Hybrid Regression–Artificial Bee Colony Optimization for PV Production Forecasting under Energy Performance Contracting

Hybrid Regression–Artificial Bee Colony Optimization for PV Production Forecasting under Energy Performance Contracting | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Hybrid Regression–Artificial Bee Colony Optimization for PV Production Forecasting under Energy Performance Contracting Adem Akbulut, Kubilay Taşdelen This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8703528/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Accurate photovoltaic (PV) energy production forecasting is essential for Energy Performance Contracts (EPCs), where financial outcomes and contractual guarantees depend on reliable performance estimates. This study proposes a hybrid forecasting framework that integrates multivariate regression analysis with the Artificial Bee Colony (ABC) algorithm to improve prediction accuracy while preserving computational efficiency and model transparency. The proposed model is validated using real operational data from a 1710.72 kWp grid-connected PV system operating under an EPC framework at Alanya Alaaddin Keykubat University (Türkiye). Key technical and economic variables, including solar irradiance, investment cost, and electricity unit price, are employed in the regression model, whose coefficients are optimized using the ABC algorithm. Results show that the hybrid Regression–ABC model achieves a MAPE of 6.82%, significantly outperforming the baseline regression model (14.67%). The predicted annual energy production closely matches measured field data, with a relative deviation of approximately 0.01%, remaining within typical measurement uncertainty. The findings demonstrate that the proposed hybrid approach provides an accurate, transparent, and practical forecasting tool suitable for EPC-based PV projects, supporting performance verification, risk management, and investment planning. photovoltaic forecasting regression analysis artificial bee colony algorithm energy performance contracts hybrid modeling renewable energy optimization sustainable investment Figures Figure 1 Figure 2 1. INTRODUCTION The global energy system is currently undergoing a profound transformation as countries intensify efforts to decarbonize their economies and reduce dependence on fossil fuels [1]. From an engineering perspective, this transition introduces new technical challenges related to power system planning, operational reliability, and integration of variable renewable energy sources. In this context, renewable energy technologies play a pivotal role in achieving long-term energy security, mitigating climate change, and supporting sustainable economic growth. Among these technologies, photovoltaic (PV) systems have emerged as one of the most widely adopted solutions due to their modular structure, scalability, and minimal environmental impact during operation [2,3]. The rapid expansion of PV installations worldwide has been driven not only by technological advancements in module efficiency and power electronics, but also by substantial reductions in investment costs and the implementation of supportive policy mechanisms at both national and international levels [4,5]. As PV penetration increases, accurate prediction of energy output becomes an essential requirement for system design, grid integration, and performance assessment. Energy Performance Contracting (EPC) has gained increasing attention as an effective framework for implementing energy efficiency and renewable energy projects, particularly in public-sector applications where capital constraints and performance accountability are critical [6,7]. EPC schemes enable project deployment without upfront capital expenditure by linking contractor remuneration directly to achieved energy performance outcomes, thereby transferring technical and financial risks to the service provider [8,9]. This performance-based structure aligns EPCs closely with sustainability and decarbonization objectives while simultaneously imposing strict requirements on measurement, verification, and forecasting accuracy. As a result, EPC frameworks demand technically reliable and transparent models that can support contractual guarantees and long-term operational planning [10,11]. In countries such as Türkiye, national energy strategies and regulatory frameworks explicitly emphasize performance verification, transparency, and market-based efficiency mechanisms, further strengthening the role of EPCs in renewable energy investments and increasing the importance of engineering-grade forecasting tools [12,13]. Accurate forecasting of energy production and savings is widely recognized as a critical factor for the success of EPC-based projects [14,15]. This requirement is particularly pronounced in public infrastructure investments, where budgeting procedures, contractual guarantees, and verification protocols are subject to strict regulatory oversight and audit processes [16,17]. Inadequate forecasting accuracy may lead to increased financial risk, reduced investor confidence, and disputes during performance verification stages. From a technical standpoint, forecasting errors can also affect system optimization, operational scheduling, and long-term asset management. Consequently, researchers and practitioners have increasingly turned to hybrid forecasting approaches that combine traditional regression techniques with metaheuristic optimization algorithms, such as Particle Swarm Optimization (PSO), Genetic Algorithms (GA), and Artificial Bee Colony (ABC) methods, to enhance predictive performance under real operating conditions [18,19]. The Artificial Bee Colony (ABC) algorithm, inspired by the collective foraging behavior of honeybee swarms, has attracted considerable attention in engineering optimization problems due to its strong global search capability, flexibility, and relatively low computational complexity [20,21]. When integrated into regression-based forecasting frameworks, ABC enables efficient optimization of model parameters and has been shown to significantly reduce prediction errors across a variety of application domains, including energy systems and power engineering [22,23]. In the context of smart grids and distributed energy systems, such hybrid models contribute to improved energy management by enabling more accurate demand-response planning, generation forecasting, and system-level decision-making [24–26]. In Türkiye, the adoption of performance-based investment models for PV systems has accelerated in recent years, supported by legal regulations and strategic roadmaps developed by institutions such as the Ministry of Energy and Natural Resources (ETKB) [27,28]. Despite this progress, several implementation challenges persist, including uncertainties related to risk allocation, data reliability, and performance verification processes [29,30]. These challenges highlight the need for robust forecasting tools that can operate effectively under real-world data limitations while maintaining transparency, repeatability, and contractual accountability. From an engineering standpoint, addressing these issues requires forecasting models that balance predictive accuracy with computational efficiency and practical deployability within EPC-based PV projects. Recent studies indicate that the integration of building automation systems, supervisory control and data acquisition (SCADA) platforms, and standardized energy management protocols within EPC models significantly improves monitoring accuracy, data reliability, and operational transparency [31,32]. From an engineering standpoint, these systems enable continuous data acquisition, real-time performance assessment, and traceable verification of energy outputs, which are essential for performance-based contractual frameworks. When aligned with ISO 50001 energy management standards, such integrated infrastructures provide a structured foundation for consistent measurement and verification procedures, thereby reducing uncertainty in performance evaluation and supporting technically sound decision-making throughout the project lifecycle. Empirical evidence from public building applications further demonstrates that incorporating reliable forecasting models at early stages of EPC project development can substantially enhance achievable energy savings and long-term performance outcomes [33,34]. Early-stage forecasting supports informed system sizing, financial feasibility analysis, and risk allocation, while also enabling more accurate baseline definition and performance guarantee structuring. From a systems engineering perspective, the integration of forecasting tools during project planning improves overall system robustness and reduces the likelihood of deviations between predicted and realized energy performance. Despite these advancements, conventional forecasting approaches based solely on regression analysis often struggle to capture nonlinear relationships, seasonal effects, and stochastic variability in solar irradiance [35–37]. Such limitations are particularly problematic in EPC-based PV applications, where even small forecasting errors may propagate into financial discrepancies and contractual disputes. These challenges have motivated a growing shift toward hybrid machine learning and optimization-based methodologies that can better accommodate complex system dynamics and nonlinear input–output relationships [38,39]. By integrating optimization algorithms with data-driven models, these approaches enable adaptive parameter tuning and improved generalization under varying operational conditions. Hybrid methodologies further allow the incorporation of practical engineering constraints, including site-specific system characteristics, meteorological uncertainty, and financial parameters that influence EPC performance metrics [40,41]. This capability is especially relevant for EPC frameworks, where forecasting models must simultaneously satisfy technical accuracy requirements and contractual performance criteria. Consequently, hybrid forecasting approaches are increasingly viewed as essential tools for engineering-grade prediction in performance-based renewable energy projects. The increasing availability of high-resolution PV production datasets has further enabled the development and validation of advanced predictive models tailored to real operational environments [42,43]. Access to detailed temporal data facilitates more rigorous model training, validation, and benchmarking under realistic conditions. Prior research indicates that improved forecasting accuracy directly supports more effective risk assessment, regulatory compliance, and capital allocation decisions within EPC-driven renewable energy projects [44–46]. In addition, accurate performance prediction contributes to enhanced investor confidence and more efficient lifecycle management of PV assets by reducing uncertainty in expected returns and operational outcomes [47–49]. At the policy and system-planning level, initiatives such as the European Union’s Clean Energy Package underscore the strategic importance of advanced forecasting tools in achieving national and regional energy transition objectives [50–52]. From an engineering perspective, these initiatives further emphasize the need for scalable, transparent, and technically robust forecasting solutions that can be integrated into existing energy management and verification frameworks. Emerging technologies, including digital twins and AI-enhanced monitoring systems, are now shaping the next generation of EPC implementations by enabling predictive maintenance, real-time performance tracking, and adaptive contract management [53–55]. These technologies rely heavily on accurate forecasting models to support proactive system control and data-driven operational decisions. Their adoption is particularly significant for emerging economies and resource-constrained municipalities, where scalable, cost-effective, and computationally efficient solutions are required to expand EPC deployment without increasing technical complexity or operational burden [56–58]. Against this background, the present study proposes a hybrid forecasting framework that combines multivariate regression analysis with the Artificial Bee Colony (ABC) optimization algorithm. The proposed model is validated using real operational data obtained from a photovoltaic installation in Türkiye, with the objective of minimizing forecasting errors while maintaining computational efficiency and practical applicability [59,60]. By operating effectively under real-world data constraints typical of EPC projects, the model addresses key engineering requirements, including transparency, performance accountability, and cost-effectiveness. In summary, this study introduces a hybrid forecasting approach that leverages the complementary strengths of regression modeling and swarm intelligence optimization to enhance PV production forecasting within EPC frameworks. Beyond its algorithmic contribution, the study provides empirical validation based on real system data, demonstrating its relevance for practical engineering applications. The proposed framework aims to support informed technical and financial decision-making and to contribute to the broader adoption of EPC-driven renewable energy projects in alignment with established energy efficiency standards and evolving system requirements. 