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ICT Express 11 (2025) 80–86
www.elsevier.com/locate/icte

Multivariate bidirectional gate recurrent unit for improving accuracy of

energy prediction
Quota Alief Sias, Rahma Gantassi, Yonghoon Choi ∗
Department of Electrical Engineering, Chonnam National University, Gwangju 61186, South Korea
Received 22 May 2024; received in revised form 1 September 2024; accepted 4 October 2024
Available online 10 October 2024

Abstract
Energy prediction is an important process in energy management, especially regarding demand response. Energy predictions are often
carried out for load forecasting or energy generation forecasting of renewable energy. This paper explains the implementation of multi-
variables in the development of recurrence neural network models to predict load energy and generation energy. The proposed main model is
a multi-variate bidirectional GRU combined with a periodic feature pattern. The proposed model will also be compared with the fundamental
bidirectional models of the GRU and LSTM models. For load prediction, the variables used are all energy supply data and periodic features.
Meanwhile, for photovoltaic generation energy predictions, additional weather data is used because energy generation is very dependent on
solar radiation and ambient conditions. Load prediction data is built using daily and hourly energy prediction data. Meanwhile, solar energy
prediction is constructed with data every minute. The results show that the proposed model obtains the best prediction results for all test data
on a daily, hourly, or minute basis. The model also shows the fastest execution time performance compared to other models.
© 2024 The Authors. Published by Elsevier B.V. on behalf of The Korean Institute of Communications and Information Sciences. This is an open
access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Keywords: Energy prediction; Load; Multivariate; Photovoltaic

1. Introduction consumed. A lack of accuracy in forecasting electric loads can

result in blackouts that partially or entirely disable the power
The energy system flows electricity from generators as the
grid. Excess power generation can result in economic losses if
supply side to consumers as the demand side, with settings
over-estimations are made.
and monitoring carried out by the energy management sys-
Modern societies are affected by many factors, including
tem (EMS). EMS can be explained in a small scope, for
example, in only one house with several generating sources electricity consumption and generation. In order to ensure
such as solar panels, grids, and generators. EMS can also be affordability and stability in the energy sector, accuracy in
represented in a broader scope, such as one country that has predictions of generation and consumption is essential. Energy
several energy resources distributing electricity to consumers. prediction can be divided into long-term forecasting [1,2],
Consumers, on the demand side, use EMS to save electricity medium-term forecasting for up to several months [3], and
costs, while power generation companies on the supply side short-term of less than one day (hourly or minutely) [4]. Dur-
use EMS to ensure the energy generation process is efficient. A ing the past decade, artificial intelligence (AI) has developed
power plant must ensure that there are enough energy sources into an excellent tool for predictions. For example, AI algo-
available to meet the energy needs of consumers. Power sys- rithms have been used to analyze vast amounts of historical
tem operations require accurate prediction of demand energy data on electricity consumption and generation, allowing for
(known as load forecasting) due to the simultaneous generation more accurate forecasts of future demand and supply. This
and consumption of electric power. The results of the load has helped energy companies optimize their operations, reduce
forecasting process can also be used to generate the amount costs, and ensure a more reliable and efficient energy grid.
of electricity needed to match the amount of load that is Some examples of popular algorithms are Gated Recurrent
Units (GRU) [5] and Long Short-Term Memory (LSTM) [6],
∗ Corresponding author.
E-mail address: yh.choi@jnu.ac.kr (Y. Choi).
which can capture complex temporal dependencies in sequen-
Peer review under responsibility of The Korean Institute of Communica- tial data, making them ideal for energy prediction tasks [7].
tions and Information Sciences (KICS). The limitations of using GRU and LSTM for energy prediction
https://doi.org/10.1016/j.icte.2024.10.002
2405-9595/© 2024 The Authors. Published by Elsevier B.V. on behalf of The Korean Institute of Communications and Information Sciences. This is an
open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Q.A. Sias, R. Gantassi and Y. Choi ICT Express 11 (2025) 80–86

