Generation of daily solar irradiation by means of artificial neural net works

Renewable Energy 35 (2010) 2406e2414

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Renewable Energy journal homepage: www.elsevier.com/locate/renene

Review

Generation of daily solar irradiation by means of artificial neural net works Adalberto N. Siqueira*, Chigueru Tiba, Naum Fraidenraich Departamento de Energia Nuclear, da Universidade Federal de Pernambuco, Av. Prof. Luiz Freire, 1000 e CDU, CEP 50.740-540 Recife, Pernambuco, Brasil

a r t i c l e i n f o

a b s t r a c t

Article history: Received 9 January 2008 Accepted 15 March 2010 Available online 14 May 2010

The present study proposes the utilization of Artificial Neural Networks (ANN) as an alternative for generating synthetic series of daily solar irradiation. The sequences were generated from the use of daily temporal series of a group of meteorological variables that were measured simultaneously. The data used were measured between the years of 1998 and 2006 in two temperate climate localities of Brazil, Ilha Solteira (São Paulo) and Pelotas (Rio Grande do Sul). The estimates were taken for the months of January, April, July and October, through two models which are distinguished regarding the use or nonuse of measured bright sunshine hours as an input variable. An evaluation of the performance of the 56 months of solar irradiation generated by way of ANN showed that by using the measured bright sunshine hours as an input variable (model 1), the RMSE obtained were less or equal to 23.2% being that of those, although 43 of those months presented RMSE less or equal to 12.3%. In the case of the model that did not use the measured bright sunshine hours but used a daylight length (model 2), RMSE were obtained that varied from 8.5% to 37.5%, although 38 of those months presented RMSE less or equal to 20.0%. A comparison of the monthly series for all of the years, achieved by means of the KolmogoroveSmirnov test (to a confidence level of 99%), demonstrated that of the 16 series generated by ANN model only two, obtained by model 2 for the months of April and July in Pelotas, presented significant difference in relation to the distributions of the measured series and that all mean deviations obtained were inferior to 0.39 MJ/m2. It was also verified that the two ANN models were able to reproduce the principal statistical characteristics of the frequency distributions of the measured series such as: mean, mode, asymmetry and Kurtosis. Ó 2010 Elsevier Ltd. All rights reserved.

Keywords: Artificial neural networks Daily solar irradiation Synthetic temporal series Simulation of solar systems Bright sunshine hours Accumulated distribution of daily solar irradiation

1. Introduction The knowledge of available solar resource in a determined locality is fundamental for diverse areas of technology such as, cattle breeding, meteorology, forestry engineering, hydro resources, particularly for taking advantage of solar energy. Sustainable development of solar technology requires detailed knowledge of solar irradiation, both spatially and temporally, because it is directly related to economic factors and to the reliability of installed energy systems. The great scarcity of global solar irradiation data for the majority of Brazilian localities, confirmed by Tiba et al. [1], is explained as much by the high cost of equipment used in obtaining these data as by the great territorial extension of the country. In the sense of overcoming these difficulties, among the

* Corresponding author. Tel.: þ5581 3453 6019; fax: þ55 81 32718250. E-mail addresses: [email protected] (A.N. Siqueira), [email protected] (C. Tiba), [email protected] (N. Fraidenraich). 0960-1481/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2010.03.019

principal proposals suggested in this work, the generating of synthetic temporal series of daily solar irradiation can be emphasized. Such series should reproduce the principal statistical characteristics of the historical series. The use of these series allows both the simulation of solar systems submitted to daily stochastic regime, and a long term evaluation of solar system performance. An estimation of solar irradiation can be considered as a classic problem to be approached by some features of ANN, such as robustness (the ANN are able to manage time series of solar irradiation with missing data) and the complexity of the physical phenomenon in the study (diverse physical parameters interrelated with irradiation). Another aspect that favors the use of ANN is the existence of a great amount of meteorological variables measured in conventional weather stations. The use of ANN for generating synthetic series of solar irradiation is very recent and has basically been used on a monthly scale, as for example, in the works presented by Alawi and Al-Hinai [2], Mohandes et al. [3], Atsu et al. [4], Adnan et al. [5] and Mellit et al. [6]. Among the few cases that address other time scales, the works

A.N. Siqueira et al. / Renewable Energy 35 (2010) 2406e2414

Table 1 Description of training, validation and test subgroups utilized for generation of synthetic series of solar irradiation via ANN for Ilha Solteira.

