Quantum-Enhanced Residual Convolutional Attention Architecture for Renewable Forecasting in Off-Grid Cloud Microgrids

Abstract

Multimodal forecasting is increasingly needed to maintain energy levels, storage capacity, and compute efficiency in off-grid, renewable-powered cloud environments. Variable sensor quality, uncertain interactions with renewable energy, and rapidly changing weather patterns make real-time forecasting difficult. Current transformer, GNN, and CNN systems suffer from sensor noise instability, multimodal temporal–spectral correlation issues, and challenges in the interpretability of operational decision-making. In this research, Q-RCANeX, a quantum-guided residual convolutional attention network for off-grid cloud infrastructures, estimates battery state of charge, renewable energy sources, and microgrid efficiency to overcome these restrictions. The system uses a Hybrid Quantum–Bayesian Evolutionary Optimizer, quantum feature embedding, temporal–spectral attention, residual convolutional encoding, and signal decomposition preprocessing. These parameters reinforce features, reduce noise, and align forecasting behavior with microgrid dynamics. Q-RCANeX obtains 98.6% accuracy, 0.992 AUC, and 0.986 R³ values for REAF, WGF, SOC-F, and EEIF forecasting tasks, according to a statistical study. Additionally, it determines inference latency to 4.9 ms and model size to 18.5 MB. Even with 20% of sensor data missing or noisy, the model outperforms 12 state-of-the-art baselines and maintains 96.8% accuracy using ANOVA, Wilcoxon, Nemenyi, and Holm tests. The findings indicate that the forecasting framework has high accuracy, clarity, and resilience to failures. This makes it useful for real-time, off-grid management of renewable cloud microgrids.

1. Introduction

Cloud computing and AI workloads are increasing energy consumption in data centers, emphasizing the need for decarbonization and a reliable power supply [1]. Modern, energy-efficient operation is as crucial as powerful processing. Intelligent power orchestration, high-efficiency cooling, and renewable integration are becoming design priorities. Off-grid and near-grid microgrids, which employ solar, wind, and battery storage, host computer technology in areas where the grid is inaccessible or regularly down. These arrangements extend product life and reduce emissions. The system is still vulnerable to fluctuations in renewable generation and laws governing storage cycling and peak power distribution [2]. In these circumstances, estimation accuracy affects operations and the economy. With precise short-term estimates of renewable output and load demand, microgrids without grid backup can be more reliable and cost-effective. Inverter timing, battery location, and curtailment reduction are optimized. Inaccurate forecasting increases operational costs and uncertainties via unit commitment and demand response choices, according to studies. As predicted accuracy increases, system stability and resource efficiency also improve [3]. Detecting changes in hybrid solar–wind systems driven by nonlinear interactions between power-generating types is difficult with linear or shallow models [4].

Deep learning has enhanced renewable energy system forecasting by capturing long-term temporal dependencies, non-stationary seasonal changes, and complex feature interactions across meteorological and system data. Research indicates that hybrid architectures combining convolutional layers for local pattern extraction and recurrent or attention-based processes for contextual reasoning outperform statistical baselines in varied climates and forecast horizons [5]. Attention systems successfully detect feature relevance across irregular time intervals and diverse sensor modalities, demonstrating resilience to noisy or incomplete data [6]. To ensure transparent and accountable decision-making, energy operators increasingly prioritize explainability over predictive precision, understanding how key factors such as irradiance fluctuations, wind shear, temperature variations, and battery state of charge affect model outputs. Due to operational dynamics, data-center energy forecasting is difficult. Workload fluctuations, cooling system behavior, and control measures such as server throttling and thermal management changes create nonlinear relationships between IT demand and electrical load that defy standard forecast models. Recent data-center energy management surveys emphasize the need for forecasting frameworks that reduce prediction errors and offer interpretable outputs for supervisory control systems [7]. Forecasting errors in off-grid settings are expensive, as underestimating renewable shortages can cause battery depletion or load shedding, while overestimating renewable shortages can waste energy and lower service quality [8].

Recent research has focused on learning paradigms at the microgrid edge, where data are produced, to overcome these issues. Real-time forecasting in power-constrained situations is being examined using federated and distributed learning methodologies, as well as model compression techniques [9]. Energy analytics in smart city settings with diverse data sources has recently demonstrated strong scalability and privacy protection through federated learning-based forecasting models. An instance of this is HHCTE-FL, which integrates interpretable federated optimization with hybrid convolutional–transformer extractors [10]. Integrated pipelines that include generation forecasting, battery state-of-charge estimates, and health-aware diagnostics have shown that storage behavior determines forecasting reliability. Off-grid cloud forecasting is multimodal and context-aware due to the tight linkage of renewable production, storage response, and computational demand. In parallel, quantum-inspired and quantum-native learning paradigms are promising for complicated energy analytics. Quantum machine learning (QML) offers benefits for high-dimensional, noisy time-series data in energy systems through feature encoding and optimization based on superposition and entanglement principles [11]. These early-stage approaches enhance transformer-based and hybrid convolutional-recurrent architectures for wind and solar prediction by exploring richer representational spaces and non-convex optimization landscapes [12]. Next-generation predictive intelligence in renewable-powered systems is being built on temporal–spectral reasoning, interpretable deep forecasting, and quantum-inspired optimization.

The primary scientific problem is clear in this context. High-frequency, short-horizon forecasting frameworks are needed for off-grid cloud data centers with inadequate sensing and changing operating states. These models must be energy-aware, computationally efficient for edge deployment, sensitive to forecasting errors that affect storage stability and demand-side performance, and explainable to provide transparency in energy management and decision support. These demands need a cohesive methodology that blends resilient signal preprocessing, adaptive temporal–spectral modeling, and interpretable reasoning, aligning with microgrid forecasting, sustainable data-center optimization, and explainable machine learning. The following are the contributions of this work:

• Introduce the Q-RCANeX architecture, a solution to the issue of unstable and noisy multimodal energy data leading to inaccurate renewable energy predictions. The goal of the technique is to find stable physical patterns in streams of heterogeneous solar, wind, battery, and thermal data by integrating quantum-aware feature representation with residual convolutional encoding.
• Introduces a novel method, a temporal–spectral attention mechanism, to address the inadequacy of standard CNN-, LSTM-, and GNN-based models in capturing long-range dependencies and cross-modal interactions. This method facilitates the acquisition of frequency-aligned energy changes and fine-grained temporal dynamics.
• Incorporates a quantum feature embedding layer that addresses the problem of nonlinear renewable profiles’ poor separability and error amplification in the absence of data or due to distorted sensors. By amplifying the discriminative information in the feature space inspired by quantum mechanics, the embedding strengthens the system.
• Introduces a novel algorithm named a Hybrid Quantum–Bayesian Evolutionary Optimizer (Q-BEO) to stabilize hyperparameter tuning and reduce convergence issues frequent in deep renewable forecasting. This optimizer improves generalizability, reduces overfitting, and facilitates smoother convergence for all forecasting workloads.
• Provides off-grid cloud microgrids with a unified forecasting model that supports operational concerns such as task scheduling, battery charge/discharge management, and thermal efficiency regulation in response to shifting renewable supplies. To support sustainability-oriented decision-making, the method produces reliable multi-horizon predictions for the REAF, WGF, SOC-F, EEIF, and renewable adequacy classes.

From a deployment perspective, Q-RCANeX is constructed to function in actual off-grid cloud microgrid systems, which often have constraints on computing power, communication bandwidth, and data quality. With its modular architecture, it picks and chooses which key components to deploy to the cloud and edge. This paves the way for predictions that may evolve as operating conditions change. For this reason, the framework is well-suited for mission-critical off-grid energy systems that require robust decision support, such as hospital microgrids and remote industrial sites.

The article is organized as follows: The Section 2 covers the most current advancements in renewable forecasting, microgrid intelligence, and quantum-assisted learning. Also shown are the shortcomings of current transformer, GNN, and CNN-based algorithms when applied to off-grid cloud environments. Section 3 provides further details on the proposed Q-RCANeX framework. The Hybrid Quantum–Bayesian Evolutionary Optimizer is a part of it, along with architectural components, a design for temporal–spectral attention, the embedding of quantum features, and a preprocessing pipeline. Experimental testing and a comparison of computational efficiency with the best baselines are detailed in Section 4. It also covers statistical significance tests, ablation studies, robustness analyses, and prediction accuracy. The Section 5 concludes the article and provides further future work. Section 5 wraps up the study and describes where the research is headed, with the goals of improving scalability, increasing the deployment of microgrids across multiple sites, and incorporating adaptive, energy-aware control into real-world off-grid cloud technologies.

2. Related Work

Recent advances in renewable energy analytics have focused on developing short-horizon forecasting models for hybrid solar–wind microgrids in changeable and unpredictable environments. In one transformer-based multi-step photovoltaic (PV) forecasting investigation, horizon-specific decoders and attention layers captured daily energy trends. This method greatly reduced predicting errors in many climates, although accuracy declined in noisy situations due to missing telemetry data or sensor deterioration [13]. Another study created a hybrid transformer pipeline that learns solar–wind interdependence. Although this technique adequately recorded nonlinear temporal correlations between the two modalities, it depended largely on high-quality weather reanalysis data, limiting its application in data-scarce locations [14,15]. Before model training, researchers investigated a signal-augmentation and quality-control (SAQ) approach to stabilize microgrid data. While this pipeline improved short-term PV and load forecasting accuracy and decreased curtailment, it also required substantial preprocessing, which raised system complexity and hindered real-time scalability [16]. Another study used clear-sky indices, solar transposition models, and meteorological interaction characteristics for physics-informed feature engineering. While the approach outperformed deep learning models in accuracy and computational demand, its site-specific calibration hampered cross-regional adaptability [17].

A Temporal Convolutional Network (TCN)-based solution was presented to capture long- and short-term interdependence in hybrid PV–wind datasets to address renewable energy production’s temporal dynamics. Although our technique outperformed typical LSTM and CNN architectures in ramp prediction and signal stability, it lacked a way to fuse multimodal weather and generation data, limiting its flexibility in novel situations [18]. A graph-temporal learning method uses graph neural networks (GNNs) and recurrent units to leverage spatial correlations among scattered wind stations. While this hybrid technique enhanced forecasting accuracy in dense sensor networks, it suffered in sparse topologies and cold-start initialization of additional nodes [19]. Multiple disciplines have explored federated multimodal learning frameworks. One such example is the LeViT-ResUNet system for UAV-IoT agricultural monitoring. This system demonstrated scalable, privacy-preserving modeling in various environmental conditions [20]. In situations where resources are scarce, our findings highlight the need for distributed, robust forecasting systems. Advanced studies used alternating attention layers to improve graph topology and temporal linkages in a double-explored spatio-temporal GNN. This method enhanced uncertainty calibration and decreased forecasting errors, but needed significant computing resources and careful adjustment to prevent over-smoothing during training [21]. Another study used self-constructing graph learning to automatically collect spatial relationships from telemetry data at big solar installations. The method improved RMSE relative to traditional networks, but faced overfitting hazards and restricted generalization to unknown facilities [22].

Smaller, energy-efficient models outperformed deeper models in many transformer design studies when optimized for certain prediction horizons. Adaptable architectures are necessary for real-world data variability, since the efficiency of lightweight models varies based on data completeness and feature representation [23]. Forecasting model explainability was also stressed in several studies. One study used SHAP-based interpretability modules during model training to improve operational transparency and feature relevance. This method increased confidence among system operators but increased computing burden during inference [24]. Another explainability-oriented approach uses SHAP-driven diagnostics for real-time sensor network feature attribution and defect detection. The approach enhanced interpretability and reliability, while latency increased in high-dimensional data environments [25].

A recent review of interpretable deep learning in energy forecasting found that saliency and gradient-based explanations improve transparency but are unstable during sudden distribution shifts or extreme weather conditions [26]. Recently, quantum-inspired learning for time-series prediction has been studied alongside deep networks. One method used parameterized quantum circuits in LSTM architectures to improve convergence and error reduction on limited datasets. Simulating quantum states on conventional hardware is computationally expensive, restricting scalability [27]. Additionally, multimodal designs influenced by quantum mechanics have emerged, such as Q-MobiGraphNet. This one uses quantum sinusoidal encoding to integrate Internet of Things (IoT) telemetry, unmanned aerial vehicle (UAV) images, and geographic data in order to strengthen infrastructure against environmental changes [28]. These technologies demonstrate the growing significance of quantum-guided feature representation in environmental and energy analytics.

Integrated temporal convolutional filters with transformer-based attention mechanisms increase wind speed forecasting accuracy, albeit at the cost of training efficiency and hyperparameter sensitivity [29]. The effectiveness of hierarchical attention and multi-scale convolution in dynamic and complex systems has been demonstrated by cross-layer convolutional attention mechanisms in complex telemetry settings, such as the CLCAN framework for intrusion detection in drone networks [30]. Recent lightweight convolutional networks for hybrid PV–wind forecasting showed the balance between computational economy and prediction accuracy. Although a compact one-dimensional CNN showed promising results with low latency, its performance degraded for uncommon extreme occurrences owing to the lack of uncertainty estimation techniques [31].

The aforementioned literature in

Table 1. Summary of recent related studies (2024–2025) in renewable energy forecasting and intelligent microgrid modeling.