2. METHODOLOGY This study proposes an integrated predictive modeling framework that combines Multiple Linear Regression (MLR) with the Artificial Bee Colony (ABC) optimization algorithm to enhance the accuracy of energy yield forecasting and cost estimation for solar photovoltaic (PV) systems operating under Energy Performance Contracts (EPCs). The primary objective of the proposed approach is to minimize forecasting errors by coupling statistical regression-based estimation with a nature-inspired optimization mechanism capable of efficiently tuning model parameters. By improving prediction accuracy, the model aims to support more reliable financial analysis and decision-making processes, which are critical for performance-based contracting structures such as EPCs. 2.1. Data Collection and Processing The proposed model was validated using real operational data obtained from a grid-connected solar PV system with an installed capacity of 1710.72 kWp, located at Alanya Alaaddin Keykubat University (ALKU). The system was commissioned in March 2024 and implemented within an EPC framework, making it representative of performance-based renewable energy applications. Electrical energy production data were recorded at 15-minute intervals using Schneider Electric ION 7650 power analyzers, ensuring high temporal resolution and measurement accuracy. These measurements were subsequently aggregated into monthly energy production values to align with EPC reporting and verification requirements. Meteorological input parameters, including solar radiation and ambient temperature, were obtained from the Turkish State Meteorological Service, providing reliable site-specific environmental data. Economic inputs required for EPC-based evaluation, such as investment cost parameters and electricity selling prices, were sourced from official EPC documentation and the 2024 national electricity tariff schedule published by the Energy Market Regulatory Authority (EMRA). This ensured consistency between technical performance modeling and the financial conditions governing EPC implementation. The final dataset consists of six key variables that directly influence PV system performance and economic evaluation: (i) annual average solar radiation (kWh/m²), (ii) investment cost (TL/kWp), (iii) electricity selling price (kr/kWh), (iv) PV panel efficiency (%), (v) system performance ratio (%), and (vi) total energy production (kWh). Prior to model development, the dataset was subjected to a systematic preprocessing procedure. Outliers were identified and removed using Z-score analysis, while minor data gaps were addressed through interpolation to preserve dataset continuity. All input variables were then normalized to a [0,1] range, which improves numerical stability and ensures efficient convergence during the ABC-based optimization process. This preprocessing step is particularly important for metaheuristic algorithms, as it prevents dominance of variables with larger numerical ranges and enhances overall optimization performance. 2.2. Regression Model Development As an initial benchmark, a Multiple Linear Regression (MLR) model was developed to estimate the unit electricity production cost (TL/kWh) of the PV system. The regression model employs three primary explanatory variables that directly influence both technical performance and economic outcomes under EPC-based PV projects: (i) solar radiation \(\:\left({X}_{1}\right)\) , (ii) investment cost \(\:\left({X}_{2}\right)\) , and (iii) electricity selling price \(\:\left({X}_{3}\right)\) . The regression coefficients were estimated using the Ordinary Least Squares (OLS) method, which provides unbiased and efficient parameter estimates under standard linear regression assumptions. To evaluate potential multicollinearity among the independent variables, the Variance Inflation Factor (VIF) was calculated for each predictor. All variables exhibited VIF values below the commonly accepted threshold of 5, indicating the absence of significant multicollinearity and confirming the suitability of the selected predictors for regression modeling. Model adequacy was assessed using multiple statistical indicators. The coefficient of determination \(\:\left({R}^{2}\right)\) was found to be 0.873, demonstrating a strong explanatory capability of the model in capturing variations in unit production cost. Residual diagnostics were further conducted to verify the underlying regression assumptions. The Breusch–Pagan test confirmed homoskedasticity of residuals, while the Durbin–Watson statistic indicated no significant autocorrelation. These results collectively validate the baseline MLR model as a reliable reference for subsequent optimization. Although the regression model is formulated in terms of unit production cost, the optimized coefficients are subsequently used to derive annual energy production estimates within the EPC performance framework. 2.3. ABC Algorithm Integration Although the baseline MLR model demonstrates strong explanatory power, its predictive accuracy is inherently constrained by the fixed nature of OLS-estimated coefficients. To further enhance forecasting performance, the regression coefficients were optimized using the Artificial Bee Colony (ABC) algorithm. The ABC algorithm is a population-based metaheuristic inspired by the foraging behavior of honeybee colonies. In the proposed framework, each candidate solution (food source) represents a potential set of regression coefficients. The optimization process aims to identify the coefficient vector that minimizes forecasting error while preserving economic consistency within the EPC framework. The optimization objective is defined by a customized fitness function: $$\:f\left(\overrightarrow{x}\right)=\alpha\:\cdot\:\text{MAPE}+\beta\:\cdot\:\mid\:\frac{{C}_{\text{actual}}-{C}_{\text{predicted}}}{{C}_{\text{actual}}}\mid\:$$ where \(\:\alpha\:=0.7\) and \(\:\beta\:=0.3\) represent weighting factors assigned to forecasting accuracy and economic deviation, respectively. This formulation ensures that the optimization process prioritizes prediction accuracy while simultaneously accounting for deviations in cost estimation, which is critical for EPC-based financial evaluation. The solution vector is defined as: \(\:\overrightarrow{x}=[{\beta\:}_{0},{\beta\:}_{1},{\beta\:}_{2},{\beta\:}_{3}]\) where \(\:{\beta\:}_{0}\) is the intercept term and \(\:{\beta\:}_{1}\) , \(\:{\beta\:}_{2}\) , and \(\:{\beta\:}_{3}\) correspond to the regression coefficients associated with \(\:{X}_{1}\) , \(\:{X}_{2}\) , and \(\:{X}_{3}\) , respectively. The ABC optimization process was executed over 1000 iterations, during which employed bees explored neighboring solutions, onlooker bees probabilistically selected promising solutions based on fitness values, and scout bees introduced new candidate solutions when stagnation was detected. This exploration–exploitation balance reduces the likelihood of entrapment in local minima and improves convergence toward a globally optimal solution. Through this integration, the regression model transitions from a purely statistical estimator to a hybrid regression–optimization framework, enhancing predictive robustness and adaptability under real-world EPC operating conditions. 2.4. Model Implementation and Evaluation The proposed hybrid regression–ABC model was implemented using MATLAB R2024b, which provides a robust computational environment for numerical optimization and statistical analysis. Based on preliminary sensitivity testing and common practices in swarm intelligence applications, the ABC algorithm parameters were configured as follows: a population size of 100 bees, a scout bee ratio of 0.5, a limit value of 100, and a maximum of 1000 iterations. These parameter settings were selected to ensure a balanced trade-off between exploration and exploitation while maintaining reasonable computational efficiency. Model performance was evaluated using the Mean Absolute Percentage Error (MAPE) as the primary accuracy metric, given its suitability for comparing forecasting performance across different scales. The optimized hybrid model achieved a MAPE value of 6.82%, representing a substantial improvement over the 14.67% obtained from the baseline MLR model. This reduction in error demonstrates the effectiveness of the ABC-based coefficient optimization in enhancing predictive accuracy beyond conventional regression estimation. To assess the generalization capability of the proposed approach, a cross-validation procedure was applied. The results confirmed that the optimized model maintained consistent performance across unseen data subsets, indicating that the observed accuracy improvements were not limited to the training dataset and that the model exhibits robust predictive behavior under varying data conditions. For practical validation, the model outputs were compared against actual field measurements obtained from the ALKU PV system operating under real EPC conditions. The predicted annual energy production was calculated as 2,423,734.26 kWh, while the measured annual production was 2,423,472.28 kWh. This corresponds to a relative deviation of approximately 0.01%, demonstrating a very close agreement between predicted and observed values. From an engineering perspective, this level of agreement indicates that the proposed model is capable of capturing the dominant performance characteristics of the PV system under real operating conditions. While minor discrepancies are expected due to measurement uncertainty and environmental variability, the results suggest that the hybrid regression–ABC framework provides sufficiently accurate forecasts to support performance verification, cost estimation, and decision-making processes within EPC-based PV projects. 3. RESULTS This section presents a detailed evaluation of the predictive performance and optimization characteristics of the integrated Regression–Artificial Bee Colony (ABC) model. The analysis is structured around three main aspects: (i) convergence behavior of the ABC algorithm, (ii) prediction accuracy of the hybrid model, and (iii) comparative assessment of performance metrics. All results are derived from real operational data obtained from a 1710.72 kWp grid-connected photovoltaic system installed at Alanya Alaaddin Keykubat University (ALKU) and operated under an Energy Performance Contract (EPC) framework. 3.1. Convergence Behavior of the ABC Algorithm The optimization process carried out using the ABC algorithm exhibited rapid and stable convergence in reducing the estimation error of the regression model. During the initial phase of the optimization, particularly within the first 40 iterations, a substantial decrease in the Mean Absolute Percentage Error (MAPE) was observed, highlighting the strong global search capability of the ABC algorithm. Figure 1 illustrates the evolution of MAPE values as a function of iteration number. The initial MAPE exceeded 2.0%, but declined sharply during the early iterations and fell below 0.5% shortly thereafter. This rapid error reduction indicates that the algorithm efficiently explores the solution space and avoids premature convergence to local optima. Following this phase, the error curve exhibits a smooth and stable behavior. Beyond approximately the 300th iteration, the MAPE values become nearly constant, suggesting that the optimization process has reached a steady-state solution. This behavior confirms the robustness of the ABC algorithm in fine-tuning regression coefficients and achieving convergence with high numerical precision. The absence of oscillations or divergence in later iterations further indicates a well-balanced exploration–exploitation mechanism within the selected algorithm parameters. 3.2. Prediction Accuracy of Energy Production The predictive accuracy of the proposed Regression–ABC model was evaluated using real operational energy production data obtained from the installed PV system. The actual annual energy production, measured by Schneider Electric ION 7650 energy analyzers, was recorded as 2,423,472.28 kWh, while the optimized model estimated an annual production of 2,423,734.26 kWh. The resulting absolute deviation between measured and predicted values is 261.98 kWh, corresponding to a relative error of approximately 0.01%. From an engineering standpoint, this deviation is negligible when compared to the overall annual energy output and falls well within typical measurement uncertainty, environmental variability, and operational fluctuations associated with large-scale PV systems. These results indicate that the proposed hybrid model is capable of accurately capturing the dominant performance characteristics of the system under real EPC operating conditions. Figure 2 presents a direct comparison between the measured and predicted annual energy production values. The visual similarity between the two results highlights the strong agreement achieved through the ABC-based optimization of regression coefficients. This level of consistency demonstrates the effectiveness of the proposed approach in reducing estimation error and improving forecasting reliability. Overall, the findings confirm that the Regression–ABC framework provides a high level of predictive accuracy suitable for applications requiring precise energy yield estimation, such as performance verification, financial reconciliation, and risk assessment in EPC-based photovoltaic projects. 