Hidden layer

ϕi

Input layer

Output layer

ϕi ϕi ϕi ϕi Fig. 1. Neural network (MLP).

developed by Hontoria et al. [7] and Reddy and Rajan [8], can be highlighted for estimating solar irradiation on hourly scale and the Tymvios et al. [9], on daily scale. The present study intends to amplify the Tymvios study and test the ANN as a tool for generating synthetic temporal series of daily solar irradiation for two Brazilian temperate climate localities, Ilha Solteira (São Paulo) and Pelotas (Rio Grande do Sul).

2. Material and methods 2.1. Data The data used in this work were measured in the Brazilian localities of Ilha SolteiraeState of São Paulo (Latitude: 20 250 23.500 S and Longitude: 51 210 12.600 W) and Pelotas-State of Rio Grande do Sul (Latitude: 31 520 0000 S and Longitude: 52 210 2400 W). The data referring to Ilha Solteira were measured during the months of January, April, July and October in the years 2000 to 2006 by department of phytosanitation, rural and soil engineering of the engineering faculty of the Ilha Solteira e UNESP. The set of data refer to the temporal series that correspond to the following daily meteorological variables, measured simultaneously: maximum, mean and minimum temperature ( C), mean and minimum humidities (%), daily global irradiation incidence on horizontal surface (MJ/m2), wind speed (m/s), pluviometric precipitation (mm) and bright sunshine hours (h). At this station the daily global irradiation was measured with a LICOR LI e 200X pyranometer and the bright sunshine hours with a Campbell-Stokes heliograph, Engineering Faculty of Ilha Solteira e UNESP [10]. Besides the variables cited previously, the daily amplitude of temperature and theoric bright sunshine hours were added to the data set. The data referring to Pelotas were measured during the months of January, April, July and October in the years 1998 to

Input vector

Hidden camada layer oculta

x(n)

Output neurônio neuron d saída kk

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yk(n) -

∑ ∑

dk(n)

+ ek(n)

Fig. 2. Diagram of MLP network trained with a supervised apprenticeship.

Training (years)

Validation

Test

02 to 05 e January 02 to 04 and 06 e January 02 to 03 and 05 to 06 e January 02 and 04 to 06 e January 03 to 06 e January 00 and 03 to 05 e April 00 and 03 to 04 and 06 e April 00 and 03 and 05 to 06 e April 00 and 04 to 06 e April 03 to 06 e April 00 to 01 and 03 to 05 e July 00 to 01 and 03 to 04 and 06 e July 00 to 01 and 03 and 05 to 06 e July 00 to 01 and 04 to 06 e July 00 and 03 to 06 e July 01 and 03 to 06 e July 00 and 03 to 05 e October 00, 03 to 04 and 06 e October 00, 03 and 05 to 06 e October 00 and 04 to 06 e October 03 to 06 e October

January mean January mean January mean January mean January mean April mean April mean April mean April mean April mean July mean July mean July mean July mean July mean July mean October mean October mean October mean October mean October mean

January 06 January 05 January 04 January 03 January 02 April 06 April 05 April 04 April 03 April 00 July 06 July 05 July 04 July 03 July 01 July 00 October 06 October 05 October 04 October 03 October 00

2006 at the agroclimatological station of the Pelotas Convention EMBRAPA/UFPe1/INMET. The data set refer to the temporal series corresponding to the following daily meteorological variables, measured simultaneously: maximum, mean and minimum temperatures ( C), relative humiditiy (%), daily global irradiation

Table 2 Description of training, validation and test subgroups utilized for generation of synthetic series of solar irradiation via ANN for Pelotas. Training (years)

Validation

Test

98 to 05 e January 98 to 04 and 06 e January 98 to 03 and 05 to 06 e January 98 to 02 and 04 to 06 e January 98 to 01 and 03 to 06 e January 98 and 00 to 06 e January 98 to 00 and 02 to 06 e January 98 to 99 and 01 to 06 e January 99 to 06 e January 98 to 05 e April 98 to 04 and 06 e April 98 to 03 and 05 to 06 e April 98 to 02 and 04 to 06 e April 98 to 01 and 03 to 06 e April 98 to 00 and 02 to 06 e April 98 to 99 and 01 to 06 e April 98 and 00 to 06 e April 99 to 06 e April 98 to 05 e July 98 to 04 and 06 e July 98 to 03 and 05 to 06 e July 98 to 02 and 04 to 06 e July 98 to 01 and 03 to 06 e July 98 to 00 and 02 to 06 e July 98 to 99 and 01 to 06 e July 98 and 00 to 06 e July 99 to 06 e July 98 to 00 and 02 to 05 e October 98 to 00, 02 to 04 and 06 e October 98 to 00, 02 to 03 and 05 to 06 e October 98 to 00, 02 and 04 to 06 e October 98 to 00 and 03 to 06 e October 98 to 99 and 02 to 06 e October 98, 00 and 02 to 06 e October 98 to 00 and 02 to 06 e October