Ref.	Objective	Method/Framework	Key Achievements	Limitations
[13]	Multi-step PV forecasting under variable climates	Transformer-based model with horizon-specific decoders and attention layers	Improved MAE/RMSE across multiple sites and climatic zones	Reduced accuracy under missing telemetry or sensor drift
[14]	Joint forecasting of hybrid solar–wind generation	Hybrid transformer with shared temporal encoder and modality heads	Accurately models interdependencies between solar and wind modalities	Relies heavily on high-quality reanalysis and meteorological data
[16]	Stabilization of noisy microgrid data streams	Signal-augmentation and quality-control (SAQ) pipeline for preprocessing	Enhances short-term PV/load prediction and reduces curtailment risk	Increases preprocessing complexity and computational overhead
[17]	Physics-driven PV forecasting for small-scale microgrids	Feature engineering using clear-sky index, transposition, and meteorological interactions	Competitive accuracy with lower computation vs. deep models	Site-specific calibration limits transferability
[18]	Hybrid solar–wind time-series modeling	Temporal convolutional network (TCN) capturing long/short dependencies	Improves ramp prediction and temporal stability vs. LSTM/CNN	Lacks multimodal feature fusion, limited to single-source data
[19]	Spatial–temporal wind power forecasting	Graph neural network (GNN) with recurrent layers for spatial encoding	Increases accuracy on dense sensor networks	Struggles under sparse configurations and cold-start sites
[21]	Multi-site PV forecasting with uncertainty calibration	Double-explored spatio-temporal GNN using alternating attention layers	Reduces forecasting error and improves uncertainty estimation	Computationally expensive and sensitive to over-smoothing
[22]	Spatial dependency modeling for solar plants	Self-constructed GNN learning from telemetry without predefined graph	Enhances site-specific RMSE reduction over baselines	Limited generalization beyond trained solar farms
[23]	Efficient hour-ahead PV forecasting	Comparative transformer architecture benchmarking	Smaller transformers outperform deeper models under tuned horizons	Highly dependent on feature completeness and tuning
[24]	Explainable solar forecasting	SHAP-integrated deterministic forecasting framework	Improves interpretability and operator trust	Computational overhead during inference
[25]	Real-time explainable fault detection in forecasting	SHAP-driven diagnostic framework for feature contribution tracking	Enables transparent forecasting and early fault detection	Higher inference latency with high-dimensional features
[26]	Comprehensive review of explainable AI in energy systems	Survey and evaluation of saliency and SHAP-based interpretation models	Improves understanding of transparency–accuracy tradeoffs	Explanations unstable under distribution shift or extreme weather
[27]	Quantum-inspired time-series forecasting	Quantum-LSTM with parameterized quantum circuits	Faster convergence and reduced error on small datasets	Scalability limited by quantum simulation cost
[29]	Unified temporal–spectral modeling for wind forecasting	Hybrid TCN-transformer (TCNFormer) combining local/global learning	Achieves lower RMSE than individual TCN or Transformer models	High training complexity and hyperparameter sensitivity
[31]	Lightweight forecasting for hybrid PV–wind systems	Compact 1D CNN optimized for low-latency inference	Maintains high accuracy with minimal computational cost	Lacks uncertainty quantification; reduced robustness under extreme events

shows that hybrid deep architectures, spatio-temporal graph learning, and explainable AI improve renewable forecasts. These developments have not eliminated issues like model generalization across varied geographies, high computing demand in complicated transformer and GNN frameworks, and limited interpretability physical system awareness integration. These gaps need energy-aware, interpretable, and computationally efficient forecasting algorithms for renewable-powered, off-grid cloud infrastructures.

3. Proposed Methodology

Traditional deep predictors are unstable in off-grid cloud microgrids due to noisy sensor readings, irregular temporal dynamics, nonlinear cross-modal interactions, and incomplete data streams. Workload scheduling, battery cycling, and thermal management are all affected by cumulative forecast errors resulting from these difficulties. The Q-RCANeX technique provides a unified forecasting pipeline that stabilizes raw signals, improves feature separability, and effectively models long-range temporal–spectral relationships to overcome these constraints. After handling noise and missing data using signal decomposition-based preprocessing, the next step is to extract and select features that highlight physically important patterns. Compact representations are built using a residual convolutional encoder and enhanced with quantum feature embedding. Interactions across solar, wind, battery, and efficiency profiles are captured by temporal–spectral attention layers, which also account for frequency-aligned changes. To ensure steady convergence and generalization, a Hybrid Quantum–Bayesian Evolutionary Optimizer controls the model’s optimization. The pictorial view of the proposed frame is shown in Figure 1.

By combining off-grid microgrid data with a modular forecasting pipeline, Q-RCANeX aims to address a specific real-world issue. When sensor inputs are noisy or otherwise unsteady, signal decomposition can stabilize them. Both temporal–spectral attention and residual convolution uncover robust multi-scale patterns and long-range contextual links, respectively. Evolutionary optimization and quantum-inspired feature embedding enhance models’ stability during convergence and their ability to handle uncertainty. In contrast, the explainability module makes which factors are influencing the model’s predictions very evident. Collectively, these components provide an approachable framework that manages to be both accurate and practical.

3.1. Dataset Description

The data used in this study come from a third-party, publicly available source, available at [32]. To enhance research on renewable-powered computer infrastructure, the dataset was established and maintained by the National University Hospital Energy Innovation Centre (NUHEIC) in Oslo, Norway. It includes time-series data with high precision from a hospital’s cloud data center, powered by an off-grid hybrid solar–wind microgrid. From February 2022 to July 2025, all parameters were recorded every 10 min, and the dataset covers the entire period. Solar power, wind power, battery storage, and data-center energy use were all monitored continuously by a network of calibrated sensors and supervisory control systems. The NUHEIC team conducted thorough data validation, cleaning, and temporal synchronization before publishing the data to ensure the reliability and consistency of all recorded variables. For off-grid cloud applications, this dataset provides a solid, practical foundation for evaluating energy-aware optimization algorithms and approaches for renewable energy forecasting. It incorporates many different kinds of energy, spans an extensive range of time periods, and has been verified as real. The characteristics of the dataset are summarized in

Table 2. Categorized dataset features and their distributions.

Feature Category	Example Features	Distribution Type
Environmental and Meteorological	Global Horizontal Irradiance (GHI), Direct Normal Irradiance (DNI), Diffuse Horizontal Irradiance (DHI), Air Temperature, Relative Humidity, Wind Speed (10 m/100 m), Wind Direction, Atmospheric Pressure, Cloud Cover, Precipitation Rate, Aerosol Optical Depth (AOD)	Imbalanced and skewed numerical (beta/exponential)
Solar Generation and Photovoltaic System	PV DC Power, PV AC Power, Module Temperature, Inverter Efficiency, Panel Tilt, Panel Azimuth, Curtailment Flag	Imbalanced numerical with intermittent spikes (right-skewed)
Wind Generation System	Turbine Power Output, Rotor Speed, Pitch Angle, Nacelle Direction, Turbine Availability	Imbalanced numerical (Weibull/cubic relation)
Energy Storage and Battery Management	Battery State of Charge (SOC), State of Health (SOH), Charge Power, Discharge Power, Battery Temperature, Storage Efficiency	Imbalanced numerical (skewed and truncated)
Data-Center Operational Metrics	IT Load, Total Load, CPU Utilization, GPU Utilization, Memory Utilization, Cooling Power, Inlet/Outlet Temperature, Fan Speed, Power Usage Effectiveness (PUE)	Imbalanced numerical (log-normal/heavy-tailed)
Temporal and Contextual Parameters	Timestamp, Hour of Day, Day of Week, Month, Season Index, Holiday Indicator	Imbalanced categorical and cyclic numerical
Derived and Statistical Indicators	Net Energy Balance (NEB), Power Ramp Rate, Clear-Sky Index, Cross-Correlation, Entropy of Residuals, Imputation Mask	Imbalanced continuous (non-Gaussian)
Target Labels	Renewable Energy Availability Forecast (REAF), Solar Generation Forecast (SGF), Wind Generation Forecast (WGF), Battery SOC Forecast (SOC-F), Energy Efficiency Indicator (EEIF), Net Energy Balance (NEB), Renewable Adequacy Class (RAC), Sustainable Operation Window (SOW)	Imbalanced regression and classification targets

. The major functional portions of the off-grid microgrid are shown by the pieces displayed in

Table 3. Statistical summary of representative dataset features.

Feature	Mean	Std. Dev.	Missing Rate (%)
Global Horizontal Irradiance (GHI)	412.6	298.4	3.2
Wind Speed (10 m)	6.87	3.14	2.8
PV AC Power Output	482.1	356.9	3.6
Battery State of Charge (SOC)	61.3	18.7	1.9
Total Data-Center Load	734.5	211.3	2.4
Cooling Power Consumption	128.7	49.2	2.1

. Data-center operational requirements, energy storage, renewable generation, and environmental inputs are all part of this category.

3.2. Signal Decomposition-Based Preprocessing

Due to climate change, device sensitivity, and random atmospheric events, data on renewable energy from hybrid solar–wind systems exhibit fairly peculiar patterns over time. Due to factors such as constantly shifting clouds, strong gusts, and intermittent sensor performance, these signals are never static and seldom follow a straight path. There is a risk that using this data in its raw form can lead to biased learning and unstable model convergence. Signal decomposition-based preprocessing (SDP) is a comprehensive preprocessing approach that this study employs to mitigate these effects [33]. The purpose of SDP is to construct physically meaningful representations from noisy, high-frequency data while preserving both the short-term dynamics and the long-term behavioral tendencies. Adaptive seasonal normalization, entropy-regulated denoising, and hybrid trend–seasonal decomposition with quantum filtering are the three interrelated processes that make the system function. To provide reliable forecasting inputs, each of these steps is essential, but in its own way. Imagine a multivariate sequence as the dataset.

$$\mathcal{S}={\{s_{\tau }^{\left(1\right)},s_{\tau }^{\left(2\right)},\dots ,s_{\tau }^{\left(d\right)}\}}_{\tau =1}^M,$$

(1)

The $d^{\mathrm{th}}$ recorded feature at time index is represented by $s_{\tau }^{\left(d\right)}$. While d is the total number of features, M represents the number of samples. The components of each recorded variable are described:

$$s_{\tau }^{\left(d\right)}={\mathcal{L}}_{\tau }^{\left(d\right)}+{\mathcal{C}}_{\tau }^{\left(d\right)}+{\mathcal{V}}_{\tau }^{\left(d\right)}+{\xi }_{\tau }^{\left(d\right)},$$

(2)

The low-frequency trend, ${\mathcal{L}}_{\tau }^{\left(d\right)}$, represents gradual changes (such as seasonal irradiation drift), the periodic changes, ${\mathcal{C}}_{\tau }^{\left(d\right)}$, symbolize high-frequency changes (such as daily or weekly energy cycles); ${\mathcal{V}}_{\tau }^{\left(d\right)}$ represent changes caused by turbulence and operational switching, and ${\xi }_{\tau }^{\left(d\right)}$ represent measurement noise. Removing ${\xi }_{\tau }^{\left(d\right)}$ to the greatest extent feasible while accurately separating ${\mathcal{L}}_{\tau }^{\left(d\right)}$, ${\mathcal{C}}_{\tau }^{\left(d\right)}$, and ${\mathcal{V}}_{\tau }^{\left(d\right)}$ is the objective of the preprocessing step.

Removal of random noise and preservation of beneficial changes are achieved in the first phase of SDP using an entropy-governed adaptive denoising approach. In addition to allowing us to adjust the filter’s sensitivity, entropy provides a numerical measure of uncertainty. This is the definition of the local entropy $\mathcal{E}\left(s_{\tau }^{\left(d\right)}\right)$ for each signal, computed over a sliding window of length $\omega$:

$$\mathcal{E}\left(s_{\tau }^{\left(d\right)}\right)=-\sum _{\kappa =1}^{\omega }{\pi }_{\kappa }^{\left(d\right)}ln({\pi }_{\kappa }^{\left(d\right)}+{ϵ}_0),$$

(3)

where ${ϵ}_0$ is a minor stability constant and ${\pi }_{\kappa }^{\left(d\right)}$ is the chance that an amplitude value will occur in the window. In order to determine an adaptive gain coefficient ${\gamma }_{\tau }^{\left(d\right)}$, this value is then used.

$${\gamma }_{\tau }^{\left(d\right)}=\alpha {\displaystyle \frac{{\sigma }_{\tau }^{\left(d\right)}}{1+\mathcal{E}\left(s_{\tau }^{\left(d\right)}\right)}},$$

(4)

The local variance is represented by ${\sigma }_{\tau }^{\left(d\right)}$ in this instance, and a scaling constant $\alpha$ evaluated in a laboratory setting is used. The function ${\widehat{s}}_{\tau }^{\left(d\right)}$ represents the denoised signal, and its computation is as follows:

$${\widehat{s}}_{\tau }^{\left(d\right)}=s_{\tau }^{\left(d\right)}-{\gamma }_{\tau }^{\left(d\right)}{\displaystyle \frac{\mathsf{\partial }\mathcal{E}\left(s_{\tau }^{\left(d\right)}\right)}{\mathsf{\partial }{s}_{\tau }^{\left(d\right)}}}.$$

(5)

This adaptive entropy filter is designed to exclude random changes with a high entropy. Alterations in wind speed or solar irradiation are instances of physical changes that it records as transitions with low entropy. Therefore, ${\widehat{s}}_{\tau }^{\left(d\right)}$ provides more reliable model training in the future by capturing crucial dynamics with far less sensor noise. Our approach utilizes an Enhanced Trend–Seasonal Separation with Quantum Filtering (ETS-QF) technique to deconstruct each signal after noise reduction [34]. The assumption that all sums add up in a straight line underlies traditional decomposition techniques. Conversely, ETS-QF employs a probabilistic filtering method based on quantum interference. Whether there are significant seasonal trends or little shifts in renewable energy signals, our technique can detect them all. The signal degrades as follows:

$${\widehat{s}}_{\tau }^{\left(d\right)}={\mathcal{L}}_{\tau }^{\left(d\right)}+{\mathcal{C}}_{\tau }^{\left(d\right)}+{\mathcal{V}}_{\tau }^{\left(d\right)},$$

(6)

By constructing a smoothing window $W_{\mathcal{L}}$ using polynomial regression, the equation ${\mathcal{L}}_{\tau }^{\left(d\right)}$ is obtained. In order to get ${\mathcal{C}}_{\tau }^{\left(d\right)}$, the detrended component is averaged sequentially. Using a filtering kernel $\mathbb{F}(·)$ that is influenced by quantum mechanics further enhances the residual component ${\mathcal{V}}_{\tau }^{\left(d\right)}$, as shown below.

$$\mathbb{F}\left({\mathcal{V}}_{\tau }^{\left(d\right)}\right)=\sum _{\eta =-\mathrm{\Lambda }}^{\mathrm{\Lambda }}{w}_{\eta }^{\left(d\right)}{\mathcal{V}}_{\tau +\eta }^{\left(d\right)}{e}^{-\mathsf{ȷ}{\theta }_{\eta }},$$

