^{1}

^{2}

^{1}

^{1}

Solar radiation is one of the most important parameters for applications, development and research related to renewable energy. However, solar radiation measurements are not a simple task for several reasons. In the cases where data are not available, it is very common the use of computational models to estimate the missing data, which are based mainly on the search for relationships between weather variables, such as temperature, humidity, precipitation, cloudiness, sunshine hours, etc. But, many of these are subjective and difficult to measure, and thus they are not always available. In this paper, we propose a method for estimating daily global solar radiation, combining empirical models and artificial neural networks. The model uses temperature, relative humidity and atmospheric pressure as the only climatic input variables. Also, this method is compared with linear regression to verify that the data have nonlinear components. The models are adjusted and validated using data from five meteorological stations in the province of Tucumán, Argentina. Results show that neural networks have better accuracy than empirical models and linear regression, obtaining on average, an error of 2.83 [MJ/m
^{2}] in the validation dataset.

Solar radiation is an important parameter for research related to solar energy. The solar energy importance is that it can play a key role in the decarbonisation of the global economy along with improvements in energy efficiency and imposing costs on greenhouse gases emissions [

Unlike other climate variables such as ambient temperature and relative humidity, the solar radiation is barely measured [

In the literature, we can find a wide variety of methods to estimate solar radiation. There are empirical models [

Many of these methods include empirical relationships between solar radiation and astronomical factors (Earth-sun distance, solar declination, hour angle, etc.), geographic factors (latitude, longitude and elevation of the site), physical factors (diffusion of air molecules, water vapor content, the spread of dust, etc.) and weather factors (sunshine, temperature, rainfall, relative humidity, cloud cover, etc.) [

The aim of this paper is to propose a method for estimating daily global solar radiation, based on an empirical model and neural network. The proposed method uses the empirical model to generate initial estimates, which are then used along with temperature, relative humidity and atmospheric pressure as input variables for the neural network to improve estimates. As part of this study, we make a comparison of different mathematical methods to determine which one provides better initial estimates of solar radiation. Both empirical models and neural network are adjusted and validated using weather data from automated weather stations located in the province of Tucumán, Argentina. Finally, the proposed method is compared with linear regression to determine if the relationship between input data and output data has indeed nonlinear components.

The rest of this paper is organized as follows: Section 2 describes the materials and methodology used for estimating daily global solar radiation; Section 3 details the results for both the empirical model and the method based on neural networks; finally in Section 4 the conclusions are presented.

The weather data used in this work were collected from five weather stations belonging to Estación Experimental Agroindustrial Obispo Colombres (E.E.A.O.C.), located in the province of Tucumán, Argentina. The dataset corresponds to average values of samples taken every 15 minutes, in the period between 01-01-2010 and 20- 11-2013. Among all the variables provided by the weather stations, in this paper we use:

・ Temperature [˚C]

・ Relative Humidity [%]

・ Atmospheric Pressure [hPa]

・ Observed Solar Radiation [W/m^{2}]

In the initial analysis of the dataset, and as usually happens in distributed sensor networks, there are records with missing or erroneous values (out of range), varying from a few days to a few weeks. This is usually caused by problems in measuring devices or data transmission and storage or poorly calibrated instrumentation [

From the database described above, a new database is generated with daily values, which was used in the tests in this paper. This new database is composed of maximum, minimum and average temperature, average relative humidity, average atmospheric pressure and global solar radiation [MJ/m^{2}].

A large percentage of empirical methods found in the literature use empirical relations to estimate the global solar radiation from climatic variables. Many of them include extraterrestrial radiation (

where ^{2}∙day)];

The factor

Weather Station | Variable | Min. | Max. | Mean | STD | Missing Values [%] | Affected Records [%] | |
---|---|---|---|---|---|---|---|---|

Santa Ana | Temperature [˚C] | −5.3 | 40.8 | 18.77 | 7.64 | 2.52 | 2.52 | |

Lat. 27˚47'21''S | Pressure [hPa] | 944.7 | 991.2 | 965.51 | 6.32 | 2.26 | ||

Lon. 65˚40'30''O | Relative Humidity [%] | 9.0 | 98.0 | 71.59 | 21.42 | 2.52 | ||

