energies
ArticleEnhanced Day-Ahead Electricity Price Forecasting Using a
Convolutional Neural Network–Long Short-Term Memory
Ensemble Learning Approach with Multimodal Data Integration
Ziyang Wang 1, * , Masahiro Mae 1 , Takeshi Yamane 2 , Masato Ajisaka 2 , Tatsuya Nakata 2 and Ryuji Matsuhashi 1
1

2*

Citation: Wang, Z.; Mae, M.; Yamane,T.; Ajisaka, M.; Nakata, T.;
Matsuhashi, R. Enhanced Day-Ahead
Electricity Price Forecasting Using a
Convolutional Neural
Network–Long Short-Term Memory
Ensemble Learning Approach with
Multimodal Data Integration.
Energies 2024, 17, 2687. https://doi.org/10.3390/en17112687
Academic Editor: Ahmed Abu-Siada
Received: 14 May 2024
Revised: 28 May 2024

Department of Electrical Engineering and Information Systems, The University of Tokyo,
Tokyo 113-8656, Japan; mmae@ieee.org (M.M.); matu@enesys.t.u-tokyo.ac.jp (R.M.)
Department of Energy Systems Research and Development, KYOCERA Corporation,
Yokohama 220-0012, Japan; takeshi.yamane.hs@kyocera.jp (T.Y.); masato.ajisaka.ke@kyocera.jp (M.A.);
tatsuya.nakata.gt@kyocera.jp (T.N.)
Correspondence: wang-ziyang@ieee.org; Tel.: +81-080-2561-3818

Abstract: Day-ahead electricity price forecasting (DAEPF) holds critical significance for stakeholders
in energy markets, particularly in areas with large amounts of renewable energy sources (RES)
integration. In Japan, the proliferation of RES has led to instances wherein day-ahead electricity
prices drop to nearly zero JPY/kWh during peak RES production periods, substantially affecting
transactions between electricity retailers and consumers. This paper introduces an innovative DAEPF
framework employing a Convolutional Neural Network–Long Short-Term Memory (CNN–LSTM)
model designed to predict day-ahead electricity prices in the Kyushu area of Japan. To mitigate
the inherent uncertainties associated with neural networks, a novel ensemble learning approachis implemented to bolster the DAEPF model’s robustness and prediction accuracy. The CNN–
LSTM model is verified to outperform a standalone LSTM model in both prediction accuracy andcomputation time. Additionally, applying a natural logarithm transformation to the target day-ahead
electricity price as a pre-processing technique has proven necessary for higher prediction accuracy. A
novel "policy-versus-policy" strategy is proposed to address the prediction problem of the zero prices,halving the computation time of the traditional two-stage method. The efficacy of incorporating asuite of multimodal features: areal day-ahead electricity price, day-ahead system electricity price,
areal actual power generation, areal meteorological forecasts, calendar forecasts, alongside the rollingfeatures of areal day-ahead electricity price, as explanatory variables to significantly enhance DAEPF
accuracy has been validated. With the full integration of the proposed features, the CNN–LSTM
ensemble model achieves its highest accuracy, reaching performance metrics of R2 , MAE, and RMSE
of 0.787, 1.936 JPY/kWh, and 2.630 JPY/kWh, respectively, during the test range from 1 March 2023
to 31 March 2023, underscoring the advantages of a comprehensive, multi-dimensional approach
to DAEPF.
Keywords: day-ahead electricity price forecasting (DAEPF); renewable energy sources (RES);
CNN–LSTM; deep learning; ensemble learning; zero day-ahead electricity priceAccepted: 29 May 2024
Published: 1 June 2024

Copyright: © 2024 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms andconditions of the Creative Commons
Attribution (CC BY) license (https://creativecommons.org/licenses/by/

1. Introduction
1.1. The Necessity of Day-Ahead Electricity Price Forecasting
In the wake of the 21st century, the global energy sector has been undergoing aparadigm shift, characterized by the massive integration of renewable energy sources (RES)such as wind and solar power into the electricity grids [1,2]. This transformation, largely
driven by the need to counteract the environmental challenges of conventional energy
systems, brings volatility and unpredictability in electricity generation. The intermittency
associated with RES significantly influences the dynamics of the day-ahead electricity4.0/).