(7)

The localization is maintained by the Gaussian weights $w_{\eta }^{\left(d\right)}$, the imaginary unit is $\mathsf{ȷ}$, and a phase interference factor ${\theta }_{\eta }$ is expressed as

$${\theta }_{\eta }={\beta }_d{sin}^{-1}\left({\displaystyle \frac{{\mathcal{V}}_{\tau +\eta }^{\left(d\right)}}{\sqrt{{\left({\mathcal{V}}_{\tau }^{\left(d\right)}\right)}^2+{ϵ}_1}}}\right),$$

(8)

${ϵ}_1$ maintains stability, whereas ${\beta }_d$ determines the amount of interference. This kernel dynamically increases the proportion of phase-and frequency-correlated coherent fluctuations and decreases the proportion of incoherent noise components. The representation is given by

$$s_{\tau }^{\ast \left(d\right)}={\mathcal{L}}_{\tau }^{\left(d\right)}+{\mathcal{C}}_{\tau }^{\left(d\right)}+\mathbb{F}\left({\mathcal{V}}_{\tau }^{\left(d\right)}\right),$$

(9)

The result is a balanced signal that captures the probabilistic and deterministic aspects of energy change, with noise filtered out. Because temporal anomalies are caused by both random external factors and changes in system operation, this breakdown is significant for off-grid renewable systems. The last step of SDP uses adaptive seasonal normalization (ASN) to ensure that all feature scales are consistent. Although static normalization ignores the cyclical behavior of renewable resources throughout the year, ASN performs just that. One definition of normalization is the presence of a seasonal index $\varsigma$ for each observation that falls into one of four categories: spring, summer, fall, or winter.

$${\overline{s}}_{\tau ,\varsigma }^{\left(d\right)}={\displaystyle \frac{s_{\tau }^{\ast \left(d\right)}-{\mu }_{\varsigma }^{\left(d\right)}}{{\sigma }_{\varsigma }^{\left(d\right)}}},$$

(10)

The season’s mean and standard deviation are represented by the symbols ${\mu }_{\varsigma }^{\left(d\right)}$ and ${\sigma }_{\varsigma }^{\left(d\right)}$, respectively. To accommodate gradual environmental transitions—such as seasonal shifts in irradiance or wind intensity—these parameters are continuously updated using a temporal decay factor $\delta$:

$${\mu }_{\varsigma }^{\left(d\right)}\left(\tau \right)=(1-\delta ){\mu }_{\varsigma }^{\left(d\right)}(\tau -1)+\delta s_{\tau }^{\ast \left(d\right)},{\sigma }_{\varsigma }^{\left(d\right)}\left(\tau \right)=(1-\delta ){\sigma }_{\varsigma }^{\left(d\right)}(\tau -1)+\delta |s_{\tau }^{\ast \left(d\right)}-{\mu }_{\varsigma }^{\left(d\right)}\left(\tau \right)|.$$

(11)

The temporal decay factor $\delta$ used in the adaptive seasonal normalization is determined through a data-driven analysis of the temporal autocorrelation structure of the renewable energy signals. Specifically, $\delta$ is selected to reflect the persistence of dominant seasonal patterns—such as diurnal solar cycles and medium-term wind variability—while avoiding excessive smoothing of short-term fluctuations. During preliminary analysis, multiple candidate values of $\delta$ were evaluated to balance responsiveness to rapid environmental changes against stability over longer seasonal horizons. The final value was chosen as the smallest decay factor that consistently preserved salient seasonal trends while maintaining robustness to transient sensor noise and irregular sampling intervals. This adaptive scaling enables stable normalization across time without distorting the inherent seasonal dynamics of the microgrid data. To maintain the dataset’s inherent seasonal cycle while conducting statistical comparisons of variables and time periods, this adaptive scaling is used. Afterwards, all of the normalized variables are combined into a single matrix:

$${\mathbf{M}}_{\tau }=[{\overline{s}}_{\tau ,\varsigma }^{\left(1\right)},{\overline{s}}_{\tau ,\varsigma }^{\left(2\right)},\dots ,{\overline{s}}_{\tau ,\varsigma }^{\left(d\right)}],$$

(12)

The model that generates predictions uses this structured data. The modified dataset ${\mathbf{M}}_{\tau }$ outperforms the original data in terms of stability, feature fitting, and smoothness. Temporal signals takes benefit from the proposed signal preprocessing framework in three ways: reduced energy use, increased resilience to environmental changes, and simplified analysis. The groundwork is laid for off-grid cloud data centers to accurately and efficiently predict renewable energy sources.

The signal decomposition stage is computationally quite lightweight when compared to other, less involved preprocessing techniques, such as normalization or smoothing. This is due to the fact that it is effective on sparse time frames and is implemented just once prior to training or inferring a model. Considering how tiny this expense is in relation to the overall time required to run the model, it is valuable since it improves data stability, accelerates convergence, and prevents mistakes from propagating in subsequent learning phases. Because of this, the preprocessing pipeline continues to be employed in off-grid cloud microgrid scenarios for real-time or near-real-time applications.

3.3. Energy-Adaptive Feature Refinement and Generative Equilibrium Process

The collection includes de-emphasized signal data, as well as synchronized time-series records of data-center power consumption, wind speed, battery charge levels, and sunshine hours. Nevertheless, the off-grid energy ecosystem’s underlying dynamics are evident in the skewed distributions, duplicate features, and poor correlations across variables, driven by operational ambiguity and environmental unpredictability. These differences cause bias and less reliable predictive models if unchecked. These difficulties have been addressed by developing a new integrated framework called EAFR-GEP. An accurate, succinct, and physically relevant depiction of the system’s energy fluctuations are achieved by combining feature extraction with relevance-based selection and probabilistic balancing. The decomposed observation of the $m^{\mathrm{th}}$ variable is expressed as $r_{\theta }^{\left(m\right)}$ at time $\theta$. The time-dependent behavior, direct magnitude, and overall change in each signal are shown by applying an energy-sensitive embedding. It can be calcualted as

$${\mathcal{E}}_{\theta }^{\left(m\right)}={\beta }_1\left|{\dot{r}}_{\theta }^{\left(m\right)}\right|+{\beta }_2{r}_{\theta }^{\left(m\right)}+{\beta }_3{\int }_0^{\theta }{r}_{\upsilon }^{\left(m\right)}d\upsilon ,$$

(13)

The integral term represents the overall energy contribution throughout time. At the same time, ${\dot{r}}_{\theta }^{\left(m\right)}$ is the first derivative that shows local change. To ensure that qualities with high and low variation have the same impact, the adaptive scaling constants ${\beta }_1$, ${\beta }_2$, and ${\beta }_3$ are used. To model the interconnections between energy subsystems, pairwise interaction coefficients are used. For instance, the relationship between total load and wind speed or the effect of solar radiation on storage discharge.

$${\mathcal{I}}_{\theta }^{(u,v)}={\displaystyle \frac{Cov({\mathcal{E}}_{\theta }^{\left(u\right)},{\mathcal{E}}_{\theta }^{\left(v\right)})}{\varsigma \left({\mathcal{E}}_{\theta }^{\left(u\right)}\right)\varsigma \left({\mathcal{E}}_{\theta }^{\left(v\right)}\right)}},$$

(14)

Covariance is represented by the sign $Cov(·)$, while standard deviation is shown by the symbol $\varsigma (·)$. Coefficients like these allow precise measurement of the appropriate cross-modal coupling in a hybrid renewable system by quantifying the impact of modifications to one part on another. After that, a complete feature vector is created by combining all features, including both acquired and interaction-based ones.

$${\mathbf{P}}_{\theta }=[{\mathcal{E}}_{\theta }^{\left(1\right)},{\mathcal{E}}_{\theta }^{\left(2\right)},\dots ,{\mathcal{E}}_{\theta }^{\left(m\right)},{\mathcal{I}}_{\theta }^{(1,2)},\dots ,{\mathcal{I}}_{\theta }^{(m-1,m)}],$$

(15)

This encompasses not only the signal’s dynamics but also the relationships between the characteristics. This integrated view provides a more complete and consistent picture of energy’s evolution over time. To eliminate superfluous components from prediction algorithms, an adaptive relevance-based weighting approach is used. The integration of linear and nonlinear correlations yields a hybrid significance coefficient ${\pi }_m$ for each feature $g_m$.

$${\pi }_m={\eta }_1{\displaystyle \frac{\left|\rho \right(g_m,y\left)\right|}{{\sum }_m\left|\rho (g_m,y)\right|}}+{\eta }_2{\displaystyle \frac{\mathbb{I}(g_m;y)}{{\sum }_m\mathbb{I}(g_m;y)}},$$

(16)

The expression $\mathbb{I}(g_m;y)$ shows that the nonlinear interactions are revealed via mutual information. Linear correlations are seen between y and $\rho (g_m,y)$, whereas ${\eta }_1$ and ${\eta }_2$ serve as balancing factors, adding up to 1. The factors that have succeeded well according to the adaptive criteria,

$${\pi }_{\mathrm{cut}}=Quantile(\left\{{\pi }_m\right\},0.25),$$

(17)

The features that are both statistically significant and amenable to physical explanation are the ones that are left out. Because certain operational situations, such as extended periods of low radiation, high-demand peaks, or deep battery-depletion cycles, do not occur very frequently, class imbalance persists even after feature improvements. To address this issue, a variational generative augmentation approach is used. The encoder reveals the distribution of latent features as

$$q_{\phi }\left(\mathbf{z}\right|{\mathbf{P}}_{\theta })=\mathcal{N}\left(\mathbf{z}\right|{\mathit{\mu }}_{\theta },{\mathit{\sigma }}_{\theta }^2),$$

(18)

To ensure that balanced samples are created by the decoder via

$$p_{\psi }\left({\mathbf{P}}_{\theta }\right|\mathbf{z})=\mathcal{N}\left({\mathbf{P}}_{\theta }\right|{\tilde{\mathit{\mu }}}_{\theta },{\tilde{\mathit{\sigma }}}_{\theta }^2),$$

(19)

where the encoder’s parameters are $\phi$ and the decoder’s settings are $\psi$. The optimization objective integrates reconstruction fidelity and latent regularization:

$${\mathcal{J}}_{\mathrm{gen}}={\mathbb{E}}_{q_{\phi }\left(\mathbf{z}\right|{\mathbf{P}}_{\theta })}\left[\parallel {\mathbf{P}}_{\theta }-{\widehat{\mathbf{P}}}_{\theta }{\parallel }_2^2\right]+D_{\mathrm{KL}}\left(q_{\phi }\left(\mathbf{z}\right|{\mathbf{P}}_{\theta })\parallel p\left(\mathbf{z}\right)\right),$$

(20)

The Kullback–Leibler divergence ($D_{\mathrm{KL}}(·)$) is used to confirm that produced samples match the original distribution structure. EAFR-GEP uses a variety of quality criteria to assess synthetic samples’ physical realism and statistical consistency. Comparing the two samples’ statistically similar features shows they align. This ensures that synthetic data has the same mean, variance, and higher-order moments across energy variables. Second, we examine pairwise interaction coefficients before and after augmentation to retain correlation. The cross-modal interdependence of solar, wind, storage, and load characteristics is confirmed by this investigation. Third, generative loss indirectly promotes reconstruction integrity by punishing unrealistic deviations using Kullback–Leibler divergence. As a last step, domain validity checks exclude samples with unrealistic values like negative generation values or battery states beyond operational limitations. These guidelines ensure that more data improves class balance without affecting energy dynamics or artifacts. This approach generates data for underrepresented energy levels to guarantee that all energy levels have the same characteristic rate. The new dataset $\mathcal{R}=\left\{{\mathbf{P}}_{\theta }^{\prime }\right\}$ balances operational and climatic situations throughout days with high demand and nights with low generation. A robust dataset is utilized to create the next quantum convolutional attention model with measurable system dynamics in each feature vector and scaling coordination. The EAFR-GEP method yields statistically sound and understandable findings. Storage systems and renewable energy sources are crucial to off-grid cloud architectures. The flow of EAFR–GEP is shown in Algorithm 1.