3.3. Comparative Evaluation of Performance Metrics To quantitatively assess the effectiveness of the proposed ABC-optimized regression model, its performance was benchmarked against the classical Multiple Linear Regression (MLR) approach using standard error metrics commonly adopted in energy forecasting studies. The evaluation criteria include the Mean Absolute Error (MAE), Mean Squared Error (MSE), and Mean Absolute Percentage Error (MAPE), which collectively provide a comprehensive assessment of prediction accuracy and robustness. Table 1 summarizes the comparative results obtained from both models. As shown, the ABC-optimized model consistently outperforms the classical regression approach across all error indicators. Specifically, the MAE was reduced from 0.054 to 0.029, corresponding to an improvement of 46.3%, while the MSE decreased from 0.0043 to 0.0019, reflecting a 55.8% reduction. The most notable improvement was observed in the MAPE metric, which declined from 14.67% to 6.82%, yielding an overall improvement of 53.5%. Table 1 Comparison of error metrics between classical regression and ABC-optimized model. Metric Classical Regression ABC-Optimized Model Improvement (%) MAE 0.054 0.029 46.3% MSE 0.0043 0.0019 55.8% MAPE (%) 14.67 6.82 53.5% The observed improvements confirm that the integration of the ABC algorithm significantly enhances the regression model’s ability to capture complex relationships within the PV energy generation process. Although the underlying regression structure remains linear, the metaheuristic optimization of coefficients enables more effective representation of nonlinear influences and parameter interactions that are not adequately addressed by conventional OLS estimation. To further evaluate model robustness, the optimized framework was tested on unseen validation data. The ABC-enhanced model achieved a test-phase MAPE of 7.4%, which is closely aligned with the training-phase value of 6.82%. This limited deviation indicates strong generalization capability and suggests that the performance gains are not attributable to overfitting. From an engineering perspective, this level of consistency supports the applicability of the proposed approach for real-world EPC-based PV projects, where reliable forecasting across varying operational conditions is essential. 4. DISCUSSION This study further underscores the effectiveness of integrating hybrid optimization algorithms with classical regression techniques—specifically through the proposed Regression–Artificial Bee Colony (ABC) framework—for achieving enhanced forecasting accuracy in energy performance assessments. The findings are consistent with broader conceptual and operational frameworks developed for the diffusion of low-carbon Energy Performance Contracts (EPCs), which increasingly prioritize technical reliability, transparent performance verification, and economic feasibility in contract-based renewable energy implementations [61]. Within such frameworks, accurate and robust forecasting models are regarded as a foundational requirement for minimizing performance risk and ensuring contractual compliance. Recent EPC applications, particularly in social housing projects and heritage-sensitive building renovations, have highlighted the growing influence of occupant behavior, usage patterns, and operational variability on energy performance outcomes [62,63]. These factors introduce additional uncertainty into energy savings calculations, reinforcing the necessity for adaptive and data-driven prediction models capable of responding to dynamic system conditions. In parallel, the deployment of deep learning–based forecasting techniques, such as those applied in multi-energy microgrids, has become increasingly important for enabling higher penetration of renewable energy sources in distributed and decentralized energy systems [64]. Within public-sector energy efficiency and renewable energy programs, the strategic relevance of EPCs continues to expand, driven by policy objectives related to decarbonization, fiscal efficiency, and long-term asset performance [65]. In this context, increasing attention is being paid to verification protocols, legal and contractual design, and the coordination of multiple stakeholders involved in EPC delivery. To support these complex requirements, advanced machine learning and deep learning techniques, including convolutional neural networks (CNNs) and long short-term memory (LSTM) architectures, are being widely adopted for solar energy forecasting due to their capability to capture nonlinear relationships, temporal dependencies, and weather-induced variability [66,67]. At the national level, ongoing efforts to improve EPC implementation systems in countries such as Türkiye further emphasize the urgency of integrating AI-driven forecasting models into policy-backed energy efficiency frameworks [68]. Hybrid artificial intelligence approaches are increasingly being employed to support both short-term time series prediction and real-time operational responsiveness in grid-connected PV and smart energy systems [69]. Within this evolving landscape, the Regression–ABC model proposed in this study offers a complementary alternative that balances predictive accuracy, computational efficiency, and transparency—attributes that are particularly valuable for EPC applications where interpretability, auditability, and contractual accountability remain critical considerations. Accurate forecasting of electrical load and renewable energy generation, particularly under unstable and highly variable operating conditions, has been consistently shown to enhance grid stability, reduce balancing costs, and support more efficient dispatch strategies [70]. Reliable forecasts enable system operators to anticipate fluctuations in renewable output and demand, thereby improving reserve allocation and mitigating the risks associated with intermittency. In power systems with high penetration of photovoltaic generation, such forecasting capabilities are increasingly viewed as an essential component of secure and resilient grid operation. In the context of building retrofits—especially within the stock of older buildings in Türkiye—forecasting accuracy plays a decisive role in determining optimal system sizing, retrofit design, and expected energy savings [71]. In such cases, inaccurate predictions may lead to over- or under-dimensioned systems, suboptimal investment decisions, and reduced confidence in projected performance outcomes. As a result, forecasting models that can reliably operate under data limitations and heterogeneous building characteristics are particularly valuable for retrofit-oriented EPC projects. Recent advances in hybrid metaheuristic and deep learning approaches, including CNN–LSTM configurations, have demonstrated significant improvements in solar radiation and energy forecasting accuracy while simultaneously reducing computational burden through efficient feature extraction and temporal learning [72]. These methods have proven effective in capturing spatial–temporal dependencies in meteorological data, which are often challenging for conventional statistical models. Complementary case studies conducted in educational institutions further confirm the effectiveness of analyzing EPC performance through consumption trends, tariff structures, and institutional usage patterns, highlighting the importance of integrating technical forecasts with economic evaluation [73]. At the regional and international levels, ongoing efforts to harmonize EPC performance indicators across Europe emphasize the need for forecasting tools that can remain robust across diverse regulatory, climatic, and market environments [74]. Models capable of adapting to varying tariff regimes, verification protocols, and policy requirements are increasingly necessary to support cross-border benchmarking and best-practice transfer. In this regard, advanced architectures such as Conv2D LSTM have been successfully applied in studies combining air quality, weather, and energy data, demonstrating their potential for integrated energy–environmental modeling frameworks [75]. Comparative studies between probabilistic and deterministic forecasting approaches reveal that advanced LSTM-based models often outperform simpler techniques under complex and rapidly changing meteorological conditions [76]. Nevertheless, enhanced regression-based methods continue to play an important role in solar energy prediction, particularly where model transparency, interpretability, and computational efficiency are prioritized [77]. These characteristics are especially relevant for EPC applications, where forecasting outputs must be auditable and easily communicated to multiple stakeholders. Beyond generation forecasting, predictive modeling increasingly extends to life-cycle energy savings estimation, particularly in retrofit projects governed by service and performance-based contracts [78]. Accurate forecasts enable better tracking of guaranteed savings, facilitate verification and measurement processes, and support long-term asset management strategies. Empirical evidence from public building applications further demonstrates that improved forecasting accuracy directly contributes to higher efficiency metrics and strengthens verification procedures in performance-based energy initiatives [79]. Collectively, these findings reinforce the central role of robust forecasting methodologies in advancing EPC implementation and achieving sustainable energy performance outcomes. Design considerations within Energy Performance Contract (EPC) models—such as balanced risk allocation, performance guarantees, and long-term alignment between contractors and building owners—require forecasting methodologies capable of supporting reliable long-term energy savings projections [80]. In EPC-based implementations, inaccurate forecasts may distort baseline definitions, compromise savings guarantees, and ultimately weaken contractual trust. Consequently, forecasting accuracy is not merely a technical concern but a structural requirement for effective EPC design and governance. In addition to energy yield and cost metrics, performance indicators such as Indoor Environmental Quality (IEQ) and broader building performance indices increasingly rely on data-driven forecasting approaches to support EPC optimization [81]. These indicators, which encompass thermal comfort, air quality, and occupant well-being, are particularly relevant in public-sector and residential applications, where energy efficiency measures must be aligned with user comfort and regulatory standards. Forecasting models that integrate such multidimensional performance criteria enhance the ability of EPC frameworks to deliver both energy and non-energy benefits. Empirical studies on thermal retrofitting projects demonstrate that EPC success is strongly dependent on the early-stage integration of forecasting tools that explicitly account for climate conditions, building envelope characteristics, and system-specific dynamics [82]. Early forecasting enables more accurate retrofit design decisions, supports realistic savings estimates, and reduces uncertainty during the contract execution phase. In parallel, intelligent energy management systems deployed within microgrids increasingly utilize AI-based forecasting techniques to optimize energy exchange, load balancing, and interaction with the main grid, further illustrating the growing operational relevance of advanced predictive models [83]. From a regulatory perspective, analyses of legal EPC frameworks, such as those applied in Poland and other European countries, highlight the institutionalization of forecasting as a regulatory and contractual necessity rather than an optional analytical tool [84]. Forecasting outputs are increasingly embedded within verification protocols, performance audits, and compliance mechanisms. Moreover, advanced forecasting tools enable complex EPC configurations—such as reactive power compensation and power quality management—to be modeled, monitored, and enforced more effectively within contractual boundaries [85]. Recent comprehensive reviews of photovoltaic power forecasting consistently highlight the central role of deep learning and hybrid modeling architectures in reducing prediction errors across a wide range of climatic and geographical conditions [86]. These studies emphasize that the increasing variability of solar resources, driven by changing weather patterns and localized atmospheric effects, necessitates forecasting approaches capable of learning complex nonlinear relationships from large and heterogeneous datasets. In this context, deep learning–based methods have emerged as powerful tools for capturing spatial–temporal dependencies that are difficult to represent using conventional statistical techniques. Among these approaches, CNN–LSTM architectures optimized through hybrid metaheuristic techniques have demonstrated particularly strong performance under conditions characterized by highly volatile solar irradiance and nonlinear weather dynamics [87]. By combining convolutional layers for spatial feature extraction with recurrent structures for temporal dependency modeling, these hybrid frameworks offer substantial accuracy gains, especially in large-scale or highly dynamic PV systems. Their effectiveness has been validated in applications ranging from utility-scale solar farms to distributed generation networks, where rapid fluctuations in irradiance pose significant forecasting challenges. Further enhancements in forecasting performance have been achieved through the integration of contextual and environmental variables, such as air quality indices, aerosol concentrations, and atmospheric pollution levels, into advanced Conv2D LSTM architectures [88]. The inclusion of such auxiliary data enables multi-feature learning and provides a more comprehensive representation of the physical processes influencing solar energy generation. These developments illustrate a broader trend toward holistic modeling strategies that extend beyond purely meteorological inputs. Beyond technical forecasting accuracy, recent studies have also explored the role of game-theoretic frameworks, including Stackelberg-based models, as analytical tools for EPC contract design and evaluation [89]. Within such frameworks, accurate energy forecasting serves as a critical input for strategic decision-making, informing contract negotiation, risk-sharing mechanisms, and performance incentive structures. By supporting equilibrium between contracting parties, forecasting-driven game-theoretic models contribute to more stable and transparent EPC arrangements. Despite the rapid advancement and demonstrated effectiveness of deep learning–based forecasting techniques, regression-based approaches continue to play a significant and complementary role in performance prediction, particularly for public buildings undergoing thermal retrofitting [90]. Their inherent transparency, interpretability, and relatively low computational requirements make them especially suitable for EPC applications operating within policy-driven, audit-intensive, and resource-constrained environments. In such contexts, the ability to clearly interpret model behavior and verify results remains as important as achieving marginal gains in predictive accuracy. 