Mean series Mean series Mean series Mean series Mean series Mean series Mean series Mean series Mean series Mean series Mean series Mean series Mean series Mean series Mean series Mean series Mean series Mean series Mean series Mean series Mean series Mean series Mean series Mean series Mean series Mean series Mean series Mean series Mean series Mean series Mean series Mean series Mean series Mean series Mean series

January 06 January 05 January 04 January 03 January 02 January 99 January 01 January 00 January 98 April 06 April 05 April 04 April 03 April 02 April 01 April 00 April 99 April 98 July 06 July 05 July 04 July 03 July 02 July 01 July 00 July 99 July 98 October 06 October 05 October 04 October 03 October 02 October 00 October 99 October 98

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Table 3 Architecture of the neural networks used for Ilha Solteira.

Table 6 RMSE for the daily series in Pelotas.

Layers Model 1

Model 2

Month of test

RMSE (model 1)

RMSE (model 2)

Input

(11 Neurons) Temperatures: maximum, minimum and mean. Humidities: maximum, minimum and mean. Daily global irradiation Wind speed Rainfall Bright sunshine hours (theoric)

January 06 January 05 January 04 January 03 January 02 January 99 January 01 January 00 January 98 April 06 April 05 April 04 April 03 April 02 April 01 April 00 April 99 April 98 July 06 July 05 July 04 July 03 July 02 July 01 July 00 July 99 July 98 October 06 October 05 October 04 October 03 October 02 October 00 October 99 October 98

10.9% 7.5% 7.2% 6.2% 9.4% 14.1% 11.6% 7.6% 16.8% 8.5% 16.6% 10.5% 14.0% 18.4% 11.3% 12.2% 7.5% 22.9% 7.5% 10.6% 16.2% 12.3% 16.1% 17.2% 8.7% 17.8% 23.2% 10.7% 7.7% 9.7% 10.1% 15.6% 17.5% 11.3% 13.2%

19.9% 12.2% 12.6% 13.1% 15.4% 20.7% 15.6% 8.5% 24.2% 15.1% 23.5% 14.3% 23.9% 28.3% 18.7% 17.6% 21.9% 34.3% 18.5% 17.0% 26.5% 21.2% 29.2% 34.0% 18.0% 24.5% 37.5% 15.4% 13.8% 20.0% 13.0% 33.7% 22.6% 18.4% 21.3%

(11 Neurons) Temperatures: maximum, minimum and mean. Humidities: maximum, minimum and mean. Daily global irradiation Wind speed Rainfall Bright sunshine hours (experimental) Amplitude of temperature

Amplitude of temperature

Hidden (20 Neurons)

(20 Neurons)

Output (01 Neuron) Daily global irradiation

(01 Neuron) Daily global irradiation

Table 4 Architecture of the neural networks used for Pelotas. Layers Model 1

Model 2

Input

(11 Neurons) Temperatures: maximum, minimum and mean. Humidity Evaporation Daily global irradiation Wind speed Rainfall

(11 Neurons) Temperatures: maximum, minimum and mean. Humidity Evaporation Daily global irradiation Wind speed Rainfall Bright sunshine hours (experimental) Bright sunshine hours (theoric) Amplitude of temperature

Bright sunshine hours (theoric) Amplitude of temperature

Hidden (20 Neurons)

(20 Neurons)

Output (01 Neuron) Daily global irradiation

(01 Neuron) Daily global irradiation

incidence on horizontal surface (cal.cm-2.), wind speed (m/s), pluviometric precipitation (mm), evaporation (mm) and bright sunshine hours (h). The instruments used for measuring daily global irradiation and bright sunshine hours were a LICOR LI e 200X pyranometer and a Campbell-Stokes heliograph, Table 5 RMSE for the daily series in lha Solteira. Month of test

RMSE (model 1)

RMSE (model 2)

January 06 January 05 January 04 January 03 January 02 April 06 April 05 April 04 April 03 April 00 July 06 July 05 July 04 July 03 July 01 July 00 October 06 October 05 October 04 October 03 October 00

5.1% 11.9% 6.6% 9.7% 10.7% 5.4% 4.8% 4.1% 3.8% 5.9% 4.6% 4.9% 5.8% 12.0% 11.8% 9.6% 10.6% 9.5% 10.5% 10.1% 10.3%

15.5% 21.5% 14.5% 15.6% 12.0% 10.4% 9.9% 14.0% 19.0% 10.0% 8.7% 10.7% 15.0% 12.4% 13.1% 16.9% 26.0% 17.5% 18.4% 19.2% 12.8%

respectively. In the same way as at the Ilha Solteira, also adding the daily amplitude of temperature and theoric bright sunshine hours to the data set.

