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\title{Short-term Power Prediction of Distributed Photovoltaic Systems Based on
Multi-scale Feature Fusion using TPE-CBiGRU}



\author[1]{Hongbo Zou}%
\author[1]{Changhua Yang}%
\author[2]{Hengrui MA}%
\author[2]{Suxun Zhu}%
\author[3]{Jialun Sun}%
\author[1]{Jinlong Yang}%
\author[2]{Jiahao Wang}%
\affil[1]{China Three Gorges University}%
\affil[2]{Qinghai University}%
\affil[3]{Zhangjiakou Power Supply Company of State Grid Jibei Electric Power Co.}%


\vspace{-1em}



  
  \date{April 25, 2026}


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\selectlanguage{english}
\begin{abstract}
To address the key challenges of insufficient comprehensive extraction
and fusion of meteorological conditions, temporal features, and periodic
characteristics of power in short-term power prediction of distributed
photovoltaic (PV) stations, a TPE-CBiGRU model prediction method based
on multi-scale feature fusion is proposed. Firstly, multi-scale feature
fusion of meteorological features, temporal features, and hidden
periodic features in PV power is performed to construct model input
features. Secondly, CNN and Bi-GRU are utilized to model the feature
relationships between PV power and its influencing factors from spatial
and temporal scales, respectively, and the spatial-temporal features
extracted are fused through an Add network. Finally, the Bayesian
hyperparameter optimization method is adopted to further optimize
network parameters, achieving the prediction of single-station PV power.
Validation using measured data from a certain PV station shows that the
proposed method enhances the comprehensiveness of feature information
extraction from both data and model layers, significantly improving the
accuracy of short-term PV power prediction. Compared with other
prediction models, the Mean Absolute Error (MAE) and Root Mean Square
Error (RMSE) are reduced by 26.11\% and 35.64\%, respectively, and the
R-squared (R2) is increased by 3.07\%.%
\end{abstract}%



\sloppy


. Short-term Power Prediction of Distributed Photovoltaic Systems Based
on Multi-scale Feature Fusion using TPE-CBiGRU

Hongbo Zou\textsuperscript{1,2},Changhua
Yang\textsuperscript{1*},Henrui Ma\textsuperscript{3,4},Suxun
Zhu\textsuperscript{3},Jialun Sun\textsuperscript{5},Jinlong
Yang\textsuperscript{1},Jiahao Wang\textsuperscript{3}

\textsuperscript{1}College of Electrical Engineering and New Energy,
China Three Gorges University, Yichang, China

\textsuperscript{2}Hubei Provincial Key Laboratory for Operation and
Control of Cascaded Hydropower Station, China Three Gorges University,
Yichang, China

\textsuperscript{3}College of Energy and Electrical Engineering, Qinghai
University, Xining City, Qinghai Province, China

\textsuperscript{4}College of Electricity and Automation, Wuhan
University, Wuhan, Hubei, China

\textsuperscript{5}Zhangjiakou Power Supply Company of State Grid Jibei
Electric Power Co.

\textsuperscript{*}18385615363@163.com

Abstract: To address the key challenges of insufficient comprehensive
extraction and fusion of meteorological conditions, temporal features,
and periodic characteristics of power in short-term power prediction of
distributed photovoltaic (PV) stations, a TPE-CBiGRU model prediction
method based on multi-scale feature fusion is proposed. Firstly,
multi-scale feature fusion of meteorological features, temporal
features, and hidden periodic features in PV power is performed to
construct model input features. Secondly, CNN and Bi-GRU are utilized to
model the feature relationships between PV power and its influencing
factors from spatial and temporal scales, respectively, and the
spatial-temporal features extracted are fused through an Add network.
Finally, the Bayesian hyperparameter optimization method is adopted to
further optimize network parameters, achieving the prediction of
single-station PV power. Validation using measured data from a certain
PV station shows that the proposed method enhances the comprehensiveness
of feature information extraction from both data and model layers,
significantly improving the accuracy of short-term PV power prediction.
Compared with other prediction models, the Mean Absolute Error (MAE) and
Root Mean Square Error (RMSE) are reduced by 26.11\% and 35.64\%,
respectively, and the R-squared (R2) is increased by 3.07\%.

\subsection*{Introduction}

{\label{introduction}}

By the end of 2023, China's installed capacity of distributed
photovoltaic (PV) systems reached 60,891.8 MW, with new capacity
surpassing centralized PV for two consecutive years {[}1{]}. Distributed
PV systems can be installed and utilized on the user side, reducing
transmission losses associated with long-distance power delivery.
However, the high penetration of distributed PV introduces new
challenges for grid operation and management {[}2-4{]}. The randomness
and volatility of distributed PV generation, especially during midday
low and evening peak periods, exacerbate the difficulty of power system
integration and supply, leading to the ''duck curve'' phenomenon in the
net load curve. This increases system uncertainty and the cost of full
absorption, impacting the economic operation of the grid {[}5{]}.
Furthermore, the large-scale grid integration of distributed PV systems
promotes the transition of distribution networks towards gridization,
activation, and automation, imposing higher requirements on power
control, voltage regulation, and communication methods in distribution
networks {[}6{]}. Additionally, as the proportion of distributed PV
installations increases, the difficulty of maintaining power balance
scheduling rises, and the demand for flexible resources becomes more
urgent. Distributed PV systems, in comparison to conventional power
sources, lack reliable substitute capabilities in supporting power and
energy, further aggravating the system balance contradiction {[}7{]}. In
this context, high-precision short-term power prediction technology for
distributed PV is crucial for optimizing power system operation
strategies, assisting power system scheduling, and reducing operational
risks. It is key to improving grid planning and operational efficiency
{[}8, 9{]}. Therefore, developing short-term power prediction methods
for distributed PV to address these challenges is particularly urgent
and significant.

Currently, in the field of photovoltaic (PV) power prediction, although
substantial research has been conducted with significant progress, the
focus has primarily been on power prediction for PV stations or PV
clusters, as summarized in Table 1. Prediction methods are mainly
divided into traditional methods and artificial intelligence (AI)
methods. Traditional methods include physical modeling and statistical
methods {[}10, 11{]}. Physical modeling typically involves creating
models based on the physical characteristics of PV generators,
meteorological conditions, and environmental factors, which align more
closely with actual physical processes. For instance, reference {[}12{]}
proposed a five-parameter PV system simulation model that combines
algebraic and analytical techniques, which has been validated to predict
the output power of PV stations under real conditions. Another study
{[}13{]} improved the accuracy of PV station power prediction by
forecasting solar radiation and temperature. While physical methods for
PV power prediction can partially elucidate the system's operating
principles, their limitations---such as complex interaction
relationships, difficulty in accurately obtaining parameters, high
computational complexity, and sensitivity to environmental
changes---restrict their reliability and accuracy in practical
applications. Consequently, an increasing number of researchers are
turning to statistical methods for modeling {[}14{]}.