5. CONCLUSION This study presents a comprehensive investigation into the development and application of a hybrid Regression–Artificial Bee Colony (ABC) model for forecasting solar energy generation within the framework of Energy Performance Contracting (EPC). The proposed methodology demonstrates high forecasting accuracy, low error margins, and robust performance under varying operational and environmental conditions. These attributes are particularly critical in EPC-based projects, where contractual guarantees, financial settlements, and risk-sharing mechanisms are directly dependent on the reliability of energy production forecasts. Compared with conventional statistical approaches and several advanced AI-based techniques reported in the recent literature, the proposed Regression–ABC hybrid framework achieves a well-balanced trade-off between predictive accuracy, computational efficiency, and model interpretability. This balance is especially relevant for stakeholders operating in financially and regulatorily constrained environments—such as energy service companies (ESCOs), public-sector authorities, and private investors—who require forecasting tools that are not only precise but also transparent, explainable, and suitable for audit and verification processes. Unlike purely data-driven black-box models, the hybrid structure preserves the interpretability of regression analysis while benefiting from the adaptive optimization capability of swarm intelligence. One of the principal contributions of this study lies in the integration of metaheuristic optimization into a regression-based forecasting framework, enabling dynamic calibration of model parameters in response to project-specific conditions. The ABC algorithm enhances the model’s flexibility by allowing it to adapt to site-dependent climatic characteristics, system design constraints, and EPC contractual requirements. This adaptability supports the generation of customized forecasting solutions that are technically robust and economically feasible, thereby strengthening the practical applicability of the model in real-world EPC implementations. From an operational perspective, the use of real production data from an operating photovoltaic system ensures that the proposed approach bridges the gap between theoretical modeling and practical deployment. The close agreement observed between predicted and measured energy outputs indicates that the model is capable of capturing the dominant performance characteristics of PV systems within the bounds of measurement uncertainty and environmental variability. Such accuracy is particularly valuable in EPC contexts, where even small deviations between predicted and actual performance may translate into financial penalties, disputes, or loss of stakeholder confidence. Beyond its technical merits, the study provides important insights into the role of data-driven forecasting as a decision-support instrument within performance-based investment frameworks. Improved forecasting accuracy directly contributes to more reliable estimation of key financial indicators, including levelized cost of energy (LCOE), payback period, and return on investment (ROI). By reducing uncertainty in these indicators, the proposed Regression–ABC model can help mitigate performance-related risks, enhance investor confidence, and support transparent measurement and verification (M&V) processes in alignment with international standards such as ISO 50001. At a broader level, the findings reinforce the strategic importance of hybrid modeling approaches in supporting policy-driven energy transitions. Accurate and transparent forecasting tools are essential for the effective implementation of EPCs aligned with national energy efficiency targets, decarbonization strategies, and green public procurement policies. In this context, the proposed framework contributes not only to methodological advancement but also to the operationalization of sustainable energy policies through reliable performance assessment mechanisms. Future research should focus on extending the proposed model across diverse climatic zones, regulatory environments, and building typologies to further evaluate its scalability and transferability. The integration of real-time Internet of Things (IoT) data streams may enable continuous model updating and improve responsiveness under rapidly changing operating conditions. Additionally, extending the framework toward probabilistic or ensemble-based forecasting could enhance its suitability for high-uncertainty scenarios commonly encountered in renewable energy systems. Comparative benchmarking against other evolutionary optimization techniques—such as Ant Colony Optimization or Differential Evolution—would also provide valuable insights into relative performance characteristics. Finally, embedding the model within digital twin platforms or smart building management systems could open new avenues for dynamic energy governance, adaptive EPC management, and policy-aligned technological innovation. Declarations Author Contribution A.A. conceptualized the study, collected and curated the data, developed the regression–ABC methodology, and performed the simulations and analysis. K.T. contributed to the methodological design, supervised the technical aspects of the study, and validated the results. A.A. drafted the original manuscript. Both authors reviewed, edited, and approved the final version of the manuscript. Data Availability The data used in this study were obtained from an operational grid-connected photovoltaic system operating under an Energy Performance Contract framework. Due to institutional and contractual confidentiality restrictions, the data are not publicly available. 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Energies, 14(6), 1565. https://doi.org/10.3390/EN14061565 Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8703528","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":584292414,"identity":"2d24dc2f-6f62-4074-b292-afb8aaa2001c","order_by":0,"name":"Adem Akbulut","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABFUlEQVRIiWNgGAWjYFCCBDCRwMAOpD4wWEBF2YjRwszA2DiDQQKhhYcYLc08xGjhb08+uoGhJi3P4DCP+WObGgl5c4nkBwwfyg4z2EsfwKpF4syztBsMx3KKgVoMm3OOSRjunJFmwDjj3GEGHr4E7NbcyDG7wcBWkbgBrIVNgnHDjQQDZt42oBYcLpO/kf/tBsM/qBaLfxL2G26kf2D+i0eLwY0cthuMbTkQLYxtEokbbuQYMDPi0WJ45pnZjcS+tGLJw2yFM3v7JJI3nHlTcLDnXDoPzxnsWuSOJz+78eFbch7f8eYNH358s7HdcDx944MfZdZy7D3YtYABasgIJDAcYMAXk5iA/wAJikfBKBgFo2AkAAC772JJTc3HhgAAAABJRU5ErkJggg==","orcid":"","institution":"Alanya Alaaddin Keykubat University","correspondingAuthor":true,"prefix":"","firstName":"Adem","middleName":"","lastName":"Akbulut","suffix":""},{"id":584292415,"identity":"034fd4d9-b9cc-4904-bcc3-64a7d3710147","order_by":1,"name":"Kubilay Taşdelen","email":"","orcid":"","institution":"Isparta University of Applied Sciences","correspondingAuthor":false,"prefix":"","firstName":"Kubilay","middleName":"","lastName":"Taşdelen","suffix":""}],"badges":[],"createdAt":"2026-01-26 19:53:42","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8703528/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8703528/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":101738699,"identity":"f23f7aa3-89eb-45fb-bffc-1352812907dd","added_by":"auto","created_at":"2026-02-03 07:53:00","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":79562,"visible":true,"origin":"","legend":"\u003cp\u003eConvergence of estimation error using ABC optimization over iterations. The mean absolute percentage error (MAPE) decreased significantly after 40 iterations.\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-8703528/v1/b8de940be16e9c5121f83ee3.png"},{"id":101753943,"identity":"b2e072f5-d43f-400a-9104-62853fc40f41","added_by":"auto","created_at":"2026-02-03 10:41:13","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":116106,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of actual and predicted annual energy production values using the integrated Regression–ABC model\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-8703528/v1/9932ea45559b70d76957b4ef.png"},{"id":107224013,"identity":"4429dea8-6d83-4f0f-9e0f-66e801661338","added_by":"auto","created_at":"2026-04-18 15:25:39","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":509765,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8703528/v1/972503d1-dd8b-48f3-953b-67dd9484a969.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Hybrid Regression–Artificial Bee Colony Optimization for PV Production Forecasting under Energy Performance Contracting","fulltext":[{"header":"1. INTRODUCTION","content":"\u003cp\u003eThe global energy system is currently undergoing a profound transformation as countries intensify efforts to decarbonize their economies and reduce dependence on fossil fuels [1]. From an engineering perspective, this transition introduces new technical challenges related to power system planning, operational reliability, and integration of variable renewable energy sources. In this context, renewable energy technologies play a pivotal role in achieving long-term energy security, mitigating climate change, and supporting sustainable economic growth. Among these technologies, photovoltaic (PV) systems have emerged as one of the most widely adopted solutions due to their modular structure, scalability, and minimal environmental impact during operation [2,3]. The rapid expansion of PV installations worldwide has been driven not only by technological advancements in module efficiency and power electronics, but also by substantial reductions in investment costs and the implementation of supportive policy mechanisms at both national and international levels [4,5]. As PV penetration increases, accurate prediction of energy output becomes an essential requirement for system design, grid integration, and performance assessment.\u003c/p\u003e \u003cp\u003eEnergy Performance Contracting (EPC) has gained increasing attention as an effective framework for implementing energy efficiency and renewable energy projects, particularly in public-sector applications where capital constraints and performance accountability are critical [6,7]. EPC schemes enable project deployment without upfront capital expenditure by linking contractor remuneration directly to achieved energy performance outcomes, thereby transferring technical and financial risks to the service provider [8,9]. This performance-based structure aligns EPCs closely with sustainability and decarbonization objectives while simultaneously imposing strict requirements on measurement, verification, and forecasting accuracy. As a result, EPC frameworks demand technically reliable and transparent models that can support contractual guarantees and long-term operational planning [10,11]. In countries such as T\u0026uuml;rkiye, national energy strategies and regulatory frameworks explicitly emphasize performance verification, transparency, and market-based efficiency mechanisms, further strengthening the role of EPCs in renewable energy investments and increasing the importance of engineering-grade forecasting tools [12,13].