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Scientific Reports volume 15, Article number: 40482 (2025)
1776
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This study proposes an optimized method for reducing operational costs by integrating a microgrid consisting of photovoltaic (PV) panels and battery energy storage systems (BESS), thereby decreasing dependence on the main grid. Traditionally, electricity demands have been met primarily by the main grid. However, with the increased use of renewable energy sources and BESS in microgrids, it’s now possible to lower generation costs, improve environmental sustainability, and enhance energy efficiency. In this paper, the optimization problem is tackled using the SPEA2 algorithm, focusing on three main Objectives: (i) minimizing technical issues like power losses and voltage fluctuations in the grid, (ii) maximizing financial returns for distribution network operators, and (iii) reducing grid imports. The paper provides a comprehensive set of numerical results, leveraging detailed data on energy demand, local solar irradiance, and energy storage systems to validate the proposed method. The obtained results, based on two case studies, confirm that the optimal energy combination between power units and the main grid at each time reduces power losses by 47%, voltage deviation by 51% and improve financial returns by 54% (compared to the reference case). The results highlight also the added value of BESS integration in minimizing grid imports, especially during peak hours. It can be said that the results underscore the remarkable efficiency and effectiveness of the proposed approach, demonstrating its capability to address the targeted challenges while achieving optimal performance metrics.
Recently, the surge in fossil fuel prices and growing concerns about climate change have driven society to re-evaluate its energy strategies. This shift has led to an increased emphasis on environmental impact assessments and a strong push towards the adoption of clean and efficient energy sources within power systems. The urgency of mitigating environmental damage has propelled the development of renewable energy technologies, such as wind and solar power, as viable alternatives to traditional fossil fuels. This transition not only addresses the environmental challenges but also aims to create a sustainable energy future for generations to come1. A microgrid, typically operating at low or medium voltage, functions as a localized energy system with a clearly defined electrical boundary. This boundary allows it to manage the distribution of power within a specific area, often encompassing a mix of residential, commercial, and industrial consumers. What makes a microgrid particularly innovative is its ability to integrate a variety of Distributed Energy Resources (DERs), such as solar panels, wind turbines, and energy storage systems, alongside traditional loads. By doing so, a microgrid not only enhances energy reliability and efficiency but also supports the transition towards a more sustainable and resilient power infrastructure. This flexibility enables microgrids to function independently from the main grid during power outages or in remote areas, making them a crucial element in the changing energy landscape2. Microgrids offer a powerful solution for generating electricity that is both resilient and eco-friendly, while also being cost-efficient. By using local renewable sources and leveraging advanced control systems, microgrids can function independent or in tandem with the utility grid, providing consistent power even in the face of disruptions. This blend of sustainability and reliability makes microgrids an appealing choice for communities and businesses looking to reduce their carbon footprint and strengthen energy security3,4. Microgrids are flexible systems capable of operating either in connection with the utility grid or independently in islanded mode. When linked to the main grid, they optimize energy usage by balancing supply and demand, often incorporating renewable energy sources. In islanded mode, they become self-reliant, delivering reliable power during grid outages or in remote locations. This dual capability boosts energy security and provides greater flexibility in managing local energy needs5. Residential microgrids connected to the main grid allow for bi-directional electricity flow, enabling homeowners to both consume and supply power as required. Hybrid microgrids, which integrate multiple renewable energy sources (RES), traditional power generation, and energy storage systems, go a step further. They help mitigate the variability of renewable energy, enhancing system efficiency and strengthening overall resilience. This combination ensures a stable and reliable energy supply, even in the face of changing weather conditions or disruptions to the main grid6. A residential microgrid enables the efficient utilization of renewable energy sources (RES) by managing power generation, consumption, and energy storage within a localized system. This study focuses on a microgrid that incorporates Battery Energy Storage Systems (BESS) and Photovoltaic (PV) panels, offering a sustainable energy solution. With global policies increasingly aimed at reducing greenhouse gas emissions and addressing climate change, the shift from fossil fuels to RES is gaining momentum, positioning microgrids as a key component of the future energy landscape7. Notably, CO2 emissions make up over 70% of total greenhouse gas emissions, positioning them as the main contributor to climate change. This underscores the pressing need to