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This study focuses on improving power system grid performance and efficiency through the integration of distributed energy resources (DERs). The study proposes an artificial intelligence (AI) based effective approach for economic dispatch and load management for three linked microgrids (MGs) that operate in both grid-connected and autonomous modes. A day-ahead scheduling method is suggested to calculate the optimal set points for various energy sources in MGs considering various system constraints for safe operation. In addition, a load management approach that shifts the controllable loads from one interval to another is applied to reduce the operating cost of MG. To handle the optimization challenges of energy scheduling and load shifting such complexity and non-linearity, an advanced meta-heuristic method known as the one-to-one based optimizer (OOBO) is used. Overall, the paper proposes a viable and efficient methodology for economical distribution in linked microgrids, which takes advantage of renewable energy resources and incorporates scheduling optimization via the OOBO algorithm. The proposed energy management strategy enhances the system performance, increases energy efficiency, and reduces the daily operational cost by 1.6% for grid connected mode and by 0.47% for islanded operation mode.
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Extending the public electricity grid to rural or peri-urban areas is sometimes very costly and unprofitable due to their remoteness, low population density and sometimes difficult accessibility. In view of this, and in the concern of a sustainable development, the autonomous PV and/or wind power systems is increasingly used. However, these fluctuating source systems remain unreliable due especially to their intermittent nature, what justifies the integration of battery storage systems to them. They are also still expensive, particularly in the African context, limiting their access to the greatest number of the population. In addition to these problems of cost and reliability, the issue of optimal sizing of such systems is essential. In this paper, energy storage technologies, performance criteria, basic energy production and storage models, configuration types, sizing and management techniques discussed in the literature for the study of stand-alone solar and/or wind power systems in isolated sites are reviewed. The findings of the present study reveals that electrochemical battery is the main technology used for energy storage in stand-alone PV-wind systems due in particular to their maturity compared to the other storage technologies. However, it also shows that while batteries are the most widely used energy storage technology for solar and wind power systems, they are still expensive. The paper also revealed that traditional methods of optimal sizing and management of autonomous solar and wind power generation systems are being used less and less, in favor of artificial intelligence methods, due mainly to their limited flexibility and inability to solve complex problems.
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Interfacial solar evaporation (ISE) has emerged as a promising technology to alleviate global water scarcity via energy-efficient purification of both wastewater and seawater. While ISE was originally identified and developed during studies of simple double-layered two-dimensional (2D) evaporators, observed limitations in evaporation rate and functionality soon led to the development of three-dimensional (3D) evaporators, which is now recognized as one of the most pivotal milestones in the research field. 3D evaporators significantly enhance the evaporation rates beyond the theoretical limits of 2D evaporators. Furthermore, 3D evaporators could have multifaceted functionalities originating from various functional evaporation surfaces and 3D structures. This review summarizes recent advances in 3D evaporators, focusing on rational design, fabrication and energy nexus of 3D evaporators, and the derivative functions for improving solar evaporation performance and exploring novel applications. Future research prospects are also proposed based on the in-depth understanding of the fundamental aspects of 3D evaporators and the requirements for practical applications.
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The energy optimization in smart power grids (SPGs) is crucial for ensuring efficient, sustainable, and cost-effective energy management. However, the uncertainty and stochastic nature of distributed generations (DGs) and loads pose significant challenges to optimization models. In this study, we propose a novel optimization model that addresses these challenges by employing a probabilistic method to model the uncertain behavior of DGs and loads. Our model utilizes the multi-objective wind-driven optimization (MOWDO) technique with fuzzy mechanism to simultaneously address economic, environmental, and comfort concerns in SPGs. Unlike existing models, our approach incorporates a hybrid demand response (HDR), combining price-based and incentive-based DR to mitigate rebound peaks and ensure stable and efficient energy usage. The model also introduces battery energy storage systems (BESS) as environmentally friendly backup sources, reducing reliance on fossil fuels and promoting sustainability. We assess the developed model across various distinct configurations: optimizing operational costs and pollution emissions independently with/without DR, optimizing both operational costs and pollution emissions concurrently with/without DR, and optimizing operational costs, user comfort, and pollution emissions simultaneously with/without DR. The experimental findings reveal that the developed model performs better than the multi-objective bird swarm optimization (MOBSO) algorithm across metrics, including operational cost, user comfort, and pollution emissions.
