Solar Irradiation Prediction Level
GIL-VERA V. D.1, QUINTERO-LÓPEZ C.2
1Department of Engineering,
Information Systems and Knowledge Society Research Group,
Luis Amigo Catholic University,
Transversal 51A #67B 90,
COLOMBIA
2Basic and Applied Neurosciences Group,
Luis Amigo Catholic University,
Transversal 51A #67B 90,
COLOMBIA
Abstract: - The discipline of Machine Learning (ML), a branch of Artificial Intelligence, enhances the ability to
model crucial variables for generating green energy, such as solar radiation. Precise prediction of solar
irradiation assists in the strategic placement of solar panels, optimizing energy production, reducing reliance on
non-renewable energy sources, and promoting environmental conservation. This research aimed to develop a
model for predicting solar irradiation using the Multiple Linear Regression (MLR) technique. The results, while
indicating a moderate performance (R²=0.56, MAE=158.23, MSE=43804.89, and RMSE=209.29), provide a
valuable starting point for future studies that seek to improve accuracy with more advanced techniques, such as
artificial neural networks (ANN) or hybrid models. This research emphasizes the importance of continuing to
investigate more sophisticated models for more accurate prediction and suggests that linear models, while
useful for understanding basic relationships, have limitations that can be overcome with more advanced
approaches.
Key-Words: - Forecasting, Irradiation, Linear Regression, Machine Learning, Meteorology, Renewable Energy,
Sun.
Received: April 12, 2024. Revised: September 5, 2024. Accepted: October 8, 2024. Published: November 7, 2024.
1 Introduction
Solar energy consists of the energy emitted by the
sun in the form of electromagnetic radiation. This
energy, when harnessed can be in the form of heat
and electricity production using different
technologies such as solar cells made from silicon
which is a better example, [1]. The sun is the
principal energy source for our planet, and it has a
major influence on many basic phenomena like
Earth's surface radiation balance, hydrological cycle
regulation or plant photosynthesis as well as
extreme weather conditions while not forgetting
climatological issues, [2]. As a result, forecasting
solar radiance is crucial in the industry of renewable
energy and meteorology. It is necessary to predict
the generation of electricity as it can help in
properly designing photovoltaic systems.
Prediction of solar irradiation is a must for the
sizing of the PV power plant as it tells how much
electricity will be generated on average. Accurate
forecasts allow plant operators to increase their
operational efficiencies, perform cost savings, and
bring increased effectiveness, [3]. The output of
solar power in one location can change with the sky
being clear or cloudy and also at morning,
afternoon, and dusk. Grid operators can use this to
predict the upcoming fluctuations in solar
generation and dispatch conventional power
supplies such that grid-energy balance is
maintained, [4].
Further, it can help energy operators make
better decisions about when to buy or sell
electricity. The ability to develop a forecast for
potential deviations of solar power produced enables
them to take appropriate measures in their trading
strategies, [5]. Solar irradiance prediction is highly
relevant to weather forecasting. It means the
weather forecasters can get more accurate sunlight
estimates. Furthermore, this is especially immediate
in zones where sun-based influence generation is
high, [6].
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DOI: 10.37394/232016.2024.19.35
Gil-Vera V. D., Quintero-López C.
E-ISSN: 2224-350X
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Volume 19, 2024
In the scientific literature, several researches
have focused on the prediction of solar irradiance.
In [7], a short-term solar prediction model was
developed with satellite data. In regions with few
meteorological observation facilities, such as the
deserts in northwest China, they applied Support
Vector Machine (SVM) techniques to enhance
prediction accuracy. The proposed model proved to
be useful as it did not require more meteorological
variables and provided better prediction when used
along with the satellite data. The most exciting
revelation was that the model significantly improved
very short-term solar forecasts. That could have a
big effect on the large deployment of solar
elsewhere in parts of the world that lack extensive
meteorological infrastructures.
In [8], only assessed dissemination performance
of predicting Solar Irradiation using multiple models
for one-hour and short-term global horizontal
irradiance (GHI) forecasting. Based on data
obtained from a weather station near Erfoud,
Morocco which is operated by the German
Aerospace Center (DLR) Solar Research Institute
and forms part of their enerMENA project they
tested ANN framework methods with deep learning
models such as Random Forest classifier model
(RF), long short-term memory (LSTM). The results
of their study indicated that the LSTM model
significantly outperformed other models consisting
of ANN and Random Forest (RF) for forecasting
GHI in advance both in terms of performance and
stability.
