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Revista Facultad de Ingeniería, Universidad de Antioquia, No.102, pp. 9-25, Jan-Mar 2022
Electricity demand forecasting in industrial
and residential facilities using ensemble
machine learning
Predicción de demanda eléctrica en instalaciones industriales y residenciales
utilizando aprendizaje automático combinado
Rodrigo Porteiro 1*, Luis Hernández-Callejo 2, Sergio Nesmachnow 1
1Universidad de la República. Av. 18 de Julio 1824-1850. C. P. 11200. Montevideo, Uruguay.
2Departamento de Ingeniería Agrícola y Forestal, Universidad de Valladolid. Campus Universitario Duques de Soria. C. P.
42004. Soria, España.
CITE THIS ARTICLE AS:
R. Porteiro, L.
Hernández-Callejo and
S. Nesmachnow.
”Electricity demand
forecasting in industrial
and residential facilities
using ensemble
machine learning”,
Revista Facultad de
Ingeniería Universidad de
Antioquia, no. 102, pp.
9-25, Jan-Mar 2022.
[Online]. Available:
https://www.doi.
org/10.17533/udea.
redin.20200584
ARTICLE INFO:
Received: February 27,
2019
Accepted: May 21, 2019
Available online: May 21,
2019
KEYWORDS:
Energy; forecasting;
articial intelligence
Energía; pronóstico;
inteligencia articial
ABSTRACT: This article presents electricity demand forecasting models for industrial and residential
facilities, developed using ensemble machine learning strategies. Short term electricity demand
forecasting is benecial for both consumers and suppliers, as it allows improving energy efciency
policies and the rational use of resources. Computational intelligence models are developed for
day-ahead electricity demand forecasting. An ensemble strategy is applied to build the day-ahead
forecasting model based on several one-hour models. Three steps of data preprocessing are
carried out, including treating missing values, removing outliers, and standardization. Feature
extraction is performed to reduce overtting, reducing the training time and improving the
accuracy. The best model is optimized using grid search strategies on hyperparameter space.
Then, an ensemble of 24 instances is generated to build the complete day-ahead forecasting
model. Considering the computational complexity of the applied techniques, they are developed
and evaluated on the National Supercomputing Center (Cluster-UY), Uruguay. Three different
real data sets are used for evaluation: an industrial park in Burgos (Spain), the total electricity
demand for Uruguay, and demand from a distribution substation in Montevideo (Uruguay). Standard
performance metrics are applied to evaluate the proposed models. The main results indicate that
the best day ahead model based on ExtraTreesRegressor has a mean absolute percentage error of
2.55% on industrial data, 5.17% on total consumption data and 9.09% on substation data.
RESUMEN: Este artículo presenta modelos de pronóstico de demanda eléctrica industriales y
residencial, aplicando aprendizaje automático combinado. El pronóstico de demanda eléctrica
a corto plazo benecia a consumidores y proveedores, ya que permite mejorar las políticas de
eciencia energética y el uso racional de los recursos. Se desarrollan modelos de inteligencia
computacional para el pronóstico diario de demanda eléctrica y una estrategia híbrida para
construir el modelo de pronóstico diario basado en modelos para la próxima hora. Se aplican tres
métodos de preprocesamiento de datos: tratamiento de valores perdidos, eliminación de valores
atípicos y estandarización. Se aplica extracción de características para reducir el sobreajuste
y el tiempo de entrenamiento, mejorando la precisión. El mejor modelo se optimiza mediante
búsqueda de grilla en el espacio de hiperparámetros. Luego se genera un conjunto de 24 instancias
para construir el modelo de pronóstico completo para el día siguiente. Las técnicas aplicadas
se desarrollan y evalúan en el Centro Nacional de Supercomputación (Cluster-UY), Uruguay.
Se utilizan tres conjuntos de datos reales para la evaluación: un parque industrial en Burgos
(España), la demanda eléctrica total de Uruguay y la demanda de una subestación de distribución
en Montevideo (Uruguay). Se aplican métricas estándar para evaluar los modelos propuestos. Los
resultados indican que el mejor modelo, basado en ExtraTreesRegressor, tiene un error porcentual
medio de 2,55% en datos industriales, 5,17% en consumo total y 9,09% en subestación.
1. Introduction
Uncertainty is a specic characteristic of the energy sector.
Although decisions in the energy sector are generally not
9
* Corresponding author: Rodrigo Porteiro
E-mail: rporteiro@ute.com.uy
ISSN 0120-6230
e-ISSN 2422-2844
DOI: 10.17533/udea.redin.20200584 9
R. Porteiro et al., Revista Facultad de Ingeniería, Universidad de Antioquia, No. 102, pp. 9-25, 2022
based on predictable outcomes, some variables that affect
decision making can be predicted, with certain degree of
condence, using information from different sources [1,2].
Examples of useful information for decision making
is that related to natural variables (temperature, wind
speed, etc.). Information related to energy consumption
and demand proles of users is valuable too. Furthermore,
new sources of renewable energy generation developed in
the last 30 years are directly related to natural variables,
and the corresponding information is often incorporated
in prediction models for decision making [3].
Due to the aforementioned reasons, a large number of
stochastic variables must be taken into account to improve
operational decision making, but also to assure that the
derived actions are feasible from an economic point of
view. When considering a large number of variables, the
complexity of the underlying models notoriously increases.
However, the increase in complexity associated with the
number of variables is partly compensated because the
hardware infrastructure to perform computations on large
volumes of data has developed strongly.