Energies 2024, 17, 2687. https://doi.org/10.3390/en17112687

https://www.mdpi.com/journal/energies

Energies 2024, 17, 2687

2 of 17market [3,4], where electricity is traded for immediate delivery, thereby escalating thecomplexity of pricing mechanisms.
In this evolving energy landscape, day-ahead electricity price forecasting (DAEPF)
in day-ahead electricity markets has emerged as a paramount concern [5]. As electricity
transaction prices are determined in the wholesale market, price fluctuations profoundly
influence the financial dynamics of electric utilities [6]. Accurate DAEPF, therefore, isinstrumental for a range of market stakeholders, from power producers and consumers totraders. It aids in energy companies’ optimized bidding, strategic planning, and insightfuldecision-making processes, especially in a market with escalating RES integration, which
introduces additional complexities in price patterns [7]. For both retailers and consumers,
accurate DAEPF can usher in substantial economic benefits, helping to craft optimized
procurement strategies and promoting proactive demand response initiatives [8]. On a
broader scale, it underpins the stability and efficiency of modern power systems, playing apivotal role in the transition to a sustainable energy future.
1.2. Day-Ahead Electricity Price Forecasting Models
Statistical models such as the Autoregressive Moving Average (ARMA) [9,10] andAutoregressive Integrated Moving Average (ARIMA) [11–13] have been widely employedin DAEPF studies. While these models provide foundational approaches, their inherent linearity can pose challenges. The increased integration of RES, along with factors
like demand fluctuations, introduces non-linear trends and sudden price anomalies thattraditional statistical models may struggle to capture accurately. On the other hand, machine learning models, particularly those that incorporate time-dependent features such as
the Long Short-Term Memory (LSTM), have gained traction in DAEPF, as evidenced bynumerous studies [7,14,15].
Furthermore, by integrating the capabilities of the Convolutional Neural Network(CNN) with the LSTM, a potent hybrid framework CNN–LSTM emerges. In this architecture, the CNN functions as a feature extractor, while the LSTM captures temporaldependencies. Notably, this hybrid approach dramatically shortens training time, a benefit
primarily derived from the convolutional operations performed by the CNN, setting itapart from standalone LSTM models. This enhanced efficiency in training, coupled withimproved predictive accuracy, positions the CNN–LSTM as superior to standalone LSTM
models across various time series forecasting domains. Notable studies evidencing thesuperior performance of CNN–LSTM over LSTM include those in diverse fields such as biosignal analysis for heart rate monitoring [16], electricity market demand bidding [17], stock
price forecasting [18], short-term photovoltaic power production prediction [19], lithium–
ion battery discharge capacity estimation [20], PM2.5 concentration [21], residential energy
consumption forecasting [22], individual household load forecasting in the short-term [23],and DAEPF [24]. Through these various applications, the CNN–LSTM model has demonstrated a commendable blend of efficiency and effectiveness, underscoring its utility overstandalone LSTM models in time series forecasting problems. Cordoni [24] compared aseries of machine learning models for DAEPF, including Random Forest (RF), Multilayer
Perceptron (MLP), CNN, Recurrent Neural Network (RNN), LSTM, and CNN–LSTM,
showing that the CNN–LSTM achieved the highest forecasting accuracy among all themodels. In addition to the day-ahead electricity price, calendar variables, total load, andzonal load were used as features. However, weather data, which has been validated as
significant for DAEPF by some studies [25,26], was not included in Cordoni’s analysis [24].
Moreover, existing studies [16–24] did not address the inherent uncertainty characteristics of the neural networks when comparing the performance between standalone LSTM
models and CNN–LSTM models, resulting in unreliable comparisons.

Energies 2024, 17, 2687

3 of 171.3. Day-Ahead Electricity Prices: Negative Trends in the US and EU and Non-Negative
Limitations in Japan

250
200
150
100
50
0

Electricity spot price (yen/kWh)Electricity spot price (yen/kWh)In recent years, the increased penetration of RES, particularly from wind and solar sources, has introduced an unprecedented phenomenon in the US and EU electricity
markets: negative day-ahead electricity price [27]. This development can be attributed primarily to two interconnected factors. First, the inherent intermittency and unpredictabilityof RES can occasionally lead to generation surpassing demand, leading to an oversupply.
Second, conventional power plants, including nuclear and coal, often find it challenging toramp down production swiftly or cost-effectively. During periods of high renewable energy
output, these plants may opt to maintain operations, effectively paying consumers to use
the excess electricity rather than incurring the costs associated with shutting down andrestarting. The occurrence of negative electricity prices has become increasingly frequent.
For instance, during the final two weeks of 2012, day-ahead electricity prices in Germany
turned negative on three occasions, an event that was considered unusual at the time, asemphasized by Shiri et al. [28]. Recent findings by Seel et al. [27] indicate that, in 2020,
solar and wind energy were principal contributors to negative prices in both the US and EU
electricity markets. Such negative prices, while posing challenges, highlight the imperative
for proficient grid management, adaptable demand–response systems, and energy storage
solutions to keep pace with the escalating contribution of RES [29,30]. However, the situation in Japan presents a distinct narrative. With the significant introduction of solar andwind energy into the Japanese power grid, the electricity wholesale day-ahead markets
have witnessed prices approaching nearly zero JPY/kWh, specifically at 0.01 JPY/kWh(referred to as zero prices in the following sections of this paper). Notably, negative prices
have been absent, a consequence of the Japanese governmental policies and regulations.
The day-ahead electricity price in the Kyushu area is depicted in Figure 1a. A closer lookat the intermittent zero prices is presented in Figure 1b. As evident from Figure 1a, theemergence of considerable zero prices became prominent from the year 2020 onward,
largely attributable to the rapid integration of RES.

Kyushu electricity spot price

2016

2017

2018

2019

2020
Time [Yearly]D

2021

2022

2023

Kyushu electricity spot price (Zoomed)
40
30
20
10
0

2022-04-01

2022-04-02

2022-04-03

2022-04-04
Time [Daily]E

2022-04-05

2022-04-06

2022-04-07

Figure 1. Kyushu areal day-ahead electricity price [JPY/kWh] (a) and zooming-in on zero-inflated
prices (b).

