Predictive Modeling of Photovoltaic Solar Power Generation

GIL-VERA V. D.

SISCO Research Group,

Luis Amigó Catholic University,

Trans. 51A N° 67 B-90, Medellín,

COLOMBIA

QUINTERO-LÓPEZ C.

NBA Research Group,

Luis Amigó Catholic University,

Trans. 51A N° 67 B-90, Medellín,

COLOMBIA

Abstract: - Photovoltaic solar power referred to as solar power using photovoltaic cells, is a renewable

energy source. The solar cells' electricity may be utilized to power buildings, neighborhoods, and even

entire cities. A stable and low-maintenance technology, photovoltaic solar power is an appealing

alternative for generating energy since it emits no greenhouse gases and has no moving components.

This paper aimed to provide a photovoltaic solar power generation forecasting model developed with

machine learning approaches and historical data. In conclusion, this type of predictive model enables

the evaluation of additional non-traditional sources of renewable energy, in this case, photovoltaic

solar power, which facilitates the planning process for the diversification of the energy matrix.

Random Forests obtain the highest performance, with this knowledge power systems operators may

forecast outcomes more precisely, this is the main contribution of this work.

Key-Words: Forecasting, Generation, Machine Learning, Predictive Modeling, Solar Power.

Received: July 16, 2022. Revised: March 11, 2023. Accepted: April 9, 2023. Published: May 3, 2023.

1 Introduction

The utilization of renewable energy sources instead

of fossil fuels has been emphasized as a way to

reduce the carbon footprint globally. Global

population growth is closely related to rising energy

consumption and while old energy sources are

becoming depleted, new energy sources are being

investigated to fill the void, [1]. As a substitute

treatment, more promotion and use of

environmentally friendly energy sources are desired.

Solar photovoltaic (PV) energy is presented by

this group. In 2010, solar energy generated less than

1% of the world's electricity, but by 2022, that

percentage is projected to rise to over 28%, [2],

throughout the last three decades. The local climate

in the area where the system will be deployed has a

strong correlation with the solar power-producing

capacity of PV systems, [3], [4]. Among the

performance models used to estimate generation, the

models of [5], [6], [7], stand out.

These models illustrate the direct link between

environmental parameters (solar radiation, air

temperature, and wind speed) and the electrical

output of a solar system. Even though these models

are initial approximations, [8], [9], they do not

sufficiently take into consideration radiation's

changing and nonlinear character.

Because meteorological data variations and

intermittencies affect energy output and the

performance index of solar systems, [10], solutions

that foresee and assess these changes are necessary.

Predictive models are one of these alternatives since

they focus on using data processing and analysis to

find relationships, patterns, and/or trends. Models

may be divided into two categories and applied to

the development of prediction models. In the first,

machine learning (ML) and artificial intelligence

(AI) are utilized, whereas classical statistics are used

in the second, [11], [12].

This work aimed to create a forecasting model

for electricity generation for the next few days. For

34 days in a row (68,788 entries), a database was

utilized to collect data on energy production from a

solar photovoltaic power plant every 15 minutes.

WSEAS TRANSACTIONS on POWER SYSTEMS

DOI: 10.37394/232016.2023.18.8

Gil-Vera V. D., Quintero-López C.

E-ISSN: 2224-350X

Volume 18, 2023

The database's variables included the date and time

of each observation, the amount of DC power the

inverter produced in 15 minutes (in kW), the

amount of AC power the inverter (source key)

produced in 15 minutes (kW), the total amount of

energy produced throughout the day, and the total

return on investment.

The other sections of this work are: section 2

provides a broad background on photovoltaic solar

power, section 3 offers the problem formulation,

section 4 generalization of ML, section 5 problem

solution, section 6 discussion, and finally

conclusions.

In conclusion, predictive models provide

improved network management, detect the need for

panel cleaning/maintenance, and locate faulty or

inefficient equipment. Predictive modeling may be

used to forecast the long-term power reserve for PV

system design and size as well as minimize

generation uncertainty.

