Smart Grid Stability Prediction with Machine Learning
GIL-VERA VICTOR DANIEL
Faculty of Engineering, Luis Amigó Catholic University,
Trans. 51 A N° 67 B-90,
COLOMBIA
Abstract: - Smart grids refer to a grid system for electricity transmission, which allows the efficient use of
electricity without affecting the environment. The stability estimation of this type of network is very important
since the whole process is time-dependent. This paper aimed to identify the optimal machine learning technique
to predict the stability of these networks. A free database of 60,000 observations with information from
consumers and producers on 12 predictive characteristics (Reaction times, Power balances, and Price-Gamma
elasticity coefficients) and an independent variable (Stable / Unstable) was used. This paper concludes that the
Random Forests technique obtained the best performance, this information can help smart grid managers to
make more accurate predictions so that they can implement strategies in time and avoid collapse or disruption
of power supply.
Key-Words: analysis; artificial intelligence; control, machine learning; smart grid; stability.
Received: June 28, 2021. Revised: July 15, 2022. Accepted: September 16, 2022. Published: October 6, 2022.
1 Introduction
Smart grids are networks that control power
delivery and provide several advantages, including
the development and effective management of
renewable power sources [1]. They are primarily
used to solve energy supply problems by ensuring
the transfer of information and electricity between
power plants and appliances [2]; they also enable
devices to communicate between suppliers and
consumers, thus managing demand, preserving the
distribution network, reducing costs, and saving
energy [3].
In essence, a smart grid has advanced technology
and incorporates information and communication
technologies (ICT), utilizing technology for
metering, communications, and control in the
facilities' generating, transmission lines, substations,
feeders (circuits), and meters [4]. The objectives of
smart grids are; to generate faster performance for
the benefit of the end consumer (services, tariffs,
quality, and continuity of supply), reduce power
outages, increase security and energy efficiency,
reduce pollution, help control energy consumption,
reduce and prevent outages by anticipating
equipment damage and making changes in the
electrical transmission path, reduce the vulnerability
of transmission networks to attacks or failures and
facilitate their rapid location in urban and rural areas
[5].
According to [6], modern electric power systems'
technical and commercial disturbances are often
referred to as "smart grid", encompassing everything
integrated into them, what uses the grid services and
what interacts with them. On the other hand, [7]
defines them as a complex system of technological,
electricity trading, and service subsystems
articulated to the business, legislative, political, and
social sectors. Technically speaking, smart grids are
comprised of transmission and distribution
networks, production, consumption, and storage
facilities, as well as related operational and
investment decision-making systems. They also
have close ties to other energy sources and domains
due to the coupling of sectors and electrification of
energy domains like building heating and cooling,
transportation, and industrial processes [7]. The key
to making the best use of abundant energy resources
is smart grid engineering, which enables the
efficient dispatching of power generated by hybrid
renewable energy sources (RES) over long distances
via DC transmission lines using high voltage DC
(HVDC) transmission technology [8].
Smart grids enable efficient and dependable
energy access using computing and digital
communication technologies by integrating
renewable energy generation technologies into the
transmission system [9]. The reality in which
utilities operate, coupled with innate values like
business culture, technology, process maturity, and
the current market, as well as the socioeconomic and
environmental situation of their concession region,
are what drive the deployment of smart grids [10].
These generate benefits for utilities, better grid
management, increased customer choice, greater
understanding of energy use, reduced electricity
cost, increased communication with customers and
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their appliances, use of more renewable energy
sources, and integration of electric vehicles [11].
They can offer various advantages that lend
themselves to a more stable and effective system,
and their primary functions include real-time
monitoring and reaction, allowing the system to
constantly change to an ideal condition. This is one
of its key qualities [12]. Self-healing enables them
to identify anomalous signals, carry out adaptive
reconfigurations, and isolate disturbances, reducing
or eliminating electrical disturbances during storms
and disasters. They can also reduce power outages
and shorten their duration when they do occur [13].
Rapid isolation enables the system to quickly isolate
affected portions of the network from the rest of the
system to prevent the spread of outages and enable
faster restoration. Anticipation enables the system to
automatically search for issues that could cause
greater disturbances [14].
While grid operators manage the system's
balance, provide supply stability and security,
physically connect producers and consumers and
facilitate energy transactions, smart grids also
provide services that enable an electricity system's
efficient and secure running [15]. Smart grids aim to
improve the functioning of energy markets, use
existing transmission infrastructures more
effectively, increase the capacity of renewable
energy sources, electric vehicles, heat pumps, and
other energy-saving technologies, and give all
stakeholdersincluding small-scale actors like
distributed energy resource ownersmore
flexibility [16]. Fig.1 presents the main benefits of
smart grids.
Smart Grids
Interaction
Increased capacity for interaction
with the energy market and users.
Self-repair
Self-healing and resilience in the
face of failure.
Prediction
Efficient forecasting for better
storage.
Security
Increased security against attacks
on the power grid.
Optimization
Optimization of resource and
equipment availability.
Coordination
Harmonious management of
resources, equipment, and
information systems beyond
geographical distribution.
Integration
Full integration of monitoring,
control, protection, maintenance,
and dispatch.
Fig. 1: Benefits of smart grids
In a smart grid, data on consumer demand is
gathered, supply circumstances are compared
centrally and customers are supplied with pricing
information to determine their usage because the
