Electricity Price Forecasting Model based on Gated

Recurrent Units
Nafise Rezaei Roozbeh Rajabi Abouzar Estebsari
Faculty of ECE Faculty of ECE School of the Built Environment and Architecture
Qom University of Technology Qom University of Technology London South Bank University
Qom, Iran Qom, Iran London, United Kingdom
rezaii.n@qut.ac.ir rajabi@qut.ac.ir estebsaa@lsbu.ac.uk

Abstract—The participation of consumers and producers in the signal cannot be determined; and ii) the same IMF contains
demand response programs has increased in smart grids, which more than two main frequencies, which limits the noise
reduces investment and operation costs of power systems. Also, reduction [6]. These problems are addressed by Ensemble
with the advent of renewable energy sources, the electricity
market is becoming more complex and unpredictable. To EMD (EEMD) in [7], where the signals are integrated with
white Gaussian noise. However, adding noise can produce
arXiv:2207.14225v1 [cs.LG] 28 Jul 2022

effectively implement demand response programs, forecasting the

future price of electricity is very crucial for producers in the varying numbers of IMFs, whose consequence would be
electricity market. Electricity prices are very volatile and change observation of residual noise in the reconstructed signals
under the influence of various factors such as temperature, after the decomposition. The problem of imbalance EMD
wind speed, rainfall, intensity of commercial and daily activities,
etc. Therefore, considering the influencing factors as dependent decomposition scale was resolved when complete EEMD
variables can increase the accuracy of the forecast. In this paper, a with Adaptive Noise (CEEMDAN) [8] added white noise
model for electricity price forecasting is presented based on Gated components in the sifting process of each IMF. Selecting the
Recurrent Units. The electrical load consumption is considered as sensitive mode to distinguish relevant and irrelevant IMFs in
an input variable in this model. Noise in electricity price seriously an efficient way is a serious challenge in EMD-based methods.
reduces the efficiency and effectiveness of analysis. Therefore, an
adaptive noise reducer is integrated into the model for noise To tackle these challenges, we use CEEMDAN method which
reduction. The SAEs are then used to extract features from the potentially avoid the spurious modes and the reduction in the
de-noised electricity price. Finally, the de-noised features are fed amount of noise contained in the modes. In the following
into the GRU to train predictor. Results on real dataset shows that sections of this paper, some related works on electricity
the proposed methodology can perform effectively in prediction price forecasting are summarized, an improved version of
of electricity price.
Index Terms—Electricity Price, Gated Recurrent Unit (GRU),
CEEMDAN as well as a GRU model is introduced, and results
Feature Extraction, Stacked Auto Encoder(SAE). on evaluating the efficiency of the new modified method are
presented. The paper is concluded then with remarks.
I. I NTRODUCTION II. L ITERATURE R EVIEW
Current technology cannot store electricity in large amounts Creating high quality and effective forecasting models is
efficiently and cost effectively. Traditionally, the production becoming challenging and difficult in the new electricity
has been following the demand to ensure the balance, markets where most of consumers and producers take
and in smart grids with integration of more intermittent active roles in the market, more renewable resources with
renewable-sourced production, the demand is also following intermittent behavior are integrated into the network, and
the generation by appropriate demand side management more fluctuations and volatility are observed in the system
schemes [1]. Electricity demand depends on temperature, [5]. Reviewing literature shows the challenges resulted in
wind speed, precipitation, intensity of business and everyday developing several different methods and models by involved
activities, etc [2], [3]. These would result in price dynamics. stakeholders and researchers. These models can be classified
The electricity market actors find it challenging to forecast into three categories: statistical methods, artificial intelligence
the electricity load [4], generation, and price accurately and methods, and hybrid methods [9]. Statistical methods such
efficiently as the systems face more uncertainty, non-linearity as autoregressive moving average (ARMA) [10], autoregres-
and volatility. [5]. There are different methods and solutions to sive integrated moving average (ARIMA) [11], generalized
tackle the above-mentioned challenges. However, each method autoregressive conditional heteroskedasticity (GARCH) [12],
comes with its pros and cons. Empirical Mode Decomposition vector auto-regression (VAR) [13], and Kalman filters (KF)
(EMD) is a technique which decomposes a signal into Intrinsic [14], outperform other methods in stable power markets [15].
Mode Functions (IMFs) series and a residual with different However, the rapid changes of electricity prices with their
frequencies. Besides the advantages of using EMDs, there are nonlinear characteristics are not considered in the electricity
two main issues: i) the very extreme values at the two ends of price, which is a limitation of these methods [5]. Comparing
to these statistical methods, artificial intelligence methods,
instead, are capable of managing the nonlinear properties and
rapid changes [16]. There are many studies on the subject
of electricity price prediction based on artificial intelligence
methods such as artificial neural network (ANN) [17], [18],
recurrent neural network (RNN) [19], [20], and Extreme
Learning Machine (ELM) [21]. Nevertheless, applying only
traditional models may overlook the complex characteristics
of the original nonlinear and non-fixed electricity prices. To
overcome the disadvantages of single models, many hybrid
models have been developed for electricity price forecasting
that use data analysis methods to preprocess nonlinear and
nonstationary electricity price data before forecasting [16]. For
example, Zhang et al [22], developed a forecasting model
using WT models, generalized regression neural network
(GRNN) and GARCH models for electricity price forecasting,
which was validated in the Spanish electricity market and
performed well [23].

