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  <front>
    <journal-meta>
      <journal-title-group>
        <journal-title>X ((I. Zaitsev);</journal-title>
      </journal-title-group>
    </journal-meta>
    <article-meta>
      <title-group>
        <article-title>High-Fidelity Photovoltaic Power Forecasting Using a Skip-Fusion DNN with GELU Activation and AdamW Optimization⋆</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Ievgen Zaitsev</string-name>
          <email>zaitsev@i.ua</email>
          <xref ref-type="aff" rid="aff1">1</xref>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Hasan Uzel</string-name>
          <email>hasan.uzel@bozok.edu.tr</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Feyyaz Alpsalaz</string-name>
          <email>feyyaz.alpsalaz@bozok.edu.tr</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Yıldırım Özüpak</string-name>
          <xref ref-type="aff" rid="aff4">4</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Emrah Aslan</string-name>
          <email>emrahaslan@artuklu.edu.tr</email>
          <xref ref-type="aff" rid="aff3">3</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Akdağmadeni Vocational School, Yozgat Bozok University</institution>
          ,
          <addr-line>Gültepe Mahallesi, Tepe 4, 66540 Yozgat</addr-line>
          ,
          <country country="TR">Turkey</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>Center for Information-Analytical and Technical Support of Nuclear Power Facilities Monitoring, National Academy of Sciences of Ukraine</institution>
          ,
          <addr-line>Akademika Palladina 34a, 03142 Kyiv</addr-line>
          ,
          <country country="UA">Ukraine</country>
        </aff>
        <aff id="aff2">
          <label>2</label>
          <institution>Institute of Electrodynamics of NAS of Ukraine</institution>
          ,
          <addr-line>Beresteyskyi 56, 03057 Kyiv</addr-line>
          ,
          <country country="UA">Ukraine</country>
        </aff>
        <aff id="aff3">
          <label>3</label>
          <institution>Mardin Artuklu University</institution>
          ,
          <addr-line>Diyarbakır Road, 5, 47200 Mardin</addr-line>
          ,
          <country country="TR">Turkey</country>
        </aff>
        <aff id="aff4">
          <label>4</label>
          <institution>Silvan Vocational School, Dicle University</institution>
          ,
          <addr-line>Gazi, 21640 Diyarbakır</addr-line>
          ,
          <country country="TR">Turkey</country>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2025</year>
      </pub-date>
      <volume>000</volume>
      <fpage>0</fpage>
      <lpage>0002</lpage>
      <abstract>
        <p>Accurate forecasting of photovoltaic (PV) power generation is essential for optimizing the operation and stability of renewable-dominated smart grids. However, the stochastic nature of solar irradiance, temperature-dependent derating, and nonlinear PV conversion dynamics pose significant challenges to model reliability and generalization. This study presents a novel deep neural network architecture, DNNv4, designed for short-term PV power forecasting using high -resolution SCADA telemetry. The proposed model integrates GELU activation, Layer Normalization, and a skip-fusion mechanism that merges multiscale dense representations to enhance feature propagation and gradient stability. Optimization is conducted through the AdamW algorithm combined with a Cosine Decay Restarts learning-rate schedule and Huber loss to improve robustness against outliers. The model was trained on a real -world dataset comprising 118,865 SCADA records with environmental and electrical features such as irradiance, temperature, wind speed, and DC/AC currents. Experimental results demonstrate superior performance with RMSE = 1.741 kW, MAE = 0.992 kW, MAPE = 1.12 %, sMAPE = 1.14 % and R² = 0.9996, significantly outperforming conventional and hybrid baselines. Beyond predictive accuracy, DNN-v4 preserves physical consistency between irradiance, temperature, and current, offering a computationally efficient and interpretable framework for real-time PV forecasting in smart-grid operations.</p>
      </abstract>
      <kwd-group>
        <kwd>eol&gt;Photovoltaic power forecasting</kwd>
        <kwd>SCADA telemetry</kwd>
        <kwd>deep neural network (DNN)</kwd>
        <kwd>skip-fusion architecture</kwd>
        <kwd>GELU activation</kwd>
        <kwd>AdamW optimization1</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>
        Accurate forecasting of photovoltaic (PV) power generation has become a cornerstone of modern
renewable energy management, particularly within smart grid environments that increasingly rely
on intermittent sources. The rapid growth of solar energy integration has introduced new challenges
for power system operators, who must maintain real-time energy balance, stability, and scheduling
efficiency despite the inherent variability of solar resources [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ]. In this context, short-term and
dayahead forecasting of PV generation are essential for economic dispatch, demand-side management,
and energy market participation. Nevertheless, achieving high forecasting accuracy remains difficult
due to the stochastic and nonlinear nature of solar power generation processes [2].
