Forecasting Hourly Solar Radiation using a Novel Hybrid Technique

based on Machine Learning Models

Hamza Ali-Ou-Salah

, Benyounes Oukarfi

, Khalid Bahani

, Mohammed Ramdani

and

Mohammed Moujabbir

Laboratory of Physic of Condensed Matter & Renewable Energy, Hassan II Casablanca University, BP 146,

Mohammedia, Morocco

Laboratory of Computer Science, Hassan II Casablanca University, BP 146, Mohammedia, Morocco

Laboratory of Computer Science, Sultan Moulay Slimane University, BP 145, Khouribga, Morocco

Keywords: Forecasting, solar radiation, photovoltaic energy, machine learning, support vector machine, artificial neural

network.

Abstract: Photovoltaic production is highly dependent on solar radiation time series, which is sporadic. Grid operators

have a significant problem integrating photovoltaic energy sources into the electrical grid due to the

unpredictability of solar radiation. To overcome this, forecasting global solar radiation can solve the

intermittency due to the variability of weather conditions. It allows the grid operators to predict photovoltaic

power production to facilitate the planning and dispatching tasks of the electric grid. In this work, we have

proposed a new hybrid method to predict one-hour solar radiation in Évora city (Portugal). The hybrid model

is based on the daily classification of global solar radiation and machine learning algorithms such as support

vector machines (SVM) and artificial neural network (ANN). We have collected five years of global

horizontal solar radiation data from the meteorological station of Évora city. We have evaluated the

performance of the proposed model using normalized root mean square error (nRMSE) and normalized mean

absolute error (nMAE). The results show that, for sunny days, the SVM model performs better than the ANN

model with nRMSE = 9.15 % and nMAE = 4.65%, while for cloudy days, the ANN model gives better results

than the SVM model with nRMSE= 42.09 % and nMAE = 25.1%. Moreover, we have carried out a

performance comparison with the recent literature. The results show the superiority of the proposed hybrid

model compared to literature’s models.

1 INTRODUCTION

The integration of photovoltaic energy into the

electric grid makes its management difficult due to

the variability of this renewable energy source. To

overcome this, the forecasting of photovoltaic

production can facilitate the task of planning and

scheduling the operations of the electric grid with the

existence of photovoltaic energy sources. The main

meteorological parameter that defines photovoltaic

production is solar radiation (Mellit, 2010).

Consequently, the forecasting of solar radiation

https://orcid.org/0000-0002-8345-2242

https://orcid.org/0000-0002-4211-6082

https://orcid.org/0000-0001-9596-3480

https://orcid.org/0000-0002-7941-6003

https://orcid.org/0000-0003-2941-4461

allows easy prediction of photovoltaic production.

Researchers have proposed various models for this

purpose, which may be divided into three groups. The

first group includes models based on numerical

weather prediction (NWP), which solve the physical

equations of the atmosphere to provide short- and

medium-term forecasts. (Mathiesen, 2011; Voyant,

2017). The second group consists of models based on

sky images and satellite images (Perez, 2010; Yang,

2014). The approaches based on sky images are used

for very short-term prediction (Voyant, 2017), while

the techniques based on satellite images are widely

Ali Ou Salah, H., Oukarﬁ, B., Bahani, K., Ramdani, M. and Moujabbir, M.

Forecasting Hourly Solar Radiation using a Novel Hybrid Technique based on Machine Learning Models.

DOI: 10.5220/0010729800003101

In Proceedings of the 2nd International Conference on Big Data, Modelling and Machine Learning (BML 2021), pages 135-142

ISBN: 978-989-758-559-3

135

utilized to generate short-term forecasts (Yagli,

2019). The third group represents machine learning

(ML) models that aim to learn the relationship

between inputs and outputs from meteorological data.

These ML models are used for very short-term and

short-term forecasting.

Recent studies on solar radiation forecasting have

paid attention to ML models because of their high

performance (Voyant, 2017; Yagli, 2019). (Benali,

2019) found that random forest (RF) is the best model

for forecasting hourly solar radiation in Algeria.

(Belaid, 2020) proposes support vector machines

(SVM) for predicting the next hour of solar radiation.

The outcomes show the superiority of the proposed

SVM approach compared to the literature’s methods.

