In recent years, 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 come . 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 landscape . Microgrids offer a powerful solution for generating electricity that is both resilient and eco-friendly, while also being cost-efficient. By harnessing local renewable energy sources and leveraging advanced control systems, microgrids can function autonomously or in tandem with the main 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 security 4]. Microgrids are flexible systems capable of operating either in connection with the main 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 needs . 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 grid . 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 landscape . 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 future . 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 future . 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 modes . 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 resilient 12]. Many researchers have focused on the design, planning, and optimization of hybrid microgrids, employing various optimization techniques. For instance, 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 as and aim to minimize the total costs and emissions of microgrids by determining the optimal configuration of Distributed Energy Resources (DERs), taking into account 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 contrast, and investigate the optimal allocation of energy storage within distribution systems. seeks to reduce system costs by enhancing voltage profiles, lowering line loading, and minimizing both active and reactive power losses. Meanwhile, 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 in . Additionally, 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 instance, optimizes the size and dispatch of Distributed Energy Resources (DERs) to lower CO₂ emissions, factoring in heat and cold storage. Similarly, presents an economic scheduling model for electricity and natural gas systems aimed at reducing CO₂ emissions, while explores cost minimization and emission reduction through DER optimization, taking into account utility rates, transportation constraints, and generator states. For industrial parks, proposes an optimal low-carbon economic dispatch model that incorporates real-time multi-energy price incentives, calculating monthly carbon emissions based on real-time monitoring and historical data. In , a Mixed Integer Quadratic Programming (MIQP) algorithm is introduced to optimize BESS capacity in grid-tied commercial microgrids with dispatchable generators and renewable energy sources (RES). Additionally, utilizes a hybrid multi-objective sensitivity analysis algorithm to optimize the sizes of PV and storage systems. In , the performance of the Grasshopper Optimization Algorithm (GOA) is compared to other optimization algorithms for DER size optimization in isolated microgrids. Lastly, 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, while 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 NEPLAN , deterministic methodologies that involve numerical and iterative techniques , and heuristic or metaheuristic optimization algorithms such as CS, GOA, and PSO . 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 evaluate 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 times to find an optimal solution .

In the literature, several metaheuristic algorithms have been developed and are extensively used to tackle microgrid-related problems. These methods are flexible and skilled at avoiding local optima, often providing better solutions than deterministic approaches . A thorough comparison of optimization methods presented in indicates that Particle Swarm Optimization (PSO) is among the most effective algorithms for microgrid planning. PSO excels at minimizing interruption costs, maximizing reliability, and exhibiting more stable convergence characteristics compared to other stochastic methods .

Extensive research has been conducted on grid-connected solar photovoltaic (PV) systems with battery integration to analyze and quantify the optimal advantages of deploying such systems at the customer level. Studies in the literature have examined various aspects of system-level optimization, including sizing, simulation and optimization of PV-battery systems focusing on self-consumption, Feed-in Tariff (FiT) incentives, wholesale electricity tariffs, and demand forecasting . While batteries have traditionally been utilized in standalone PV systems , there is a growing interest in integrating batteries into grid-connected PV systems, particularly under FiT and time-of-use tariffs . Despite the initially high installation costs, domestic solar PV systems have witnessed significant adoption rates, largely propelled by energy policies such as FiT schemes in Europe and other regions . Moreover, large-scale installations in the form of solar farms are becoming increasingly prevalent due to favorable energy policies . As per sources , integrating battery technology into energy systems characterized by high levels of fluctuating distributed energy resources offers a solution to mitigate against frequent interruptions resulting from specific electricity demand patterns or grid-connected distributed energy systems. A key concern in this domain is the rationale behind the necessity for battery storage within electricity networks. The escalating peak electricity demands in power systems, coupled with the proliferation of distributed energy resources, lead to a disparity between generation and demand, resulting in underutilization of generation, transmission, and distribution infrastructure . Leveraging battery storage alongside PV systems enables utility operators to optimize existing network capacity utilization and defer costly network investments. 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 in , the impact of active demand-side management and battery storage systems on self-consumption levels was investigated. The analysis highlighted the significance of the relationship between electricity energy flows and battery storage capacity as a critical decision variable in optimizing system performance. The optimization model described in is tailored for scenarios involving aggregated demand profiles, allowing aggregators to participate in the day-ahead market. In various other contexts, the minimization of costly demand charges (kVA charges) has been a primary motivation for the deployment of PV-battery systems, as highlighted in references . Exploring the disparity between flat retail electricity prices and FiT export tariffs for PV, investigated the potential value of deploying battery storage to maximize FiT revenue streams. This involved optimizing battery storage deployment to capitalize on periods of peak electricity prices for discharging and periods of lowest prices for charging. In , a Mixed-Integer Linear Programming (MILP) model was developed to manage and size residential heat pumps, aiming to maximize self-consumption of PV generation. The PV generation profile was generated based on irradiation data. Furthermore, presented a case study that utilized economic optimization of battery storage size to assist customers in selecting the most suitable battery storage technology for their specific requirements.

