Comparative Analysis of Energy Storage Technologies for Microgrids

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Introduction
Energy storage systems (ESSs) stock electricity when there is a surplus of electricity, or when electricity rates are low, and provide the stocked electricity to the unit when electricity is in high demand or prices are high.Terefore, for the successful functioning of power facilities, the algorithm development of an energy management system (EMS) is mandatory.Battery specifcations and EMS design sizing have been thoroughly studied, as the battery represents a major part of the project cost when designing EMSs [1].Such battery choice and control are important, as aging problems caused by improper battery management account for a large part of the total replacement budget.With the development of new sources of renewable energy [2][3][4][5], microgrids (MGs) and optimization techniques related to these areas have appeared.An MG [6][7][8] can be defned as an isolated or connected network that can produce electrical energy from diferent hybrid sources and deliver or store it in an electrical ESS [9][10][11].Several studies have already been carried out to develop the productivity of this type of network through the development of maximum power point tracking (MPPT) algorithms [12][13][14].Te development of these technologies requires a low ESS compatible with this type of network in terms of lifetime costs, response time, and the amount of energy produced [15][16][17].Tere are several studies that have worked on the behavior and mode of operation of batteries, with electrical and physical modeling citing or demonstrating models of equivalent circuits of Liion batteries, while including mathematical equations characterizing their operational behavior.Similar research can be found with other types of batteries, such as lead-acid and nickel-cadmium [18][19][20][21].Other studies have highlighted a comparative study between the diferent battery technologies applied in this feld and technical-commercial studies [22].Tese studies focused on investment costs, life span, and price of units and neglected the specifc needs of MGs in terms of response time, recharge time, and operational safety.A comparison between the nature of batteries, their chemical compositions, and their manufacturing technology [23,24] helps understand such a technology using chemical equations, materials layers, energy density, etc.However, each study focused only on one type of batteries.With the appearance of new concepts such as smart grids, MGs, battery ESSs (BESSs), and systems of network management [25,26], it is required to operate the ESS in terms of density of energy compatibility with networks.In addition, some studies have compared the BEES applied in MGs, showing the operating behavior of certain types of batteries in MGs in terms of commercial technologies, chemical compositions, physical modeling, etc.However, there is a lack of results in terms of comparison between diferent charging technologies as regards climatic conditions, fast charging, and storage.Te objective of this work is to investigate the impact of ambient temperature on the behavior of lithium-ion, lead-acid, and supercapacitor batteries in terms of state of charge (SOC) and response time as a function of power value.Tis work aims to fll this research gap by studying the behavior of diferent types of batteries under varying ambient temperature and power levels.

Presentation of the Used Approach
Several research studies have been conducted on energy storage systems on both technology and technical characteristics or on energy management systems and algorithms, such as MPPT or BMS for ESSs, without considering the diferent batteries used in MGs and their conditions and requirements.
Tis work presents the modeling of the diferent types of ESSs for MGs (Li-ion, lead-acid, nickel-cadmium, nickelmetal hybrid, and supercapacitor).Tis modeling starts by physical-electrical modeling for the diferent batteries studied.Ten, a study of the recharging behavior with various levels of low/high current will make an analogy of fast recharge systems.Tis technology has become a scientifc research feld, where the recharging time became a key factor for system reliability.On the other hand, we validate the comparative study by applying a BMS system to observe the charging behavior and its efect on the SOC for each type.Moreover, the efects of the external conditions on the mode of operation of BESSs, such as the ambient conditions, the SOC, and the response time, have been studied.
Figure 1 shows a comparative study of the charging and discharging response time for fast-charging techniques and the efect of elevated temperature on battery operations, which is critical for understanding battery performance under diferent conditions.Charge and discharge rates can have a signifcant impact on battery performance.Rapid charging and discharging can increase the internal resistance of the battery, reduce its capacity, and shorten its life.Terefore, it is critical to evaluate the response time of rapidcharging techniques to determine their impact on battery performance.In addition, a high temperature can have a signifcant impact on battery performance.Heat can increase the internal resistance of the battery, reduce its capacity, and increase the rate of chemical reactions, which accelerates its aging.Terefore, it is essential to study the efect of elevated temperature on battery operations to determine the optimal operating temperature range.A comparative study of these factors can help to identify the most efcient and reliable battery technologies for various applications.For example, batteries used in electric vehicles require fast charge and discharge rates, but the efect of a high temperature on battery operations can be a limiting factor.Terefore, a comparative study can help to determine the optimal battery technology for that application.

