Applied Science, Faculty of
Non UBC
Electrical and Computer Engineering, Department of
DSpace
Batteries 11 (5): 169 (2025)
Zhao, Yiming
Li, Hongrui
Wan, Changsheng
Du, Dong
Chen, Bo
There are many challenges in incorporating the attenuation cost of energy storage into the optimization of microgrid operations due to the randomness of renewable energy supply, the high cost of controlled power generation, and the complexity associated with calculating the cost of battery attenuation. Therefore, this paper proposes a microgrid energy management scheme considering the attenuation cost of energy storage. This scheme analyzes the power generation mode and uncertainty factors of distributed generators in detail. The influence of charge and discharge depth on the cycle life and residual value of the energy storage system was analyzed, and the energy storage attenuation cost model was established. Finally, considering the cost of power generation, environmental treatment, and the deterioration cost of energy storage systems, the objective function of the comprehensive operation cost of microgrids is formulated. The improved sine cosine algorithm (SCA) is used to simulate the energy output optimization of various distributed generators in the microgrid. The results show that the algorithm can effectively reduce the comprehensive operation cost of microgrids and improve their energy utilization efficiency, which proves the practical significance and reference value of the method for microgrid energy management.
Received: 28 March 2025Revised: 13 April 2025Accepted: 22 April 2025Published: 23 April 2025Citation: Zhao, Y.; Li, H.; Wan, C.;Du, D.; Chen, B. Microgrid EnergyManagement Considering EnergyStorage Degradation Cost. Batteries2025, 11, 169. https://doi.org/10.3390/batteries11050169Copyright: © 2025 by the authors.Licensee MDPI, Basel, Switzerland.This article is an open access articledistributed under the terms andconditions of the Creative CommonsAttribution (CC BY) license(https://creativecommons.org/licenses/by/4.0/).ArticleMicrogrid Energy Management Considering Energy StorageDegradation CostYiming Zhao 1,2,3 , Hongrui Li 1,* , Changsheng Wan 1 , Dong Du 1,2,3 and Bo Chen 41 School of Cyber Science and Engineering, Southeast University, Nanjing 210096, China;230229561@seu.edu.cn (Y.Z.)2 Inner Mongolia Electric Power (Group) Co., Ltd., Hohhot 010000, China3 Inner Mongolia Electric Power Group Mengdian Information and Communication Industry Co., Ltd.,Hohhot 010000, China4 Department of Electrical and Computer Engineering, University of British Columbia,Vancouver, BC V6T 1Z4, Canada; cbhp1993@ece.ubc.ca* Correspondence: 220225058@seu.edu.cnAbstract: There are many challenges in incorporating the attenuation cost of energy storageinto the optimization of microgrid operations due to the randomness of renewable energysupply, the high cost of controlled power generation, and the complexity associated withcalculating the cost of battery attenuation. Therefore, this paper proposes a microgridenergy management scheme considering the attenuation cost of energy storage. Thisscheme analyzes the power generation mode and uncertainty factors of distributed genera-tors in detail. The influence of charge and discharge depth on the cycle life and residualvalue of the energy storage system was analyzed, and the energy storage attenuation costmodel was established. Finally, considering the cost of power generation, environmentaltreatment, and the deterioration cost of energy storage systems, the objective function ofthe comprehensive operation cost of microgrids is formulated. The improved sine cosinealgorithm (SCA) is used to simulate the energy output optimization of various distributedgenerators in the microgrid. The results show that the algorithm can effectively reduce thecomprehensive operation cost of microgrids and improve their energy utilization efficiency,which proves the practical significance and reference value of the method for microgridenergy management.Keywords: microgrid; optimal scheduling; renewable energy sources; degradation costs1. IntroductionAgainst the backdrop of rapid development in renewable energy, traditional powersystems are continuously optimizing their energy structures by introducing new cleanenergy sources and integrating them into the grid. Nowadays, the distributed generation ofrenewable energy, such as wind and solar power, is widely regarded as an environmentallyand economically beneficial solution for future smart grids. The integration of clean energyinto distributed power systems effectively enhances energy efficiency and the penetrationrate of renewable energy. This significantly reduces the emissions of carbon dioxideand other harmful gases associated with traditional fossil fuel-based power generation,thereby helping to mitigate climate change and improve environmental quality. Withthe development and application of clean energy technologies, it is foreseeable that cleanenergy generation will become an integral part of the global energy system in the future.Simultaneously, the introduction of clean energy is driving the development of mi-crogrids. Microgrids integrate traditional generators with new energy sources to provideBatteries 2025, 11, 169 https://doi.org/10.3390/batteries11050169Batteries 2025, 11, 169 2 of 22power services to users in a decentralized manner [1]. With the ability to generate powerindependently and the flexibility to connect or disconnect from the utility grid, microgridsoffer new avenues for the utilization of new energy sources. Microgrids effectively alleviatethe supply pressure and environmental pollution of traditional power units. Moreover,during utility grid failures, microgrid systems can independently supply power to main-tain normal operation. Compared to traditional power systems, microgrids have strongerlocal consumption capabilities. By managing the output of distributed power sources andscheduling energy usage rationally [2], clean energy can be utilized more effectively.Microgrids typically consist of various distributed power sources, energy storagedevices, energy conversion equipment, loads, and various protective devices, forminga power supply system capable of achieving internal power balance [3]. Distributedpower sources generally consist of both renewable and traditional energy sources, whichcomplement each other to support load balancing. Energy storage devices effectively storeelectricity from renewable sources and release it when needed to meet grid demands orprovide backup power. Common energy storage devices include battery energy storagesystems (such as lithium ion batteries, sodium sulfur batteries, etc.), pumped hydro storage,and compressed air energy storage. These devices not only improve the stability andreliability of microgrids but also help regulate load and balance differences between supplyand demand in the power system, thereby achieving more effective grid management.Although microgrids are considered crucial components of future power systems,they still encounter various challenges in practical applications. The main issues facingmicrogrid systems currently include:(1) Reliability: The generation of renewable energy sources in the system is greatly af-fected by weather fluctuations, leading to unstable power generation in microgrid systems.