2.2. Artificial neural networks In this work, the implementation of the neural networks was carried out from the division of the temporal series of the measured data, in three distinct subgroups: training, validation and test. The training group was used during the beginning phase to capture the existing interrelationships between solar irradiation and the rest of the available variables. The use of a validation group as a stop criteria, aimed to avoid the network becoming addicted in the training group, therefore, improving its generalization capacity for data that do not make up part of that group. During the generation of the synthetic series of solar irradiation, from the rest of the available variables, a test group was used to evaluate the performance of the models.

Table 7 Variability of daily solar irradiation in the two localities. Locality

Month

Monthly mean

Standard deviation (%)

Ilha Solteira Ilha Solteira Ilha Solteira Ilha Solteira Pelotas Pelotas Pelotas Pelotas

January April July October January April July October

21.5 18.6 15.8 21.3 21.0 11.3 7.9 16.1

28.7% 21.9% 21.5% 27.0% 33.1% 42.1% 43.1% 44.4%

A.N. Siqueira et al. / Renewable Energy 35 (2010) 2406e2414

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Ilha Solteira July 2003

22 20 18

14

2

Irradiation (MJ/m .day)

16

12 10 8 6 4 2 0 5

10

15

20

Day Mod1

Data

25

30

mod2

Fig. 3. Daily series for July 2003 in Ilha Solteira.

The solar irradiation estimates, for two localities were taken from two distinct models that differ only by use or not of the quantified bright sunshine hours as an input variable: model 1 used it and model 2 excluded it and in its place daylight length was used. In the two models the multiple layer perceptron (MLP) of ANN were used, whose input layer possessed a number of neurons defined by the quantity of input variables used, the hidden layer possessed a number of empirically defined neurons in function of the size of the training group and the output layer is composed of only one neuron, that is responsible for solar irradiation estimation. A MLP network has its neurons (units of information processing) organized in layers without lateral connections and the input signals propagate from behind to the front, through the network, which is trained by a retropropagation algorithm. In Fig. 1, a structure of this type of network is presented. In the MLP type neural networks, Fig. 1, the activation of the neurons in the hidden and output layers is achieved from the use of sigmoid (fi) type activation function. The ANN used in the study were trained from the back-propagation algorithm which is an interactive training method that is

Ilha Solteira

22

supervised for multi-layer networks with propagation of signal from behind to front, which minimizes the square mean error between the network output (yk(n)) and the desired output (dk(n)), Fig. 2. Before the k neuron is activated by a state vector x(n), produced by the layer of hidden neurons, that in turn were activated by an applied input vector (stimulated) to the neural network input layer,, the algorithm determined the connecting weights between the neurons in the following way: the implementation of the network was initiated with a training example, and by using the existing weights, calculated the output or the output example, then, the algorithm calculated the (ek(n)) error, taking the difference between the calculated result and the expected result (true result), and finally, the error was feedback to the network and the weights adjusted aiming to minimize the error. 2.3. Development of the models Considering the importance of the seasonal character of meteorological variables for the months of January, April, July and

July 2006 Pelotas July 1998

20 14

16

12

14 Radiation (MJ/m .day)

2

Irradiation (MJ/m .day)

18

10

2

12 10 8 6 4

8 6 4 2

2 0

5

10

15

20

25

30

0 5

10

15 Day

Data

Mod1

Day Data

Mod1

Mod2

Fig. 4. Daily series for July 2006 in Ilha Solteira.

20 Mod2

Fig. 5. Daily series for July 1998 in Pelotas.

25

30

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A.N. Siqueira et al. / Renewable Energy 35 (2010) 2406e2414

Pelotas July 2006

Ilha Solteira - July

25

14

20

10

2.

Radiation (MJ/m day)

2

Solar Irradiation (MJ/m )

12

8 6 4

15

2

R =0.83

10

5

2 0

0 5

10

15

20

25

30

0

5

10

Day Data

Mod1

15

20

25

Solar Irradiation (MJ/m2)

Mod2

Fig. 8. Comparison for the 1 model for July in Ilha Solteira.