      </p>
      <p>The main difficulty in PV power prediction arises from the complex dependencies between
environmental and electrical variables. Solar irradiance, ambient temperature, wind speed, and
humidity interact in nonlinear ways that directly influence the current and voltage output of PV
modules. These relationships are further complicated by panel aging, inverter efficiency, and sensor
noise in Supervisory Control and Data Acquisition (SCADA) systems [3]. Consequently, developing
models that can effectively represent these multivariate dependencies is essential for reliable
forecasting across different temporal scales and environmental conditions.</p>
      <p>A large body of research has explored data-driven approaches for PV power forecasting, with
machine learning and deep learning methods dominating recent literature [4]. Traditional machine
learning algorithms such as Support Vector Regression (SVR), Random Forests (RF), and Gradient
Boosting (XGBoost) have demonstrated acceptable performance for certain datasets and horizons.
However, these methods often struggle to model the high-dimensional and nonlinear feature
interactions present in real-world PV systems [5]. Their performance typically depends on careful
feature engineering, which can limit scalability and adaptability to new environments.</p>
      <p>To overcome these limitations, deep learning (DL) architectures have gained increasing attention
due to their ability to automatically learn hierarchical feature representations. Models such as
Convolutional Neural Networks (CNNs) and Long Short-Term Memory (LSTM) networks have
shown superior capabilities in capturing both spatial and temporal dependencies in time-series data
[6]. CNNs are particularly effective at extracting local patterns from multivariate SCADA signals,
while LSTMs are adept at modeling sequential dependencies and long-term temporal correlations.
However, these architectures are not without drawbacks. Deep models often require substantial
computational resources, complex hyperparameter tuning, and large quantities of labeled data.
When applied to relatively small or noisy SCADA datasets, they may overfit, leading to reduced
generalization capability and unstable predictions [7].</p>
      <p>Another significant limitation of existing approaches is their lack of physical interpretability.
Most purely data-driven methods neglect the underlying physical relationships between irradiance,
temperature, and current, which govern the photovoltaic conversion process [8]. As a result, model
outputs can violate known physical constraints or behave inconsistently under varying
environmental conditions. This reduces the trustworthiness of predictions, especially in operational
settings that demand both accuracy and explainability. Bridging this gap between data-driven
learning and physics-based modeling remains a major challenge in the field.</p>
      <p>In response to these issues, the present study introduces a novel deep neural network
architecture, termed DNN-v4, designed specifically for accurate and physically consistent PV power
forecasting using SCADA telemetry [9]. The proposed framework is built upon a compact yet
expressive design that integrates several modern components from state-of-the-art deep learning
research. It employs the Gaussian Error Linear Unit (GELU) activation function, which offers
smoother nonlinear transformations and improved gradient behavior compared to conventional
ReLU-based activations. To further enhance training stability, Layer Normalization is applied across
layers, reducing internal covariate shift and ensuring consistent convergence during optimization.</p>
      <p>A key innovation of DNN -v4 lies in its skip-fusion mechanism, which merges multi-scale dense
feature representations from intermediate layers. This design promotes richer information flow
through the network while mitigating vanishing gradient problems. By combining shallow and deep
features, the model effectively captures both short-term fluctuations and long-term dependencies in
PV power output. This hybrid representation improves generalization and robustness across diverse
meteorological conditions.</p>
      <p>The optimization process also integrates several advanced techniques. Model training is
conducted using the AdamW optimizer, which decouples weight decay from gradient updates,
leading to more controlled regularization and improved generalization [10]. Furthermore, a Cosine
Decay Restarts (CDR) learning rate scheduler is adopted to dynamically modulate the learning rate,
preventing premature convergence and enabling the model to explore more optimal regions of the
loss landscape. This adaptive scheduling strategy encourages smoother convergence and better