(2) Power Quality: Due to the inclusion of various distributed energy sources andloads, issues related to power quality within the microgrid (such as voltage fluctuationsand harmonics) may affect power supply quality and equipment lifespan.(3) Energy Management: Microgrids require the effective management of multipledistributed energy sources, including solar, wind, and batteries, to ensure stable powersupply. This involves complex energy scheduling and optimization problems.(4) Economic: The construction and operation costs of microgrids are relatively high,especially considering the constant technological updates and intense market competition.Thus, reducing costs and achieving economic feasibility are key issues.Addressing the above problems, this paper proposes a series of solutions. To ensurethe reliability of microgrid system operation, energy storage systems, diesel generators,and grid power are introduced to meet electricity loads during fluctuations in renewableenergy generation, thus ensuring system stability. To tackle power quality, operationalconstraints are set for various distributed energy sources to control their output powerlimits, preventing drastic energy fluctuations that could affect equipment lifespan. As forenergy management and economic issues, this paper introduces metaheuristic algorithmsfor optimizing microgrid energy management and overall costs.The rapid solving capability and precise calculation ability of metaheuristic algorithmsprovide feasible solutions for optimizing microgrid energy management, sparking a surgein research on microgrid operation optimization. However, previous optimization pro-cesses often only considered economic and environmental pollution factors, neglecting thedegradation costs of energy storage systems. In reality, in microgrid systems, due to theuncertainty of wind and solar power generation, energy storage systems undergo frequentcharging and discharging, accelerating battery degradation. Thus, strategically planningthe timing and depth of battery charging and discharging to reduce storage degradationcosts is crucial for overall energy scheduling in microgrids. This paper considers the degra-Batteries 2025, 11, 169 3 of 22dation costs of energy storage systems as a key element of microgrid system operatingcosts, together with economic costs and environmental costs, forming the comprehensiveoperating costs of microgrids, and uses an improved SCA to optimize them.The main contributions of this paper are as follows:(1) Establishing a microgrid energy storage system represented by lithium batter-ies, constructing degradation costs, and integrating them into the total operation costsof microgrids;(2) Improving the SCA using two strategies: circle chaos mapping and Levy flight,and demonstrating the effectiveness of the improved algorithm through test functions;(3) Using the improved SCA to simulate and optimize the operating costs of micro-grid systems, demonstrating that the improved algorithm effectively reduces the overalloperating costs of microgrids.The structure of the article is as follows: Section 2 reviews previous work, Sections 3 and 4introduce the degradation model of energy storage and the design of the comprehensive op-erating cost function of microgrids, Section 5 introduces the improved SCA, and Sections 6and 7 present the experiments and conclusions of this paper, respectively.2. Related WorkWind power generation, as a significant form of renewable energy, holds a crucialposition in today’s energy sector, and wind energy has now become one of the primarysources of global electricity supply [4]. Wind power generation refers to the process ofconverting wind energy into mechanical energy and then into electrical energy throughwind turbines. Wind power generation utilizes the wind to drive the rotation of turbineblades, which are connected to the generator rotor. The rotating rotor induces electricalcurrent within the generator through magnetic field induction, thereby generating electricalenergy. In recent years, the manufacturing cost of wind turbines has continuously decreased,and they are commonly equipped with smart sensors, resulting in improved operationalefficiency and further reduction in usage costs.Photovoltaic (PV) power generation is the process of directly converting sunlightradiation into electrical energy and is an important form of renewable energy. The corecomponent of photovoltaic power generation is the solar panel, which consists of multiplesolar cells. These cells can convert photons from sunlight into electrons, thus generatingelectrical current. Photovoltaic technology features renewable, non-polluting, and low-noise characteristics, playing a significant role in sustainable development and climatechange mitigation [5]. With continuous technological advancements and cost reductions,photovoltaic power generation has been widely deployed globally.Wind power and photovoltaic power, as major clean energy technologies, play acritical role in addressing climate change and energy security challenges. Their generationprocesses involve minimal direct greenhouse gas emissions, contributing to improvedenvironmental quality and exhibiting significant renewability. Additionally, their relativelylow operation and maintenance costs contribute to enhanced economic benefits. How-ever, wind and photovoltaic power generation are significantly influenced by weatherfactors, resulting in substantial output power fluctuations within microgrids, necessitatingcoordinated operation with other generation equipment.Duan, YZ [6] proposed a fully distributed algorithm that does not rely on the initializa-tion process to solve the dynamic scheduling problem of hybrid microgrids. The optimalsolution satisfies the supply and demand constraints and the constraints of unequal produc-tion capacity at each time limit. Dey, B et al. [7] proposed a demand response (DR) model tomaximize the advantages of microgrids, taking into account various aspects of utility andelasticity, as well as customer behavior. The optimization model can reduce the overall costBatteries 2025, 11, 169 4 of 22of the microgrid system. Zhao, ZL [8] proposed a new autonomous multi-microgrid intra-day robust energy management framework based on the distributed dynamic managementmodel predictive control (DD-TMPC) method. The proposed strategy can dynamicallycapture the safe operating range of the microgrid system based on set theory. Wongdet,P [9] proposed a capacity optimization method and cost analysis considering the life cycleof a battery energy storage system (BESS), which is conducive to reducing the total cost.Hemmati, M [10] proposed a new energy management method for MMG networks inthe presence of battery storage, renewable energy, and demand response (DR) plans. Theuncertainty associated with the load and power output of wind and solar energy is handledby adopting the chance constrained programming (CCP) optimization framework in theMMG energy management model. Ref. [11] investigated the smart control problem ofautonomous microgrids to ensure voltage safety and maximize economic and environmen-tal benefits. Ref. [12] aimed to minimize total investment costs and technological factorsand explored the design problem of microgrids composed of various types of distributedenergy sources using the movable damping wave algorithm. Ref. [13] focused on the energymanagement of microgrid systems in islanded mode, considering demand forecasting, andutilized the strawberry optimization algorithm for optimized scheduling. Dong Haiyan [14]optimized the charging and discharging states of distributed energy sources in microgridsover multiple time ranges based on seasonal differences, aiming to achieve low carbonemissions under the low-carbon operation mode of microgrids. Wang et al. [15] proposed amixed-integer second-order cone optimization problem and demonstrated the performanceoptimization of the integrated energy system for fault recovery.The aforementioned studies in microgrid optimization scheduling did not take intoaccount the impact of battery degradation factors on costs. Unlike generation resources,the short-term scheduling of energy storage systems (ESSs) significantly affects their long-term lifespan; for instance, frequent charging and discharging can greatly reduce batterylife. On the other hand, the conflict between cost and benefit further complicates theenergy management problem of microgrids. Increasing ESS capacity can provide greateroperational reserves, making microgrid operations smoother, but at the cost of additionalcapital investment [15]. Additionally, most microgrid optimization scheduling problemsuse intelligent search algorithms for solutions; however, basic intelligent search algorithmssuffer from slow convergence, weak global search capability, and susceptibility to localoptima, necessitating improvements to enhance algorithm performance.This paper incorporates battery degradation costs into the overall operating costsof microgrids, considering the depth of charge and discharge of batteries, the number ofcharge and discharge cycles, and cost losses during usage, and utilizes an improved SCAto optimize microgrid operating costs.3. Energy Storage DegradationThe degradation of energy storage systems (ESSs) is crucial for analyzing and evalu-ating the economic operation of microgrids [16]. In order to accurately simulate the costcharacteristics of microgrid energy management, this section discusses the structure ofmicrogrids and the degradation costs of ESSs.3.1. Microgrid StructureMicrogrid systems are complex and typically composed of distributed energy sources,energy storage devices, and loads [17]. Distributed energy sources are divided into con-trollable and uncontrollable categories. Uncontrollable distributed energy sources usuallyinclude renewable energy generation devices such as wind turbines and photovoltaicgenerators, while controllable distributed energy sources include micro gas turbines, dieselBatteries 2025, 11, 169 5 of 22generators, and gas boilers. The variety of distributed energy sources in microgrids, eachwith its own operational characteristics, significantly increases the complexity of microgridscheduling [18].There is a classic microgrid in Figure 1 that includes wind power generation, pho-tovoltaic power generation, diesel generators, energy storage batteries, and electricityprocurement from the utility grid. This configuration involves multiple sources of elec-tricity and a combination of diverse power equipment working in unison to ensure stableload operation.Batteries 2025, 11, x FOR PEER REVIEW 5 of 23 3.1. Microgrid Structure Microgrid systems are complex and typically composed of distributed energy sources, energy storage devices, and loads [17]. Distributed energy sources are divided into controllable and uncontrollable categories. Uncontrollable distributed energy sources usually include renewable energy generation devices such as wind turbines and photo-voltaic generators, while controllable distributed energy sources include micro gas tur-bines, diesel generators, and gas boilers. The variety of distributed energy sources in mi-crogrids, each with its own operational characteristics, significantly increases the com-plexity of microgrid scheduling [18]. There is a classic microgrid in Figure 1 that includes wind power generation, photo-voltaic power generation, diesel generators, energy storage batteries, and electricity pro-curement from the utility grid. This configuration involves multiple sources of electricity and a combination of diverse power equipment working in unison to ensure stable load operation. Figure 1. Microgrid structure. The characteristics of the mixed generation are reflected in the differences among various devices in terms of power density, energy density, lifespan, and cost. Batteries have high energy density and can store large amounts of electrical energy; diesel genera-tors have high power density and can respond quickly to charging events. The combined characteristics of different power generation ends support the stable operation of mi-crogrids. At the same time, when interacting with the utility grid, microgrids can transmit the electricity they generate to the utility grid, reducing energy consumption. When the elec-tricity generation of the microgrid is insufficient, the utility grid can also provide neces-sary electricity support. Microgrids can flexibly decide whether to sell or buy electricity from the utility grid based on their own electricity generation and load demand. Addi-tionally, various means such as peak shaving and energy storage can be used to optimize electricity scheduling. During the interaction between microgrids and the utility grid, it is necessary to ensure stable and safe electricity quality and monitor and control electricity to prevent problems such as voltage fluctuations and momentary blackouts. 3.2. Factors Affecting Battery Life Battery degradation mainly manifests in two aspects: cycle life, which reflects the to-tal number of cycles that a battery unit can achieve, and capacity wear of battery units [19]. Cycle conditions, such as the frequency of charge–discharge cycles, charge–discharge rates, and maintenance schedules, have a significant impact on battery life. Battery life may accelerate degradation under unreasonable cycle conditions [20]. In addition to cycle Figure 1. Microgrid structure.The characteristics of the mixed generation are reflected in the differences among vari-ous devices in terms of power density, energy density, lifespan, and cost. Batteries have highenergy density and can store large amounts of electrical energy; diesel generators have highpower density and can respond quickly to charging events. The combined characteristicsof different power generation ends support the stable operation of microgrids.At the same time, when interacting with the utility grid, microgrids can transmit theelectricity they generate to the utility grid, reducing energy consumption. When the elec-tricity generation of the microgrid is insufficient, the utility grid can also provide necessaryelectricity support. Microgrids can flexibly decide whether to sell or buy electricity fromthe utility grid based on their own electricity generation and load demand. Additionally,various means such as peak shaving and energy storage can be used to optimize electricityscheduling. During the interaction between microgrids and the utility grid, it is necessaryto ensure stable and safe electricity quality and monitor and control electricity to preventproblems such as voltage fluctuations and momentary blackouts.3.2. Factors Affecting Battery LifeBattery degradation mainly manifests in two aspects: cycle life, which reflects the totalnumber of cycles that a battery unit can achieve, and capacity wear of battery units [19].Cycle conditions, such as the frequency of charge–discharge cycles, charge–discharge rates,and maintenance schedules, have a significant impact on battery