Statistical methods include time series analysis, regression analysis,
and machine learning, with commonly used techniques such as support
vector machines (SVM){[}15{]} and random forests (RF){[}16{]}. These
methods generally have lower computational costs and do not require
complex physical modeling and simulation. For instance, reference
{[}17{]} developed a hybrid model combining an Improved Whale
Optimization Algorithm (IMWOA) with SVM (IMWOASVM) for short-term PV
power prediction. The IMWOA optimizes the kernel function parameters and
penalty coefficients in SVM, enhancing prediction accuracy. Another
study {[}18{]} proposed an improved Markov Chain model, which
effectively increased the accuracy and applicability of probabilistic PV
power output prediction by integrating conditional probability
structures of influencing factors, rough set theory-based factor
selection, and K-nearest neighbor similar sample mining. However,
distributed PV systems, composed of numerous small PV generation units
located in various geographic locations, are more dispersed and flexible
compared to traditional centralized PV stations. This dispersion results
in significant local microclimate impacts on distributed PV systems.
Traditional methods have limited capacity to handle such complex
nonlinear issues, making it challenging to fully exploit the nonlinear
feature mapping relationships between various characteristics and PV
power in the data, thus hindering improvements in prediction accuracy
{[}19{]}.

With the rapid development of artificial intelligence technologies, deep
learning has gained significant attention from researchers due to its
powerful nonlinear fitting and generalization capabilities. It is now
widely applied in various fields, including power system fault diagnosis
and prevention {[}20{]}, energy prediction and optimization {[}21{]},
power market analysis and decision support {[}22{]}, and renewable
energy power prediction {[}23{]}. Common deep learning algorithms
include Long Short-Term Memory (LSTM) networks and Gated Recurrent Units
(GRU). For instance, reference {[}24{]} proposed a multivariate
ultra-short-term centralized wind farm power prediction method based on
LSTM networks, enhancing prediction accuracy by selecting variables
highly correlated with power using a distance analysis method. Another
study {[}25{]} introduced a centralized PV power prediction model based
on a dual-attention mechanism GRU network and similar sequence
correction. This model enhances feature extraction by incorporating
feature and temporal attention modules and improves prediction accuracy
by correcting the prediction results with future values of similar power
sequences. However, the aforementioned studies primarily considered
meteorological features such as solar irradiance, wind speed, and wind
direction, without deeply exploring the periodic characteristics of
power, limiting further improvement in model fitting performance.
Additionally, LSTM networks, while powerful, are complex,
computationally intensive, and time-consuming to train, often leading to
overfitting. Although GRU simplifies the structure, it still has
limitations in capturing long-range dependencies and bidirectional
long-term sequence features. In contrast, Bidirectional GRU (Bi-GRU)
combines forward and backward GRU layers, better capturing the
bidirectional dependencies in PV power time series, thereby improving
prediction accuracy and model generalization capabilities while
maintaining high computational efficiency.

Compared to manual parameter tuning, hyperparameter optimization
algorithms offer significant advantages. For instance, reference
{[}26{]} proposed an ultra-short-term centralized PV power prediction
method combining the Whale Optimization Algorithm (WOA) and a parallel
deep learning model (PMCI-PCNN-BiLSTM). This method improved prediction
accuracy and model generalization by extracting temporal and spatial
features from historical data through similar day clustering, multi-mode
decomposition, and multi-channel input. Another study {[}27{]}
introduced a PV power prediction method based on short-term power
feature clustering, utilizing the K-ISSA-LSTM model, which optimizes the
hyperparameters of the Long Short-Term Memory (LSTM) network by
combining the K-means clustering algorithm and an improved sparrow
search algorithm (ISSA).The Whale Optimization Algorithm (WOA) is known
for its strong global search capability and fast convergence speed, but
it has insufficient local search ability and is sensitive to parameters.
The Improved Sparrow Search Algorithm (ISSA) enhances the ability to
escape local optima by balancing exploration and exploitation, although
it is more complex and has unstable convergence speeds. In contrast, the
Bayesian hyperparameter optimization algorithm based on Tree-structured
Parzen Estimator (TPE) constructs and optimizes a probabilistic model,
efficiently exploring the hyperparameter space and achieving rapid
convergence. It also offers automated tuning and strong robustness,
making it significantly superior to WOA and ISSA in terms of efficiency,
accuracy, and applicability in hyperparameter optimization.

Centralized and distributed photovoltaic (PV) systems exhibit
significant differences in the spatial characteristics between
meteorological features and power output. Centralized PV systems are
concentrated at single sites where meteorological conditions are
relatively uniform, and spatial features are simple, relying primarily
on temporal variations for prediction. For example, reference {[}28{]}
proposed a Dynamic Convolutional Generative Adversarial Network (DC-GAN)
method based on satellite cloud image video frames, which combined
radiative data from centralized PV stations, spatial correlations of
distributed stations, and cloud cover characteristics to construct a
prediction model, thereby improving prediction accuracy. Another study
{[}29{]} presented a regional distributed PV output prediction method
based on spatial correlation. This method equated distributed stations
within a region to a virtual centralized station, using the Adaptive
Neuro Fuzzy Inference System (ANFIS) to predict the output of the
centralized station and then using polynomial fitting to predict the
output of distributed stations.However, these methods focus on
predicting the output of distributed PV stations within a certain region
and do not address predictions for single distributed PV stations. The
diverse geographical locations of individual distributed PV systems lead
to significant differences in meteorological conditions, characterized
by complex spatial heterogeneity and lower correlation. Therefore, it is
crucial to handle and fully utilize the spatiotemporal feature
correlations between meteorological characteristics and power output in
individual distributed PV systems to enhance prediction accuracy.