entire process is time-dependent, it is crucial to
understand and plan for disturbances and
fluctuations in energy consumption and production
introduced by system participants dynamically,
considering not only technical considerations but
also how participants react to changes in energy
prices [17].
In power system operation and planning,
dynamic security assessment and prediction are
critical to ensure uninterrupted electricity supply to
consumers and improve system reliability [18]. The
ability of smart grids to maintain balance over time
is referred to as stability, i.e., avoid blackouts
regardless of consumer demand (Hz) [19].
Globally, 50 Hz / 60 Hz frequencies are employed
in electric power distribution and generation
systems, the frequency of the electric signal
increases in times of excess generation, therefore,
measuring the frequency of the grid at each
customer's location is sufficient to give the manager
the necessary information on the present grid energy
balance, so that it can price its energy supply and
alert consumers, while it reduces in times of
underproduction [19].
In the review of the state of the art, the scientific
databases Scopus and WoS were used, only research
articles were considered and the fields of knowledge
were delimited to energy, engineering, and
computer science, the search period was from 2019
to September 2022. The search equation used was:
TITLE-ABS-KEY ("smart grid" AND "stability"
AND ("prediction" OR "forecasting")) AND
(LIMIT-TO (PUBYEAR, 2022) OR LIMIT-TO
(PUBYEAR, 2021) OR LIMIT-TO (PUBYEAR,
2020) OR LIMIT-TO (PUBYEAR, 2019)) AND
(LIMIT-TO (DOCTYPE, "ar")) AND (LIMIT-TO
(SUBJAREA, "COMP) OR LIMIT-TO
(SUBJAREA, "ENER")) AND (LIMIT-TO
(SRCTYPE, "j"))
The research question considered was: Q1. How
has the prediction/forecasting of smart grid stability
been performed?
Most of the identified research related to smart
grid stability prediction uses simulated data and
deep learning techniques. In the research developed
by [20], they claim that measuring the grid
frequency of each customer is sufficient to provide
the grid manager with all the necessary information
about the energy balance so that it can price its
energy supply and inform consumers. According to
[21], grid stability is affected by the fluctuating
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nature of renewable energy sources, in this research
they employed the Simulated Annealing (SA)
algorithm to optimize the hyperparameters and
improve the predictability of the grid stability
prediction model, which obtained high performance.
In the research conducted by [22], they predict the
stability of smart grids using multidirectional short-
term memory (LSTM). Meanwhile, [23] employed
a symmetric non-negative latent factor model based
on matrix factorization. In the research developed
by [24], they concluded that neural networks can
achieve high performance in predicting network
stability; however, they claim that most existing
machine learning-based approaches can only
examine a specific type of stability, and feature
engineering is hardly performed due to the limited
size of the training data, which may present a
misleading indicator of the stability status.
As mentioned above, this paper aimed to train
different models to predict the stability of smart
grids using machine learning techniques (Random
Forests, Support Vector Machine (SVM), Logistic
Regression, K-Nearest Neighbors (KNN), Decision
Trees, ANN-MLP, Naïve Bayes), compare the
performance of each technique and identify the
optimal one to predict the stability of this type of
grids. The utility of this study in practical
applicability is the identification of the optimal
technique in terms of accuracy that can help smart
grid managers worldwide to make more accurate
predictions about the stability of this type of
network so that they can implement strategies in
time to avoid collapse or breakdowns in the power
supply to the nodes that make up the network. A
free database of 60,000 observations with
information from consumers and producers on 12
predictive characteristics (reaction times, power
balances, and gamma-price elasticity coefficients)
and an independent variable (stable/unstable) was
used. The rest of the paper contains the following
sections: in the second section generalities about
smart grids are presented, in the third section
generalities about machine learning, in the fourth
section the method used in the models’ training, and
the fifth section the results and the discussion.
Finally, the paper concludes.
2 Machine Learning
It is a subfield of computer science and artificial
intelligence (AI) that focuses on using data and
algorithms to simulate how people learn, increasing
their accuracy gradually [25]. Machine learning
models are used to learn patterns from data in two
ways: supervised or unsupervised learning. The
former starts from a labeled data set, i.e., the value
of the target variable is known, while the latter uses
unlabeled data, i.e., the value of the target variable is
unknown. Machine learning and data analytics are
interdependent and related fields of study that
primarily focus on acquiring decisive knowledge
[26]. Models are developed using training data and
evaluated with test data. Machine learning is
currently widely employed in many fields of
knowledge to generate predictions and facilitate
decision-making. The objective of Machine
Learning is to let computers learn how to carry out
tasks without being explicitly taught to do so [27].
It is viable to construct algorithms that instruct a
machine to carry out the steps required to solve a
problem for simpler tasks, but for activities with a
greater level of complexity, it is more beneficial to
assist the machine in developing its algorithm rather
than outlining each step [28]. Machine learning can
be used for classification (to predict the membership
of a class or label) and regression (to predict a
numerical value) tasks. Threesome several
specialized tools or programs allow the use of
machine learning; some of them are Keras,
TensorFlow, KNIME, Shogun, IBM Watson,
Apache Mahout, R, Apache Spark MLlib, Weka,
Oryx 2, RapidMiner, H20.ai, and Pytorch.
There are several techniques (Random Forests,
Support Vector Machine (SVM), Logistic
Regression, K-Nearest Neighbors (KNN), Decision
Trees, ANN-MLP, Naïve Bayes), that can be
employed in the construction of classification or
regression models, each of these differing from the
others in terms of parameterization. Different
research focused on predictive modeling has
employed machine learning techniques, specifically,
the logistic regression assumes that the independent
variable y can take the discrete values {0,1.
Equations (1) and (2) describe the relationship
between the dependent and independent variables.
󰇛

