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New predictive model of hourly global solar component
S. Belaid 1*, A. Boualit 1, M. Zaiani 1 and A. Mellit 2
1Unité de Recherche Appliquée en Energies Renouvelables, URAER Centre de Développement des Energies Renouvelables, CDER
47133, Ghardaia, Algeria
2 Renewable Energy Laboratory, Jijel University, 18000 Jijel, Algeria
Abstract - A prior knowledge of solar energy available on the studied site is necessary, to make the best use of the energy production of different solar installations. For this, several predictive techniques are available in the literature. In this work, new predictive model is proposed using support vector machine (SVM) with the principle of simple and partial autocorrelations, to predict the hourly global solar radiation (HGSR) at one hour step ahead. Two approaches have been adopted; the first by considering five meteorological parameters as inputs for the model at past time (Hour-1 and Hour-2) to predict the future HGSR (Hour H) and the second one is directly inspired from the time series principle. From all the developed models, accurate predictions were obtained with the second approach with order of two in autocorrelation. His performances are such as mean absolute percentage error (MAPE) is equal to 19.72 %, correlation coefficient R = 99 % and normalized root mean square error NRMSE= 13.08 %. As a final task, the predictive performances of this selected model are compared with those of some ones cited in the literature based on other methodologies. This comparison is just to prove the ability of SVM technique in prediction of hourly global solar radiation time series.
Keywords: Hourly solar component - Prediction - SVM - Autocorrelations - Time series.
1. INTRODUCTION
The exploitation of the solar energy field requires some technical challenges because of its intermittent and random nature, where its integration into the operating networks (electrical or thermal) poses problems in maintaining the balance between production and consumption. Therefore, a good forecast is needed for a better use of this form of energy. Thus, the current challenge of researchers is to develop predictive models which achieve better performance.
So, a wide range of techniques are used for modelling and predicting the different components of solar radiation (direct, global, and diffuse). These techniques can be divided into four major classes;
The first, involves complex models of radiative transfers that take into account the interactions between solar radiation and the earth's atmosphere, such as Rayleigh scattering, radiative absorption by ozone, by water vapour or by aerosols [1]. These models have been adopted by some authors, such as; [2], [3], and [4].
But, for more knowledge on these models, we can refer to the works of Gueymard [5], where are summarized a list of radiative models existing in the literature and which are applicable to the prediction of the three components of solar radiation at different scales of time.
The second class includes empirical models that are based on some meteorological and/or geographical parameters. These models come directly from Angström's original equation (1924) [6] which defines the relation existing between the index of clarity (ratio of the solar radiation to the surface of the earth and that outside the terrestrial atmosphere H/H0) and the report of insolation (the duration of sunshine over the
*sboualit@uraer.dz
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duration of maximum sunlight S/S0). Several models result from this Angstrom formulation with more or less parameters to adapt them to a given site and climate.
For example, for Spain; Palomo (1989), for Italy; Mustacchi et al. (1979), for Athènes; Balouktsis et al. (1986), for Singapore; Goh et al. (1977), for Canada; Graham et al. (1987) and for USA; Knight (1988) [7].
The third class of predictive models is based on the principle of statistical learning (ANN, SVM ...). These techniques have only been developed in recent decades and have proven their efficiency in the modelling and forecasting of phenomena that are very complex or too noisy as the case of solar radiation. According to the literature, the majority of proposed models are primarily based on artificial neural networks, [8-13].
The last class is based on the time series principle, which consists to study cross- correlations of the observed time series. These methods are parametric of the moving average type (MA), autoregressive (AR), or a combination of both (ARMA) and others;
ARIMA, SARIMA, ARCH, GARCH, ARMAX…
In this work, a new approach was adopted to predict Hourly Global horizontal Solar Radiation (HGSR) in a Saharan site of Algeria. One technique recently applied in this area of meteorology which is Support Vector Machine (SVM) is exploited with a principle of times series (ARMA) to construct the predictive model.
We note that the first investigations concerning the prediction of the solar component by the SVM were only conducted in 2011 by Chen et al. [14] by proposing a predictive model of average monthly global solar radiation (MGSR). Then, in 2013 these same authors (Chen, Li et al. 2013) propose to apply the SVM to estimate Daily Global Solar Radiation (DGSR) in China, and recently in 2016 [15] elaborate SVM based predictive models for daily and monthly global solar radiation (DGSR, MGSR) on horizontal surface in Ghardaïa (Algeria).