are that they are heavily dependent on historical data and can patterns as features to improve prediction results. For solar
struggle to adapt to sudden changes [8]. panel energy predictions, the model also uses historical data
from the weather. The model is tested with data from three
1.1. Related worked different countries and different forecasting ranges. Based on
these proposed models for conducting energy forecasting, this
LSTM and GRU are based on Recurrence Neural Network paper has the following contributions:
(RNN) so that historical information can be retained in the
1. Develops a multi-variable input model of the bi-direc-
output or used to generate a new result [9]. A vanishing
tional GRU model based on the proposed feature’s
severe/exploding gradient problem prevents the basic RNN
priority correlation in order to improve the accuracy of
from maintaining long-term temporal dependence [10]. This
the energy prediction.
problem is addressed by an improved RNN called LSTM,
2. Proposes new importance features that are all energy
which is based on long short-term memory [11]. By introduc-
data, periodic pattern, and weather of time-series data
ing a cell memory into the RNN, the LSTM network offers a
in order to predict energy recurrently.
promising solution for inhibiting gradient disappearance [12].
3. Predicts not only the consumption of energy based on
The next development is a GRU network that was found to
perform better than an LSTM network based on its minor its features but also the generation of energy using
errors and fewer training parameters [5]. This results in GRUs weather conditions as features.
being able to be trained faster and being better suited for large- 4. Provides big historical data simulations from three dif-
scale occupancy prediction [7]. GRU and LSTM models flow ferent countries to predict the energy at every minute,
information only in one direction, usually from the past into hour, and day.
the future [13]. Some tasks, however, can benefit from com-
bining information from previous and future contexts using a 2. Model development
bidirectional model [8].
Univariate time series analysis may be helpful when ana- 2.1. Basic RNN and LSTM network
lyzing individual variables, but it fails to capture real-world
systems’ complexity and make suboptimal predictions. Al- RNN is proposed to handle sequential time-series prob-
ternatively, multivariate analysis provides a more complete lems with the advantage of remembering historical informa-
understanding of dynamics by incorporating multiple vari- tion. However, the gradient vanishing and exploding limit
ables’ interactions and dependencies. This paper proposes its application in long-term dependencies due to the single
the use of multivariate inputs to predict energy demand and structure and parameter-solving algorithm based on backprop-
supply. Electric generation data from all electricity sources is agation through time [10]. Deriving from RNN, LSTM [11]
used to forecast load, while weather data is used to forecast and GRU [9] overcome the limitation of RNN. Fig. 1 shows
renewable energy. The main model developed is bidirectional the internal cell structure of RNN, LSTM, and GRU. On the
GRU and will be validated by comparing it with more fun- basis of RNN, a memory cell and three gates named forget
damental models. The recurrence algorithm is implemented gate, input gate, and output gate are introduced into LSTM,
based on periodic patterns to improve prediction results. which control the flow of information across LSTM cells
and determine the input, retention, and output of information,
1.2. Contributions respectively.

The contribution of this article is to propose energy fore- 2.2. Bidirectional gate recurrent unit
casting using more complete data and prioritizing the model
features. The important idea is a more comprehensive analysis The GRU fundamental equations are as follows:
based on the law of energy supply and demand balance.
z t = σ (Wz xt + Uz h t−1 + bz ), (1)
Electricity companies often try to increase the number of
energy consumers (demand) even though the energy sources rt = σ (Wr xt + Ur h t−1 + br ), (2)
in nature are limited. It is impossible to follow the pattern of h̃ t = tanh(Wh xt + Uh (rt ⊙ h t−1 ) + bh ), (3)
increasing consumer energy needs that are always increasing,
h t = (1 − z t ) ⊙ h t−1 + z t ⊙ h̃ t . (4)
while energy is limited. Energy forecasting is usually done
only from one side, only demand or only supply based on GRUs are RNN architectures with gating mechanisms that
previous data, which will not describe the real conditions regulate information flow within them. GRU uses special
according to the law of conservation of energy. gates, such as update and reset, to enable long-term memory
This journal proposes a discussion of energy forecasting and minimize computation loss. The update gate z t functions
with a more comprehensive data set between the balance of in the same way as input and forget gates in LSTM, determin-
supply and demand as well as weather and periodic patterns. ing how much of the previous information is retained for the
This paper explains how to build a modified GRU model present forecasting, which is expressed as (1). xt represents the
for energy prediction or forecasting using multi-variable in- input at time step t, h t is the hidden state at time step t, and σ
put from historical data. This paper also includes periodic denotes the sigmoid function. The rt in (2) is the reset gates,
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Fig. 1. Fundamental flowchart of a unit cell on RNN, LSTM, and GRU.

h̃ t in (3) is the candidate hidden state, and ⊙ represents dot

product of the multiplication process. The Bidirectional Gated
Recurrent Unit (Bi-GRU) is an extension of the GRU that
processes the input sequence in both forward and backward
directions, allowing the model to capture dependencies from
both past and future contexts. The backward pass equations for
Bi-GRU are similar to the forward pass equations. The process
of Bi-GRU is given in Algorithm 1.