(Aljanad, 2021) developed a hybrid artificial neural

network (ANN) model using the particle swarm

optimization (PSO) algorithm for predicting global

solar irradiance in Malaysia. The findings

demonstrated the effectiveness of the hybrid

approach for very short term intervals. (Marzouk,

2020) used an evolutionary algorithm to optimize the

ANN model for solar radiation prediction for up to six

hours. The results show that the proposed hybrid

approach outperforms several models such as smart

persistence, regression tree and RF. In reality,

comparing the performance of all these techniques

described above appears challenging because each

model has its dataset, its prediction horizon, and its

evaluation criteria which differ from model to model.

(Voyant, 2017) showed that support vector machines

(SVM) are a very promising forecasting method and

have not been sufficiently investigated by

researchers. In addition, the artificial neural network

model (ANN) is the most used approach for solar

radiation prediction. We have applied the SVM and

ANN models to the dataset of Évora city. The

obtained outcomes enable us to comprehend better

how these ML algorithms perform with the data of

this site which leads to enriching the literature.

This article compares SVM and ANN techniques

for predicting one hour of global solar radiation using

endogenous data from Évora. We have utilized the

auto mutual information function to identify delayed

values of solar radiation that are the most relevant for

prediction. Furthermore, we have performed a

comparison study according to three timescales:

yearly, seasonally, and daily. These comparisons

enable us to comprehend better the performances of

the proposed ML models under different

meteorological conditions. The final results

demonstrate that there isn’t just one optimal

approach, but the two ML techniques complement

each other in such a manner that the SVM approach

gives good results on sunny days while the ANN

technique performs well on overcast days.

The remainder of this work is structured as

follows: Section 2 outlines the suggested technique.

Section 3 covers the empirical results, and Section 4

closes the study and offers some future research

directions.

2 METHODOLOGY

2.1 Solar Radiation Measurements

In this work, we have used global horizontal solar

radiation hourly time series data from 2012 to 2016

to forecast one hour in advance of the solar radiation

in Évora (Portugal). These data have been collected

from the meteorological station of the Évora city

(38°34 N, 07°54 W) using an Eppley pyranometer. In

this study, we have used only daytime hours from

6:00 to 20:00. In addition, we have applied the auto

mutual information function (AMIF) to identify the

delayed values that have a linear and nonlinear

relationship with the future values of solar radiation

(Benali, 2019; Ali-Ou-Salah, 2021). The results show

that eight historical values have a strong correlation

with future global solar radiation.

2.2 Support Vector Machines

Support vector machines (SVM) is a supervised

learning algorithm used for classification and

regression. It was first introduced by Vladimir Vapnik

and his co-workers in 1992 (Boser, 1996). SVM has

been widely employed by researchers for solar

radiation prediction due to its good generalization

capabilities and their capacity to lead with nonlinear

time series. The nonlinear SVM regression is based on

kernel functions that map inputs into high dimensional

feature space, in which linear regression is carried out

by minimizing the -insensitive loss function (Urraca,

2016). Figure 1 shows the nonlinear transformation

using a kernel function.

Figure 1: Transformation into high dimensional feature

space using the kernel function.

BML 2021 - INTERNATIONAL CONFERENCE ON BIG DATA, MODELLING AND MACHINE LEARNING (BML’21)

136

In addition, the SVM also minimizes the model

error to increase accuracy. As a result, the SVM

minimizes the following function that regroups the -

insensitive loss function and the model error.

𝑚𝑖𝑛







∥𝑤∥



 ∁

∑

𝜉



𝜉



∗









(1)

𝑠𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜



𝑦





⟨

𝑤,𝑥



⟩

𝑏𝜀𝜉



⟨

𝑤,𝑥



⟩

𝑏



𝑦



𝜀 𝜉



∗

𝜉



,𝜉



∗

 0 𝑐𝑙𝑒𝑎𝑟

(2)

Where 𝑥



and 𝑦



are respectively the set of inputs

and the set of targets. 𝑤 is the weight vector, and 𝑏 is

the bias. 𝜀 is the epsilon margin. 𝜉



,𝜉



∗

are the slack

variables, and C is the cost parameter (Perez, 2010).

The training inputs are mapping into high

dimensional feature space using nonlinear mapping

function 𝜑𝑥 (Jiménez-Pérez, 2016). In this work,

we used the radial basis function (RBF) as a kernel

function. The RBF is described as follow:

𝐾𝑥



,𝑥



exp∥𝑥



𝑥



∥



/2𝜎





(3)

where 𝜎 is a free parameter that controls the width

of the Gaussian function.

The generalization performance of the SVM

model depends on the epsilon margin 𝜀, the cost

parameter (C), and the free parameter (𝜎. We have

applied the grid search strategy to determine the best

values of 𝜀,C,and 𝜎 (Torres-Barrán, 2019).