BESS Modeling
Tere are many available battery designs developed by scientists with various intricacies to address battery performance for particular goals, e.g., battery design, performance estimation, and circuit simulation.Tree main groups can be distinguished: electrochemical, mathematical, and electric models [27].In order to better understand the operation mode of each type of ESSs, it is necessary to go through the physical/electrical modeling stage, which describes all the variables and characteristic parameters of diferent battery models.Te variation in these parameters has an infuence on the operation mode.Tis part of the work focuses on the physical modeling of the battery types already mentioned in the previous section.

Lead-Acid Battery Model.
Te modeling of lead-acid batteries as a complete system is based on the electrochemical ESS.However, due to the nonlinearities, interconnected reaction, and relationships involved, this approach requires signifcant computational power to simulate the entire system in detail [28].Tevenin's model, shown in Figure 2, provides a simplifed representation of the lead-acid battery behavior in an electrical circuit.Tis model represents the battery as a voltage source in series 2 International Transactions on Electrical Energy Systems with an internal resistance.Te voltage source represents the battery's open-circuit voltage, which is the voltage measured when the battery is not being discharged.Te internal resistance represents the resistance that the electric current encounters as it passes through the electrolyte and plates of the battery.Te Tevenin model is useful for simulating and optimizing the battery performance under various conditions.By using this model, engineers and researchers can design BMS, predict battery life, and optimize battery performance.In summary, Tevenin's model is a simplifed electrical model used to represent the behavior of a lead-acid battery in an electrical circuit, representing the battery as a voltage source in series with an internal resistance, which is useful for simulating and optimizing the battery's performance under diferent conditions.Tevenin's model of a lead-acid battery can be represented by the following equation: where V is the battery voltage, E is the open-circuit voltage of the battery, I is the current fowing through the battery, and R i is the internal resistance of the battery.Te internal resistance of the battery can be expressed as where R o is the resistance when the battery is fully charged, K c is the capacity coefcient, and SOC is the state of charge of the battery.Te capacity coefcient can be expressed as where K 1 , K 2 , and K 3 are empirical constants that depend on the battery chemistry and construction.Te SOC of the battery is a critical factor in determining the internal resistance and voltage of the battery.Te calculation of the SOC should be as precise as possible.Te SOC of the battery can be determined as the ratio of the amp-hours left in the battery to the total amp-hours of the battery, as shown in the following equation [30,31]: Te ampere hour discharged is given by equation ( 5), while the main reaction current in the battery (I mr ) and the ampere hour discharged at the start of the process are, respectively, given by equations ( 6) and ( 7): Te typical gravity of the battery is very important for the internal or open-circuit voltage.It is calculated through Te gassing efect causes a loss of energy in the battery.Te gassing current under a load status is given by Te internal resistance during charging and discharging operations is a result of the SOC, the type of the electrolyte, and the electrodes.It is given by where Te Tevenin model of lead-acid has, however, some disadvantages, such as not considering the battery's nonlinear behavior and the dependency of its internal resistance on SOC and temperature.In contrast, the RC model of the lead-acid battery considers the battery's nonlinear behavior  3 shows the equivalent circuit of the RC model, which includes two RC branches.
Te model is composed of a voltage source in series with an internal resistance and a capacitor.In a more advanced version of the model, there are two RC branches [32][33][34].Te voltage source represents the battery's opencircuit voltage, while the internal resistance represents the resistance that the electric current encounters as it passes through the electrolyte and plates of the battery.Te two RC branches represent the charge transfer resistance and difusion resistance within the battery, respectively.
Te mathematical equations for the two-branch RC model of a lead-acid battery are as follows.
Te voltage across the battery terminals at time t is given by Te charge stored in the frst RC branch at time t is given by Te voltage across the second RC branch at time t is given by the following equation: V 1 is the voltage across the frst RC branch given at time t by where: Te charge Q stored in the frst RC branch is related to voltage V 1 by the following equation: 3.2.Li-Ion Battery.Due to the increasing use and continuous technological improvement in Li-ion batteries, the battery design is a valuable tool for various research and product development tasks.Studies such as battery designs can be categorized into electrochemical and equivalent circuit designs [35].Te mathematical relation of the cells of a lithium-ion battery to their V-I property, the SOC, the internal resistance, the duty cycle, and the self-discharge is represented in