As a function of solar irradiance, temperature, efficiency coefficient of solar panel and many other parameters, the output produced photovoltaic power $P_{\mathit{PV},i}^t$ at time t and injected at bus i is described in equation (1).

$G^t$ is defined as the global solar irradiance at time t, $P_{\mathit{PVr}}$ 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 follows:

$P_{\mathit{BESS}}$ represents the nominal power of the storage system. ${\eta }_{\mathit{ch}},$ ${\eta }_{\mathit{dis}}$, $P_{\mathit{ch},i}^t$ and $P_{\mathit{dis},i}^t$ 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 $\mathit{\Delta t}$ is the time step.

The BESS power $P_{\mathit{BESS},i}^t$at each instant t and each bus I$$is then expressed as follows:

Industrial, residential, and commercial loads are considered in order to simulate the variation of the load. The load power $P_{\mathit{load}}^t$ 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 that aims to minimize hourly power losses and average voltage deviation and maximize Distribution Network Operator (DNO) revenues, as expressed in equations (5-7).

The objective function developed in this work includes three main functions, expressed below:

Minimize hourly power losses P^t_L:

Minimize average voltage deviation V^t_{D, average}:

Maximize DNO’s revenue R^t_DNO:

$I_{i,k}^{\mathrm{t}}\mathrm{ }$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.

$P_{\mathit{PV}}^t$, $P_{\mathit{ch}}^t$ and $P_{\mathit{dis}}^t$are respectively the total PV, charging and discharging BESS powers at time t, defined by:

$P_{\mathit{grid},\mathit{import}}^t$ and $P_{\mathit{grid},\mathit{export}}^t$ are respectively the imported and exported energy from and to the utility grid at time t and $C_{\mathit{import}}^t$ and $C_{\mathit{export}}^t$ are their corresponding costs. $C_{\mathit{load}}^t$ is the cost of the energy sold to costumers, $C_{\mathit{PV}}$ and $C_{\mathit{dis}}$ are the costs of energy purchased from PV and BESS respectively (to support the loads) and $C_{\mathit{ch}}$ 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).

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.

The proposed energy management strategy is implemented on a modified IEEE 33-bus distribution network, as depicted in Figure 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 study, 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. 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.

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 hour. This setup allowed for detailed tracking of load demands and renewable energy (RE) output on a summer and a winter day, as illustrated in Figures 6 and 9.

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 the following tables, offering a clear overview of the inputs driving the analysis and results.

The purchased and sold energy prices from and to the grid are represented in Figure 4.

In order to investigate the effectiveness of the model, the simulation is done for a typical day in summer and winter with three different scenarios:

1) Reference: no PV and BESS are integrated to the network (only the main grid supports the loads).

2) PV without BESS: only 4 PVs are integrated to the network.

3) PV with BESS: both PVs and BESSs are integrated to the network.

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 Figure 5 and Figure 6.

On a typical summer day without grid-integrated BESS, the main grid supplies the load during early morning and evening hours (from 6:00 p.m.) when solar irradiance is absent. PV systems begin contributing around 11:00 a.m., and from 12:00 p.m. to 6:00 p.m., they fully meet electricity demand, with any excess energy sold back to the grid.

When BESSs are integrated into the network, the main grid continues to supply power in the early morning to meet demand. As irradiance increases, PV generation covers the demand, charges the BESS, and exports surplus energy to the main grid (4:00 p.m. to 7:00 p.m.). The amount of stored energy in the BESS is illustrated in Figure 7. In this scenario, PV generation is higher, and main grid imports are lower. Additionally, BESS charges from PV production between 12:00 p.m. and 6:00 p.m., then discharges during peak grid hours (7:00 p.m. to 10:00 p.m.).

Optimal values for power losses, voltage deviation, and revenue maximization across the three scenarios are presented in Table 5.

Winter days are characterized by low solar irradiance, explaining the results shown in Figures 8 and 9 and Table 6. Without integrating BESSs into the network, the system yields results similar to 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.

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.

From the results of tables and figures above, it is 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).

This paper introduces an optimal planning and energy management approach for a microgrid (MG) system that takes into account 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.

The authors declare no conflicts of interest.