III. P ROPOSED M ETHOD

Increasing attention to the prediction of time series such
as Electricity Price indicates its potential application in
many fields. However, predicting time series is not an easy
task. How to deal with noise and extract features from
time series are the two main challenges to obtain accurate
predictions. Because time series are unstable and often contain
noise, data processing is necessary to reduce the effect of
noise on prediction. To solve these issues, a framework
for noise removing and feature extraction for electricity
price forecasting is proposed. In this framework, CEEMDAN
technique is used to decompose time series and eliminate
noise. A combination of stacked encoders and GRU is also
used for feature extraction and prediction. The diagram of the
proposed model is presented in Figure 1.

A. Adaptive Noise Reduction

Fig. 1. The proposed ANR-SAE-GRU method.
First, CEEMDAN technique [8] is used to decompose
electricity price into IMFs and a residual (R). This technique
can decompose a signal into a set of IMFs that include noise Step 2: When k = 1, 2, · · · , I the remaining kth residue is
modes and information modes. Therefore, it can be a powerful calculated as rk = rk−1 − IM Fk and r0 = X. Then rk +
compatible tool for extracting IMFs for signal reconstruc- 0 Ek (wi )(i = 1, 2, · · · , I) is decomposed by EMD to obtain
tion. The main issue is how to choose a sensitive mode to the first state of EMD and the definition of the (k + 1)th of
distinguish between IMFs and unrelated IMFs in an efficient the IMF is as follows:
way. residual has the lowest frequency and the frequency
distribution of IMFs is from top to bottom. It is assumed that I
the electricity price time series are X = {x1 , x2 , . . . , xm } [24]. 1X
IM Fk+1 = E1 (rk + k Ek (wi )) (2)
Step 1: The amount of Gaussian noise 0 wi (i = 1, 2, · · · , I) I i=1
is added to the electricity price and X + 0 wi is decomposed
by the EMD technique to obtain the first IMF: Step 3: Step 2 are repeated until the residue cannot be
decomposed anymore. The final residue is as follows:
I
1X
IM F1 = E1 (X + 0 wi ) (1)
I i=1 K
X
R=X− IM Fk (3)
In this relation, 0 is the adaptive coefficient and I is the k=1
number of adding Gaussian noise. In this paper, the value of
I is considered equal to 100. Where K is the IMF number and the electricity price time
series can be rewritten as follows: and converting it to labeled data is costly and requires
K
X professional knowledge. unsupervised learning, can learn a
X= IM Fk + R (4) feature display layer from unlabeled data. In addition, these
k=1 layers can be stacked to create deep grids. The proposed
In the next step, noisy and no-noise IMF must be model uses automatic stack encoder (SAE), which is a kind of
separated. To do this, the permutation entropy method is used. unsupervised learning method. Figure 2 shows the structure of
Permutation Entropy (PE) [25] is a method of calculating the a typical encoder. SAE consist of two parts, the encoder and
complexity of time series. The permutation entropy measures the decoder. In this paper, an auto encoder with three hidden
the randomness of time series. The higher the permutation layers is used, which extracts the required features to increase
entropy, the more noise will present in time series. IMF the accuracy of forecasting.
classification is based on the PE value of each IMF. The PE
value threshold is set at 0.7 based on several experiments in
different methods. If the PE value of an IMF is higher than the
threshold, the IMF contains noise; otherwise, the IMF is noise-
free. Assuming that P is the point of separation between high-
frequency noise IMFs and low-frequency noise-free IMFs, the
decomposed series can be expressed as follows:
P
X −1 K
X
X= IM F (k) + IM F (k) + R (5)
k=1 k=p