Table 1 Comparison of forecasting methods\selectlanguage{english}
\begin{longtable}[]{@{}llll@{}}
\toprule
Literature number & Model & Innovation point & Scope of
application\tabularnewline
\midrule
\endhead
{[}12{]} & Physics Model & Proposed a five-parameter photovoltaic system
simulation model combining algebraic and analytical techniques, which
has been validated to accurately predict the performance of photovoltaic
systems under actual conditions. & Photovoltaic power
plant\tabularnewline
{[}13{]} & Physics Model & Improved prediction accuracy by forecasting
solar radiation and temperature using only current solar radiation and
temperature values as inputs. & Photovoltaic power plant\tabularnewline
{[}17{]} & IMWOASVM & Developed a hybrid improved whale optimization
algorithm (IMWOA) combined with support vector machine (SVM) model for
short-term photovoltaic power prediction. The IMWOA optimized the kernel
function parameters and penalty coefficients in SVM, thereby enhancing
prediction accuracy. & Photovoltaic power plant\tabularnewline
{[}18{]} & IMC & Innovatively proposed an improved Markov chain model,
which effectively improves the accuracy and applicability of
photovoltaic power output probability prediction by combining the
conditional probability structure of influencing factors, influencing
factor selection based on rough set theory, and K-nearest neighbor
similar sample mining. & Photovoltaic power plant\tabularnewline
{[}24{]} & LSTM & Proposed a multivariate wind power plant
ultra-short-term power generation prediction method based on long
short-term memory network (LSTM). This method improves the accuracy of
wind power prediction by selecting highly correlated multivariate time
series through Pearson correlation coefficient and utilizing LSTM
network's dynamic time modeling capability. & Centralized wind
farms\tabularnewline
{[}25{]} & DA-GRU & Proposed a photovoltaic power prediction model based
on dual attention mechanism GRU network and similar sequence correction.
By introducing feature attention and time attention modules, the model's
ability to extract effective information is enhanced, and the prediction
accuracy is improved by correcting the prediction results with future
values of similar power sequences. & Centralized Photovoltaic Power
Plant\tabularnewline
{[}26{]} & WOA-PMCI-PCNN-BiLSTM & Proposed a centralized photovoltaic
power prediction method combining whale optimization algorithm (WOA) and
parallel deep learning model (PMCI-PCNN-BiLSTM). Through similar day
clustering, multi-mode decomposition, and multi-channel input, the
prediction accuracy and model generalization ability are effectively
improved. & Centralized Photovoltaic Power Plant\tabularnewline
{[}27{]} & K-ISSA-LSTM & Proposed a photovoltaic power prediction method
based on short-term power feature clustering of K-ISSA-LSTM. By
combining the K-means clustering algorithm and the improved sparrow
search algorithm to optimize the hyperparameters of long short-term
memory network, the accuracy of photovoltaic power prediction under
complex weather conditions is effectively improved. & Centralized
Photovoltaic Power Plant\tabularnewline
{[}28{]} & DC-GAN & Introduced an innovative dynamic convolutional
generative adversarial network (DC-GAN) method based on satellite cloud
map video frames. By combining radiation data from centralized
photovoltaic power stations, spatial correlations of distributed
stations, and cloud coverage features, the prediction accuracy is
enhanced through model construction. & Distributed Photovoltaic Power
Plants\tabularnewline
{[}29{]} & ANFIS & Proposed a region-based distributed photovoltaic
output prediction method based on spatial correlation. By equivalenting
distributed stations within the region to virtual centralized stations
and using ANFIS method to predict the output of centralized stations,
distributed station output prediction is achieved through polynomial
fitting. & Distributed PV Cluster\tabularnewline
\bottomrule
\end{longtable}

Although methods for predicting centralized PV power output can be
referenced, distributed PV systems exhibit fundamental differences in
system characteristics. Centralized PV power stations, due to their
scale and geographic diversity, can achieve a certain level of output
complementarity, thereby reducing overall output fluctuations. In
contrast, distributed PV systems consist of small, dispersed units whose
outputs are affected by local microclimatic conditions such as smoke and
shadows, necessitating individual predictions. The geographic diversity
of distributed PV systems leads to complex meteorological conditions
with significant spatial heterogeneity and low correlation. Current
methods are inadequate in handling and fully leveraging the
spatiotemporal correlations between meteorological features and power
output.Therefore, distributed PV power prediction methods need to be
specifically designed to effectively capture and utilize these complex
spatiotemporal features. Additionally, existing methods in model
construction and power mapping processes fail to fully exploit the
comprehensive situation and trends in the power generation dataset
across different time scales and power cycle scales. They overlook
important features in the sequence information, resulting in significant
deviations between the predicted and actual power curves, thereby
reducing prediction accuracy. Thus, developing short-term power
prediction methods tailored for distributed PV systems to address these
challenges is particularly urgent and important.

In summary, addressing the key challenges in short-term power prediction
for distributed photovoltaic (PV) stations, this paper proposes a
TPE-CBiGRU model prediction method based on multi-scale feature fusion.
Feature fusion is performed at both the data and model layers, utilizing
Convolutional Neural Networks (CNN) for spatial feature extraction,
Bi-GRU networks for time series feature modeling, and an Add layer for
feature fusion. Additionally, a Bayesian hyperparameter optimization
method based on Tree-structured Parzen Estimator (TPE) is employed to
fine-tune model parameters. The main contributions of this paper are as
follows:

1. Comprehensive Feature Engineering Process: A comprehensive feature
engineering process is proposed, integrating multi-scale features such
as meteorological conditions, temporal characteristics, and the periodic
features of PV power generation. Compared to models that only consider
meteorological conditions, this integration improves the fitting degree
R2 by 3.07\%, enhancing the accuracy of short-term PV power prediction.

2. Bayesian Hyperparameter Optimization with TPE: The application of
Bayesian hyperparameter optimization using TPE in the CBiGRU model is
demonstrated. This method efficiently searches for the optimal
hyperparameter combination, with a total experimental duration of 21
hours, 35 minutes, and 55 seconds, significantly reducing the time
required compared to manual methods and improving the efficiency and
accuracy of model optimization.

3. TPE-CBiGRU Model for Distributed PV Short-term Power Prediction: The
TPE-CBiGRU model is proposed for short-term power prediction of
distributed PV systems. By capturing spatial and temporal features using
CNN and Bi-GRU networks, respectively, and fusing features through an
Add layer, the model reduces the Mean Absolute Error (MAE) and Root Mean
Square Error (RMSE) by 26.11\% and 35.64\%, respectively. It also
demonstrates higher prediction concordance across multiple time scales,
validating the model's effectiveness in uncovering intrinsic data
relationships.

The structure of the remaining sections of this paper is as follows: The
introduction section introduces the research background and significance
of distributed photovoltaic (PV) power prediction. Next, the first part
delves into the concept of multi-scale feature fusion, including a
detailed description of feature fusion at both the data layer and the
model layer. The second part elaborates on the TPE-CBiGRU short-term PV
power prediction model, covering the model framework, parameter
optimization strategies, and prediction process. The third part provides
a case study analysis, including experimental platform configuration,
data sources, selection of evaluation metrics, comparative analysis of
parameter optimization methods, performance comparison of different
prediction models, and validation of the effectiveness of model key
components through ablation experiments. Finally, the conclusion section
summarizes the research findings of this paper.

\subsection*{Multi-scale Feature
Fusion}

{\label{multi-scale-feature-fusion}}

In the field of distributed photovoltaic (PV) power generation, the
unique geographic locations and operating mechanisms mean that power
generation is influenced not only by meteorological conditions, such as
solar irradiance and temperature variations, but also by temporal
characteristics, such as seasonal changes and different times of the
day. The dynamic interactions of these multi-dimensional features pose
challenges to the stable operation of the grid while providing potential
information sources for accurate PV power prediction. To fully exploit
and effectively utilize this information, improving the accuracy and
robustness of prediction models, this study proposes an innovative
multi-scale feature fusion strategy.

Feature fusion is a critical technique in time series data analysis,
aiming to merge features from multiple time scales or different sources
into a unified feature set to enhance the model's capability to
represent data and improve prediction accuracy {[}30, 31{]}. This
process includes steps such as feature extraction, transformation,
fusion, and selection. By effectively integrating multi-source features,
the model can better capture the spatiotemporal characteristics of the
data. Additionally, feature fusion plays a noise reduction role in data
analysis. By integrating information from multiple time scales or
feature sources, it can reduce noise interference in the data,
extracting more stable and reliable feature representations, thereby
improving the performance and robustness of the model {[}32, 33{]}.
Feature fusion has broad application prospects in time series
prediction, signal processing, financial analysis, and other fields.