transition to cleaner energy sources, such as those employed in microgrids, which can substantially lower our carbon footprint and promote a more sustainable future8. The growing integration of Renewable Energy Sources (RES) marks a pivotal step toward a significantly decarbonized power system. In the United States, this shift is clear, with RES penetration rising from 9% in 2004 to 13% in 2014. This increase highlights the continued efforts to decrease dependence on fossil fuels and progress toward a cleaner, more sustainable energy future9. However, the variability in RES generation and the switching between grid-tied and off-grid modes in residential microgrids can pose stability challenges. To overcome these issues and ensure a consistent power supply, Battery Energy Storage Systems (BESS) are employed to balance fluctuations between energy generation and consumption. BESS helps maintain the stability and reliability of the microgrid, even when renewable energy production fluctuates or during transitions between operating modes10. Addressing the technical and economic constraints of microgrids is crucial for maintaining a balanced relationship between available resources and load demands. Achieving this balance requires optimal planning and design, with components of hybrid microgrids accurately sized to meet specific load requirements. Careful sizing is vital for ensuring both efficiency and reliability, as demonstrated in numerous studies. Properly tailored microgrid components not only improve performance but also optimize costs, making the system both economically feasible and technically resilient11,12. Many researchers have focused on the design, planning, and optimization of hybrid microgrids, employing various optimization techniques. For instance13, examines how to optimize the design, selection, and operation of different Distributed Energy Resources (DERs) in commercial buildings. These studies focus on improving the efficiency and reliability of microgrids by strategically selecting and managing resources to meet specific energy needs, showcasing the potential for customized solutions across various environments. Research efforts such as14 and15 aim to minimize the total costs and emissions of microgrids by determining the optimal configuration of Distributed Energy Resources (DERs), considering constraints within local distribution networks, like voltage profiles and energy losses. However, these studies primarily focus on optimizing voltage profiles and do not fully address the reliability of microgrids. In contrast16, and17 investigate the optimal allocation of energy storage within distribution systems16. seeks to reduce system costs by enhancing voltage profiles, lowering line loading, and minimizing both active and reactive power losses. Meanwhile17, focuses on reducing costs associated with energy storage installation, energy losses, maintenance, interruptions, and system upgrades. The techno-economic advantages of Battery Energy Storage Systems (BESS) and Photovoltaic (PV) systems under feed-in tariff (FiT) incentives and time-varying electricity rates are analyzed in18. Additionally19, addresses energy storage sizing and operational strategies, considering economic incentives for storage owners. Various studies also emphasize efforts to reduce CO2 emissions in microgrid operations. For instance20, optimizes the size and dispatch of Distributed Energy Resources (DERs) to lower CO2 emissions, factoring in heat and cold storage. Similarly21, presents an economic scheduling model for electricity and natural gas systems aimed at reducing CO2 emissions, while22 explores cost minimization and emission reduction through DER optimization, taking into account utility rates, transportation constraints, and generator states. For industrial parks23, proposes a low-carbon economic dispatch model that incorporates multi-source prices, calculating monthly CO2 emissions based on real-time monitoring. In24, an algorithm is introduced to manage BESS capacity in commercial microgrids with generators and renewable energy sources (RES). Additionally25, utilizes a multi-objective analysis algorithm to find the optimal sizes of PV and storage systems. In26, the Grasshopper Optimization Algorithm (GOA) is tested to other optimization algorithms for DER size optimization in isolated microgrids. Lastly27, employs meta-heuristic algorithms such as the Imperialistic Competitive Algorithm (ICA), Genetic Algorithm (GA), and Particle Swarm Optimization (PSO) to optimize the size and location of DERs in distribution networks, while28 focuses on implementing the PSO algorithm for DER optimization with consideration for various load types. Various strategies are used to optimize the allocation of Distributed Energy Resources (DERs), including simulation software tools like HOMER, DER-CAM, and NEPLAN29,30,31, deterministic method-ologies that involve numerical and iterative techniques19,32, and heuristic or metaheuristic optimization algorithms such as CS, GOA, and PSO26,33,34. While simulation tools provide valuable insights into DER sizing, they are limited by the modeling assumptions of their components and are mainly used for feasibility studies. As a result, simulation software is often utilized as a comparative tool to analyze the sensitivity of sizing outcomes across different studies. Deterministic sizing methods generally outperform simulation software tools when it comes to DER sizing. However, the complex nature of microgrid design and planning can cause these deterministic approaches to get stuck in local optima, leading to longer time to find the economic solution26.