In [9], they have proposed a novel mechanism
for solar irradiation prediction by integrating ANN,
support vector regression (SVR), and convolutional
neural network (CNN) models. Data from several
weather stations were employed to enhance the
accuracy of forecasted solar irradiation. The most
important result of this study is that the solar
irradiation forecasting model, using hybrid
SVR+CNN models, provides a very effective
prediction and outperforms existing methodologies.
This result endorses the suitability of a neighbor
data-based strategy for more accurate solar
irradiation prediction and indicates that this
approach may be a practical instrument in field
deployment.
In [10], they proposed a new system called
AOHDL-SRP to ensure true prediction of solar
irradiation based on deep learning technique (i.e.,
the fusion between Attention-based Long Short-
Term Memory Network models (ALSTMs) and
Convolutional Neural Networks (CNNs) as well as
hyperparameter optimization by using Particle
Swarm Optimization algorithms, namely ALSTM-
PSO. They have experimented on a large scale and
with different data sets, the results obtained from
experimental analysis of the AOHDL-SRP model
show a maximum R²=100%, which is better than
some contemporary models in terms of accuracy.
This result points to the potential for AOHDL-SRP
as a valuable tool in improving solar irradiation
forecasting, with notable implications for renewable
energy systems programming and control.
In [11], 78 existing models were tested and 4
new ones were derived with observations at each of
the weather stations available (105) for daily solar
irradiation prediction in a temperature difference
(ΔT, zonal approach over five zones. These models
were utilized to assess their performances, and
generalized coefficients for the superior model (N1-
4) were derived as it showed higher accuracies at
individual ΔT zones along with a combined ΔT
zone.
The most pertinent discovery was the fact that
the N1-4 model, along with its generalized
coefficients at national and zonal levels have a
reasonable level of accuracy to indirectly forecast
daily solar irradiation for long-term high ΔT zones
or intermittently low ΔT sunny days which has
valuable implications in photovoltaic /solar thermal
systems design as well as agricultural, ecological
and climatic investigations. They argue that the
importance of sophisticated solar energy forecasting
models will rise increasingly in coming years to
maximize wind power plant operation and control.
Moreover, the performance of advanced models
needs to be compared with those of traditional
statistical models to substantiate the justification for
having a more sophisticated forecasting model.
In [12], a hybrid model that integrates radiative
transfer with ML techniques for estimating diffuse
solar irradiation at different observation sites in
China was analyzed. Moreover, the accuracy of
several RTM-RF (RTM model based on RF),
RTMXGBoost, RTMMultilayer perceptron (MLP),
ResNet50-Deep neural network (RTM mask holder
DNN), and Residual Convolutional Neural Network
(RCNN) modeling methods were assessed by
comparing with ground-based reference
observations. The results showed that the meta-
hybrid models RTM-RF and RTM-XGBoost
obtained considerably more accurate estimates than
RNN, LSTM, or MLPs. This conclusion indicates
that using the radiative transfer model and ML is
competent in any domain lacking ground-based
observation for attaining credible indirect normal
solar irradiance values. In summary, all the above
require solar irradiation forecasting to efficiently
and effectively operate these plants successfully
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DOI: 10.37394/232016.2024.19.35
Gil-Vera V. D., Quintero-López C.
E-ISSN: 2224-350X
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allowing grid system strength stability as well assist
in energy trading decisions. Solar irradiation affects
the extremes of weather phenomena and
temperature, along with global mean sea level so it
is crucial to appropriately investigate geography-
based (spatial) and time-varying trends in solar
radiative climate.
2 Multiple Linear Regression (MLR)
MLR is a supervised learning algorithm used in ML
and statistics to model the relationship between a
dependent scalar variable “Y” with one or more
explanatory variables X(1),…,X(n). A MLR model is
represented by Eq. (1):
(1)
Y is the output, Xi are independent variables or
input parameters, and is a cut-off point with the
coordinate of y-axis. The error is evaluated as the
function of location points along with their
corresponding actual output Y-value in this ML
model. Learning this algorithm tries to minimize the
cost of a quadratic error function and these
coefficients are equivalent to the line which should
be optimal. Datasets of the construction RLM model
in this work are disclosed in [13].
Several works found in the review of the
scientific literature have used this technique in
topics related to solar energy. In [14], compared the
performance of the ANFIS method and the MLR
method in forecasting solar irradiation intensity. The
findings indicate that the ANFIS method
outperformed the MLR method in predicting solar
irradiation intensity, with better RMSE and MAE
values. The results show that the ANFIS method
provided a more accurate solar irradiation intensity
prediction than the MLR method.