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As environmental energy harvesting gains increasing importance in self-powered systems and large-scale energy demands, wind energy, as a clean, pollution-free, and renewable source, has garnered widespread attention. However, achieving efficient wind energy collection remains challenging. This study proposes a high-performance rotating structure triboelectric-electromagnetic hybrid nanogenerator designed for environmental wind energy harvesting. By optimizing the magnetic circuit design of the electromagnetic generator, the dispersed radial magnetic field is converted into a unified axial magnetic field, enabling efficient power generation with only a single annular coil, thereby simplifying the generator design and reducing manufacturing and maintenance costs. Additionally, a triboelectric nanogenerator design with soft contact friction between polycarbonate (PC) fur and fluorinated ethylene propylene (FEP) film was implemented, optimizing the spacing between the electrode and friction layers, thus enhancing output performance and device durability. Furthermore, we simulated and experimentally tested the output waveform of the designed hybrid generator structure, with the results showing a high degree of similarity, further validating the rationality of the device design and providing guidance for structural optimization. Subsequently, we achieved efficient energy storage using an energy management circuit (EMC). With the integration of the EMC, the generator successfully powered a Bluetooth temperature and humidity sensor at a wind speed of 10 m/s, achieving wireless transmission, and demonstrating its potential application in traffic signal systems and other natural environmental systems. This research provides an important reference for further exploration of novel wind energy harvesting technologies.
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This research proposes a day-ahead scheduling utilizing both demand side management (DSM), and Energy Management (EM) in a grid-tied nanogrid comprises of photovoltaic, battery, and diesel generator for optimizing the generation cost and the energy not supplied (at grid-outage). Wider terminology is introduced to combine both load controllability (considered in traditional DSM), and interval capability to accommodate additional loads defined as flexible, non-flexible, and semi-flexible intervals. Moreover, the user selection for EM or combined operation of EM with DSM at different degrees of interval flexibility is defined as user preference. In addition, three utility's operations are considered denoted as fixed rate pricing (FRP), time-of-use (ToU) pricing, and FRP with grid-outage. Hence, the suggested framework utilizes the opportunities of generation diversity, the electricity pricing strategy, and the load flexibility. The obtained result show that, DSM with flexible intervals reduces the cost by 21.02%, 25.23%, and 18.15% for FRP, ToU, and FRP with grid-outage scenarios respectively. And cost reduction by 20.41%, 22.42%, and 17.81% for DSM with semi-flexible intervals and 16.24%, 21.15%, and 13.8% for DSM with non-flexible intervals. This cost reduction is associated with full utilization of renewable energy generation and reduction of the energy from/to battery which enhances its lifetime or reduces the required battery size during design stage for cost and provisions saving in flexible and semi-flexible intervals. A hybrid optimization technique of Moth-flame optimization algorithm, and Lagrange's multiplier is proposed and confirms its effectiveness with detailed comparison with other techniques.
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This paper introduces the design and comprehensive performance evaluation of a novel Multi-Load and Multi-Source DC-DC converter tailored for electric vehicle (EV) power systems. The proposed converter integrates a primary battery power source with a secondary renewable energy source-specifically, solar energy-to enhance overall energy efficiency and reliability in EV applications. Unlike conventional multi-port converters that often suffer from cross-regulation issues and limited scalability, this converter ensures stable power distribution to various EV subsystems, including the motor, air conditioning unit, audio systems, and lighting. A key feature of the design is its ability to independently manage multiple power loads while maintaining isolated outputs, thus eliminating the inductor current imbalance that is common in traditional systems. Experimental validation using a 100 W prototype demonstrated the converter's ability to deliver stable 24 V and 48 V outputs from a 12 V input, with output voltage deviations kept within ± 1%, significantly improving upon the ± 5% deviations typically seen in existing converters. Furthermore, the system achieved an impressive 93% efficiency under variable load conditions. The modular nature of the converter makes it not only suitable for EV applications but also for a broader range of industries, including renewable energy systems and industrial power supplies. This paper concludes by discussing optimization strategies for future improvements and potential scaling of the technology for commercial use in sustainable energy applications.