B. Noise Reduction
To reduce noise in the IMF with high-frequency noise, the
adaptive threshold and the threshold function are determined
using the following equations:
Fig. 2. Auto Encoder Structure.
s
2ln(m)
λ=σ
ln(k + 1) E. GRU Predictor
( (6)
sgn(w)(|w| − λ), |w| ≥ λ Gated Recurrent Unit (GRU) is especially effective in
wλ = learning the characteristics of longer time series, because
0, |w| < λ
learning the properties of long sequences requires less training
where σ, m and K are the standard deviation, length and weights and faster calculations compared to LSTM. The GRU
number of IMFs, respectively. The notation w is a noise value is therefore used here to process and learn the time domain
in the IMF. If the absolute value of w is greater than λ, it characteristics of the electricity prices extracted by SAE and
takes the value sgn(w)(|w| − λ), otherwise it takes 0 [24]. to improve the accuracy of the final model forecast.
C. Reconstruction
IV. E VALUATION AND R ESULTS
Noise-free time series are obtained by adding high-
frequency and low-frequency noise-free IMFs. Noise-free time In this section, the proposed framework is compared with
series are obtained as follows: the framework, which used LSTM to predict electricity price.
First, the dataset is described, and then the method for data
P
X −1 K
X sampling for evaluation is described. Three criteria are used
X= IM F (k) + IM F 0(k) + R (7) to evaluate the prediction models, including root mean square
k=1 k=p error (RMSE) and mean absolute error (MAE).
Where IM F 0(k) (k = P, P + 1, · · · , K) is equivalent to the
A. Dataset
high-frequency noise-free IMF and IM F (k) is equivalent to
low frequency noise-free IMF and R is the residue. The data used in this article are related to the price
of electricity consumed in Iran over three years. In this
D. Unsupervised Learning dataset, hourly electricity prices are collected. In total, the
To effectively analyze the price of electricity, an important size of the electricity price data set is 35040. In this study,
method is to extract the features and their interdependence information for 1186 days is used for training (28032 data
between variables. Feature extraction methods can be divided samples, one sample per hour) and 292 days for testing
into supervised learning methods and unsupervised learning (7008 samples). Iran electricity market price dataset is public
methods. Supervised learning method extracts functions from and can be downloaded from https://www.igmc.ir/Electronic-
labeled datasets. However, electricity price are often unlabeled Services/Power-Market-Deputy/Reports.
 TABLE I
C OMPARISON R ESULTS BASED ON RMSE AND MAE.

Measure RMSE MAE

Model
Horizon (Hour) 3 6 9 12 3 6 9 12
Proposed Method 2.86 3.89 5.18 6.48 1.8 2.83 3.92 5
ANR-SAE-LSTM 4.33 5.28 6.39 7.5 2.09 2.94 4 5.42

B. Evaluation Measures
The evaluation process was performed using evaluation
indicators named RMSE and MAE for both training and test
sets. Eqs. 8, 9 show these criteria, respectively.
v
u
u1 X N
RMSE = t (yi − yˆi )2 (8)
N i=1
N
1 X
MAE = |yi − yˆi | (9)
N i=1
where N is the total number of sample points. yi and yˆi are
the actual and predicted values of ith sample respectively. Fig. 3. Prediction results compared to actual values.