Energies 2024, 17, 2687

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1.4. Paper Contributions and Organization
The contributions of this paper are summarized as follows. To address the challenges
previously mentioned, this research investigates multimodal data as novel features to enhance DAEPF in Kyushu area, Japan, and compare the performance between the standalone
LSTM model and the CNN–LSTM model in terms of both prediction accuracy and computation time, by utilizing a novel ensemble learning approach to address their inherent
uncertainties. Moreover, to address the "zero-inflated" problem in the Japan Electric Power
Exchange (JEPX) day-ahead electricity market, a novel "policy-versus-policy" strategy is
employed to forecast the zero prices to half the computation time, which a traditional
two-stage method requires. Furthermore, a natural logarithm transformation is utilized
to improve the Skewness and Kurtosis of the electricity price to enhance the prediction
accuracy. Moreover, a novel method for extracting meteorological forecast data by utilizing
Google Maps is introduced. To the best of the authors’ knowledge, no prior work has
combined these specific features together for accurate DAEPF.
The remainder of this paper is organized as follows. Section 2 details the methodology
adopted in this study and presents the comprehensive structure of the LSTM and CNN–
LSTM models used for DAEPF. Section 3 describes the data architecture underpinning
the DAEPF models. Section 4 reports the performance metrics of the DAEPF results andvalidates the efficacy of the proposed feature sets. Finally, Section 5 concludes the paperand discusses potential directions for future research.
2. Methodology
2.1. LSTM and CNN–LSTM Forecasting Models
An LSTM model and a CNN–LSTM model were designed and employed for DAEPF
and for comparison using the Python Tensorflow Keras library, given their demonstrated
performance in time series forecasting, as discussed in Section 1.2. The architectures of
the LSTM and CNN–LSTM models are delineated in Figure 2, and the hyperparameters
were selected empirically based on optimal performance. The LSTM model comprises two
LSTM layers with the same number of units, followed by a fully-connected (FC) Layer.
The initiation of the CNN–LSTM model begins with an input layer that accommodates
the input data. Following this, the data traverses through a one-dimensional convolution
layer, employing the Rectified Linear Unit (ReLU) activation function. Subsequently, a
max pooling layer is applied to the convolutional output, assisting in reducing the spatial
dimensions of the output feature maps. Another convolution layer follows, facilitating
further feature extraction from the data. The ensuing layer is an LSTM Layer, with thesame number of units as the LSTM layers in the LSTM model, adept at capturing the
temporal dependencies in the time-series data. The output of the LSTM Layer is thenrouted through an FC layer, producing the final output of the model. The LSTM and
CNN–LSTM models are compiled using the Adam optimizer with a learning rate of 0.001,
with the mean absolute error (MAE) chosen as both the loss function and the metric. To
prevent overfitting, the batch size and number of training epochs for both models were set
to 2048 and 50, respectively, for each training iteration. Subsequently, the performance of
the LSTM and CNN–LSTM models are then compared.
2.2. Ensemble Learning Strategy
Given the inherent variability of neural network models, which stems from their
sensitivity to initial conditions and the stochastic nature of their training, training thesame neural network multiple times and averaging the predictions can mitigate individualmodel errors. This leads to enhanced prediction performance, as different models will
not make the same errors on the identical test set [31,32]. Based on this understanding,a novel ensemble learning approach was implemented. The LSTM and CNN–LSTM
models underwent multiple training iterations for each feature set defined in Section 3.4.
Subsequently, all individual predictions were aggregated using a simple averaging method
to construct the final ensemble prediction. The ensemble learning process is describedEnergies 2024, 17, 2687

5 of 17in Equation (1), where N represents the total number of predictions, and k denotes theindex of each individual prediction. In accordance with the central limit theorem, which
posits that the distribution of the average of a large number of independent, identically
distributed variables will approximate normality, this study selected N = 30 as the numberof training iterations for ensemble predictions.
ŷensemble =

1 N
ŷk
N k∑
=1

(1)

For clarity, the pseudo-code for the ensemble learning procedure is outlined in
Algorithm 1.
Algorithm 1 Ensemble Learning Procedure
1: Perform natural logarithm transformation of the day-ahead electricity price using

Equation (6).
2: Normalize the training and test data.
3: for i = 1 to N do
4:
Train the model to generate prediction ŷi .
5: end for
6: Restore the predicted values to their original scale (reverse data normalization).
7: Apply the exponential transformation to the predicted values using Equation (7) (re-verse of the log transformation).
8: Calculate the ensemble prediction ŷensemble using Equation (1).
9: Calculate the zero price for ŷi and ŷensemble using Equation (2).

FC Layer(M6 × 1)

LS

LS

TM

Input Layer(N × F )LSTM Layer(M5 × 1)TM

LSTM Layer(M5 × 1)

Output Layer(48 × 1)
M6

48

e

LS

F features

ec
Fo
r

TM
LS

LS

TM

as

te

d

LS

TM

M5

TM

M5

pr
ic

Past N -step data

N(a)
LSTM Layer(M5 × 1)

M3

Output Layer(48 × 1)

M1 /2

48

LS

M2 /2
M4

F features

ec
Fo
r

LS

TM

as
te
d

M2

M6

TM

M5

e

Past N -step data

N

ic

Max Pooling Layer(M1 /2 × M2 /2)

FC Layer(M6 × 1)pr

M1

Convolution Layer(M3 × M4 )TM

Input Layer(N × F )LS

Convolution Layer(M1 × M2 )(b)Figure 2. Schematic of the architectures of the (a) LSTM and (b) CNN–LSTM models.