New challenges have emerged from the described
reality. A very relevant one is related to the development
of an intelligent system to take advantage of new sources
of information and available data. Classic statistical
models, that were useful for making predictions some
decades ago, have limitations in this new context.
Computational intelligence methods have demonstrated
excellent forecasting accuracy in different areas, in recent
years [4–6]. These methods are robust and tolerant to
uncertainty, and they are able to learn the most relevant
features of the considered data to provide a precise
forecast, thus providing excellent results by excluding
non-relevant information and focusing on the most useful
data.
In this line of work, this article presents the application
of several prediction algorithms based on computational
intelligence to forecast the electricity demand of an
industrial park in Spain, the electricity demand of a
substation in Uruguay and the total electricity demand of
Uruguay. The modeled scenarios are based on historical
demand data of the industrial park (from 2014 to 2017),
historical demand data of the substation in Uruguay (from
2017 to 2018) and historical total demand data of Uruguay
(from 2010 to 2018). For the industrial park, a forecasting
model for the next 24 hours is built by optimizing the
algorithm that presented the best results for the one hour
forecast.
Overall, the major contributions of the research reported
in this article are: i) the evaluation and comparison of
computational intelligence models applied to forecasting
the demand of an industrial park in Spain, the demand of
a substation in Uruguay and the total demand of Uruguay.
Also ii) the optimization of the proposed models using
the high performance computing infrastructure of the
National Supercomputing Center, in Uruguay.
This work extends our previous article Short term
load forecasting of industrial electricity using machine
learning [7], presented at II Ibero-American Congress on
Smart Cities, Soria, Spain, 2019. The main contributions
of the extended version are: i) a residential demand
forecasting scenario applying the studied techniques on
a substation and incorporating climate variables and ii) a
total demand forecasting scenario of Uruguay including
residential and industrial consumers. Both new instances
are analyzed in order to evaluate different consumer
proles as well as different types of inuence of weather
variables.
The article is organized as follows. Section 2presents the
formulation of the electricity demand forecasting problem
and a review of related works. Section 3describes
the proposed approach to solve the proposed problem.
Section 4reports the experimental analysis of the studied
methods, and Section 5reports analysis of the best
method and extension to 24-hour demand forecast is
presented. Finally, Section 6formulates the conclusions
and main lines for future work.
2. Energy demand forecasting
This section introduces the energy demand forecasting
problem, describes forecasting techniques, and reviews
related works.
2.1 General considerations
The energy demand forecasting problem is usually solved
applying mathematical methods using historical data for
prediction. There is no a general method that can be
used in all types of energy demand forecasting. Thus,
an appropriate method must be found for each demand
prole. Using historical data of a particular demand
prole is common in practice to determine the most
effective algorithm. The problem can be classied by
the time horizon to forecast: ultra short-term demand
forecasting (up to a few minutes ahead), short-term
demand forecasting (up to few days ahead), medium-term
demand forecasting (up to few month ahead), and
long-term demand forecasting (years ahead). Different
techniques are applied when considering each time
horizon. This work focuses on short-term demand
forecasting using historical data.
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R. Porteiro et al., Revista Facultad de Ingeniería, Universidad de Antioquia, No. 102, pp. 9-25, 2022
The energy management and operation of electric
grids becomes highly difcult and uncertain, particularly
when new technologies are incorporated. The power
demand of end customers is versatile and changes on
hourly, daily, weekly, and seasonally basis. Hence, there is
a real need of developing models for accurately forecasting
at different time horizons, depending on the management
goals.
This work focuses on both industrial and residential
power consumption. Residential power proles are
usually variable, mainly depend on the time of the day and
the day of the week, but they also depend on occasional
vacations and other factors [8]. On the other hand,
industrial power proles tend to be stable, due to the
needs of industrial processes themselves.
There are two classes of forecasting models for predicting
power demand proles: statistical and physical models.
The main goal of both classes is to predict the power
prole at a future time frame. Statistical models can be
built for time series analysis.
They are less complex than physical models and are
suitable for short term prediction. Physical models are
based on differential equations for relating the dynamics
of the environment and generally are applied for long term
forecasting. In this article, statistical models are selected
for short term forecasting due to their very good prediction
accuracy and lower complexity.
2.2 Problem formulation and strategies
This section describes the problem formulation and the
studied strategies for electric demand forecasting.
Relation between one hour and 24 hour forecasting.
This article focuses on applying computational intelligence
methods to develop a model for forecasting electricity
demand 24 hours ahead. When historical data are
available with hourly frequency, is natural to develop
a model that predicts next hour. From that model, a
multi-step forecasting model can be constructed (i.e., 24
steps in the future).
Four strategies are typically applied for multi-step
forecasting starting from a one-step model:
•Direct strategies develop a different model for
each time step to be predicted. Assuming past
observations of the variable to be predicted are used,
this strategy implies, in case of 24 steps, developing
24 models with the structure dened in Equation 1,
where predtis the prediction of time tvalue and obst
is the observed value at time t.
pred(t+1) =model1(obst, obs(t−1) , ..., obs(t−n))
pred(t+2) =model2(obst, obs(t−1) , ..., obs(t−n))
. . .
pred(t+24) =model24 (obst, obs(t−1), ..., obs(t−n))
(1)
Unfortunately, a direct strategy implies developing
a model for each time step to be predicted and
consequently is very expensive computationally. In
addition, temporary dependencies are not explicitly
preserved between consecutive time steps.