Solar Radiation [W/m^{2}] | 0.0 | 1511.0 | 167.17 | 266.88 | 2.52 | |||

Pueblo Viejo | Temperature [˚C] | −4.0 | 41.2 | 19.38 | 6.88 | 10.84 | 10.84 | |

Lat. 27˚11'56''S | Pressure [hPa] | 940.0 | 985.8 | 960.46 | 6.17 | 10.46 | ||

Lon. 65˚37'10''O | Relative Humidity [%] | 10.0 | 96.0 | 69.44 | 19.44 | 10.84 | ||

Solar Radiation [W/m^{2}] | 0.0 | 1410.0 | 174.38 | 274.30 | 10.84 | |||

Monte Redondo | Temperature [˚C] | −6.9 | 43.6 | 19.48 | 8.16 | 0.06 | 0.07 | |

Lat. 26˚49'10''S | Pressure [hPa] | 942.7 | 991.2 | 964.70 | 6.57 | 0.06 | ||

Lon. 64˚50'58''O | Relative Humidity [%] | 9.0 | 100.0 | 66.30 | 23.40 | 0.07 | ||

Solar Radiation [W/m^{2}] | 0.0 | 1414.0 | 189.16 | 286.20 | 0.06 | |||

El Colmenar | Temperature [˚C] | −2.6 | 42.5 | 19.69 | 6.98 | 0.01 | 0.08 | |

Lat. 26˚47'21''S | Pressure [hPa] | 934.1 | 980.4 | 955.04 | 6.27 | 0.00 | ||

Lon. 65˚11'13''O | Relative Humidity [%] | 9.0 | 100.0 | 64.10 | 20.58 | 0.08 | ||

Solar Radiation [W/m^{2}] | 0.0 | 1470.0 | 182.95 | 281.27 | 0.02 | |||

Casas Viejas | Temperature [˚C] | −6.2 | 42.2 | 19.14 | 7.92 | 0.06 | 0.06 | |

Lat. 27˚46'56''S | Pressure [hPa] | 943.6 | 992.9 | 966.05 | 6.66 | 0.00 | ||

Lon. 65˚30'24''O | Relative Humidity [%] | 9.0 | 98.0 | 66.17 | 21.71 | 0.07 | ||

Solar Radiation [W/m^{2}] | 0.0 | 1444.0 | 190.34 | 288.09 | 0.06 | |||

Earth-Sun distance (

where

The solar declination

where

The hour angle of the sun

To choose a method for the initial estimates of global solar radiation, different models based only on temperature were tested. To adjust the empirical parameters of these models, a local search algorithm was implemented, Hill Climbing [

where

An Artificial Neural Network (ANN) is an abstract model formed by a structure of interconnected processing units, called neurons. The links connecting neurons transmit information between themselves, where mathematical transformations are applied to provide the expected result. The inputs of each neuron have associated

Empirical Model | RMSE | R | MBE |
---|---|---|---|

Hargreaves & Samani, 1982 | 3.69 | 0.87 | 0.23 |

Annandale, 2002 | 3.69 | 0.87 | 0.18 |

Bristow & Campbell, 1984 | 3.69 | 0.87 | 0.30 |

Donatelli & Capbell, 1998 | 3.77 | 0.86 | 0.26 |

Goodin, 1999 | 3.73 | 0.87 | 0.33 |

Winslow, 2001 | 3.67 | 0.87 | 0.19 |

Mahmood & Hubbard, 2002 | 4.13 | 0.86 | 0.54 |

weights, which are adjusted iteratively by a training algorithm. For each iteration (or step), the algorithm compares the output and target values, so as to minimize the error. The training process ends when the network is capable of reproducing the outputs corresponding to the input parameters.

Multilayer Feedforward is a kind of neural network, which consist of a number of layers: the first has neurons directly connected to the input data, and they are linked to one or more neurons in a hidden layer, or directly connected to the neurons in the output layer. In this kind of network, all neurons in one layer are full connected to all neurons of the next layer, and there are no feedbacks or recurrent connections.

