SPECIAL SECTION ON KEY ENABLING TECHNOLOGIES FOR PROSUMER ENERGY MANAGEMENT

Received June 29, 2020, accepted July 30, 2020, date of publication August 4, 2020, date of current version August 17, 2020.
Digital Object Identifier 10.1109/ACCESS.2020.3014241

A Deep Learning Based Hybrid Framework for

Day-Ahead Electricity Price Forecasting
RONGQUAN ZHANG 1,2 , GANGQIANG LI 3, AND ZHENGWEI MA 1,2
1 College of Urban Transportation and Logistics, Shenzhen Technology University, Shenzhen 518118, China
2 College of Mechatronics and Control Engineering, Shenzhen University, Shenzhen 518060, China
3 College of Electronics and Information Engineering, Shenzhen University, Shenzhen 518060, China

Corresponding author: Zhengwei Ma (mazhengwei@sztu.edu.cn)

This work was supported in part by the National Natural Science Foundation of Guangdong Province under Grant 2018A030310523,
in part by the Special Innovation Project in Higher Education of Guangdong Province under Grant 2018KTSCX351, and in part by the
Teaching Reform Project in Higher Education of Guangdong Province (Title: Study on the Practical Teaching System of Multi-Integration
of School-Enterprise and Industry-Education for Automotive Service Engineering Major Under the Background of New Engineering).

ABSTRACT With the deregulation of the electric energy industry, accurate electricity price forecast-
ing (EPF) is increasingly significant to market participants’ bidding strategies and uncertainty risk control.
However, it remains a challenging task owing to the high volatility and complicated nonlinearity of electricity
prices. Aimed at this, a novel hybrid deep-learning framework is proposed for day-ahead EPF, which includes
four modules: the feature preprocessing module, the deep learning-based point prediction module, the error
compensation module, and the probabilistic prediction module. The feature preprocessing module is based
on isolation forest (IF), and least absolute shrinkage and selection operator (Lasso), which is used to detect
outliers and select the correlated features of electricity price series. The point prediction module combines
the deep belief network (DBN), long-short-term memory (LSTM) neural network (RNN), and convolutional
neural network (CNN), and is employed to extract complicated nonlinear features. The residual error between
forecasting price and actual price can be reduced based on the error compensation module. The probabilistic
prediction module based on quantile regression (QR) is used to estimate the uncertainty under various
confidence levels. The PJM market data is employed in case studies to evaluate the proposed framework,
and the results revealed that it has a competitive advantage compared with all of the considered comparison
methods.

INDEX TERMS Electricity market, day-ahead electricity price forecasting, feature preprocessing, deep
learning, error compensation, probabilistic forecasting.

I. INTRODUCTION influence of competitors’ bidding behavior and power system

Distributed energy resources (DERs), such as wind power operating conditions, EPF presents typical non-linearity and
and photovoltaic power, play a vital role in the electricity high volatility [5]. Facing these challenges, the day-ahead
market [1]. In order to improve congestion management, electricity price prediction methods that have been published
promote clean energy, and optimize resource allotment of in literature can be divided into three categories, which are
the power market, deregulations of the electric energy indus- physical methods, statistical methods, and machine learning
try that encourages market participants to boost competition methods.
and capture electricity prices have been established in many Physical methods are based on security-constrained unit
regions [2]. Following market rules, day-ahead electricity commitment (SCUC) and security-constrained economic dis-
price forecasting (EPF) is a top priority for proper bidding patch (SCED) models, which simulate the day-ahead elec-
strategies and risk-control [3]. If the market participant has a tricity market clearing in terms of boundary conditions and
preferable day-ahead EPF, it can provide a reasonable bidding physical theories [6]. Although physical methods is efficient
strategy to maximize its payoff [4]. However, due to the from a forecasting logic perspective, the major issues here
is that SCUC and SCED models require massive volumes of
The associate editor coordinating the review of this manuscript and real-time operating data, such as the transmission capability
approving it for publication was Jiayong Li. of lines, electricity load, and competitors’ bidding, which