a lithium-ion battery model.Te equivalent circuit design of a lithium-ion battery is a design performance model that uses one or more parallel combinations of resistance, capacitance, and other circuit components to build an electrical circuit in order to reproduce the dynamic characteristics of Li-ion batteries.Equation (18) states that the terminal voltage v is instantaneously proportional to the open-circuit voltage V oc [35,36]: Te SOC of a cell is 100% when the cell is completely charged, and the SOC is 0% when the cell is completely discharged.Te quantity of charge dropping from 100% to 0% is the full capacity measured in Ah or mAh. Figure 4 Voc  A fully charged battery has a much greater open-circuit voltage than a discharged battery.Te design of R int seems quite straightforward, but it overlooks the variable character of the internal resistance related to the temperature, the SOC, and the electrolyte concentration.Figure 3 depicts the circuit schematic of Tevenin's resistive battery design.Tis design has two kinds of internal resistances, R 0 and R 1 , which are, respectively, related to the charge and discharge characteristics of the battery.Te electrical and nonelectrical leakage losses are modeled by the internal resistance R 0 and R 1 .Te scattering voltages can also be precisely derived using one or more parallel RC branches.Tis method gives better results than the R int method, but transient states such as the efect of capacitance are not taken into consideration.Terefore, this model is nondynamic and not suitable for applications involving electrical vehicles and hybrid electrical vehicles.In a relaxation mode, the voltage progressively decreases to zero, which is called the difusion voltage that can be accurately approximated using parallel RC branches: Figure 5 presents a precise design of an electric battery, modeling of the battery capacity, the SOC, and the operating time using a capacitor and a current-controlled source.Te circuit considers battery life as well as its slow and fast transient responses.A voltage-controlled source as a function of SOC is used to break the barrier between SOC and V oc .
3.3.Supercapacitor.Supercapacitors, situated in the midhierarchy of energy storage units, have some key advantages that make them essential for applications that need highpower delivery in a small amount of time.Determining the suitability of strategies for the use of these devices involves understanding the characteristics of the supercapacitor under diferent loads and its control [37].Te double-layer capacitor is a physical device that has not only a required capacitance but also an inevitable parasitic inductance thanks to its physical geometry.It also has a series resistance caused by the ohmic resistance of the electronic and ionic conductors, as well as a parallel resistance caused by the leakage current between the electrodes.On the other hand, it can be modeled by an RC branch, where the capacitor is represented by the capacitance C, the series resistance by R S , and the parallel resistance by R p .Te RC circuit equation [38][39][40] is given by where V is the voltage across the supercapacitor, Q is the charge stored in the capacitor, and I Leak is the leakage current.Te voltage response of the RC model for a supercapacitor can be described by the following equation: where V(t) is the voltage across the supercapacitor at time t, V 0 is the initial voltage, R eq is the equivalent resistance of the supercapacitor (Rs + Rp), and C eq is the equivalent capacitance of the supercapacitor.Equation (21) shows that the voltage across the supercapacitor exponentially decays with time, with a time constant given by the product of R eq and C eq .Te value of R eq and C eq can be determined experimentally or through modeling and simulation.However, in real cases, we cannot represent a supercapacitor solely from an RC assembly.In certain situations, it is not sufcient to simulate a real supercapacitor only by International Transactions on Electrical Energy Systems one of the RC models discussed above.Te designs listed previously can be extended to a more generic model.Te number of branches can be optimally extended to infnity.In addition, the supercapacitor has an inductance efect that must also be modeled, particularly at higher operating frequencies.Finally, the leaking current efect has been ignored in previous designs.Figure 6 shows a typical RC circuit design with parallel shunting.In this fgure, resistor R p stands for the leakage current losses, and the series inductance L gives the high-frequency inductance efect.Te equivalent impedance (Z eq ) of the RC model of a supercapacitor can be calculated using the following equation: where R is the series resistance, C is the capacitance of the supercapacitor, ω is the angular frequency of the AC signal, and j is the imaginary unit.Te frst term R represents the ohmic resistance of the supercapacitor, whereas the second term 1/(jCω) represents the capacitive reactance.Te impedance of the supercapacitor is frequency-dependent, decreasing as the frequency increases due to the decrease in the capacitive reactance.
To obtain high power, it is absolutely necessary to have a low ESR.Te parallel resistance Rp only has a visible efect at very low frequencies (below the millihertz range).It is responsible for the self-discharge time of the capacitor.Its value must be as high as possible to limit the leakage current.Te self-discharge time constant t is equal to τ � C × Rp.