2. METHODOLOGY
2.1 Case study
Saharan sites which is Ghardaïa (latitude = +32.37°, longitude = +3.77° and altitude
= 450 m) has chosen to be studied because it’s considered as an experimental platform for solar energy applications. So, prior knowledge of solar radiation in situ is very important, for better management, sizing and control of solar energy installations.
Consequently, the goal of this study is forecasting the hourly solar radiation for Ghardaïa which is characterized by an arid climate; daily average temperatures ranging from 25°C up to 41 °C during the period from May to October, and daily horizontal solar radiation is arranged between 2500 Wh/m2/day and 8000 Wh/m2/day. The cumulative yearly energy is more than 2 MWh/m2 [15].
2.2 Data and proposed networks
The measured data used in this study are recorded at the Research Unit for Renewable Energy Applications (RUREA) at Ghardaïa. The data are recorded every 1 h with a high precision by a radiometric station installed at the rooftop of the RUEA and the measures taken during 2013 have been exploited.
Two approaches were adopted to predict the HGSR for one step ahead, in the study zone. Each one of these approaches is presented by an appropriate network (R1 and R2) which are illustrated in the figure 2. The first approach consist to use five inputs of meteorological parameters at hour H-1 or H-2, that are temperature (T°C), relative humidity (Rh %),wind speed (V m/s), pressure (P Pa), and HGSR (Wh/m2) (figure 2).
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Fig. 1: Autocorrelogram and partial autocorrelogram of differentiated HGSR time series
Fig. 2: Two types of proposed networks to predict hourly global horizontal solar radiation (HGSR)
The second one (R2), is based on the time-series principle, considering that an autocorrelation relation is already present in this phenomenon of hourly solar radiation.
So, the correlograms of the considered time series after having stationarized it by seasonal differentiation, prove that the phenomenon repeats itself in time and a maximum order of autocorrelation which is of order 2 (H-1 and H-2) has been considered for learn the networks (figure 1).
For evaluate the performances of forecasting models, correlation coefficient (R), root mean square error (RMSE), normalized root mean square error (NRMSE), normalized mean bias error (NMBE) and mean absolute percentage error (MAPE) were calculated.
2.3 Machine learning algorithms
SVM (Support Vector Machine), often translated by Separator at Vast Marge, is a class of learning algorithms, initially defined for classification problems. This approach stems directly from Vapnik's works in learning theory in 1995. Subsequently, these learning techniques were generalized for regression problems (prediction).
The particularity of SVM is that employs the Structural Risk Minimization (SRM) principle, which has been proved that is superior compared to the traditional Empirical Risk Minimization (ERM) principle employed in conventional learning algorithms (e.g.
neural networks).
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SRM minimizes an upper bound on the generalization error as opposed to ERM, which minimizes the error on the training data. This difference makes SVM more attractive in statistical learning applications [16].
The principle of this method is to find a function f of a hyper plane characterized by (w*, b* ) by a structural risk minimization (SRM). f establish a relationship between the variables x and grandeur to model it y;
b ) x ( w ) x ( f
y from the set of measurements.
) x
( is the high dimensional feature space which is nonlinearly mapped from the input space.
n
1 i
2 i
b ,
w (y w (x) b)
min arg )
* b
*, w
( (1)
By introducing Lagrange multipliers and exploiting the optimality constraints to solve {Eq (1)}, we have to solve quadratic problem with constraints (For more detailed information could be found in (Vapnik 1995 and 1998), and we have to find the Lagrange multipliers αi and αi* , i = 1, n by minimizing
n 1 i
n 1
j * i j
j
* j i i
n
1 i
* i i i n
1 i
* i i i
* i i
) x , x ( K ) (
) (
2 / 1
) (
y )
( y )
, ( L min
(2)
With constraints:
n1 i
*i i
* i i
0 ) (
n , ...
, 1 i C ,
0
(3)
C is referred to as the regularized constant and determines the trade-off between the empirical risk and the regularization term.
Finally, the regression function is given by,
n
1
i * i
i i
* i
i, ˆ ) (ˆ ˆ )K(x,x ) b*
, ˆ x (
f (4)
) x ( ) x ( ) x , x (
K i i j is defined as the kernel function, her value is equal to the inner product of two vectors xi and xj in the feature space (xi) and (xj). The using of the kernel function allows dealing with feature spaces of arbitrary dimensionality without having to compute the map (x) explicitly. Any function satisfying Mercer’s condition can be used as kernel function [17]. In general, RBF function is recommended because it handles the case where the relationship between the labels and attributes is nonlinear
.