life. Battery life may accel-erate degradation under unreasonable cycle conditions [20]. In addition to cycle conditions,state parameters also play an important role in battery life. Overcharging or underchargingstates of charge (SOCs) can severely affect the charge–discharge performance of batteries.Temperature can also have adverse effects, especially under high-temperature conditions,where the degradation process of batteries may accelerate. In practical applications, atemperature controller is typically included in battery management systems. Therefore, wecan assume that battery degradation caused by temperature factors can be ignored.Batteries 2025, 11, 169 6 of 22Furthermore, charge–discharge rates also affect battery life, but as long as the currentdoes not exceed the limits specified by the manufacturer’s specifications, it should not beconsidered a long-term impact; hence, it is not considered in this paper.Therefore, the primary determinants of battery life are the actual full capacity anddepth of discharge (DOD). Depending on different cycling events, there are typically twoways to define DOD. The first definition refers to the output energy at full capacity (100%SOC), while the second definition refers to a complete cycle composed of one charge–discharge event [21]. In this paper, we define DOD as the ratio of the energy change inone charge or discharge event to the energy at full battery capacity. Simultaneously, wedefine the actual full capacity of the battery as the energy that can be stored at 100% SOC.It should be noted that a cycle event is counted whenever the operating mode (chargingand discharging) switches to the opposite side. The relationship between the number ofbattery cycles and DOD is illustrated in Figure 2. The fit of battery life is optimal whenDOD = dB [22]:LB(dB) = a ∗ dB−b ∗ e−cdB (1)where a, b, c > 0 are curve fitting coefficients, LB is battery life, and dB is the depth of charge.The number of cycles in the battery’s lifespan decreases with an increase in DOD. Withouta loss of generality, this expression is also applicable to batteries of different parametertypes. Standards for battery life are typically determined according to manufacturingspecifications; however, it should be noted that all charge–discharge cycles in standard dataare conducted under the assumption of constant depth of discharge (DOD). However, inpractical operations, the assumption of constant DOD is evidently unrealistic. Estimatingbattery degradation costs using the above information would introduce significant errors;hence, there is a need to further consider expressions for battery life under actual operatingconditions and provide more accurate assessments of battery life.Batteries 2025, 11, x FOR PEER REVIEW 6 of 23 conditions, state parameters also play an important role in battery life. Overcharging or undercharging states of charge (SOCs) can severely affect the charge–discharge perfor-mance of batteries. Temperature can also have adverse effects, especially under high-tem-perature conditions, where the degradation process of batteries may accelerate. In practi-cal applications, a temperature controller is typically included in battery management sys-tems. Therefore, we can assume that battery degradation caused by temperature factors can be ignored. Furthermore, charge–discharge rates also affect battery life, but as long as the current does not exceed the limits specified by the manufacturer’s specifications, it should not be considered a long-term impact; hence, it is not considered in this paper. Therefore, the primary determinants of battery life are the actual full capacity and depth of discharge (DOD). Depending on different cycling events, there are typically two ways to define DOD. The first definition refers to the output energy at full capacity (100% SOC), while the second definition refers to a co plete cycle co posed of one charge–discharge event [21]. In this paper, we define DOD as the ratio of the energy change in one charge or discharge event to the energy at full battery capacity. Si ultaneously, e define the actual full capacity of the battery as the energy that can be stored at 100 SOC. It should be noted that a cycle event is counted henever the operating ode (charging and discharging) s itches to the opposite side. The relationship bet een the nu ber of battery cycles and is illustrated in Figure 2. The fit of battery life is opti al hen = 𝑑஻ [22]: 𝐿஻ሺ𝑑஻ሻ ൌ 𝑎 ∗ 𝑑஻ି௕ ∗ 𝑒ି௖ௗಳ (1)here 𝑎, 𝑏, 𝑐 ൐ 0 are curve fitting coefficients, 𝐿஻ is battery life, and 𝑑஻ is the depth of charge. The number of cycles in the battery’s lifespan decreases with an increase in DOD. Without a loss of generality, this expression is also applicable to batteries of different pa-rameter types. Standards for battery life are typically determined according to manufac-turing specifications; however, it should be noted that all charge–discharge cycles in standard data are conducted under the assumption of constant depth of discharge (DOD). However, in practical operations, the assumption of constant DOD is evidently unrealis-tic. Estimating battery degradation costs using the above information would introduce significant errors; hence, there is a need to further consider expressions for battery life under actual operating conditions and provide more accurate assessments of battery life. Figure 2. Relationship between battery life cycle and DOD. 3.3. Battery Degradation Cost Model To make the battery degradation cost model more practical, it is reasonable to assume that empirical data on lifespan are sufficiently accurate to estimate long-term degradation i r . l ti s i t tt r lif l .3.3. Battery Degradation Cost ModelTo make the battery degradation cost model more practical, it is reasonable to assumethat empirical data on lifespan are sufficiently accurate to estimate long-term degradationeffects, meaning that the impact of each charge–discharge cycle event on lifespan is inde-pendent of historical charge–discharge curves. At the same time, this paper assumes thatthe degradation cost of each charge and discharge cycle event at different SOC levels is thesame under the same DOD level [23].The battery degradation cost model represents the direct depreciation of its actualcapacity and lifespan. Considering a charging event starting at time t, with the averageBatteries 2025, 11, 169 7 of 22power during a time interval ∆t denoted as PB(t), the depth of charge dB(∆t) over this timeinterval can be expressed as:dB(∆t) = PB(t)∆t/EBC(t) (2)The actual capacity at time t is denoted as EBC(t). The efficiency coefficients of chargingand discharging, ηBc and ηBd, respectively, are defined. The average degradation cost perunit energy can be expressed as [24]:CBAC(t, dB(∆t)) = CB∆t/2LB(dB)EBC(t)dB(∆t)ηBcηBd (3)This term refers to the average degradation cost of each charging and dischargingevent of DOD = dB, where CB represents the cost of battery replacement. Therefore, we canobtain the degradation cost of the battery corresponding to this discharge event by simplymultiplying the energy output of the battery:CBDC(t, dB(∆t)) = CBAC(t, dB(∆t)) ∗ PB(t)∆t= CBPB(t)∆t/2LB(dB)EBC(t)dB(∆t)ηBcηBd(4)As the battery degrades, its health status also changes. This article defines the batteryhealth status (SOH), where Erand is the rated capacity of the battery:SOH(t) =EBC(t)Erand(5)After a complete cycle event, the actual capacity of the battery at t + ∆t is depreciatedproportionally. At