To fully exploit the key information in the data, this paper extracts
and fuses feature information at both the data layer and the model
layer:

Data Layer: First, based on resampling techniques, features related to
time scales and periodic scales in the data are extracted to construct
time feature matrices and periodic feature matrices. These feature
matrices are then aligned to the same granularity and concatenated.
Finally, they are merged with the original input data matrix to obtain
the multi-scale feature input matrix at the data layer.

Model Layer: The data is input into CNN and Bi-GRU models, where
high-dimensional spatial features are extracted by the CNN model and
multi-dimensional temporal features are extracted by the Bi-GRU model.
These feature layers are then combined using an Add layer to further
integrate the feature information. This approach leverages the strengths
of both CNN in capturing spatial dependencies and Bi-GRU in modeling
temporal sequences, enhancing the overall prediction performance of the
model.

Data-level Feature Fusion

The core of feature fusion at the data layer lies in constructing the
time feature matrix and the periodic feature matrix. The time scale
feature matrix includes time series features closely related to
photovoltaic (PV) power, which can provide systematic time series data
for model training. In this strategy, time features encompass year,
season, month, date, hour, and minute. These time features
comprehensively reflect the operating environment of the PV system and
external influencing factors. Specifically, changes in the year reflect
long-term trends and variations in the system environment, seasonal
changes, and months reflect variations in daylight duration. Dates and
hours reflect daily peak and off-peak electricity consumption periods,
directly related to the power demand of the PV system.

Additionally, compared to centralized PV plants typically located in
remote and open areas, distributed PV systems are often installed in
urban environments, making them more susceptible to local microclimate
factors such as chimney emissions, shadows from tall buildings, and
other local microclimatic conditions. By introducing high time
resolution (15 minutes) data features, the model can more accurately
capture the subtle fluctuations in the environment of distributed PV
generation, which is crucial for improving the accuracy of distributed
PV power prediction models. These features are summarized in Table 2:

Table 2 Temporal Scale Features\selectlanguage{english}
\begin{longtable}[]{@{}lll@{}}
\toprule
Feature Column & Function & Encoding Method\tabularnewline
\midrule
\endhead
Year & Represents overall trends and annual variations in power
generation over time. & Encoded as numerical features: 2022,
2023\tabularnewline
Season & Provides critical clues about seasonal changes. & Spring: 1,
Summer: 2, Autumn: 3, Winter: 4\tabularnewline
Month & Captures monthly variation patterns and periodic characteristics
of power generation. & Encoded as numerical features: 1 to
12\tabularnewline
Day & Describes fluctuations in power generation on different days of
the month. & Date encoding: 1 to 31\tabularnewline
Hour & Represents power generation variations across different times of
the day. & 1. Numerical features: 0 to 23 2. Converted to sine and
cosine values\tabularnewline
Minute & Provides detailed information on fine-grained fluctuations in
distributed photovoltaic power generation. &
0min,15min,30min,45min\tabularnewline
\bottomrule
\end{longtable}

The periodic scale feature matrix aims to explore the characteristics of
photovoltaic (PV) power generation on an hourly basis, uncovering
periodic features within a 24-hour cycle. Five features are calculated
for each 24-hour cycle: average value, maximum value, minimum value,
standard deviation, and variance of the generated power. The average
value represents the central tendency of the dataset, reflecting the
typical level of power generation within a given time period. The
maximum value indicates the highest level of power generation during
that period, while the minimum value denotes the lowest level. The
standard deviation measures the extent to which values deviate from the
mean, its magnitude reflecting data volatility, which is crucial for
understanding power generation fluctuations within a given cycle.
Variance, the average of the squared differences from the mean,
similarly measures the dispersion of data points. These statistical
features provide insights into the overall condition and variation
trends of the power generation dataset across different time periods.
The specific steps are illustrated in Figure 1.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

Figure 1 Power cycle feature matrix extraction and splicing

As illustrated in Figure 1, the process begins with resampling to
extract the average value, maximum value, minimum value, standard
deviation, and variance of power generation over periods ranging from 1
hour to 24 hours, resulting in 24 feature matrices. These 24 feature
matrices are then aligned with the input data's time granularity (15
minutes). Finally, the 24 matrices are concatenated to construct the
periodic scale feature input matrix for power generation.

In summary, by concatenating the raw data features, temporal scale
features, and power cycle features, we construct the model's input
feature matrix. This fusion method integrates diverse characteristics to
enhance the model's predictive capability. The detailed feature
information is presented in Table 3.

Table 3 Model Input Features\selectlanguage{english}
\begin{longtable}[]{@{}ll@{}}
\toprule
Feature Category & Feature Name\tabularnewline
\midrule
\endhead
Original Data Features &
Power\begin{CJK}{UTF8}{gbsn}、\end{CJK}\selectlanguage{english}Irradiance\begin{CJK}{UTF8}{gbsn}、\end{CJK}\selectlanguage{english}Temper\begin{CJK}{UTF8}{gbsn}、\end{CJK}\selectlanguage{english}Pressure\begin{CJK}{UTF8}{gbsn}、\end{CJK}\selectlanguage{english}Humidity\tabularnewline
Temporal Scale Features &
Year\begin{CJK}{UTF8}{gbsn}、\end{CJK}\selectlanguage{english}Season\begin{CJK}{UTF8}{gbsn}、\end{CJK}\selectlanguage{english}Month\begin{CJK}{UTF8}{gbsn}、\end{CJK}\selectlanguage{english}Day\begin{CJK}{UTF8}{gbsn}、\end{CJK}\selectlanguage{english}Hour\begin{CJK}{UTF8}{gbsn}、\end{CJK}\selectlanguage{english}Hour-sin\begin{CJK}{UTF8}{gbsn}、\end{CJK}\selectlanguage{english}Hour-cos\begin{CJK}{UTF8}{gbsn}、\end{CJK}\selectlanguage{english}Minute\tabularnewline
Power Period Features (with cycles of 1, 2, \ldots{}, 24 hours) &
\begin{CJK}{UTF8}{gbsn}、、、、 、、、、 \end{CJK}\selectlanguage{english}\ldots{}\ldots{} \begin{CJK}{UTF8}{gbsn}、、、、\end{CJK}\selectlanguage{english}\tabularnewline
\bottomrule
\end{longtable}

Model-level Feature Fusion

To further enhance the model's performance, this study employs a CNN
network and a Bi-GRU network to extract spatial and temporal features
from the input dataset, respectively. On this basis, an Add network is
used to fuse feature tensors from different network layers element-wise,
constructing a high-dimensional spatiotemporal feature matrix. This
enables the model to learn deeper and more comprehensive feature
information.

\emph{1)CNN architecture:} Convolutional Neural Networks (CNNs) are
renowned for their advantages in spatial information processing, and the
structure of the CNN model is illustrated in Figure 2. By leveraging
local perception and weight sharing, CNN models can map input data into
high-dimensional space and efficiently extract key features from the
input data {[}34{]}. In the structure of the CNN model, the
convolutional layer plays a crucial role, using convolutional kernels
with shared weights to extract features from the input data and applying
activation functions to perform nonlinear mapping of neurons, thereby
capturing complex relationships within the data. The pooling layer then
reduces the dimensionality of the features obtained from the convolution
operation through methods such as max pooling or average pooling,
thereby compressing the feature quantity and reducing the risk of
overfitting.