2.3 Artificial Neural Network

Artificial Neural Network (ANN) is a heuristic model

that simulates two human brain functions: learning

and generalization. In the first process, the network is

trained with examples representing the problem, then

the knowledge acquired by the network is tested

during the generalization process with unseen

examples.

ANN models offer an alternative solution to

traditional models that cannot solve complex

problems precisely. Their application had been

proven effective in various fields such as engineering,

telecommunication, economics, medicine,

environment, etc. (Safi, 2013). The basic neural

network architecture is the feed-forward neural

network (FFNN). It comprises three layers: the input

layer, one or many hidden layers, and the output

layer. Each layer contains many neurons which are

interconnected to other layer’s neurons by weighted

connections (Teo, 2015). Figure 2 shows the single

layer FFNN architecture.

Figure 2: Single layer FFNN architecture.

The process of learning consists of adjusting the

connection weights iteratively according to a training

algorithm. Among ML algorithms, we find

supervised learning techniques that reduce the error

between real output and desired output. This

operation is repeated until the ANN model reaches an

acceptable performance. Subsequently, the

generalization process tests the network on new data

to evaluate the learning procedure.

The model’s accuracy depends on several

parameters such as the used dataset, the number of

hidden layers, the number of hidden neurons, and the

activation functions. Further, the dataset is divided

into training, testing and validation sets. The training

set is used in the learning process to update network

weights and biases, while the validation set is used to

stop the training process. The testing set is utilized to

test the network performance, which allows

comparison between different network architectures.

Furthermore, the used training algorithm impacts the

learning process significantly; that’s why it should be

chosen carefully (Teo, 2015). As reported by (Wang,

2011), any nonlinear problem whose samples are not

too large can be solved by an ANN network with one

hidden layer having a sufficient number of neurons.

The number of hidden neurons

(Num_Hidden_neurons) represents the most critical

parameter in network architecture. In addition, the

Levenberg Marquardt training algorithm (LM) is

used to train the ANN model. This algorithm gives

accurate predictions when it is used with hyperbolic

tangent sigmoid transfer function in the hidden layer

and linear transfer function in the output layer

(Yadav, 2014).

2.4 The Architecture of ML Models

The grid search strategy was applied to determine the

best architectures of the SVR and ANN models.

Several combinations of user-defined

hyperparameters were investigated to identify the

Forecasting Hourly Solar Radiation using a Novel Hybrid Technique based on Machine Learning Models

137

best model with the lowest 5-fold cross-validation

error (Ali-Ou-Salah, 2021). In reality, the 5-fold

cross-validation approach splits the dataset randomly

into five folds (Mellit, 2010; Hassan, 2017). Each fold

is used as a testing set, and the rest folds are used as a

training set. Each fold serves as a testing set, while

the remaining folds serve as a training set. The

average of the errors of all testing sets is the 5-folds

cross-validation error. Figure 3 depicts the grid search

technique's steps.

Figure 3: The grid search technique.

The ‘fitnet' function was used for the ANN

method, whereas the ‘fitrsvm' function was utilized to

design the SVR approach. These functions are

available in the Statistics and Machine learning

Toolbox of Matlab software. The ranges of

hyperparameters for the SVR and ANN model are as

follow:

For the ANN model:

 Hidden_neurons = [10, 20, 30, 40, 45, 50,

55, 60, 65, 70, 75, 80, 90, 100]

For the SVR model:

 C = [100, 200, 300, 400, 500, 600, 700].

 𝜀 = [10, 20, 30, 40, 50, 60, 70].

 𝜎 = [0.5, 1.23, 1.5, 2, 3].

2.5 Statistical Indicators

The proposed models have been evaluated using the

root mean square error (RMSE), the normalized root

mean square error (nRMSE), the mean absolute error

(MAE) and the normalized mean absolute error

(nMAE) (Benali, 2019; Voyant, 2017). The lower

their values, the more the forecasts are accurate.

