International Journal of Photoenergy

Volume 2015, Article ID 968024, 13 pages

http://dx.doi.org/10.1155/2015/968024

## A Model for Hourly Solar Radiation Data Generation from Daily Solar Radiation Data Using a Generalized Regression Artificial Neural Network

^{1}Department of Energy Engineering and Environment, An-Najah National University, Nablus, State of Palestine^{2}Institute of Networked and Embedded Systems, University of Klagenfurt, 9020 Klagenfurt, Austria

Received 29 June 2015; Accepted 13 September 2015

Academic Editor: Wilfried G. J. H. M. Van Sark

Copyright © 2015 Tamer Khatib and Wilfried Elmenreich. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper presents a model for predicting hourly solar radiation data using daily solar radiation averages. The proposed model is a generalized regression artificial neural network. This model has three inputs, namely, mean daily solar radiation, hour angle, and sunset hour angle. The output layer has one node which is mean hourly solar radiation. The training and development of the proposed model are done using MATLAB and 43800 records of hourly global solar radiation. The results show that the proposed model has better prediction accuracy compared to some empirical and statistical models. Two error statistics are used in this research to evaluate the proposed model, namely, mean absolute percentage error and root mean square error. These values for the proposed model are 11.8% and −3.1%, respectively. Finally, the proposed model shows better ability in overcoming the sophistic nature of the solar radiation data.

#### 1. Introduction

Solar energy is the portion of the sun’s energy available at the earth’s surface for useful applications, such as raising the temperature of water or exciting electrons in a photovoltaic cell, in addition to supplying energy to natural processes. This energy is free, clean, and abundant in most places throughout the year. Its effective harnessing and use are of importance to the world, especially at a time of high fossil fuel costs and degradation of the atmosphere by the use of fossil fuels. Solar radiation data provide information on how much of the sun’s energy strikes a location on the earth’s surface during a particular time period. These data are needed for effective research into solar energy utilization [1].

In general, solar radiation that reaches the earth surface is called extraterrestrial solar radiation (above the atmosphere). In the meanwhile, the attenuated solar radiation within the atmosphere is called global solar radiation. Global solar radiation incident on a horizontal surface has two components, namely, direct (beam) and diffuse solar radiation. Both components of solar radiation are usually measured by pyranometers, solarimeters, or actinography. Direct (beam) solar radiation is measured by a pyrheliometer while diffuse solar radiation is measured by placing a shadow band over a pyranometer [1]. In addition, solar radiation can be modeled using different techniques.

Many models of solar radiation were presented in the literature. These methods can be mathematical such as linear and polynomial functions, heuristic methods, fuzzy logic techniques, or other individual methods such as Fourier series and Markov chain. However, recently, artificial intelligence techniques based models such as artificial neural networks (ANNs) were used for solar radiation prediction. According to [1, 2], ANNs were used many times for solar radiation modeling, prediction, and forecasting. Different types of ANNs were utilized for this purpose. Examples for these models are feedback back forward ANN, cascade-forward back propagation ANN, generalized regression ANN, neurofuzzy ANN, and optimized ANN-genetic algorithm. In general, most of the conducted work was done for solar radiation prediction using ground measured meteorological variables such as ambient temperature, sunshine ratio, relative humidity, wind speed, and other solar geometry angles such as hour angle and angle of declination. The main purpose of the aforementioned models is to generate synthetic solar radiation data at a specific location where there are no measuring devices in order to be utilized in solar energy system design, to restore a solar radiation data set in case of having missing data due to monitoring system outages, or to predict the performance of a solar energy system. In 1990s, ANNs were proposed for predicting monthly or daily solar radiation utilizing monthly or daily meteorological variables due to the availability of such data. However, hourly solar radiation prediction is currently more important in order to optimally design solar energy systems. Hourly solar radiation data can be used to optimally design solar power and thermal systems. By using hourly solar radiation data in the design of solar energy systems, the stochastic nature of the solar radiation is considered. In other words, the reliability of the solar power/thermal systems designed based on hourly solar radiation data is greater than systems designed based on daily or monthly solar radiation profiles [3]. The need for hourly solar radiation data for accurate system’s design and control led researchers to utilize hourly meteorological variables for predicting hourly solar radiation. However, there is a big debate regarding the availability of hourly meteorological data such as ambient temperature, relative humidity, and sunshine ratio for this purpose [1]. On the other hand, some of pioneer researchers have proposed empirical equations that can predict hourly solar radiation in terms of daily or monthly solar radiation, hour angle, and sunrise/sunset hour angle. Examples of these models are Liu and Jordan’s model [4], Collares-Pereira and Rabel’s model [5], Garg and Garg’s model [6], Jain’s model [7], Baig’s model [8], and Kaplanis’s model [9, 10]. Proposing these equations has made a big advantage in predicting hourly solar radiation without the need for other meteorological variables. These models are reviewed and discussed in detail in Section 2. Most of these models are either empirical or statistical models that implying complex calculations are required. Therefore, these empirical models can be further enhanced in terms of accuracy and simplicity by utilizing novel learning machine such as generalized artificial neural network (GRNN) where GRNN has been recommended for solar radiation prediction in previous researches according to [1]. There is consequently a need to develop GRNN based models that predict hourly solar radiation using daily or monthly solar radiation without the need for hourly meteorological data. The main objective of this paper is to present a novel model for predicting hourly solar radiation using global solar radiation and other solar angles. This model is developed using a generalized regression artificial neural network and is designed to be more accurate than other models. The proposed model is able to generate hourly solar radiation data from daily solar radiation data at sites where only daily averages of solar radiation are available. These data can be used in optimal sizing of photovoltaic systems. The optimal sizing of such systems requires hourly prediction of system performance for at least one-year time in order to provide optimal sizes of photovoltaic array and storage units, for example. Moreover, such a model can be used to optimally manage photovoltaic based distributed generation (DG) units. The output of DG systems needs to be predicted in order to optimally operate the penetrated power system in terms of optimal power flow and system’s stability, protection, and power quality. This work is done utilizing solar radiation data for Sohar city, Oman. The city has a desertic climate and it is located on Gulf of Oman with latitude of 24.34 N, longitude of 56.73 E, and elevation of 13 ft. The utilized solar radiation data are measured at Sohar University Weather Station.

#### 2. Hourly Solar Radiation Data Mining

Data mining (knowledge discovery in databases) is the process that attempts to discover patterns in large data sets. Based on this, mean hourly solar radiation data mining is the process that attempts to estimate, predict, or obtain mean hourly solar radiation from a solar radiation data set. This solar radiation data set ideally contains measurements such as mean daily solar radiation and solar angles such as hour angle, sunset angle, and angle of declination. The importance of mean hourly solar radiation data mining is to obtain these data for sites that have only mean daily solar radiation. Mean hourly data represents considerable more information and therefore is more useful for the already mentioned applications. Figure 1 shows a typical profile of mean hourly solar radiation versus time. The mean daily solar radiation is indicated here as a horizontal line.