This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
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will lead to complex computation [7]. And it will grow belief network (DBN) [21], deep reinforcement learning [22],
worse when physical methods encounter unexpected inputs long short-term memory (LSTM) [23] and convolutional
during prediction. Therefore, physical methods maybe not neural network (CNN) [24]. In [25], the authors developed
very suitable for day-ahead EPF. Statistical methods aim to multi-input and multi-output LSTM models to forecast elec-
unveil the dynamic trend between historical electricity price tricity load for the time specified by the user. Numerical
series using curve fitting. This method has advantages in results demonstrate that the LSTM exhibits the ability to
high-speed performance, model simplicity, and convenience. improve forecasting accuracies compared to SVM, ANN, and
Statistical models include Autoregressive Moving Average recurrent neural network (RNN). In [26], [27], the authors
(ARMA) [8], generalized autoregressive conditionally het- proposed a novel hybrid method based on wavelet trans-
eroskedastic (GARCH) [9], and fuzzy theory [10]. In [8], form and CNN for renewable energy forecasting. Wavelet
the authors proposed a novel EPF algorithm that includes transform was employed to decompose the raw renewable
the results from multiple linear regression (MLR) model energy data into a set of better outlines series, and CNN was
with an ARMA and Holt-Winters models. In [9], the authors applied to extract the complicated nonlinear features. The
exploited the GARCH methodology to predict next-day elec- experimental results also demonstrated that the forecasting
tricity prices. The authors in [10] proposed a hybrid model performance of deep learning models performed all of the
combining wavelet, firefly algorithm, and fuzzy adaptive considered shallow learning models in terms of seasons and
resonance theory map (ARTMAP) for day-ahead EPF. How- prediction horizons. To the authors’ knowledge, deep learn-
ever, since the prerequisites for using statistical methods are ing method for day-ahead EPF has received little attention
mainly linear modeling, most of them become more diffi- compared with wind energy forecasting, load forecasting,
cult for predicting the high-dimensional nonlinear electricity and photovoltaic power forecasting in the field of energy
price series. system.
Machine learning methods can broadly split into two types: The existing studies only focus on the application of
shallow learning models and deep learning models [40]. feature extraction for point prediction, there are other
Shallow learning models are based on the principle of error issues unresolved. First, the raw features with outliers and
minimization, and usually have better performance than high-dimensional data can make the feature extractions
physical methods and statistical methods. Due to their notable more complex. Therefore, feature preprocessing techniques
capabilities in extracting features, they has been one of the will be crucial to anomaly detection (reduce outliers) and
most common methods for electricity prices forecasting. identify the correlated features to the corresponding fore-
Shallow learning models include support vector regression cast time (reduce the dimension) [28]. Second, the single
(SVR) [11], artificial neural network (ANN) [12] and regres- forecasting model may result in large forecasting residu-
sion tree [13]. In [14], the authors employed the hybrid model als between the forecast and actual values. Therefore, it is
based on SVR and feature selection techniques to predict reasonable to reduce the forecasting residuals by an error
the electricity price spikes. In [15], [16], the authors utilized compensation model, which is perceived as a post-processing
ANN and similar daily load and prices of the corresponding learning model to forecasting error shifting trends. Finally,
forecasting day to predict day-ahead electricity prices in the considering the model misspecification and data noise, point
PJM market. The simulation results show that the average prediction models fail to evaluate the forecasting uncertainty
of mean absolute percentage error (MAPE) for the proposed presented in electricity prices, which is not conducive to
method is up to 9.75%. The authors in [17] developed a counteractive risk. Consequently, the probabilistic day-ahead
hybrid forecasting model based on a seasonal component EPF model that can describe these uncertainties becomes
auto-regressive model and an ANN model, which is applied more meaningful [29].
to forecast day-ahead electricity prices with tolerable perfor- In light of this, we need to combining feature preprocess-
mance. ing techniques, deep learning-based point prediction mod-
However, the above methods for EPF concentrate only on els, error compensation module, and probabilistic prediction
shallow learning models. Because shallow machine learning model to rethink and design a hybrid deep learning frame-
models are prone to over-fitting and gradient disappearance, work for day-ahead EPF in this article. The main contribu-
they are restricted in processing big data and complicated tions of this article are presented as follows:
nonlinear problems [18]. With the development of intel- (1) A novel feature preprocessing module consisting
ligence optimization theories and computer technology in of isolation forest (IF) [30] and least absolute shrinkage
recent years, deep learning methods, as a potential forecast- and selection operator (Lasso) [31] is proposed, which
ing technology, is experiencing rapid growth to circumvent helps to anomaly outliers and identify the correlated
these problems, and successful applications to pattern recog- features.
nition, text processing, and fault location [19]. In addition, (2) The deep learning-based point prediction module com-
deep learning methods have also been widely employed bining three types of deep-learning models (DBN, LSTM,
for short-term renewable energy forecasting and electric- and CNN) is developed and contrasted to extract complicated
ity load forecasting in the energy system. Deep learning nonlinear features of electricity price, and their forecasting
methods combine deep neural network (DNN) [20], deep performance is compared with shallow learning models.