In the context of time series data, CNN models also demonstrate powerful
feature extraction capabilities {[}35{]}. Although CNNs were initially
designed for image data processing, their applicability to time series
data stems from their ability to effectively extract spatial features.
Time series data can be viewed as spatial data points arranged
sequentially along the time axis, allowing CNNs to utilize their local
perception and weight sharing properties to discover and exploit spatial
correlations among data points within the time series. This capability
enables CNNs to capture important features in time series data, thereby
enhancing the model's performance and generalization ability.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image17/image17}

\end{center}
\end{figure}

Figure 2 CNN architecture

\emph{2)Bi-GRU structure:} The Bidirectional Gated Recurrent Unit
(Bi-GRU) is a specialized variant of the standard GRU architecture,
comprising two GRU layers with identical outputs but opposite directions
of information flow. The Bi-GRU model simultaneously considers
information from both past and future time steps, thereby fully
exploiting the temporal characteristics of photovoltaic power data and
enhancing data utilization and prediction accuracy {[}36, 37{]}. The
structure of a single-layer GRU is illustrated in Figure 3.

In Equation (1), represents the input to the GRU model at time step ;
and denote the sigmoid and hyperbolic tangent activation functions,
respectively; is the reset gate, which indicates the influence of the
input at time and the hidden state output from the previous time step on
the candidate hidden state ; is the update gate, indicating the extent
to which the hidden state output from the previous time step influences
the hidden state output at time ; is the candidate hidden state,
computed from the input and the hidden state output from the previous
time step; is the hidden state output at time . The weight matrices ,
and correspond to the reset gate, update gate, and candidate hidden
state, respectively.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image40/image40}

\end{center}
\end{figure}

Figure 3 Single layer GRU structure

Based on the aforementioned GRU model, a Bi-GRU model can be constructed
by setting up forward and backward GRU layers. The basic structure of
the Bi-GRU model is illustrated in Figure 4. In this figure, represents
the output of the forward GRU model at time , and represents the output
of the backward GRU model at time .\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image45/image45}

\end{center}
\end{figure}

Figure 4 Bi-GRU structure

The Bi-GRU model\selectlanguage{ngerman}·computational equation can be expressed as:

Where: and are the positive-order GRU model input weight matrix and time
output weight matrix, respectively; and are the negative-order GRU model
input weight matrix and time output weight matrix, respectively; and are
the positive-order GRU model and the negative-order GRU model output
weight matrix, respectively.

\subsection*{TPE-CBiGRU Short-term Photovoltaic Power Prediction
Model}

{\label{tpe-cbigru-short-term-photovoltaic-power-prediction-model}}

\begin{enumerate}
\tightlist
\item
  Model Framework
\end{enumerate}

This paper leverages the superior spatial feature extraction
capabilities of Convolutional Neural Networks (CNN) and the long-term
sequential feature extraction capabilities of Bidirectional Gated
Recurrent Units (Bi-GRU). Additionally, it employs the Tree-structured
Parzen Estimator (TPE)-based Bayesian optimization algorithm to
fine-tune the parameters of the CBiGRU prediction model. The detailed
structural framework is illustrated in Figure 5.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image57/image57}

\end{center}
\end{figure}

Figure 5 TPE-CBiGRU Structure

Input Layer: The raw data is combined with the extracted temporal and
power cycle features for the first fusion (data-level feature fusion) to
construct the model's input feature matrix.

Feature Extraction Layer: The feature matrix is input into the CNN and
Bi-GRU networks. The hyperparameters of both CNN and Bi-GRU are
optimized using the TPE-based Bayesian hyperparameter search. The CNN
outputs high-dimensional spatial features, while the Bi-GRU outputs
high-dimensional temporal features.

Feature Fusion Layer: The extracted multi-dimensional abstract
spatio-temporal features are fused at the Add layer, completing the
second fusion (model-level feature fusion).

Output Layer: The feature matrix obtained after the second fusion is
input into the Dense layer to generate the prediction results.

TPE Parameter Optimization

Bayesian Optimization (BO) is an active optimization method and one of
the black-box optimization algorithms. Proposed by Snoek et al. in 2012
{[}38{]}, BO aims to solve extremum problems for functions with unknown
expressions. Research has shown that Bayesian optimization outperforms
traditional grid search and random search methods, particularly by
avoiding local optima. However, traditional BO algorithms can suffer
from the curse of dimensionality when handling large parameter spaces,
which can degrade their performance {[}39{]}.

To address the hyperparameter selection problem for the CBiGRU model,
this paper proposes a CBiGRU parameter optimization method based on the
Tree-Structured Parzen Estimator (TPE). The performance of the CBiGRU
model is influenced by parameters such as the number of network units,
the number of network layers, and the learning rate. TPE is a
non-standard Bayesian optimization algorithm that employs a
tree-structured Parzen density estimator {[}40{]}. Compared to
traditional Bayesian optimization algorithms, TPE can more effectively
handle large parameter spaces, thus avoiding the adverse effects of the
curse of dimensionality on the algorithm's performance. Its core idea is
to model and optimize the parameter space by constructing a
tree-structured model, thereby achieving an efficient parameter search
and optimization process. TPE has been widely applied in hyperparameter
optimization and automated machine learning, yielding impressive
results. In traditional Bayesian optimization theory, the process
involves:

The density function represents the observations where the loss of is
less than the threshold , while denotes the density formed by the
remaining observation values. In the Tree-structured Parzen Estimator
(TPE) algorithm, the Bayesian formula is utilized to optimize the
expected improvement function :

Let , representing a certain quantile of the TPE algorithm, which is
used to partition and , and then construct:

Subsequently, based on equations (6) and (7), we obtain:

Finally, can be simplified to:

From equation (9), it is evident that to maximize , it is necessary to
ensure that the probability of is high and the probability of is low at
point . TPE utilizes the ratio to evaluate the selected candidate
objects, and after a certain number of iterations, the algorithm returns
the candidate with the maximum .

Prediction Process

The prediction process in this paper is divided into six steps, as
illustrated in Figure 6:\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image79/image79}

\end{center}
\end{figure}

Figure 6 Forecasting Flowchart

1) Data preprocessing: The K-Nearest Neighbors (KNN) interpolation
method is utilized to automatically calculate and fill in missing values
in the data based on the neighboring values of the missing points.
Outliers are replaced by the average of the values before and after the
outlier at the preceding and following time steps.

2) Construction of input feature matrix: The input feature matrix
consists of three parts: the original processed data, the time feature
matrix, and the power cycle feature matrix. The original processed data
refers to the data processed in step 1). The time feature matrix
includes features extracted from the original data, such as the year and
season. The power cycle feature matrix consists of periodic features
extracted from the original data, such as the average, maximum, and
minimum values of power. These three parts of feature matrices are
concatenated to achieve data-level feature fusion.