Fig. 6. Daily series for July 2006 in Pelotas.

12 2

3. Results and discussion

10 8

2

R =0.89

6 4 2 0

0

3.1. Estimations of daily solar irradiation

2

4

6

8

10

12

14

Solar Irradiation (MJ/m2)

After carrying out the ANN training, with the corresponding weights to each duly adjusted neuron, estimates of daily solar irradiation series for each month were carried out. The values referring to RMSE among the daily solar irradiation measured values and those for each month can be seen in Tables 5 and 6 respectively, for the localities of Ilha Solteira and Pelotas. From the results above it can be seen that when measured bright sunshine hours is used as input, the results obtained as much for Pelotas as for Ilha Solteira are satisfactory. For the 56 months tested the RMSE obtained were lower or equal to 23.2%, although 43 of those months presented RMSE lower or equal to 12.3%. The estimates obtained when excluding observed

Fig. 9. Comparison for the 1 model for July in Pelotas.

bright sunshine hours in input, presented inferior precision, as expected. For the 56 months tested RMSE were found to vary from 8.5% to 37.5%, although 38 of those months presented RMSE lower or equal to 20.0%. In Pelotas, the good performance of ANN could not be proved for a few months, as for example, July, 1998 and October 2002. One of the reasons that produced the low performance of the models for these months, may be that the series referring to these months were atypical for the time of the year in the locality.

Ilha Solteira - April

25

Pelotas - July

14

Solar Irradiation (MJ/m )

October the variables were analyzed individually. The analysis was carried out for a long term period that evaluated the possible combinations between the same month and the diverse years, in the sense of reducing the risk of an equivocal evaluation of ANN performance occasioned by the occurrence of an atypical month. Each monthly data set was divided into three distinct subgroups: training, validation and test conforming to Table 1, for Ilha Solteira and Table 2, for Pelotas. Tables 3 and 4 show the architecture used by the ANN models that were developed during the achievement of this study.

Pelotas - October

30 25 2.

Solar Irradiation (MJ/m )

2

Solar irradiation (MJ/m )

20

2

R = 0 .9 5

15

10

5

0

20 2

R =0.93

15 10 5 0

0

5

10

15

20

Solar Irradiation (MJ/m2 .) Fig. 7. Comparison for the 1 model for April in Ilha Solteira.

25

0

5

10

15

20

25

Solar Irradiation (MJ/m2.) Fig. 10. Comparison for the 1 model for October in Pelotas.

30

A.N. Siqueira et al. / Renewable Energy 35 (2010) 2406e2414 Table 8 Coefficients of determination (R2) obtained for the correlation between measured daily solar irradiation and estimated with the ANN 01 model, for different months. Month

Locality

R2

January January April April July July October October

Ilha Solteira Pelotas Ilha Solteira Pelotas Ilha Solteira Pelotas Ilha Solteira Pelotas

0.91 0.91 0.95 0.90 0.83 0.89 0.85 0.93

Table 9 Mean deviations for the two localities (all period). Month

January April July October January April July October

Locality

Mean Deviation

Ilha Solteira Ilha Solteira Ilha Solteira Ilha Solteira Pelotas Pelotas Pelotas Pelotas

RMSE

Model 1 (MJ/m2)

Model 2 (MJ/m2)

Model 1 (MJ/m2)

Model 2 (MJ/m2)

0.01 0.08 0.02 0.15 0.26 0.34 0.16 0.22

0.08 0.14 0.35 0.38 0.39 0.68 0.20 0.11

8.7% 4.8% 8.8% 10.3% 9.9% 13.4% 14.5% 12.0%

15.1% 13.0% 13.4% 19.0% 15.3% 20.5% 24.4% 19.5%

Also, it was verified that the results obtained for Ilha Solteira were better than those observed for Pelotas. In relation to the probable cause of this difference, it is believed that in spite of the monthly historical series, used for Pelotas (nine years), being longer than those used for Ilha Solteira (five years) the size of this series is still insufficient for representing the variability of daily solar