Nickel-Metal Hybrid and Ni-Cd Battery Models.
Ni-Mh and Ni-Cd are the type of reloadable batteries, whose chemical reaction is the same [41].Te only diference between these two batteries is that the capacity of Ni-Mh is 2 or 3 times as big as that of Ni-Cd.Te electrical modeling of Ni-Mh is like that of Ni-Cd, derived by Notten and based on [42].

Results and Discussion
Tis part of the work highlights the efect of changing the supply current of BESSs and their efect on the charging/ discharging behavior, where it focuses on the change of the SOC of each type of energy storage system.Tis indicates by analogy of the system response time, where the latter sets a key factor in the design of the MG.Tis is because some users require a very fast response time for the charging and discharging phases.Furthermore, this kind of simulation ofers the opportunity to observe two vital parameters for all ESS types, which are depth of charge (DOC) and depth of discharge (DOD).Tese two factors have a relation to the life span of the batteries and their operational status.Te cycling conditions, such as the number of frequent discharging/ charging events and the charging/discharging rates, have a great impact on the battery lifetime [43].In the second part, the results of the use of BMS are presented and discussed.Te BMS is essential to ensure the safe and reliable operation of the batteries [44] and for the implementation of the ESS in the system.An in-depth review of the years 2006 to 2020 is performed in the area of BMSs.Several functions, advantages, and disadvantages of the approaches used in the BMS for cell equilibration, thermal control, battery overvoltage and overcurrent protection, state-of-health estimation, and battery SOC estimation are discussed.In addition, some critical defciencies are identifed, and a framework for the design of an efective BMS is suggested.Te implementation of smart technologies, such as a digital twin of a battery, cyber-physical systems, battery swap technologies, nondestructive testing, self-reconfgurable batteries, and prudent recycling/reuse through automation are also addressed.In summary, critical gaps, advanced technologies, and the framework that researchers can use to build complete systems including advanced BMSs, real-time battery monitoring, and battery reuse and recycling as a complete 6 International Transactions on Electrical Energy Systems unit are presented [45].In the last part of simulation, the work is directed towards the efect of an external factor which has a great infuence on the mode and working behavior of the BESS, which is the ambient temperature.Tis factor has an impact on battery aging.