2.3. “Policy-Versus-Policy” Zero Prices Forecasting Strategy
As is shown in Figure 1b, the considerable durations of zero prices in the target variable
create a zero-inflated regression problem in machine learning after data normalization.
However, it is almost impossible for most machine learning models, including Random

Energies 2024, 17, 2687

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Forest (RF), Support Vector Regression (SVR), and neural networks, to continuously output
zeros. The traditional method to solve the zero-inflated regression problem typically applies
a two-stage approach: one binary classification model to identify the zeros and another
regression model to predict the non-zero values, which doubles the computation time andtraining cost. In this study, we introduce a novel method to address this issue. The solution
begins with an understanding of broader trends in global day-ahead electricity markets.
As highlighted by Seel et al. [27], the abundance of RES can lead to negative day-ahead
electricity prices in the US and EU. Drawing from this, we infer that negative pricing isa natural consequence of RES abundance. In Japan, the current policy dictates that dayahead electricity prices cannot drop below 0.01 JPY/kWh, thereby preventing them fromturning negative. Assuming that the circumstances leading to negative prices in the US
and EU are similar to those in Japan, it is reasonable to infer that the explanatory variables
in both scenarios would exhibit similar patterns. Feeding these Japanese explanatory
variables into a machine learning regression model would naturally produce negative
prices, as the model is not constrained by Japan’s minimum pricing policy. Hence, byleveraging this premise, zero prices can be forecast by translating any negative outputs
from the model to zeros. This novel approach effectively functions as a policy-versus-policy
forecasting strategy, reflecting real-world conditions. Equation (2) illustrates the zero pricecalculation procedure.
(2)ŷi = max(0, ŷi )2.4. Performance Evaluation
Performance metrics, including MAE, root mean squared error (RMSE), and thecoefficient of determination (R2 ), were utilized for evaluation. The computational formulaefor MAE, RMSE, and R2 are specified in Equations (3)–(5), respectively.
MAE(y, ŷ) =∑nt=1 |yt − ŷt |
n

r

(3)

RMSE(y, ŷ) =∑nt=1 (yt − yˆt )2n(4)

R2 (y, ŷ) = 1 −∑nt=1 (yt − yˆt )2∑nt=1 (yt − ȳ)2(5)

3. Data Preparation
This study utilizes multimodal data to enhance DAEPF, comprising the areal dayahead electricity price (Kyushu), day-ahead system electricity price, rolling features of areal
day-ahead electricity price, areal actual power generation (Kyushu), areal meteorologicalforecast data (Kyushu), and calendar forecast data. In this study, since photovoltaic (PV)power is the primary RES in the Kyushu area due to its substantially greater installedcapacity compared to wind power, features pertaining to wind power are not incorporated
into the current investigation.
The overall data architecture and the corresponding time frame are illustrated in
Figure 3. The input data are segmented by their temporal delay into three green blocks.
To maintain consistency with the JEPX day-ahead electricity price data, all input data
were linearly interpolated to a time resolution of 30 min. A 7-day moving window wasapplied to the input data before being fed into the DAEPF models. In the JEPX day-ahead
electricity market, all transactions must be finalized by the bidding deadline of 10:00 JST.
Given the computational requirements and the complexities of the forecasting process, a
5 h buffer before the deadline has been established. The explanatory variables include data
up to 05:00 JST on the day before the forecast day. The forecasting period covers the entire
following day, from 00:00 JST to 23:30 JST, encompassing a total of 48 time frames.

Energies 2024, 17, 2687

7 of 17JEPX day-aheadmarket bidding
deadline

Forecasting point(5 h ahead)

7-day-long historical data (05:00 - 05:00]
Actual power generation (Kyushu), actual solar power generation(Kyushu)

Interval(19 h)

Prediction period[00:00 - 00:00)

7-day-long forecast data ① [00:00 - 00:00)
Day-ahead areal price (Kyushu), day-ahead areal price rolling features(Kyushu), day-ahead system price7-day-long forecast data ② [00:00 - 00:00)
Meteorological forecast data (Kyushu), calendar forecast data

05:00

00:00

00:00

・・・・・・

05:00 10:00

00:00

00:00

Figure 3. Illustration of the data architecture of the explanatory variables, highlighting the timedelays among different data.

Regarding the outliers issue, extreme values in day-ahead electricity prices and power
generation data are considered significant and not anomalies. For meteorological forecast
data, since individual forecast points have forecasting errors, the outliers are mitigated byaveraging the data over the Kyushu area. This approach reduces the impact of individual
errors and ensures stable input for the DAEPF model.
3.1. Electricity Data
3.1.1. Day-Ahead Electricity Price
The day-ahead electricity prices (JPY/kWh) at a 30 min resolution, encompassing
both the areal day-ahead electricity price and the day-ahead system electricity price, wereobtained from the JEPX official website [33]. The distribution of the Kyushu areal day-ahead
electricity price, as illustrated in Figure 4a, exhibits pronounced Skewness and Kurtosis,
indicating a skewed distribution. Neural network models typically assume that input data
are normally distributed or at least exhibit symmetry, as this facilitates the model’s learning
process by providing a standardized scale for the input features. Deviations from normality,
such as Skewness and Kurtosis, can introduce biases in the model’s predictions and affectthe efficiency of the learning algorithm. To mitigate these effects, a natural logarithm
transformation was applied to the day-ahead Kyushu areal electricity price, as detailedin Equation (6). This transformation, a common technique in statistical normalization,
reduces the impact of Skewness and Kurtosis by compressing the scale of the distribution,
thereby enhancing symmetry and reducing the influence of outliers. The effectivenessof the natural logarithm transformation is quantitatively evidenced by the reduction in
Skewness and Kurtosis of the price data, as shown in Table 1 and Figure 4b. Following themodel’s prediction output, an exponential back-transformation, defined in Equation (7), isapplied to convert the forecast values back to their original scale.
y = loge (y + 1)

(6)

y = ey − 1(7)Energies 2024, 17, 2687

8 of 17Frequency

0.3
0.2
0.1
0.0

0

50
100
150
200
Electricity spot price [yen/kWh]D

250

Frequency

0.06
0.04
0.02
0.00

0
1
2
3
4
5
Natural logarithm-transformed electricity spot priceE

Figure 4. Distribution of Kyushu areal day-ahead electricity price (a) and the corresponding distribution after the natural logarithm transformation (b).
Table 1. Skewness and Kurtosis of the original and natural logarithm-transformed Kyushu areal
day-ahead electricity prices during 5 April 2016 to 31 December 2021.