the same time, the health status of the battery will also affect the actualcapacity. A lower SOH will accelerate battery decay. The formula for the actual capacitychange of the battery is as follows, where γ is the capacity decay acceleration factor:EBC(t+ ∆t) = EBC(t)− ErandLB(dB(∆t)) · γ(SOH(t)) (6)Of particular concern is that prolonged operation at an excessively high or low SOCcan lead to increased internal impedance of the battery and electrolyte decomposition,thereby resulting in capacity loss and power attenuation. However, it is worth emphasizingthat such degradation is relatively negligible in the short term compared to degradationcaused by long-term charge–discharge events.4. Microgrid Energy ManagementThis section focuses on the economic costs, environmental management costs, andstorage degradation costs of microgrids, establishing a comprehensive cost function formicrogrid operation, laying the foundation for subsequent energy management analysis.Simultaneously, it analyzes the specific operational characteristics of various distributedenergy resources in microgrids and establishes operational constraints for distributedenergy resources to ensure the reliability and stability of system operation.4.1. Objective FunctionThis paper adopts the comprehensive operation cost of microgrids as the objectiveoptimization function. Under the condition of ensuring the balance between electricitysupply and demand in the microgrid, it not only considers operating costs and environ-mental benefits but also incorporates battery degradation costs as a long-term influencingBatteries 2025, 11, 169 8 of 22factor into the consideration of comprehensive costs. It establishes the objective functionfor minimizing comprehensive operation costs, as follows:fmin =∑Tt=1 (CDG(t) + CB(t) + CGrid(t) + CEM(t)) (7)where fmin represents the minimum comprehensive operation cost of the microgrid system,CDG denotes the generation cost of diesel generators, CB represents the battery degradationcost, CGrid signifies the cost of using grid electricity, and CEM represents the cost requiredfor environmental governance of the system. The following is a detailed analysis of thegeneration costs of various distributed energy sources.4.1.1. Diesel Generator Power Generation CostIn microgrid systems, diesel generators play a crucial role in maintaining supply–demand balance. With a lengthy developmental history, diesel generators have reacheda considerable level of technical maturity and find extensive application as conventionalpower sources capable of swift startup and rapid shutdown in emergencies. They arecharacterized by their ability to generate stable electricity, exhibiting resilience to externalinfluences and boasting high reliability. However, they incur high operational costs due tocontinuous fuel supply requirements, and the combustion of fuel leads to the emission ofpollutants.The relationship between diesel generator fuel costs and power output is described bythe following equation, where α, β, and γ are constants, PDG represents the output powerof the diesel generator, and CDG denotes the generator’s operating cost:CDG(t) = α ∗ PDG(t)2 + β ∗ PDG(t) + γ (8)4.1.2. Battery Degradation CostThe uncertainty and variability inherent in renewable energy generation pose chal-lenges to the reliability and security of the power supply in microgrid systems. Energystorage systems, widely employed in microgrids, offer solutions for load balancing andenergy regulation [25]. These systems possess the capability to dynamically absorb andrelease energy, enabling bidirectional energy control within specific time frames. Whenexcess electricity is generated from wind and solar sources, energy storage systems canstore surplus energy while meeting load demands. Conversely, when renewable energygeneration falls short, these systems can provide power support to the microgrid.Energy storage systems are primarily classified into three categories: chemical energystorage, physical energy storage, and electromagnetic energy storage. Physical energystorage encompasses forms such as flywheels, pumped hydro, and compressed air. Electro-magnetic energy storage includes superconducting magnetic energy and supercapacitorenergy storage, among others. Chemical energy storage encompasses technologies suchas lead acid batteries, lithium ion batteries, flow batteries, and sodium sulfur batteries.Among these, lithium ion batteries, due to their relatively low cost and mature technology,have found widespread application in power systems. This paper focuses on the analysis ofenergy storage systems represented by lithium ion batteries. In Section 3.3 of this paper, thedegradation cost of battery cycling events has been provided, considering charge–dischargeefficiency. The energy variation equation of the battery over discrete time is given as:EB(t) ={EB(t− 1)− PB(t)∆tηBc, PB(t) ≤ 0EB(t− 1)− PB(t)∆tηBd , PB(t) > 0(9)Batteries 2025, 11, 169 9 of 22Due to the fact that the degradation cost of the battery within each time interval canonly be determined after the end of the charging or discharging event, it is necessary tospecify the power flow direction of the battery. To address this, we first represent g(t) as anauxiliary binary variable, indicating the state transition of charging or discharging eventsbetween two consecutive time intervals:g(t) ={1, PB(t)PB(t− 1) ≤ 00, PB(t)PB(t− 1) > 0(10)Ea(t) represents the cumulative energy in kilowatt-hours (kWh) before the change ofcycling events. Correspondingly, the cumulative energy Ea(t) can be expressed as:Ea(t) = (1− g(t))Ea(t− 1) + PB(t)∆t (11)Therefore, the degradation cost of the battery over consecutive time intervals can beexpressed in terms of the state transition signal g(t) and the cumulative energy Ea(t):CB(t) = CBDC(t,Ea(t)EB(t))− (1− g(t))CBDC(t,Ea(t− 1)EB(t− 1))(12)4.1.3. Utility Grid Power Generation CostThe cost of grid electricity generation can be represented as follows:CM(t) = cm(t)PGrid(t)∆t (13)The cost of utility grid generation at time t, denoted by cm, is influenced by the poweroutput PGrid from the grid. In this paper, the utility grid is priced based on time-of-use(TOU) tariffs, which are divided into off-peak, standard, and peak periods. The fluctuationof electricity prices is also a significant parameter affecting the optimization of fmin.4.1.4. Environmental Governance CostIn the optimization scheduling of microgrids, traditional models only consider eco-nomic costs while disregarding environmental considerations [26]. To better achieve thescheduling objectives of microgrid systems, it is imperative to comprehensively consider en-vironmental factors. In this context, this paper precisely quantifies the pollutants generatedby various types of generation units to achieve the goal of pollution reduction.In the microgrid system studied in this paper, only photovoltaic and wind powergeneration can achieve zero emissions of pollutants. Other power generation devices releasea certain amount of pollutants during the generation process. In this study, environmentalcosts are defined as the expenses required to mitigate the harmful gases produced bymicrogrid systems. These harmful gases include CO, CO2, SO2, NOx, etc. The cost ofpollutant treatment CEM is expressed as follows:CEM(t) =I∑i=1(σi(γiGridPtgrid + γiDGPtDG))(14)where γiGrid and γiDG are the emission coefficients of the i-th type of pollutants from thepublic power grid and