BESS Charging/Discharging
Behavior.In this section, we compare the response time of the studied BEESs with identical dimensions.Tese systems have a capacity of 48 Ah and 12 V for batteries and 500 Farad and 48 V for the supercapacitor and are subjected to a variable continuous current.Te charge/discharge response time of each type of BEES is simulated using MATLAB/Simulink software.
From Figures 8 and 9, it is shown that Li-ion batteries and SCs have the fastest charging time compared to other BEESs.For instance, at t � 90 s, the SOC of Li-ion batteries is approximately 12%, and they have a steeper recharge slope than the other BEESs.Te closest candidate is lead-acid batteries, with an SOC of approximately 10% under the same conditions and period.However, Ni-Mh and Ni-Cd have an SOC of less than 10% at this instant.Terefore, for fast charging, Li-ion batteries are the preferred choice.However, if we consider the speed of recharging with energy density, Li-ion victory is uncertain.Under the same simulation conditions, at t � 90 s, the supercapacitor with a capacity of 500F reaches almost 80% of the SOC (see Figure 9), with a signifcant slope.Terefore, to design an energy storage system with a rapid response to recharging and high-energy density, we must use a combination of Li-ion batteries and SCs.
Figures 10 and 11 present the response time of the diferent BESSs and the supercapacitor under variable loads.At t � 70 s, the discharge phase ends as the SOC of Li-ion reaches approximately ±94%, the SOC of lead-acid reaches approximately ±95%, and the SOC of Ni-Cd reaches 95%.Indeed, both the SOC of Ni-Mh and the SOC of the supercapacitor are below 60%.Based on these results, the combination of Li-ion batteries and SCs is validated as the optimal choice, as previously discussed.
Te charging and discharging of an ESS can be represented by a charge/discharge curve, as shown in Figure 12.Fast charging techniques may lead to variations in the charge/discharge curve of diferent types of batteries, such as Li-ion, lead-acid, Ni-Cd, Ni-Mh, and supercapacitors, due to diferences in their chemistry, construction, and operating conditions.Te depth of charge and discharge and the response time are crucial factors that impact battery performance.Te depth of charge refers to the amount of energy that can be stored in the battery, while the depth of discharge refers to the amount of energy that can be released.Te response time is the duration required for the battery to reach its complete SOC or state of discharge, infuenced by factors such as the charging/discharging rate, temperature, and battery health.Te ESS charging/discharging curve is an essential tool for assessing the performance of diferent batteries and supercapacitors.When utilizing fast-charging techniques, it is vital to consider the depth of charge and discharge, the response time, and the potential impacts on the battery performance and life span.

Mathematical Modeling and Simulation of Battery Faults in Energy Storage
Systems.Te use of failure models in battery simulation research ofers many advantages.By incorporating realistic failure conditions, these models enable more accurate and representative simulations of battery behavior.Researchers can assess battery performance under various failure scenarios, such as capacity decay or increased internal resistance, providing valuable information on the impact of failures.Failure simulations help diagnose specifc failure patterns and can be used to optimize battery design for improved fault tolerance and safety.Running simulations with failure models is cost-efective and accelerates research progress by efectively exploring multiple failure scenarios.In addition, robust failure models prepare researchers to meet future challenges in battery technologies, contributing to the development of reliable and efcient energy storage solutions for a variety of applications.
In this section, we present mathematical models for diferent battery types, including Li-ion, lead-acid, supercapacitor, Ni-Cd, and Ni-Mh batteries.Tese models account for the behavior of faulty batteries under various conditions, such as capacity decay and increased internal resistance.Te mathematical equations describe the response of battery voltage over time, taking into account the specifc characteristics and parameters of each battery type.By integrating these failure models into a simulation International Transactions on Electrical Energy Systems framework, we can simulate and analyze the performance of faulty batteries in energy storage systems.Te simulation framework provides a powerful tool for assessing the impact of battery failures on system performance, such as voltage degradation, power output reduction, and energy efciency.It enables us to evaluate the efectiveness of diferent fault mitigation strategies and optimize the operation of energy storage systems in the presence of faulty batteries.By performing simulations under various operating conditions and failure scenarios, we can better understand the behavior of faulty batteries and make informed decisions regarding battery management and system design.Overall, this section presents a comprehensive approach to the mathematical modeling and simulation of battery faults in energy storage systems.It highlights the importance of accurately representing battery faults in simulations in order to assess their impact on system performance and guide the development of robust and reliable energy storage systems.Te results of these simulations can inform the design and optimization of battery management strategies,  International Transactions on Electrical Energy Systems helping to improve the performance and longevity of energy storage systems in a variety of applications.
(1) Capacity fade (Li-ion battery) [46,47]: (i) Te efective capacity C eff of the battery can be modeled as a decreasing function over time or cycles, such as where C_max is the initial maximum capacity and k is a degradation rate constant.
(2) Internal resistance increase (Li-ion battery) [48,49]: (i) Te internal resistance (R int (t)) of the battery can be modeled as an increasing function over time or cycles, such as where R initial is the initial internal resistance and k is a degradation rate constant.
(3) Sulfation (lead-acid battery) [50][51][52]: (i) Te efective capacity (C eff ) of the battery can be modeled as a decreasing function due to sulfation, such as where C_max is the initial maximum capacity and k is a degradation rate constant.
(5) Capacitance loss (supercapacitor) [55,56]: (i) Te efective capacitance (C eff ) of the supercapacitor can be modeled as a decreasing function over time or cycles, such as where C_initial is the initial capacitance and k is a degradation rate constant.
(6) Increased equivalent series resistance (ESR) (supercapacitor) [57,58]: (i) Te equivalent series resistance (ESR) of the supercapacitor can be modeled as an increasing function over time or cycles, such as where ESR_initial is the initial ESR and k is a degradation rate constant.