Algorithm 1 Bidirectional GRU

Fig. 2. Forward and backward of bidirectional process.
Input: Input sequence X = {x1 , x2 , ..., x T }
Output: Output sequence Y = {y1 , y2 , ..., yT }
Initialize h 0 to zeros; such as slow convergence, selection of learning rates, and
for t = 1 to T do computation efficiency [8]. Each iteration of Adam’s learn-
Compute update gate z t using (1) ing rate is clearly defined, resulting in smooth parameter
Compute reset gate rt using (2) weight changes [9]. A further advantage of this method is
Compute candidate hidden state h̃ t using (3) its robustness to noisy gradients and ability to handle large
Update hidden state h t using (4) data sets [6,12]. The dropout regularization is set to 0.2, and
Concatenate forward and backward hidden states h t = the loss function uses mean absolute or squared error. The
t , ht
[h fwd bwd
] Compute output yt using yt = f (h t ) proposed model also uses a dense layer to be more prone to
end overfitting and the model parameters are shown in Table 1.
Korea meteorological administration (KMA) collects
2.3. Proposed multivariate Bi-GRU weather data on temperature, sunlight, humidity, precipitation,
and so on. KMA’s data center processes and manages collected
For an energy forecasting model to be effective, impor- data, which is then shown to the public on a daily basis. It is
tant features and complex variances must be extracted from possible to access PV power generation data and consumption
the data. GRU, however, can access only forward-looking energy from the Korean power exchange through the ministry
information and ignore valuable information coming from the of interior and safety (MIS). Our data are gathered from
reverse direction. To analyze data effectively between output the KMA and Grida Energy in Gwangju metropolitan city,
and input variables, this paper uses the Bi-GRU algorithm especially at Sinhyochon village, to become raw data as the
since it is a composite of forward and backward processes, Korean dataset.
as shown in Fig. 2. This paper has employed dropouts to
resolve problems like underfitting [10] and overfitting from 2.4. Model performance evaluation
the prior layer output [14]. A portion of unnecessary neurons
are eliminated temporarily by returning zero output from the The main data used is the history of one year, 2023, of
hidden layer to reduce model complexity [7]. As a result, it electrical energy in three different countries with testing data
can be used in the construction of a more robust network that from the last 1 month. The first data from Türkiye [15] was
is less affected by fluctuations in the input [13]. recorded every hour with 8760 rows and 16 columns. The
Adaptive moment estimation (Adam) optimizers are used second data is from energy records in Germany [16], which
because of their ability to accommodate many limitations, span 15 min and have a total of 35,040 rows and 21 columns
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Algorithm 2 Proposed Multivariate Bi-GRU

Input: Training dataset {(x (i) , y (i) )}i=1
T
, input x can be a
single-variable or multi-variables
Output: Trained multi-variate model
Training process:
Initialize multivariate input and select periodic features:
for i ← 1 to n do
Grouping data by chosen periodic pattern m for j ← 1
to m do
Compute z t using (1) , rt using (2) , h̃ t using (3) , h t
using (4) , Concatenate forward and backward hidden
t , ht
states h t = [h fwd bwd
] Fig. 3. Germany dataset.
end
end
Testing process:
Use multivariate input and select periodic features for i ← 1
to n do
Grouping data based on periodic pattern m for j ← 1 to
m do
Prediction by Multivariate Bi-GRU models by output
yt using yt = f (h t )
end
end

Fig. 4. Turkey dataset.