•Recursive strategies apply a one-step model
(recursively), multiple times. Predictions for previous
time steps are used as input for the prediction on the
following time step. The structure to develop for a
recursive strategy is presented in Equation 2.
pred(t+1) =model1(obst, obs(t−1), ..., obs(t−n))
pred(t+2) =model1(pred(t+1) , obst, obs(t−1), ...,
obs(t−n+1))
. . .
pred(t+24) =model1(pred(t+23) , pred(t+22) , ...,
pred(t+1), obs(t−n+23))
(2)
In this strategy predictions are used instead of
observations. A single model is trained, but the
recursive structure allows prediction of errors to
accumulate; also, the performance of the model can
quickly degrade as the time horizon increases.
•Hybrid strategies combine the previously described to
get benets form both methods. A separate model is
constructed for each time step to be predicted. Each
model may use the predictions made by models at
prior time steps as input values. For example, using
all known prediction, a hybrid strategy produces the
structure in Equation 3.
pred(t+1) =model1(obst, obs(t−1), ...,
obs(t−n))
pred(t+2) =model1(pred(t+1) , obst, ...,
obs(t−n))
.
.
.
pred(t+24) =model1(pred(t+23) , pred(t+22) , ...,
obst, ..., obs(t−n))
(3)
•Multiple output strategies develop a model that has as
output all time steps to be predicted (in this case 24).
Multiple output models are more complex as they can
learn the dependence structure between inputs and
outputs as well as between outputs. For this reason,
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they are slower to train and require more data to
avoid overtting. Equation 4shows the corresponding
structure.
pred(t+1,...,t+24) =model1(obs(t), obs(t−1), ...,
obs(t−n))
(4)
In this work, hybrid strategies are applied for solving the
forecasting problem.
One hour forecasting model training. Section 2.3
reviews different approaches and methods for short
term demand forecasting. This work explores the use
of machine learning techniques, mainly those based on
model ensembles. Feature selection is commonly applied
in this kind of problems due to several reasons. Simpler
models are easier to interpret, and have shorter training
times. Also, the size of the model using less features is
smaller, mitigating the curse of dimensionality [9]. But
the main reason to apply feature selection is to reduce
overtting, enhancing generalization of the model to
unseen data.
Once established the strategy to extend the next hour
forecasting models to twenty four hours model, the main
issue is to obtain the best possible model for the next
hour. With this purpose, standard steps are taken: i)
data gathering, ii) data preparation, iii) choosing a model,
iv) training, v) evaluation, vi) parameter tuning, and vii)
testing. Each of these steps is described in detail in
Section 3.
Complete model. After obtaining a one-hour model with
optimized parameters, it is trained for the next hour taking
all steps mentioned. Thus, 24 four different instances of
this model are trained, one for each of the next 24 hours.
Then, the hybrid strategy described in Equation 3is applied
to build a 24-hour forecasting model. The complete model
is evaluated on testing data and results are reported.
2.3 Related works
Several methods have been proposed for electricity
demand forecasting, applying short, medium and
long-term predictions. These methods are classied
in statistical models and machine learning models. This
work focuses on short-term demand forecasting using
machine learning.
Most used forecasting techniques include auto regressive
models (AR), moving average models (MA), auto regressive
moving average models (ARMA) and auto regressive
integrated moving average (ARIMA) models [10]. These
kind of models are easy to implement. ARIMA models
for short-term demand forecasting [11] were initially
proposed by Hagan and Behr.
Taylor and McSharry compared different ARIMA
implementations using load data from multiple
countries [12]. Dudek proposed applying a linear
regression technique [13]. However, linear models
are inadequate to represent the non-linear behavior
of electricity demand series and fail to predict the
accurate future demand values. Thus, their forecasting
accuracy tends to be poor. Some studies try to overcome
the aforementioned difculties considering nonlinear
components, obtaining good accuracy metrics [14].
Several studies have been conducted on short-term
demand forecasting using non-linear models. For
example, Do et al. described a model for predicting hourly
electricity demand considering temperature, industrial
production levels, daylight hours, day of the week, and
month of the year to forecast electricity consumption [15].
Results suggested that consumption is better modeled
considering each hour separately. In our work, this
strategy is developed and applied. Son and Kim proposed
a method based on support vector regression preceded
by feature selection for the short-term forecasting of
electricity demand for the residential sector. For feature
selection, twenty inuential variables were considered and
the quality of the model improved substantially [16].
Other mid-term demand forecasting studies consider
variables such as GDP and prove that are highly correlated
with the demand [17]. Peak demand estimation is also
crucial to determine future demand, in order to assist
future investment decisions [18]. In this article, the
decision to consider ensemble models was taken based in
the work presented by Burger and Moura, who applied a
gated ensemble learning method for short-term electricity
demand forecasting and showed that the combination of
multiple models yielded better results than the use of
a single model [19]. Silva presented a complex feature
engineering to build gradient boosted decision trees
and linear regression models for wind forecasting;
in our work several similar ideas were developed for
demand forecasting [20]. De Felice et al. applied several
separate models for each hourly period. Each of those
models measure variations in electricity demand based
on multiple variables [21]. Recent studies in trafc
prediction in the context of Internet of Things have shown
promising results using advanced articial intelligence
techniques related to those applied in our work [22,23].
Computational intelligence has also been applied to
forecasting and dissagregation of residential energy
consumption [8,24].
The analysis of the related works allowed to conclude that
two main issues impact on the forecasting capabilities and
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the results quality: the model itself and other preparation
and pre-processing techniques.
Several works applied techniques like data normalization,
ltering of outliers, clustering of data or decomposition by
transformations [25–28] to improve prediction results.