In the review, many methods have been developed and are extensively used as metaheuristic algorithms to tackle microgrid problems. These approaches are adaptable and skilled at avoiding unit optima, often providing better solutions than deterministic approaches35. A simple comparison of optimization approaches conducted in36 reveals that PSO stands out as one of the most significant algorithms for microgrid planning. PSO demonstrates the ability to minimize obstruction costs, rise reliability, and exhibit more significant convergence than other stochastic methods and quantify the optimal advantages of improving such systems at the customer level37,38 (Fig. 1). Studies in the literature have examined various aspects of system-level optimization 39, including simulation and optimization of PV-battery systems focusing on self-consumption, Feed-in Tariff (FiT) incentives, wholesale electricity tariffs, and demand forecasting40,41,42,43,44,45. While batteries have traditionally been utilized in standalone PV systems46, there is a growing interest in integrating batteries into grid-connected PV systems, particularly under FiT and time-of-use tariffs47,48. Moreover, large-scale installations in the form of solar farms integrating battery technology into energy systems are becoming increasingly prevalent due to favorable energy policies49,50,51. The rising electricity demands in grid systems, coupled with the proliferation of distributed resources to optimize existing network capacity utilization, lead to a disparity between production and load, resulting in underutilization of production and distribution infrastructure52,53. Consequently, the ability of residential electricity consumers to dynamically respond to fluctuating electricity prices becomes increasingly valuable for seamlessly integrating high levels of distributed energy resources, such as PV, into future electricity networks. In a study outlined in54,55,56,57, the effect of load management with storage systems was examined on self-consumption levels. The study highlighted the significance of the association between energy flows and storage capacity as important variable in optimizing process. In56,57, a Mixed-Integer Linear Programming (MILP) model was improved to manage and size residential heat pumps, aiming to maximize self-consumption of PV production with economic optimization of battery storage.
Schematic structure of the microgrid system.
This article proposes a system that promotes strong and optimal insertion of renewable energies and BESS as well, while limiting imports from the main grid. It is capable of ensuring effective network management based on technical and economical parameters. For many scenarios, the system not only minimizes technical parameters such as voltage deviation and power losses, but also provides significant economic benefits to the Distribution Network Operator (DNO). The article is structured as follows; section I mathematical modeling; section II optimization problem formulation. In addition, the proposed strategy method has been carefully analyzed and restructured to provide a clearer understanding of the performance and limitations of the evaluated methods. This reformulation highlights key trends and areas for improvement, while also paving the way for discussions on new evaluation criteria. Section III evaluates the results obtained from the techniques. Finally, Section IV outlines the conclusion.
This section provides an overview of the PV system, highlighting the mathematical concepts and design principles of the selected compensation topology, with a particular focus on the ESS configuration.
Equations As a function of solar irradiance, temperature, efficiency coefficient of solar panel and many other parameters, the output produced photovoltaic power (:{P}_{PV,i}^{t}) at time t and injected at bus i is described in Eq. (1)58.
(:{G}^{t}) is defined as the global solar irradiance at time t, (:{P}_{PVr}) is the nominal power of the PV, (:{T}_{C}) is the temperature of the PV cell and (:{K}_{T}) is the PV temperature coefficient.