Table 1
Models parameters.
Parameters Value
energy in the future. Energy supply data for renewable energy
Batch size 64
(wind, solar, etc.) is obtained from the generation energy
Max epochs 300
Optimizer Adam forecast based on weather conditions. The energy supply data
Activation Swish is already available online on the open data platform for the
Loss function mae, mse German and Turkish datasets. In both of these data, the energy
Regularization dropout 0.2 sources used differ based on the power plants installed in each
dataset partition 80% training, 20% testing
country. The energy sources in Germany are shown in Fig. 3
and Turkey in Fig. 4. The weather data for the Korean dataset
is obtained from forecasting data sourced from KMA. The
of data. The latest data is Korean energy data [5], which data can be obtained from the weather are hour, precipitation,
is obtained every minute, so there are 525,600 rows and 13 wind speed, wind direction, humidity, ambient temperature,
columns of data. As part of the daily energy demand prediction dew point temperature, ground temperature, ground pressure,
test, Turkiye data is used to test the predictions. German data vapor pressure, local atmospheric pressure, sea level pressure,
is used to test hourly energy predictions from energy demand. sunlight, solar radiation (MJ/m2), cloud cover, and snow cover.
Korean data is used to test predictions of solar energy that can All training data is used to obtain proper weight and bias
be generated within time span of every minute. Preprocessing values for the proposed models. Next, testing is partitioned
data combines several tables into one dataset. For load energy first based on features and the periodic patterns chosen to carry
prediction, it combines electricity consumption and generation out forecasting, and a detailed process is given in Algorithm
data. For supply energy prediction, it combines generation and 2. Model evaluation regarding the error can be performed by
weather data. Data normalization is also applied to have clean calculating the root mean square error (RMSE), the mean
consistently formatted data. The dataset used is the result of average error (MAE), and the mean average percentage ac-
preprocessing grouping adjusted to the specified time scenario, curacy (MAPA) of the model. MAPA is calculated by sub-
Turkey for daily, Germany for hourly, and Korea for minutely. tracting 100% accuracy from the mean average percentage
Thus, these three data can represent predictions of accuracy error (MAPE) to calculate the model’s accuracy. In statistics,
testing every minute, every hour, and every day. the R-squared refers to the proportion of variance in the
The types of input data needed to forecast the energy dependent variable, which can be predicted by the independent
proposed in this article are energy supply and weather data. variable(s).
Energy supply data for non-renewable energy (gas, oil, coal, √∑
n 2
etc.) can be obtained from the fuel stock available in the i=1 (yi − ŷi )
RMSE = (5)
power plant warehouse or that is scheduled to be produced into n
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Fig. 5. Evaluation model performances of Turkiye, Germany, and Korea Dataset.

∑n ⏐ yi − ŷi ⏐2
⏐ ⏐
Table 2
i=1
M AE = (6) Result of model performances.
n
∑n | yi − yˆi | Model RMSE MAE MAPA R 2 score Time
i=1 yi Turkiye Dataset
M A P A = (1 − ) × 100% (7)
∑n n RNN 46.09 37.60 99.955 0.47 16.46
(yi − ŷi )2 LSTM 26.93 36.82 99.967 0.66 16.46
R 2 scor e = 1 − ∑i=1
n 2
(8) GRU 33.94 45.56 99.958 0.48 15.96
i=1 (yi − ȳ) Bi-LSTM 31.50 43.38 99.962 0.52 19.32
Here, yi represents the actual values, ŷi represents the pre- Bi-GRU 29.54 37.54 99.964 0.64 18.34
MBi-GRU 22.33 16.23 99.981 0.87 15.80
dicted values, and ȳ represents the mean of the actual values.
The summation is over n data points. R 2 scor e is equal to 1 Germany Dataset
RNN 446.3 372.3 99.927 0.39 16.85
when the predicted value is the same as the actual value and
LSTM 227.5 301.1 99.955 0.72 16.17
when the model perfectly fits the data. GRU 317.5 385.1 99.937 0.55 15.76
Bi-LSTM 319.6 382.7 99.936 0.56 16.98
3. Experimental result Bi-GRU 247.1 327.0 99.952 0.68 18.05
MBi-GRU 244.9 213.5 99.959 0.82 15.61
The proposed MBi-GRU model is tested by comparing the
Korea Dataset
prediction performance with the basic bidirectional models,
RNN 7.155 16.33 99.651 0.80 69.56
Bi-GRU and Bi-LSTM. Apart from that, we also use the basic LSTM 6.899 15.80 99.651 0.81 51.73
GRU, LSTM, and RNN models to validate the results of the GRU 7.048 16.03 99.635 0.81 71.49
model performance measurement. The results of the R 2 score Bi-LSTM 6.790 15.48 99.649 0.82 48.77
calculation do not need to be converted into a percentage by Bi-GRU 7.011 16.10 99.676 0.81 81.73
MBi-GRU 5.379 12.05 99.694 0.89 35.81
multiplying it by 100% like MAPA because the difference
in value can be observed well in each model. Meanwhile,
MAPA in percentage form is presented with 3 digits after the
comma because some of the values are almost the same. The
calculation of the simulation time for each model will also be for the Turkish data, while the daily periodic pattern is more
presented to see the prediction speed of each model. Fig. 5 important for the German and Korean data. This periodic
shows the RMSE, MAE, and Rsquare performance values of pattern is then used to predict as a feature of the model
all models presented in Table 2. according to algorithm 2 for both training data and testing
data. For data from Turkiye and Germany, load predictions are
3.1. Features analysis carried out using energy supply variables from all sources plus
a periodic pattern. Meanwhile, for the Korean dataset, solar
Data period patterns from daily, weekly, monthly, and quar- energy predictions are carried out not only with periodic loads
terly are analyzed in the three big datasets and sorted based or periodic patterns but also with weather data. Weather data
on the priority of their correlation value to energy predictions. is used because solar energy is very dependent on weather
Fig. 1 shows that the weekly periodic pattern is very important conditions.
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Fig. 7. Real and prediction energy of Korea dataset.

