Elsevier

Energy

Volume 35, Issue 9, September 2010, Pages 3751-3762
Energy

Radial Basis Function Network-based prediction of global solar radiation data: Application for sizing of a stand-alone photovoltaic system at Al-Madinah, Saudi Arabia

https://doi.org/10.1016/j.energy.2010.05.024Get rights and content

Abstract

In this paper, Radial Basis Function network (RBF) is used for modelling and predicting the daily global solar radiation data using other meteorological data such as air temperature, sunshine duration, and relative humidity. These data were recorded in the period 1998–2002 at Al-Madinah (Saudi Arabia) by the National Renewable Energy Laboratory. Four RBF-models have been developed for predicting the daily global solar radiation. It was found that the RBF-model which uses the sunshine duration and air temperature as input parameters, gives accurate results as the correlation coefficient in this case is 98.80%. A comparative study between developed RBF, Multilayer perceptron and conventional regression models are presented and discussed in this paper, In addition, an application for estimating the sizing of a stand-alone PV system at Al-Maidinah is presented in order to show the effectiveness of the developed RBF-model.

Introduction

Daily global solar radiation (HG), measured on horizontal surface, is considered as the most important parameter in meteorology, solar conversion, and renewable energy applications, particularly for the sizing photovoltaic (PV) systems [1]. The knowledge of the amount of solar radiation falling on the surface of the earth is of prime importance to engineers and scientists involved in the design of solar energy systems. In particular, many design methods for thermal and photovoltaic systems require the information about the daily radiation on a horizontal surface, in order to predict the energy production of the system [1]. In practice, it is very important to appreciate the order of measurements prior to any modelling study for both solar radiation and sunshine duration or daylight. There is a relative abundance of sunshine duration data and therefore it is a common practice to correlate the solar radiation to sunshine duration measurements. In many countries, sunshine duration is measured at a wide number of locations.

Artificial Neural Network (ANN) has been applied for modelling, identification, optimization, prediction, forecasting and control of complex systems. Many studies concerning the solar radiation modelling and prediction have been performed using ANNs. Most of these studies use the geographical coordinates and meteorological data, such as relative humidity (RH), air temperature (T), pressure (P), sunshine duration (S) as input parameters of the neural network for estimation of the global solar radiation. In fact, few studies were interested in using only the meteorological data for estimation of the global solar radiation.

This paper presents the use of RBF networks for modelling and predicting the global solar radiation data. Due to their better approximation capabilities, simpler network structures and faster learning algorithms, RBF networks have been widely applied in many science and engineering fields [1]. Therefore, in the present study, four RBF-models are proposed, the first one has as input parameters the sunshine duration and the day of the year (t), (HG=f˜(t,S)). The second model has input parameters both sunshine duration, temperature and the day of the year (HG=f˜(t,S,T)). In the third model and in addition to the above parameters, the relative humidity (RH) is used as input parameter (HG=f˜(t,S,T,RH)). Finely, the fourth model is similar to the third model except that the sunshine duration is not included in its input parameters HG=f˜(t,T,RH). The output of these models is the daily global solar radiation data. In order to show the potential of the proposed RBF-models, we will make a comparison between MLP network, and some conventional regression models. Additionally, an application for sizing of the stand-alone PV system in this location is presented and discussed.

This paper is organized as follows: in Section 2 we provide a database description, as well as a correlation between solar radiation, sunshine duration, air temperature and relative humidity. In Section 3 we give a brief introduction to the radial basis function network that used in this study. Section 4 deals with the implementation of the RBF-models for predicting daily global solar radiation from other meteorological parameters. Results and discussion are given in Section 5. While an application for sizing PV system is presented in the final section.

Section snippets

Review on the using of ANN for modelling and predicting of solar radiation

Alawi and Hinai [2] used ANNs to predict solar radiation in areas that are not covered by direct measurement instrumentation. The input data used by the network are the location, and the monthly values of the pressure, the temperature, the relative humidity, the wind speed and the sunshine duration. The monthly-predicted values using the ANN model compared to the actual global radiation values for this independent data set produced an accuracy of 93% and a mean absolute percentage error of

Database and correlation between different meteorological parameters

The experimental data used in this work are the global solar radiation, the sunshine duration, the air temperature and the relative humidity. These data are available from 1998 to 2002 at the National Renewable Energy Laboratory (NREL) [17].

Fig. 1a shows the daily evolution of the global solar radiation and the sunshine duration fallen on a horizontal surface. Fig. 1b shows the daily evolution of the air temperature and the relative humidity, at Al-Madinah (Latitude:24.55 N°,

Radial basis function networks

The radial basis function network is considered as a 3-layers network (see Fig. 4), because the learning process has done in two different stages, referred to as layers [18]. A key aspect is the distinction between the first and second layers of weights. In the first stage, the input data set xn alone is used to determine the parameters of the basis functions, the first-layer weights.

When only the input data are used, the training method is called unsupervised. The first layer weights are then

RBF-based implementation of solar radiation models

The main objective of this study is to model and predict the global solar radiation from other parameters (e.g. sunshine duration, air temperature and relative humidity) by using RBF network. In fact, we will develop four solar radiation models based on the RBF network, which have the same output which is the daily global solar radiation, and they differ only in their inputs data.

In the first model, we estimate the global solar radiation from the sunshine duration and the day t of year, so:HG=f˜

Results and discussion

A computer codes for different RBF-models were developed in the MatLab software (Version 7.5). Each RBFNs were trained until the best performance is obtained (the MSE should equal or less than the fixed error, 0.001). Once this criterion is achieved the optimal parameters (weights and bias) of the network are saved and used for testing and validating the RBF-models.

Fig. 5 (a), (b), (c), and (d) show a comparison between measured and estimated daily global solar radiation for the first RBF-model

Application for estimating the sizing curve of a stand-alone PV system at Al-Madinah

The size of the stand-alone PV system is a general concept which includes the sizing of PV-array and the accumulator [22], [23]. A useful definition of such dimensions relates to the load: in daily basis, the PV array peak power (CA) is defined as the ratio between average PV-array energy production and the average load energy demand. The storage capacity (CS) is defined as the maximum energy that can be taken out from the accumulator divided by the average energy demand.

A basic configuration

Conclusion

In this paper, RBF-models for estimating the daily global solar radiation data at Al-Madinah (Saudi Arabia) have been developed. The measured daily global solar radiation was compared with those estimated using different designed RBF-models. The obtained results indicate that the second RBF-model (HG=f˜(t,S,T)) provides better accurate results than the other proposed RBF-models. However, for the different developed RBF-models the correlation coefficient r is more than 98%, except in the fourth

Acknowledgement

The authors would like to thank the International Centre for Theoretical Physics (ICTP), Trieste, (Italy) for providing facilities for achieving the present work.

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Present address: The Abdus Salam, International centre for Theoretical Physics (ICTP), Strada-Costiera, 1134014 Trieste, Italy.

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