In [15], different methods have been applied to
estimate solar irradiation, where empirical
equations, ANN, and MLR are the examined
prediction techniques. These results indicate that the
models are consistent with those presented in review
articles, and include specific variables associated
with increased diagnostic performance. The
comparison between ANN and MLR models is
observed to be consistent.
In [16], a regression model was built to provide
short-term prediction on solar irradiance; another
functional relationship between solar and air
temperature/humidity would be able also
established, got three equations were presented for
relating the trend concerning temperature.
In [17], performed a vast comparison between
regression model and ANN forecasting models for
predicting global solar irradiation. Results revealed
that ANN models produced lower mean absolute
percent error values and higher R values than
regression models. Results reveal the best
performance of ANN in predicting global solar
radiation.
In [18], a new methodology for estimating solar
irradiation was recommended. From the
meteorological data by the Hargreaves method and
linear regression there are some missing data in
these records. The results compared and analyzed
the observed solar insolation with predicted or
modeled values in terms of statistical measures such
as CRM, RMSE, NSE values, and percent errors.
These results reveal that the proposed method has
good performance, it can be used successfully
because of CRM near zero, RMSE low values NSE
close to unit, and less percentage error.
In [19], compared various ML models in
predicting solar irradiation. The results confirmed
that the proposed GBT model has a better capability
to predict solar radiation and can be used
successfully for short-term prediction of solar
irradiation using only meteorological parameters as
input. Several ML algorithms were used for
predicting global horizontal solar irradiation in [20].
Results show that the root mean square error of
MLP models was less than those encountered using
regression-based models, but worse compared to
ANFIS and SVM for global irradiation interpolated
over a distance. In addition, it assesses the
performance of decision trees in solar irradiation
modeling temperature and day number-based
models depict similar R² > 85%, especially when no
sunshine records are at hand.
3 Method
This work aimed to build a predictive model for
solar irradiation based on historical data, including
solar irradiation measurements and various
meteorological variables such as wind direction (°),
temperature (°F), barometric pressure (Hg),
humidity (%) and wind speed (Mi/h). The multiple
linear regression (MLR) technique was employed
for this purpose. The historical data set comprised
measurements of solar irradiation (W/m²) and
meteorological variables (Table 1).
The MLR technique was used, adjusting
hyperparameters and performing cross-validation.
Python programming language and libraries such as
LinearRegression, Pandas, Numpy, Matplotlib, and
Seaborn were utilized to build the model. The code
is available in [21]. The final model was evaluated
using test data not involved in the training process.
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The ability of the model to generalize to new and
unseen data was analyzed, and its performance was
compared to traditional solar irradiation prediction
methods.
An accurate predictive model for solar
irradiation can significantly impact various sectors,
including solar energy management, agriculture,
urban planning, and climatology. A reliable model
enhances the efficiency and sustainability of solar
energy usage, aiding in informed decision-making
in sectors influenced by solar irradiation.
Table 1. Database description
Nomenclature
Variable
Description
Y
Solar irradiation
Watts per square meter
(W/m²)
V1
Temperature
Degrees Fahrenheit (°F)
V2
Humidity
Percentage (%)
V3
Barometric
pressure
mmHg
V4
Wind direction
Degrees °
V5
Wind speed
Miles per hour (Mi/h)
4 Results
Table 2 presents the correlation matrix. This
indicated that irradiation has a positive correlation
with temperature (0.73), pressure (0.12), and wind
speed (0.074), and a negative correlation with
humidity (-0.23) and wind direction (-0.23).
Table 2. Correlation matrix
Y
V1
V2
V3
V4
V5
Y
1
0.73
0.12
-0.23
-0.23
0.074
V1
0.73
1
0.31
-0.29
-0.26
-0.031
V2
0.12
0.31
1
-0.22
-0.23
-0.084
V3
-0.23
-0.29
-0.22
1
-0.0018
-0.21
V4
-0.23
-0.26
-0.23
-0.0018
1
0.073
V5
0.074
-0.031
-0.084
-0.21
0.073
1
The distribution diagram (Figure 1) showed a
bell-shaped (normal distribution) pattern, suggesting
good model predictions.