Skewness
Kurtosis

Original

Log-Transformed

8.77
123.00−0.68
3.81

Feature engineering was conducted to the day-ahead Kyushu areal electricity priceusing a method that involves calculating rolling statistics (minimum, maximum, mean, andstandard deviation) with a rolling window. This method is crucial for capturing temporal
patterns and trends, which are essential for time series feature extraction. The equations forthese calculations are provided in Equations (8)–(11), where t indicates the current time
step, and w indicates the length of the rolling window. The length of the rolling window
was chosen to be 3 days, i.e., w = 144.
Mint = min(yt−w+1 , yt−w+2 , . . . , yt )(8)

Maxt = max(yt−w+1 , yt−w+2 , . . . , yt )

(9)

t
1
y
∑
w i = t − w +1 i

(10)

t
1
(y − Meant )2∑
w − 1 i = t − w +1 i

(11)Meant =vuu
Stdt = tEnergies 2024, 17, 2687

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3.1.2. Actual Power Generation
The actual power generation data (MW) at a 5-min resolution in the Kyushu area
were obtained from the Organization for Cross-regional Coordination of Transmission
Operators, Japan (OCCTO) [34], including the actual total power generation and actual
solar power generation.
3.2. Meteorological Forecast Data
The meteorological forecast data at a 1-h resolution were obtained from the Japan
Meteorological Business Support Center (JMBSC) [35]. The Mesoscale Model Grid Point
Value (MSM-GPV) consists of ten categories of meteorological data: the U-Component ofWind (UGRD), representing wind speed in the east–west direction with positive values
indicating westerly winds; the V-Component of Wind (VGRD), representing wind speed in
the north–south direction with positive values indicating southerly winds; temperature(TMP); relative humidity (RH); Low Cloud Cover (LCDC), indicating low-level cloudiness;
Middle Cloud Cover (MCDC), indicating mid-level cloudiness; High Cloud Cover (HCDC),
indicating high-level cloudiness; Total Cloud Cover (TCDC); Accumulated Precipitation(APCP); and Downward Shortwave Radiation Flux (DSWRF), indicative of solar radiation
reaching the Earth’s surface.
The JMBSC issues meteorological forecasts six times daily at 03:00, 06:00, 09:00, 15:00,
18:00, and 21:00 UTC, providing high-resolution, hourly updates at the surface level. These
forecasts cover a geographic area from 22.4° N, 120° E to 47.6° N, 150° E, encompassing
the whole area of Japan, and are disseminated on an equal latitude–longitude grid witha resolution of 0.05° × 0.0625° (505 by 481 grid points). The data are distributed in the
GRIB2 format, with each 39 h forecast file approximately 293 MB in size, resulting in about
1758 MB of data per 1 day. According to the forecasting time point of 05:00 JST, data up to
18:00 UTC were utilized.
The Kyushu area map was a rectangular screenshot from the Google Maps Styling
Wizard [36]. The identification of the land areas from the Kyushu area map was conductedusing the Python OpenCV library [37]. Figure 5a displays the original screenshot of the
Kyushu area map. In this step, pixels that are not within the defined blue color range, specifically lower-bound HSV values of [100, 50, 50] and upper-bound values of [130, 255, 255],
are identified as land. Subsequently, Figure 5b showcases the delineated land areas from
Figure 5a, with red dots marking these regions. After the identification of land areas, themeteorological data of all the land area pixels were averaged as input features.

D

E

Figure 5. Kyushu area map (a) and the identified land areas (b). Map data: ©2024 Google, TMap
Mobility.