2 Photovoltaic Solar Power

A set of electrical and electronic components called

a photovoltaic array uses sun radiation to generate

electricity. The photovoltaic module, which is made

up of cells capable of converting incident light

energy into direct electrical energy, is the main

component of this system, [13], [14].

The rest of the equipment in a photovoltaic

system is primarily determined by the system's

intended use. Grid-connected, off-grid, and pumped

storage systems are the three basic categories under

which photovoltaic systems may be categorized.

Grid-connected systems generate electricity that

is supplied to the traditional grid; they are exempt

from the requirement for energy storage as they are

not directly responsible for meeting customer

demand or ensuring consumption, [15], [16]. These

systems, which may be separated into ground-

mounted systems and building-mounted systems,

comprise inverter equipment that adjusts the

electricity supplied by the solar generator to the

circumstances of the traditional grid to permit the

proper linkage with the electrical grid, [17].

Above-ground systems often have more power

than 100 kW and are entirely intended for energy

generation and related economic efficiency. In-

building systems perform tasks in addition to

generating energy, such as replacing architectural

elements, creating aesthetically pleasing effects,

shading glass, etc.

They generally have power ratings of less than 100

kW and are smaller than ground-mounted systems,

[18], [19].

The requirement to satisfy a particular energy

demand unites the many uses for stand-alone

systems. Because of this, almost all standalone

systems have energy storage technology, [20].

According to their related applications, these

systems may be divided into three groups:

professional, rural electrification, and modest

consumption. Little photovoltaic modules,

frequently built of amorphous silicon, are used in

modest consumption applications to power

electronic devices like calculators or watches,

mobile phone chargers, tiny power tools, household

beacons, etc., [21], [22].

There are many professional applications,

including radio links, cathodic protection of gas

pipelines, hotels, traffic signals, air navigation,

refrigeration of vaccines, equipment for remote data

acquisition and transmission, and even power

supply for satellites and other space equipment,

[23].

Due to the extremely high costs associated with

power failures in all of these applications, it is

typically chosen to add solar generators and

electrochemical accumulators that are bigger than

technically necessary, [24], [25]. This reduces the

likelihood of failure.

Often included in development cooperation

projects and funded by nonprofit organizations or

institutions like the World Bank or the European

Union, rural electrification systems provide energy

to rural communities that are located distant from

traditional power lines, [26], [27]. Solar home

systems (SHS), hybrid power plants, and pumped-

storage systems are the most common types of rural

electrification systems. Lighting devices, radio,

television, and small power tools may all be

respectively, [28], [29].

WSEAS TRANSACTIONS on POWER SYSTEMS

DOI: 10.37394/232016.2023.18.8

Gil-Vera V. D., Quintero-López C.

E-ISSN: 2224-350X

Volume 18, 2023

Domestic systems with 100 W or 200 W power

ratings are often found in a family home, however,

occasionally they can also be found in community

centers or medical facilities. A rural village's

electrical grid is provided by hybrid power plants

with a solar generator, an electrochemical

accumulator, and a generator set or wind turbine.

The size of these plants depends on the population

they serve, with capacity ranging from 10 kW to

100 kW, [30], [31]. Pumping systems employ a

motor pump to raise and move water from an

aquifer to a reservoir or distribution system by using

the electrical energy generated by the solar

generator, [32]. These systems often store energy in

the form of potential energy from the water stored in

the raised reservoir to minimize costs and boost

dependability. Pumping systems can be used to

desalinate water that has been extracted using

reverse osmosis systems, deliver water for human or

animal use, and irrigate private or public

plantations, [33], [34].

An electrical configuration designed to employ

photovoltaics to generate useable solar power is

known as a photovoltaic system. A photovoltaic cell

is a type of electrical device that directly transforms

light energy into electricity by harnessing the

physical and chemical phenomena known as the

photovoltaic effect, [35], [36]. Moreover, it is the

fundamental photovoltaic component that serves as

the

foundation for solar modules.

When a substance is exposed to light, the

photovoltaic effect occurs, which produces voltage

and electric current, [37]. Several solar cells linked

in series and/or parallel and enclosed in an

ecologically friendly laminate make up a

photovoltaic module, [38]. A solar array's

fundamental building component is a photovoltaic

panel, a collection of modules, [39], [40]. A

collection of solar panels that together form the

entire photovoltaic-producing unit is called a

photovoltaic array, [41], [58].