by obtaining the smallest error values, 5.379 for RMSE and

12.05 for MAE. The highest R 2 score is also obtained from the
proposed model at 0.89, indicating that the proposed model is
the most fit to accept variations in input data. The simulation
time of 35.81 s of the proposed model is also proven to
outperform all other comparison models.
The proposed model in this article adds seasonal weather
data and the periodic pattern. They are analyzed based on
Fig. 6. Real and prediction energy of Turkiye and German dataset. regression priorities so that the most influential trends will
be used as input features in the model. This feature priority
analysis is repeated to train the model so that over time the
3.2. Model performances model will be able to follow the ongoing trend according to
the proposed algorithm. External factors such as economic
The performance model in the prediction of the Turkiye crises, political natural disasters, and others will produce new
data set for one month from the testing data set shows that data that allow changes in trends from previous data. New
the smallest error obtained by the proposed model is 22.33 data will provide different trends that produce different priority
RMSE and 16.23 MAE. The highest R 2 score is also obtained feature analyses. By following the proposed algorithm, the
from this model with a figure of 0.87. The fastest time in model features will always continue to be changed according
one iteration cycle is also obtained by the proposed model of to the latest data trends to produce accurate predictions.
15.80 s. If the prediction results are zoomed in, as shown in
Fig. 6, the largest error value occurs on December 17. The
4. Conclusion
proposed model shows the best performance on that date with
values close to the actual load data. The proposed model explains the multi-variable imple-
Testing on German data shows that the RSME and MAE mentation of the Bi-GRU model to predict load energy and
values are greater than Turkish data because there is more generation energy from solar panels. Multivariate are con-
training data. The execution time in one iteration cycle also structed from several variables and selected based on priority
remains similar as shown in Table 2. Performances testing on in the feature selection process, and training and testing will be
the German data set for one month from the testing data set carried out according to the proposed periodic pattern. Predic-
shows that the smallest error obtained by the proposed model tions with only one variable (time series) can be improved with
is 244.9 of RMSE and 213.5 of MAE. The highest R 2 score is multiple variables based on essential features. The data used
also obtained from this model with a figure of 0.82, indicating consists of three countries: Turkey, Germany, and Korea. This
that the proposed model is the most fit to accept variations work evaluated the performance of all models by calculating
in input data. The fastest time in one iteration cycle is also errors of RMSE, MAE, MAPA, and Rsquare. The prediction
obtained by the proposed model of 15.61 s. execution times of all models are also compared, and the
The results of model testing on photovoltaic energy predic- proposed model shows the fastest time for all data sets. Thus,
tions for the Korean dataset over a period of one week (24 h the proposed model is proven to be able to predict the energy
× 7 days) from December 13 to 19 are shown in Fig. 7. Solar of demand and supply every minute, every hour, or every day.
energy is only generated around the time period from 06.00
to 18.00. The predictions of all models remain close to the CRediT authorship contribution statement
actual values even though there was a drop in solar energy
on December, 16, according to actual data. The predictions Quota Alief Sias: Writing – original draft, Visualization,
of the proposed model appear to be more precise following Methodology, Formal analysis, Data curation. Rahma Gan-
the generation energy data values on that date. This is proven tassi: Conceptualization. Yonghoon Choi: Validation.
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Declaration of competing interest [8] X. Li, X. Ma, F. Xiao, C. Xiao, F. Wang, S. Zhang, Time-series
production forecasting method based on the integration of Bidirec-
The authors declare that they have no known competing tional Gated Recurrent Unit (Bi-GRU) network and Sparrow Search
financial interests or personal relationships that could have Algorithm (SSA), J. Pet. Sci. Eng. 208 (2022) 109309.
appeared to influence the work reported in this paper. [9] Y. Yu, G. Hu, C. Liu, J. Xiong, Z. Wu, Prediction of solar irradiance
one hour ahead based on quantum long short-term memory network,
Acknowledgments IEEE Trans. Quantum Eng. (2023).
[10] S. Mahjoub, L. Chrifi-Alaoui, B. Marhic, L. Delahoche, Predicting
This research was supported by the Ministry of Educa- energy consumption using LSTM, multi-layer GRU and drop-GRU
tion of the Republic of Korea and the National Research neural networks, Sensors 22 (11) (2022) 4062.
Foundation of Korea (NRF-2023S1A5C2A07096111). [11] S. Emshagin, W.K. Halim, R. Kashef, Short-term prediction of
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