In our research, several data preparation techniques
are applied for building a robust approach for short term
energy utilization forecasting. Next section describes the
proposed approach.
3. The proposed approach for day
ahead demand forecasting
This section describes the proposed approach to solve the
day-ahead electricity demand forecasting for an industrial
park in Spain, a substation in Uruguay, and for the total
demand of Uruguay applying the strategies described in
Section 2.2. In addition, implementation details of the
proposed models are presented.
3.1 General approach
This subsection describes the data and the proposed
methodology for electricity demand forecasting.
Data description, preparation, and metrics
Data description. Data for the three studied scenarios
are described next. Industrial park in Burgos, Spain. The
rst scenario reported in this article considers historical
hourly energy consumption data from an industrial park
in Spain. Data were collected between January 2014
and December 2017. The dataset consists of industrial
energy consumption measurements. Each measurement
is composed of the following elds:
•Year (integer), representing the year on which the
measure was taken.
•Month (integer), indicating the month on which the
measure was taken.
•Day (integer), indicating the day on which the measure
was taken.
•Hour (integer), indicating the hour on which the
measure was taken.
•Dayofweek (integer), indicating the day on which the
measure was taken.
•Workingday (boolean), indicating whether the
measure was taken in a working day or not.
•Useful (boolean), indicating whether the measure is
valid.
•Demand (oat), indicating the real power measured.
Substation SB1872 in Montevideo, Uruguay. The second
scenario studied in this article considers historical hourly
energy consumption data from a substation in Tres Cruces
neighborhood in Montevideo, Uruguay. Tres Cruces is
a neighborhood located near the centre of Montevideo
that serves 390 citizens distributed in 117 homes with
medium socio-economic level [29]. The studied dataset
contains residential energy consumption measurements
collected between January 2017 and December 2018. Each
measurement is composed of the following elds:
•Year (integer), representing the year on which the
measure was taken.
•Month (integer), indicating the month on which the
measure was taken.
•Day (integer), indicating the day on which the measure
was taken.
•Hour (integer), indicating the hour on which the
measure was taken.
•Dayofweek (integer), indicating the day on which the
measure was taken.
•Workingday (boolean), indicating whether the
measure was taken in a working day or not.
•Useful (boolean), indicating whether the measure is
valid.
•Temperature (oat), indicating the temperature.
•Humidity (oat), indicating humidity.
•Wind speed (oat), indicating the average wind of a
specic hour.
•Demand (oat), indicating the real power measured.
Total demand of Uruguay. The third scenario studied in
this article considers the historical hourly energy total
demand from Uruguay for a total period of nine years (data
were collected between January 2010 and December 2018).
Each measurement is composed of the following elds:
•Year (integer), representing the year on which the
measure was taken.
•Month (integer), indicating the month on which the
measure was taken.
•Day (integer), indicating the day on which the measure
was taken.
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•Hour (integer), indicating the hour on which the
measure was taken.
•Dayofweek (integer), indicating the day on which the
measure was taken.
•Workingday (boolean), indicating whether the
measure was taken in a working day or not.
•Useful (boolean), indicating whether the measure is
valid.
•Temperature (oat), indicating the temperature.
•Humidity (oat), indicating humidity.
•Wind speed (oat), indicating the average wind of that
hour.
•Demand (oat), indicating the real power measured.
Data preparation. For the three studied scenarios, data
preparation consists in eliminating useless measurements
and replacing outliers. A few useless measurements were
found (less than 0.0001%) in each dataset, and none of
them corresponded to consecutive hours. Thus, they were
replaced by the average measure of the previous and next
hour. A measurement is considered an outlier when it
deviates from the mean by more than three times the
standard deviation [30].
Outliers were replaced by the value of the mean, adding or
subtracting three times the standard deviation, depending
on whether the outlier is higher or smaller than the mean.
Feature standardization was applied to the three scenarios
data to avoid typical scale issues. For instance, if a feature
in the dataset has a different order of magnitude compared
to others then in algorithms where a metric is involved
this big scaled feature becomes dominating and needs to
be standardized [31].
Finally, from in each of the scenarios, new features
were generated from datasets associated with past
demand measures to train the models. In particular,
the last 48 measures were considered for each record to
capture at least two days of consumption pattern directly
in the features.
Several visualization analysis were performed to gain
an intuitive insight of the information contained in
each feature. The most relevant fact conrmed in this
preliminary analysis was the daily periodicity of the
demand value in all scenarios. The diagram shown in
Figure 1reports the high correlation between actual
demand and the demand of the same hour of two days
before in the case of the industrial park scenario. Weather
data was not considered in the industrial scenario because
of the very low correlation. However, in both scenarios that
contain residential consumption data, weather variables
are highly correlated with demand. Figure 2presents the
relation between temperature and total consumption for
the scenario of total demand of Uruguay showing that
demand values are higher in extreme temperatures. Data
preprocessing was performed using pandas library [32].
A linear regression model Msim was trained using the
sklearn toolkit [33], congured with default parameters as
benchmark model. New training and test datasets were
produced keeping only the relevant features, according
to the analysis performed to determine the relative
importance of each feature.
Metrics. Three standard metrics were used for
evaluation: Mean absolute percentage error (MAPE,
Equation 5), root mean square error (RMSE, Equation 6)
and mean absolute error (MAE, Equation 7); reali
represents the measured value for t=i,predirepresents
the predicted value and nrepresents the predicted horizon
length.