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FIGURE 1. The structure of the proposed framework.

(3) For the first time, the residuals between the forecasting reduction (this is, features selection). This article concen-
electricity price and actual electricity price are trained to trates on IF based anomaly detection and Lasso based features
correct the error from the point predicted values of electricity selection, as described in Section III-A.
price by an error compensation module, for which the inputs
are the validation set errors. B. DEEP LEARNING-BASED POINT PREDICTION MODULE
(4) The uncertainties registered in electricity price are Point prediction module based on DBN, LSTM, and CNN
initially evaluated using a probabilistic prediction module aims to extract complicated nonlinear features of day-ahead
concerning data noise and model misspecification (inspired electricity prices. DBN is semi-supervised learning for
by quantile regression (QR)) [32]. weight initialization, but CNN and LSTM belong to a kind
The rest of the paper is organized as follows. Section II of supervised learning. Furthermore, what their similar char-
introduces the proposed forecasting framework; Section III acter is: a quadratic loss function to compute weights can be
describes the experimental methods; Section IV describes the minimized by using BP based on various gradient descent
assessment indicators of point and probabilistic forecasting methods [33], such as stochastic gradient descent (SGD),
performance; Section V shows and discusses case studies of momentum gradient descent (MGD), Ada gradient descent
the PJM electricity market. Finally, Section VI presents the (Ada), and RMSProp gradient descent (RMSProp). The
concluding remarks. details are described in Section III-B.

II. THE DESCRIPTION OF THE PROPOSED FORECASTING C. ERROR COMPENSATION MODULE

FRAMEWORK Error compensation module can help to reduce the residual
In this section, a novel day-ahead EPF framework, which error between the forecasted and actual values. In order to
includes feature preprocessing module, deep learning-based reflect error changing trends, the inputs for the error correc-
point prediction module, error compensation module, and tion module should interlink with the validation set errors,
probabilistic prediction module, is proposed. Besides, except for correlated features obtained from the point predic-
the electricity price data is divided into three parts: training tion module. To simplify the discussion, the feature extrac-
set, validation set, and test set, as shown in Figure 1. tion method of error correction module remains the same as
point prediction module, which means that if point prediction
A. FEATURE PREPROCESSING MODULE module uses CNN, error correction module also uses CNN,
The raw data gathered from different websites are as shown in Figure 1.
prone to various clutters, such as high dimensions, out-
liers, and missing values, et al., resulting in undesirable D. PROBABILISTIC PREDICTION MODULE
forecasting performance. Therefore, this clutter must be The uncertainty showed in electricity price data are inevitable
preprocessed to guarantee application potential for the because of model misspecification and the lack of all
deep-learning point prediction module. Typically, feature the correlated features of the corresponding forecasting
preprocessing techniques incorporates anomaly detection, day.
removing outliers, filling missing data (regularly takes Consequently, in this article, a probabilistic prediction
the similar-day value as fillers), normalization (applies to module is to describe these uncertainties according to the QR,
net-work training of backpropagation (BP)), and dimensional as described in Section III-C.

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III. THE DESCRIPTION OF EXPERIMENTAL METHODS and activation probability of each neuron for the visible layer
A. FEATURE PREPROCESSING MODULE (binary state v and offset a) and the hidden layer (binary state
1) ISOLATION FOREST h and offset b) can be respectively deduced as follows:
Conventional anomaly detection methods are generally based X X XX
E(v, h) = − aTs vs − bTk hk − hk Wk,s vs (3)
on a hypothesis that better outlines follow a given region, such
s k k s
as mean-square error method and quartile method, which X
could result in false valuation or partial detection. Conversely, p(vs = 1|h) = σ (as + wk,s hk ) (4)
IF without making any prior assumptions (contain multiple k
X
isolation trees of no child node or two child nodes) utilizes p(hk = 1|v) = σ (bk + wk,s vs ) (5)
anomaly score to isolate outliers [34], which is defined as s
follows: where E(v, h) is the energy function. σ is the logistic sigmoid
E(h(x))
S(x, n) = 2 c(n) (1) function. P(hk = 1|v) and P(vs = 1|h) respectively represent
the activation probability of v at a given h and the activation
where E(h(x)) is the average length of sample x from a set of probability of h at a given v.
isolation trees. c(n) represents the average path length with Once the energy function and activation probability for
n samples obtained from a binary search tree [34]. Once each neuron of RBM are required, the objective function Lθ,s
anomaly scores for each sample x are solved, lower val- of DBN is defined as follows:
ues (outliers) can manually be exclude based on the abnormal X X E(v, h)
proportional coefficient ζ . Lθ,S = log( ) (6)
s
Z
k
2) LEAST ABSOLUTE AND SELECTION OPERATOR where Z is the partition function.
In general, feature selection aims to choose the attributes Then, the model parameters of the visible and hidden layers
relevant to the corresponding forecast day. Compared to tradi- can be updated using the derivative of Lθ,s based on Bayesian
tional methods such as Pearson correlations, chi-square tests, statistics theory and Gibbs sampling [39], as shown below:
and information gain, Lasso can effectively tackle continuous n o
time series and parameter estimation problems [35]. There- Wk,s = Wk,s +η P(hk = 1|v)vT − P(h∗k = 1|v∗ )(v∗ )T (7)
fore, feature selection based on Lasso is introduced in this a = a + η(v − v∗ ) (8)
article, which is as follows:
  2  b = b + η{p(hk = 1|v) − P(h∗k = 1|v∗ )} (9)