 󰇜
(1)
󰇛󰇜

(2)
This technique is used primarily for classification
tasks. The composition of a sigmoidal function
φ(sig): R [0, 1] over the class of linear functions
is the logistic regression class hypothesis [29]. The
K-Nearest Neighbors (K-NN) technique saves all
the data in the training set and classifies the test
sample data based on the Euclidean distance (3),
this technique calculates the distance between the
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data points in the training set, chooses the K entries
that are closest to the new data point, and then
assigns the label with the highest frequency in the K
entries as the class label for the new data point [29].
󰇛󰇜󰇛󰇜
(3)
The Support Vector Machines (SVM) technique,
optimally divides two classes by determining the
distance between the nearest points in any class'
training set [29]. It is possible to map features from
a finite-dimensional space into a higher-dimensional
space, enabling linear separation despite the
dimensional space. This technique provides the best
decision boundary that separates the space into
classes [30]. The Bayes' Theorem (4), on the other
hand, forms the foundation of the Naive Bayes
technique, to find the probability when certain other
probabilities are known [30].
󰇛󰇜󰇛󰇜󰇛󰇜
󰇛󰇜
(4)
P(Y|X): the probability that Y occurs when X
occurs. P(X|Y): the probability that X occurs when
Y occurs.
P(Y): the probability that Y occurs.
P(X): the probability that X occurs.
The X variable represents the set of
characteristics and is given as X = (X1, X2, X3, ...
Xn). See equation (5):
󰇛󰇜󰇛󰇜󰇛󰇜
󰇛󰇜󰇛󰇜
(5)
The decision tree technique refers to classifiers,
h: X Y, that move from the root node to a leaf to
forecast the label associated with an instance of
variables; these are built as branch-like fragments.
This technique includes all the predictors with the
dependence assumptions between the predictors,
and each tree has nodes (root and leaves) that
represent the class labels, with the data attribute
with the highest priority in decision making being
selected as the root node [31]. For the construction
of decision trees, it is necessary to calculate two
types of entropy using one-attribute (6) and two-
attribute (7) frequency tables.
󰇛󰇜󰇛󰇜