MAPE = 100 ×∑n
i=1|reali−pr edi
reali|
n(5)
RMSE =√∑n
i=1 (reali−predi)2
n(6)
MAE =∑n
i=1|reali−predi|
n(7)
Training the one hour ahead forecasting models
Once all data were prepared for model training, a four-step
procedure was applied for training and evaluation in all the
scenarios studied. The four steps are:
1. Training and test sets were generated in a 3:1
proportion. In the industrial park scenario, the
training set considered data from 2014 to 2016 and
the test set considered data from 2017. In the
substation scenario, the training set considered data
from January 2017 to June 2018 and the test set from
July 2018 to December 2018. In the total demand
scenario, the training set uses data from 2010 to 2016
and the test set considered data from 2017 to 2018.
2. A simple base model was trained for benchmarking.
Using the trained model, a recursive feature
elimination process was performed. The ten most
important features are preserved.
3. Several models were trained and compared with the
benchmark model.
4. The best model according to MAPE metric was
chosen.
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Figure 1 Correlation diagram between actual demand and 48 last demand measures
Figure 2 Relation between temperature and total demand of Uruguay
5. An optimization of hyperparameters of the best model
was performed using grid search techniques.
Finally, the best model found with the optimized
hyperparameters was used as a reference to train
the 24 hour forecasting model.
Generation of the 24 hour model
The best model congured with the best hyperparameters
obtained in the previous step, was used to generate twenty
four models M1, M2, ..., M24 to forecast day ahead hours.
The twenty four models were generated by applying the
following procedure:
1. Training and test sets were generated using the same
procedure described in Section 3.1. In the industrial
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R. Porteiro et al., Revista Facultad de Ingeniería, Universidad de Antioquia, No. 102, pp. 9-25, 2022
park scenario, the training set considered data from
2014 to 2016 and the test set considered data from
2017. In the substation scenario, the training set
considered data from January 2017 to June 2018 and
the test set from July 2018 to December 2018. In the
total demand scenario, the training set uses data from
2010 to 2016 and the test set considered data from
2017 to 2018.
2. Model Miwas trained using yias output, where yi
consists of the demand value corresponding to ihours
ahead, and input Xis enriched for models Mi, i > 2
with a new column consisting of the i−1prediction
obtained by the trained model Mi−1
3. Models Miare assembled to get a complete model M
to forecast the next 24 hours altogether.
3.2 Implementation
This section describes the implementation of the approach
described in Section 3.1.
Computational platform and software
The experimental evaluation was performed in an HP
ProLiant DL380 G9 high end server with two Intel Xeon
Gold 6138 processors (20 cores each) and 128 GB RAM,
from the high performance computing infrastructure of
National Supercomputing Center, Uruguay (Cluster-UY)
[34].
The proposed approach was implemented in Python.
Several scientic packages were used to handle data, train
models and visualize results. Used packages included
pandas, sklearn, and keras.
A generic module was implemented to train various
type of models following a pipeline processing.
Parameter tuning of the studied models were performed
using RandomizedSearchCV and GridSearchCV modules
from sklearn. The main details of the implementation
of the studied models are provided in the following
subsections.
Implementation of one-hour model
All one hour models described in this section use training
and test sets and data preprocessing presented in Section
3.1.
Base model: Linear regression. A linear regression
model was trained to be used as a baseline for the results
comparison. A recursive feature selection strategy [35]
was also applied on this model for each of the three
scenarios to determine the most important features. The
rest of features were removed from the dataset.
Ten features were selected based on their relative
importance in the industrial demand scenario:
•T1,T2,T24,T25 : demand values lagged.
•workingday: ag indicating whether the day of
measured value is a working day
•month: month on which the measure was taken.
•hour: hour of the day on which the measure was taken.
•dayofweek: day of the week on which the measure was
taken.
•day: day of month on which the measure was taken.
•year: year on which the measure was taken.
For the two residential scenarios, the ten most important
features were:
•T1,T2,T24,T25 : demand values lagged.
•temperature forecast: temperature external forecast
for the hour to be considered.
•workingday: ag indicating whether the day of
measured value is a working day
•month: month on which the measure was taken.
•hour: hour of the day on which the measure was taken.
•dayofweek: day of the week on which the measure was
taken.
•year: year on which the measure was taken.
The most relevant past demand values are T1,T2,T24, and
T25 because the current demand is highly correlated with
the immediate past demands and also with the demands
of the previous day at the same time, due to the daily
periodicity. It is worth noting that temperature is the fth
most important feature in scenarios that involve residential
demand, in spite of being excluded of the industrial model
due to the very low correlation with demand in that case.
When training hourly models, temperature external
forecast is considered for the corresponding hour.
The full analysis of feature selection experiments is
presented and discussed in Section 4.1.
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Selection of the best method. Seven regression models
were trained for each scenario, including the base model
considering the ten most important features and default
parameters. The studied models included trained using
the scikit-learn API [36]:
Linear Regression, MLP, Extra Trees, Gradient Boosting,
Random Forest, K-Neighobors and Ridge.
These models were evaluated using the MAPE metric
and the linear regression model was used to determine a
baseline performance value. The most accurate method
was chosen for further evaluation (this method is called
Mbest).
pred(t+1) =Mopt,(t+1)(obst, obs(t−1), ...,
obs(t−n))
pred(t+2) =Mopt,(t+2)(M(t+1), obst, ...,
obs(t−n))
. . .
pred(t+24) =Mopt,(t+24)(M(t+23), M(t+22) , ..., obst, ...,
obs(t−n))
(8)
Optimization of the best method. Parameter search
techniques were applied for each scenario to optimize
a model based on the best method obtained (Mbest).
