A variety of renewable energy sources (RESs) play
important roles in the global energy markets, they gradually
replace conventional fossil fuel-based power plants which
leads to reduce carbon emissions [1]. The problem with
RESs is that the produced energy is not easily predictable in
advance, it varies with weather conditions such as cloud,
humidity, precipitation, wind speed and temperature [2]. This
problem can be overcome by using accurate forecasting [3].
The RESs are sustainable and are low in environmental
pollution. Growing load requirement need efficient energy
management to enhance the real time wide area monitoring
systems in order to increase the power system efficiency and
performance [4]. Phasor measurement units (PMUs) also
known Synchrophasors measure the magnitude and phase of
transmission line voltage and current at a reporting rate up to
120 times per second. As shown in figure 1, a time reference
provided by a global positioning system (GPS) is used to
synchronize measurements from all the PMUs in a power
system to provide an accurate, real-time picture of an entire
transmission system [5]. PMU measurements are aggregated
by a phasor data concentrator and relayed to the grid
protection and control system. PMU systems are expected be
installed at solar energy plants to enhance the wide-area
situational awareness and to facilitate integration of RESs
[6].
Energy forecasting methods play a vital role in power
system developments. Introducing smart grid technologies is
becoming very essential especially when the level of
renewables penetration is high (Capacity penetration level
exceeds 30% on any section of the power grid) to ensure
reliable and stable operation of the power grid [7]. The
transition from traditional grid into smart grid requires
upgrades of traditional grid systems and new innovative
solutions to accommodate the nature of renewable energy
generation [8].
Fig.1 PMU unit structure [9]
Worldwide, Solar power plants is progressively being
integrated into electric power grids. However, the integration
of RESs into the power systems suffers of two problems,
namely, the intermittent electricity delivery and
unpredictability. Therefore, solar power forecasting is now
very important for the stabile operation of electric grid and
optimal dispatch. Machine learning techniques are employed
to overcome these problems and successfully integrate these
PV sources into the national electric grid [10].
In literature, the PV energy output forecasting can be
classified into three main methods, mainly, physical, time-
series statistical [11], and hybrid methods [12]– [15]. The
physical method uses the meteorological data obtained by
numerical weather predictions to build forecasting models.
The more accurate the weather parameters related to the solar
irradiance, the more accurate is the forecasting of the amount
of the solar energy produced.
Time series models use a large amount of historical data
statistical approach to forecast the average hourly solar
irradiance; it does not require geographic information of PV
power plants. These models provide accurate forecasts of the
average monthly or annual production [16]. The time series
models used in solar power forecasting include
autoregressive model, moving-average model,
autoregressive–moving-average model, autoregressive
integrated moving average model. The statistical methods
such as Artificial Neural Network (ANN), Support Vector
Machine (SVM), Markov chain are capable to extract and
model unseen relationships and features [17]. They are easy
to build with good prediction accuracy. Major Network
Architectures of Deep learning are
Deep Belief Networks (DBNs)
Convolutional Neural Networks (CNNs)
Recurrent Neural Networks (RNN)s –(LSTM)
Recursive Neural Networks.
The Solar Energy Forecasting by Pearson Correlation using Deep
Learning Techniques
1TAMER MUSHA’L AL-JAAFREH, 2ABDULLAH AL-ODIENAT
1Mutah University, Kark, JORDAN
2Electrical Engineering Department, Mutah University, Karak, JORDAN
Abstract: Solar energy is one of the most important renewable energy sources (RES) with many advantages as compared
to other types of sources. Climate change is gradually becoming a global challenge for the sustainable development of
humanity. There will potentially be two key features, for future electricity systems, high penetration or even dominance of
renewable energy sources for clean energy e.g., onshore/offshore wind and solar PV. Solar energy forecasting is essential
for the energy market. Machine learning and deep learning techniques are commonly used for providing an accurate
forecasting of the energy that will be produced. The weather factors are related to each other in terms of influence, a wide
range of features that are necessary to consider in the prediction process. In this paper, the effect of some atmospheric
factors like Evapotranspiration and soil temperature are investigated using deep learning techniques. Higher accuracy is
achieved when new features related to solar irradiation were considered in the forecasting process.
Keywords: Pearson correlation, Deep Learning, Solar irradiation, Forecasting process, Solar energy.
Received: June 29, 2021. Revised: March 25, 2022. Accepted: July 7, 2022. Published: August 2, 2022.
1. Introduction
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The accuracy of these forecasting methods depends
mainly on the variables used. Hybrid methods use both
previous approaches at the same time. The hybrid approach
significantly improves the efficiency and quality of forecasts.
According to the Renewable Energy Policy Network for the
Twenty-First Century (REN21), Solar energy is expected to
reach 8000 GW in 2050 [18-21].