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In contemporary society, commercial buildings, as a crucial component of urban development, face increasingly prominent energy consumption issues, posing significant challenges to the environment and sustainable development. Traditional energy management methods rely on empirical models and rule-based approaches, which suffer from low prediction accuracy and limited applicability. To address these issues, this study proposes a commercial building energy consumption prediction and energy-saving strategy model based on hybrid deep learning and optimization algorithms. This model integrates convolutional neural networks (CNN), gated recurrent units (GRU), and the clonal selection algorithm (CSA), aiming to enhance the accuracy and efficiency of energy consumption predictions. Experimental results demonstrate that the CNN-GRU-CSA Network (CGC-Net) model achieves mean absolute errors (MAE) of 17.12, 16.73, 16.62, and 15.94 on the Building Data Genome Project (BDGP), Commercial Building Energy Consumption Survey (CBECS), Nonresidential Building Energy Performance Benchmark (NEPB), and Building Energy Efficiency Benchmark (BEBDEE) datasets, respectively, significantly outperforming traditional methods and other models. Additionally, the model exhibits faster inference and training times. These results validate the stability and superiority of the CGC-Net model, providing an innovative solution and essential technical support for commercial building energy management.
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Hydrogen energy, due to its clean and efficient nature, has shown great potential during the current transition period in the shipbuilding industry. However, the application of hydrogen energy in ship energy systems is influenced by variations in operational load and the integration of new energy sources during actual navigation. To address these issues, this paper focuses on optimizing and scheduling the operation of ships under various navigation conditions, considering the distributed nature of hydrogen energy. System simulations were conducted to model the photovoltaic (PV), proton exchange membrane fuel cells (PEMFCs), lithium batteries (LIBs), electrolytic cells (ECs), and energy storage modules of yacht energy systems. Component boundaries and objective functions were set, and two cases (excess photovoltaic state and constant power state) were designed to optimize and regulate the energy balance of hydrogen-powered yachts, enhancing their comprehensive utilization of renewable energy. By comparing the changes in ship energy under the two cases, it was concluded that case 1 ensures the maximum utilization of renewable energy. When photovoltaic power generation is insufficient, the PEMFC and LIB in the system provide the required power to achieve a supply-demand balance. Moreover, when PV power generation is sufficient, hydrogen energy is used to store renewable energy. The optimization method designed in this study can, to some extent, maximize the application of renewable energy in new energy yachts, ensuring the efficiency of the comprehensive energy system of new energy yachts, reducing emissions, and improving the sustainability and economic efficiency of the ships.
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To satisfy the electricity needs of a village in Tangi, northwest Pakistan, the present research can design and evaluate the environmental and economical aspects of an optimal hybrid photovoltaic-biogas-hydropower-battery energy sustainable system (PV-BG-HP-BESS). This framework integrates various renewable energy sources, delivering a modern, efficient approach to sustainable energy solutions. The HOMER Pro software is utilized to optimize the most economical and effective hybrid energy system. The results showed that the proposed hybrid system comprising 91.4 kWp PV modules, 19.6 kW hydropower, a 50 kW biogas generator (BG), 36 batteries, and a 60.6 kW converter was the most economical choice. This system, which used the cyclic charging (CC) method, had a cost of energy (COE) of 0.0728 $/kWh and a total net present cost (NPC) of $152,242. The suggested hybrid energy system for rural areas of Pakistan includes photovoltaic (PV), biogas (BG), hydro, and battery components to provide a dependable and sustainable power supply. This system minimizes the need for expensive fossil fuels while simultaneously minimizing environmental impact by lowering pollutants and greenhouse gas emissions. The system's annual electricity production is 294,782 kWh, with PV leads at 59.4%, BG at 6.02%, and hydro at 34.6%, ensuring uninterrupted power generation even in remote areas. The unmet load, extra electricity, and capacity shortage illustrate the reliability of the system and make it possible to address rural electrification challenges while supporting sustainable development and economic growth. Moreover, the outcomes of the proposed hybrid system dominate the previous studies in multiple objectives, including cost and sensitivity analysis, when compared.