𝑅𝑀𝑆𝐸



𝑛

𝑦



𝑦











(4)

𝑛𝑅𝑀𝑆𝐸



𝑛

∑

𝑦





𝑦











𝑛

∑

𝑦







 100

(5)

𝑀𝐴𝐸

𝑛



𝑦



𝑦









(6)

𝑛𝑀𝐴𝐸

𝑛

∑|

𝑦





𝑦







𝑛

∑

𝑦







 100

(7)

3 RESULTS AND DISCUSSION

In this study, the auto mutual information function

was utilized to identify the most relevant historical

values for predicting one hour in advance of solar

radiation. Indeed, the obtained findings demonstrate

that eight delayed variables may predict future solar

radiation reliably. Moreover, the optimal architecture

of the SVM and ANN models was determined using

the 5-fold cross-validation approach. For the SVM

model, different combinations of 𝐶,𝜀, and 𝛾 have

been tested to find the optimal combination that gives

the best 5-fold cross-validation error. Similarly,

different values of neurons have been utilized to find

the best number of neurons of the ANN model. Table

1 summarizes the obtained architectures of the SVM

and ANN models.

Table 1: Architectures of the SVM and ANN models.

Mdl Configuration

RMSE

(W/m

)

SVM 𝐶600;𝜀10; 𝜎2 62.35

ANN

Num_Hidden_Layers = 1;

Num_Hidden_neurons = 60

63.82

3.1 Annual Analysis

Using one year of the testing set, a comparison of the

SVM and ANN techniques was carried out. The

results of the yearly comparison between the SVM

and ANN approaches are presented in Table 2.

BML 2021 - INTERNATIONAL CONFERENCE ON BIG DATA, MODELLING AND MACHINE LEARNING (BML’21)

138

Table 2: The outcomes of the yearly comparison of the

SVM and ANN techniques.

Error metrics SVM ANN

RMSE (W/m

) 62.80 62.73

nRMSE (%) 18.73 18.70

MAE (W/m

) 32.52 33.94

nMAE (%) 9.69 10.12

As shown in Table 2, According to nRMSE, the

ANN method outperforms the SVM approach.

However, in terms of nMAE, the SVM technique

outperforms the ANN method. In reality, comparing

these two ML techniques appears to be challenging

because the ANN method performs well according to

nRMSE while the SVM approach performs well

according to nMAE.

As a result, an in-depth comparative analysis of

the SVM and ANN techniques was conducted

utilizing seasonal testing sets to evaluate the

prediction performance of each ML approach

according to seasons.

3.2 Seasonal Analysis

The testing set is divided into four testing subsets,

each representing a different season of the year. For

each season, Table 3 summarizes the findings of the

comparison between the SVM and ANN techniques.

Table 3: A comparative study between the SVM and ANN techniques utilizing testing subsets based on seasons.

Error metrics

Winter Spring Summer Autumn

SVM ANN SVM ANN SVM ANN SVM ANN

RMSE (W/m

) 48.76 50.06 94.43 93.89 42.01 41.97 51.97 51.42

nRMSE (%) 24.31 24.96 22.84 22.71 8.41 8.40 23.76 23.51

MAE (W/m

) 27.84 29.12 57.09 59.04 17.88 20.24 27.36 27.42

nMAE (%) 13.88 14.52 13.81 14.28 3.58 4.05 12.51 12.54

As shown in Table 3, it is found that the SVM model

gives better results than the ANN model in the winter

in terms of nRMSE and nMAE. Moreover, the SVM

approach outperforms the ANN in terms of nMAE,

and they have slightly the same nRMSE in summer.

Finally, in spring and autumn, the ANN is slightly

better than the SVM according to nRMSE, but the

SVM approach outperforms the ANN according to

nMAE. This finding does not allow us to conclude the

most efficient ML technique for the spring and

autumn seasons. As a result, a more comparative

study based on daily testing sets is necessary, to

investigate more deeply the performance of each ML

technique.

3.3 Daily Analysis

Daily testing sets generated from the daily

categorization of global solar radiation were used to

compare the SVM and ANN techniques. This

classification was performed using the daily clearness

index (kt), which is given as the daily quotient

between global solar radiation and extraterrestrial

radiation. (Yousif, 2013). Several 𝑘𝑡 intervals have

been employed to classify the daily sky conditions

into two types: sunny or very sunny sky conditions

( 𝑘𝑡 0.6) and overcast or partly cloudy sky

conditions (𝑘𝑡 0.6) (Yousif, 2013). Then, using

the daily clearness index of Évora city provided by

power project data sets supported by NASA (The

POWER Project, 2021), one year of testing data was

split into two daily testing subassemblies. The

findings of the comparison between the SVM and

ANN models utilizing 147 overcast days and 219

sunny days are shown in Table 4.

Table 4: Comparison between the SVM and ANN models

using daily testing sets.