(6)
󰇛󰇜 󰇛󰇜󰇛󰇜


(7)
The gain function (8) is obtained as follows:
󰇛󰇜 󰇛󰇜󰇛󰇜
(8)
In equation (8) T represents the target variable, X
the feature on which it will be divided, and (T, X)
the entropy calculated after dividing the data on the
feature X. Random Forests is a technique based on
decision trees, which are assembled by bags and
trained independently [32]; this technique forecasts
an output based on features using a collection of
decision trees. The prediction is the outcome of
consecutive binary decisions that are divided
orthogonally in the multivariate space of variables;
in essence, it is a meta-learning of numerous
separately built trees [32].
Finally, artificial neural networks are
parameterized nonlinear regression models that seek
to emulate the way the human brain processes
information, i.e., a large number of interconnected
processing units that play the role of biological
neurons, which work simultaneously to process
information. The activation function (softmax, tanh,
relu) is in charge of returning output from an input
value, often the set of output values in a certain
range such as (0,1) or (-1,1) [33]. As universal
approximators, multilayer perceptrons are neural
network models that can approximate any
continuous function. They are made up of
perception, which is neurons. A perceptron takes n
characteristics as input (x = x1, x2, ..., xn), and each
of these features is associated with a weight (9).
Since a perceptron requires numeric input features,
non-numeric input features must be translated
before being used [33].
󰇛󰇜