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irradiation in this locality which is clearly superior to Ilha Solteira, as in agreement with what can be seen in Table 7. Figs. 3e6 show the daily series of solar irradiation generated by two models for the months of July 2006 and July 2003 (Ilha Solteira) and July 2006 and July 1998 (Pelotas). In Figs. 3e6 it is verified that in general way, with few exceptions in Pelotas, the models were able to produce irradiation variability in a satisfactory way. Besides this, model 1 presented better performance, as was expected. 3.2. Utilization of synthetic series for long term simulation of solar systems The good performance of ANN methodology, for generation of daily solar irradiation can be proved by the comparisons of measured and estimated values. Figs. 7e10 show the comparisons between measured (ordinate) and estimated values (abscissa), for the months of April and July (Ilha Solteira) and July and October (Pelotas). The coefficient of determination (R2) for the linear expression that relates to measured values as opposed to estimated values in the two localities, as can be seen in Table 8. In Table 9 the values referring to mean deviations are represented and the RMSE obtained for each model, are calculated from the series corresponding to all the period of study. In spite of the tendency to underestimate the solar irradiation for Pelotas, Table 8, this methodology showed that it was able to reproduce, in a satisfactory way, the variability of the measured series in the two localities with or without the use of measured bright sunshine hours as input. In the case of model 1 RMSE lower or equal to 14.5% was obtained for the 8 months, being that 6 of these months had RMSE lower or equal to 9.9%. When measured bright sunshine hours is not used as input, model 2, RMSE were estimated for 8 months that were lower or equal to 24.4%, 4 of these months having RMSE lower or equal to 20.0%.

Table 10 Descritive statistics for Ilha Solteira. Month

Séries

Méan

Median

Standard deviation

Minimum

Maximum

Monthly Sum

January January January April April April July July July October October October

Data Model Model Data Model Model Data Model Model Data Model Model

21.5 21.5 21.5 18.6 18.5 18.8 15.8 15.8 16.2 21.3 21.5 21.7

21.5 22.4 21.7 19.9 19.9 20.0 16.7 16.9 17.1 23.3 23.4 23.1

6.2 5.8 5.0 4.1 4.0 3.5 3.4 3.1 2.8 5.8 5.3 4.6

3.2 7.6 4.8 4.5 6.9 4.1 3.2 5.5 1.1 4.1 7.0 9.4

31.5 29.8 29.7 23.6 23.4 22.3 21.0 19.2 19.2 29.7 27.9 27.6

2928.4 2929.7 2916.9 2626.2 2614.7 2646.7 2814.6 2819.0 2877.3 3028.3 3049.8 3082.1

1 2 1 2 1 2 1 2

Table 11 Descritive statistics for Pelotas. Month

Séries

Méan

Median

Standard deviation

Minimum

Maximum

Monthly Sum

January January January April April April July July July October October October

Data Model Model Data Model Model Data Model Model Data Model Model

21.0 20.8 20.6 11.3 11.0 10.6 7.9 7.7 7.7 16.1 15.9 16.0

22.7 23.1 22.1 11.9 12.1 11.8 8.6 8.5 8.2 17.1 17.3 17.1

7.0 6.6 6.2 4.8 4.5 4.2 3.4 3.1 2.9 7.2 6.7 6.1

2.8 4.5 4.6 0.5 0.8 0.5 0.6 1.3 0.7 1.1 1.4 2.2

31.9 29.0 30.5 20.9 17.5 17.3 13.5 11.9 13.0 28.3 25.3 25.2

5848.0 5788.1 5751.6 3004.6 2913.5 2824.4 2172.2 2130.1 2119.5 3892.8 3838.9 3865.9

1 2 1 2 1 2 1 2

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A.N. Siqueira et al. / Renewable Energy 35 (2010) 2406e2414

Ilha Solteira - January

20

Pelotas - January

30

25

15

Frequency (%)

Frequency (%)

20

10

15

10

5 5

0

0 0

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30

0

32

2

4

6

8

Data

Mod1

10

12

14

16

18

20

22

24

26

28

30

32

2

2

Irradiation (MJ/m .day)

Irradiation (MJ/m .day) Mod2

Data

Mod1

Mod2

Fig. 11. Histogram of the series of daily solar irradiation calculated by ANN and measured series for January, in Ilha Solteira.

Fig. 13. Histogram of the series of daily solar irradiation calculatated via ANN and measured series for January, in Pelotas.