3) Data standardization: The input feature matrix constructed in step 2)
is standardized using Z-Score normalization to eliminate the influence
of different magnitudes and dimensions. This process ensures that the
mean of the data is 0 and the standard deviation is 1, while preserving
the relative differences in the data without altering the distribution
shape or the relative relationships of the data.

In the formulas, represents a selected feature or column from the matrix
X. denotes the mean of all values for feature (), and represents the
standard deviation of feature (). The standardized data are then divided
into training, validation, and test sets to facilitate model training
and evaluation.

4) Hyperparameter optimization: The dataset constructed in step 3) is
input into the TPE-CBiGRU model, with the highest performance metric as
the optimization objective. The Tree-Structured Parzen Estimator (TPE)
based Bayesian hyperparameter optimization algorithm is then employed to
search for and optimize the hyperparameters of the TPE-CBiGRU model,
returning the optimal hyperparameter combination.

5) Training the optimal TPE-CBiGRU model: The standardized feature
matrix from step 3) and the optimal hyperparameters obtained in step 4)
are input into the TPE-CBiGRU model to extract high-dimensional temporal
and spatial features. These high-dimensional spatiotemporal features are
then superimposed and fused through the Add layer network (feature
fusion at the model layer) for deep feature fusion. Subsequently, the
fused features are processed by the Dense layer to produce the model's
training output, while monitoring overfitting using the validation set.

6) Analysis of prediction results: The test set data are input into the
optimized TPE-CBiGRU model obtained in step 5) to obtain the
photovoltaic power prediction results. By comparing the prediction
results with those of the comparative models using error evaluation
metrics, an in-depth analysis of the prediction performance of the
TPE-CBiGRU model is conducted to validate its effectiveness and
accuracy.

\subsection*{Case Study Analysis}

{\label{case-study-analysis}}

\begin{enumerate}
\tightlist
\item
  Experimental Platform Configuration and Data Sources
\end{enumerate}

The experiment was conducted using PyCharm 2023.2 (Community Edition) as
the development platform, with an integrated development environment
constructed using Miniconda3. The short-term photovoltaic power
prediction model was built on a deep learning framework based on Python
3.8, utilizing TensorFlow 2.6.0 and Keras 2.7.0. The model was validated
using real-world data from a distributed photovoltaic (PV) power station
in China. The dataset includes one year of power generation and
meteorological data from February 21, 2022, to February 21, 2023, with a
data sampling interval of 15 minutes. The data were split into training,
validation, and test sets with proportions of 75\%, 15\%, and 15\%,
respectively.The experimental setup was as follows: the operating system
was Windows 10, the CPU was a 12th Gen Intel(R) Core(TM) i5-12490F, the
GPU was an NVIDIA GeForce RTX 3060, and the system had 16GB of RAM.

Evaluation Metrics

Due to the presence of zero values in photovoltaic power, the mean
absolute percentage error (MAPE), commonly used in photovoltaic power
prediction, becomes meaningless. Therefore, this paper selects the mean
absolute error (MAE), root mean square error (RMSE), and coefficient of
determination () as the primary evaluation metrics to comprehensively
represent the model's prediction accuracy {[}41{]}. The MAE, RMSE, and
are calculated as follows:

where , , and represent the actual photovoltaic power value, the mean of
the actual photovoltaic power values, and the predicted photovoltaic
power value, respectively; is the number of data points in the
validation set; and is the index of the predicted data points.

Comparison of Parameter Optimization Methods

This paper employs the Bayesian hyperparameter optimization method based
on Tree-Structured Parzen Estimator (TPE) within the Optuna optimization
framework to optimize the critical hyperparameters of the CBi-GRU model
{[}42{]}. The fundamental principle involves defining the hyperparameter
search space and optimization objective. Through Bayesian optimization,
the algorithm iteratively explores and updates the optimal
hyperparameters within the search space to minimize the loss function.
Based on an analysis of the CBi-GRU model, eight hyperparameters with
the most significant impact on the model's performance were selected for
optimization through experimental analysis. Since the output structure
of the last layer of the Bi-GRU only requires returning the predicted
data of the last timestep, hyperparameter search was conducted
exclusively for the last layer. The hyperparameters and their respective
search spaces are shown in Table 4:

Table 4 Hyperparametric search space\selectlanguage{english}
\begin{longtable}[]{@{}lll@{}}
\toprule
& Hyperparameterization & Searched Interval\tabularnewline
\midrule
\endhead
Global Parameters & learning\_rate & {[}1e-5,1e-1{]}\tabularnewline
Bi-GRU & bigru\_num\_layers & {[}1,4{]}\tabularnewline
& bigru\_unit\_final & {[}32,256{]}\tabularnewline
& units\_per\_layer & {[}32,256{]}\tabularnewline
& bigru\_dropout & {[}0.1,0.5{]}\tabularnewline
& bigru\_dropout\_final & {[}0.1,0.5{]}\tabularnewline
CNN & cnn\_unit & {[}32,256{]}\tabularnewline
& cnn\_dropout & {[}0.1,0.5{]}\tabularnewline
\bottomrule
\end{longtable}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image98/image98}

\end{center}
\end{figure}

Figure 7 Histogram of importance of model hyperparameters

Figure 7 illustrates the importance of the eight hyperparameters on the
loss of the CBi-GRU model after 80 experimental runs. As shown in Figure
7, the dropout rate for the CNN network (cnn\_dropout) has the most
significant impact on model accuracy, accounting for 31.0\%. This is
followed by the number of units in the first layer of the Bi-GRU network
(bigru\_units\_layer0), the dropout rate for the Bi-GRU network
(bigru\_dropout), and the learning rate (learning\_rate), with impacts
of 10.0\%, 8.0\%, and 7.0\%, respectively. The term ''first layer units
(bigru\_units\_layer0)'' refers to the number of units in the first
layer within the searched interval {[}1,4{]} for the number of layers
(bigru\_num\_layers). Subsequently, the dropout rate for the final layer
of the Bi-GRU network (bigru\_dropout\_final) and the number of units in
the final layer (bigru\_unit\_final) impact the model by 5.0\% and
4.0\%, respectively. The number of units in the CNN network (cnn\_unit)
and the number of layers in the Bi-GRU network (bigru\_num\_layers) have
the smallest impact, each accounting for 3.0\%.

The detailed breakdown of the hyperparameters and their respective
impacts on the model's performance underscores the critical elements
influencing the CBi-GRU model's accuracy and provides a clear path for
targeted optimization. This analysis emphasizes the significance of
fine-tuning dropout rates and layer configurations to enhance predictive
performance effectively.

The total experimental duration was 21 hours, 35 minutes, and 55
seconds, significantly reducing the time required compared to manual
trials. The major advantage of automated hyperparameter optimization
lies in its efficiency and accuracy. Utilizing the Bayesian optimization
algorithm based on Tree-Structured Parzen Estimator (TPE), parameter
adjustments during the experimental process are completed in a shorter
timeframe with more precise results. Compared to manual experimentation,
the automated optimization method significantly improves experimental
efficiency, reduces resource wastage, and facilitates easier replication
and adjustment. This automated approach not only accelerates research
progress but also enhances the reliability of experimental results,
thereby providing strong support for scientific research and engineering
applications.