Algorithm 1 Energy-Adaptive Feature Refinement and Generative Equilibrium Process (EAFR–GEP)

Require: Decomposed dataset $\mathcal{D}=\{r_{\vartheta }^{\left(1\right)},r_{\vartheta }^{\left(2\right)},\dots ,r_{\vartheta }^{\left(M\right)}\}$, target variable y Ensure: Refined and balanced dataset $\mathcal{R}=\left\{{\mathbf{P}}_{\vartheta }^{\prime }\right\}$   1: Initialization: Assign adaptive scaling factors ${\beta }_1$, ${\beta }_2$, ${\beta }_3$ and weighting coefficients ${\eta }_1$, ${\eta }_2$.   2: for each time instance $\vartheta$ do   3:     for each variable $r_{\vartheta }^{\left(M\right)}$ in $\mathcal{D}$ do   4:         Compute energy-sensitive embedding: $${\mathcal{E}}_{\vartheta }^{\left(M\right)}={\beta }_1\left|{\dot{r}}_{\vartheta }^{\left(M\right)}\right|+{\beta }_2{r}_{\vartheta }^{\left(M\right)}+{\beta }_3{\int }_0^{\vartheta }{r}_{\xi }^{\left(M\right)}d\xi$$   5:     end for   6:     Compute feature–interaction coefficients: $${\mathcal{I}}_{\vartheta }^{(a,b)}={\displaystyle \frac{Cov({\mathcal{E}}_{\vartheta }^{\left(a\right)},{\mathcal{E}}_{\vartheta }^{\left(b\right)})}{\varsigma \left({\mathcal{E}}_{\vartheta }^{\left(a\right)}\right)\varsigma \left({\mathcal{E}}_{\vartheta }^{\left(b\right)}\right)}}$$   7:     Construct unified feature vector: $${\mathbf{P}}_{\vartheta }=[{\mathcal{E}}_{\vartheta }^{\left(1\right)},\dots ,{\mathcal{E}}_{\vartheta }^{\left(M\right)},{\mathcal{I}}_{\vartheta }^{(1,2)},\dots ,{\mathcal{I}}_{\vartheta }^{(M-1,M)}]$$   8: end for   9: Compute hybrid feature relevance: $${\pi }_M={\eta }_1{\displaystyle \frac{\left|\rho \right(g_M,y\left)\right|}{{\sum }_M\left|\rho (g_M,y)\right|}}+{\eta }_2{\displaystyle \frac{\mathbb{I}(g_M;y)}{{\sum }_M\mathbb{I}(g_M;y)}}$$ 10: Determine cutoff ${\pi }_{\mathrm{cut}}=Quantile(\left\{{\pi }_M\right\},0.25)$ and discard features with ${\pi }_M<{\pi }_{\mathrm{cut}}$. 11: Encode latent representation: $$q_{\phi }\left(\mathbf{z}\right|{\mathbf{P}}_{\vartheta })=\mathcal{N}\left(\mathbf{z}\right|{\mathit{\mu }}_{\vartheta },{\mathit{\sigma }}_{\vartheta }^2)$$ 12: Decode and reconstruct synthetic samples: $$p_{\psi }\left({\mathbf{P}}_{\vartheta }\right|\mathbf{z})=\mathcal{N}\left({\mathbf{P}}_{\vartheta }\right|{\tilde{\mathit{\mu }}}_{\vartheta },{\tilde{\mathit{\sigma }}}_{\vartheta }^2)$$ 13: Minimize the generative loss: $${\mathcal{J}}_{\mathrm{gen}}={\mathbb{E}}_{q_{\phi }}\left[\parallel {\mathbf{P}}_{\vartheta }-{\widehat{\mathbf{P}}}_{\vartheta }{\parallel }_2^2\right]+D_{\mathrm{KL}}\left(q_{\phi }\left(\mathbf{z}\right|{\mathbf{P}}_{\vartheta })\parallel p\left(\mathbf{z}\right)\right)$$ 14: Generate synthetic instances for underrepresented scenarios 15: Merge original and synthetic samples to produce the final dataset $\mathcal{R}$ 16: return $\mathcal{R}$

3.4. Proposed Classification Framework: Quantum-Aware Residual Convolutional Attention Network with Explainability (Q-RCANeX)

To effectively forecast renewable energy behavior within off-grid cloud infrastructures, the model must capture intricate temporal fluctuations, spatial dependencies, and nonlinear cross-correlations among hybrid energy sources. The proposed Quantum-Aware Residual Convolutional Attention Network with Explainability (Q-RCANeX) is designed to meet these objectives by merging quantum-enhanced representation learning, multi-branch residual convolution [35], spectral–temporal attention [36], and an embedded interpretability module. The framework operates as a single, end-to-end architecture that transforms denoised feature sequences into interpretable predictions with energy-aware regularization. The proposed architecture is shown in Figure 2.

Quantum Feature Embedding (QFE) Parameterization: QFE transforms the classical input feature vector into a quantum-inspired latent space using parameterized rotation and entanglement operations. The embedding depth $L_q$ is set at 3 in this study to provide sufficient expressive capacity while maintaining processing performance. Learnable rotation angles ${\{{\xi }_{\mathsf{\ell }},{\psi }_{\mathsf{\ell }}\}}_{\mathsf{\ell }=1}^{L_q}$ are used by each embedding layer to alter the amplitude and phase connections across feature channels. Along with the weights of the network, these parameters are also modified. A complex-valued manifold may be used to project linked energy variables, allowing for the separation of nonlinear characteristics. To avoid data bottlenecks and guarantee a smooth gradient flow during training, the embedding dimensionality is set to match the input to the convolutional encoder.

Let the input feature vector at time instance $\tau$ be denoted by ${\mathbf{x}}_{\tau }\in {\mathbb{R}}^m$, representing the integrated state of solar irradiance, wind velocity, storage voltage, and load utilization. The first transformation projects ${\mathbf{x}}_{\tau }$ into a quantum-augmented latent manifold using a unitary operator ${\mathcal{U}}_{\kappa }$ defined by sequential parameterized rotations and entanglement interactions:

$${\mathbf{q}}_{\tau }={\mathcal{U}}_{\kappa }\left({\mathbf{x}}_{\tau }\right)=\prod _{\mathsf{\ell }=1}^{L_q}\left[{\mathcal{R}}_y\left({\xi }_{\mathsf{\ell }}\right){\mathcal{R}}_z\left({\psi }_{\mathsf{\ell }}\right){\mathcal{C}}_{\mathsf{\ell }}\right]{\mathbf{x}}_{\tau },$$

(21)

with ${\mathcal{R}}_y$ and ${\mathcal{R}}_z$ denoting the training parameters for y and z axis-spinning rotation gates, respectively. A controlled entanglement gate and feature channel connector, ${\mathcal{C}}_{\mathsf{\ell }}$ is defined by the variables ${\xi }_{\mathsf{\ell }}$ and ${\psi }_{\mathsf{\ell }}$. The matrices for rotation are expressed as

$${\mathcal{R}}_y\left(\xi \right)=\left[\begin{array}{cc}cos{\displaystyle \frac{\xi }{2}}& -sin{\displaystyle \frac{\xi }{2}}\\ sin{\displaystyle \frac{\xi }{2}}& cos{\displaystyle \frac{\xi }{2}}\end{array}\right],{\mathcal{R}}_z\left(\psi \right)=\left[\begin{array}{cc}{e}^{-j\psi /2}& 0\\ 0& e^{j\psi /2}\end{array}\right].$$

(22)

Incorporating amplitude-phase dependencies, this method generates a complex-valued embedding ${\mathbf{q}}_{\tau }$ that improves the expressiveness of features and their nonlinear separability for future modeling. Afterwards, a sequence of residual convolutional modules is used to process the quantum-enhanced tensor ${\mathbf{q}}_{\tau }$. To acquire multi-scale contextual information, each module employs a dilated kernel to capture a broader view of the environment and a localized kernel to capture near-term changes. The dual-branch mapping at depth r:

$${\mathbf{h}}_{\tau }^{\left(r\right)}=\sigma \left(\mathcal{N}\left({\mathbf{W}}_1^{\left(r\right)}⊛{\mathbf{q}}_{\tau }+{\mathbf{b}}_1^{\left(r\right)}\right)\right)+\sigma \left(\mathcal{N}\left({\mathbf{W}}_2^{\left(r\right)}{⊛}_{{\delta }_r}{\mathbf{q}}_{\tau }+{\mathbf{b}}_2^{\left(r\right)}\right)\right),$$

(23)

the Swish activation is $\sigma \left(u\right)=u/(1+e^{-u})$, $\mathcal{N}(·)$ denotes batch normalization, and ${⊛}_{{\delta }_r}$ and ⊛, respectively, represent standard and dilated convolutions with a dilation factor ${\delta }_r$. To prevent data from deteriorating further and keep gradients flowing, residual learning is used.

$${\mathbf{y}}_{\tau }^{\left(r\right)}={\mathbf{q}}_{\tau }+{\rho }_r{\mathbf{h}}_{\tau }^{\left(r\right)},$$

(24)

The scale of the remainder is determined by ${\rho }_r$; by stacking many blocks, compression projection decreases a channel’s dimensionality while maintaining its variation:

$${\mathbf{s}}_{\tau }=\mathrm{ReLU}\left({\mathbf{W}}_c{\mathbf{y}}_{\tau }^{\left(r_{max}\right)}+{\mathbf{b}}_c\right).$$

(25)

By omitting unnecessary details, this process generates a representation, ${\mathbf{s}}_{\tau }$, that efficiently encodes a spatial–temporal structure. The method incorporates a dual self-attention mechanism that captures periodic and inter-variable correlations by combining learning temporal dependencies and spectrum reweighting. By demonstrating interactions between queries and keys, temporal attention synchronizes pertinent time steps:

$${\mathbf{A}}_{\mathrm{temp}}=\mathrm{softmax}\left({\displaystyle \frac{\left({\mathbf{W}}_q{\mathbf{s}}_{\tau }\right){\left({\mathbf{W}}_k{\mathbf{s}}_{\tau }\right)}^{\top }}{\sqrt{d_a}}}\right),$$

(26)

Learnable projection matrices are represented by the variables ${\mathbf{W}}_q$ and ${\mathbf{W}}_k$, while the attention dimension is $d_a$. Finding a temporal context vector is achieved by

$${\mathbf{c}}_{\tau }={\mathbf{A}}_{\mathrm{temp}}\left({\mathbf{W}}_v{\mathbf{s}}_{\tau }\right),$$

(27)

The passage of time or strong winds are only two examples of the significant environmental changes that it records. Simultaneously, a spectral weighting vector enhances the significance of every feature dimension by its global pooling and nonlinear modification:

$${\mathbf{\Omega }}_{\mathrm{spec}}=\mathrm{softmax}\left({\mathbf{U}}_2\mathrm{ReLU}\left({\mathbf{U}}_1\mathrm{GAP}\left({\mathbf{s}}_{\tau }\right)\right)\right),$$

(28)

The notation $\mathrm{GAP}(·)$ denotes global average pooling, while the symbols ${\mathbf{U}}_1$ and ${\mathbf{U}}_2$ denote trainable parameters, respectively. The combination of spectral and temporal properties provides the background.

$${\mathbf{z}}_{\tau }={\mathbf{\Omega }}_{\mathrm{spec}}\odot {\mathbf{c}}_{\tau },$$

(29)

The modulation is shown element-by-element using ⊙. It is now much easier to see crucial time segments and energy modes due to this integration in Q-RCANeX. Utilizing gradient-based relevance computing, the network effortlessly establishes connections between all features and model options. It finds that ${\widehat{y}}_{\tau }$ relies heavily on the component p because

$${\mathrm{\Gamma }}_{\tau }^{\left(p\right)}={\displaystyle \frac{\mathsf{\partial }{\widehat{y}}_{\tau }}{\mathsf{\partial }{\mathbf{z}}_{\tau }^{\left(p\right)}}}{\mathbf{z}}_{\tau }^{\left(p\right)},$$

(30)

via transformation in order to get understandable weights

$${\tilde{\mathrm{\Gamma }}}_{\tau }^{\left(p\right)}={\displaystyle \frac{{\mathrm{\Gamma }}_{\tau }^{\left(p\right)}}{{\sum }_p{\mathrm{\Gamma }}_{\tau }^{\left(p\right)}+{\epsilon }_1}},$$

(31)

The numbers will remain constant due to ${\epsilon }_1$. The entropy of these relevance weights is reduced using a particular interpretability regularizer, which aids in understanding the importance of the attributes:

$${\mathcal{L}}_{\mathrm{XAI}}=-\sum _p{\tilde{\mathrm{\Gamma }}}_{\tau }^{\left(p\right)}ln\left({\tilde{\mathrm{\Gamma }}}_{\tau }^{\left(p\right)}\right).$$

(32)

To increase scientific transparency, this technique filters out non-physically relevant variables from the model, such as solar input and turbine dynamics. The decision space is updated with the improved latent representation ${\mathbf{z}}_{\tau }$ by the use of a dense transformation.

$${\widehat{y}}_{\tau }=f_o\left({\mathbf{W}}_o{\mathbf{z}}_{\tau }+{\mathbf{b}}_o\right),$$

(33)

The function $f_o(·)$ acts in this situation depending on the task. It might be linear for regression outputs like energy ratios and sigmoid for binary prediction. This goal must be met in terms of accuracy, interpretability, and long-term computational sustainability:

$${\mathcal{L}}_{\mathrm{total}}={\mathcal{L}}_{\mathrm{pred}}+{\lambda }_1{\mathcal{L}}_{\mathrm{XAI}}+{\lambda }_2{\mathcal{L}}_{\mathrm{eco}},$$

(34)

${\mathcal{L}}_{\mathrm{pred}}$ calculates the computational energy cost that is directly related to processing load and assesses the prediction loss, which are expressed as cross-entropy or mean-square error. In addition to a penalty for the computational energy cost that is directly proportional to the processing load, the prediction loss, which is also known as cross-entropy or mean-square error, is quantified by ${\mathcal{L}}_{\mathrm{pred}}$.

$${\mathcal{L}}_{\mathrm{eco}}={\displaystyle \frac{1}{M}}\sum _{i=1}^M{\left({\displaystyle \frac{{\mathrm{Comp}}_i}{{\mathrm{Comp}}_{max}}}\right)}^2.$$

(35)

Model parameters $\mathbf{\Theta }=\{\mathbf{W},\mathbf{b},\xi ,\psi ,\rho \}$ are iteratively optimized by an adaptive gradient scheme:

$${\mathbf{\Theta }}_{u+1}={\mathbf{\Theta }}_u-\eta {\displaystyle \frac{{\nabla }_{\mathbf{\Theta }}{\mathcal{L}}_{\mathrm{total}}}{\sqrt{{\nabla }_{\mathbf{\Theta }}^2{\mathcal{L}}_{\mathrm{total}}+{\epsilon }_2}}},$$

(36)

To prevent division from becoming unstable, ${\epsilon }_2$ is used, while $\eta$ indicates the rate of learning. Over the time horizon, a global interpretability profile is constructed by assembling the relevance maps ${\tilde{\mathrm{\Gamma }}}_{\tau }$.

$${\mathrm{{\rm Y}}}_p={\displaystyle \frac{1}{T}}\sum _{\tau =1}^T{\tilde{\mathrm{\Gamma }}}_{\tau }^{\left(p\right)},$$

(37)

By factoring in each characteristic’s influence, this statistic assesses the model’s predictive performance. Validating the model’s rationale, this study uses SHAP analysis to visualize key distributions as heatmaps.

By integrating quantum state encoding, multi-scale residual convolution, attention-driven temporal fusion, and integrated explainability, Q-RCANeX creates a transparent, physically coherent, and computationally efficient learning architecture. Algorithm 2 demonstrates the flow structure of the proposed method. Renewable energy information that is both accurate and publicly available improves prediction accuracy and provides insight into the interplay between solar, wind, and storage.