Photovoltaic inverters convert DC electricity

from batteries or solar arrays to AC power for use

with standard utility-powered appliances. The

inverter acts as the brain of photovoltaic systems

since the solar array is a DC source and it takes one

to convert DC electricity to the common AC power

used in our homes and offices, [42]. It is crucial to

understand how weather conditions might affect the

output of the two solar power plants since

photovoltaic systems are heavily impacted by the

weather; in good weather, we receive the most yield,

while in bad weather, we get the least yield, [43],

[44], [45]. The transition from a solar cell to a

photovoltaic system is shown in Figure 1.

Cell Module Panel

Array – PV_System

Electricity Meter

Inverter

Generation Meter

Mounting

AC Isolator

Battery

DC Isolator

Tracking System

Fusebox

Charge Controller

Cabling

Fig. 1: From a solar cell to a PV system

3 Problem Formulation

Throughout 34 days, generation data were acquired

at 15-minute intervals at the inverter level, where

each inverter was connected to several lines of solar

panels. Table 1 presents the variables that make up

the power plant database.

Table 1. Database description

Variable Description

Date_Time

Each observation's date and time.

Observations were made and recorded every

15 minutes.

Plant_ID Plant identification.

Source_Key Inverter identification.

DC_Power Amount of DC power produced over 15

minutes by the inverter (source key) (kW).

AC_Power Amount of AC power produced over 15

minutes by the inverter (source key) (kW).

Daily_Yield The total amount of energy produced in a

day.

Total_Yield Total investor return.

In the following GitHub link are available the

generation database of the PV plant was analyzed

for 34 consecutive days: https://acortar.link/w8yUqp

Sunlight is the cause of the Plant's Direct Current

(DC) power production between 05:33:20 and

18:00:00, but else there is none. There are 22

inverters in the facility, each linked to several PV

arrays. Each inverter captures its data every 15

minutes. Hence, to determine how much electricity

the plant produced in an hour, we just compute the

contribution of the 22 inverters. There are 22

inverters for data time on May 15, 2020, at 0:00.

Except for the curve of May 20 and 25, which

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DOI: 10.37394/232016.2023.18.8

Gil-Vera V. D., Quintero-López C.

E-ISSN: 2224-350X

Volume 18, 2023

provides a consistent shape, nearly all the curves are

the same despite some variation between 11 am and

2 pm. DC electricity is only at its peak on 2020-05-

25. Data provides us with a logistics-like function,

but after 18:00 the energy progressively declines

until breaking down completely at 00:00. As you

can see, certain daily yield dates (2020-02-06, 2020-

05-19, etc.) have a logistic shape with missing

values, but not others (2020-02-06, 2020-05-19,

etc.). Data are logged every 15 minutes, and then we

receive a fresh yield. Figure 2, presents the DC

Power Plot.

300000

250000

200000

150000

100000

50000

00:00 05:33 11:06 16:40 22:13

Fig. 2: DC Power Vs Time

Figure 3 presents the Daily DC Power on each

day of the considered period (34 days).

Fig. 3: Daily DC Power

4 Machine Learning

This computer science area is characterized by an

artificial intelligence (AI) method, which is applied

in many different disciplines of study, including

biology, economics, and the energy sector, [46]. ML

enables the creation of models that can make

judgments that are challenging for explicit methods,

such as straightforward numerical and analytical

techniques, to describe, [47]. In [48], the authors

assert that if representation is feasible, ML models

can identify correlations between predictor variables

and target variables.

Three steps make up ML: the first stage is the

pre-processing and categorization of the data, the

second stage is the data input, and the third stage is

the handling of the discrepancy between the

estimated and measured data, [49]. By taking into

account the fact that the deviation and forecasting

abilities of the models depend not only on the

climatic conditions but also on the prediction

horizon, criteria like the treatment of non-linearity,

the behavior when using multiple inputs, the

prediction horizon, the treatment of the deviation

associated with the prediction, and flexibility,

provide guidelines in model development, [50].