(9)
3 Problem Formulation
Smart grids are the future of energy supply. Their
instability can cause problems in the supply of
energy to consumption nodes, for this reason, is
important to predict their stability. In this type of
network, generation must match demand at all
times, a reserve must be maintained for immediate
outages, and sufficient capacity must be provided
for voltage stability.
Identifying the optimal machine learning
technique (higher accuracy) to predict the stability
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of this type of network, allows for building reliable
predictive models, which can be used in the
prediction of their stability (Stable / Unstable). This
study aimed to compare various machine learning
approaches to identify the best technique for
predicting a smart grid's stability. The database used
contains the results of stability simulations of a star
network (three consumption nodes and one
generation node) as presented in Fig.3.
Fig. 2: 4-Node Star Smart Grid
4 Problem Solution and Discussion
A free database accessible from the following link
was used to build the models: https://onx.la/46d79,
the dataset contains 60,000 observations, twelve
primary predictive characteristics, and one
dependent variable. The database's structure is
shown in Table 1.
Table 1. Database structure
Variable
Description
V0
Target Variable
(Unstable=0/Stable=1)
V1
Reaction
time
Power producer
V2
Consumer 1
V3
Consumer 2
V4
Consumer 3
V5
Power
balance
Power producer
V6
Consumer 1
V7
Consumer 2
V8
Consumer 3
V9
Price
elasticity
coefficient
(gamma)
Power Producer
V10
Consumer 1
V11
Consumer 2
V12
Consumer 3
It should be made clear that the price elasticity
coefficient refers to the percentage variation in
electricity demand in response to small percentage
variations in price data, and the reaction time refers
to the response time of network participants to
adjust consumption and/or production in response to
price changes, and the power balance refers to the
nominal power produced or consumed at each
network node. The models were trained in a ratio of
75/25 (75% for training and 25% for testing), thanks
to this division it is possible to identify the accuracy
of the models, which were developed in Python
using Google Colab. This tool provides free virtual
machines with graphics cards to perform machine
learning algorithms, which have the same power as
platforms such as AZURE or AMAZON Web
Services. These Google virtual machines are
restarted every 12 hours, allow running and
programming in Python in a web browser, do not
require configuration, allow free access to Graphics
Processing Units (GPUs), and allow sharing content.
This tool can be used by students, data scientists, or
artificial intelligence researchers.
Colab files are Jupyter notebooks that enable the
blending of executable code and rich text in a single
document, as well as graphics, HTML, and LaTeX.
These notebooks are stored in a Google Drive
account and can be shared with others for comments
or editing. Colab allows the use of the most popular
Python libraries to analyze and visualize data, such
as Pandas, Numpy, Matplotlib, Keras, and
Tensorflow, among others. This tool allows
importing own data from a Google Drive account
and GitHub, it also allows importing image datasets,
training image classifiers, and evaluating
classification and regression models. It should be
noted that these notebooks run code on Google's
cloud servers, which allows taking advantage of the
power of Google hardware regardless of the
computer power on which it is used. Table 2
presents the libraries and optimal parameters for
each of them.
Table 2. Optimal parameters and libraries
Model
Library & Optimal Parameters
Decision
Trees
DecisionTreeClassifier:
{'criterion':'gini','class_weight':
'balanced', 'max_depth': 5,
'max_features': 'log2, 'splitter': 'best'}
k-Nearest
Neighbors
KNeighborsClassifier: {'n_neighbors':
4}
Logistic
Regression
LogisticRegression: {'C': 17, 'max_iter':
9600, 'penalty': 'l2', 'tol': 1e-2}
SVM
SVC: {'C': 120, 'kernel': 'RBF', 'tol':
0.01}
Naive
Bayes
GaussianNB: {'max_features': 'auto',
'var_smoothing':1e-8}
Random
Forests
RandomForestClassifier: {'n_estimators':
60}
ANN -
MLP
MLPRegressor: {'activation': 'relu',
'hidden_layer_sizes': 4, 'learning_rate':
'constant', 'solver': 'adam',
'learning_rate_init': 0.5}
A confusion matrix, which is a matrix
representation of the prediction’s outcomes made,
was used to assess the accuracy of the constructed
models (Table 3).
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Table 3. Confusion matrix
Current
Predicted
Negative
Positive
Negative
TN
FP
Positive
FN
TP
TN: values that were negative in the prediction and
were also negative in the real values.
TP: values that were positive in the prediction and
were also positive in the real values.
FN: values that were negative in the prediction and
were not negative in the real values.
FP: values that were positive in the prediction and
were not positive in the real values.
From the values of the confusion matrix, the
metrics presented in equations (10), (11), (12), (13),
(14), and (15) were calculated.
Accuracy: percentage of correct predictions.
 󰇛󰇜

(10)
Sensitivity, Exhaustiveness, or Recall:
percentage of positive cases detected.
 
󰇛󰇜
(11)
Specificity: percentage of negative cases
detected.
 
󰇛󰇜
(12)
Precision: percentage of correct positive
predictions
 
󰇛󰇜
(13)
F1 Score: a harmonic measure of precision and
completeness, 1 denotes perfect completeness and
accuracy.
 

(14)
Receiver operating characteristics curve (ROC):
where AUC=1 is ideal, AUC = 0.5 the model cannot
differentiate between classes, and AUC = 0 means
that the prediction matches the classes.
 