Solar radiation is the energy or radiation received from
the sun, it is measured in kW or W. The Insolation (solar
irradiation) is the total quantity of solar radiation energy
received on a particular surface area over a particular period.
solar irradiation is commonly measured and expressed it in
watt-hour per square meter (Wh/m²) [22]. It is more
convenient to quantify it in days (Wh/m² per day). The
distance between the sun and the Earth ranges from
1.47x10^8 km to 1.52x10^8 km. The solar irradiance, E,
ranges from 1325 to 1420 W/m
2
. The solar constant E:
E
=
1.367kW / m² (1)
The solar irradiation is normally absorbed, scattered, and
reflected by the different components of atmosphere such as
ozone, carbon dioxide, and water vapor, as well as other
gases and particles. About 30% of the solar irradiation passes
through the atmosphere, resulting in an insolation at the
earth's surface of about 1 kW/m² at sea level [24].
In this paper, many features or weather conditions are
incorporated, to the best of author’s knowledge, some of
them have never been considered before, such as Sunshine
Duration, Precipitation, Wind Speed and Direction on 10m
height, Wind Speed [900 milli bar], Wind Direction [when
the atmospheric pressure equal 900 milli bar], Cloud Cover
Total, temperature, CAPE [180-0 milli bar above ground],
Soil Moisture [0-10cm down], Mean Sea Level Pressure
[MSL], Evapotranspiration, Relative Humidity. Long Short-
Term Memory (LSTM) algorithm is used as a deep learning
technique, it is a type of Recurrent Neural Network that has
been specifically developed for the use of handling
sequential prediction problems, like weather forecasting for
wind and solar energy. Many researchers assured that LSTM
is very convenient for regression of time series data.
The data set used in the study is between January 1, 2015,
and January 1, 2021, for Basel city irradiation, in
Switzerland. The weather observation data measured with a
resolution of 1-hour intervals during all day. The free data
was collected from “meteoblue” weather website which can
be applied to research purpose.
The data set include many meteorological parameters
such as humidity precipitation, temperature, wind speed on
high 10 m, wind direction on high 10 m, wind speed [900
mb], wind direction [900 mb], relative humidity, cloud cover
total, convective available potential energy (CAPE) [180-0
mb above gnd], sunshine duration, soil moisture [0-10 cm
down], evapotranspiration and mean sea level pressure
(MSL) [26-29]. The dataset contains 52632 values for 6
years, separated in 42105 samples for training process, and
10527 samples for testing process. The dataset is split up into
train and test subsets with an 80:20 ratio according to the
Pareto principle; the learning model uses 80% of the dataset
for training and 20% (test subset) for the solar radiation
prediction [30].
The weather classification algorithm, Support Vector
Machine (SVM) and solar panel output prediction algorithm
are nonlinear models [23]. the prediction accuracy is
significantly reduced if these data are directly used as the
input variables. The data normalization is required, it will
extract the small range for same data, with range limited
between 0 and 1 [24-26]. It can be calculated as follows:
𝑥
=
(2)
Where 𝑥
is the initial, 𝑥
is the normalized input data,
and 𝑥
and 𝑥
are the input data's minimum and
maximum values, respectively.
In figure 2 the y axis shows the normalized values of the
humidity on 2 m elevation corrected during 6 years from
Basel site, the measurements were taken for full duration of
the day and measured at 1- hour intervals.
Fig. 2 Basel Relative Humidity [2 m] For 6 years
Figure 3 shows the normalized values of the Wind Speed
at 900 mb corrected during 6 years from Basel site. The
measurements taken for full duration of the day and
measured at 1-hour intervals. The y axis shows the
normalized values of the Wind Speed.
Fig. 3 Basel Wind Speed [900 mb] For 6 years
Figure 4 shows the convective available potential energy
(CAPE) [180-0 mb above ground] corrected during 6 years
from Basel site the measurements taken for full duration of
the day and measured at 1-hour intervals. the y axis shows
the normalized values of the (CAPE).
2. The Data Set Description
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Fig. 4 Basel CAPE [180-0 mb above gnd] For 6 years
In figure 5, the x axis shows the samples of measurements
for 6 years and y axis show the normalized values of the
MSL pressure. The MSL pressure values are collected during
6 years from Basel site the measurements for full duration of
the day and measured at 1-hour intervals.
Fig.5 Basel Mean Sea Level Pressure for 6 years
When an Artificial Neural Network (ANN) model with a
strong nonlinear fitting function is used to predict solar
energy output, then selecting ANN's input variables will be
the key issue [27]. In case of the coexistence of multiple
meteorological factors, it is important to identify the
meteorological factors with a greater impact on solar power
output. The PCC method is a very common method for main
feature extraction [28]. PCC is a measure of linear correlation
between two sets of data. It is the ratio between the
covariance of two variables and the product of their standard
deviations; thus, it is essentially a normalized measurement
of the covariance, such that the result always has a value
between −1 and 1.