Through the analysis of 80 trials, the results are shown in Figure 8.
The highest value of 96.00\% was achieved in the 51st experiment,
indicating the highest fitting degree between the predicted curve and
the actual values. Therefore, the hyperparameter combination with an
value of 96.00\% was selected to build the model, with the parameter
combination detailed in Table 5. Figure 9 shows the loss curves of the
training and validation sets for the selected hyperparameter
combination, demonstrating that the errors for both the training and
validation sets are below 0.1, indicating a well-fitted model.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image101/image101}

\end{center}
\end{figure}

Figure 8 TPE search experiment

Table 5 Hyperparameter search results\selectlanguage{english}
\begin{longtable}[]{@{}lll@{}}
\toprule
& Hyperparameterization & Search results\tabularnewline
\midrule
\endhead
Global Parameters & learning\_rate &
0.00036579169481258444\tabularnewline
Bi-GRU & bigru\_num\_layers & 1\tabularnewline
& bigru\_num\_layer0 & 32\tabularnewline
& bigru\_unit\_final & 128\tabularnewline
& bigru\_dropout & 0.33999999999999997\tabularnewline
& bigru\_dropout\_final & 0.14\tabularnewline
CNN & cnn\_unit & 32\tabularnewline
& cnn\_dropout & 0.22\tabularnewline
\bottomrule
\end{longtable}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image103/image103}

\end{center}
\end{figure}

Figure 9 Model loss curves

Comparison of Prediction Models

To further validate the superiority of the proposed model in
photovoltaic power prediction, comparisons were made with Bi-LSTM,
Bi-GRU, GRU, LSTM, and C-LSTM models. The overall performance comparison
between the proposed model and other models is shown in Table 6. To
illustrate the comparison of actual power values and power prediction
results of different models under clear and cloudy weather conditions,
Figure 10 (a) and (c) display continuous clear days from February 16,
2023, 0:00 to February 17, 2023, 24:00, while Figure 10 (b) and (d)
compare cloudy days on January 20, 2023, 0:00--24:00 and February 5,
2023, 0:00--24:00.

Table 6 Model Comparison Experimental Effects\selectlanguage{english}
\begin{longtable}[]{@{}llll@{}}
\toprule
& MAE & RMSE &\tabularnewline
\midrule
\endhead
TPE-CBiGRU & 0.5273 & 1.0710 & 96.03\%\tabularnewline
Bi-LSTM & 0.6635 & 1.4180 & 93.05\%\tabularnewline
Bi-GRU & 0.5762 & 1.2564 & 94.54\%\tabularnewline
GRU & 0.7884 & 1.4274 & 92.96\%\tabularnewline
LSTM & 0.6195 & 1.3244 & 93.94\%\tabularnewline
C-LSTM & 0.7207 & 1.2407 & 94.68\%\tabularnewline
\bottomrule
\end{longtable}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image105/image105}

\end{center}
\end{figure}

Figure 10 Power prediction curve \textbf{(a) (c)} Sunny \textbf{(b) (d)}
Cloudy

Combining Table 6 and Figure 10, a comparative analysis of the
performance of each model was conducted. Overall, the TPE-CBiGRU model
achieved the best performance in terms of mean absolute error (MAE) and
root mean square error (RMSE), with the highest coefficient of
determination (R\selectlanguage{ngerman}²). The C-LSTM and Bi-GRU models followed in
performance. The proposed TPE-CBiGRU model excelled across multiple
metrics, demonstrating the highest accuracy and the closest fit of the
prediction curve to the actual curve.

Specifically, compared to traditional deep learning models, the proposed
TPE-CBiGRU model shows a reduction in mean absolute error (MAE) by
4.89\% and 9.22\% compared to the Bi-GRU and LSTM models, respectively.
The reductions are even more pronounced for the Bi-LSTM, GRU, and C-LSTM
models, at 13.62\%, 26.11\%, and 19.34\%, respectively, indicating an
improvement in model accuracy. In terms of root mean square error
(RMSE), the TPE-CBiGRU model exhibits a significant reduction of 18.54\%
and 16.97\% compared to the Bi-GRU and C-LSTM models, respectively. The
largest reductions are observed when compared to the Bi-LSTM, GRU, and
LSTM models, at 34.70\%, 35.64\%, and 25.34\%, respectively.From Figure
10, under sunny conditions (a) and (c), the TPE-CBiGRU model's
prediction curve fits well with the actual data, with the other models
performing slightly worse. This trend is even more evident under cloudy
conditions (b) and (d), highlighting the advantage of lower errors in
the proposed model. Regarding the coefficient of determination (R²), the
Bi-GRU and C-LSTM models perform closely to the TPE-CBiGRU model, with
R² values of 94.54\% and 94.68\%, respectively. The lowest R² values are
observed for the Bi-LSTM, GRU, and LSTM models, at 93.05\%, 92.96\%, and
93.94\%, respectively. This demonstrates that the feature fusion
component of the model effectively integrates the spatial and temporal
features extracted by CNN and Bi-GRU, enhancing the model's prediction
accuracy.

Furthermore, comparing the conditions depicted in Figure 10 (a) and (c)
under sunny conditions with (b) and (d) under cloudy conditions, the
following observations can be made: under sunny conditions, all six
predictive models demonstrate relatively high prediction accuracy, with
minimal performance differences among them. In sunny conditions, the
photovoltaic power exhibits a relatively stable curve with minimal
fluctuations. Therefore, each model only needs to focus on the overall
trend and offset of the prediction curve without considering subtle
fluctuations extensively. This simplifies the prediction task as the
models only need to capture the general shape of the curve without
dealing with complex fluctuations. In contrast, under cloudy conditions,
the proposed TPE-CBiGRU model exhibits the highest prediction accuracy.
Although other models also demonstrate high accuracy in sunny
conditions, albeit slightly lower than the TPE-CBiGRU model, considering
the predictive performance across various scenarios, the model proposed
in this study shows superior performance.

In summary, the fusion of features at the data layer to extract temporal
and power cycle characteristics and construct input feature matrices can
effectively enhance prediction accuracy. Simultaneously, feature fusion
at the model layer effectively integrates high-dimensional
spatiotemporal features extracted by CNN and Bi-GRU networks. This
further explores the mapping relationship between input features and
photovoltaic power, thereby improving the model's predictive accuracy.
As a result, the predicted power variations closely align with the
actual power variations, demonstrating a consistent trend.

Ablation Experiments

To further validate the effectiveness of each component of the
TPE-CBiGRU model, ablation experiments were conducted for analysis. By
reducing components, the contribution of each component to the model
performance was evaluated. There are three scenarios in total: (a)
TPE-CBiGRU0 model only inputs raw feature data without data layer
feature mining, verifying the effectiveness of data layer fusion; (b)
TPE-BiGRU model inputs raw data and data layer feature mining features,
validating CNN's ability to extract spatial features; (c) TPE-CNN model
inputs raw data and data layer feature mining features, validating the
feature extraction ability of the Bi-GRU network for time-series data.
The TPE-CBiGRU1 model proposed in Section 2 was established as a
comparison to test the effectiveness of the data layer feature fusion
component and the model layer feature fusion component. The missing
modules in (b) and (c) were replaced by Dense with the same parameters.
The experimental comparison results are shown in Table 7, and the power
prediction curves of each component model are compared in Figure 11,
with the prediction date selected as February 16, 2023, from 0:00 to
24:00.