The model Mbest trained with default parameters
was optimized using two standard tools available in
scikit-learn:
• GridSearchCV: combines an estimator with a grid
search preamble to tune hyper-parameters. The
method picks the optimal parameter from the grid
search and uses it with the estimator selected
according to a predetermined metric.
• RandomizedSearchCV: sets up a grid of
hyperparameter values and selects random
combinations to train the model and score. After
that, the method nds the best parameters setting
according to a predetermined metric.
The best parameter set obtained for Mbest are used
in an optimal model Mopt. The main details of the
implementation of the complete model are described in the
next subsection.
3.3 Implementation of the complete model
Model Mopt was optimized for predicting the next hour
and used for predicting any of the following 24 hours to
build the complete model. This decision was adopted
assuming that the forecasting quality of the parameter
setting obtained in the previous phase is independent of
the hour used as output.
To build the complete model, 24 instances of the optimized
model Mopt were trained. These instances are called
Mopt,i, dening the model trained to forecast the ith hour
ahead. The output yiused to train the model consisted of
the demand value for the i-th hour ahead.
For i > 2, the input Xiis enriched with a new set of
columns consisting in all predictions obtained by models
Mopt,1, ..., Mopt,i−1. Then, the complete solution uses a
different model for each time step to predict. Predictions
for previous time steps are used as input for the prediction
on the following time step.
This way, a hybrid strategy is applied to Mopt, described in
Equation 8.
Finally, the complete model Mopt is computed by
Equation 9. The output of the model is a 24 valued vector,
one prediction for each hour.
Mopt(t) = (pred(t+1), pred(t+2), ..., pred(t+24))(9)
4. Experimental analysis
This section presents the results of the experimental
analysis of the proposed computational intelligence
methods for day ahead electricity demand forecasting in
industrial and residential scenarios.
4.1 Recursive feature elimination
A feature selection analysis was performed using the
recursive feature elimination tool available in sklearn.
A model is specied and a number of features are
selected, and the tool works by recursively removing
features and building a new model (of the specied type)
on those remaining features.
The accuracy of the new model is used to identify the
features or combination of features that contribute the
most to predicting the target attribute.
The recursive feature selection tool was applied over
the linear regression method described in Subsection 3.2
in each of the three scenarios, to study up to ten features.
Figure 3,4and 5summarize the main results of the
analysis, reporting the relative importance of the ten most
important features for each scenario.
The most relevant conclusion of the feature selection
analysis is the high relative importance of temperature in
17
R. Porteiro et al., Revista Facultad de Ingeniería, Universidad de Antioquia, No. 102, pp. 9-25, 2022
T1T2working
day
T24 month hour T25 day of
week
day year
0 %
10 %
20 %
30 %
40 %
50 % 50.9%
17.4%
4.2%3.8%2.7%1.5%1.1%0.8%0.6%0.5%
Relative importance
Figure 3 Relative importance of most important features (percentage values), industrial scenario
T2T24 working
day
tempera-
ture
day of
week
hour T25 day year
0 %
10 %
20 %
30 %
40 %
50 % 46.9%
13.6%
7.8%6.6%5.8%
2.8%1.7%1.1%0.8%0.3%
Relative importance
Figure 4 Relative importance of most important features (percentage values), substation scenario
both scenarios related with residential demand. This is a
expected result due to the high incidence of temperature
on residential energy consumption, in contrast to its low
incidence on industrial energy consumption.
4.2 Experimental results on preliminary
models
Performance metrics dened in Section 3.1 were used to
evaluate the implementation of the one hour models as
described in Section 3.2.
Tables 1–3report the obtained results of the studied
forecasting models for each scenario. The best results are
reported in cells with green background.
Results reported in Table 1for the industrial scenario
indicate that three of the studied methods achieved the
best results regarding the analyzed metrics. Focusing on
MAPE, Extratreesregressor improved over MLP by 4.16%
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R. Porteiro et al., Revista Facultad de Ingeniería, Universidad de Antioquia, No. 102, pp. 9-25, 2022
T2T24 working
day
tempera-
ture
day of
week
hour T25 day year
0 %
10 %
20 %
30 %
40 %
50 %
54.1%
17.6%
7.2%6.7%4.5%2.1%0.8%0.7%0.6%0.4%
Relative importance
Figure 5 Relative importance of most important features (percentage values), total demand of Uruguay
and over RandomForest by 6.54%.
In turn, results reported in Table 2for the substation
scenario and in Table 3for the total demand scenario
indicate that Extratreesregressor was also the best model
in both cases. Additionally, in all scenarios the training
time of Extratreesregressor was approximately three
times shorter than RandomForest and six times smaller
than MLP.
Overall, ExtraTreesRegressor was the most effective
model for forecasting the next hour, outperforming all
the other methods regarding the three standard metrics
studied in each scenario. According to these results,
ExtraTrees was selected as the best method for showing
the best performance and a low training time. Thus, in
following sections Mbest =ExtraTreesRegressor.
4.3 Parameter tuning
Parameter tuning techniques described in Section 3.2
were applied on the best model Mbest.
The input for both grid search studied techniques in
the three data scenarios was generated using the
following values:
•n_estimators: [10, 50, 75, 100, 150];
•max_features: [auto, sqrt, log2];
•max_depth: [50, 100,150, 200, 250]
GridSearchCV achieved the best results with the same
parameters setting for all scenarios. The best parameter
setting found by the algorithm was n_estimators=50,
max_features=auto and max_depth=250.