The behavior of the battery energy storage system is reflected by its state of charge SoC, expressed in % as a function of time as follows59,60:
(:{P}_{BESS}) represents the nominal power of the storage system. (:{eta:}_{ch}:), (:{eta:}_{dis}), (:{P}_{ch,i}^{t}) and (:{P}_{dis,i}^{t}) are respectively the charging and discharging efficiencies and powers of BESS at time t and bus i. SD is the self-discharge of the BESS and (:varDelta:t) is the time step. While Eq. (2) is the main equation used to update the battery SoC during operation, Eq. (3) models the self-discharge effect, which causes the reduction of the SoC over time by a factor proportional to the self-discharge rate SD. In order to accurately update the battery SoC over time, these two equations were combined.
The BESS power (:{P}_{BESS,i}^{t}:)at each instant t and each bus i is then expressed in Eq. (4), used to model the net BESS power injection at each bus and time step.
Industrial, residential, and commercial loads are considered in order to simulate the variation of the load. The load power at time t is equal to the IEEE 33 bus typical load power at each bus multiplied by the sum of the coefficients of proportions of the 3 types of loads. The exchange of energy with the main grid depends on the state of the PV sources and BESSs as well as the loads; energy is purchased from the grid in the case of a deficit and sold in the case of excess. The network is therefore modeled by an infinite source.
In this section, the proposed optimization model for distribution networks with integrated decentralized PV-BES systems is described. It is a multi-objective non-linear optimization problem involving discrete decision variables and aims to minimize hourly power losses and average voltage deviation and maximize Distribution Network Operator (DNO) revenues, as expressed in Eqs. (5)-(7).
The objective function developed in this work includes three main functions, expressed below:
Minimize hourly power losses PtL:
Minimize average voltage deviation VtD, average :
Maximize DNO’s revenue RtDNO :
(:{I}_{i,k}^{text{t}}:)is the current that transits between nodes i and k at time t and (:{R}_{i,k}) is the branch resistance. (:{V}_{i}^{t}) represents the nodal voltage at time t and N is the number of the network nodes.
(:{P}_{PV}^{t}), (:{P}_{ch}^{t}) and (:{P}_{dis}^{t}:)are respectively the total PV, charging and discharging BESS powers at time t, defined by:
(:{P}_{grid,import}^{t}) and (:{P}_{grid,export}^{t}) are respectively the imported and exported energy from and to the utility grid at time t and (:{C}_{import}^{t}) and (:{C}_{export}^{t}) are their corresponding costs. (:{C}_{load}^{t}) is the cost of the energy sold to costumers, (:{C}_{PV}) and (:{C}_{dis}) are the costs of energy purchased from PV and BESS respectively (to support the loads) and (:{C}_{ch}) is the cost of energy sold to the BESS (to charge it).
The DNO revenue includes purchased electricity from PV, BESS (when discharging) and the main grid and sold electricity to BESS (to be charged), customers and the main grid (when there is an excess of energy).
In this optimization framework, the decision vector is a 9-dimension vector containing variables that are optimized by the algorithm in order to minimize the objective functions above. They include the active power injected from PV 1, 2, 3 and 4 at their respective buses and time t, the charging and discharging power of BESS at bus i and time t, and the active power supplied by the utility grid.
The control parameters that influence system behavior, in this study include the nominal capacity of PV and BESS units, the charging/discharging efficiencies of BESS, the time step and simulation horizon, maximum charging/discharging power, tariff structure and SPEA2 settings.
Based on many technical parameters of PV systems, BESS and utility grid, many restrictions are established in order to simulate the real operation of the system.
The energy management strategy presented in this paper is designed to optimize power losses and voltage deviation while maximizing revenue for the Distribution Network Operator (DNO). To achieve this, the study employs the Strength Pareto Evolutionary Algorithm 2 (SPEA2), an advanced method within the category of Evolutionary Algorithms (EAs), which are inspired by the concept of “survival of the fittest.” Evolutionary Algorithms, including genetic algorithms (GAs), evolutionary strategies (ESs), and evolutionary programming (EP), draw on biological principles from Darwin and Mendel, simulating natural selection and adaptation processes.