In Tables 10 and 11, the principal statistical characteristics of the measured series are represented and estimated for the two localities. The units are (MJ/m2.day), except the last which is given in (MJ/m2.month). The comparison of descriptive statistics of the measured and calculated values can be seen in Table 10. The results demonstrate the capacity of the ANN in reproducing measured values without presenting significant differences in: the mean, the median and the accumulated monthly values, which differ at a maximum of 6.0%, 4.0% and 6.0% respectively. Regarding the minimum values of monthly daily solar irradiation, the deviations are expected while these minimum values are measured with instrumental errors greater than 100% in the best of the hypotheses. The error of measurement in an Eppley PSP Pyranometer is typically 25 W/m2, which integrated along one day

(10 hours) results in 0.9 MJ/m2. In addition, the threshold of the heliographs e when well calibrated e are in the order of 120 W/m2. and therefore, in the range of low irradiation the errors will be quite elevated. In Figs. 11e14 the histograms of the series generated by the ANN model and the measured series are represented for the months of January and April in the two localities. The data were grouped in classes with amplitude of 2 MJ/m2. day, corresponding to an instrumental field error of 10%. The evaluation of the histograms referring to the four months in each locality, show that, with the exception of Ilha Solteira (April and July) the two ANN models managed to reproduce, in a satisfactory way, the statistical characteristics regarding the distribution frequency format. The comparisons of asymmetry and Kurtosis of measured and calculated time series can be seen in Table 12.

Ilha Solteira - April

50

Pelotas - April

30

45 25

40

20

Frequency (%)

Frequency (%)

35 30 25 20 15 10

15

10

5

5 0

0 0

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30

32

2

Irradiation (MJ/m .day) Data

Mod1

Mod2

Fig. 12. Histogram of the series of daily solar irradiation calculated by ANN and measured series for April, in Ilha Solteira.

0

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30

32

2

Irradiation (MJ/m .day) Data

Mod1

Mod2

Fig. 14. Histogram of the series of daily solar irradiation calculated via ANN and measured series for April, in Pelotas.

A.N. Siqueira et al. / Renewable Energy 35 (2010) 2406e2414 Table 12 Assymmetry and kurtosis of the series. Asymmetry

January (Ilha Solteira) April (Ilha Solteira) July (Ilha Solteira) October (ilha Solteira) January (Pelotas) April (Pelotas) July (Pelotas) October (Pelotas)

Curtose

Data

Model 1 Model 2 Data

Model 1 Model 2

0.40 2.50 1.43 0.85 0.69 0.35 0.43 0.41

0.37 1.52 1.81 0.85 0.72 0.44 0.45 0.43

1.08 3.13 2.50 0.38 0.77 1.12 1.23 1.24

0.62 1.60 2.39 0.96 0.72 0.52 0.54 0.43

0.43 6.56 2.02 0.10 0.43 0.84 0.92 1.03

0.24 2.10 6.88 0.02 0.35 0.84 0.51 0.95

80

60

40

20

0

Ilha Solteira - January

100

Pelotas - January

100

Acumcumulative distribution (%)

Month

2413

0

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30

32

Irradiation (MJ/m2.d a y) Mod2

60

40

100

20

80

0 0

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30

32

2

Irradiation (MJ/m .day) Data

Mod1

Mod2

Fig. 15. Comparison between calculated accumulated distribution function and measured series for January in Ilha Solteira.

The comparison between the accumulated distribution function of measured and calculated time series for the months of January and April for the two localities are represented, in Figs. 15e18. The evaluation of the temporal series calculated via ANN, in which the accumulated distribution probability is referred to, in KolmogoroveSmirnov Test (IC ¼ 99%), demonstrated that of the 16 generated series only two, obtained by model 2 for the months of

Pelotas - April

60

40

20

0 0

2

4

6

8

10

12

14

16

18

20

22

24

Irradiation (MJ/m2.d a y) Data

Mod1

Mod2

Fig. 18. Comparison between calculated accumulated distribution function and measured series for April in Pelotas.

April and July in Pelotas, presented significant differences between the distributions of the measured series and the synthetic generated series. The capacity of the model 1, for reproducing the sequential characteristics of the series, was analyzed comparing the partial auto correlation coefficient of first order (f1), calculated with measured values, Table 13. The models reproduce the partial auto correlation coefficient of first order with maximum deviation of 5.3% in relation to the measured values, for April, July and October for Ilha Solteira and with maximum desviation of 15.4% for January, April, July and October for Pelotas.

Ilha Solteira - April

100

Acumcumulative distribution (%)

Mod1

Fig. 17. Comparison between calculated accumulated distribution function and measured series for January in Pelotas.

Acumcumulative distribution (%)

Acumcumulative distribution (%)

Data 80

80

60

40

20

Table 13 Comparison the partial auto correlation coefficient of first order (f1), monthly average of the period, calculated with measured values.

0 0

2

4

6

8 10 12 14 16 Irradiation (MJ/m2.day)

Data

Mod1

18

20

22

24

Mod2

Fig. 16. Comparison between calculated accumulated distribution function and measured series for April in Ilha Solteira.