\u003c/p\u003e \u003cp\u003eAccurate forecasting of energy production and savings is widely recognized as a critical factor for the success of EPC-based projects [14,15]. This requirement is particularly pronounced in public infrastructure investments, where budgeting procedures, contractual guarantees, and verification protocols are subject to strict regulatory oversight and audit processes [16,17]. Inadequate forecasting accuracy may lead to increased financial risk, reduced investor confidence, and disputes during performance verification stages. From a technical standpoint, forecasting errors can also affect system optimization, operational scheduling, and long-term asset management. Consequently, researchers and practitioners have increasingly turned to hybrid forecasting approaches that combine traditional regression techniques with metaheuristic optimization algorithms, such as Particle Swarm Optimization (PSO), Genetic Algorithms (GA), and Artificial Bee Colony (ABC) methods, to enhance predictive performance under real operating conditions [18,19].\u003c/p\u003e \u003cp\u003eThe Artificial Bee Colony (ABC) algorithm, inspired by the collective foraging behavior of honeybee swarms, has attracted considerable attention in engineering optimization problems due to its strong global search capability, flexibility, and relatively low computational complexity [20,21]. When integrated into regression-based forecasting frameworks, ABC enables efficient optimization of model parameters and has been shown to significantly reduce prediction errors across a variety of application domains, including energy systems and power engineering [22,23]. In the context of smart grids and distributed energy systems, such hybrid models contribute to improved energy management by enabling more accurate demand-response planning, generation forecasting, and system-level decision-making [24\u0026ndash;26].\u003c/p\u003e \u003cp\u003eIn T\u0026uuml;rkiye, the adoption of performance-based investment models for PV systems has accelerated in recent years, supported by legal regulations and strategic roadmaps developed by institutions such as the Ministry of Energy and Natural Resources (ETKB) [27,28]. Despite this progress, several implementation challenges persist, including uncertainties related to risk allocation, data reliability, and performance verification processes [29,30]. These challenges highlight the need for robust forecasting tools that can operate effectively under real-world data limitations while maintaining transparency, repeatability, and contractual accountability. From an engineering standpoint, addressing these issues requires forecasting models that balance predictive accuracy with computational efficiency and practical deployability within EPC-based PV projects.\u003c/p\u003e \u003cp\u003eRecent studies indicate that the integration of building automation systems, supervisory control and data acquisition (SCADA) platforms, and standardized energy management protocols within EPC models significantly improves monitoring accuracy, data reliability, and operational transparency [31,32]. From an engineering standpoint, these systems enable continuous data acquisition, real-time performance assessment, and traceable verification of energy outputs, which are essential for performance-based contractual frameworks. When aligned with ISO 50001 energy management standards, such integrated infrastructures provide a structured foundation for consistent measurement and verification procedures, thereby reducing uncertainty in performance evaluation and supporting technically sound decision-making throughout the project lifecycle.\u003c/p\u003e \u003cp\u003eEmpirical evidence from public building applications further demonstrates that incorporating reliable forecasting models at early stages of EPC project development can substantially enhance achievable energy savings and long-term performance outcomes [33,34]. Early-stage forecasting supports informed system sizing, financial feasibility analysis, and risk allocation, while also enabling more accurate baseline definition and performance guarantee structuring. From a systems engineering perspective, the integration of forecasting tools during project planning improves overall system robustness and reduces the likelihood of deviations between predicted and realized energy performance.\u003c/p\u003e \u003cp\u003eDespite these advancements, conventional forecasting approaches based solely on regression analysis often struggle to capture nonlinear relationships, seasonal effects, and stochastic variability in solar irradiance [35\u0026ndash;37]. Such limitations are particularly problematic in EPC-based PV applications, where even small forecasting errors may propagate into financial discrepancies and contractual disputes. These challenges have motivated a growing shift toward hybrid machine learning and optimization-based methodologies that can better accommodate complex system dynamics and nonlinear input\u0026ndash;output relationships [38,39]. By integrating optimization algorithms with data-driven models, these approaches enable adaptive parameter tuning and improved generalization under varying operational conditions.\u003c/p\u003e \u003cp\u003eHybrid methodologies further allow the incorporation of practical engineering constraints, including site-specific system characteristics, meteorological uncertainty, and financial parameters that influence EPC performance metrics [40,41]. This capability is especially relevant for EPC frameworks, where forecasting models must simultaneously satisfy technical accuracy requirements and contractual performance criteria. Consequently, hybrid forecasting approaches are increasingly viewed as essential tools for engineering-grade prediction in performance-based renewable energy projects.\u003c/p\u003e \u003cp\u003eThe increasing availability of high-resolution PV production datasets has further enabled the development and validation of advanced predictive models tailored to real operational environments [42,43]. Access to detailed temporal data facilitates more rigorous model training, validation, and benchmarking under realistic conditions. Prior research indicates that improved forecasting accuracy directly supports more effective risk assessment, regulatory compliance, and capital allocation decisions within EPC-driven renewable energy projects [44\u0026ndash;46]. In addition, accurate performance prediction contributes to enhanced investor confidence and more efficient lifecycle management of PV assets by reducing uncertainty in expected returns and operational outcomes [47\u0026ndash;49].\u003c/p\u003e \u003cp\u003eAt the policy and system-planning level, initiatives such as the European Union\u0026rsquo;s Clean Energy Package underscore the strategic importance of advanced forecasting tools in achieving national and regional energy transition objectives [50\u0026ndash;52]. From an engineering perspective, these initiatives further emphasize the need for scalable, transparent, and technically robust forecasting solutions that can be integrated into existing energy management and verification frameworks.\u003c/p\u003e \u003cp\u003eEmerging technologies, including digital twins and AI-enhanced monitoring systems, are now shaping the next generation of EPC implementations by enabling predictive maintenance, real-time performance tracking, and adaptive contract management [53\u0026ndash;55]. These technologies rely heavily on accurate forecasting models to support proactive system control and data-driven operational decisions. Their adoption is particularly significant for emerging economies and resource-constrained municipalities, where scalable, cost-effective, and computationally efficient solutions are required to expand EPC deployment without increasing technical complexity or operational burden [56\u0026ndash;58].\u003c/p\u003e \u003cp\u003eAgainst this background, the present study proposes a hybrid forecasting framework that combines multivariate regression analysis with the Artificial Bee Colony (ABC) optimization algorithm. The proposed model is validated using real operational data obtained from a photovoltaic installation in T\u0026uuml;rkiye, with the objective of minimizing forecasting errors while maintaining computational efficiency and practical applicability [59,60]. By operating effectively under real-world data constraints typical of EPC projects, the model addresses key engineering requirements, including transparency, performance accountability, and cost-effectiveness.\u003c/p\u003e \u003cp\u003eIn summary, this study introduces a hybrid forecasting approach that leverages the complementary strengths of regression modeling and swarm intelligence optimization to enhance PV production forecasting within EPC frameworks. Beyond its algorithmic contribution, the study provides empirical validation based on real system data, demonstrating its relevance for practical engineering applications. The proposed framework aims to support informed technical and financial decision-making and to contribute to the broader adoption of EPC-driven renewable energy projects in alignment with established energy efficiency standards and evolving system requirements.\u003c/p\u003e"},{"header":"2.\tMETHODOLOGY","content":"\u003cp\u003eThis study proposes an integrated predictive modeling framework that combines Multiple Linear Regression (MLR) with the Artificial Bee Colony (ABC) optimization algorithm to enhance the accuracy of energy yield forecasting and cost estimation for solar photovoltaic (PV) systems operating under Energy Performance Contracts (EPCs). The primary objective of the proposed approach is to minimize forecasting errors by coupling statistical regression-based estimation with a nature-inspired optimization mechanism capable of efficiently tuning model parameters. By improving prediction accuracy, the model aims to support more reliable financial analysis and decision-making processes, which are critical for performance-based contracting structures such as EPCs.\u003c/p\u003e\n\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\n \u003ch2\u003e2.1. Data Collection and Processing\u003c/h2\u003e\n \u003cp\u003eThe proposed model was validated using real operational data obtained from a grid-connected solar PV system with an installed capacity of 1710.72 kWp, located at Alanya Alaaddin Keykubat University (ALKU). The system was commissioned in March 2024 and implemented within an EPC framework, making it representative of performance-based renewable energy applications.\u003c/p\u003e\n \u003cp\u003eElectrical energy production data were recorded at 15-minute intervals using Schneider Electric ION 7650 power analyzers, ensuring high temporal resolution and measurement accuracy. These measurements were subsequently aggregated into monthly energy production values to align with EPC reporting and verification requirements. Meteorological input parameters, including solar radiation and ambient temperature, were obtained from the Turkish State Meteorological Service, providing reliable site-specific environmental data.\u003c/p\u003e\n \u003cp\u003eEconomic inputs required for EPC-based evaluation, such as investment cost parameters and electricity selling prices, were sourced from official EPC documentation and the 2024 national electricity tariff schedule published by the Energy Market Regulatory Authority (EMRA). This ensured consistency between technical performance modeling and the financial conditions governing EPC implementation.\u003c/p\u003e\n \u003cp\u003eThe final dataset consists of six key variables that directly influence PV system performance and economic evaluation:\u003c/p\u003e\n \u003cp\u003e(i) annual average solar radiation (kWh/m\u0026sup2;),\u003c/p\u003e\n \u003cp\u003e(ii) investment cost (TL/kWp),\u003c/p\u003e\n \u003cp\u003e(iii) electricity selling price (kr/kWh),\u003c/p\u003e\n \u003cp\u003e(iv) PV panel efficiency (%),\u003c/p\u003e\n \u003cp\u003e(v) system performance ratio (%), and\u003c/p\u003e\n \u003cp\u003e(vi) total energy production (kWh).\u003c/p\u003e\n \u003cp\u003ePrior to model development, the dataset was subjected to a systematic preprocessing procedure. Outliers were identified and removed using Z-score analysis, while minor data gaps were addressed through interpolation to preserve dataset continuity. All input variables were then normalized to a [0,1] range, which improves numerical stability and ensures efficient convergence during the ABC-based optimization process. This preprocessing step is particularly important for metaheuristic algorithms, as it prevents dominance of variables with larger numerical ranges and enhances overall optimization performance.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\n \u003ch2\u003e2.2. Regression Model Development\u003c/h2\u003e\n \u003cp\u003eAs an initial benchmark, a Multiple Linear Regression (MLR) model was developed to estimate the unit electricity production cost (TL/kWh) of the PV system. The regression model employs three primary explanatory variables that directly influence both technical performance and economic outcomes under EPC-based PV projects:\u003c/p\u003e\u003cspan\u003e\n \u003cp\u003e(i) solar radiation \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\left({X}_{1}\\right)\\)\u003c/span\u003e\u003c/span\u003e,\u003c/p\u003e\n \u003c/span\u003e \u003cspan\u003e\n \u003cp\u003e(ii) investment cost \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\left({X}_{2}\\right)\\)\u003c/span\u003e\u003c/span\u003e, and\u003c/p\u003e\n \u003c/span\u003e \u003cspan\u003e\n \u003cp\u003e(iii) electricity selling price \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\left({X}_{3}\\right)\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e\n \u003c/span\u003e\n \u003cp\u003eThe regression coefficients were estimated using the Ordinary Least Squares (OLS) method, which provides unbiased and efficient parameter estimates under standard linear regression assumptions. To evaluate potential multicollinearity among the independent variables, the Variance Inflation Factor (VIF) was calculated for each predictor. All variables exhibited VIF values below the commonly accepted threshold of 5, indicating the absence of significant multicollinearity and confirming the suitability of the selected predictors for regression modeling.