𝑐𝑜𝑟𝑟 =
∑(
)
∑(
)
∑(
)
(3)
where m is the sample size, 𝑠
k
, 𝑡
k
are the individual
sample points indexed with k the sample point and s, t is the
average value of S and T [29] .
The correlation coefficient technique shows the most
features effected with irradiation forecasting and that will
help for our aim to provide the highest accuracy of
forecasting with our model [30-33].
Figure 6 shows all possible correlations between the 16
features and irradiation, the most correlation with irradiation
is evapotranspiration with 0.89 correlation, then temperature
and sunshine duration with 0.68, soil temperature with 0.52,
temperature at 2 meters with 0.5, them the correlation start
decrees like CAPA with 0.18, wind speed with 0.041, wind
direction with 0.014, pressure with -0.018, soil moisture with
-0.16, cloud cover with -0.25, humidity with -0.62,
precipitation with -0.093.
The most common forecasting indices are root mean
squared error (RMSE) and mean square error (MSE) as given
in equations (4) and (5), respectively [34-35]. They are used
to evaluate the prediction performance of the solar radiation;
they are an excellent general-purpose error metric for
numerical predictions. However, RMSE is more robust since
it is less sensitive to extreme values than MSE. The error
between predicted and actual values in the test set is
calculated using these formulae. Actual and predicted values
are denoted by Y and X, respectively
𝑀𝑆𝐸 =(
.∑(𝑌−𝑋)
) (4)
MSE =
.∑ (Y−X)
(5)
The random number seed is usually fixed to ensure the
reproducibility of the results. Using suitable number for
modeling with a neural network to load the data set as
pandas’ data frame by extracting the Numpy array from data
frame, then getting the floating-point values by converting
the integer values from Numpy array [36-37].
The sequence of the numbers is very important for time
series data. Using a simple technique, the ordered data set are
divided into train and test datasets with 80% of the
observations suitable for training and the remaining 20%
suitable for testing [38-39]. The LSTM model is built for this
forecasting, with 3 hidden layers selected. By
‘earlystopping’, LSTM can avoid over fitting with 50 epochs
using 200 neurons with ‘relu’ activation in first hidden layer,
100 neurons with ’relu’ activation in the second hidden layer,
and 50 neurons with’ relu ‘activation in the last hidden layer.
then single output layer with ‘sigmoid’ activation [40].
In this paper, LSTM learning models are used to predict
the amount of solar radiation available. The data sets for 6
years contained about 16 weathers measurements. The PCC
is used to determine the most measurements affecting
irradiation forecasting. In the first step, 6 features that
normally applied in previous research are used to predict the
irradiation. In the second step, more features with different
irradiation correlation are added until we use all features to
predict the irradiation. The RMSE and MSE are calculated
each time. The process is repeated twice to confirm the
results.
3. The Pearson Correlation
Coefficient (PCC)
4. Accuracy Evaluation
5. Results
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Fig.6 correlation coefficient heatmap
It is clear from the figure 6 that the correlations between
the 16 features and irradiation may vary from small values up
to values near to one, the most correlation with irradiation is
evapotranspiration with 0.89 correlation. There are very
interesting results like the correlation of evapotranspiration
with soil temperature, it is 0.59 and with temperature 0.66.
The results of RMSE and MSE show that there is a
significant impact of some of the features that have been
introduced with the participation of irradiation for the
forecasting process, this affects the accuracy of the
forecasting process. The RMSE decreases when the 16
features are used for forecasting.
Table 1 presents the experiments that are conducted to
calculate the RMSE and MSE.
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TABLE 1 THE ACCURACY RESULT OF FORECASTING
%
Training
Layers Datasets
(type) MSE
RMSE
80% 200
100
50
Full day
6 years
Real time
6 Features
0.03160809
0.1777866
80% 200
100
50
Full day
6 years
Real time
11 Features
0.00397981 0.0630857
80% 200
100
50
Full day
6 years
Real time
14 Features
0.00188 0.0433988
80% 200
100
50
Full day
6 years
Real time
16 Features
0.00125388 0.0354102
This work presents forecast solar energy radiation using
LSTM model. The model processed meteorological data for
the last 6 years from the Meteobleu site. Many new factors
are considered in our study. The PCC is applied to identify
the most effective factors correlated with solar radiation to
facilitate the training process.
In this study, the results clearly show that there are some
atmospheric factors have greater effect on the forecasting
process than other factors. Considering these differences will
greatly improve the accuracy of the forecasting process.
some of these important weather factors are the
evapotranspiration and soil temperature. The study affirms
that the LSTM model is superior for solar radiation
forecasting when the PCC is not high.
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