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The global transportation electrification commerce sector is now booming. Stakeholders are paying an increased attention to the integration of electric vehicles and electric buses into the transportation networks. As a result, there is an urgent need to invest in public charging infrastructure, particularly for fast charging facilities. Consequently, and to complete the portfolio of the green environment, these fast-charging stations (FCSs) are designed using 100% of renewable energy sources (RESs). Thus, this paper proposes an optimization model for the techno-economic assessment of FCSs comprising photovoltaic and wind turbines with various energy storage devices (ESDs). In this regard, the FCS performance is evaluated using flywheels and super capacitors due to their high-power density and charging/discharging cycles and rates. Then, optimal sizing of these distributed generators is attained considering diverse technical and economical key performance indicators. Afterwards, the problem gets more sophisticated by investigating the effect of RES's uncertainties on the selection criterion of the FCS's components, design and capacity. Eventually, as an effort dedicated to an online energy management approach, a deep learning methodology based on radial basis network (RBN) is implemented, validated, and carried out. In stark contrast to conventional optimization approaches, RBN demonstrates its superiority by obtaining the optimum solutions in a relatively short amount of time.
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The advent of multi-Microgrid (MG) energy systems necessitates the optimization of management strategies to curtail operational costs. This paper introduces an innovative MG energy management strategy that integrates Chaotic Local Search (CLS) with Particle Swarm Optimization (PSO) to fulfill this requirement. Our approach leverages PSO for extensive global exploration and subsequently employs CLS to refine local searches, thereby ensuring the attainment of optimal global outcomes. To further enhance performance, we have crafted a PSO algorithmic framework underpinned by chaotic local search principles, aimed at circumventing regions of local optima. The study presents a comprehensive MG energy system model that encompasses a photovoltaic generation unit, battery energy storage, and a micro gas turbine. The experimental data corroborates that our proposed algorithm secures optimal solutions within a range of 48.2-51.7, outperforming others in achieving these optimal resolutions. When juxtaposed with Scenario 1, there is a significant reduction in both operational and primary energy conversion costs by 24.22 % and 31.39 %, respectively. In comparison to Scenario 2, these figures are reduced by an additional 3.08 % and 6.05 %, respectively. The research findings underscore the strategy's exceptional performance in optimization tasks, as illustrated by the simulation outcomes. The methodology's application to a micro-energy network substantiates its practical relevance. Collectively, this research offers a holistic solution for the optimization of MG energy systems, effectively merging theoretical progress with tangible practical applications.
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The need to incorporate renewable energy generators (REGs) into the electrical grid has become increasingly crucial due to the push for a more sustainable environment. This study advocates an innovative strategy for optimizing inertia-integrated generation and transmission expansion planning (GTEP) to implement feed-in tariffs (FiT). The application of the GAMS CPLEX solver to the model, which tested on an IEEE 6/IEEE 16 system, reveals that using FiT results in a 12.1 % drop in system cost ($599 million to $526 million) and a 7.91 % rise in total system inertia. Sensitivity analysis highlights the correlation between increased REG integration and FiT payment reduction at 50 % penetration. The model outperforms soft computing optimization techniques, showcasing rapid convergence and computational efficiency. The proposed model's validated superiority in rapid convergence and computational efficiency is demonstrated by comparing its results with those obtained from other soft computing optimization techniques.
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Microgrids offer an optimistic solution for delivering electricity to remote regions and incorporating renewable energy into existing power systems. However, the energy balance between generation and consumption remains a significant challenge in microgrid setups. This research presents an adaptive energy management approach for grid-interactive microgrids. The DC microgrid is established by combining solar PV with a battery-supercapacitor (SC) hybrid energy storage system (HESS). The proposed approach integrates the frequency separation strategy with a rule-based algorithm to ensure optimal power sharing among sources while maintaining the safe operation of storage units. Specifically, the battery meets steady-state energy demands, the SC addresses transient power requirements, and the grid support is tailored to system needs. The method employs the dq reference frame technique to control the grid inverter (VSC). The key merits include efficient power allocation, fast regulation of the DC link voltage irrespective of load or generation variations, seamless transition between scenarios, and introduction of a straightforward battery state of charge (SOC)-based coefficient for allocating power between the battery and the grid while enhancing the power quality within the grid. Moreover, safety measures prevent the SC from overcharging, the battery from high current, overcharging, and deep discharging, potentially extending their lifespan. Validation and implementation of the method are conducted using MATLAB/Simulink.