Energies 2024, 17, 2687

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The reason for utilizing the aforementioned meteorological data is as follows. According to the American Society of Heating, Refrigerating and Air-Conditioning Engineers(ASHRAE) [38], an occupant’s thermal comfort is influenced by air temperature and relative
humidity (RH). The utility of air temperature and RH in modeling thermal comfort has been
substantiated in previous studies [39,40]. Solar radiation significantly impacts the output
of photovoltaic (PV) panels, thereby necessitating the inclusion of Downward Shortwave
Radiation Flux (DSWRF) data. Additionally, cloud cover at different levels, represented
by Low Cloud Cover (LCDC), Middle Cloud Cover (MCDC), High Cloud Cover (HCDC),
and Total Cloud Cover (TCDC), also affects solar radiation. Hence, these factors were
included in the analysis. The U-Component (UGRD) and V-Component (VGRD) of Windare relevant for modeling wind power generation, which is why they were considered.
Lastly, Accumulated Precipitation (APCP) influences the generation of hydropower andsmall-scale hydro power, making it a pertinent variable for inclusion.
3.3. Calendar Forecast Data
The calendar forecast data which integrate the cyclic features and Japanese holidays,
aimed to enhance the DAEPF accuracy by accounting for the unique electricity consumption
behaviors associated with specific time periods, were used as features.
3.3.1. Cyclic Features
When modeling time series data, capturing the inherent cyclicity of time-related
features is essential. Many features, such as hours of the day, days of the week, or monthsof the year, exhibit periodic behavior. For instance, the pattern of human activity at 06:00 JST
is more similar to 06:00 JST of the next day. Traditional linear representations of time failto capture this cyclical relationship. One effective method to account for this cyclicity
is to transform time-related features using trigonometric functions, specifically sine andcosine transformations. By representing features like days, weeks, months, and years
as points on a unit circle using sine and cosine values, we can maintain the closeness ofcyclical times as adjacent. In this study, we employ sine and cosine transformations withperiods corresponding to common cyclical patterns: 1 day, 1 week, 1 month, and 1 year.
For instance, the sine and cosine waves with a period of 1 year is shown in Figure 6. Suchtransformations have been acknowledged in foundational time series literature as a robust
method to encapsulate periodic patterns in data [41–45].

sin_yearcos_year

1.0
0.5
0.0
0.5
1.0
2016 2017 2018 2019 2020 2021 2022 2023
Time [year]
Figure 6. Sine and cosine waves with a period of 1 year.

3.3.2. Holiday Features
Japanese holidays and non-holidays were encoded into numerical labels, with holidays
labeled as 1 and non-holidays as 0. These holidays include national holidays, Golden Week
from 29 April–5 May, and the New Year’s period from 29 December–3 January.

Energies 2024, 17, 2687

11 of 173.4. Multiple Feature Sets
To analyze and compare the validity of the proposed features, a strategy is proposedthat involves removing each feature set one at a time from all proposed features and using
the remaining features to evaluate and compare prediction accuracy, as shown in Table 2.
Table 2. Performance metrics of the CNN–LSTM and LSTM ensemble learning models using different
combinations of the proposed features during the test period (1 January 2022–31 December 2022).
The highest prediction accuracies are highlighted in bold.
Feature Set

Model

Prediction
MethodLog Transformation

EnsembleTimes

Training
Time

R2

MAE
[JPY/kWh]

RMSE[JPY/kWh]All
No actual power generation
No holidays
No meteorological data
No rolling features
No cyclic features
No system price
All
All
All

CNN-LSTM
CNN-LSTM
CNN-LSTM
CNN-LSTM
CNN-LSTM
CNN-LSTM
CNN-LSTM
CNN-LSTM
LSTM
LSTM

(a)
(a)
(a)
(a)
(a)
(a)
(a)
(a)
(a)
(a)

Yes
Yes
Yes
Yes
Yes
Yes
Yes
No
Yes
Yes

30
30
30
30
30
30
30
30
15
30

52 min50 min51 min40 min46 min42 min51 min53 min58 min
117 min

0.592
0.583
0.575
0.572
0.561
0.530
0.558
0.535
0.581
0.587

5.112
5.216
5.231
5.200
5.328
5.489
5.233
5.490
5.112
5.070

6.941
7.020
7.088
7.117
7.207
7.457
7.226
7.411
7.034
6.986

3.5. Prediction Methods
Two prediction methods were utilized, as illustrated in Figure 7. Prediction method(a) is used to validate the performance of proposed features as it requires much lesstraining time compared with the day-by-day prediction method (prediction method (b))
shown in Figure 7b. For validation of the proposed features, the training data span from
5 April 2016—the date marking the full liberalization of the electricity retail market—to
31 December 2021. The testing period ranges from 1 January 2022 to 31 December 2022.
Considering that the test data span an entire year, the probability of the results being
attributable to random chance is considerably minimized.
Data set
Training data

Test data

・・・・・・

Day i

Day i+1

Day i+2

・・・・・・

Day i+365

・・・・・・

Day i+365(a)Data set
Training data

Test data

Training data

Test data

Training data

Test data
・・・・・・・・・・・・

Day i

Day i+1

Day i+2(b)

Figure 7. Schematics of the one-time prediction method (a) and the day-by-day prediction method (b).

After selecting the features with the best prediction performance, the day-by-day
prediction method was conducted to explore the actual prediction accuracy in real-world
application scenarios using these optimal features. Specifically, the test range is the next
whole day for each training data range, and the training data are updated for every
predicted next whole day. For the day-by-day prediction method, the testing period ranges
from 1 March 2023 to 31 March 2023, and the training data span from 5 April 2016 to the day

Energies 2024, 17, 2687

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before the predicted day. For comparison during the same testing period, the prediction
method (a) was also used, as shown in Table 3.
Table 3. Performance metrics of prediction methods (a) and (b) using the CNN–LSTM ensemble
learning model using all proposed features. The highest prediction accuracies are highlighted in bold.
FeatureSet

Model

Prediction
MethodTest Period

Log
Transformation

Ensemble Times

R2

MAE

RMSE

All

CNN-LSTM(a)

1 March 2023–31
March 2023

Yes

30

0.750

2.197

2.851

All

CNN-LSTM(b)

1 March 2023–31
March 2023

Yes

30

0.787

1.936

2.630

3.6. Model Training Platform
The models were trained using two NVIDIA Quadro RTX 8000 GPUs on a Windows OS.
4. Results and Discussion
4.1. Ensemble Learning Prediction Results
Table 2 presents the performance metrics for the prediction outcomes by adjustingmodels, features, pre-processing (natural logarithm transformation), and ensemble learning
iteration times. By observing Table 2, significant results can be summarized as follows.
1.