Statistical

indicators

Sunny days

(𝑘𝑡0.6)

Cloudy days

(𝑘𝑡 0.6)

SVM ANN SVM ANN

RMSE

(W/m

)

38.80 40.77 87.05 85.56

nRMSE (%) 9.15 9.61 42.82 42.09

MAE

(W/m

)

19.72 22.47 51.58 51.02

nMAE (%) 4.65 5.30 25.37 25.1

Forecasting Hourly Solar Radiation using a Novel Hybrid Technique based on Machine Learning Models

139

Table 4 compares the SVM and ANN models

using sunny and cloudy testing sets. For sunny days,

the SVM outperforms the ANN model according to

nRMSE and nMAE. In contrast, for cloudy days, the

ANN yields better results than the SVM in terms of

nRMSE and nMAE. Unlike the annual and seasonal

comparisons, the daily comparison better shows the

forecasting accuracy of each model, allowing us to

draw firm conclusions about the ANN and SVM

models. Consequently, a novel hybrid model is

created by combining the SVM model for sunny days

and the ANN model for cloudy days. Figure 4 shows

the forecasted values versus the measured values

using the ANN and SVR techniques for predicting

one hour in advance of global solar radiation.

(a)

(b)

Figure 4: Forecasted values versus measured values using

the ANN model with cloudy days (a) and the SVR model

with sunny days (b).

Performance comparison with the existing

approaches in recent literature has been performed.

Table 5 shows the annual comparison of one hour in

advance of global solar radiation prediction between

the developed hybrid method and the other

approaches available in the recent literature (Benali,

2019; Benmouiza, 2019; Ibrahim, 2017). The

proposed hybrid model outperforms the models of

other studies according to the nRMSE and RMSE.

The suggested hybrid model takes advantage of both

SVR and ANN models and uses them to forecast daily

data in which they perform well. The limitations of

this work are the lack of some important

meteorological variables such as the clearness index

and the low computing capacity that allow us to find

more optimal ML architectures.

4 CONCLUSIONS

This study offers a novel hybrid method for

predicting one hour in advance of global horizontal

solar radiation in the region of Évora based on the

SVR and ANN techniques. In fact, the auto mutual

information function was utilized to identify the most

relevant delayed values of solar radiation, allowing

for reliable prediction of future values. In addition,

different comparisons have been carried out to

highlight the performances of each model. Firstly, an

annual comparison study between the SVM and ANN

models has been conducted using one year of the

testing set. The results show that the ANN approach

is superior to the SVM technique in terms of nRMSE,

while the SVM technique is superior in terms of

nMAE.

Subsequently, a seasonal comparison study has

been undertaken using four seasonal testing subsets.

It has been found that the SVM gives better results

than the ANN for the winter and summer seasons.

Further, in spring and autumn, it has been

demonstrated that comparing ML techniques is

challenging because there is a discrepancy between

the nRMSE and the nMAE. For this reason, a daily

comparison study has been performed using daily

testing subsets. Using the daily clearness index, one

year of testing data was split into two daily testing

subgroups. The results indicate that, for sunny days,

the SVM model performs better than the ANN model.

In contrast, for cloudy days, the ANN model

outperforms the SVM method. Based on these results,

it can be concluded that the daily assessment of ML

techniques is the most effective method to evaluate

the forecasting accuracy of the suggested ML models.

Further work will focus on comparing the

suggested hybrid methods with deep learning and

recurrent neural network techniques, which are very

promising ML approaches.

0 15 30 45 60 75 90 105 120 135 150 165 180 195 210 225

Time (hours)

200

400

600

800

1000

1200

Global solar radiation (W/m

)

Forecasted

Measured

0 15 30 45 60 75 90 105 120 135 150 165 180 195 210 225

Time (hours)

100

200

300

400

500

600

Global solar radiation (W/m

)

Forecasted

Measured

BML 2021 - INTERNATIONAL CONFERENCE ON BIG DATA, MODELLING AND MACHINE LEARNING (BML’21)

140

Table 5: Annual comparison of the proposed models with the approaches in the recent literature.

Study Models Locations nRMSE (%) RMSE (W/m

)

(Benali, 2019) RF France 19.65 88.62

(Benmouiza, 2019) FCM-ANFIS Algeria NA 112

(Ibrahim, 2017) RF-FA Malaysia 18.97 68.84

This paper Hybrid model Portugal 18.70 62.73

ACKNOWLEDGEMENTS

Daily clearness index data used in this article were

obtained from the NASA Langley Research Center

(LaRC) POWER Project funded through the NASA

Earth Science/Applied Science Program.

FUNDING

This work was supported by the National Centre for

Scientific and Technical Research, Morocco [grant

number 4UH2C2017].

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