\u003c/p\u003e\n \u003cp\u003eModel adequacy was assessed using multiple statistical indicators. The coefficient of determination \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\left({R}^{2}\\right)\\)\u003c/span\u003e\u003c/span\u003ewas found to be 0.873, demonstrating a strong explanatory capability of the model in capturing variations in unit production cost. Residual diagnostics were further conducted to verify the underlying regression assumptions. The Breusch\u0026ndash;Pagan test confirmed homoskedasticity of residuals, while the Durbin\u0026ndash;Watson statistic indicated no significant autocorrelation. These results collectively validate the baseline MLR model as a reliable reference for subsequent optimization. Although the regression model is formulated in terms of unit production cost, the optimized coefficients are subsequently used to derive annual energy production estimates within the EPC performance framework.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\n \u003ch2\u003e2.3. ABC Algorithm Integration\u003c/h2\u003e\n \u003cp\u003eAlthough the baseline MLR model demonstrates strong explanatory power, its predictive accuracy is inherently constrained by the fixed nature of OLS-estimated coefficients. To further enhance forecasting performance, the regression coefficients were optimized using the Artificial Bee Colony (ABC) algorithm.\u003c/p\u003e\n \u003cp\u003eThe ABC algorithm is a population-based metaheuristic inspired by the foraging behavior of honeybee colonies. In the proposed framework, each \u003cstrong\u003ecandidate solution (food source)\u003c/strong\u003e represents a potential set of regression coefficients. The optimization process aims to identify the coefficient vector that minimizes forecasting error while preserving economic consistency within the EPC framework.\u003c/p\u003e\n \u003cp\u003eThe optimization objective is defined by a customized fitness function:\u003c/p\u003e\n \u003cdiv id=\"Equa\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e$$\\:f\\left(\\overrightarrow{x}\\right)=\\alpha\\:\\cdot\\:\\text{MAPE}+\\beta\\:\\cdot\\:\\mid\\:\\frac{{C}_{\\text{actual}}-{C}_{\\text{predicted}}}{{C}_{\\text{actual}}}\\mid\\:$$\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\alpha\\:=0.7\\)\u003c/span\u003e\u003c/span\u003eand \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\beta\\:=0.3\\)\u003c/span\u003e\u003c/span\u003erepresent weighting factors assigned to forecasting accuracy and economic deviation, respectively. This formulation ensures that the optimization process prioritizes prediction accuracy while simultaneously accounting for deviations in cost estimation, which is critical for EPC-based financial evaluation.\u003c/p\u003e\n \u003cp\u003eThe solution vector is defined as: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\overrightarrow{x}=[{\\beta\\:}_{0},{\\beta\\:}_{1},{\\beta\\:}_{2},{\\beta\\:}_{3}]\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{0}\\)\u003c/span\u003e\u003c/span\u003eis the intercept term and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{1}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{2}\\)\u003c/span\u003e\u003c/span\u003e, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{3}\\)\u003c/span\u003e\u003c/span\u003ecorrespond to the regression coefficients associated with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{X}_{1}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{X}_{2}\\)\u003c/span\u003e\u003c/span\u003e, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{X}_{3}\\)\u003c/span\u003e\u003c/span\u003e, respectively.\u003c/p\u003e\n \u003cp\u003eThe ABC optimization process was executed over 1000 iterations, during which employed bees explored neighboring solutions, onlooker bees probabilistically selected promising solutions based on fitness values, and scout bees introduced new candidate solutions when stagnation was detected. This exploration\u0026ndash;exploitation balance reduces the likelihood of entrapment in local minima and improves convergence toward a globally optimal solution.\u003c/p\u003e\n \u003cp\u003eThrough this integration, the regression model transitions from a purely statistical estimator to a hybrid regression\u0026ndash;optimization framework, enhancing predictive robustness and adaptability under real-world EPC operating conditions.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\n \u003ch2\u003e2.4. Model Implementation and Evaluation\u003c/h2\u003e\n \u003cp\u003eThe proposed hybrid regression\u0026ndash;ABC model was implemented using MATLAB R2024b, which provides a robust computational environment for numerical optimization and statistical analysis. Based on preliminary sensitivity testing and common practices in swarm intelligence applications, the ABC algorithm parameters were configured as follows: a population size of 100 bees, a scout bee ratio of 0.5, a limit value of 100, and a maximum of 1000 iterations. These parameter settings were selected to ensure a balanced trade-off between exploration and exploitation while maintaining reasonable computational efficiency.\u003c/p\u003e\n \u003cp\u003eModel performance was evaluated using the Mean Absolute Percentage Error (MAPE) as the primary accuracy metric, given its suitability for comparing forecasting performance across different scales. The optimized hybrid model achieved a MAPE value of 6.82%, representing a substantial improvement over the 14.67% obtained from the baseline MLR model. This reduction in error demonstrates the effectiveness of the ABC-based coefficient optimization in enhancing predictive accuracy beyond conventional regression estimation.\u003c/p\u003e\n \u003cp\u003eTo assess the generalization capability of the proposed approach, a cross-validation procedure was applied. The results confirmed that the optimized model maintained consistent performance across unseen data subsets, indicating that the observed accuracy improvements were not limited to the training dataset and that the model exhibits robust predictive behavior under varying data conditions.\u003c/p\u003e\n \u003cp\u003eFor practical validation, the model outputs were compared against actual field measurements obtained from the ALKU PV system operating under real EPC conditions. The predicted annual energy production was calculated as 2,423,734.26 kWh, while the measured annual production was 2,423,472.28 kWh. This corresponds to a relative deviation of approximately 0.01%, demonstrating a very close agreement between predicted and observed values.\u003c/p\u003e\n \u003cp\u003eFrom an engineering perspective, this level of agreement indicates that the proposed model is capable of capturing the dominant performance characteristics of the PV system under real operating conditions. While minor discrepancies are expected due to measurement uncertainty and environmental variability, the results suggest that the hybrid regression\u0026ndash;ABC framework provides sufficiently accurate forecasts to support performance verification, cost estimation, and decision-making processes within EPC-based PV projects.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"3. RESULTS","content":"\u003cp\u003eThis section presents a detailed evaluation of the predictive performance and optimization characteristics of the integrated Regression\u0026ndash;Artificial Bee Colony (ABC) model. The analysis is structured around three main aspects: (i) convergence behavior of the ABC algorithm, (ii) prediction accuracy of the hybrid model, and (iii) comparative assessment of performance metrics. All results are derived from real operational data obtained from a 1710.72 kWp grid-connected photovoltaic system installed at Alanya Alaaddin Keykubat University (ALKU) and operated under an Energy Performance Contract (EPC) framework.\u003c/p\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e3.1. Convergence Behavior of the ABC Algorithm\u003c/h2\u003e \u003cp\u003eThe optimization process carried out using the ABC algorithm exhibited rapid and stable convergence in reducing the estimation error of the regression model. During the initial phase of the optimization, particularly within the first 40 iterations, a substantial decrease in the Mean Absolute Percentage Error (MAPE) was observed, highlighting the strong global search capability of the ABC algorithm.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e illustrates the evolution of MAPE values as a function of iteration number. The initial MAPE exceeded 2.0%, but declined sharply during the early iterations and fell below 0.5% shortly thereafter. This rapid error reduction indicates that the algorithm efficiently explores the solution space and avoids premature convergence to local optima. Following this phase, the error curve exhibits a smooth and stable behavior.\u003c/p\u003e \u003cp\u003eBeyond approximately the 300th iteration, the MAPE values become nearly constant, suggesting that the optimization process has reached a steady-state solution. This behavior confirms the robustness of the ABC algorithm in fine-tuning regression coefficients and achieving convergence with high numerical precision. The absence of oscillations or divergence in later iterations further indicates a well-balanced exploration\u0026ndash;exploitation mechanism within the selected algorithm parameters.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e3.2. Prediction Accuracy of Energy Production\u003c/h2\u003e \u003cp\u003eThe predictive accuracy of the proposed Regression\u0026ndash;ABC model was evaluated using real operational energy production data obtained from the installed PV system. The actual annual energy production, measured by Schneider Electric ION 7650 energy analyzers, was recorded as 2,423,472.28 kWh, while the optimized model estimated an annual production of 2,423,734.26 kWh.\u003c/p\u003e \u003cp\u003eThe resulting absolute deviation between measured and predicted values is 261.98 kWh, corresponding to a relative error of approximately 0.01%. From an engineering standpoint, this deviation is negligible when compared to the overall annual energy output and falls well within typical measurement uncertainty, environmental variability, and operational fluctuations associated with large-scale PV systems. These results indicate that the proposed hybrid model is capable of accurately capturing the dominant performance characteristics of the system under real EPC operating conditions.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e presents a direct comparison between the measured and predicted annual energy production values. The visual similarity between the two results highlights the strong agreement achieved through the ABC-based optimization of regression coefficients. This level of consistency demonstrates the effectiveness of the proposed approach in reducing estimation error and improving forecasting reliability.\u003c/p\u003e \u003cp\u003eOverall, the findings confirm that the Regression\u0026ndash;ABC framework provides a high level of predictive accuracy suitable for applications requiring precise energy yield estimation, such as performance verification, financial reconciliation, and risk assessment in EPC-based photovoltaic projects.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e3.3. Comparative Evaluation of Performance Metrics\u003c/h2\u003e \u003cp\u003eTo quantitatively assess the effectiveness of the proposed ABC-optimized regression model, its performance was benchmarked against the classical Multiple Linear Regression (MLR) approach using standard error metrics commonly adopted in energy forecasting studies. The evaluation criteria include the Mean Absolute Error (MAE), Mean Squared Error (MSE), and Mean Absolute Percentage Error (MAPE), which collectively provide a comprehensive assessment of prediction accuracy and robustness.\u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e summarizes the comparative results obtained from both models. As shown, the ABC-optimized model consistently outperforms the classical regression approach across all error indicators. Specifically, the MAE was reduced from 0.054 to 0.029, corresponding to an improvement of 46.3%, while the MSE decreased from 0.0043 to 0.0019, reflecting a 55.8% reduction. The most notable improvement was observed in the MAPE metric, which declined from 14.67% to 6.82%, yielding an overall improvement of 53.5%.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eComparison of error metrics between classical regression and ABC-optimized model.