Next, we provide a summary of the ML models

examined in this work:

4.1 Naïve-Bayes

This probabilistic ML method is frequently

employed for classification problems. It is founded

on the Bayes theorem, which calculates an event

probability using information about prior

confounding variables. This model assumes that the

features used to categorize instances are

independent of one another in the context of

classification, i.e., one feature’s existence or

absence does not affect the presence or absence of

any other feature, [51]. This model is based on the

Bayes Theorem.

P󰇛A|B󰇜󰇛|



󰇜.󰇛



󰇜



󰇛



󰇜

(1)

Where P(A) and P(B) are the odds of seeing A

and B in the absence of any provided circumstances.

P(A│B) is the probability that event A occurs given

that B is true, and P(B│A) is the probability of the

contrary case. A and B are events, and P(B) is

different from zero.

4.2 Artificial Neural Network

ANN was developed based on how the human brain

functions. Neurons, the linked layers of nodes that

make up ANNs, process and transfer information

via mathematical operations. A neuron is the

fundamental unit of an ANN. It receives input from

other neurons or external sources, computes an

output using the weighted sum of the inputs, and

then applies a nonlinear activation function. Using

methods like backpropagation, the weights of the

connections between neurons are learned using

training data, [52]. Equation (2), presents the

general equation of this model.

a󰇛󰇜a.



 

(2)

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DOI: 10.37394/232016.2023.18.8

Gil-Vera V. D., Quintero-López C.

E-ISSN: 2224-350X

Volume 18, 2023

4.3 Support Vector Machine

This model is employed for classification and

regression problems. When dealing with high-

dimensional datasets and non-linear decision

boundaries, SVMs are especially successful.

Finding the hyperplane that optimally separates the

various classes in the input data is fundamental in

this model. When there are more than two classes,

the hyperplane may be a plane or a higher-

dimensional manifold, [53]. In a two-class

classification issue, the hyperplane is a line that

divides the two classes. Equation (3) presents a

feature vector.

󰇛󰇜 (3)

For a binary classification problem , , if

󰇛󰇜0 then x ∈ , else x ∈ .

4.4 Logistic Regression

This model is a typical statistical learning approach

for binary classification problems, where the

objective is to predict the likelihood that an event

will belong to one of two classes. A probability

score may be the threshold for a binary logistic

regression prediction result. The logistic function,

on which this model is built, converts an output

resulting from a linear combination of input data

into a probability score between 0 and 1.

Weights are used to model the linear

combination of input characteristics, and they are

learned from training data via maximum likelihood

estimation, [54]. Equation (4) presents the general

equation of this model, where μ is the midpoint of

the curve and s is a scale parameter.

p󰇛󰇜 1

1󰇛󰇜/ (4)

4.5 Decision Tree

This model is employed for classification and

regression problems. Each leaf node represents a

class label or a numeric value, and each interior

node represents a decision based on a feature or

attribute, [55]. Recursively dividing the input space

into subsets based on the values of the input

characteristics is how decision trees are built, the

data is divided into two or more subsets via top-

down partitioning, where the most informative

feature is chosen at each internal node, [55].

A decision tree may be easily converted into a

collection of rules by mapping from the root node to

the leaf nodes one by one. This model may be

trained using many techniques, including ID3, C4.5,

CART, and Random Forests, [55]. The objective is

to reduce the impurity or entropy of the subsets,

which quantifies the level of homogeneity of the

class labels or values, [55]. In this model, entropy is

a measure of the randomness in the information

being processed and information gain (IG) is a

decrease in entropy (equation 5).

IGEntropy󰇛󰇜Entropy󰇛,󰇜





(5)

4.6 Random Forest

This model is used for supervised learning tasks

including classification, regression, and others. An

extensive number of decision trees are constructed

during training using this ensemble learning

approach, which results in a class that reflects the

average of the predictions (regression) or

classifications produced by the individual trees.

This technique works by building a collection of

decision trees, each of which is trained using a

portion of the input features and training data that is

randomly chosen. The random forest aggregates all

of the individual trees’ predictions throughout the

prediction phase to provide a final prediction, [56].