2.
3.

4.

Using all features, the ensemble learning prediction with the CNN–LSTM model
achieved the highest performance metrics, underscoring the efficacy and validity ofthe proposed features in enhancing DAEPF accuracy.
Applying the natural logarithm transformation to the target day-ahead electricity
price significantly improved performance.
The CNN–LSTM model (30 iterations ensemble) outperformed the LSTM model(15 iterations ensemble, special case for comparison), requiring less than the training
time of the LSTM model.
Using the same ensemble learning of 30 iterations, the CNN–LSTM model outperformed the LSTM model in terms of R2 and RMSE, though slightly weaker in MAE,
requiring less than half of the training time of the LSTM model.

Table 4 shows performance metrics of individual predictions using the optimal featureset (All features) from Table 2, LSTM and CNN–LSTM models, natural logarithm transformation pre-processing, and prediction method (a). It is noteworthy in Table 4 that eachtraining iteration results in a unique individual prediction on the test set, underscoring theinherent uncertainty in the neural network training process. Tables 2 and 4 demonstratethat the performance metrics of ensemble predictions significantly outperform the simple
average of the performance metrics from individual predictions, as well as the best individual prediction, highlighting the efficacy of the ensemble learning strategy. In addition,
the average individual prediction performance of the CNN–LSTM model outperformedthat of the LSTM model. Furthermore, it is evident from Table 4 that a certain individual
CNN–LSTM prediction can underperform a certain individual LSTM prediction, indicatingthat comparing individual predictions between CNN–LSTM and LSTM models is notreliable, thereby highlighting the necessity of the ensemble learning approach.
4.2. Day-by-Day Prediction Result
The day-by-day prediction results are shown in Figure 8. The ensemble learning
metrics for prediction methods (a) and (b) are presented in Table 3. As is shown in Table 3,
using the day-by-day prediction method, where the training data are incremented daily toinclude the most recent information, significantly enhanced performance compared withthe prediction method (a), as the model consistently integrates the latest data up to the day
before the prediction.

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As can be observed from Figure 8, ensemble learning effectively reduces the variability
inherent in individual model predictions. Although some individual predictions may
diverge markedly from the actual values, the ensemble method, described in Equation (1),averages these forecasts to produce a more reliable final prediction. This technique aligns
with the principle outlined by GoodFellow et al. [31]: averaging models is beneficial
because distinct models are unlikely to repeat the same errors on the test set. On theother hand, as shown in Figure 8, the model is capable of predicting zero prices to someextent, indicating the validity of the “policy-versus-policy” zero prices forecasting strategy.
Though not all instances of zero prices were successfully captured.
Table 4. Performance metrics of individual predictions using the CNN–LSTM and LSTM models withall proposed features and natural logarithm transformation pre-processing employing prediction
method (a).
No.

CNN-LSTM
R2

MAE [JPY/kWh]

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30

0.501
0.554
0.437
0.529
0.529
0.530
0.538
0.565
0.538
0.554
0.525
0.545
0.517
0.504
0.525
0.499
0.529
0.517
0.531
0.544
0.547
0.530
0.550
0.547
0.477
0.544
0.519
0.497
0.546
0.548

Min
Max
Average

0.437
0.565
0.527

LSTM
RMSE [JPY/kWh]

R2

MAE [JPY/kWh]RMSE [JPY/kWh]

5.569
5.360
5.996
5.455
5.442
5.541
5.420
5.284
5.421
5.365
5.486
5.329
5.533
5.575
5.441
5.452
5.343
5.605
5.390
5.349
5.320
5.437
5.436
5.388
5.680
5.347
5.505
5.547
5.404
5.384

7.677
7.261
8.159
7.463
7.460
7.454
7.388
7.170
7.389
7.260
7.493
7.334
7.557
7.657
7.495
7.698
7.463
7.554
7.448
7.341
7.315
7.451
7.290
7.317
7.866
7.340
7.537
7.711
7.327
7.309

0.496
0.463
0.462
0.510
0.522
0.447
0.490
0.544
0.447
0.487
0.518
0.500
0.501
0.518
0.534
0.495
0.497
0.493
0.473
0.494
0.527
0.522
0.502
0.514
0.500
0.485
0.513
0.519
0.495
0.544

5.507
5.661
5.691
5.483
5.401
5.760
5.582
5.269
5.776
5.629
5.492
5.570
5.634
5.498
5.446
5.543
5.501
5.527
5.652
5.591
5.390
5.356
5.595
5.433
5.521
5.599
5.469
5.543
5.533
5.402

7.720
7.967
7.978
7.614
7.514
8.084
7.761
7.343
8.086
7.787
7.549
7.687
7.677
7.551
7.419
7.722
7.713
7.743
7.896
7.737
7.474
7.514
7.671
7.583
7.686
7.799
7.584
7.541
7.723
7.340

5.284
5.996
5.460

7.170
8.159
7.473

0.447
0.544
0.500

5.269
5.776
5.535

7.340
8.086
7.682

Spot price (yen/kWh)

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Individual Predictions

Ensemble Prediction

Actual20
1002023-03-01

2023-03-05

2023-03-09

2023-03-13

2023-03-17
Time [Daily]

2023-03-21

2023-03-25

2023-03-29 2023-04-01

Figure 8. Individual and ensemble predictions for the test range from 1 March 2023 to 31 March 2023,
using the CNN–LSTM model and all proposed features with the natural logarithm transformation
pre-processing and the day-by-day prediction method.