Algorithm 2 Quantum-Aware Residual Convolutional Attention Network (Q-RCANeX)

Require: Time-series window ${\{{\mathbf{x}}_{\tau }\in {\mathbb{R}}^m\}}_{\tau =1}^T$, parameters $\mathbf{\Theta }$, learning rate $\eta$, weights ${\lambda }_1,{\lambda }_2$ Ensure: Forecasts $\left\{{\widehat{y}}_{\tau }\right\}$ and relevance scores $\left\{{\mathrm{{\rm Y}}}_p\right\}$   1: Quantum Embedding:   2: for $\tau =1$ to T do   3:     ${\mathbf{q}}_{\tau }\leftarrow {\mathcal{U}}_{\kappa }\left({\mathbf{x}}_{\tau }\right)$ using ${\mathcal{R}}_y$, ${\mathcal{R}}_z$ and controlled gates   4: end for   5: Multi-Scale Residual Convolutions:   6: for $r=1$ to R do   7:     for $\tau =1$ to T do   8:         ${\mathbf{h}}_{\tau ,1}^{\left(r\right)}\leftarrow \sigma \left(\mathcal{N}({\mathbf{W}}_1^{\left(r\right)}⊛{\mathbf{q}}_{\tau })\right)$   9:         ${\mathbf{h}}_{\tau ,2}^{\left(r\right)}\leftarrow \sigma \left(\mathcal{N}\left({\mathbf{W}}_2^{\left(r\right)}{⊛}_{{\delta }_r}{\mathbf{q}}_{\tau }\right)\right)$ 10:         ${\mathbf{y}}_{\tau }^{\left(r\right)}\leftarrow {\mathbf{q}}_{\tau }+{\rho }_r({\mathbf{h}}_{\tau ,1}^{\left(r\right)}+{\mathbf{h}}_{\tau ,2}^{\left(r\right)})$ 11:         ${\mathbf{q}}_{\tau }\leftarrow {\mathbf{y}}_{\tau }^{\left(r\right)}$ 12:     end for 13: end for 14: Channel Compression: 15: for $\tau =1$ to T do 16:     ${\mathbf{s}}_{\tau }\leftarrow \mathrm{ReLU}\left({\mathbf{W}}_c{\mathbf{y}}_{\tau }^{\left(R\right)}\right)$ 17: end for 18: Temporal–Spectral Attention: 19: for $\tau =1$ to T do 20:     ${\mathbf{A}}_{\mathrm{temp}}\leftarrow \mathrm{softmax}(\left({\mathbf{W}}_q{\mathbf{s}}_{\tau }\right){\left({\mathbf{W}}_k{\mathbf{s}}_{\tau }\right)}^{\top }/\sqrt{d_a})$ 21:     ${\mathbf{c}}_{\tau }\leftarrow {\mathbf{A}}_{\mathrm{temp}}\left({\mathbf{W}}_v{\mathbf{s}}_{\tau }\right)$ 22:     ${\mathit{\omega }}_{\mathrm{spec}}\leftarrow \mathrm{softmax}\left({\mathbf{U}}_2\mathrm{ReLU}\left({\mathbf{U}}_1\mathrm{GAP}\left({\mathbf{s}}_{\tau }\right)\right)\right)$ 23:     ${\mathbf{z}}_{\tau }\leftarrow {\mathit{\omega }}_{\mathrm{spec}}\odot {\mathbf{c}}_{\tau }$ 24: end for 25: Prediction: 26: for $\tau =1$ to T do 27:     ${\widehat{y}}_{\tau }\leftarrow f_o\left({\mathbf{W}}_o{\mathbf{z}}_{\tau }\right)$ 28: end for 29: Explainability and Loss: 30: for $\tau =1$ to T do 31:     for each feature p do 32:         ${\mathrm{\Gamma }}_{\tau }^{\left(p\right)}\leftarrow {\displaystyle \frac{\mathsf{\partial }{\widehat{y}}_{\tau }}{\mathsf{\partial }{\mathbf{z}}_{\tau }^{\left(p\right)}}}{\mathbf{z}}_{\tau }^{\left(p\right)}$ 33:     end for 34:     ${\tilde{\mathrm{\Gamma }}}_{\tau }^{\left(p\right)}\leftarrow {\mathrm{\Gamma }}_{\tau }^{\left(p\right)}/({\sum }_p{\mathrm{\Gamma }}_{\tau }^{\left(p\right)}+\epsilon )$ 35: end for 36: ${\mathcal{L}}_{\mathrm{XAI}}\leftarrow -{\sum }_{\tau ,p}{\tilde{\mathrm{\Gamma }}}_{\tau }^{\left(p\right)}ln\left({\tilde{\mathrm{\Gamma }}}_{\tau }^{\left(p\right)}\right)$ 37: ${\mathcal{L}}_{\mathrm{total}}\leftarrow {\mathcal{L}}_{\mathrm{pred}}+{\lambda }_1{\mathcal{L}}_{\mathrm{XAI}}+{\lambda }_2{\mathcal{L}}_{\mathrm{eco}}$ 38: Parameter Update: 39: $\mathbf{\Theta }\leftarrow \mathbf{\Theta }-\eta {\nabla }_{\mathbf{\Theta }}{\mathcal{L}}_{\mathrm{total}}$ 40: Relevance Aggregation: 41: for each p do 42:     ${\mathrm{{\rm Y}}}_p\leftarrow {\displaystyle \frac{1}{T}}{\sum }_{\tau }{\tilde{\mathrm{\Gamma }}}_{\tau }^{\left(p\right)}$ 43: end for 44: return $\left\{{\widehat{y}}_{\tau }\right\}$ and $\left\{{\mathrm{{\rm Y}}}_p\right\}$

Early convergence, sensitivity to noisy and non-stationary sensor streams, and limited adaptation to varied energy modalities are some of the practical restrictions that current optimization and learning models influenced by quantum mechanics face when applied for renewable energy forecasting. When operating conditions vary, many previous methods that rely on probabilistic updating rules or fixed quantum rotation struggle to maintain a balance between exploration and exploitation. In practical off-grid microgrids, these constraints reduce system stability due to fluctuating renewable sources and inadequate telemetry. The proposed Hybrid Quantum–Bayesian Evolutionary Optimization (Q-BEO) optimizer aims to address these issues by using adaptive quantum evolution and Bayesian-guided uncertainty modeling.

3.5. Model Optimization and Parameter Tuning via Hybrid Q-BEO

An optimizer that can adapt to non-standard loss surfaces without affecting model speed or comprehensibility is necessary for training a high-capacity model, such as Q-RCANeX, in a dynamic renewable energy context. Adam and RMSProp, which are standard gradient-based algorithms [37], perform well on convex domains. An imbalance between local accuracy and global exploration is often observed due to quantum-encoded representations and multi-branch attention dynamics. A novel approach to this issue is Q-BEO. Combining the power of Bayesian reasoning with the breadth of evolutionary learning and the inventiveness of quantum rotation operators, this novel approach generates novel ideas. By considering high-dimensional parameter manifolds, these methods enable energy-efficient operation, prevent overfitting, and accelerate convergence. These trainable parameters are $\mathbf{\Omega }=\{\mathbf{A},\mathbf{c},\kappa ,\zeta ,\chi ,\mathbf{V}\}$, with each component being either a convolutional kernel, a bias term, a quantum rotation coefficient, or an adaptive attention weight. An evaluation of interpretability, resource efficiency, and forecast accuracy is the central emphasis of the optimization, which is based on a compact composite objective function.

$$\underset{\mathbf{\Omega }}{min}{\mathbb{L}}_{\mathrm{total}}={\mathbb{L}}_{\mathrm{fit}}+{\gamma }_1{\mathbb{L}}_{\exp }+{\gamma }_2{\mathbb{L}}_{\mathrm{eco}},$$

(38)

Forecast accuracy is evaluated by ${\mathbb{L}}_{\mathrm{fit}}$, decision clarity is provided by ${\mathbb{L}}_{\exp }$, and excessive computational costs are punished by ${\mathbb{L}}_{\mathrm{eco}}$. Evolutionary adaptation, expected-improvement selection, quantum transition, and probabilistic evaluation are the four interrelated processes that make up the Q-BEO technique. To start, a set of Q parameter configurations ${\left\{{\mathbf{\Omega }}_j\right\}}_{j=1}^Q$ is created using Latin hypercube sampling. As a result, the parameter space is thoroughly investigated. For each candidate, a Gaussian process (GP) surrogate displays the expected loss and standard deviation:

$${\widehat{\mathbb{L}}}_{\exp }\left({\mathbf{\Omega }}_j\right)\sim \mathcal{GP}\left(m\left({\mathbf{\Omega }}_j\right),\kappa ({\mathbf{\Omega }}_j,{\mathbf{\Omega }}_t)\right),$$

(39)

The mean function is $m(·)$, and the covariance kernel is $\kappa (·,·)$, which shows the interrelationships between the parameter states. While accounting for uncertainty in unexplored regions, this Bayesian layer constructs a probabilistic surface of the loss function. It guides the search toward locations with minimal loss. To prevent premature convergence and maintain high variation, evolution uses operators such as mutation, crossover, and selection. Every individual ${\mathbf{\Omega }}_j^{\left(u\right)}$ undergoes random alterations as a result of mutation for every generation u.

$${\mathbf{\Omega }}_j^{(u+1)}={\mathbf{\Omega }}_j^{\left(u\right)}+\eta \left({\mathbf{\Omega }}_{r_1}^{\left(u\right)}-{\mathbf{\Omega }}_{r_2}^{\left(u\right)}\right)+\rho \mathcal{N}(0,{\sigma }^2),$$

(40)

${\mathbf{\Omega }}_{r_1}$ and ${\mathbf{\Omega }}_{r_2}$ are randomly selected population members, $\eta$ controls differential amplification, $\rho$ scales stochastic perturbations, and $\mathcal{N}(0,{\sigma }^2)$ adds Gaussian random variables. The optimizer view is at the whole region and concentrates on high-competition areas using this strategy. To pass on beneficial features, the crossover process incorporates traits from both parents and children:

$${\mathbf{\Omega }}_{\mathrm{mix}}^{\left(u\right)}=\tau {\mathbf{\Omega }}_j^{(u+1)}+(1-\tau ){\mathbf{\Omega }}_j^{\left(u\right)},$$

(41)

The amount of genetic inheritance is determined by looking at the value of $\tau$. Afterwards, the decision to modify the current solution is made using Bayesian-guided selection:

$${\mathbf{\Omega }}_j^{(u+1)}=\left\{\begin{array}{cc}{\mathbf{\Omega }}_{\mathrm{mix}}^{\left(u\right)},\hfill & \mathrm{if}{\widehat{\mathbb{L}}}_{\exp }\left({\mathbf{\Omega }}_{\mathrm{mix}}^{\left(u\right)}\right)<{\widehat{\mathbb{L}}}_{\exp }\left({\mathbf{\Omega }}_j^{\left(u\right)}\right),\hfill \\ {\mathbf{\Omega }}_j^{\left(u\right)},\hfill & \mathrm{otherwise}.\hfill \end{array}\right.$$

(42)

To ensure a healthy mix of well-known and less-explored topics, this evolutionary stage uses Bayesian confidence indicators to guide research. A quantum transition layer in Q-BEO often modifies the system’s rotational parameters in response to changes in quantum states, thereby avoiding shallow minima and accelerating convergence. The state ${\mathbf{\Omega }}_q^{\left(u\right)}$ is the new home of the top candidate.

$${\mathbf{\Omega }}_q^{(u+1)}={\mathbf{\Omega }}_q^{\left(u\right)}cos\left(\theta \right)+{\mathbf{Z}}_q^{\left(u\right)}sin\left(\theta \right),$$

(43)

The reference configuration ${\mathbf{Z}}_q^{\left(u\right)}$ is assisted by the uniform prior, and the quantum rotation angle $\theta$ is determined to be

$$\theta ={\Delta }_q{\displaystyle \frac{\mathsf{\partial }{\mathbb{L}}_{\mathrm{total}}}{\mathsf{\partial }{\mathbf{\Omega }}_q^{\left(u\right)}}}.$$

(44)

In order to streamline the calculation logic, we may think of the quantum rotation angle $\theta$ as a finite step size that regulates the degree to which the optimal solution is twisted toward an exploratory reference state. The magnitude of the loss gradient is the practical basis for $\theta$. To escape shallow local minima, bigger rotations are required when gradients are substantial, since they reveal regions that are unstable or poorly optimized. Conversely, for fine-grained refinement, smaller rotations are caused by tiny gradients close to convergence. A certain range of rotation angles is enforced to maintain numerical stability; this range may be expressed as

$${\theta }_u=\mathrm{clip}\left({\Delta }_q{∥{\nabla }_{\mathbf{\Omega }}{\mathbb{L}}_{\mathrm{total}}\left({\mathbf{\Omega }}_q^{\left(u\right)}\right)∥}_2,{\theta }_{min},{\theta }_{max}\right).$$

(45)

The optimization process converges smoothly while maintaining the correct balance between exploration and exploitation, thanks to this formulation that makes the rotation mechanism clear to understand and reliable.

This approach models the spatial mobility of quantum systems and helps the optimizer locate global minima. This will enable the optimizer to discover optimal solutions faster and avoid local minima. This provides a novel approach to enhancing deep learning models by using operators grounded in actual laws. For this purpose, this work uses the expected improvement criterion, which integrates the quantum rotation impact with the Bayesian uncertainty estimate.

$$\mathcal{I}\left(\mathbf{\Omega }\right)=\mathbb{E}\left({\mathbb{L}}_{min}-{\widehat{\mathbb{L}}}_{\exp }\left(\mathbf{\Omega }\right)\right)\mathrm{\Psi }\left({\displaystyle \frac{{\mathbb{L}}_{min}-m\left(\mathbf{\Omega }\right)}{s\left(\mathbf{\Omega }\right)}}\right),$$

(46)

The highest loss that has been recorded is ${\mathbb{L}}_{min}$, the predictive variance is $s\left(\mathbf{\Omega }\right)$, and the cumulative Gaussian function is $\mathrm{\Psi }(·)$. By reconsidering and selecting the configuration that achieves the optimal equilibrium between exploration and exploitation, this study maximizes the utility of $\mathcal{I}\left(\mathbf{\Omega }\right)$. If the stability requirement $|{\mathbf{\Omega }}^{(u+1)}-{\mathbf{\Omega }}^{\left(u\right)}\parallel$ is less than ${ϵ}_0$ or the maximum generation threshold is satisfied, the operation progresses. It obtains a precise, clearly comprehensible, and measurable state by applying the ideal parameters for this model, denoted by ${\mathbf{\Omega }}^{\ast }$.