the diesel generator, respectively; PtDG is the output power of thediesel generator; Ptgrid is the output power of the utility grid; σi is the treatment cost of thei-th type of pollutant.Batteries 2025, 11, 169 10 of 224.2. System RestrictionsIn the operation of microgrids, ensuring the satisfaction of load balance constraints iscrucial. Load balance refers to the matching and equilibrium between the power outputof various electrical components (such as generators, storage devices, renewable energygeneration units, etc.) within the microgrid system and the load demand. At any givenmoment, the microgrid must maintain a balance between power supply and demand toensure the stable operation of the power system. The power balance equation in this papercan be expressed as:PL(t) = PGrid(t) + PB(t) + PDG(t) + PPV(t) + PWT(t) (15)where PPV(t), PWT(t) represent the output power of the photovoltaic and wind turbines attime t, PL(t) denotes the electrical load, and PGrid(t) denotes the power output from theutility grid.The inequality constraints include power limits for the grid, battery, and diesel genera-tors, as well as capacity limits for the battery, expressed as follows:PminGrid(t) ≤ PGrid(t) ≤ PmaxGrid(t) (16)PminB (t) ≤ PB(t) ≤ PmaxB (t) (17)PminDG (t) ≤ PDG(t) ≤ PmaxDG (t) (18)SOCmin(t) ≤ SOC(t) ≤ SOCmax(t) (19)PmaxGrid(t), PminGrid(t), PmaxB (t), PminB (t), PmaxDG (t), and PminDG (t) represent the upper andlower limits of power generation for the grid, battery, and diesel generator, respectively.SOCmax(t) and SOCmin represent the upper and lower limits of the energy storage capacity.5. Solving Optimization Problems Based on CLSCAIn addressing optimization problems in microgrids, metaheuristic algorithms arewidely applied due to their strong dimensional handling capability and fast convergencespeed. Among the plethora of metaheuristic algorithms, the SCA stands out for its advan-tages such as fewer parameters, simplicity in structure, and relatively fast convergencespeed, demonstrating excellent performance in solving practical problems. This algorithmtargets the oscillatory and periodic nature of sine and cosine functions as the design ob-jective of its implementation operators, seeking optimal solutions through search anditeration [27].While the SCA absorbs some advantages of traditional intelligent optimization algo-rithms in its iterative strategy, it still suffers from drawbacks such as slow convergence of theinitial population and susceptibility to local optima, suggesting potential for improvement.In this study, we employ two strategies, circle chaotic mapping and Levy flight, to enhancethe original SCA, aiming to achieve better performance in solving real-world problems.5.1. Sine Cosine AlgorithmThe sine cosine algorithm consists primarily of three steps: initialization, update, andselection. In the initialization phase, a set of initial individuals is generated based on arandom algorithm, where each individual represents a solution in the search space. Inthe update phase, the iteration strategy of the SCA is categorized into two steps: globalexploration and local exploitation. In global exploration, significant random fluctuationsare applied to the solutions in the current population to explore unknown regions of thesolution space. In local exploitation, weak random perturbations are applied to thoroughlyBatteries 2025, 11, 169 11 of 22search the neighborhood of the current solutions. Finally, in the selection phase, individualswith superior fitness values are selected for the next iteration through fitness comparison.The SCA utilizes the periodic oscillations of sine and cosine functions to constructiteration equations that realize the functionalities of global exploration and local exploita-tion. These concise update equations impose perturbations and update the solution set.Specifically, the iteration equations are divided into two types: sine iteration or cosineiteration equations.xi(t+ 1) ={xi(t) + r1 ∗ sin (r2) ∗ |r3Pi(t)− xi(t)|, r4 ≤ 0.5xi(t) + r1 ∗ cos (r2) ∗ |r3Pi(t)− xi(t)|, r4 > 0.5(20)where r1, r2, r3, and r4 are random numbers between 0 and 1; Pi(t) represents the fittestindividual from the previous iteration.5.2. Circle Chaos MapThe SCA adopts a random generation of initial populations. Although convenient, thisapproach may lead to uneven population distribution and overall lower quality, resultingin instability in the early stages of algorithm execution. To address these issues, chaoticmodels are commonly employed during population generation to improve populationquality. Currently used chaotic mappings include tent mapping, logistic mapping, andChebyshev mapping [28]. Both Chebyshev and logistic mappings represent typical chaoticsystems, where the mapping points exhibit high values at the ends and low values in themiddle, causing uneven distribution, thereby affecting the algorithm’s search efficiency.Compared to the dense distribution of boundary values in the logistic mapping range,tent chaotic mapping possesses both uniform probability density and good characteristics.Therefore, initializing populations using tent mapping can generate a more uniformlyrandom distribution. However, tent mapping exhibits unstable periodic points in certainintervals. Meanwhile, circle mapping shares similar uniformity with tent mapping butoffers a more balanced distribution at the ends of intervals [29]. The formula for calculatingcircle chaotic mapping is as follows:xi+1 = mod(xi + 0.2− 0.52π sin (2πxi), 1) (21)This paper selects the circle mapping, which exhibits a more uniform distributionand greater stability, to enhance the SCA. This enhancement aims to increase individualdiversity, thus accelerating the convergence speed of the algorithm. It facilitates betterexploration of the solution space, improves stability, and achieves higher convergenceaccuracy. The distribution of random mapping, tent chaotic mapping, and circle mappingis illustrated in Figure 3 below:Batteries 2025, 11, x FOR PEER REVIEW 12 of 23 . Figure 3. Three random mappings. 5.3. Levy Flight The Levy distribution is a probability distribution model proposed by the renowned French mathematician Paul Levy. It can be utilized to describe the flight trajectories of flying animals in nature, providing crucial insights for scientific research [30]. Levy flight represents a highly scalable stochastic process, enabling movements spanning multiple distances, thereby significantly expanding the search domain and enhancing the global search capabilities of algorithms. The Levy distribution is defined as follows: 𝐿𝑒𝑣𝑦ሺ𝛽ሻ ൌ 𝑢|𝑣|ଵఉ (22)𝑢~𝑁ሺ0,𝜎௨2ሻ,𝑣~𝑁ሺ0,𝜎௩2ሻ 𝜎௨ ൌ ቎𝛤ሺ1 ൅ 𝛽ሻ ∗ sin ሺ𝛽𝜋2 ሻ𝛤ሺ1൅ 𝛽ሻ ∗ 𝛽 ∗ 2ఉି12቏1ఉ ,𝜎௩ୀ1 The Levy distribution with parameter β is denoted as Levy(β), representing a random variable following this distribution. Levy(β) is defined by Equation (20), where u and v are normally distributed, and β is set to 1.5. The updated formula for SCA position, incor-porating Levy flight trajectories, is presented as follows: 𝑥௜ሺ𝑡 ൅ 1ሻ ൌ 𝑥௜ሺ𝑡ሻ ൅ 𝐿𝑒𝑣𝑦ሺ𝛽ሻ⨁𝑥௜ሺ𝑡ሻ (23)The pseudo-code of the improved algorithm is as follows (see Algorithm 1): Algorithm 1 The pseudo-code of the CLSCA Initialize the population 𝑥௜ (i = 1, 2, …, N) with circle chaos mapping Calculate the fitness values of the initial search individuals while t< G Update rand1 for i = 1: N for j = 1:d Calculate the parameters rand2, rand3 and rand4 Update the positions of the search agents by Equation (19) End j Perform