0.0025–
0.0020–
0.0015–
0.0010–
0.0005–
0.0000–
-750
-500
-250
0
250
500
750
1000
Density Vs Radiation
Fig. 1: Distribution diagram
The model's performance was evaluated using
several regression metrics. Among these, the
coefficient of determination (R²) stands out as it
measures the proportion of variance in the
dependent variable that the independent variables
account for, as outlined in Eq. (2):
(2)
Additionally, the performance was evaluated
using the Mean Absolute Error (MAE), which
reflects the average magnitude of prediction errors,
as detailed in Eq. (3):
(3)
The Mean Squared Error (MSE) was also
utilized, offering insight into the average of the
squared differences between predicted and actual
values, as indicated in Eq. (4):
(4)
Lastly, the Root Mean Squared Error (RMSE)
was considered, which represents the square root of
the average squared discrepancies between the
observed and predicted values, Eq. (5):
(5)
In Eq. (2) to (5), n is the number of data points,
ym_t and yo_t respectively for predicted and
observed solar irradiation. The former is denoted as
and the latter by
. The value of R² is
interpreted as a correlation between the observed
and predicted values. What more you get with
RMSE and MAE is that a closer value to 0 indicates
better, in other words, the prediction values have
been predicted as it was found. Multiple
performance measures (RMSE, MAE) should be
used to get the full vision of how well your model is
performing.
Table 3 presents the R², MAE, MSE, and RMSE
metrics, showing an R²=0.56, MAE=158.23,
MSE=43804.89, and RMSE=209.29. These metrics
indicate that the MLR model explains a moderate
percentage of the variability in solar irradiation but
still has considerable error.
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Table 3. Results of the MLR model
Metric
Value
R²
0.56
MAE
158.23
MSE
43804.89
RMSE
209.29
An R² of 0.56 means that approximately 56% of
the variability in solar irradiation can be explained
by the linear regression model. An MAE of 158.23
indicates that, on average, the model predictions
have an absolute error of approximately 158.23
units of the solar irradiation measurement. An MSE
of 43804.89 indicates that the average of the squares
of the prediction errors is approximately 43804.89
units of the solar irradiation measure.
An RMSE of 209.29 indicates that, on average,
the model predictions have an error of
approximately 209.29 units of the solar irradiation
measure. These statistics indicate that the MRLM
explains a moderate percentage of the variability in
solar irradiation, but the model predictions still have
considerable error, as evidenced by the relatively
high MAE, MSE, and RMSE. Table 4 presents the
coefficients of the MLR model.
Table 4. Coefficients of the MLR model
Variable
Description
Coefficient
V1
Temperature
38.22
V2
Pressure
-749.95
V3
Humidity
-0.28
V4
Wind direction (Degrees)
-0.27
V5
Speed
8.44
Eq. (6) predicts solar irradiation (Y) as a
function of the variables temperature(V1),
pressure(V2), humidity(V3), wind direction(V4), and
wind speed(V5).
(6)
A one-unit temperature increase is related to a
38.22-unit increase in solar irradiation, holding all
other model variables constant. A one-unit increase
in pressure is related to a 749.95-unit decrease in
solar irradiation, holding all other model variables
constant. A one-unit increase in humidity is related
to a 0.28-unit decrease in solar irradiation, holding
all other model variables constant. A one-unit
increase in wind direction is related to a 0.27-unit
decrease in solar irradiation, holding all other model
variables constant. A one-unit increase in wind
speed is related to an 8.44-unit increase in solar
irradiation, holding all other model variables
constant.
Higher temperature and wind speed tend to be
related to higher solar irradiation, while higher
atmospheric pressure and humidity tend to be
associated with lower solar irradiation. Wind
direction has a negative, but weaker influence
compared to the other variables, in other words,
although wind direction negatively affects solar
irradiance, its impact is minor compared to the other
factors analyzed.
5 Discussion
Using the MLR method, an R² of 0.56 is moderate
for forecasting solar irradiance in this study. These
values are consistent with previous studies that have
implemented regression models to correct solar
insolation such that coefficients of determination
were also in the mid-range. On the other hand,
modern methods like deep neural networks and
hybrid learning can achieve huge improvements in
predicting solar irradiance by achieving R² values
close to or higher than 0.85 considering new
research outputs (As compared with only 82% from
older methods) structures are shown, [22]. Although
MLR is a valuable tool for entry-level modeling and
explaining the relationships among variables, this
also indicates that more advanced techniques could
greatly enhance predictive capability.