X n p 

If pre-trained weights have concluded in an unsupervised
X
(r, βj ) = arg min y−r − βj xij  ,

 i=1 j=1

 manner, as described in Section III-B, the whole network
weights for DBN can finally be tuned by BP algorithm.
p
X
s.t. βj ≤ ϕ (2) 2) CONVOLUTIONAL NEURAL NETWORK
j=1
Convolutional neural network (CNN) is proposed based on
where xi,j is the time-shared load or historical electricity biological information transfer, in which the connection
prices for the jth feature in the ith time series. r and βj are relation among neurons references the cat’s cerebral opti-
regression coefficients. cal cortex, and it is found that it can effectively lessen
From (2), it can be obviously seen that time-shared uncor- the complexity of network structures [40]. Based on this,
related features could be eliminated when a feature selection CNN has two advantages, which is translation invariance and
coefficient ϕ is smaller. shared-weights technique [41]. Typical CNN consists of an
input layer, stacking convolutional layers with sub-sampling
B. DEEP LEARNING-BASED POINT PREDICTION MODULE layers, a fully connected layer, and an output layer, as shown
1) DEEP BELIEF NETWORK in Figure 4.
Deep belief network (DBN) contains stacked restricted Boltz-
mann layers (RBM) for unsupervised pre-training and a logis- a: INPUT LAYER
tic regression layer for forecasting outputs [36], which is Compared with pattern recognition, EPF has distinct char-
shown in Figure 2. As an important part of DBN, RBM is acteristics. Its input features are 1-dimensional (1D) data,
a simple binary network model which includes a visible layer whereas the stacking convolutional and down-sampling lay-
to accept inputs from the upper hidden layer, and a hidden ers for CNN are two-dimensional (2D) data. Thus, the input
layer to extract features from the visible layer, as shown layer serves as a dimension transducer to convert the 1D day-
in Figure 3. There is no interconnection between neurons ahead electricity price data series into a 2D image, and the
in the visible layer and hidden layer, but fully connected size of the image should be determined by the number of
neural networks exist neurons between various layers [37]. correlated features from feature preprocessing module. The
According to Boltzmann distribution [38], energy function process is described as follows: (1) The size of the image

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FIGURE 2. DBN architecture.

FIGURE 5. The architecture of LSTM.

c: SUB-SAMPLING LAYER
Sub-sampling layer aims to achieve an information filtering
task, in which the single point statistical result is obtained
by replacing the pooled feature map with sub-sampling
function to avoid over-fitting due to no specificity deduc-
tions [42]. As a sub-sampling function, the max-pooling
function max(kijl−1 ) can easily keep the invariance of the local
FIGURE 3. RBM architecture. extraordinary feature, which is as follows:
l−1
ylj = f (βjl∗ max(xi,j ) + clj ) (11)

d: FULLY CONNECTED LAYER

Full connected layer for CNN is equivalent to the hidden layer
of the traditional feedforward neural network. Compared with
convolutional and pooling layers, the fully connected layer
has the most network parameters and can handle 1D data.
Here, the full connection layer can be applied to convert the
2D image from the sub-sampling layer into 1D electricity
FIGURE 4. The architecture of CNN. price data, which acts as the input of the output layer and
executes the final forecasting outputs.

m∗ m is pre-determined by the number of correlated features 3) LONG-SHORT-TERM MEMORY NEURAL NETWORK