C. Results and discussion

In this section, the proposed GRU-based method is methods becomes larger as the forecast horizon increases. On
compared with the LSTM-based method on a electricity price average, for different forecast horizons, the proposed method
dataset to demonstrate the superiority of the proposed method is 1.54 and 0.3 superior to the other method in terms of RMSE
in electricity price prediction. Simulations are performed in and MAE criteria, respectively.
Python using NumPy, PyEEMD, and Keras libraries. Our approach is only to forecast electricity prices using
In our experiment, the prediction horizon is set to 3, 6, 9, historical electricity price data. However, since the price of
12 and the corresponding input data length is set to 24. Table I electricity depends on several factors, the effect of several
summarizes the prediction results according to different values dependent variables on the price forecast can be considered. In
of the forecast horizon. It can be seen that as the forecast future work, we will further explore the possible methods of
horizon increases, the forecasting error for both methods multi-objective forecasting. In the proposed method, only one
becomes larger, but the proposed method works better for all GRU predictor is used in the aggregation stage, while several
three criteria and has the least error growth. On average, for predictors such as LSTM and GRU can combine consumption
different forecast horizons, the proposed method is 1.54 and patterns in a group.
0.3 superior to the other method in terms of RMSE and MAE R EFERENCES
criteria, respectively.
[1] J. Bauer, Upgrading Leadership’s Crystal Ball. CRC Press, 2013.
Figure 3 shows the forecast results of the methods compared [2] R. Weron, Modeling and forecasting electricity loads and prices: A
to the actual cost values for 12 days. We can see that the statistical approach. John Wiley & Sons, 2007.
proposed method provides the predicted values closer to the [3] A. Estebsari and R. Rajabi, “Single residential load forecasting using
deep learning and image encoding techniques,” Electronics, vol. 9, no. 1,
actual values than the ANR-SAE-LSTM. 2020. [Online]. Available: https://www.mdpi.com/2079-9292/9/1/68
[4] R. Rajabi and A. Estebsari, “Deep learning based forecasting of
V. C ONCLUSION individual residential loads using recurrence plots,” in 2019 IEEE Milan
To deal with noise in electricity price, an ANR method PowerTech, 2019, pp. 1–5.
[5] S.-C. Chan, K. M. Tsui, H. Wu, Y. Hou, Y.-C. Wu, and F. F. Wu,
was used in this paper. Permutation Entropy (PE) is used to “Load/price forecasting and managing demand response for smart
determine the boundary point between noisy and low-noise grids: Methodologies and challenges,” IEEE signal processing magazine,
IMFs, and an adaptive threshold function is constructed to vol. 29, no. 5, pp. 68–85, 2012.
[6] J. Zhang, Y. Guo, Y. Shen, D. Zhao, and M. Li, “Improved ceemdan–
eliminate noise from high-frequency IMFs. SAE was used wavelet transform de-noising method and its application in well logging
to extract features that fully take into account electricity noise reduction,” Journal of Geophysics and Engineering, vol. 15, no. 3,
price forecasting performance and prevent overfitting, the pp. 775–787, 2018.
[7] Z. Wu and N. E. Huang, “Ensemble empirical mode decomposition:
GRU model was employed to obtain a robust forecaster. The a noise-assisted data analysis method,” Advances in adaptive data
proposed GRU-based method was compared with the LSTM- analysis, vol. 1, no. 01, pp. 1–41, 2009.
based method on a power consumption price dataset. Two [8] M. E. Torres, M. A. Colominas, G. Schlotthauer, and P. Flandrin, “A