In this work, we decided to use a Multilayer Feedforward Neural Network with 4 neurons in a single hidden layer, as show in

The input vector of the neural network consists of global solar radiation estimates (H) calculated with Equation (6), the solar zenith angle (

Additionally, in order to improve the accuracy of estimates, information from the previous day is included as new independent variables called lagged variables [

As is usual when using neural networks, we normalize the data by applying a scaling minmax to

In other works [

The inclusion of past information as lagged variables in the input vector generates a strong correlation between some of the input variables. For this reason, the linear systems involved can be ill-conditioned (produce a strong variation in the output for small changes in the input) [

In order to evaluate the performance of the implemented models, the errors obtained are analyzed using different metrics commonly used in the literature, comparing the calculated solar radiation values (

The errors obtained using the simple empirical model, using linear regression and using a neural network are shown in

Model | WeatherStation | RMSE | R | MBE | RMSE% |
---|---|---|---|---|---|

Empirical Model | El Colmentar^{a} | 3.69 | 0.87 | 0.17 | 11.71 |

Santa Ana | 4.28 | 0.88 | −2.54 | 14.80 | |

Pueblo Viejo | 3.78 | 0.89 | −1.54 | 12.14 | |

Monte Redondo | 4.19 | 0.88 | −2.00 | 13.04 | |

Casas Viejas | 3.57 | 0.89 | −1.23 | 11.28 | |

Linear Regression | El Colmentar^{a} | 2.92 | 0.92 | 0.01 | 9.28 |

Santa Ana | 3.26 | 0.92 | −1.56 | 11.28 | |

Pueblo Viejo | 3.15 | 0.92 | −0.97 | 10.12 | |

Monte Redondo | 3.39 | 0.91 | −1.05 | 10.56 | |

Casas Viejas | 2.93 | 0.92 | −0.55 | 9.26 | |

Neural Network | El Colmentar^{a} | 2.55 | 0.94 | 0.07 | 8.11 |

Santa Ana | 2.91 | 0.93 | −1.37 | 10.06 | |

Pueblo Viejo | 2.72 | 0.94 | −0.80 | 8.72 | |

Monte Redondo | 2.96 | 0.92 | −0.28 | 9.21 | |

Casas Viejas | 2.74 | 0.93 | −0.16 | 8.65 |

^{a}Values used for training or parameter adjustment.

Colmenar were used to adjust the empirical model, obtain the linear regression coefficients and train the neural network. Furthermore, comparing the results obtained, you can see that the error reduction when using neural networks regarding linear regression is 6.6% for training set (data from El Colmenar) and 10.0% on average for the validation cases. These differences show that the relationship between solar radiation and the input variables present nonlinear components.

The use of lagged variables allows improving the estimates accuracy. According to preliminary tests, which are not detailed in this work, use these additional variables allows a reduction between 10% and 15% in the estimates obtained with neural networks. Since the total amount of variables is not excessive (in total 12 input variables were used), it was not necessary to implement a method for selecting variables.

The use of lagged variables allows improving the estimates accuracy. According to preliminary tests, which are not detailed in this work, use these additional variables allows a reduction between 10% and 15% in the estimates obtained with neural networks. Since the total amount of variables is not excessive (in total 12 input variables were used), it was not necessary to implement a method for selecting variables.

^{2}], and a slight overestimation for values less than 5 [MJ/m^{2}]. This model behavior occurs for both the training set and the validation set. However, in general the trained model achieves correctly grasp the trend of the data, and this is reflected in the R values near 1 in

This paper presented a methodology for estimating solar radiation based on empirical models and artificial neural networks, using temperature, relative humidity and atmospheric pressure as unique climatic input variables. From the results obtained, we present the following conclusions:

・ The proposed methodology is used to estimate the daily global solar radiation satisfactorily, even without some of the variables considered critical that the literature reports as necessary for a good estimate.

・ Using the neural network significantly improves the accuracy over estimates obtained only using the empirical model.

・ By using lagged variables is possible to improve the result. Considering more time backwards the number of variables increases, but in some cases this allows to increase the accuracy of the estimates. However, the use of too many variables may increases the complexity of the problem, so it is recommended the use of some variable selection method to avoid these problems.

・ The error obtained is slightly higher than the error obtained in other works that estimate solar radiation in Tucumán [

In this work, a single empirical model is included as input to the neural network. However, the methodology used allows us to include more than one.

This work was partially supported by grants PID-UTN 25/P051 UTI 1757. We also wish to extend thanks to Estación Experimental Agroindustrial Obispo Colombres to provide the data necessary to make this paper.

Victor Adrian Jimenez,Amelia Barrionuevo,Adrian Will,Sebastián Rodríguez, (2016) Neural Network for Estimating Daily Global Solar Radiation Using Temperature, Humidity and Pressure as Unique Climatic Input Variables. Smart Grid and Renewable Energy,07,94-103. doi: 10.4236/sgre.2016.73006