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Background. People with kidney failure who undergo hemodialysis treatment and experience chronic fatigue identify negative effects on occupational performance and participation as a key aspect of their illness experience. Purpose. To describe the occupational performance and participation problems of people treated with hemodialysis who live with debilitating fatigue. Method. Fifteen participants, who were randomized to participate in an energy management intervention as part of a randomized controlled trial, completed two occupation-based assessments at baseline and chose three priority occupational performance or participation problems to address as goals during the intervention. Results were analyzed using descriptive statistics (counts and percentages). Findings. Fifteen participants (mean age 60, 53% male) completed the occupation-based assessments. Participants stated that they wanted or needed more energy for a median of 22 of 55 occupations. Going out for food/drinks (n = 11), going to a movie/concert/performance (n = 10), and food preparation/clean-up (n = 10) were the top occupations for which participants required more energy. Prioritized occupational performance and participation problems most often fell within the household management (14 goals), self-care (6 goals), and hobbies (5 goals) domains. Conclusion. Occupational performance and participation problems are extensive among people treated with hemodialysis who live with debilitating fatigue. There is a clear need for occupation-based interventions that optimize occupational performance and participation in this population.
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Solar desalination is a promising solution for alleviating water scarcity due to its low-cost, environmentally friendly, and off-grid capabilities. However, simultaneous salt rejection and heat localization remain challenging, as the rapid salt convection often results in considerable heat loss. Herein, this challenge is overcome via a facile design: i) isolating high-temperature and high-salt zones by rationally designing morning glory-shaped wick structures and ii) bridging high-salt zones and bulk water with low-tortuosity macrochannels across low-temperature surfaces. The salinity gradient in the macrochannels passively triggers convective flow, facilitating the rapid transfer of salt ions from the high-salt zone to the bulk water. Meanwhile, the macrochannels are spatially isolated from the high-temperature zone, preventing heat loss during salt convection and thereby achieving a high evaporation rate (≈3 kg m-2 h-1) and superior salt rejection even in highly concentrated real seawater. This work provides new insights into salt rejection strategies and advances practical applications for sustainable seawater desalination.
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The growing integration of renewable energy sources into grid-connected microgrids has created new challenges in power generation forecasting and energy management. This paper explores the use of advanced machine learning algorithms, specifically Support Vector Regression (SVR), to enhance the efficiency and reliability of these systems. The proposed SVR algorithm leverages comprehensive historical energy production data, detailed weather patterns, and dynamic grid conditions to accurately forecast power generation. Our model demonstrated significantly lower error metrics compared to traditional linear regression models, achieving a Mean Squared Error of 2.002 for solar PV and 3.059 for wind power forecasting. The Mean Absolute Error was reduced to 0.547 for solar PV and 0.825 for wind scenarios, and the Root Mean Squared Error (RMSE) was 1.415 for solar PV and 1.749 for wind power, showcasing the model's superior accuracy. Enhanced predictive accuracy directly contributes to optimized resource allocation, enabling more precise control of energy generation schedules and reducing the reliance on external power sources. The application of our SVR model resulted in an 8.4% reduction in overall operating costs, highlighting its effectiveness in improving energy management efficiency. Furthermore, the system's ability to predict fluctuations in energy output allowed for adaptive real-time energy management, reducing grid stress and enhancing system stability. This approach led to a 10% improvement in the balance between supply and demand, a 15% reduction in peak load demand, and a 12% increase in the utilization of renewable energy sources. Our approach enhances grid stability by better balancing supply and demand, mitigating the variability and intermittency of renewable energy sources. These advancements promote a more sustainable integration of renewable energy into the microgrid, contributing to a cleaner, more resilient, and efficient energy infrastructure. The findings of this research provide valuable insights into the development of intelligent energy systems capable of adapting to changing conditions, paving the way for future innovations in energy management. Additionally, this work underscores the potential of machine learning to revolutionize energy management practices by providing more accurate, reliable, and cost-effective solutions for integrating renewable energy into existing grid infrastructures.
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Given the complex powertrain of fuel cell electric vehicles (FCEVs) and diversified vehicle platooning synergy constraints, a control strategy that simultaneously considers inter-vehicle synergy control and energy economy is one of the key technologies to improve transportation efficiency and release the energy-saving potential of platooning vehicles. In this paper, an energy-oriented hybrid cooperative adaptive cruise control (eHCACC) strategy is proposed for an FCEV platoon, aiming to enhance energy-saving potential while ensuring stable car-following performance. The eHCACC employs a hybrid cooperative control architecture, consisting of a top-level centralized controller (TCC) and bottom-level distributed controllers (BDCs). The TCC integrates an eco-driving CACC (eCACC) strategy based on the minimum principle and random forest, which generates optimal reference velocity datasets by aligning the comprehensive control objectives of the platoon and addressing the car-following performance and economic efficiency of the platoon. Concurrently, to further unleash energy-saving potential, the BDCs utilize the equivalent consumption minimization strategy (ECMS) to determine optimal powertrain control inputs by combining the reference datasets with detailed optimization information and system states of the powertrain components. A series of simulation evaluations highlight the improved car-following stability and energy efficiency of the FCEV platoon.