N from the feature preprocessing module. (2) Taking the first Long short-term memory neural network (LSTM RNN) is
m correlated features as the first row of the image, the next an improved RNN. LSTM RNN is proposed to process the
m correlated features as the second column of the image, time series data with long time span, because RNN may cause
et al. (3) Putting the maximally correlated feature to fill in the problems of vanishing gradient and gradient explosion in
the gaps of null elements m∗ m – N for the last row of the it [43]. The hidden layer of LSTM RNN is composed of mem-
image. ory/forget gates, input gates, and output gates replace, which
are to control the information flows process and therefore has
b: CONVOLUTIONAL LAYER
the memory capacity for long historical time series [44]. The
Convolution layer adopts the convolutional function as the structure of LSTM RNN for information flows is shown in
operator to convolve network weights with its previous Figure 5.
layer’s feature maps with a small receptive field via weight In Figure 5, tanh and σ are respectively the hyperbolic
sharing technique, and forms an output feature map in terms tangent activations and sigmoid function. xt and Ct is respec-
of a user-defined activation function as follows: tively input and cell states at the moment of t. Ct−1 and ht−1
are respectively cell states and output at the moment of t−1.
X
ylj = f ( xil−1∗ kijl + blj ) (10)
i∈Im
The output values of the forget gate ft uses xt & ht−1 as input
to remember the effective information Ct−1 according to a
where Im is the number of feature map. kijl and blj are respec- sigmoid function. The output value of the input gate it uses
tively the weight and offset for the ith input map and the jth xt & ht−1 as input to determine cell states Ct by a combination
output map corresponding to the lth convolution layer respec- of a candidate cell state Ct 0 . The output value of the output
tively. f is a user-defined activation function. ∗ represents a gate ot is used to adjust the output value ht of based on Ct
convolutional operation. with a sigmoid function and tanh function. The mathematical

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TABLE 1. The advantages and disadvantages of various gradient descent probabilistic electricity price tends to follow given distribu-
methods.
tions, such as Gaussian [47], [48] and logistic [49]. Neverthe-
less, this solution may be improper because it is difficult to
follow a prior distribution [50]. Therefore, QR is introduced
as a kind of nonparametric approaches to estimate these
uncertainties from electricity prices, which is as follows,
X
min ρτ (yj − xj0 β1,τ − β0,τ − r) (19)
βτ ∈R
j

where yj and xj0 are the forecasting and real values for sample
j, respectively. β1 , τ and β0 , τ are linear optimal parameters
according to τ (quantile value). ρτ is a piecewise linear loss
function, which is defined by:
(
τr if r > 0
ρτ = (20)
−(1 − τ )r otherwise
description is as follows:
Once the parameters are estimated, the uncertainty for
ft = σ (Wf [ht−1 , xt ]) + bf ) (12) point forecasting results of day-ahead electricity prices can
it = σ (Wi [ht−1 , xt ]) + bi ) (13) be evaluated at different quantiles, as follows:
Ct 0 = tanh(Wc [ht−1 , xt ]) + bc ) (14)
yτ = β0,τ + β1,τ xj0 (21)
Ct = ft∗ Ct−1 + i∗t Ct 0 (15)
ot = σ (Wo [ht−1 , xt ]) + bo ) (16) IV. PERFORMANCE ASSESSMENT
ht = o∗t tanh(Ct ) (17) In this section, some judgment indexes are introduced to
evaluate point and probabilistic forecasting performance and
4) BACK PROPAGATION ALGORITHM demonstrate the superiority of the proposed hybrid forecast-
To improve the accuracy and stability of the day-ahead EPF, ing framework.
the network parameters of DBN, LSTM RNN, and CNN, the
weights, and biases, are trained and updated based on the BP A. ASSESSMENT OF POINT FORECASTING PERFORMANCE
algorithm using gradient descent methods with a mini-batch Mean absolute percentage error (MAPE), mean absolute error
form. Table 1 shows the advantages and disadvantages of (MAE), and root mean square error (RMSE) are utilized to
various gradient descent methods in the application of the evaluate the point forecasting performance. MAPE represents
weight updating. Compared with the batch form, the key the absolute average forecasting deviation between forecasts
focus of the mini-batch form presents two main benefits: the and targets. MAE and RMSE are to assess the forecasting
first is that the calculation iteration numbers have reduced accuracy and capability of the point forecasting results, which
to better convergence and stability; the second is that matrix are as follows:
optimization is more efficient [45]. Thus, BP algorithm to 1 X |rt − pt |
minimize the mean squared error between the outputs value MAPE = × 100% (22)
T rt
pm,t and target value rm,t can be described as follows, t∈T
1X
M T MAE = |rt − pt | × 100% (23)
1 XX T
J= (rm,t − pm,t )2 (18) t∈T
M s
1X
m=1 t=1
RMSE = (rt − pt )2 × 100% (24)
T
t∈T
C. PROBABILISTIC PREDICTION MODULE
Though feature preprocessing module, deep learning-based B. ASSESSMENT OF PROBABILISTIC FORECASTING
point prediction module, and error compensation module PERFORMANCE
have been proposed to improve the accuracy of the day-ahead Average coverage percentage (ACP) and interval
EPF, the point forecasting results are still uncertain. However, sharpness (IS) are considered as the criteria for probabilistic
this uncertainty can be depicted by a probabilistic predic- forecasting performance assessment. ACP is to evaluate the
tion module to diminish the bidding risk for market partic- coverage value cαt of the observed values located in a pre-
ipants [29]. In general, probabilistic forecasting methods can diction interval (PI) at the given prediction interval nominal
be grouped into parametric and nonparametric approaches, confidence (1−α) %. IS is to comprehensively measure the
with or without prior distribution assumptions [46]. The offset between PI and out-of-range observed values, and the
premise condition of parametric approaches for modeling width wαt for PI at the given the prediction interval nominal