finetuning across training epochs.</p>
      <p>For the loss function, the Huber loss is employed instead of the standard mean squared error
(MSE). The Huber loss provides a balance between L1 and L2 penalties, making it particularly robust
to noisy or outlier data samples frequently encountered in SCADA measurements [11]. Together,
these optimization choices enable the DNN-v4 model to achieve high predictive accuracy without
sacrificing computational efficiency or stability.</p>
      <p>Comprehensive experiments demonstrate that the proposed DNN-v4 model outperforms existing
benchmarks in both accuracy and robustness, while maintaining a lightweight architecture suitable
for real-time forecasting applications [5]. Compared to deeper or more complex models, DNN-v4
requires fewer parameters and exhibits faster convergence, making it practical for deployment in
embedded or edge computing environments. Beyond raw prediction accuracy, the model exhibits
strong physical consistency, aligning with known PV power generation principles. This hybrid
modeling philosophy—combining physical insights with data-driven learning—contributes to
improved interpretability and reliability under unseen weather scenarios [11].</p>
      <p>The study also emphasizes the importance of data preprocessing and exploratory analysis prior
to model training. Raw SCADA data often contain missing values, noise, and inconsistencies due to
sensor faults or communication errors. Therefore, careful data cleaning, normalization, and feature
selection are critical for ensuring stable training performance. Additionally, exploratory data
analysis (EDA) enables the identification of statistical patterns and correlations between
environmental and electrical parameters, which can guide both model design and evaluation.</p>
      <p>The remainder of this paper is organized as follows. Section 2 details the dataset description,
preprocessing workflow, and exploratory data analysis conducted on the SCADA telemetry. Section
3 introduces the architecture of the proposed DNN-v4 model, highlighting its key layers, activation
functions, optimization strategy, and learning rate scheduling mechanism. Section 4 outlines the
experimental setup, including training configurations, baseline comparisons, and evaluation metrics.
Section 5 presents and discusses the experimental results, focusing on predictive performance,
learning dynamics, and residual analyses to assess model robustness. Finally, Section 6 concludes the
paper by summarizing the main findings and suggesting potential avenues for future research,
including model interpretability, transfer learning, and integration with hybrid physics-informed
frameworks.</p>
      <p>The proposed DNN-v4 framework represents a significant step toward compact, stable, and
physically consistent PV power forecasting. By combining the strengths of modern deep learning
techniques with physics-aware design principles, it bridges the gap between black-box prediction
models and interpretable renewable energy analytics. The results highlight that accurate, efficient,
and explainable deep learning models can substantially enhance the reliability of smart grid
operations in an era increasingly dominated by renewable energy sources.</p>
    </sec>
    <sec id="sec-2">
      <title>2. Dataset and Exploratory Data Analysis (EDA)</title>
      <p>The proposed model was trained and evaluated using a real-world SCADA dataset collected from
a grid-connected photovoltaic (PV) power plant [13]. The dataset contains 118,865 records with nine
continuous variables, including module temperature, ambient temperature, wind speed,
plane-ofarray irradiance (W/m²), DC current, three-phase AC currents (Ir, Iy, Ib), and the target variable AC
power (kW) [4]. The dataset was obtained from the publicly available SolarGeneration dataset shared
by Arun Kanagolkar on the Kaggle platform [13].</p>
      <p>
        Descriptive statistics of all input features are summarized in Table 1. The results indicate that
irradiance and string current exhibit the highest magnitudes within the numerical range (with mean
values of approximately 428 W/m² and 356 A, respectively), reflecting their dominant influence on
photovoltaic energy generation. Meanwhile, the module temperature shows an average of 37 °C,
which is roughly 14 °C above the mean ambient temperature. This temperature differential aligns
well with the expected thermal behavior of PV modules under standard outdoor operating
conditions, where solar absorption and electrical loading typically elevate the module temperature
beyond the surrounding environment [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ].