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Researchers are increasingly focusing on renewable energy due to its high reliability, energy independence, efficiency, and environmental benefits. This paper introduces a novel multi-objective framework for the short-term scheduling of microgrids (MGs), which addresses the conflicting objectives of minimizing operating expenses and reducing pollution emissions. The core contribution is the development of the Chaotic Self-Adaptive Sine Cosine Algorithm (CSASCA). This algorithm generates Pareto optimal solutions simultaneously, effectively balancing cost reduction and emission mitigation. The problem is formulated as a complex multi-objective optimization task with goals of cost reduction and environmental protection. To enhance decision-making within the algorithm, fuzzy logic is incorporated. The performance of CSASCA is evaluated across three scenarios: (1) PV and wind units operating at full power, (2) all units operating within specified limits with unrestricted utility power exchange, and (3) microgrid operation using only non-zero-emission energy sources. This third scenario highlights the algorithm's efficacy in a challenging context not covered in prior research. Simulation results from these scenarios are compared with traditional Sine Cosine Algorithm (SCA) and other recent optimization methods using three test examples. The innovation of CSASCA lies in its chaotic self-adaptive mechanisms, which significantly enhance optimization performance. The integration of these mechanisms results in superior solutions for operation cost, emissions, and execution time. Specifically, CSASCA achieves optimal values of 590.45 ct for cost and 337.28 kg for emissions in the first scenario, 98.203 ct for cost and 406.204 kg for emissions in the second scenario, and 95.38 ct for cost and 982.173 kg for emissions in the third scenario. Overall, CSASCA outperforms traditional SCA by offering enhanced exploration, improved convergence, effective constraint handling, and reduced parameter sensitivity, making it a powerful tool for solving multi-objective optimization problems like microgrid scheduling.
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The use of plug-in hybrid electric vehicles (PHEVs) provides a way to address energy and environmental issues. Integrating a large number of PHEVs with advanced control and storage capabilities can enhance the flexibility of the distribution grid. This study proposes an innovative energy management strategy (EMS) using an Iterative map-based self-adaptive crystal structure algorithm (SaCryStAl) specifically designed for microgrids with renewable energy sources (RESs) and PHEVs. The goal is to optimize multi-objective scheduling for a microgrid with wind turbines, micro-turbines, fuel cells, solar photovoltaic systems, and batteries to balance power and store excess energy. The aim is to minimize microgrid operating costs while considering environmental impacts. The optimization problem is framed as a multi-objective problem with nonlinear constraints, using fuzzy logic to aid decision-making. In the first scenario, the microgrid is optimized with all RESs installed within predetermined boundaries, in addition to grid connection. In the second scenario, the microgrid operates with a wind turbine at rated power. The third case study involves integrating plug-in hybrid electric vehicles (PHEVs) into the microgrid in three charging modes: coordinated, smart, and uncoordinated, utilizing standard and rated RES power. The SaCryStAl algorithm showed superior performance in operation cost, emissions, and execution time compared to traditional CryStAl and other recent optimization methods. The proposed SaCryStAl algorithm achieved optimal solutions in the first scenario for cost and emissions at 177.29 ct and 469.92 kg, respectively, within a reasonable time frame. In the second scenario, it yielded optimal cost and emissions values of 112.02 ct and 196.15 kg, respectively. Lastly, in the third scenario, the SaCryStAl algorithm achieves optimal cost values of 319.9301 ct, 160.9827 ct and 128.2815 ct for uncoordinated charging, coordinated charging and smart charging modes respectively. Optimization results reveal that the proposed SaCryStAl outperformed other evolutionary optimization algorithms, such as differential evolution, CryStAl, Grey Wolf Optimizer, particle swarm optimization, and genetic algorithm, as confirmed through test cases.