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FIGURE 6. Electricity prices autocorrelation of PJM market. FIGURE 7. Correlation between electricity prices and load in PJM market.

TABLE 2. The parameter settings of the proposed and contrast models.

confidence (1−α) %. They can be expressed as follows:

1X α
ACP = ct × 100% (25)
T
t∈T
α Ltα < rt < Utα

1 −2αwt ,

−2αwαt − 4 Ltα − rt Ltα ≥ rt
X
IS = (26)
T
t∈T −2αwα − 4 U α − r Utα ≤ rt


t t t

V. CASE STUDIES
A. EXPERIMENTAL SETTINGS
The proposed hybrid framework for day-ahead EPF are eval-
uated using PJM market data [51]. In this study, the day-
ahead electricity prices data covers a period from June 2018 to
December 2019 at an interval of one hour. The whole data set
is classified into a training set, a validation set, and a testing
set, in which the testing set contains the seven-day of each
season in 2019 (7 days before March, December, June, and corresponding to the forecasting day is acknowledged easily.
September). In the whole data set except the test set, 60% is Therefore, we can choose the correlated features derived
divided into training set, whereas the rest 40% is divided into from the historical price at a lag of more than 24-h, and
validation set. combine the forecast day and historical load as input data
The parameters of the feature preprocessing module for the forecasting models in this article. In addition, the
include an abnormal proportional coefficient ζ for IF and a data dimension is related to the correlation degree of the
feature selection coefficient ϕ for Lasso. Simulation results correlated features and the structure of forecasting models.
show that an abnormal proportional coefficient ζ within the In order to verify the effectiveness of the hybrid deep-learning
range of 0.005-0.1 performs well, because a high value would framework, the forecasting results are compared with the
result in the loss of information relating to the significance light gradient boosting machine (LGBM) [53], BPNN [16],
attributes, whereas a low value would affect the overall k-nearest neighbor (KNN) [54], and SVR [14]. Some vital
forecasting performance. According to stability analysis, the parameter settings of the proposed and contrasted models are
abnormal proportional coefficient ζ is set to 0.015 in winter listed in Table 2.
and 0.0015 in other seasons. The feature selection coefficient
ϕ is used to characterize the correlation degree of the impact B. NUMERICAL RESULTS
features, and is fixed at 0.00005. In order to evaluate the effectiveness of the proposed frame-
Figure 6 and Figure 7 give 20 better correlation values from work, the comparison of the three deep-learning forecasting
historical electricity price and load over the week, respec- models (DBN, LSTM RNN, and CNN) and four contrast
tively. Other influential factors, such as bidding behavior, forecasting models are conducted, and the simulation results
congestion and maintenance schedule, can not be quantified over various seasons are presented in Table 3. It can be
as input values of feature extractors. From the figures, it can seen that the MAPE value of CNN varies from 0.0587 to
be seen that the electricity prices autocorrelation coefficients 0.0988 with an average of 0.0814, the MAPE value of
increase slowly as the number of forecasting hours reduce, DBN varies from 0.0613 to 0.1085 with an average of
and it performs well when it lags by 1 hour, but it can not be 0.0902, and the MAPE value of LSTM varies from 0.0608 to
used for day-ahead EPF with a lag of 0-23 hours. According 0.1073 with an average of 0.0896. The average MAPE results
to [52], the day-ahead load forecasting has touched a satisfac- for LGBM, BPNN, SVR, and KNN are 0.1233, 0.1271,
tory forecasting accuracy with a 1%∼2% error, so the load 0.3169, and 0.1252, respectively. Compared with LSTM

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TABLE 3. The forecasting statistical results for various contrast models in various seasons.