5. Conclusions and Future WorkDAEPF is pivotal for stakeholders in the energy market. This study has proposed an
innovative DAEPF framework utilizing a CNN–LSTM ensemble learning model, incorporating areal day-ahead electricity price, day-ahead system electricity price, areal actual
power generation, areal meteorological forecasts, calendar forecasts, alongside the rollingfeatures of areal day-ahead electricity price, as explanatory variables to enhance DAEPF
accuracy in the Kyushu area of Japan. The effectiveness of these multimodal features
has been validated by comparing the prediction accuracy of different combinations of the
proposed features.
Given that individual predictions vary significantly, it is unwise to ignore the uncertainty characteristics of neural networks in DAEPF or the feature selection process, and
it is unreliable to compare single individual predictions between CNN–LSTM and LSTM
models. However, by employing an ensemble learning approach, the uncertainty can be
minimized and the prediction accuracy can be significantly increased. In the ensemble
learning, the CNN–LSTM model outperforms the LSTM model in both prediction accuracy
and computation time. The average individual prediction performance of the CNN–LSTM
model surpasses that of the LSTM model.
Applying the natural logarithm transformation to the electricity price to improve
the Skewness and Kurtosis has proven crucial for DAEPF prediction accuracy. The novel“policy-to-policy” strategy has been proposed and verified for zero prices forecasting,halving the computation time compared with the traditional two-stage method. Utilizing
all features, the ensemble learning method achieved the highest performance metrics
during the test range from 1 January 2022 to 31 December 2022.
Moving forward, by using the day-by-day prediction approach, the CNN–LSTM
model achieved performance metrics of R2 , MAE, and RMSE of 0.787, 1.936 JPY/kWh,2.630 JPY/kWh, respectively, during the test range from 1 March 2023 to 31 March 2023.
Moreover, while this study averaged meteorological data across the land areas, future work
could leverage the entire spectrum of meteorological data to preserve more comprehensive
information, potentially leading to even higher precision in DAEPF. In this study, ensemble
learning of 30 iterations were conducted with the CNN–LSTM model. In future work, thebalance between ensemble learning iteration times, computation time, increased prediction
accuracy, and potential profits from the predictions should also be considered.
Author Contributions: Conceptualization, Z.W. and R.M.; methodology, Z.W.; software, Z.W.; validation, Z.W. and M.M.; formal analysis, Z.W., M.M., T.Y., M.A. and T.N.; investigation, Z.W., M.M., T.Y.,
M.A., T.N. and R.M.; resources, T.Y., M.A., T.N. and R.M.; data curation, Z.W., T.Y., M.A. and T.N.;
writing—original draft preparation, Z.W.; writing—review and editing, Z.W. and M.M.; visualization,
Z.W.; supervision, R.M.; project administration, R.M.; funding acquisition, R.M. All authors haveread and agreed to the published version of the manuscript.
Funding: This research was funded by KYOCERA Corporation.
Data Availability Statement: All data generated or analyzed during this study are included in thisarticle.

Energies 2024, 17, 2687

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Conflicts of Interest: Authors Takeshi Yamane, Masato Ajisaka, Tatsuya Nakata were employed by
the company Department of Energy Systems Research and Development, KYOCERA Corporation.
The remaining authors declare that the research was conducted in the absence of any commercial or
financial relationships that could be construed as a potential conflict of interest.

Abbreviations
DAEPF
RES
OCCTO
JMBSC
JEPX
ASHRAE
PV
ARMA
ARIMA
RF
SVR
MLP
CNN
LSTM
CNN–LSTM
FC
ReLU
MAE
RMSE
R2
MSM-GPV
UGRD
VGRD
TMP
RH
LCDC
MCDC
HCDC
TCDC
APCP
DSWRF
Symbols
e
Mint
Maxt
Meant
Stdt
y
ŷ
ŷensemble
n
N
t
i
k
w

Day-ahead electricity price forecasting
Renewable energy sources
Organization for Cross-regional Coordination of Transmission Operators, Japan
Japan Meteorological Business Support Center
Japan Electric Power Exchange
American Society of Heating, Refrigerating and Air-conditioning Engineers
Photovoltaic
Autoregressive Moving Average
Autoregressive Integrated Moving Average
Random Forest
Support Vector Regression
Multilayer Perceptron
Convolutional Neural Network
Long Short-Term Memory
Convolutional Neural Network6-Long Short-Term Memory
Fully-connected
Rectified Linear Unit
Mean absolute error
Root mean squared error
Coefficient of determination
Mesoscale Model Grid Point Value
U-Component of Wind
V-Component of Wind
Temperature
Relative humidity
Low Cloud Cover
Middle Cloud CoverHigh Cloud CoverTotal Cloud CoverAccumulated Precipitation
Downward Shortwave Radiation Flux
Natural logarithm
Minimum value of the day-ahead electricity price over a rolling window
Maximum value of the day-ahead electricity price over a rolling window
Mean value of the day-ahead electricity price over a rolling window
Standard deviation of the day-ahead electricity price over a rolling window
Target variable
Predicted target variable
Ensemble prediction of the target variable
Sequence length of the target variable
Total training times of the modelt-th value in a variable sequencei-th value in a variable sequencek-th individual prediction after k-th training of the model
Rolling window length

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