These evolutionary-based methods have attracted attention across diverse fields such as computer science, engineering, and finance, where optimization is critical. By leveraging Darwinian principles, these algorithms explore vast “fitness landscapes,” efficiently navigating through potential solutions to identify the best candidates. The increased computational power available today makes EAs particularly efficient in finding optimal solutions for complex problems, often achieving results faster and more flexibly than traditional optimization techniques. SPEA2 specifically is well-suited for handling multiple objectives, providing a robust approach for managing trade-offs between competing goals, such as minimizing power losses and maximizing revenue. This flexibility has made Darwinian-based optimization techniques highly attractive to researchers. Figure 2 illustrates a basic flowchart that captures the core structure of Evolutionary Algorithms, highlighting the iterative selection, mutation, and crossover processes that drive the search for optimal solutions. This evolutionary framework offers a powerful, adaptable approach for solving both single and multi-objective optimization problems, as further explored in this study. Evolutionary Algorithms embody the fittest concept, converting it into a mathematical approach that provides a stochastic approach for solving single or multi-objective optimization problems58. Figure 2 shows a flowchart illustrating the proposed energy management strategy.
Flowchart of the proposed Algorithm.
The proposed model solves an optimization problem involving multiple conflicting objectives; namely, minimizing power losses, voltage deviation, and maximizing profit. To manage the trade-offs among these objectives, the SPEA2 Pareto-based multi-objective optimization technique was adopted. Unlike weighted sum methods, SPEA2 generates a Pareto front containing diverse non-dominated solutions. For decision-making, TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) method was used in order to evaluate the solutions based on operational priorities.
The proposed energy management strategy is implemented on a modified IEEE 33-bus distribution network, as depicted in Fig. 3. This network incorporates four decentralized photovoltaic (PV) systems and two Battery Energy Storage Systems (BESSs), strategically placed to optimize performance. The locations and sizes of these units were determined based on findings from a prior study61, detailed in Table 1, which identified configurations that maximize efficiency while balancing energy supply and demand. For simplicity and to streamline power flow calculations, it is assumed that both PV and BESS units operate at a unity power factor, supplying purely active power. This assumption ensures that reactive power effects are minimal, allowing a clearer focus on optimizing active power flows within the network and assessing the direct impact of these distributed energy resources. While it is noted that reactive power plays an important role in voltage regulation, its effects are not considered in this work to reduce model complexity. The role of reactive power will be investigated in future work, especially in scenarios including wind turbines. This setup provides a practical and scalable framework to test the proposed strategy’s effectiveness in managing real-time power distribution across a decentralized energy grid.
The modified IEEE 33 bus test network.
For the simulations in this study, solar irradiance data specific to Casablanca, Morocco, was utilized to reflect realistic conditions for the region. Casablanca, known for its diverse climate and variable irradiance levels across seasons, provided an ideal basis for analyzing the performance of a microgrid under different weather scenarios. The simulations were conducted in MATLAB on a computer equipped with an Intel Core i7 processor and 8 GB of RAM, with each simulation covering a full 24-hour period and a time step of 1 h. This setup allowed for detailed tracking of load demands and renewable energy (RE) output on a summer and a winter day, as illustrated in Figs. 4 and 5. Since 2017, electricity prices in Morocco have shown moderate fluctuations, ranging between 97.54 USD/MWh in 2022 and 108.48 USD/MWh in 2021. These price variations influence both the economic viability and optimization strategies for microgrid energy management. Table 2 provides a breakdown of energy costs across different customer categories, illustrating the cost structure within the Moroccan energy market. All technical, economic, and simulation parameters used in this study are comprehensively listed in Tables 3 and 4, offering a clear overview of the inputs driving the analysis and results.
Optimal power profiles for energy management with BESS – case 1.
Optimal power profiles for energy management with BESS – case 2.
The purchased and sold energy prices from and to the grid are represented in Fig. 6.
Purchased and sold energy prices from and to the grid.