Locality

January

April

July

October

Ilha Solteira (data) Ilha Solteira (Model 1) Pelotas (data) Pelotas (Model 1)

0.30 0.38 0.21 0.22

0.45 0.44 0.42 0.41

0.38 0.40 0.38 0.43

0.38 0.39 0.26 0.30

2414

A.N. Siqueira et al. / Renewable Energy 35 (2010) 2406e2414

localities were there only exists conventional meteorological information. The model 1 which included the measured bright sunshine hours presented a performance superior to model 2, as was expected. However, the results obtained with model 2 demonstrated that only with the knowledge of daylight length and other meteorological variables is it possible to estimate the daily solar irradiation, for the objective of long term solar system simulation purpose. Finally, this study confirms the viability of the use of ANN for carrying out estimates of daily solar irradiation for climatologically distinct localities such as, Ilha Solteira e SP and Pelotas e RS, from data of other meteorological variables that are generally more available.

Ilha Solteira - July 2003

22 20

2

Solar irradiation (MJ/m )

18 16 14 12 10 8 Mean Data

6 4

Mod1 Mod2

2 5

10

15

20

25

30

Day Fig. 19. Comparison between daily series and series mean for July 2003 in Ilha Solteira.

Pelotas - July 2006

Acknowledgements To the National Research Council (CNPQ), the São Francisco Hydroeletric Company (CHESF) and Brazilian Electric Centers S.A. (ELETROBRAS) for the support in the solar energy researches, particularly regarding the themes referring to measurements, evaluation and solar irradiation mapping.

14

References

2

Solar irradiation (MJ/m )

12 10 8 6 4 2

Mean Data

Mod1 Mod2

5

10

0 15

20

25

30

Day Fig. 20. Comparison between daily series and series mean for July 2006 in Pelotas.

During the use of the ANN, temporal or spatial interpolation, the generation of a smoothed series was verified, with lower standard deviations than the measured ones. It is believed that the smoothing occurs because the size of the training groups is not big enough for the ANN to satisfactorily learn the great variability of the measured series. In Figs. 19 and 20, besides the measured and calculated series, the daily mean global solar irradiation series for the period of training for the two localities are represented. 4. Conclusions The models for generation of synthetic series of solar irradiation via ANN presented a good performance demonstrating the viability of the methodology for generating daily solar irradiation in

[1] Tiba C, Fraindenraich N, Grossi H, Lyra F. Atlas solarimétrico para localidades brasileiras. Recife: Editora Universitária UFPE; 2001 [in Portuguese]. [2] Al-Alawi SM, Al-Hinai HA. An ANN-based approach for predicting global radiation in locations with no direct measurement instrumentation. Renewable Energy 1998;14(4):199e204. [3] Mohandes M, Balghonaim A, Kassas M, Rehman S, Halawani TO. Use of radial basis functions for estimating monthly mean daily solar radiation. Solar Energy 2000;68(2):161e8. [4] Atsu SSD, Joseph AJ, Al-Lawati Ali. Solar radiation estimation using artificial neural networks. Solar Energy 2002;71:307e19. [5] Adnan S, Erol A, Mehemet O, Galip EK. Use of artificial neural networks for mapping of solar potential in Turkey. Applied Energy 2004;77:273e86. [6] Mellit A, Benghanem M, Hadj AA, Guessoum A. A simplied model for generating sequences of global solar radiation data for isolated sites: Using artificial neural network and a library of Markov transition matrices approach. Solar Energy 2005;79(5):469e82. [7] Hontoria L, Aguilera J, Zufiria P. Generation of hourly irradiation synthetic series using the neural network multilayer perceptron. Solar Energy 2002;72 (5):441e6. [8] Reddy KS, Rajan M. Solar resource estimation using artificial neural networks and comparison with other correlation models. Energy Conversion and Management 2003;44:2519e30. [9] Tymvios FS, Jacovides CP, Michaelides SC, Scouteli C. Comparative study of Angstrom’s and artificial neural networks’ methodologies in estimating global solar radiation. Solar Energy 2005;78:752e62. [10] Engineering Faculty of Ilha Solteira e UNESP, http://www.agr.feis.unesp.br/ sensor.ilha.htm, access 2006.

Nomenclature ANN: artificial neural network dk(n): desired output ek(n): error between the calculated result and the expected result MLP: multiple layer perceptron yk(n): network output RMSE: root mean square error x(n): state vector f1: partial auto correlation coefficient of first order