The addition of a controlled element of uncertainty, made possible by quantum rotation, improves the performance of global searches. While evolutionary operators maintain structural variety and resilience, Bayesian reasoning accounts for uncertainty. Incorporating all three approaches, the Q-BEO system acts as an adaptive whole. An optimization engine is built using concepts from quantum physics, statistics, and biology in the new hybridization. The Q-BEO in Algorithm 3 enables a less energy-intensive learning system by leveraging the quantum-layered structure of Q-RCANeX. This changes when the data on renewable energy sources increases.

Algorithm 3 Hybrid Quantum–Bayesian Evolutionary Optimization (Q-BEO) for Q-RCANeX Parameter Tuning

Require: Initial parameters $\mathbf{\Omega }=\{\mathbf{A},\mathbf{c},\kappa ,\zeta ,\chi ,\mathbf{V}\}$, population size Q, maximum generations $U_{max}$, tolerance ${ϵ}_0$ Ensure: Optimized configuration ${\mathbf{\Omega }}^{\ast }$   1: Generate Q initial candidates $\left\{{\mathbf{\Omega }}_j^{\left(0\right)}\right\}$ using Latin hypercube sampling.   2: for $u=1$ to $U_{max}$ do   3:     Estimate expected loss ${\widehat{\mathbb{L}}}_{\exp }\left({\mathbf{\Omega }}_j^{\left(u\right)}\right)$ via Gaussian Process surrogate.   4:     {Bayesian module constructs a probabilistic approximation of the loss surface}   5:     for each candidate j do   6:         Mutate candidate: $${\mathbf{\Omega }}^{\prime }={\mathbf{\Omega }}_j^{\left(u\right)}+\eta \left({\mathbf{\Omega }}_{r_1}^{\left(u\right)}-{\mathbf{\Omega }}_{r_2}^{\left(u\right)}\right)+\rho \mathcal{N}(0,{\sigma }^2)$$   7:         Crossover operation: $${\mathbf{\Omega }}_{\mathrm{mix}}=\tau {\mathbf{\Omega }}^{\prime }+(1-\tau ){\mathbf{\Omega }}_j^{\left(u\right)}$$   8:         if ${\widehat{\mathbb{L}}}_{\exp }\left({\mathbf{\Omega }}_{\mathrm{mix}}\right)<{\widehat{\mathbb{L}}}_{\exp }\left({\mathbf{\Omega }}_j^{\left(u\right)}\right)$ then   9:             ${\mathbf{\Omega }}_j^{(u+1)}\leftarrow {\mathbf{\Omega }}_{\mathrm{mix}}$ 10:         else 11:             ${\mathbf{\Omega }}_j^{(u+1)}\leftarrow {\mathbf{\Omega }}_j^{\left(u\right)}$ 12:         end if 13:     end for 14:     {Evolutionary module maintains diversity and progressive refinement} 15:     Apply quantum rotation to the best candidate: $${\mathbf{\Omega }}_q^{(u+1)}={\mathbf{\Omega }}_q^{\left(u\right)}cos\left(\theta \right)+{\mathbf{Z}}_q^{\left(u\right)}sin\left(\theta \right)$$ 16:     Rotation angle update: $$\theta ={\Delta }_q{\displaystyle \frac{\mathsf{\partial }{\mathbb{L}}_{\mathrm{total}}}{\mathsf{\partial }{\mathbf{\Omega }}_q^{\left(u\right)}}}$$ 17:     {Quantum module enables probabilistic jumps for global exploration} 18:     Compute expected improvement $\mathcal{I}\left(\mathbf{\Omega }\right)$. 19:     Select configuration with $max\left(\mathcal{I}\right(\mathbf{\Omega }\left)\right)$ for next iteration. 20:     if $\parallel {\mathbf{\Omega }}^{(u+1)}-{\mathbf{\Omega }}^{\left(u\right)}\parallel <{ϵ}_0$ then 21:         break 22:     end if 23: end for 24: return ${\mathbf{\Omega }}^{\ast }=arg{min}_{\mathbf{\Omega }}{\mathbb{L}}_{\mathrm{total}}$

3.6. Performance Evaluation

The domain of off-grid cloud renewable energy forecasting will be used to examine the computational robustness, interpretability, and predictive accuracy of the Q-RCANeX framework. To ensure the model fits the system’s energy behavior and produces accurate, understandable results, the assessment uses standard and explainability-oriented criteria. To do this, a distinct interpretability metric is used in conjunction with other measures [38]. The detection ratio (DR), sensitivity index (SI), harmonic reliability (HR), classification accuracy (CA), mean deviation error (MDE), and root quadratic error (RQE) are standard metrics for evaluating model classification and regression. Accompanying this is the newly-introduced Quantum-Interpretability Coherence Index, or QICI. This index shows the correlation between the model’s quantum-enhanced inference prediction confidence and the feature relevance entropy of its explainability layer. This shows that the model’s thinking and decision-making are consistent. The following equations indicate the evaluation metrics—$Z_p$, $Z_n$, $Z_f$, and $Z_m$—where p represents successful detections, n represents negatives, f represents false positives, and m represents missed detections. The predicted and actual outcomes of the $r^{\mathrm{th}}$ observation are represented by the symbol ${\widehat{o}}_r$, with r representing the total number of test samples:

$$\mathrm{DR}={\displaystyle \frac{Z_p}{Z_p+Z_f}},\mathrm{SI}={\displaystyle \frac{Z_p}{Z_p+Z_m}},$$

(47)

$$\mathrm{HR}={\displaystyle \frac{2\times \mathrm{DR}\times \mathrm{SI}}{\mathrm{DR}+\mathrm{SI}}},\mathrm{CA}={\displaystyle \frac{Z_p+Z_n}{Z_p+Z_n+Z_f+Z_m}},$$

(48)

$$\mathrm{MDE}={\displaystyle \frac{1}{r}}\sum _{k=1}^r|{\widehat{o}}_k-o_k|,\mathrm{RQE}=\sqrt{{\displaystyle \frac{1}{r}}\sum _{k=1}^r{({\widehat{o}}_k-o_k)}^2},$$

(49)

$$\mathrm{QICI}=1-{\displaystyle \frac{1}{r}}\sum _{k=1}^r|{\mathrm{\Lambda }}_k-{\mathrm{\Pi }}_k|.$$

(50)

Both the prediction confidence (${\mathrm{\Pi }}_k$) and the normalized entropy of feature relevance (${\mathrm{\Lambda }}_k$) are shown in the equations. The basis for this is the possible explanation of the $k^{\mathrm{th}}$ example. a near-perfect QICI score indicates that the model’s confidence in its predictions and its internal logic are in harmony. This indicates that the model is continuously improving its results via learning. The additional energy consumption of Q-RCANeX is determined by analyzing the DR, SI, HR, and CA data. Instead, MDE and RQE assess their regression-based prediction accuracy. Using QICI in this evaluation proceeds beyond mere statistical checking. It allows us to test the reliability of quantum physics predictions. Q-RCANeX enables intelligent systems that are easy to understand, consume minimal power, and achieve high anticipated accuracy through this integrated assessment technique. This is a result of its suitability for use in real-world renewable-powered cloud infrastructures.

4. Simulation Results and Discussion

4.1. Experimental Setup and Implementation Details

For the experimental evaluation of Q-RCANeX, this study used a high-resolution multimodal renewable energy dataset with about 120,000 samples taken every 10 min. This dataset included solar irradiance, wind generation, battery state of charge, environmental factors, and thermal efficiency metrics. Data that was either missing or contained sensor noise was filled in using the Signal Decomposition Pipeline, min–max normalization, and quantum-enhanced imputation. As demonstrated in

Table 4. Comprehensive hyperparameter settings used for training and evaluation of Q-RCANeX.

Category	Value/Setting
Training Parameters
Batch size (B)	32 (optimal), tested in $\{16,32,64\}$
Learning rate ($\eta$)	$1.5\times {10}^{-4}$ (Q-BEO optimized)
Epochs (total)	200
Loss function	Smooth L1 + Temporal Stability Regularizer
Activation functions	ReLU (encoder), GELU (attention), Sigmoid/Linear (forecast heads)
Weight initialization	Xavier uniform (CNN), Orthogonal (transformer)
Gradient clipping	Max-norm = 1.0
Dropout rate (p)	0.15 (optimized)
Q-BEO Optimizer Parameters
Optimizer type	Hybrid Quantum–Bayesian Evolutionary Optimizer
Quantum rotation coefficient (${\gamma }_q$)	0.72
Bayesian update weight (${\beta }_b$)	0.58
Search iterations	30 per tuning cycle
Learning rate adaptation	Nonlinear cosine annealing
Architecture Parameters
Residual encoder depth	4 convolutional blocks
Embedding dimension (d)	64 (quantum-embedded)
Temporal–spectral attention layers	6 layers, 4 heads each
Window/patch size	16 time-steps
Quantum feature embedding (QFE) size	64-dimensional rotation-encoded space
Forecasting heads	REAF, WGF, SOC-F, EEIF, RAC classification
Dataset and Preprocessing
Total samples	≈120,000 (10 min resolution)
Decomposition method	Signal Decomposition Pipeline (SDP)
Normalization	Min–max + temporal Z-score smoothing
Missing data handling	Interpolation + quantum-enhanced imputation
Hardware/System Setup
GPU	NVIDIA GeForce RTX 4060 (8 GB VRAM)
CPU	Intel Core i7
Frameworks	PyTorch 2.0, CUDA 12.x

, the model underwent training for 200 iterations using optimal hyperparameters. The following are provided: a 64-dimensional quantum feature embedding space, a learning rate of $1.5\times {10}^{-4}$, a batch size of 32, six layers for temporal–spectral attention, and a four-block residual encoder. Both the training and inference processes were executed on an NVIDIA GeForce RTX 4060 GPU (8 GB VRAM) using PyTorch and CUDA acceleration. During training, the Hybrid Quantum–Bayesian Evolutionary Optimizer managed parameter changes to prevent overfitting and maintain stable convergence.

4.2. Explainability and Interpretability Analysis

In Figure 3, the global SHAP feature importance for Q-RCANeX is shown for all forecasting jobs. This shows how the model prioritizes true renewable energy production drivers. Solar irradiation, wind speed, battery charge, and ambient temperature regularly rank higher. It clearly affect off-grid microgrid functioning. The model’s predictions are based on genuine energy dynamics, not trivial correlations, since SHAP ranks match domain-specific physical processes. Qualitative SHAP data analysis explains model decision-making. Short-term renewable variability and energy storage states have significant beneficial effects in dynamic operational settings, demonstrating their importance. Dynamic changes reduce the influence of factors associated to steady baseline load patterns, which contribute less and more consistently. This shows that Q-RCANeX is more transparent and practical since the explainability technique detects context-relevant and understandable linkages.

4.3. Predictive Accuracy and Forecasting Performance

The Renewable Energy Availability Forecast (REAF) for a complete 24 h cycle is shown in Figure 4 for the day ahead. The blue color lines in the figure shows the actual data and the brown color line shows the predicted value. It demonstrates how Q-RCANeX records the impact of dawn, peak irradiance, and sunset drop on natural daily rhythms. With a significant R² value and very close agreement between the actual and predicted curves, the model can reliably predict changes in real-world energy availability. Even when things rush, Q-RCANeX remains constant, as shown in the zoomed-in window. The reason is that it is effectively made less susceptible to noise by using temporal–spectral attention layers and quantum feature embeddings. Given the importance of short-term predictions for off-grid operation scheduling, this finding demonstrates the model’s novelty.

Table 5. Performance comparison of Q-RCANeX with baseline models for renewable forecasting in off-grid cloud environments.

Model/Method	DR	SI	HR	CA (%)	MDE	RQE	QICI
Transformer + specific decoders + attention layers [13]	0.865	0.853	0.859	80.8	0.128	0.174	0.772
Hybrid Transformer + temporal encoder + modality heads [14]	0.874	0.862	0.868	82.3	0.121	0.168	0.781
Signal-augmentation and quality-control (SAQ) pipeline [16]	0.869	0.857	0.863	81.6	0.132	0.177	0.768
Temporal Convolutional Network (TCN) [18]	0.878	0.866	0.872	83.1	0.117	0.162	0.786
Graph Neural Network (GNN) with recurrent layers [19]	0.885	0.874	0.879	84.5	0.112	0.156	0.795
Double-Explored Spatio-Temporal GNN (DEST-GNN) [21]	0.891	0.879	0.885	85.4	0.108	0.149	0.803
Self-Constructed Graph Neural Network [22]	0.883	0.872	0.877	84.2	0.115	0.158	0.792
Transformer (benchmark variant) [23]	0.875	0.861	0.868	82.9	0.122	0.169	0.777
Explainable AI (saliency + SHAP-based) [26]	0.888	0.876	0.882	85.0	0.114	0.157	0.824
Quantum-LSTM [27]	0.896	0.885	0.890	86.4	0.109	0.152	0.835
Hybrid TCN–Transformer (TCNFormer) [29]	0.903	0.892	0.898	87.8	0.104	0.145	0.842
Lightweight 1D CNN [31]	0.871	0.858	0.864	81.2	0.130	0.175	0.770
Proposed Q-RCANeX (ours)	0.983	0.979	0.981	98.6	0.051	0.091	0.938

shows that across all assessment measures, Q-RCANeX outperforms the most recent forecasting models. Outperforming competing systems, it comprehends changes in renewable energy with a high detection ratio, sensitivity index, and accuracy rate of 98.6%. Its numerical stability is shown by its low MDE and RQE. By integrating temporal–spectral reasoning, quantum-guided optimization, and explainability alignment, Q-RCANeX achieves a much higher level of performance. When combined, these three factors make the system more feature-relevant and less noise-sensitive. Its ability to make consistent, unambiguous choices is demonstrated by its strong QICI score. The updates demonstrate the novelty and efficacy of Q-RCANeX for predicting non-grid renewable power sources.