complete ensemble empirical mode decomposition with adaptive noise,”
criteria of RMSE and MAE were considered for the results in 2011 IEEE international conference on acoustics, speech and signal
comparsion. The results showed that the forecast error for both processing (ICASSP). IEEE, 2011, pp. 4144–4147.
 [9] M. Lei, L. Shiyan, J. Chuanwen, L. Hongling, and Z. Yan, “A review forecasting via the application of artificial neural network based models,”
on the forecasting of wind speed and generated power,” Renewable and Applied Energy, vol. 172, pp. 132–151, 2016.
sustainable energy reviews, vol. 13, no. 4, pp. 915–920, 2009. [19] S. Anbazhagan and N. Kumarappan, “Day-ahead deregulated electricity
[10] F.-L. Chu, “Forecasting tourism demand with arma-based methods,” market price forecasting using recurrent neural network,” IEEE Systems
Tourism Management, vol. 30, no. 5, pp. 740–751, 2009. Journal, vol. 7, no. 4, pp. 866–872, 2012.
[11] T. Jakaša, I. Andročec, and P. Sprčić, “Electricity price [20] U. Ugurlu, I. Oksuz, and O. Tas, “Electricity price forecasting using
forecasting—arima model approach,” in 2011 8th International recurrent neural networks,” Energies, vol. 11, no. 5, 2018. [Online].
Conference on the European Energy Market (EEM). IEEE, 2011, pp. Available: https://www.mdpi.com/1996-1073/11/5/1255
222–225. [21] X. Chen, Z. Y. Dong, K. Meng, Y. Xu, K. P. Wong, and H. Ngan,
[12] R. C. Garcia, J. Contreras, M. Van Akkeren, and J. B. C. Garcia, “A “Electricity price forecasting with extreme learning machine and
garch forecasting model to predict day-ahead electricity prices,” IEEE bootstrapping,” IEEE Transactions on Power Systems, vol. 27, no. 4,
transactions on power systems, vol. 20, no. 2, pp. 867–874, 2005. pp. 2055–2062, 2012.
[13] H. Nyberg and P. Saikkonen, “Forecasting with a noncausal var model,” [22] J. Zhang, Z. Tan, and C. Li, “A novel hybrid forecasting method using
Computational statistics & data analysis, vol. 76, pp. 536–555, 2014. grnn combined with wavelet transform and a garch model,” Energy
[14] H. Takeda, Y. Tamura, and S. Sato, “Using the ensemble kalman filter Sources, Part B: Economics, Planning, and Policy, vol. 10, no. 4, pp.
for electricity load forecasting and analysis,” Energy, vol. 104, pp. 184– 418–426, 2015.
198, 2016. [23] D. Wang, H. Luo, O. Grunder, Y. Lin, and H. Guo, “Multi-step ahead
[15] F. J. Nogales, J. Contreras, A. J. Conejo, and R. Espı́nola, “Forecasting electricity price forecasting using a hybrid model based on two-layer
next-day electricity prices by time series models,” IEEE Transactions decomposition technique and bp neural network optimized by firefly
on power systems, vol. 17, no. 2, pp. 342–348, 2002. algorithm,” Applied Energy, vol. 190, pp. 390–407, 2017.
[16] W. Yang, J. Wang, T. Niu, and P. Du, “A novel system for multi-step [24] F. Liu, M. Cai, L. Wang, and Y. Lu, “An ensemble model based on
electricity price forecasting for electricity market management,” Applied adaptive noise reducer and over-fitting prevention lstm for multivariate
Soft Computing, vol. 88, p. 106029, 2020. time series forecasting,” IEEE Access, vol. 7, pp. 26 102–26 115, 2019.
[17] D. Singhal and K. Swarup, “Electricity price forecasting using artificial [25] C. Bandt and B. Pompe, “Permutation entropy: A natural complexity
neural networks,” International Journal of Electrical Power & Energy measure for time series,” Phys. Rev. Lett., vol. 88, p. 174102, Apr
Systems, vol. 33, no. 3, pp. 550–555, 2011. 2002. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevLett.
[18] I. P. Panapakidis and A. S. Dagoumas, “Day-ahead electricity price 88.174102