      </p>
      <sec id="sec-2-1">
        <title>MODULE_TEM P</title>
      </sec>
      <sec id="sec-2-2">
        <title>Amb_Temp</title>
      </sec>
      <sec id="sec-2-3">
        <title>WIND_Speed</title>
        <p>IRR (W/m²)</p>
      </sec>
      <sec id="sec-2-4">
        <title>DC Current (A) AC Ir (A) AC Iy (A) AC Ib (A)</title>
      </sec>
      <sec id="sec-2-5">
        <title>AC Power (kW)</title>
        <p>Count
118 865
118 865
118 865
118 865
118 865
118 865
118 865
118 865</p>
      </sec>
    </sec>
    <sec id="sec-3">
      <title>3. Proposed Method (DNN-v4 Model Architecture)</title>
      <p>The proposed DNN-v4 model was designed to provide a robust and interpretable framework for
short-term photovoltaic (PV) power forecasting using high-frequency SCADA telemetry. The
architecture follows a fully connected deep neural network structure optimized through extensive
experimentation. The input layer receives eight standardized environmental and electrical variables,
which are propagated through three hidden blocks with 512, 256, and 128 neurons, respectively. Each
dense layer employs the GELU (Gaussian Error Linear Unit) activation to ensure smooth gradient
flow and better handling of nonlinear patterns compared to ReLU. To enhance internal stability and
mitigate covariate shift, each layer output is normalized via Layer Normalization, followed by a
Dropout (rate = 0.1) for regularization.</p>
      <p>The intermediate representations are fused using a Skip-Fusion mechanism, where multi-scale
latent outputs extracted from the preceding neuron layers (with 512, 256, and 128 units, respectively)
are concatenated into a unified feature tensor. This architectural strategy ensures that both
highlevel abstract patterns and lower-level fine-grained cues are preserved throughout the forward pass,
preventing the loss of relevant information that may occur in conventional deep compression
pipelines. The concatenated representation is subsequently fed into a compact refinement block
composed of a Dense-128 layer, followed by Layer Normalization and a Dense-64 layer, which
reduces redundancy and enforces feature decorrelation. Such refinement helps to stabilize the
training process, reduce internal covariate shift, and facilitate faster model convergence.</p>
      <p>By integrating hierarchical features from different abstraction levels, the Skip-Fusion design
promotes stronger generalization, especially under varying environmental and operational
conditions, while also maintaining interpretability — since contributions from each feature scale
remain traceable within the fused latent space. Finally, the processed representation is mapped to
the predictive output through a single-neuron regression layer with linear activation, enabling
continuous estimation of the AC power (kW) without artificially constraining the output domain.</p>
      <p>Optimization is handled by the AdamW optimizer combined with a Cosine Decay Restarts
learning-rate schedule (initial LR = 8×10⁻⁴, first_decay_steps = 80, t_mul = 1.5, m_mul = 0.8), which
ensures efficient convergence and prevents over-fitting. The Huber loss (δ = 1.2) function was chosen
instead of MSE to reduce the sensitivity to outliers commonly found in SCADA data. To stabilize
training and guarantee reproducibility, deterministic operations and fixed random seeds
(random_state = 42) were applied across all layers.</p>
      <p>The network was trained for up to 400 epochs with a batch size of 32, monitored by early stopping
(patience = 40, restore_best_weights = True). Model training and evaluation were executed on a Tesla
P100 GPU (16 GB), achieving an average epoch time of approximately 1.2 seconds. The entire training
completed in about 4.2 minutes, indicating that the architecture is both computationally efficient and
suitable for real-time PV forecasting applications.</p>
      <p>Figure 4 illustrates the complete architecture of the proposed DNN-v4 framework, including the