FIGURE 8. Day-ahead electricity forecasting results of different forecasting models in spring.

FIGURE 9. Day-ahead electricity forecasting results of different forecasting models in summer.

RNN and DBN, the MAPE of CNN is averagely improved To graphically verify the supremacy of three deep-learning
by 10.81% and 10.11%, respectively. Compared with LGBM, forecasting models, the comparison of day-ahead electricity
BPNN, SVR, and KNN, the MAPE of CNN is averagely forecasting results of different forecasting models under vari-
increased by 51.46%, 56.16%, 289.40%, and 53.86%, respec- ous seasons is carried out and presented in Figure 8-Figure 11.
tively. Compared with LSTM, DBN, LGBM, BPNN, SVR It can be seen that the results of CNN performs best in terms
and KNN, the MAE of CNN is averagely increased by of the MAPE, MAE, and RMSE, followed by LSTM RNN,
10.26%, 10.26%, 39.83%, 43.22%, 232.19% and 45.95%, DBN, LGBM, BPNN, KNN, and SVR. The reason may be
respectively, and the RMSE is averagely increased by that the CNN model holds a weight-sharing technique to
9.06%, 8.53%, 31.38%, 29.91%, 167.35% and 59.84%, extract local complicated nonlinear features during training.
respectively. The inferior performance of the SVR model is mainly driven

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FIGURE 10. Day-ahead electricity forecasting results of different forecasting models in fall.

FIGURE 11. Day-ahead electricity forecasting results of different forecasting models in winter.

FIGURE 12. Hourly absolute percentage error results of CNN with and without ECM in spring.

by following abnormal distribution of kernel and worsened (2) Error compensation module: Because the proposed
by low feature extraction capability. It’s worth noting that the deep learning forecasting models contain an error compensa-
three deep-learning forecasting models have a competitive tion module, a small deviation between the forecast and actual
benefit than four contrast forecasting models. There are two electricity prices may be corrected.
reasons for this: To further demonstrate the advantages with the error
(1) Feature extraction capability: Shallow machine learn- compensation module (ECM), several simulations using the
ing models (four contrast forecasting models) need to make proposed and contrast models with and without ECM are per-
full use of feature selection to identify shifting trends, formed in spring, as an example of illustration. Hourly abso-
whereas deep learning models are well versed in the high lute
nonlinear mapping capability, especially for the volume of percentage error results of different deep learning models
data increases. in spring are shown in Figure 12-Figure 14. The statistical

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FIGURE 13. Hourly absolute percentage error results of DBN with and without ECM in spring.

FIGURE 14. Hourly absolute percentage error results of LSTM RNN with and without ECM in Spring.

TABLE 4. Statistical results of hourly absolute percentage error for the effect of ECM in spring.

TABLE 5. The ACPs and ISs with 80% confidence level using various models in various seasons.

results of them are listed in Table 4. It can be seen that and a variance of 0.0045. The hourly absolute percentage
the hourly absolute percentage error results of CNN with error results of DBN with ECM vary from 0.0054 to 0.3405
ECM vary from 0.0007 to 0.3743 with an average of 0.0820, with an average of 0.0877, and a variance of 0.0042. The

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FIGURE 15. PIs with confidence level 80% for March 1 using various forecasting models.

TABLE 6. The average ACPs and ISs with various confidence level ranging from 2% to 98% level using various models in various seasons.