󰇛󰇜
(15)
Table 4 presents a summary of the metrics
obtained by each of the models evaluated; these
metrics are ordered from the model with the best F1
score to the model with the lowest score.
Table 4. Training results
Model
Accuracy
Precision
Recall
Specificity
F1-Score
Random_Forest
0.935
0.930
0.967
0.885
0.948
Decision Tree
0.920
0.910
0.962
0.856
0.936
ANN - MLP
0.890
0.870
0.954
0.802
0.910
SVM
0.873
0.858
0.937
0.783
0.896
K- NN
0.780
0.761
0.878
0.659
0.815
Naive-Bayes
0.509
0.537
0.637
0.361
0.583
Logistic
Regression
0.476
0.402
0.643
0.365
0.495
This result allows us to identify that the model
with the best performance was Random Forest
(Accuracy=0.935, F1-Score=0.948). Other models
that performed well were Decision Trees
(Accuracy=0.920, F1-Score=0.936) and ANN-MLP
(Accuracy=0.890, F1-Score=0.910). The ANN-
MLP obtained an F1-Score>0.90; however, its
Accuracy=0.870, which shows that the ability to
make correct positive predictions is lower than the
previous two models. The Naive Bayes and Logistic
Regression models were the models that registered
the lowest capacity to identify negative cases
(Specificity), for these two models this metric was
lower than 0.40, which makes these models not very
efficient when making predictions. Finally, the least
efficient model was the Logistic Regression, with an
Accuracy=0.476. The F1-Score metric is reliable
when the classes are balanced. Fig.5 presents the
ROC/AUC curve (Receiver Operating
Characteristics Curve) of the Random Forest model,
it can be seen that it has an adequate fit in the upper
left corner, moving away from the main diagonal.
Fig. 5: Positive rates comparison
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Volume 17, 2022
These findings coincide with the results of the
research conducted by [34], where they employed
the Random Forest technique to categorize smart
grid zones depending on energy usage (high/low),
each zone was subdivided into several subzones and
assigned to Random Forest branches. In this
research, the authors confirm the effectiveness of
this technique compared with others (SVM, K-NN,
and Naïve Bayes) and conclude that it can identify
the exact location of energy availability in minimum
time, which allows providing quick responses to
grid users.
In the research developed by [35] on the
prediction of customer abandonment using machine
learning, where they point out that the least accurate
techniques are Naïve Bayes and Logistic
Regression. Additionally, it is consistent with the
study done by [36] on the performance comparison
of machine learning algorithms to detect dementia
from clinical datasets, where they highlight that the
Random Forests technique is one of the most
accurate.
It should be noted that the objective of
employing this type of technique in predictive
modeling is that they discover by themselves
patterns that generalize well the data that were not
analyzed instead of memorizing data that they
learned during training; all accuracy metrics should
be evaluated to decide which is the best and not only
focus on the accuracy metric. You should also
analyze the models that are more separated from the
random case, and not only rely on high accuracies
since it is possible to have an imbalance in the
classes and/or problems of under-or over-training,
i.e., if in the smart grid training database most of the
measurements are classified in the "Stable" category
and only a few in the "Unstable" category, it is easy
to guess that a new smart grid measurement will
also be "Stable". There must be a balance between
the number of "Stable" and "Unstable"
measurements in the training database.
5 Conclusion
Smart grid stability needs to be predicted to increase
supply reliability, efficiency, and consistency. There
are great advantages to implementing smart grids in
urban and rural areas, as they encourage the
development of renewable energies, contribute to
the reduction of polluting gases, reduce
environmental impact and damage to the ecosystem
caused by the construction of electrical
infrastructure works, which is why it is vital to
predicting their stability in advance to avoid failures
and collapses in the system.
In this study, a comparison of various machine
learning techniques for predicting the stability of the
smart grid was conducted. The Random Forests
technique obtained the best results in the metrics
that were studied (Accuracy, Precision, Recall,
Specificity, and F1 Score). When one class is less
frequent than others, this technique can
automatically balance data sets; it is less
computationally expensive and does not require a
graphics processing unit (GPU). This technique is
commonly used in classification exercises since,
unlike artificial neural networks, it doesn't need a lot
of data to be effective. However, it is not correct to
state that this technique is superior to others for
making predictions/forecasts in any area of
knowledge; the objective of the researcher and the
quantity and quality of the available data plays a
very important role. In addition, aspects such as
non-normalization of the data, non-identification of
optimal parameters, and inadequate processing can
considerably affect its performance, is very
important to normalize the data, fill in missing data
with null values and eliminate inconsistencies
before training the classification models.
Future research can focus on the construction of
constructing predictive models using combined
Machine Learning techniques (Bagging, Boosting,
Random Subspaces, and others) and compares
presented in this work. Finally, Google Colab
facilitated the training of models and the
identification of the optimal model for predicting
the stability of smart grids, as it has advanced
libraries for data analysis pre-installed and allows
cloud saving and code compilation in blocks.
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Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
Victor Daniel Gil Vera has performed the
normalization of the database, trained the predictive
models in Python, and performed the statistical
analysis.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
This research was funded by the Universidad
Católica Luis Amigó and was one of the results of
the research project entitled "Implementation of
Smart Grids in Colombia: a multidimensional
analysis" - Cost Center [0502020950].
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: 10.37394/232016.2022.17.30
Gil-Vera Victor Daniel
E-ISSN: 2224-350X
305
Volume 17, 2022