Table 7 Comparison of ablation experiments\selectlanguage{english}
\begin{longtable}[]{@{}llll@{}}
\toprule
& MAE & RMSE &\tabularnewline
\midrule
\endhead
TPE-CBiGRU1 & 0.5273 & 1.0710 & 96.03\%\tabularnewline
TPE-CBiGRU0 & 0.8528 & 1.5773 & 91.40\%\tabularnewline
TPE-BiGRU & 0.5762 & 1.2564 & 94.54\%\tabularnewline
TPE-CNN & 1.0272 & 1.4799 & 92.43\%\tabularnewline
\bottomrule
\end{longtable}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image108/image108}

\end{center}
\end{figure}

Figure 11 Power prediction curves for each component model\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image110/image110}

\end{center}
\end{figure}

Figure 12 Ablation test performance comparison chart

Analyzing the comparison between Table 7 and Figure 11,12 the
TPE-CBiGRU0 model compared to the TPE-CBiGRU1 model, due to the removal
of data layer feature mining input, the TPE-CBiGRU0 model lacks key
feature perception of time scale and power cycle scale in the data,
resulting in a significant decrease in model performance. Compared to
the TPE-CBiGRU1 model, the MAE and RMSE of the TPE-CBiGRU0 model
increased by 32.55\% and 50.63\%, respectively, indicating a significant
increase in errors, with a decrease in the coefficient of determination
(R\selectlanguage{ngerman}²) by 4.63\%. The poor fit between the curves of TPE-CBiGRU0 and
TPE-CBiGRU1 in Figure 11 also confirms this, indicating that data layer
feature fusion can effectively extract multi-scale features in the data,
thereby improving model prediction accuracy.

Comparing the TPE-BiGRU model with the TPE-CBiGRU1 model, the
performance of the model decreases when the spatial features extracted
from the data by the CNN network are missing. By contrasting Figure 12,
the MAE and RMSE increase by 4.89\% and 18.54\%, respectively,
indicating an increase in errors, with a decrease in the coefficient of
determination (R²) by 1.49\%. Combined with Figure 11, the comparison
indicates that the presence of the CNN network can improve the
smoothness of the prediction curve, and prediction models with CNN tend
to fit the real power curve better than models without CNN. The spatial
features extracted by the CNN network from the data have a beneficial
effect on the proposed model. Comparing the TPE-CNN model with the
TPE-CBiGRU1 model, the model's performance decreases significantly when
lacking the temporal feature information extracted from long-time series
data by the Bi-GRU network. The MAE and RMSE increase by 49.99\% and
40.89\%, respectively, indicating a significant increase in errors, with
a decrease in the coefficient of determination (R²) by 3.60\%. This
demonstrates the critical role of the Bi-GRU network in extracting
temporal features, especially for long sequences. Through the comparison
between the TPE-CBiGRU1 model and the TPE-BiGRU, TPE-CNN models, it is
evident that the Add layer, which fuses the spatial-temporal feature
matrices extracted by the TPE-BiGRU and TPE-CNN networks, effectively
mines the crucial spatial-temporal features of the data, significantly
reducing model errors and further improving the model's fit.

\subsection*{Conclusion}

{\label{conclusion}}

This study addresses the challenge of improving the prediction accuracy
of distributed photovoltaic (PV) power generation. Considering the
multidimensional features and predictive performance, a short-term PV
power generation prediction model based on multiscale feature fusion
TPE-CBiGRU hybrid network is proposed. This model utilizes data-level
fusion to construct the input feature information of the model and
model-level feature fusion to extract high-dimensional spatial-temporal
features from the CBiGRU network. By integrating the TPE Bayesian
hyperparameter automatic optimization method, the model further enhances
the accuracy of PV power prediction.

The main conclusions of this study are as follows:

The proposed TPE-based Bayesian hyperparameter automatic optimization
method effectively searches for the optimal parameter combination of the
model. Compared to manual parameter adjustment methods, the
computational experiments consumed only 21 hours, 35 minutes, and 55
seconds. The model's training and validation set MAE iterated rapidly,
remaining below 0.1. The highest validation accuracy reached 96.00\%,
significantly enhancing the model's fitting capability and improving the
efficiency of parameter adjustment.

Data-level fusion provides crucial features for the TPE-CBiGRU model,
while model-level fusion combines the advantages of CNN spatial feature
extraction and BiGRU model's temporal prediction, enabling deep
exploration of the correlation between data and temporal output, thereby
enhancing the accuracy of temporal prediction. The results indicate that
the TPE-CBiGRU model outperforms the other five models in evaluation
metrics. Compared to the GRU model, the MAE and RMSE of the TPE-CBiGRU
model decrease significantly by 26.11\% and 35.64\%, respectively, while
R2 increases by 3.07\%.

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\textbf{Hosted file}

\verb`Table 1 Comparison of forecasting methods.xlsx`  available at \url{https://authorea.com/users/818321/articles/1218143-short-term-power-prediction-of-distributed-photovoltaic-systems-based-on-multi-scale-feature-fusion-using-tpe-cbigru}

\textbf{Hosted file}

\verb`Table 2 Temporal Scale Features.xlsx`  available at \url{https://authorea.com/users/818321/articles/1218143-short-term-power-prediction-of-distributed-photovoltaic-systems-based-on-multi-scale-feature-fusion-using-tpe-cbigru}

\textbf{Hosted file}

\verb`Table 3 Model Input Features.xlsx`  available at \url{https://authorea.com/users/818321/articles/1218143-short-term-power-prediction-of-distributed-photovoltaic-systems-based-on-multi-scale-feature-fusion-using-tpe-cbigru}

\textbf{Hosted file}

\verb`Table 4 Hyperparametric search space.xlsx`  available at \url{https://authorea.com/users/818321/articles/1218143-short-term-power-prediction-of-distributed-photovoltaic-systems-based-on-multi-scale-feature-fusion-using-tpe-cbigru}

\textbf{Hosted file}

\verb`Table 5 Hyperparameter search results.xlsx`  available at \url{https://authorea.com/users/818321/articles/1218143-short-term-power-prediction-of-distributed-photovoltaic-systems-based-on-multi-scale-feature-fusion-using-tpe-cbigru}

\textbf{Hosted file}

\verb`Table 6 Model Comparison Experimental Effects.xlsx`  available at \url{https://authorea.com/users/818321/articles/1218143-short-term-power-prediction-of-distributed-photovoltaic-systems-based-on-multi-scale-feature-fusion-using-tpe-cbigru}

\textbf{Hosted file}

\verb`Table 7 Comparison of ablation experiments.xlsx`  available at \url{https://authorea.com/users/818321/articles/1218143-short-term-power-prediction-of-distributed-photovoltaic-systems-based-on-multi-scale-feature-fusion-using-tpe-cbigru}

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