In this model, the Gini Index (equation 6) is used to

identify how much impurity has a particular node.

1󰇛󰇜



 (6)

Where  is the proportion of samples belonging to

class c for a given node.

4.7 K-Nearest Neighbors

In supervised learning, this model is used for

classification and regression applications. It is a

non-parametric approach because it makes no

assumptions about the distribution of the

underlying data. Based on a selected distance

metric, such as Euclidean distance, the K-NN

method finds the K data points in the training set

that is closest to a given data point. The majority

class or mean value of the K nearest neighbors in

the training set is then used to forecast the output of

the supplied data point, [57], [58]. The distance

functions used in this model can be Euclidean

(equation 7), Manhattan (equation 8), or

Minkowski (equation 9).

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DOI: 10.37394/232016.2023.18.8

Gil-Vera V. D., Quintero-López C.

E-ISSN: 2224-350X

Volume 18, 2023

󰇛󰇜



  (7)

||



 (8)

󰇛||󰇜



 / (9)

Two current strategies utilized in photovoltaic

solar power generation forecasting models are deep

learning and statistical approaches. The authors of

[59], propose a hybrid model that blends machine-

learning approaches with the Theta statistical

method to more accurately anticipate future solar

power output from renewable energy facilities.

Long short-term memory (LSTM), gate recurrent

unit (GRU), AutoEncoder LSTM (Auto-LSTM),

and a recently suggested Auto-GRU are among the

ML models.

In [60], the authors suggest a fast-track

methodology to handle two essential issues: long-

term solar resource assessment and photovoltaic

energy forecasting when investigating prospective

locations for PV plant construction. These writers

employed data clustering and probability techniques

while exploring potential sites for PV plant

construction.

In [61], the authors used numerous time-series

algorithms to predict PV power generation output to

respond swiftly to equipment and panel problems.

The Long Short-Term Memory (LSTM) model

exhibited the lowest error rate when compared to

other models for quick PV power generation

estimates, according to the study's findings.

5 Problem Solution

Many variables, including geographic location,

sunshine intensity, solar panel efficiency, and

meteorological conditions, can have an impact on

the production of photovoltaic energy. However,

even within the same place, it might change from

day to day.

There are, however, a few approaches to foresee

PV power generation at a certain site and time. One

method is to employ solar radiation prediction

models, which calculate the quantity of solar

radiation that will arrive at a certain location at a

specific time using meteorological and satellite data.

Based on the amount of sunshine and the present

weather, real-time PV monitors may also be used to

measure current generations and forecast future

generations. Another approach is to estimate using

previous PV generation data from the same site and

season. In this work, the latter is utilized. After

cross-validation. Table 2 lists the optimal

parameters for each model examined.

Table 2. Optimal libraries and parameters

Model Library & Optimal Parameters

Random

Forest RandomForestClassifier: {'n_estimators': 49}

Decision

Tree

DecisionTreeClassifier:

{'criterion':'gini','class_weight':

'balanced', 'max_depth': 5, 'max_features':

'log2, 'splitter': 'best'}

ANN-

MLP

MLPRegressor: {'activation': 'relu',

'hidden_layer_sizes': 4, 'learning_rate':

'constant', 'solver': 'adam', 'learning_rate_init':

0.5}

K-NN KNeighborsClassifier: {'n_neighbors':6}

Naïve

Bayes

GaussianNB: {'max_features': 'auto',

'var_smoothing':1e-8}

Logistic

Regression

LogisticRegression: {'C': 15, 'max_iter':6800,

'penalty': 'l2', 'tol': 1e-7}

SVM SVC: {'C': 88, 'kernel': 'RBF', 'tol': 0.001}

Table 3 displays the findings for each of the

examined accuracy measures.

