 15 10 5 0 1

37

73

109

145

181 217 Days

253

289

325

361

Figure 4 Estimated and measured GSR on testing data (ANN2-1) (color figure available online).

(a)

HS estimated GSR (MJ m-2 day-1)

35 y = 0.863x + 1.206 r = 0.943

30 25 20 15

Best fit

10 5 0

0

10 20 30 Measured radiation (MJ m−2 day−1)

40

ANN2-1 estimated GSR (MJ m−2 day−1)

(b)

35 30

y = 0.936x + 3.5978 r = 0.968

25 20 15 10

Best fit

5 0

0

10 20 30 Measured radiation (MJ m−2 day−1)

40

Figure 5 Predicted versus measured radiation values for HS model (a) and ANN2-1 (b) model (color figure available online).

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RAMEDANI, OMID, AND KEYHANI Table 4 Validation Between ANN2-1 and HS Models Estimated model ANN2-1 HS

r

RMSE

MAE

0.968 0.943

3.09 2.44

2.57 1.96

is second to that of model ANN2-1.Three parameters, n, Ra , and J are common parameters for both models. In other word, each day of the year has a special sunshine duration and extraterrestrial radiation that determine the amount of GSR. ANN1, ANN4, and ANN5 do not have the accuracy required for modeling GSR. Relative humidity and precipitation are included in these models. So, these parameters are not good representative and should not be used for estimation of the solar radiation. In order to analyze the performance of HS model, the scatter plot considering measured daily values of GSR and estimated solar radiation values is shown in Figure 5a. Considering statistical criterions, differences between ANN models and HS model are shown in Tables 3 and 4. Figure 5 shows best fit between measured GSR and HS model estimates with r value of 0.943. In comparison of ANN1-1, . . . , ANN5-3 with HS, higher correlation coefficients for ANN2 and ANN3 were observed. But HS model had better estimation than ANN1, ANN4, and ANN5 models. As said, ANN2-1 ANN, and ANN3-1 are best ANN model for prediction GSR for estimation solar potential in Tehran province. Although determining GSR is main factor in designing solar heating PV systems in any region but due to high initial cost of solar heating and PV systems in Iran, these will not be sufficiently profitable without any credit for owners of renewable technologies to encourage them to invest in such a project. At present, such systems are not economically viable in agriculture buildings such as greenhouses without carbon trading option taken into account. Therefore, government support through financial investment and subsidy is an effective way for extending these systems in agricultural sections. CONCLUSIONS The prediction performance of various ANNs was assessed by comparing their predictions to actual data available in the IRIMO data center. By using correlation coefficient (r), mean absolute error (MAE), and root mean square error (RMSE), the results were compared. ANN with maximum and minimum temperature, sunshine duration, daylight hours, extraterrestrial radiation and number of day in the year as inputs lead to maximum r and minimum RMSE and MAE with the structure of 6-37-1. ANN with a single hidden layer and 37 neurons showed the best structure among other models. ANN models with n, Ra , and J as inputs gave higher correlation coefficient, and model with RH and P had lower accuracy even than HS model. The results indicate that the ANN model seems promising for evaluating the solar resource potential at the places where there are no monitoring stations. ACKNOWLEDGMENT This study was financially supported by the Department of Agricultural Machinery Engineering, Faculty of Agricultural Engineering and Technology, University of Tehran, Karaj, Iran

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APPENDIX A The inverse relative distance earth-sun, dr , and solar declination, δ, are given by Equation (A.1) and Equation (A.2) respectively (FAO 2008):  dr = 1 + 0.033 cos

2π J 365

 ,

(A.1)

 2π δ = 0.409 sin J − 1.39 , 365

(A.2)



where J is the number of the day in the year between 1 (January 1st) and 365 or 366 (December 31st).

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Also, the sunset hour angle, ωs , and daylight hours, N, are given by Equations (A.3) and (A.4), respectively (FAO 2008): ωs = arccos(−tan ϕ tan δ),

N=

24 ωs . π

(A.3)

(A.4)