International Transactions on Electrical Energy Systems
Increased internal resistance fault model: Let V_nominal be the nominal voltage of the Ni-Mh battery (e.g., V_nominal � 1.2 V per cell).Let R_int_nominal be the nominal internal resistance of the Ni-Mh battery (e.g., R_int_nominal � 0.01 ohms).Let R_int_fault be the increased internal resistance due to the fault (e.g., R_int_fault � 0.02 ohms).Let t be the time in seconds.
Te voltage across the Ni-Mh battery with increased internal resistance can be expressed as Te developed MATLAB code provides a comprehensive battery modeling framework for simulating the behavior of diferent battery types, including Li-ion, lead-acid, supercapacitor, Ni-Cd, and Ni-Mh.It allows for the characterization of normal battery operation as well as the introduction of fault models, such as capacity fade and increased internal resistance.By specifying the battery model parameters and utilizing voltage equations, the code enables the analysis of battery voltage variations over time.Te resulting plots showcase the comparison between normal and faulty battery scenarios, ofering valuable insights into the impact of these faults on battery performance.Tis code By incorporating failure models into our simulation framework, we gain valuable insights into the behavior of energy storage systems under various failure scenarios.Tese failure models enable us to study the robustness and reliability of proposed fast-charge strategies and to assess system response under failure conditions.In addition, the simulation results highlight the importance of selecting the right battery types and strategies to optimize microgrid performance and ensure their smooth operation in real-life environments.

Battery Simulator Test.
Te process of simulating battery behavior stands as a cornerstone in modern energy research and development.Within our comprehensive battery simulator test platform, we ofer a seamless solution for replicating the performance of a wide array of battery cells housed in our extensive database.By a simple selection from the dropdown menu, researchers gain access to an array of prestored cells, each ripe for simulation, as exemplifed in Figure 18.In a practical demonstration, we harnessed the power of controlled pulses, generating 50 ampere-hours (Ah) for charging and an equal and opposite −50 Ah for discharging, thus emulating the dynamic charging and discharging phases of an NCA lithium cell.Tis section ventures into the heart of battery simulator testing, exploring how it empowers researchers to scrutinize and fne-tune battery performance under diverse conditions.Te ensuing fgures (Figure 19 for discharging and Figure 20 for charging) present the simulation outcomes, vividly capturing the essence of these critical battery phases for existing cells.