stacked dense feature extraction blocks, the multi-scale skip-fusion mechanism, and the associated
training configuration. The diagram visualizes the sequential information flow from the standardized
input features through hierarchical latent representations to the final output layer responsible for
continuous AC power prediction. Additionally, Figure 4 highlights critical implementation details
that ensure robust performance and reproducibility, such as the adopted optimization strategy,
regularization components, and inference-time constraints, thereby providing a comprehensive
overview of the designed deep learning pipeline.</p>
    </sec>
    <sec id="sec-4">
      <title>4. Results and Discussion</title>
      <p>The proposed DNN-v4 model demonstrated excellent predictive accuracy and robustness across
all evaluation metrics. On the test dataset, the model achieved RMSE = 1.741 kW, MAE = 0.992 kW,
MAPE=1.12 %, sMAPE = 1.14 %, and R² = 0.9996, confirming an almost perfect alignment between
predicted and measured AC power outputs.</p>
      <p>Table 2</p>
      <p>Performance metrics of the proposed DNN-v4 model
RMSE (kW) (kWM)AE
1.741 0.992</p>
      <p>MAPE (%)
1.12
sMAPE (%)
1.14</p>
      <p>R²</p>
      <p>The parity comparison between the predicted and actual AC power values is illustrated in Figure
5. The dense clustering of points along the diagonal demonstrates that the proposed DNN-v4
accurately learns nonlinear irradiance–temperature–current interactions without overfitting.</p>
      <p>Residual behavior is analyzed in Figures 6 and 7. The residual histogram in Figure 6 is narrow,
symmetric, and centered around zero, indicating unbiased predictions and consistent variance. The
Q–Q plot in Figure 7 further confirms that the residuals follow an approximately normal distribution,
validating the absence of heteroscedasticity or systematic error patterns.</p>
      <p>Collectively, these findings confirm that the proposed DNN-v4 framework effectively combines
high predictive accuracy, strong interpretability, and robust training stability. Compared with
existing deep learning-based PV forecasting approaches, which often prioritize accuracy at the cost
of transparency or exhibit sensitivity to data variability, DNN-v4 demonstrates a more favorable
balance between performance and explainability. Such characteristics make the framework
wellsuited for operational photovoltaic (PV) power forecasting based on real-world SCADA telemetry,
ensuring reliable deployment under diverse environmental and system operating conditions.</p>
    </sec>
    <sec id="sec-5">
      <title>5. Conclusion</title>
      <p>This study proposed an explainable and high-fidelity deep learning framework, DNN-v4, for
photovoltaic (PV) power forecasting using SCADA telemetry. The model integrates GELU-activated
dense blocks, layer normalization, and a skip-fusion mechanism optimized via the AdamW optimizer
with cosine decay restarts. Experimental results demonstrated exceptional predictive accuracy
(RMSE=1.74 kW, R² = 0.9996) and strong stability across 118,865 records, confirming that the
architecture effectively captures nonlinear irradiance–temperature–current interactions without
overfitting. Residual analyses validated the unbiased and near-Gaussian error behavior, further
supporting the model’s reliability. Owing to its interpretability and reproducibility, the proposed
DNN-v4 framework provides a practical foundation for operational PV power forecasting and can
be extended to multi-plant prediction or hybrid XAI-integrated configurations in future research.</p>
    </sec>
    <sec id="sec-6">
      <title>Declaration on Generative AI</title>
      <sec id="sec-6-1">
        <title>The author(s) have not employed any Generative AI tools.</title>
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      </sec>
    </sec>
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