Table 3. Training results

Model

Accuracy*

Precision*

Recall*

Specificity*

F1-Score*

Random-Forest .843 .848 .875 .793 .854

Decision Tree .837 .827 .869 .773 .843

ANN-MLP .707 .787 .861 .798 .882

SVM .780 .765 .844 .690 .703

K-NN .697 .675 .785 .566 .722

Naïve Bayes .588 .537 .622 .476 .672

Logistic Regression .543 .532 .521 .432 .563

This finding enables us to determine that

Random Forest (Accuracy=.843, F1-Score=.854)

was the model that performed the best. Decision

Trees (Accuracy=.837, F1-Score=.843) and ANN-

MLP (Accuracy=.707, F1-Score=.882) were two

more models that did well. The accuracy of the

positive predictions made by the ANN-MLP is

lower than that of the first two models.

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DOI: 10.37394/232016.2023.18.8

Gil-Vera V. D., Quintero-López C.

E-ISSN: 2224-350X

Volume 18, 2023

The models with the lowest ability to recognize

negative instances (Specificity) were Naive Bayes

and Logistic Regression; for both of these models,

this measure was below .50, making them

ineffective prediction models. The Logistic

Regression model has the lowest efficiency, with an

Accuracy of .543.

6 Discussion

Solar power projections will have a huge impact on

the future of large-scale renewable energy

installations. Predicting solar electricity generation

is strongly reliant on changing weather patterns.

Beyond climatic and altitude factors, the total

amount of energy produced by a solar station

depends on its capacity; thus, the total amount of

energy produced by each solar power plant depends

on its capacity.

A solar plant with a higher kilowatt peak (kWp)

capacity will produce more energy than a plant with

a lower kWp capacity. Because the variables that

affect PV power generation are unpredictable, it can

be difficult to predict it with any degree of accuracy.

With the use of machine learning (ML), it is now

feasible to forecast power generation for the

upcoming few days to manage the grid better,

recognize the need for panel cleaning and

maintenance, and spot broken or underperforming

machinery.

Future studies might concentrate on estimating

the yearly solar energy that a solar power plant is

anticipated to yield based on site attributes and local

meteorological data. Other environmental variables

that may impact daily solar power output, in

addition to the height of a solar power station's

location, include temperature, wind speed, vapor

pressure, solar radiation, day length, precipitation,

and snowfall.

7 Conclusion

Forecasting photovoltaic power output is crucial for

grid planning and management because it enables

operators to better plan and manage energy supply

and demand, which leads to lower costs and higher

system efficiency. Due to weather fluctuation, the

difficulty of detecting solar radiation, system

capacity uncertainty, and a lack of historical data,

this task may be challenging. It helps to increase

prediction accuracy to utilize sensors and modeling.

The Random Forests method demonstrated the

highest performance (Accuracy=.843,

Precision=.848, Recall=.875, Specificity=.793, and

F1-Score=.854); with this knowledge, power

systems operators may forecast outcomes with more

precision.

This ML model is a robust algorithm that can

handle a large number of features, missing values,

and noisy data. It is less prone to overfitting than

other algorithms, such as decision trees, thanks to

the use of bagging and feature randomness.

Random Forests is known for its high accuracy in

predicting outcomes, making it a popular choice for

many applications.

This ML model is adaptable and may be used for

both classification and regression problems. It can

offer crucial insights into the link between the

characteristics and the outcome, increasing the

model's interpretability. Overall, ML integration can

result in improved efficiency, reliability, and cost

reductions in the photovoltaic power generation

sector.

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Gil-Vera V. D., Quintero-López C.

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E-ISSN: 2224-350X

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Contribution of Individual Authors to the

Creation of a Scientific Article (Ghostwriting

Policy)

-Victor Daniel Gil Vera has performed the literature

review, the normalization of the database, training

the predictive models in Python, and the statistical

analysis.

-Catalina Quintero López has performed the

literature review and the analysis of the results.

Sources of Funding for Research Presented in a

Scientific Article or Scientific Article Itself

This research was funded by the Luis Amigó

Catholic University and was one of the results of the

research project entitled "Implementation of Smart

Grids in Colombia: a multidimensional analysis" -

Cost Center [0502020950].

Conflict of Interest

The authors have no conflict 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

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WSEAS TRANSACTIONS on POWER SYSTEMS

DOI: 10.37394/232016.2023.18.8

Gil-Vera V. D., Quintero-López C.

E-ISSN: 2224-350X

Volume 18, 2023