To investigate the effectiveness of the model, the simulation is done for a typical day in summer and winter with three different scenarios:
Reference: no PV and BESS are integrated to the network (only the main grid supports the loads).
PV without BESS: only 4 PVs are integrated to the network.
PV with BESS: both PVs and BESSs are integrated to the network.
In terms of computation time, the runtime depends on many factors such as number of generations, population size, and problem size. In this study. The required average time to reach convergence was approximately 2–4 min per run. This demonstrates the computational feasibility of the approach for day-ahead planning.
In this case study, a typical summer day is selected to evaluate the results of the proposed algorithm for the PV systems with and without BESS, as shown in Figs. 7 and 4.
Optimal power profiles for energy management without BESS – case 1.
On a typical summer day and without grid-integrated BESS, the loads are supplied by the main grid in the morning and evening (from 6:00 p.m.) when there is no solar irradiance. The PVs begin to take it over from 11:00 a.m. From 12:00 p.m to 6:00 p.m, only PVs meet the electricity demand and excess energy is sold to the main grid.
When BESSs are integrated to the network, the grid import is always required in the early morning to meet the electricity demand. Once the irradiance starts to increase, the PV generation is used to meet demand, charge the battery systems and the surplus is exported to the main grid (4:00 p.m. − 7:00 p.m.). The amount of stored power in the battery systems is shown in Fig. 8.
BESSs stored power – case 1.
In this case, PV generation is higher and the main grid imports are lower. Furthermore, BESSs charge from the PV between hours 12:00 p.m.–6:00 p.m. and discharge at the peak grid hours (7:00 p.m.–10:00 p.m.).
Optimal power losses, voltage deviation and maximized revenues for the three scenarios are listed in Table 5.
Winter days are characterized by low solar irradiance, explaining the results shown in Figs. 9 and 5; Table 6. Without integrating BESSs into the network, the system yields results like those observed on summer days, albeit with greater reliance on the main grid and a reduction in the amount of energy sold back to it.
Optimal power profiles for energy management without BESS – case 2.
When BESSs are considered, they charge from the grid at low cost during early morning hours and discharge during peak hours, when electricity prices are higher. From 10:00 a.m. to 9:00 p.m., PV systems primarily supply the demand, with any excess energy sold back to the main grid. Additionally, the main grid supports demand at various times throughout the day, alongside PVs and BESSs, as on-site generation alone was insufficient to fully meet consumption needs (Fig. 10).
BESSs stored power – case 2.
In order to illustrate the performance of the proposed strategy, Table 7 summarizes the results obtained from the three scenarios: (i) reference, (ii) grid with integrated PV generation, and (iii) grid with both PV and BESS, for typical winter and summer days to highlight seasonal variations. Total average power losses, average voltage deviation, and the daily DNO profit are compared across scenarios.
The results of tables and figures above, for both cases, demonstrate that integrating PV and BESS into the distribution network reduces power losses effectively and improves voltage profiles throughout the day. While the BESS discharges during peak demand periods, decreasing consequently power losses and stabilizing voltages, voltage deviations are notably mitigated during peak solar generation hours.
In addition to technical improvements, economic ones are also achieved. Profits increased mainly during peak hours thanks to the ability of BESS, minimizing expensive grid imports and shifting loads.
Due to higher PV output, these improvements are more pronounced in summer and considered significant in winter as well. These results highlight the value of the coordinated operation of PV and BESS in enhancing overall system efficiency and reliability.
It is also noted that the storage systems are highly involved during peak hours after being recharged during the day, which optimizes all objective functions during this period. It can be said that the integration of storage systems into the network is cost-effective (compared to the system without storage).
While the proposed method demonstrates promising and efficient results, several limitations should be pointed. First, the assumption of power factor, for PV and BESS, doesn’t consider reactive power support, which may have an effect on voltage regulation accuracy. Second, the proposed model is tested for typical winter and summer days rather than a long-term analysis, which limit the stochastic variations. Moreover, the ability of the tested model to handle complex trade-offs was limited for only 3 objectives without testing it for more objectives. Future work will aim to study these limitations by considering reactive power control and extended time horizons.