hourly absolute percentage error results of LSTM RNN with average ACPs for CNN+QR, DBN+QR, and LSTM+QR
ECM vary from 0.0015 to 0.3490 with an average of 0.0837, are 79.46%, 79.31%, and 79.31%, respectively. The aver-
and a variance of 0.0048. Correspondingly, the variance of age ACPs for LGBM+QR, BPNN+QR, SVR+QR, and
CNN without ECM, DBN without ECM, and LSTM with- KNN+QR are 79.16%, 79.02%, 79.12%, and 79.31%,
out ECM are 0.0046, 0.0058, and 0.0077, respectively, and respectively. Meanwhile, The ISs of CNN + QR range from
their averages are 0.0883, 0.0903, and 0.0881, respectively. −3.79 to −1.92 with an average of −3.07 to. The ISs
Compared with contrast models without ECM, it is found of DBN+QR range from −4.17 to −2.13 with an aver-
that the average index of CNN with ECM, DBN with ECM, age −3.32. The ISs of LSTM + QR range from −1.53
and LSTM RNN with ECM are improved by 2.44%, 2.96%, to −0.90 with an average of −3.48. The average ISs of
and 5.26%, respectively, and their variances are increased LGBM+QR, BPNN+QR, SVR+QR, and KNN+QR are
by 7.68%, 38.10%, and 60.42%, respectively. Moreover, −3.72, −3.67, −4.32, and −3.67, respectively. Compared
the green dashed lines in Figure12-Figure 14 also show with DBN+QR, LSTM +QR, LGBM+QR, BPNN+QR,
that the ECM can cut the hourly absolute percentage error SVR+QR, and KNN+QR, the IS of CNN+QR is improved
arising from a deep learning-based point prediction module. by 8.48%, 13.61%, 21.27%, 19.72%, 40.75%, and 19.64%,
Therefore, these diagrams results demonstrate that the ECM respectively.
can not only enhance forecasting accuracy but also manifest Take the case on March 1, the constructed prediction inter-
higher stability and robustness. vals with confidence level 80% under various forecasting
According to the results above, it is noticed that fore- models are also diagrammatically presented and illustrated
casting data of day-ahead electricity prices always exist in Figure 15. It has three distinct characteristics for different
indelibility errors (uncertainties), and have an adverse influ- forecasting models. The first is that the observed values
ence on market participants’ bidding strategy. Therefore, in the prediction intervals with various forecasting models
a probabilistic prediction module with QR is introduced in have similar numbers. The second is that the offset distance
this work to describe these uncertainties. Table 5 presents between prediction interval and the out-of-range observed
each seasonal result with a confidence level of 80% by value of CNN+QR is the smallest than that of DBN+QR, and
using the proposed and contrasted models. In Table 5, the LSTM+QR, as the green dotted lines indicate. The third is

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FIGURE 16. The ACPs with various confidence level using various forecasting models in various seasons.

FIGURE 17. The ISs with various confidence level using various forecasting models in various seasons.

that the width of various contrast forecasting models is longer 11.95%, 21.70%, 22.20%, 38.22%, and 24.46%, respec-
compared with the proposed forecasting models, as the red tively, compared with DBN+QR, LSTM+QR, BPNN+QR,
dotted lines show. It is clear from these charts that ACP results LGBM+QR, KNN+QR, and SVR+QR. Therefore, it can be
of various forecasting models represent almost consistency in concluded that the ISs of CNN+QR exhibit the best forecast-
each season, and IS results of CNN+QR perform best in each ing performance compared with other forecasting models,
season, followed by DBN+QR, LSTM+QR, BPNN+QR, while the ACPs of CNN+QR changed little. Figure 16 and
LGBM+QR, KNN+QR, and SVR+QR. This is mainly due Figure 17 respectively show the statistical results in terms of
to that the CNN model presents more petite errors, and is various confidence levels ranging from 2% to 98% in each
easier to predict these uncertainties than other forecasting season. Obviously, it is in good agreement with figure results.
models. From the cases above, it can be concluded that the day-ahead
Considering that market participants may have differ- EPF framework with high-accuracy is great attractive for
ent risk preferences (here is confidence level), probabilis- implementation.
tic forecasting performance with various confidence level
are compared using the different forecasting models in VI. CONCLUSION
each season to demonstrate the effectiveness and feasibil- In this article, a novel deep-learning based hybrid framework,
ity. Table 6 shows the average ACE and IS results with composed of feature preprocessing module, deep-learning
various confidence levels ranging from 2% to 98%. The based point prediction module, error compensation module,
results show that the ACPs of CNN+QR are averagely and probabilistic prediction module, is presented for forecast-
improved by 0.12%, 0.09%, 0.27%, 0.27%, 3.7%, and ing day-ahead electricity prices. The usage of the first mod-
2.7%, respectively, compared with DBN+QR, LSTM+QR, ules is applied to detect outliers and identify the correlated
LGBM+QR, BPNN+QR, SVR+QR, and KNN+QR. And features of electricity price series. The three deep learning
the ISs of CNN+QR is averagely improved by 9.49%, models, DBN, LSTM RNN, and CNN in the second module,
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