Regarding MAPE metric, results computed using the
best conguration signicantly outperformed results of
the second best conguration: improvements were 14%
for the industrial demand scenario, 11% in the substation
demand scenario, and 12% in the total demand scenario.
4.4 Experimental results after parameter
tuning
Tables 4–6report the results of the ExtraTreesRegressor
model before and after parameter tuning for each
scenario. The best results are highlighted (cells with
green background).
Results computed by the tuned conguration of
ExtraTreesRegressor considerably improved the baseline
(non-tuned) version, regarding the three studied metrics.
In particular, MAPE reduced from 3.00% to 1.79%.
The performance improvement just demanded a negligible
increase on training time increases after parameter tuning
from 1.2s to 1.7s.
5. Experimental results of the
complete model
The forecast accuracy of the nal model was validated
by applying MAPEtot a metric that extends MAPE. Let
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Table 1 Results for each regression method in the industrial scenario
Regression method MAE MAPE RMSE Score Time (s)
LinearRegression 127.63 3.60 176.00 0.96 1.72
Ridge 127.63 3.60 176.00 0.97 0.09
KNeighbors 180.54 5.03 253.20 0.93 0.07
RandomForest 108.20 3.21 151.54 0.98 3.10
GradientBoosting 121.97 3.38 166.17 0.97 1.99
MLP 111.08 3.13 154.23 0.97 6.21
ExtraTrees 105.44 3.00 148.61 0.99 1.21
Table 2 Results for the studied regression method in the substation scenario
Regression method MAE MAPE RMSE Score Time (s)
LinearRegression 472.33 14.60 511.00 0.86 1.71
Ridge 473.11 14.91 521.11 0.85 0.11
KNeighbors 533.41 17.31 593.10 0.79 0.08
RandomForest 453.50 12.90 583.15 0.91 5.01
GradientBoosting 466.73 13.83 599.72 0.88 2.19
MLP 448.18 12.74 576.35 0.93 6.91
ExtraTrees 441.14 11.24 558.33 0.95 1.43
Table 3 Results for the studied regression method in the total demand scenario
Regression method MAE MAPE RMSE Score Time (s)
LinearRegression 255.13 6.60 317.10 0.91 1.62
Ridge 262.34 6.73 296.00 0.93 0.10
KNeighbors 367.44 10.33 501.33 0.88 0.17
RandomForest 228.44 6.12 321.43 0.95 3.15
GradientBoosting 261.2 6.48 284.71 0.94 1.79
MLP 244.03 6.18 274.30 0.94 6.11
ExtraTrees 208.14 5.99 265.11 0.96 1.26
Table 4 Comparative results of ExtraTrees before and after parameter tuning
Regression method MAE MAPE RMSE Score Time(s)
ExtraTrees before tuning 105.44 3.00 148.61 0.99 1.2
ExtraTrees after tuning 87.52 1.79 111.08 0.99 1.7
Table 5 Comparative results of ExtraTrees before and after parameter tuning
Regression method MAE MAPE RMSE Score Time(s)
ExtraTrees before tuning 414.14 11.24 558.33 0.95 1.43
ExtraTrees after tuning 220.12 6.38 269.81 0.97 5.71
MAPEhbe the MAPE value for a predicted horizon h, the
extension of MAPE to the complete testing set is dened by
Equation 10.
M AP Etot =∑k
i=1 M AP Eh
k(10)
Tables 7–9report the results for each one of the 24 models.
The expected behaviour is that the models trained
for highly correlated hours in the future respect to the
current hour, perform better than less correlated.
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R. Porteiro et al., Revista Facultad de Ingeniería, Universidad de Antioquia, No. 102, pp. 9-25, 2022
Table 6 Comparative results of ExtraTrees before and after parameter tuning
Regression method MAE MAPE RMSE Score Time(s)
ExtraTrees before tuning 208.14 5.99 265.11 0.96 1.26
ExtraTrees after tuning 100.08 5.17 131.83 0.98 1.28
This fact is due to predictability, and it is enhanced
when the correlation between input features and predicted
values is higher.
According to Figure 1, highly correlated demand values
correspond to the immediately preceding hours and from
the same hours of the day before.
Analyzing the obtained results for the MAPEtot metric for
each one of the 24 hourly models, the performance got
worse from i= 1 to 17 and then improved from i= 18
to 24. These results show that highly correlated demand
values performed better, as expected.
Finally, the complete model ETopt was applied. A
day-ahead hourly forecast demand curve was generated
for each time window for the testing set and the MAPEtot
value was calculated.
The nal result for the complete model was
MAPEtot = 2.55% in the industrial scenario,
MAPEtot = 5.17% in the industrial scenario and
MAPEtot = 9.09% in the substation scenario.
These results imply that the model obtained for the
day ahead demand forecasting of the industrial park
analyzed incurs in an error that is considered very low for
most of the studies that rely on these types of models [5,6].
For the substation scenario, there are no known previous
analysis in Uruguay to compare, but considering that the
group of homes connected to the substation is small, an
error of MAPEtot = 9.09% is considered acceptable.
For the total demand scenario, a relevant baseline for
comparison is provided by the prediction models currently
used by the National Administration of the Electric Market,
Uruguay (ADME, adme.com.uy). According to public
information reported in the ADME website, currently
used prediction models have errors (MAPEtot ) between
5.00% and 7.00%, with an average of MAPEtot = 5.52%.