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMetric\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eClassical Regression\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eABC-Optimized Model\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eImprovement (%)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMAE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.054\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.029\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e46.3%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMSE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.0043\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0019\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e55.8%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMAPE (%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e14.67\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e6.82\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e53.5%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe observed improvements confirm that the integration of the ABC algorithm significantly enhances the regression model\u0026rsquo;s ability to capture complex relationships within the PV energy generation process. Although the underlying regression structure remains linear, the metaheuristic optimization of coefficients enables more effective representation of nonlinear influences and parameter interactions that are not adequately addressed by conventional OLS estimation.\u003c/p\u003e \u003cp\u003eTo further evaluate model robustness, the optimized framework was tested on unseen validation data. The ABC-enhanced model achieved a test-phase MAPE of 7.4%, which is closely aligned with the training-phase value of 6.82%. This limited deviation indicates strong generalization capability and suggests that the performance gains are not attributable to overfitting. From an engineering perspective, this level of consistency supports the applicability of the proposed approach for real-world EPC-based PV projects, where reliable forecasting across varying operational conditions is essential.\u003c/p\u003e \u003c/div\u003e"},{"header":"4. DISCUSSION","content":"\u003cp\u003eThis study further underscores the effectiveness of integrating hybrid optimization algorithms with classical regression techniques\u0026mdash;specifically through the proposed Regression\u0026ndash;Artificial Bee Colony (ABC) framework\u0026mdash;for achieving enhanced forecasting accuracy in energy performance assessments. The findings are consistent with broader conceptual and operational frameworks developed for the diffusion of low-carbon Energy Performance Contracts (EPCs), which increasingly prioritize technical reliability, transparent performance verification, and economic feasibility in contract-based renewable energy implementations [61]. Within such frameworks, accurate and robust forecasting models are regarded as a foundational requirement for minimizing performance risk and ensuring contractual compliance.\u003c/p\u003e \u003cp\u003eRecent EPC applications, particularly in social housing projects and heritage-sensitive building renovations, have highlighted the growing influence of occupant behavior, usage patterns, and operational variability on energy performance outcomes [62,63]. These factors introduce additional uncertainty into energy savings calculations, reinforcing the necessity for adaptive and data-driven prediction models capable of responding to dynamic system conditions. In parallel, the deployment of deep learning\u0026ndash;based forecasting techniques, such as those applied in multi-energy microgrids, has become increasingly important for enabling higher penetration of renewable energy sources in distributed and decentralized energy systems [64].\u003c/p\u003e \u003cp\u003eWithin public-sector energy efficiency and renewable energy programs, the strategic relevance of EPCs continues to expand, driven by policy objectives related to decarbonization, fiscal efficiency, and long-term asset performance [65]. In this context, increasing attention is being paid to verification protocols, legal and contractual design, and the coordination of multiple stakeholders involved in EPC delivery. To support these complex requirements, advanced machine learning and deep learning techniques, including convolutional neural networks (CNNs) and long short-term memory (LSTM) architectures, are being widely adopted for solar energy forecasting due to their capability to capture nonlinear relationships, temporal dependencies, and weather-induced variability [66,67].\u003c/p\u003e \u003cp\u003eAt the national level, ongoing efforts to improve EPC implementation systems in countries such as T\u0026uuml;rkiye further emphasize the urgency of integrating AI-driven forecasting models into policy-backed energy efficiency frameworks [68]. Hybrid artificial intelligence approaches are increasingly being employed to support both short-term time series prediction and real-time operational responsiveness in grid-connected PV and smart energy systems [69]. Within this evolving landscape, the Regression\u0026ndash;ABC model proposed in this study offers a complementary alternative that balances predictive accuracy, computational efficiency, and transparency\u0026mdash;attributes that are particularly valuable for EPC applications where interpretability, auditability, and contractual accountability remain critical considerations.\u003c/p\u003e \u003cp\u003eAccurate forecasting of electrical load and renewable energy generation, particularly under unstable and highly variable operating conditions, has been consistently shown to enhance grid stability, reduce balancing costs, and support more efficient dispatch strategies [70]. Reliable forecasts enable system operators to anticipate fluctuations in renewable output and demand, thereby improving reserve allocation and mitigating the risks associated with intermittency. In power systems with high penetration of photovoltaic generation, such forecasting capabilities are increasingly viewed as an essential component of secure and resilient grid operation.\u003c/p\u003e \u003cp\u003eIn the context of building retrofits\u0026mdash;especially within the stock of older buildings in T\u0026uuml;rkiye\u0026mdash;forecasting accuracy plays a decisive role in determining optimal system sizing, retrofit design, and expected energy savings [71]. In such cases, inaccurate predictions may lead to over- or under-dimensioned systems, suboptimal investment decisions, and reduced confidence in projected performance outcomes. As a result, forecasting models that can reliably operate under data limitations and heterogeneous building characteristics are particularly valuable for retrofit-oriented EPC projects.\u003c/p\u003e \u003cp\u003eRecent advances in hybrid metaheuristic and deep learning approaches, including CNN\u0026ndash;LSTM configurations, have demonstrated significant improvements in solar radiation and energy forecasting accuracy while simultaneously reducing computational burden through efficient feature extraction and temporal learning [72]. These methods have proven effective in capturing spatial\u0026ndash;temporal dependencies in meteorological data, which are often challenging for conventional statistical models. Complementary case studies conducted in educational institutions further confirm the effectiveness of analyzing EPC performance through consumption trends, tariff structures, and institutional usage patterns, highlighting the importance of integrating technical forecasts with economic evaluation [73].\u003c/p\u003e \u003cp\u003eAt the regional and international levels, ongoing efforts to harmonize EPC performance indicators across Europe emphasize the need for forecasting tools that can remain robust across diverse regulatory, climatic, and market environments [74]. Models capable of adapting to varying tariff regimes, verification protocols, and policy requirements are increasingly necessary to support cross-border benchmarking and best-practice transfer. In this regard, advanced architectures such as Conv2D LSTM have been successfully applied in studies combining air quality, weather, and energy data, demonstrating their potential for integrated energy\u0026ndash;environmental modeling frameworks [75].\u003c/p\u003e \u003cp\u003eComparative studies between probabilistic and deterministic forecasting approaches reveal that advanced LSTM-based models often outperform simpler techniques under complex and rapidly changing meteorological conditions [76]. Nevertheless, enhanced regression-based methods continue to play an important role in solar energy prediction, particularly where model transparency, interpretability, and computational efficiency are prioritized [77]. These characteristics are especially relevant for EPC applications, where forecasting outputs must be auditable and easily communicated to multiple stakeholders.\u003c/p\u003e \u003cp\u003eBeyond generation forecasting, predictive modeling increasingly extends to life-cycle energy savings estimation, particularly in retrofit projects governed by service and performance-based contracts [78]. Accurate forecasts enable better tracking of guaranteed savings, facilitate verification and measurement processes, and support long-term asset management strategies. Empirical evidence from public building applications further demonstrates that improved forecasting accuracy directly contributes to higher efficiency metrics and strengthens verification procedures in performance-based energy initiatives [79]. Collectively, these findings reinforce the central role of robust forecasting methodologies in advancing EPC implementation and achieving sustainable energy performance outcomes.\u003c/p\u003e \u003cp\u003eDesign considerations within Energy Performance Contract (EPC) models\u0026mdash;such as balanced risk allocation, performance guarantees, and long-term alignment between contractors and building owners\u0026mdash;require forecasting methodologies capable of supporting reliable long-term energy savings projections [80]. In EPC-based implementations, inaccurate forecasts may distort baseline definitions, compromise savings guarantees, and ultimately weaken contractual trust. Consequently, forecasting accuracy is not merely a technical concern but a structural requirement for effective EPC design and governance.\u003c/p\u003e \u003cp\u003eIn addition to energy yield and cost metrics, performance indicators such as Indoor Environmental Quality (IEQ) and broader building performance indices increasingly rely on data-driven forecasting approaches to support EPC optimization [81]. These indicators, which encompass thermal comfort, air quality, and occupant well-being, are particularly relevant in public-sector and residential applications, where energy efficiency measures must be aligned with user comfort and regulatory standards. Forecasting models that integrate such multidimensional performance criteria enhance the ability of EPC frameworks to deliver both energy and non-energy benefits.\u003c/p\u003e \u003cp\u003eEmpirical studies on thermal retrofitting projects demonstrate that EPC success is strongly dependent on the early-stage integration of forecasting tools that explicitly account for climate conditions, building envelope characteristics, and system-specific dynamics [82]. Early forecasting enables more accurate retrofit design decisions, supports realistic savings estimates, and reduces uncertainty during the contract execution phase. In parallel, intelligent energy management systems deployed within microgrids increasingly utilize AI-based forecasting techniques to optimize energy exchange, load balancing, and interaction with the main grid, further illustrating the growing operational relevance of advanced predictive models [83].\u003c/p\u003e \u003cp\u003eFrom a regulatory perspective, analyses of legal EPC frameworks, such as those applied in Poland and other European countries, highlight the institutionalization of forecasting as a regulatory and contractual necessity rather than an optional analytical tool [84]. Forecasting outputs are increasingly embedded within verification protocols, performance audits, and compliance mechanisms. Moreover, advanced forecasting tools enable complex EPC configurations\u0026mdash;such as reactive power compensation and power quality management\u0026mdash;to be modeled, monitored, and enforced more effectively within contractual boundaries [85].\u003c/p\u003e \u003cp\u003eRecent comprehensive reviews of photovoltaic power forecasting consistently highlight the central role of deep learning and hybrid modeling architectures in reducing prediction errors across a wide range of climatic and geographical conditions [86]. These studies emphasize that the increasing variability of solar resources, driven by changing weather patterns and localized atmospheric effects, necessitates forecasting approaches capable of learning complex nonlinear relationships from large and heterogeneous datasets. In this context, deep learning\u0026ndash;based methods have emerged as powerful tools for capturing spatial\u0026ndash;temporal dependencies that are difficult to represent using conventional statistical techniques.\u003c/p\u003e \u003cp\u003eAmong these approaches, CNN\u0026ndash;LSTM architectures optimized through hybrid metaheuristic techniques have demonstrated particularly strong performance under conditions characterized by highly volatile solar irradiance and nonlinear weather dynamics [87]. By combining convolutional layers for spatial feature extraction with recurrent structures for temporal dependency modeling, these hybrid frameworks offer substantial accuracy gains, especially in large-scale or highly dynamic PV systems. Their effectiveness has been validated in applications ranging from utility-scale solar farms to distributed generation networks, where rapid fluctuations in irradiance pose significant forecasting challenges.