Although it was a very useful tool, the linear
nature of this study's MLR model also limits its
applicability. The MLR model fits a linear
relationship between the independent variables i.e.,
temperature, humidity (absolute), barometric
pressure, wind direction, and wind speed with the
dependent variable of solar irradiance. This
assumption of linear relation in meteorological data
is likely an oversimplification, as nonlinear
relationships between weather variables can be
complex. In addition, the model performance
(MAE=158.23, MSE=43804.89, and
RMSE=209.29) suggests significant scope for
improvement in the accuracy of models as well. ML
models that capture nonlinearity and interaction
between variables like the ANN-based model or
tree-based model can give a better image of
contributing factors to solar irradiance.
The analysis performed in this study allowed the
identification of relationships between solar
irradiance and meteorological variables, which
contributes to improving solar energy management
and photovoltaic system planning. The main
contribution of this study lies in the detailed
evaluation of how these meteorological variables
influence solar irradiance and in the validation of
the model with a historical data set.
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DOI: 10.37394/232016.2024.19.35
Gil-Vera V. D., Quintero-López C.
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Volume 19, 2024
This research underscores the need for further
research into advanced modeling techniques for
solar irradiance prediction. The development of
more accurate models will not only contribute to the
optimization of solar power generation but will also
enable better planning and management of energy
resources. In particular, future research could focus
on the integration of hybrid techniques that combine
the robustness of traditional models with the
learning capabilities of modern artificial intelligence
methods. In addition, the improvement in the quality
and quantity of meteorological data, together with
the use of advanced ML algorithms, can lead to a
deeper understanding of climate dynamics and
better utilization of renewable energies at a global
level.
6 Conclusion
Based on the evaluation results, this study shows
that the MLR method is an effective approach for
solar irradiation prediction by meteorological
variables. Although it has medium performance
metrics, the MLR model can give us meaningful
information about the relationships between solar
irradiation and some factors like temperature,
humidity, atmospheric pressure wind direction, or
average speed of air. The research underlines the
need to consider these ML techniques for solar
energy resources to be handled efficiently. It also
proposes that innovative models must be explored
further to increase both the precision and robustness
of predictions involved with solar irradiation.
Through the use of ML models, solar energy
utilization can become more efficient and
sustainable with less dependence on non-renewable
resources which ultimately helps to reduce global
carbon footprint. These results illustrate that solar
irradiation forecasting has come a considerable way,
but faces many challenges regarding prediction
reliability. The MLR model seemed to be
promising, but more extensive research is needed to
investigate advanced ML methods such as deep-
learning models and ensemble techniques that have
achieved better performances in the studies.
Furthermore, it is necessary for the improvement of
data collection methodologies and validation
techniques that could lead to an increment in solar
irradiation prediction accuracy which can increase
overall reliability to expand the properties of
renewable energy sources across a larger portion of
the global energy portfolio.
The model built in this work, by providing
accurate estimates of solar irradiance, allows for
better planning and management of solar energy
systems, helping operators to optimize the location
of solar panels, adjust energy production according
to climatic conditions, and reduce dependence on
non-renewable energy sources such as fossil fuels.
By improving energy efficiency, the need to resort
to polluting energy sources is reduced, which in turn
helps mitigate environmental impact, reducing
greenhouse gas emissions and promoting more
sustainable development. These models therefore
play a key role in the transition to a cleaner and
more environmentally friendly energy future.
Declaration of Generative AI and AI-assisted
Technologies in the Writing Process
During the preparation of this work, the authors
used ChatGPT 4.0 to improve the manuscript's
readability and language. After using ChatGPT 4.0,
the authors reviewed and edited the content as
needed and took full responsibility for the
publication's content.
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WSEAS TRANSACTIONS on POWER SYSTEMS
DOI: 10.37394/232016.2024.19.35
Gil-Vera V. D., Quintero-López C.
E-ISSN: 2224-350X
415
Volume 19, 2024
Contribution of Individual Authors to the
Creation of a Scientific Article
- Gil-Vera, V. D. carried out the development of the
model, implemented the Python libraries, has
organized and executed the statistical analysis.
- Quintero-López, C. assisted in the writing,
editing, and interpretation of the results.
Sources of Funding
This work was funded by Luis Amigó Catholic
University - Cost Center [0502020965].
Conflict of Interest
The authors have no conflicts of interest to declare.
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the
Creative Commons Attribution License 4.0
https://creativecommons.org/licenses/by/4.0/deed.en
_US
WSEAS TRANSACTIONS on POWER SYSTEMS
DOI: 10.37394/232016.2024.19.35
Gil-Vera V. D., Quintero-López C.
E-ISSN: 2224-350X
416
Volume 19, 2024