Application of BMS on Behavior of ESS.
Te integration of an optimization of ESSs more specifcally improves the battery-charging mode.An algorithm controls a converter which applies a rapid-charging mode [62] of the batteries and SC.Either it will play on the recharging frequency parameter or the converter is controlled by a PWM generator which will modulate the signal coming from the DC source.Tis technique can be also used in EV stations [63].For the confguration of the systems, the initial SOC of the diferent BESSs must be at 10%.Te systems go through four phases (stand-by, recharge, discharge, and stand-by) for the period ([0, 10 s], [10 s, 50 s], [50 s, 90 s], and [90 s, 100 s]), which gives an overview of the operating mode of the BESS managed by the BMS.
Figure 21 presents the algorithm for battery charge and discharge management.Te BMS oversees monitoring and controlling various battery parameters, such as the SOC, current, voltage, and temperature, to optimize its performance and extend its life.Te BMS can improve battery performance by ensuring that the battery is charged and discharged within safe limits and avoiding overcharging and overdischarging.Tis allows the battery to achieve higher SOC levels than without the BMS, as the BMS can accurately measure the battery SOC and control the charge/discharge process to optimize its performance.In addition, the BMS can also help balance the cells in the battery, ensuring that each cell is charged and discharged equally.Tis prevents cell imbalance and extends the life of the battery.Overall, the charge/discharge curve of a BESS managed by a BMS can demonstrate the benefts of using a BMS to monitor and optimize battery performance.Te BMS can help the battery achieve higher SOC levels, extend the life of the battery, and ensure that it is operating securely and efectively.
In Figure 22, the response of the diferent BESSs to recharge/discharge is shown, but in a mode controlled by the BMS.For the response to the load, the proposed algorithm improves the response of Ni-Mh and Ni-Cd and on everything for the lead-acid battery that can be seen over the period between [10 s-90 s].On the other hand, for the response to the discharge, the Li-ion battery is the best solution, which is demonstrated in the last phase (stand-by) for the period [90, 100 s] and the discharge phase between [60, 90 s].

Efect of Ambient Temperature on Charging and Discharging Behavior of Batteries. Simulation takes another path
, where the work focuses on the efect of ambient temperature on the mode and behavior of the BESS work, more precisely on the SOC and the internal cell temperature [64].Figure 23 shows that the BMS algorithm considers ambient temperature as a critical parameter and adjusts the charge and discharge parameters accordingly.Te algorithm continuously monitors the battery temperature and adjusts the charge and discharge current limits to keep the temperature within a safe range.When temperature is too high, the algorithm reduces the charge current to prevent overcharging and the discharge current to prevent overdischarging, as these conditions can cause thermal runaway and damage the battery.On the other hand, when temperature is too low, the algorithm increases the charge and discharge current to maintain battery performance and avoid self-discharge.
Figure 24 presents the simulation results of the infuence of the ambient temperature on the SOC of batteries.When varying the ambient temperature of the function of the leadacid battery, it observes a slight increase in the DOC between time t � 3000 s and t � 4000 s.It also observes a rise in the sensitivity of response to recharge at T � 80 °C (the recharge slope) compared to T � 25 °C.On the other hand, with the increase in temperature, it observes a decrease in the DOD and consequently a decrease in temperature less than 0 °C (in the present case, the simulation is performed at T � −25 °C and T � 80 °C), which improves the sensitivity of battery discharge, hence the low response time for the request of the load.
Another test highlights the efect of temperature on the mode of operation of the Li-ion battery when compared with another battery of the same type with a mode of operation at stable temperature at T � 25 °C.Tese tests are described below for diferent cases.

Case 1 (T � ±60 °C).
Te experiment demonstrates the temperature-dependent performance of the Li-ion battery model (battery A) when the surrounding temperature goes from 60 °C to −60 °C and then to 0 °C.Battery B is the case where the impact of temperature is ignored.Te results of the experiment are visualized in Figure 25, which compares the variation in the SOC between the two batteries at varying ambient temperature, and in  (v) At t � 2500 s, batteries A and B are charged with 3 Amp at an environmental temperature of 0 °C.Tis leads to an elevation of the internal temperature due to heat dissipation during the charging procedure, which raises the charging voltage of battery A. Ten, batteries A and B continue to charge until they are completely charged.
Te above experiment exhibits the impact of ambient temperature on the performance of both battery A and battery B. Te temperature-dependent battery A exhibits variations in the output voltage and the SOC as a function of the ambient temperature, while battery B demonstrates a consistent discharge behavior.