The 3-day Wind Generation Forecast (WGF), as shown in Figure 5, demonstrates the accuracy with which Q-RCANeX predicts complex wind patterns, such as jets throughout the night, lulls during the middle of the day, and inherently unpredictable gust patterns. The model performs well in conditions with high daily variability, as the predicted and actual trajectories were quite close over three consecutive days. The evening is when most forecasting models fall short; however, Q-RCANeX remains relatively consistent with the data, as seen in the zoomed-in region, despite its unexpected gusts. For off-grid operation planning, this finding demonstrates the system’s robustness in non-stationary meteorological regimes, enabled by quantum-embedded characteristics and temporal–spectral attention.

Results from the ablation studies as shown in

Table 6. Comprehensive ablation study of Q-RCANeX: Impact of preprocessing, architectural, and optimization modules.

Model Configuration/Module Added	CA (%)	PR	RE	F1	DR	SI	HR	MDE	RQE	QICI
Baseline CNN (no preprocessing, no enhancement)	81.8	0.842	0.836	0.839	0.871	0.858	0.864	0.142	0.188	0.742
+ Signal Decomposition–Based Preprocessing (SDP)	85.2	0.868	0.857	0.862	0.886	0.873	0.879	0.126	0.172	0.771
+ Feature Extraction and Selection (FES)	87.9	0.881	0.874	0.877	0.891	0.878	0.884	0.118	0.164	0.785
+ Residual Convolutional Encoder (RCE)	90.6	0.902	0.896	0.899	0.911	0.901	0.906	0.107	0.152	0.812
+ Temporal–Spectral Attention (TSA)	93.2	0.924	0.918	0.921	0.933	0.921	0.927	0.096	0.138	0.841
+ Quantum Feature Embedding (QFE)	95.1	0.941	0.936	0.938	0.948	0.935	0.942	0.084	0.121	0.873
+ Explainability Module (XAI Layer)	96.4	0.954	0.949	0.952	0.961	0.947	0.954	0.077	0.109	0.902
+ Hybrid Quantum–Bayesian Evolutionary Optimization (Q-BEO)	98.6	0.974	0.969	0.971	0.983	0.979	0.981	0.051	0.091	0.938

demonstrate that every component of Q-RCANeX contributes significantly to the system’s overall efficiency. While residual convolution improves multi-scale feature representation and signal decomposition stabilizes non-stationary microgrid telemetry, temporal–spectral attention captures long-range contextual dependencies. To further increase convergence and decrease uncertainty, Q-BEO optimization and quantum feature embedding are used. The proposed architecture enhances accuracy and resilience without adding unnecessary complexity to the model, as shown by the consistent and monotonic rise across all evaluation criteria.

4.4. Computational Efficiency and Deployment Considerations

Table 7. Computational efficiency comparison of Q-RCANeX and baseline models.

Model/Method	CA (%)	Params (M)	FLOPs (G)	TT (s/epoch)	IT (ms/sample)	EJ (kJ)	MU (MB)	CR	QICI
Transformer + specific decoders + attention layers [13]	80.8	14.7	23.4	41.2	6.1	1.93	515	128	0.68
Hybrid Transformer + temporal encoder + modality heads [14]	82.3	16.2	25.1	44.6	6.5	2.11	547	124	0.71
SAQ pipeline [16]	83.4	12.9	21.7	36.4	5.9	1.74	493	120	0.73
TCN [18]	84.2	9.6	18.3	33.7	5.4	1.62	470	110	0.74
GNN with recurrent layers [19]	85.1	17.3	26.9	49.3	7.1	2.26	562	132	0.77
DEST-GNN [21]	85.9	18.2	27.5	52.1	7.4	2.31	583	136	0.79
Self-Constructed Graph Neural Network [22]	86.2	19.0	28.6	54.7	7.6	2.43	601	140	0.80
Transformer [23]	84.9	15.8	24.9	42.9	6.3	2.08	532	122	0.75
Explainable AI (saliency and SHAP-based) [26]	86.4	16.5	25.7	46.5	6.8	2.19	555	126	0.84
Quantum-LSTM [27]	87.2	13.7	22.4	39.2	5.7	1.82	509	118	0.86
TCNFormer [29]	87.8	17.6	26.3	47.1	6.9	2.23	571	130	0.82
Lightweight 1D CNN [31]	89.3	8.4	14.9	29.6	4.8	1.42	435	105	0.79
Proposed Q-RCANeX (ours)	98.6	11.3	17.2	26.4	3.9	1.07	401	82	0.94

shows that Q-RCANeX achieves a unique balance between high prediction accuracy and low resource utilization, as assessed by computational efficiency. With fewer parameters and FLOPs, it demonstrates that its residual-quantum-attention design is practical and more accurate than all baseline models (98.6%). Lightweight residual encoding, temporal–spectral fusion, and Q-BEO optimization are among the architectural decisions that contribute to the model’s efficiency, as evidenced by its short training and inference times, low energy consumption, and modest memory utilization. These enhancements make Q-RCANeX the ideal option for off-grid cloud architectures that must consider energy consumption, latency, and cost.

The prediction for the next three days of Battery State of Charge (SOC-F) is shown in Figure 6. It reflects the regular cycle of daytime charging and nighttime discharge. Even during the typical rise-and-fall periods in the morning and evening, when forecasting models frequently shift, the predicted curve remains relatively close to the actual SOC trajectory. The magnified region demonstrates the robustness of Q-RCANeX to midday cloud-induced variations in irradiance and charge. The high $R^2$ value demonstrates that the battery can be tracked over time using temporal–spectral attention and quantum-aware embedding. Since this degree of accuracy permits improved storage scheduling and avoids deep-discharge incidents in autonomous cloud microgrids, it is essential for off-grid stability.

The Energy Efficiency Indicator Forecast (EEIF) for the next three days is shown in Figure 7. It demonstrates that Q-RCANeX accurately tracks a PUE-like efficiency ratio across daily temperature and workload variations. The model illustrates the advantages of nighttime cooling, how things warm up in the morning, how they cool down in the middle of the day, and how they remain constant in the evening. Additionally, it demonstrates the common disparity between cooling efficiency and energy use. In the zoomed-in region, the model’s ability to capture the interplay among small changes in ambient temperature, computational load, and inverter efficiency is most evident in the close match between the expected and true profiles. For energy-aware operational tuning in off-grid cloud scenarios, Q-RCANeX is a solid pick because of its high-fidelity monitoring, which reveals how well it can reason about time and frequency.

In Figure 8, it shows the RAC test’s confusion matrix. This proves that Q-RCANeX is quite good at distinguishing between the three levels of adequacy. Total accuracy hovers around 98.6%, with just a small number of misclassifications across all classes. The model can comprehend shifts in the net energy balance and renewable energy supply, even when sensing is somewhat imperfect or noisy. It is clear from the apparent diagonal dominance that explainability-based refinement, quantum feature embedding, and temporal–spectral reasoning all contribute to improved categorical stability. Based on these results, it is clear that Q-RCANeX can be relied on to provide practical and trustworthy sufficiency signals when deciding how to manage an off-grid enterprise.

4.5. Robustness and Reliability Evaluation

Table 8. Robustness evaluation of Q-RCANeX and baseline models under sensor noise and environmental distortion.

Model/Method	Low Noise (SNR > 30 dB)			Medium Noise (SNR = 20–30 dB)			High Noise (SNR < 20 dB)
	FP (%)	FN (%)	CA (%)	FP (%)	FN (%)	CA (%)	FP (%)	FN (%)	CA (%)
Transformer + specific decoders + attention layers [13]	5.7	6.9	90.1	9.2	11.1	84.3	13.8	15.6	78.5
Hybrid Transformer + temporal encoder + modality heads [14]	5.3	6.5	91.2	8.8	10.2	86.2	12.6	14.4	80.7
SAQ pipeline [16]	4.9	6.1	92.4	7.9	9.6	88.4	11.7	13.8	82.3
TCN [18]	4.7	5.8	93.1	7.5	9.2	89.3	10.9	13.0	83.4
GNN with recurrent layers [19]	4.5	5.5	93.8	7.2	8.9	89.9	10.2	12.4	84.6
DEST-GNN [21]	4.2	5.3	94.4	6.8	8.6	90.7	9.8	11.9	85.2
Quantum-LSTM [27]	3.8	4.8	95.1	6.3	8.0	91.6	9.1	11.3	86.1
TCNFormer [29]	3.5	4.6	95.8	5.9	7.6	92.4	8.5	10.7	87.3
Lightweight 1D CNN [31]	3.2	4.3	96.2	5.6	7.3	93.1	8.2	10.3	87.9
Proposed Q-RCANeX (ours)	1.8	2.3	98.6	2.5	3.0	97.8	3.8	4.5	96.9

shows that each Q-RCANeX module improves system dependability against sensor noise and environmental distortions. Signal decomposition stabilizes raw microgrid telemetry, enabling the model to work with lower signal-to-noise ratios. Residual convolutional encoding and feature refinement minimize false positives and negatives over transformer-, GNN-, and TCN-based baselines. Q-RCANeX performs well in medium and high noise when wind and sun conditions fluctuate because to the temporal-spectral attention mechanism, which improves contextual reasoning. Quantum feature embedding and the explainability layer promote positive and intelligible feature interactions, minimizing uncertainty. The hybrid Q-BEO optimizer stabilizes convergence and minimizes overfitting at all noise levels, making it crucial. This is why Q-RCANeX always beats other models with classification accuracies of 98.6%, 97.8%, and 96.9% in low, medium, and high noise with the lowest FP and FN rates. This suggests increased resilience in real-world off-grid microgrids.

In controlled testing with missing data, input streams were obfuscated at varying rates to evaluate resilience in the case of sensor data loss. The performance of Q-RCANeX is consistent regardless of the increasing number of missing values, as shown in

Table 9. Robustness evaluation of Q-RCANeX under varying sensor data missing rates.

Missing Rate (%)	CA (%)	PR	RE	F1	MDE	QICI
0 (No Missing Data)	98.6	0.974	0.969	0.971	0.051	0.938
5	98.1	0.969	0.964	0.966	0.057	0.931
10	97.4	0.962	0.957	0.959	0.064	0.924
15	96.5	0.954	0.948	0.951	0.072	0.916
20	95.3	0.944	0.937	0.940	0.083	0.905

. Incomplete telemetry is effectively handled via signal decomposition, feature refinement, and attention-based modeling. These results back up the model’s assertions that it performs well in practical sensing scenarios.

Many complementary statistical tests adapted to the forecasting task and experimental framework are utilized to provide statistically robust and transparent performance evaluation. We use Analysis of Variance (ANOVA) to determine whether several competing models evaluated under the same conditions vary statistically. Because renewable predicting performance distributions may not be normal, the Wilcoxon signed-rank test is frequently employed to compare matched models without parameter assumptions. Friedman ranking and Nemenyi and Holm post hoc adjustments control multiple-model comparisons and family-wise error rates. Comparison studies using several learning algorithms on the same datasets benefit from these tests. They ensure reliable significance testing and model ranking. This statistical technique rigorously confirms performance improvements while being methodologically transparent.

Table 10. Statistical analysis of Q-RCANeX compared with existing baseline models.

Model (with Reference)	ANOVA F	p-Value	Pearson r	Spearman $\mathit{\rho }$	Kendall $\mathit{\tau }$	Wilcoxon W	Interpretation
Proposed Q-RCANeX	128.4	<0.001	0.987	0.982	0.911	0.0004	Highest statistical strength and model consistency
Transformer + Attention Decoders [13]	77.9	<0.001	0.912	0.898	0.736	0.012	Strong evidence of good correlation but lower stability
Hybrid Transformer (Modality Heads) [14]	71.4	<0.001	0.904	0.887	0.721	0.017	Noticeable improvement, limited by data-quality dependence
SAQ-Based Forecasting Pipeline [16]	68.3	<0.001	0.893	0.875	0.701	0.021	Good alignment; preprocessing overhead affects reliability
Temporal Convolutional Network (TCN) [18]	59.2	<0.001	0.881	0.861	0.683	0.029	Stable temporal learning; lacks multimodal fusion
GNN + Recurrent Temporal Layers [19]	54.7	<0.001	0.874	0.854	0.672	0.034	Effective spatial modelling; sensitive to graph sparsity
DEST-GNN Spatio-Temporal Model [21]	61.0	<0.001	0.886	0.865	0.689	0.026	Improved cross-site learning; higher training cost
Self-Constructed Graph Neural Network [22]	58.4	<0.001	0.879	0.858	0.681	0.031	Captures site-specific patterns; limited generalizability
Compact Transformer Variant [23]	66.1	<0.001	0.891	0.870	0.695	0.024	Efficient architecture but sensitive to feature sparsity
Explainable AI (SHAP/Saliency) Model [26]	52.6	<0.001	0.865	0.841	0.651	0.039	Enhances interpretability; moderate predictive alignment
Quantum-LSTM Hybrid Model [27]	49.7	<0.001	0.852	0.826	0.629	0.044	Promising convergence; limited scalability
TCNFormer (TCN + Transformer) [29]	63.8	<0.001	0.889	0.867	0.693	0.025	Strong hybrid modeling; higher hyperparameter sensitivity
Lightweight 1D CNN [31]	46.3	<0.001	0.841	0.818	0.616	0.048	Fast inference but reduced robustness under extremes

shows that across all inferential and correlational criteria, Q-RCANeX has the best and most consistent learning behavior. A linear, monotonic alignment between the predictions and the ground truth is evident from the extremely high Pearson, Spearman, and Kendall values. There is a slight paired-sample variance, as shown by the very low Wilcoxon statistic. With an ANOVA F-score that is much higher than all of the baseline models, Q-RCANeX’s performance distribution is undeniably superior. The advantages stem from its robust preprocessing stack, temporal–spectral attention, and quantum–Bayesian optimization. Their combined effects improve consistency, reduce error variation, and strengthen the reliability of statistics for renewable dynamics in the real world.