Lévy flight operator using Equation (22) to generate a candidate search agent 𝑥௜ሺ𝑡ሻ Update the 𝑥௜ሺ𝑡 ൅ 1ሻ Amend the position of the current search individual based on lb and ub Figure 3. Three random map i .Batteries 2025, 11, 169 12 of 225.3. Levy FlightThe Levy distribution is a probability distribution model proposed by the renownedFrench mathematician Paul Levy. It can be utilized to describe the flight trajectories offlying animals in nature, providing crucial insights for scientific research [30]. Levy flightrepresents a highly scalable stochastic process, enabling movements spanning multipledistances, thereby significantly expanding the search domain and enhancing the globalsearch capabilities of algorithms. The Levy distribution is defined as follows:Levy(β) =u|v|1β(22)u ∼ N(0, σ2u), v ∼ N(0, σ2v )σu =[Γ(1+β)∗sin( βπ2 )Γ(1+β)∗β∗2β−12] 1β, σv=1The Levy distribution with parameter β is denoted as Levy(β), representing a randomvariable following this distribution. Levy(β) is defined by Equation (20), where u andv are normally distributed, and β is set to 1.5. The updated formula for SCA position,incorporating Levy flight trajectories, is presented as follows:xi(t+ 1) = xi(t) + Levy(β)⊕xi(t) (23)The pseudo-code of the improved algorithm is as follows (see Algorithm 1):Algorithm 1 The pseudo-code of the CLSCAInitialize the population xi (i = 1, 2, . . ., N) with circle chaos mappingCalculate the fitness values of the initial search individualswhile t < GUpdate rand1for i = 1: Nfor j = 1:dCalculate the parameters rand2, rand3 and rand4Update the positions of the search agents by Equation (19)End jPerform Lévy flight operator using Equation (22) to generate a candidate searchagent xi(t)Update the xi(t+ 1)Amend the position of the current search individual based on lb and ubEnd iReturn the best solution obtained so far as the global optimum5.4. Performance TestingTo validate the performance of the CLSCA, this study conducts tests using the bench-mark functions from CEC2005. Four test functions are selected, comprising two unimodalfunctions and two multimodal functions. A comparison is made with classical PSO and theSCA to demonstrate the feasibility and effectiveness of CLSCA optimization. The unimodalfunctions assess the convergence speed and accuracy of the optimization algorithm, whilethe multimodal functions evaluate the global search capability. The test functions used areshown in Table 1:Batteries 2025, 11, 169 13 of 22Table 1. Benchmark Functions.Fun Limitation Optimal Value Function Typef1 =n∑i=1x2i [−100, 100] 0 Unimodal functionf2 =n∑i=1(i∑j−1xj)2[−100, 100] 0 Unimodal functionf3 =n∑i=1ix4i + random[0, 1] [−1.28, 1.28] 0 Multimodal functionf4 =n∑i=1[x 2i − 10cos (2πxi) + 10][−5.12, 5.12] 0 Multimodal functionAll tested algorithms were iterated one thousand times with an initial population sizeset to 30. To mitigate experimental errors, each algorithm underwent 100 simulations tocompute both the minimum and average values.The objective space and convergence curves for unimodal functions are depicted inFigure 4:Batteries 2025, 11, x FOR PEER REVIEW 13 of 23 End i Return the best solution obtained so far as the global optimum 5.4. Performance Testing To validate the performance of the CLSCA, this study conducts tests using the bench-mark functions from CEC2005. Four test functions are selected, comprising two unimodal functions and two multimodal functions. A comparison is made with classical PSO and the SCA to demonstrate the feasibility and effectiveness of CLSCA optimization. The uni-modal functions assess the convergence speed and accuracy of the optimization algo-rithm, while the multimodal functions evaluate the global search capability. The test func-tions used are shown in Table 1: Table 1. Benchmark Functions. Fun Limitation Optimal Value Function Type 𝑓ଵ ൌ෍𝑥௜ଶ௡௜ୀଵ [−100, 100] 0 Unimodal function 𝑓ଶ ൌ෍ሺ෍𝑥௝௜௝ିଵሻଶ௡௜ୀଵ [−100, 100] 0 Unimodal function 𝑓ଷ ൌ෍𝑖𝑥௜ସ௡௜ୀଵ൅ randomሾ0, 1ሿ [−1.28, 1.28] 0 Multimodal function 𝑓ସ ൌ෍ሾ𝑥௜ଶ െ 10 cosሺ2𝜋𝑥௜ሻ ൅ 10ሿ௡௜ୀଵ [−5.12, 5.12] 0 Multimodal function All tested algorithms were iterated one thousand times with an initial population size set to 30. To mitigate experimental errors, each algorithm underwent 100 simulations to compute both the minimum and average values. The objective space and convergence curves for unimodal functions are depicted in Figure 4: Figure 4. Unimodal function graph and convergence curve. The target space diagram and convergence curve diagram of the multi-peak function are shown in Figure 5: Figure 4. ni odal function graph and convergence curve.e t rget s ace ia ra a c ergence c rve iagra of t e lti- ea f ctiare sho n in Figure 5:Batteries 2025, 11, x FOR PEER REVIEW 14 of 23 Figure 5. Multimodal function graph and convergence curve. The minimum and average values after iteration of the three algorithms are shown in Table 2: Table 2. Results of benchmark functions. Fun PSO SCA CLSCA MIN AVG MIN AVG MIN AVG 𝑓1 1.1941 × 101 7.6338 × 101 0.0000 5.1024 × 10−3 0.0000 6.0900 × 10−4 𝑓2 5.7839 × 102 4.6783 × 103 3.8354 × 101 1.1352 × 103 1.7648 × 101 8.0729 × 102 𝑓3 1.0346 × 10−2 9.4999 × 10−1 3.5981 × 10−3 3.1686 × 10−2 2.0114 × 10−4 1.5173 × 10−2 𝑓4 8.6515 × 101 1.6198 × 102 9.31 × 10−5 1.5819 × 101 0.0000 6.3108 The test results indicate that the CLSCA significantly outperforms both the SCA and PSO algorithm in terms of convergence speed and accuracy. Additionally, the CLSCA demonstrates effective avoidance of falling into the trap of local optima, exhibiting robust-ness and optimization capability. This paper employs the improved CLSCA to solve the proposed microgrid optimi-zation problem. The objective is to minimize the overall operational cost of the microgrid using the CLSCA, aiming for better planning of energy output in the microgrid. 6. Experiment 6.1. Experimental Parameters In the electricity market, the selling prices of the public grid are typically determined by upper-level system operators in either a static or dynamic manner. Static pricing schemes, such as fixed prices and time-of-use pricing, are usually predetermined and do not vary with network conditions. This paper employs time-of-use pricing as the pricing standard for the public grid. Time-of-use pricing is an important concept in the electricity market, often used to refer to the fluctuation of electricity prices during different time periods of the day. These fluctuations reflect the variation in the load of the power system during different time periods, closely related to the supply–demand relationship and the real-time operation status of the system. The core idea of time-of-use pricing is to provide lower electricity prices (off-peak prices) during periods of low demand, encouraging consumers to consume electricity dur-ing these periods to smooth the load curve, and to provide higher electricity prices (peak prices) during periods of high demand to incentivize users to reduce electricity consump-tion. The introduction of time-of-use pricing aims to achieve efficient operation and re-source utilization of the power system. Through differentiated pricing, time-of-use pricing stimulates users’ time-elastic responses to electricity consumption, reducing the system’s peak load and thus enhancing the stability and reliability of the power system. Figure 5. Multimodal function graph and convergence curve.The ini fter iteration of the thre algorithms are shown inTable 2:Batteries 2025, 11, 169 14 of 22Table 