This paper introduces an optimal planning and energy management approach for a microgrid (MG) system that considers diverse configurations of distributed energy resources (DERs). The strategy is designed to tackle three main objectives: minimizing power losses, reducing voltage deviations, and maximizing revenue for the Distribution Network Operator (DNO). Achieving this delicate balance requires sophisticated optimization, and to this end, the Strength Pareto Evolutionary Algorithm 2 (SPEA2) is applied as a robust multi-objective meta-heuristic. This algorithm effectively navigates complex, competing objectives to identify solutions that best fulfill the overall energy management goals. In this paper, SPEA2 demonstrates once again its efficiency and gives promising results in terms of optimization. For each time step, the model proposes the optimal energy mix that reduces losses in the system and increases the benefit of network operators A key focus of the study is the role of Battery Energy Storage Systems (BESS) within the MG. By integrating BESS, the strategy enhances the microgrid’s flexibility and efficiency. The effects of BESS on essential MG parameters, such as stability, efficiency, and financial return, were rigorously evaluated across both summer and winter case studies. The results underscore the added value of BESS integration: it not only increases revenue for the DNO by improving energy trading opportunities but also significantly reduces power losses and mitigates voltage deviation. This demonstrates the critical role that optimized DER configurations, combined with advanced energy storage solutions, play in modern microgrid management.
A comparative study of SPEA2 will be the subject of future work to evaluate its capability against other multi-objective algorithms in solving this optimization problem. The effectiveness of the model for scalable and larger networks in different climates will be also investigated and tested for more complex scenarios and longer-term operational performance.
The datasets used and/or analysed during the current study is available from Prof. Badre BOSSOUFI through badre.bossoufi@usmba.ac.ma.
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Acknowledgement: The authors extend their appreciation to the Deanship of Research and Graduate Studies at King Khalid University for funding this work through Large Group Project under grant number RGP. 2/510/46
SMARTILAB Laboratory, Moroccan School of Engineering Sciences (EMSI), Rabat, Morocco
Anas Aksbi & Safae Merzouk
Superior School of Technology in Khenifra, Sultan Moulay Slimane University, Beni Mellal, Morocco
Ismail Elkafazi
Engineering sciences laboratory Ensa, Ibn Tofail University, Kenitra, Morocco
Anas Aksbi & Rachid Bannari
Faculty of Science and Technic, Sultan Moulay Slimane University, Beni Mellal, Morocco
Abdelfettah Bannari
Laboratory of Engineering Modelling and Systems Analysis, Sidi Mohamed Ben Abdellah University, Fes, 30000, Morocco
Badre Bossoufi & Mourad Yessef
Electrical Engineering Department, Computer Engineering Section, College of Engineering, King Khalid University, Abha, 61421, Saudi Arabia
Salman Arafath Mohammed
College of Computer Science, King Khalid University, Abha, 61421, Saudi Arabia
Naim Ahmad
Department of Electrical Engineering, College of Engineering, King Khalid University, Abha, 61421, Saudi Arabia
Z. M. S. Elbarbary
Center for Engineering and Technology Innovations, King Khalid University, Abha, 61421, Saudi Arabia
Z. M. S. Elbarbary
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Conceptualization, A.K.; methodology, A.K.; software, A.K.; validation, A.K., B.B. and I.E.; formal analysis, R.B.; investigation, R.M.; resources, A.B., M.Y; data curation, I.E., S.A.M.; writing—original draft preparation, A.K., B.B.; writing—review and editing, Z.M.S.E., N, A.; visualization, B.M.; supervision, B.M., B.B; project administration, R.B., S.M.
Correspondence to Badre Bossoufi.
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Aksbi, A., Elkafazi, I., Bannari, R. et al. Optimum energy management of distribution networks with integrated decentralized PV-BES systems using SPEA2-based optimization approach. Sci Rep 15, 40482 (2025). https://doi.org/10.1038/s41598-025-24413-w
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