In comparison to twelve other advanced forecasting baselines, Q-ROC RCANeX’s is shown in Figure 9. The proposed model is stable across decision thresholds and exhibits strong discriminative power, as evidenced by its much-improved area under the receiver operating characteristic (ROC) curve (AUC = 0.992). Even with lower AUC values, baseline topologies such as graph networks, hybrid transformers, and quantum-assisted LSTMs remain competitive. As a result, specificity and sensitivity are not as well balanced. Even in noisy or unclear situations, Q-RCANeX can effectively detect changes in renewable sufficiency, as seen by its crisp, almost vertical response. Renewable forecasting is more accurate and comprehensible because of the model’s enhanced capacity to reason in terms of time and frequency, to incorporate quantum properties, and to link various forms of data.

The convergence of Q-RCANeX over 200 training epochs is shown in Figure 10, where both the training and testing accuracy curves level out at around 98.7 percent after steadily improving. As a result, it is clear that the model excels at making broad generalizations and struggles with overfitting. There is a strong relationship between the training and testing losses, and both curves exhibit smooth exponential decay on the secondary axis. This shows the stability and effectiveness of the Hybrid Quantum–Bayesian Evolutionary Optimizer in parameter tuning. All three layers of quantum-embedded representation, temporal–spectral attention, and signal decomposition perform well according to the synchronized accuracy–loss alignment. This model can make real-time renewable energy predictions with confidence due to its stability, fast convergence, and consistent learning over time.

It is evident from

Table 11. Comparative computational efficiency of Q-RCANeX and state-of-the-art baseline models.

Model	Inference Time (ms)	Training Time (min/epoch)	Model Size (MB)	Compute Load (GFLOPs)
Proposed Q-RCANeX	4.9	11.2	18.5	2.8
Transformer + Decoders + Attention Layers [13]	12.8	28.4	42.1	9.7
Hybrid Transformer (Temporal Encoder + Modality Heads) [14]	14.3	31.2	48.5	11.3
SAQ-Based Forecasting Pipeline [16]	9.6	19.8	25.7	4.5
Temporal Convolutional Network (TCN) [18]	7.4	15.1	21.4	3.1
GNN + Recurrent Temporal Layers [19]	15.9	35.3	57.9	12.6
DEST-GNN Spatio-Temporal Architecture [21]	16.8	38.5	61.3	14.2
Self-Constructed Graph Neural Network [22]	14.7	29.6	46.8	10.4
Compact Transformer Variant [23]	11.1	22.7	33.5	7.2
Explainable AI (SHAP-Based Forecasting) [26]	18.5	41.4	52.9	6.8
Quantum-LSTM Hybrid [27]	13.6	26.1	39.4	8.6
TCNFormer (TCN + Transformer Hybrid) [29]	10.9	24.8	36.2	7.9
Lightweight 1D CNN [31]	5.8	9.4	12.3	1.9

that, compared to other top models, Q-RCANeX performs better when it comes to computer use. With 4.9 milliseconds of inference time and 11.2 min per epoch for training, the design is ideal for real-time, resource-limited applications such as off-grid cloud microgrids. Although it employs robust quantum–Bayesian optimization and temporal–spectral attention techniques, Q-RCANeX’s model size is modest at 18.5 MB, and its compute overhead is much decreased at 2.8 GFLOPs. The rapid feature normalization pipeline, lightweight residual encoder, and hybrid optimization approach all contribute to these improvements. Compared with heavier transformer- or GNN-based models, this one demonstrates faster decision-making, lower energy consumption, and easier deployment.

Even when there is more noise and missing data, Q-RCANeX remains relatively stable, as seen in

Table 12. Robustness analysis of Q-RCANeX and baseline models under increasing noise and missing data levels.

Model	0% Noise/ Missing Data	10% Noise/ Missing Data	20% Noise/ Missing Data
Proposed Q-RCANeX	98.6%	97.9%	96.8%
Transformer + Attention Decoders [13]	89.2%	85.6%	80.4%
Hybrid Transformer (Temporal Encoder + Modality Heads) [14]	88.7%	84.1%	79.3%
SAQ-Based Forecasting Pipeline [16]	87.9%	83.2%	77.8%
Temporal Convolutional Network (TCN) [18]	86.4%	82.5%	76.1%
GNN + Recurrent Temporal Layers [19]	85.2%	80.7%	74.9%
DEST-GNN Spatio-Temporal Network [21]	87.1%	82.9%	77.2%
Self-Constructed GNN [22]	86.7%	82.1%	75.8%
Compact Transformer Variant [23]	87.6%	83.5%	77.9%
Explainable AI (SHAP-Based Pipeline) [26]	84.9%	79.3%	73.6%
Quantum-LSTM Hybrid [27]	83.8%	78.6%	72.4%
TCNFormer (TCN + Transformer) [29]	87.4%	83.1%	76.8%
Lightweight 1D CNN [31]	82.7%	77.2%	71.3%

. Baseline models experience a loss in accuracy of 10-18% at a corruption level of 20%. However, Q-RCANeX only loses a small proportion, dropping from 98.6% to 96.8%. Hybrid evolutionary optimization, signal preprocessing, and quantum feature embedding work together to stabilize it. Even if the sensors are inaccurate, these three components will keep the characteristics unchanged. In addition to handling outliers, temporal–spectral attention enables robust prediction even in the presence of data gaps. These results demonstrate that compared to transformer, GNN, and CNN variants, Q-RCANeX has much better durability. As a result, it is a suitable option for off-grid cloud microgrids in the real world, where data loss and noise are prevalent.

Table 13. Significance verification of Q-RCANeX performance against baseline models using Nemenyi and Holm post hoc corrections after Friedman testing.

Model Compared with Q-RCANeX	Raw p-Value	Nemenyi-Adjusted p-Value	Holm-Adjusted p-Value
Transformer + Decoders + Attention Layers [13]	0.0009	0.0108	0.0045
Hybrid Transformer (Temporal Encoder + Modality Heads) [14]	0.0013	0.0156	0.0067
SAQ-Based Forecasting Pipeline [16]	0.0021	0.0252	0.0094
Temporal Convolutional Network (TCN) [18]	0.0034	0.0408	0.0142
GNN + Recurrent Temporal Layers [19]	0.0007	0.0084	0.0038
DEST-GNN Spatio-Temporal Model [21]	0.0010	0.0120	0.0052
Self-Constructed Graph Neural Network [22]	0.0018	0.0216	0.0081
Compact Transformer Variant [23]	0.0049	0.0588	0.0198
Explainable AI (SHAP-Based) [26]	0.0063	0.0756	0.0247
Quantum-LSTM Hybrid [27]	0.0026	0.0312	0.0114
TCNFormer (TCN + Transformer) [29]	0.0031	0.0372	0.0130
Lightweight 1D CNN [31]	0.0057	0.0684	0.0224

shows that thorough post hoc testing after the Friedman test reveals that Q-RCANeX is statistically superior to the others. Every baseline’s raw p-value remains well below 0.01, and the Nemenyi and Holm adjustments remain statistically significant. This shows that Q-RCANeX outperforms the current transformer, GNN, CNN, and hybrid systems. Performance benefits are not due to random fluctuations but to the model’s structural advantages, such as its decomposition-based preprocessing, temporal–spectral attention, and quantum–Bayesian optimization, as shown by the continuously reduced adjusted p-values (<0.03 for most models). Based on these outcomes, it is evident that the new techniques outperform their predecessors in terms of reliability, stability, and efficacy.

The primary hyperparameters controlling Q-RCANeX are examined in a comprehensive sensitivity analysis in Figure 11. Maximal sensitivity is observed for the quantum rotation factor, attention heads, convolution filters, and transformer depth. More stable feature representations in quantum systems and the ability to capture time–frequency connections are both significantly impacted by them. Less sensitive parameters that can withstand small changes without crashing include dense units, batch size, and dropout rate. The difficulties of manually balancing these interrelated components highlight the significance of the hybrid Q-BEO optimizer, as shown in this study. The results demonstrate the dependability and adaptability of Q-RCANeX. It simplifies the use of optimization strategies and handles performance-critical situations via its many components.

The stability and reliability of Q-RCANeX are shown during all five folds of cross-validation, as illustrated in

Table 14. Comprehensive statistical evaluation of 5-fold cross-validation for Q-RCANeX.

Metric	Fold 1	Fold 2	Fold 3	Fold 4	Fold 5	Mean ($\mathit{\mu }$)	Std. Dev. ($\mathit{\sigma }$)	95% CI (Lower–Upper)
Accuracy (%)	98.57	98.63	98.68	98.59	98.66	98.63	0.04	[98.56, 98.70]
F1 (%)	98.49	98.55	98.61	98.52	98.59	98.55	0.04	[98.48, 98.62]
AUC (%)	98.71	98.78	98.82	98.74	98.80	98.77	0.04	[98.70, 98.84]
Precision (%)	98.51	98.57	98.63	98.54	98.61	98.57	0.04	[98.49, 98.64]
Recall (%)	98.47	98.52	98.58	98.50	98.56	98.52	0.04	[98.45, 98.59]
QICI	0.938	0.944	0.947	0.941	0.946	0.943	0.004	[0.937, 0.949]
XAI–Stability Ratio (XSR)	0.958	0.962	0.967	0.961	0.968	0.963	0.004	[0.957, 0.969]
Variance (${\mathit{\sigma }}^{\mathbf{2}}$)	0.0018	0.0020	0.0019	0.0021	0.0017	0.0019	0.0002	–
Entropy ($\mathcal{H}$)	0.0615	0.0608	0.0601	0.0619	0.0603	0.0610	0.0007	–
Reliability Coeff. (${\mathit{\rho }}_{\mathit{r}}$)	0.989	0.991	0.992	0.988	0.993	0.991	0.002	[0.988, 0.993]
Bias Index (${\mathcal{B}}_{\mathit{\beta }}$)	0.0041	0.0044	0.0040	0.0045	0.0039	0.0042	0.0002	[0.0039, 0.0045]
Coeff. of Variation (${\mathbf{CV}}_{\mathbf{\%}}$)	0.10	0.11	0.12	0.11	0.09	Mean CV ≈ 0.11 (high cross-fold consistency)
Generalization Entropy (${\mathcal{G}}_{\mathit{e}}$)	0.0785 (Low entropy → strong generalization capability)
Stability Index ($\mathbf{{\rm Y}}=\mathbf{1}-{\displaystyle \frac{\mathit{\sigma }\left(\mathrm{Acc}\right)}{\mathit{\mu }\left(\mathrm{Acc}\right)}}$)	0.9996 (Excellent statistical homogeneity)

. The fact that there are only minor discrepancies in accuracy, F1, AUC, and precision ($\alpha$ = 0.04) indicates that the model generalizes effectively and does not overfit. With strong QICI and XSR scores, interpretability and prediction confidence remain well-matched even when the data undergoes fold-to-fold variations. The data are highly homogeneous, as shown by the stability index of 0.9996 and low entropy and variance, both indicators of a stable internal representation. Results like these demonstrate that the combination of hybrid preprocessing, temporal–spectral reasoning, and quantum–Bayesian optimization in Q-RCANeX improves forecast accuracy and stability.

4.6. Limitations and Practical Deployment Considerations

Across a range of experimental settings, the proposed Q-RCANeX framework demonstrates high levels of accuracy, robustness, and computational efficiency. On the other hand, we need to address specific practical concerns. An off-grid microgrid dataset with high resolution is utilized to evaluate the model. However, when used on a large scale across multiple sites, the model could struggle with additional geographic variations, communication delays, and synchronization issues that are not evident in this study. Improving Q-RCANeX’s functionality in federated or geographically scattered microgrid environments is a logical next step for further research. Second, access to well-calibrated sensor streams is essential for the framework. Even with resilience measures derived from signal decomposition and attention-based modeling, prediction reliability may decrease in severe deployment scenarios such as extended sensor outages, significant hardware failures, or persistent adversarial noise. These scenarios might be made even more robust with the addition of adaptive fault-detection layers or confidence-gating mechanisms that account for uncertainty.

Finally, Q-RCANeX outperforms the top models at the moment, but further model compression or quantization techniques could be required for real-time use on ultra-low-power edge devices. Addressing these concerns would make the proposed design better suited to large-scale off-grid cloud microgrid systems and improve its scalability.

5. Conclusions

This work has presented Q-RCANeX, addressing the challenge of accurate renewable energy forecasting in cloud microgrids operating independently of the primary grid. The major objective was to address existing issues in deep learning architectures, including unstable performance when data is missing or sensors are distorted, a lack of cross-modal coupling, irregular temporal patterns, and noisy multimodal inputs. Q-RCANeX proved strong temporal reasoning, represented features, and generalized across renewable forecasting tasks using a Hybrid Quantum–Bayesian Evolutionary Optimizer, temporal–spectral attention, quantum feature embedding, and residual convolutional encoding. According to experimental results, the model performs well across all assessment metrics, including 98.6% predicted accuracy, an almost-perfect area under the curve, modest error magnitudes, and high interpretability. The framework’s multi-horizon predictions for REAF, WGF, SOC-F, EEIF, and renewable adequacy classification show that it can capture fine-grain changes, long-range dependencies, and cross-modal interactions that directly affect operational dependability in off-grid scenarios. In noisy and missing data conditions, Q-RCANeX outperforms the transformer, CNN, LSTM, GNN, and hybrid baselines in robustness testing. The proposed architecture achieves high compute load, rapid inference, and low mean training cost, making it excellent for energy-aware task scheduling and real-time microgrid control, according to computational efficiency studies. The aim of creating an accurate, interpretable, resource-efficient, and robust renewable forecasting architecture is achieved. In renewable energy-powered cloud infrastructures, the integrated predictive framework improves stability, thermal efficiency, battery charge–discharge cycles, and scheduling.

Future work includes reinforcement-driven scheduling layers that enable autonomous decision-making control over the forecasting engine. An analysis of microgrid data from multiple locations can improve ecological and geographic generalizability. Lastly, lightweight neurosymbolic reasoning modules can improve operational traceability and explainability in edge deployments.