3. RESULTATS AND DISCUSSION 3.1 First approach
The principle of this approach is to predict HGSR at time H using as inputs to the SVM model five climatic parameters such as; temperature (T°C), relative humidity (Rh
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%),wind speed (V m/s), pressure (P Pa), and HGSR (Wh/m2) at instant H-1, then at H-2, and finally by combining the both (H-1 and H-2).
The results of the different performance tests of the models obtained are shown in Table 1.
Table 1. Predictive performances of HGSR using several climatic parameters as inputs to the model SVM (R1)
NB: To be able to compare the performance of the statistical tests calculated for the different models, the size of the samples used must be the same. In our case, time series of more than four months (from 01/01/13 to 15/05/13) of data has been exploited in the learning of SVM models and the same sample, size was reserved for validation or prediction (test from 16/05/13). Calculations are made with Matlab software using the LSSVM toolbox. The sample size is limited to four and half months of time data, which equals to 3200 hourly data, because the number of variable cells of Matlab is limited.
3.2 Second approach
For this approach, the time series principle is used. The SVM models thus developed tend to predict HGSR from D-day on H-time using hourly global solar radiation values from the same day at instants H-1, H-2 or H-1 and H-2. Predicted and measured values are shown in figure 3 and models performances are illustrated on Table 2.
Table 2. Predictive performances of HGSR from SVM model with time series principle (R2)
3.3 Discussion
The technique SVM chosen for the development of this work has already proved its effectiveness in this last decade and shown as a powerful tool used for many machine learning tasks and has been widely applied in different fields of research [15].
From all the displayed results (Tables 1 and 2), a better prediction was obtained by combining the inputs at time H-1 and those at time H-2. Because, it has been proved that the phenomenon of hourly solar radiation repeat itself in time with an order of autocorrelation that maximum is two (figure 1).
Also, by exploiting a time series of 4 months and using the approach R2, one SVM model is developed, and used to make the hourly prediction for all the days of the year.
Its performance are; MAPE = 19.72 % and the correlation coefficient reaches 99%.
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The correlations between the measured and predicted data for 4 months (3200 hours) for Ghardaïa city by the SVM models developed by the second approach (R2) are presented in figure 4. The line of the first bisector is also drawn on each of the figures to better illustrate the good correlations existing between the measured values and those evaluated by the model thus developed.
Fig. 3: Predicted and measured hourly global solar radiation data for Ghardaïa Algeria from time series principle (R2), (a) inputs at instants H-1 and H-2
(b) inputs at instant H-1, (c) inputs at instant H-2
Fig. 4: Measured and predicted solar radiation values using SVM model according to both approaches (R1 and R2)
4. COMPARATIF STUDY
Table 3 resume the predictive performances of some models cited in the literature with those of the model proposed in this work. The techniques used are different;
Artificial Neural Network (ANN), Firefly Fourier Algorithm (FFA), Random Forest
45 (RF), Auto Regressive Moving Average (ARMA) and Support Vector Machine (SVM) with the principle of time series.
From this Table 3, it can be seen clearly that proposed approach (R2) outperforms the conventional methods. In conclusion, the SVM technique proves competitive in the field of time series prediction of solar radiation.
Table 3. Statistical values of some hourly solar radiation predictive methods
5.CONCLUSION
In this work, novel short-term prediction methodologies are developed by two different approaches to predict HGSR at Ghardaïa city in south of Algeria.
The first (R1) used five climatic parameters as inputs of models such as temperature (T °C), relative humidity (Rh %),wind speed (V m/s), pressure (P Pa) and HGSR (Wh/m2) in past time to predict new value of HGSR in future time with one hour step ahead.
The second methodology (R2) is inspired directly from time-series prediction principle by using SVM technique. Results have shown that a better prediction was done by combining data of two previous times to predict hourly solar radiation at a future time.
It has been proved that the phenomenon of solar radiation repeats itself in time and an order of autocorrelation which is 2 shall be considered (H-1 and H-2) to have better predictions in this site.
Also, the second approach which based on time series principle gives better results compared to the first. The performances of this selected model are; R = 0.99 %, NRMSE = 13.08 % and MAPE = 19.72 %.
Finally, a comparative study has been conducted by comparing the performances of the developed models to those of some ones that were cited in the literature by different approaches. This proved the effectiveness of the SVM technique used and its competitiveness compared to others technics in the prediction of solar component time series.
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