Case 2 (T � ±80 °C).
Te experiment illustrates the response of the model temperature-dependent lithium-ion battery (battery A) when the surrounding temperature ranges between 80 °C and −80 °C and then at 0 °C.Battery B is the case where the efect temperature is neglected.Te results of the experiment are visualized in Figure 27, which compares the variation in the SOC between the two batteries at varying ambient temperature, and in Figure 28, which shows the efect of the ambient temperature on the internal      International Transactions on Electrical Energy Systems (v) At t � 2500 s, batteries A and B are charged with 3 Amp at an air temperature of 0 °C.Tis leads to an increase in inner temperature due to the heat dissipation during the charging operation, which raises the charging voltage of battery A. Ten, batteries A and B continue to charge until they are fully charged.
With the high level of temperature variation, the Li-ion battery loses its storage energy capacity, which can be seen between t � 500 s and t � 1500 s, where the curve varies from +60 °C to −60 °C.For the SOC of battery B (battery how infuenced by temperature) in the discharge phase, battery B loses power more quickly than battery A (normal T � 25 °C).When temperature increases from t � 2500 s to t � 4000 s (charging phase), battery B returns to gain its SOC, with all its performance.Even for SCs under the same test conditions on Simulink (T � 25 °C, T � 80 °C, T � −25 °C, and T � −80 °C), the ambient temperature has no efect whatsoever.

Conclusion
Diferent battery storage technologies for MGs have been analyzed and compared in this study.Te development of an energy storage system for MGs is essential to ensure their successful functioning.Tis research has shown that the choice of a suitable combination of batteries and supercapacitors is highly dependent on the charging needs and the feld of application of the MG.A combination of Li-ion batteries and SC ofers high-energy density and a fast response time using the instantaneous response of SGs.International Transactions on Electrical Energy Systems However, commercial factors and life span should also be considered when selecting a suitable ESS.Moreover, our research has highlighted the sensitivity of battery performance to ambient temperature changes.We have observed that most battery types, including Li-ion, lead-acid, and SCs, are afected by temperature variations, with an increase or decrease in storage capacity depending on the battery type.Terefore, optimizing the charging strategies of ESSs under diferent temperature conditions is an important research area that needs further investigation.In our future research, we will prioritize the integration of ESSs with renewable energy sources and explore MG optimization techniques to enhance the efciency and reliability of MG systems.In addition, the development of new battery technologies with improved energy density, longer life span, and fast response time can enhance the performance of ESSs and MGs.Voltage across the battery terminals at time t V oc :

Nomenclature
Open-circuit voltage of the battery at time t I(t): Current fowing through the battery at time t R 0 : Resistance of the charge-transfer reaction in the battery R 1 : Resistance of the difusion process in the battery C 0 : Double-layer capacitance of the battery C 1 : Capacitance of the frst RC branch C 2 : Capacitance of the second RC branch

Q(t):
Charge stored in the frst RC branch at time t V 1 (t): Voltage across the frst RC branch at time t V 2 (t): Voltage across the second RC branch at time t V c (t): Voltage across the double-layer capacitance at time t.
Figure 7 demonstrates the model of the battery, where E Nieq and E Meq , respectively, represent the balance voltages of the nickel and metal electrodes, R Ni and R M are, respectively, the connection resistances of the nickel and metal electrodes, R e is the resistance of the electrolyte, and C dt-Ni and C dt-M are the double-layer capacitors.Te diodes represent the charge-transfer phenomenon.Te combination of (C dif-Ni //R dif-Ni ) and (C dif-M //R dif-M ) is related to the diffusion efect.

Figure 7 :
Figure 7: Battery model of Ni-MH based on the Notten model for Ni-Cd.
Li-ion Battery Voltage -Normal vs Capacity FadeLi-ion Battery Voltage -Normal vs Increased Internal

Figure 24 :Figure 25 :Figure 26 :
Figure 24: Variation in SOC as a function of ambient temperature.

Figure 27 :Figure 28 :
Figure 27: Comparison between the SOC of battery A and the SOC of battery B for case 2.

4
International Transactions on Electrical Energy Systems illustrates the common battery design used.It is an ideal battery with an open-circuit voltage V oc , a constant equivalent internal resistance R int , and a terminal voltage v(t).Once fully charged, the terminal voltage v(t) can be measured by measuring the open-circuit voltage, and R int can be measured by attaching a load and sensing both the terminal voltage and the current.

R
Ni and E M : Connective resistances of nickel and metal E Ni and E M : Battery energy C dlNi and E dlM :