The model evaluated in this article reported an error of
MAPEtot = 5.17%, which constitutes an excellent result,
improving over baseline ADME methods by 6.34%. This is
a very encouraging result for total demand prediction in
Uruguay.
Figures 6–8present samples of the real demand curve
and the predicted demand curve using the best model, for
a subset of the testing set considered in the experiments.
For the industrial demand scenario, the presented subset
corresponds to the complete data from year 2017. For the
substation scenario prediction, data from September 1st,
2019 to December 10th, 2019 are used. Finally, for the
total demand scenario the subset is the complete data
from year 2018.
The scenarios analyzed are representative of the studied
industrial and residential demands. The results obtained
with the model created were very good for all three cases.
6. Conclusions and future work
This article presented an approach to address the problem
of day ahead electricity demand forecasting.
Several machine learning models were presented
and studied for next hour forecasting. Recursive
feature selection was applied to select the most relevant
features to train the studied models. After a comparative
evaluation, the best model was optimized using random
search and grid search techniques.
A hybrid strategy (combining direct and recursive
approaches) was built based on the optimized model for
single hour prediction. It was applied to build a complete
day ahead electricity demand hourly forecasting model
in three scenarios: an industrial demand forecasting
scenario in Spain, a residential demand forecasting
scenario for a substation in Montevideo, and a total
demand forecasting scenario of Uruguay, including both
residential and industrial consumers.
The experimental evaluation was performed considering
data from January 1st, 2010 to December, 10th, 2019. An
extension of the MAPE metric was used to evaluate the
complete model for the three scenarios using testing sets.
For the industrial demand scenario, the evaluation of
the complete model reported a value of MAPEtot = 2.55%.
This is a very effective prediction result, which indicates
that the proposed algorithm is effective for addressing
the problem of day-ahead industrial demand forecasting,
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Table 7 MAPEtot score for each ETopt,i single hour model, industrial scenario
hour
1 2 3 4 5 6 7 8 9 10 11 12
MAPEtot 1.79 1.84 1.90 1.97 2.09 2.19 2.39 2.52 2.68 2.75 2.80 2.86
hour
13 14 15 16 17 18 19 20 21 22 23 24
MAPEtot 2.93 3.02 3.05 3.08 3.09 3.02 2.88 2.77 2.63 2.49 2.32 2.17
Table 8 MAPEtot score for each ETopt,i single hour model, substation scenario
hour
1 2 3 4 5 6 7 8 9 10 11 12
MAPEtot 6.38 6.55 6.77 7.02 7.45 7.80 8.5 8.98 9.55 9.80 9.98 10.19
hour
13 14 15 16 17 18 19 20 21 22 23 24
MAPEtot 10.44 10.76 10.87 10.98 11.015 10.76 10.27 9.87 9.37 8.87 8.27 7.73
Table 9 MAPEtot score for each ETopt,i single hour model, total demand scenario
hour
1 2 3 4 5 6 7 8 9 10 11 12
MAPEtot 3.63 3.73 3.85 3.99 4.24 4.44 4.85 5.11 5.43 5.58 5.68 5.80
hour
13 14 15 16 17 18 19 20 21 22 23 24
MAPEtot 5.94 6.13 6.18 6.25 6.26 6.13 5.84 5.61 5.33 5.05 4.70 4.40
Figure 6 Predicted demand and testing data curves of industrial demand
despite of using a model that do not consider weather
variables.
For the substation scenario, the evaluation of the
complete model reported a value of MAPEtot = 9.09%.
In this case, the proposed algorithm considered weather
variables due to the high correlation detected between
them and electricity demand. Results indicated that the
complete model can predict the demand with an acceptable
accuracy, in line with results from the literature, especially
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Figure 7 Predicted demand and testing data curves of substation demand
Figure 8 Predicted demand and testing data curves of total demand
considering that the variation of residential demand of
a small group of houses is signicantly higher than the
variation of industrial demand.
Finally, the application of the complete model to the
total demand scenario in Uruguay reported a value of
MAPEtot = 5.17%. In this scenario, only one weather
variable (temperature) was considered (humidity and wind
speed were excluded due to low relative importance).
Results obtained are very promising considering that
the models currently used in Uruguay, from the National
Administration of the Electric Market has a MAPEtot error
between 5.00% and 7.00%.
The main lines for future work are related to consider
deep learning techniques (e.g., recurrent/long-short term
memory neural networks) for enhancing the prediction,
since they can provide accurate results in scenarios that
are difcult for other simpler methods, i.e. when handling
large volumes of historical data. These techniques have
been successfully applied to forecasting problems with
complex state structures in explanatory variables, so they
can be useful tools to deal with uncertainty in electricity
demand.
Another line of future work consists in enriching the
studied models to generate mid-term and long-term
synthetic demand scenarios that preserve the statistical
structure of historical data. These kinds of models are very
relevant to be included in planning and operation models
based on new computational intelligence techniques
such as reinforcement learning or approximate dynamic
programming. Furthermore, prediction results can be
applied in practice for household energy planning by using
intelligent recommendation systems [37].
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R. Porteiro et al., Revista Facultad de Ingeniería, Universidad de Antioquia, No. 102, pp. 9-25, 2022
7. Declaration of competing interest
We declare that we have no signicant competing interests
including nancial or non-nancial, professional, or
personal interests interfering with the full and objective
presentation of the work described in this manuscript.
8. Acknowledgements
The research reported in this article was partly supported
by CYTED-CITIES network “Ciudades Inteligentes
Totalmente Integrales, Ecientes y Sostenbiles”.
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