\u003c/p\u003e \u003cp\u003eFurther enhancements in forecasting performance have been achieved through the integration of contextual and environmental variables, such as air quality indices, aerosol concentrations, and atmospheric pollution levels, into advanced Conv2D LSTM architectures [88]. The inclusion of such auxiliary data enables multi-feature learning and provides a more comprehensive representation of the physical processes influencing solar energy generation. These developments illustrate a broader trend toward holistic modeling strategies that extend beyond purely meteorological inputs.\u003c/p\u003e \u003cp\u003eBeyond technical forecasting accuracy, recent studies have also explored the role of game-theoretic frameworks, including Stackelberg-based models, as analytical tools for EPC contract design and evaluation [89]. Within such frameworks, accurate energy forecasting serves as a critical input for strategic decision-making, informing contract negotiation, risk-sharing mechanisms, and performance incentive structures. By supporting equilibrium between contracting parties, forecasting-driven game-theoretic models contribute to more stable and transparent EPC arrangements.\u003c/p\u003e \u003cp\u003eDespite the rapid advancement and demonstrated effectiveness of deep learning\u0026ndash;based forecasting techniques, regression-based approaches continue to play a significant and complementary role in performance prediction, particularly for public buildings undergoing thermal retrofitting [90]. Their inherent transparency, interpretability, and relatively low computational requirements make them especially suitable for EPC applications operating within policy-driven, audit-intensive, and resource-constrained environments. In such contexts, the ability to clearly interpret model behavior and verify results remains as important as achieving marginal gains in predictive accuracy.\u003c/p\u003e"},{"header":"5. CONCLUSION","content":"\u003cp\u003eThis study presents a comprehensive investigation into the development and application of a hybrid Regression\u0026ndash;Artificial Bee Colony (ABC) model for forecasting solar energy generation within the framework of Energy Performance Contracting (EPC). The proposed methodology demonstrates high forecasting accuracy, low error margins, and robust performance under varying operational and environmental conditions. These attributes are particularly critical in EPC-based projects, where contractual guarantees, financial settlements, and risk-sharing mechanisms are directly dependent on the reliability of energy production forecasts.\u003c/p\u003e \u003cp\u003eCompared with conventional statistical approaches and several advanced AI-based techniques reported in the recent literature, the proposed Regression\u0026ndash;ABC hybrid framework achieves a well-balanced trade-off between predictive accuracy, computational efficiency, and model interpretability. This balance is especially relevant for stakeholders operating in financially and regulatorily constrained environments\u0026mdash;such as energy service companies (ESCOs), public-sector authorities, and private investors\u0026mdash;who require forecasting tools that are not only precise but also transparent, explainable, and suitable for audit and verification processes. Unlike purely data-driven black-box models, the hybrid structure preserves the interpretability of regression analysis while benefiting from the adaptive optimization capability of swarm intelligence.\u003c/p\u003e \u003cp\u003eOne of the principal contributions of this study lies in the integration of metaheuristic optimization into a regression-based forecasting framework, enabling dynamic calibration of model parameters in response to project-specific conditions. The ABC algorithm enhances the model\u0026rsquo;s flexibility by allowing it to adapt to site-dependent climatic characteristics, system design constraints, and EPC contractual requirements. This adaptability supports the generation of customized forecasting solutions that are technically robust and economically feasible, thereby strengthening the practical applicability of the model in real-world EPC implementations.\u003c/p\u003e \u003cp\u003eFrom an operational perspective, the use of real production data from an operating photovoltaic system ensures that the proposed approach bridges the gap between theoretical modeling and practical deployment. The close agreement observed between predicted and measured energy outputs indicates that the model is capable of capturing the dominant performance characteristics of PV systems within the bounds of measurement uncertainty and environmental variability. Such accuracy is particularly valuable in EPC contexts, where even small deviations between predicted and actual performance may translate into financial penalties, disputes, or loss of stakeholder confidence.\u003c/p\u003e \u003cp\u003eBeyond its technical merits, the study provides important insights into the role of data-driven forecasting as a decision-support instrument within performance-based investment frameworks. Improved forecasting accuracy directly contributes to more reliable estimation of key financial indicators, including levelized cost of energy (LCOE), payback period, and return on investment (ROI). By reducing uncertainty in these indicators, the proposed Regression\u0026ndash;ABC model can help mitigate performance-related risks, enhance investor confidence, and support transparent measurement and verification (M\u0026amp;V) processes in alignment with international standards such as ISO 50001.\u003c/p\u003e \u003cp\u003eAt a broader level, the findings reinforce the strategic importance of hybrid modeling approaches in supporting policy-driven energy transitions. Accurate and transparent forecasting tools are essential for the effective implementation of EPCs aligned with national energy efficiency targets, decarbonization strategies, and green public procurement policies. In this context, the proposed framework contributes not only to methodological advancement but also to the operationalization of sustainable energy policies through reliable performance assessment mechanisms.\u003c/p\u003e \u003cp\u003eFuture research should focus on extending the proposed model across diverse climatic zones, regulatory environments, and building typologies to further evaluate its scalability and transferability. The integration of real-time Internet of Things (IoT) data streams may enable continuous model updating and improve responsiveness under rapidly changing operating conditions. Additionally, extending the framework toward probabilistic or ensemble-based forecasting could enhance its suitability for high-uncertainty scenarios commonly encountered in renewable energy systems. Comparative benchmarking against other evolutionary optimization techniques\u0026mdash;such as Ant Colony Optimization or Differential Evolution\u0026mdash;would also provide valuable insights into relative performance characteristics. Finally, embedding the model within digital twin platforms or smart building management systems could open new avenues for dynamic energy governance, adaptive EPC management, and policy-aligned technological innovation.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eA.A. conceptualized the study, collected and curated the data, developed the regression\u0026ndash;ABC methodology, and performed the simulations and analysis. K.T. contributed to the methodological design, supervised the technical aspects of the study, and validated the results. A.A. drafted the original manuscript. Both authors reviewed, edited, and approved the final version of the manuscript.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eThe data used in this study were obtained from an operational grid-connected photovoltaic system operating under an Energy Performance Contract framework. Due to institutional and contractual confidentiality restrictions, the data are not publicly available. However, aggregated or anonymized data may be made available from the corresponding author upon reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003ePedro, H. T. C., \u0026amp; Coimbra, C. F. M. (2012).Assessment of forecasting techniques for solar power production with no exogenous inputs.Solar Energy, 86(7), 2017\u0026ndash;2028.https://doi.org/10.1016/j.solener.2012.04.004\u003c/li\u003e\n\u003cli\u003eAchnib, A., Altaf, Q. H., \u0026amp; Badar, H. (2024). A comparative analysis of meta-heuristic algorithms for energy management in smart grids. Proceedings of CoDIT, 791\u0026ndash;795. https://doi.org/10.1109/codit62066.2024.10708179\u003c/li\u003e\n\u003cli\u003eAcuner, E., Cin, R., \u0026amp; Onaygil, S. (2021). Energy service market evaluation by Bayesian belief network and SWOT analysis: case of Turkey. Energy Efficiency, 14(6), 1\u0026ndash;20. https://doi.org/10.1007/S12053-021-09973-W\u003c/li\u003e\n\u003cli\u003eAkbulut, A.; Niemiec, M.; Tasdelen, K.; Akbulut, L.; Komorowska, M.; Atılgan, A.; Co\u0026cedil;sgun, A.; Okreglicka, M.; Wiktor, K.; Povstyn, O.; et al. Economic Efficiency of Renewable Energy Investments in Photovoltaic Projects: A Regression Analysis. Energies 2025, 18, 3869. https://doi.org/10.3390/en18143869.\u003c/li\u003e\n\u003cli\u003eAkko\u0026ccedil;, H. N., Onaygıl, S., Acuner, E., \u0026amp; Cin, R. (2023). Implementations of energy performance contracts in the energy service market of Turkey. Energy for Sustainable Development, 76, 101303. https://doi.org/10.1016/j.esd.2023.101303\u003c/li\u003e\n\u003cli\u003eAksin, F. N., \u0026amp; Sel\u0026ccedil;uk, S. A. (2021). Energy Performance Optimization of School Buildings in Different Climates of Turkey. 7(1). https://doi.org/10.5334/FCE.107\u003c/li\u003e\n\u003cli\u003eAl‑Ali, E. M., Hajji, Y., Said, Y., Hleili, M., Alanzi, A. M., Laatar, A. H., \u0026amp; Atri, M. (2023). Solar energy production forecasting based on a hybrid CNN‑LSTM‑Transformer model. Mathematics, 11(3), 676. https://doi.org/10.3390/math11030676\u003c/li\u003e\n\u003cli\u003eAlatawi, M. N. (2024). Optimization of home energy management systems in smart cities using bacterial foraging algorithm and deep reinforcement learning for enhanced renewable energy integration. International Transactions on Electrical Energy Systems. https://doi.org/10.1155/2024/2194986\u003c/li\u003e\n\u003cli\u003eAlorf, A. (2025). 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Improving the Energy Performance of Public Buildings Equipped with Individual Gas Boilers Due to Thermal Retrofitting. Energies, 14(6), 1565. https://doi.org/10.3390/EN14061565\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"photovoltaic forecasting, regression analysis, artificial bee colony algorithm, energy performance contracts, hybrid modeling, renewable energy, optimization, sustainable investment","lastPublishedDoi":"10.21203/rs.3.rs-8703528/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8703528/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eAccurate photovoltaic (PV) energy production forecasting is essential for Energy Performance Contracts (EPCs), where financial outcomes and contractual guarantees depend on reliable performance estimates. This study proposes a hybrid forecasting framework that integrates multivariate regression analysis with the Artificial Bee Colony (ABC) algorithm to improve prediction accuracy while preserving computational efficiency and model transparency. The proposed model is validated using real operational data from a 1710.72 kWp grid-connected PV system operating under an EPC framework at Alanya Alaaddin Keykubat University (T\u0026uuml;rkiye). Key technical and economic variables, including solar irradiance, investment cost, and electricity unit price, are employed in the regression model, whose coefficients are optimized using the ABC algorithm. Results show that the hybrid Regression\u0026ndash;ABC model achieves a MAPE of 6.82%, significantly outperforming the baseline regression model (14.67%). The predicted annual energy production closely matches measured field data, with a relative deviation of approximately 0.01%, remaining within typical measurement uncertainty. The findings demonstrate that the proposed hybrid approach provides an accurate, transparent, and practical forecasting tool suitable for EPC-based PV projects, supporting performance verification, risk management, and investment planning.\u003c/p\u003e","manuscriptTitle":"Hybrid Regression–Artificial Bee Colony Optimization for PV Production Forecasting under Energy Performance Contracting","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-03 07:52:56","doi":"10.21203/rs.3.rs-8703528/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"d83e9a7e-e9a0-4b0f-9219-8f85bf137dbf","owner":[],"postedDate":"February 3rd, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-04-18T15:25:21+00:00","versionOfRecord":[],"versionCreatedAt":"2026-02-03 07:52:56","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8703528","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8703528","identity":"rs-8703528","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}