2. Results of benchmark functions.FunPSO SCA CLSCAMIN AVG MIN AVG MIN AVGf1 1.1941 × 101 7.6338 × 101 0.0000 5.1024 × 10−3 0.0000 6.0900 × 10−4f2 5.7839 × 102 4.6783 × 103 3.8354 × 101 1.1352 × 103 1.7648 × 101 8.0729 × 102f3 1.0346 × 10−2 9.4999 × 10−1 3.5981 × 10−3 3.1686 × 10−2 2.0114 × 10−4 1.5173 × 10−2f4 8.6515 × 101 1.6198 × 102 9.31 × 10−5 1.5819 × 101 0.0000 6.3108The test results indicate that the CLSCA significantly outperforms both the SCA andPSO algorithm in terms of convergence speed and accuracy. Additionally, the CLSCAdemonstrates effective avoidance of falling into the trap of local optima, exhibiting robust-ness and optimization capability.This paper employs the improved CLSCA to solve the proposed microgrid optimiza-tion problem. The objective is to minimize the overall operational cost of the microgridusing the CLSCA, aiming for better planning of energy output in the microgrid.6. Experiment6.1. Experimental ParametersIn the electricity market, the selling prices of the public grid are typically determined byupper-level system operators in either a static or dynamic manner. Static pricing schemes,such as fixed prices and time-of-use pricing, are usually predetermined and do not varywith network conditions. This paper employs time-of-use pricing as the pricing standardfor the public grid. Time-of-use pricing is an important concept in the electricity market,often used to refer to the fluctuation of electricity prices during different time periods ofthe day. These fluctuations reflect the variation in the load of the power system duringdifferent time periods, closely related to the supply–demand relationship and the real-timeoperation status of the system.The core idea of time-of-use pricing is to provide lower electricity prices (off-peakprices) during periods of low demand, encouraging consumers to consume electricityduring these periods to smooth the load curve, and to provide higher electricity prices(peak prices) during periods of high demand to incentivize users to reduce electricityconsumption. The introduction of time-of-use pricing aims to achieve efficient operationand resource utilization of the power system. Through differentiated pricing, time-of-usepricing stimulates users’ time-elastic responses to electricity consumption, reducing thesystem’s peak load and thus enhancing the stability and reliability of the power system.The time-of-use pricing utilized in this study consists of three pricing periods. Addi-tionally, during peak generation periods in the microgrid, surplus electricity can be soldback to the public grid, optimizing power distribution and enhancing economic benefits.Table 3 shows the pricing for grid generation and microgrid electricity sales:Batteries 2025, 11, 169 15 of 22Table 3. Time-of-use Pricing.Stage Time Purchase Price/Yuan Sales Price/Yuanoff-peak 0:00–7:0023:00–24:00 0.38 0.32standard7:00–10:0021:00–23:0012:00–15:000.83 0.67peak 10:00–12:0015:00–21:00 1.38 1.09Environmental costs need to consider the gases that may be harmful to the environ-ment generated by each distributed power source during operation, as well as the costsrequired to control these gases. The average values of North China are selected for differentpollutant emission coefficients and their control cost standards. North China includes3 provinces and 2 cities, namely Beijing, Tianjin, Hebei, Shanxi, and Inner Mongolia Au-tonomous Region. It has a large population and belongs to the temperate humid andsemi-humid continental monsoon climate. It has abundant new energy sources such aswind and light. There are also a large number of high-energy-consuming industries suchas steel and chemical industries. The overall industrial foundation is good, the pollutantemissions are also not small, and the annual changes are not large. The selected pollutantsCO, CO2, SO2, and NOx basically include pollutants involved in production and life. Theselection of this region is representative. The different pollutant emission coefficients andtheir control cost standards are shown in Table 4:Table 4. Emission Coefficients and Governance Costs.Type of Pollutant Governance Costs(yuan/kg)Pollutant Emission Coefficient (g/kwh)DG GridCO 0.047 0.081 10.49CO2 0.023 680 724SO2 6 0.306 1.8NOx 8 10.09 1.6In this study, storage batteries employ technologically mature lithium battery modules.The battery has a capacity of 100 kWh, with a price of 2000 per kWh. The initial batterycapacity is 50 kWh.6.2. Simulation ExperimentThis paper uses the actual data of a microgrid in a certain area of Inner Mongolia,North China as an example, combines the microgrid model and optimization schedulingstrategy proposed in the previous article, and simulates the microgrid system with thecomprehensive operation cost as the goal. The microgrids in this area not only have urbaninterconnection modes connected to the public power grid, but also some grassland farmingand pastoral areas that cannot be connected to the public power grid due to their distancefrom towns and environmental protection factors, forming an isolated farming and pastoralmode. Compared with the urban interconnection mode, the power load in the isolatedfarming and pastoral mode is relatively low. In terms of the cost function, the isolatedfarming and pastoral mode does not need to calculate the public grid power generationcost. This paper uses the improved SCA to simulate and calculate the comprehensivecost on the Matlab (2018b version) simulation platform, and simulates and compares theoptimization scheduling results of microgrids under different algorithms to verify that theBatteries 2025, 11, 169 16 of 22improved SCA can optimize the operation cost of microgrids and achieve good results. Thetypical daily data for 24 h of wind power generation power, photovoltaic power generationpower, and load power in towns and farming and pastoral areas in this area are shown inFigures 6 and 7 below:Batteries 2025, 11, x FOR PEER REVIEW 16 of 23 isolated farming and pastoral mode does not need to calculate the public grid power gen-eration cost. This paper uses the improved SCA to simulate and calculate the comprehen-sive cost on the Matlab (2018b version) simulation platform, and simulates and compares the optimization scheduling results of microgrids under different algorithms to verify that the improved SCA can optimize the operati n c st of microgrids and achieve good results. The typical daily data for 24 h of wind power generation power, photovoltaic power gen-eration power, and load power in towns a d farming and pastoral areas in this area are shown in Figures 6 and 7 below: Figure 6. Urban photovoltaic, wind power generation, and user load curves. Figure 7. Photovoltaic, wind power generation, and user load curves in agricultural and pastoral areas. When the system is interconnected and operating, problems such as excessive or in-sufficient power output may occur in microgrids. For these two scenarios, the costs arising from the energy exchange between the microgrid and the utility grid must be fully con-sidered. Therefore, when optimizing the scheduling of interconnected microgrid systems, it is necessary to consider not only the structure and operational characteristics of the mi-crogrid system itself but also factors such as utility grid power and electricity prices. Figure 6. rban photovoltaic, ind po er generation, and user load curves.Batteries 2025, 11, x FOR PEER REVIEW 16 of 23 isolated farming and pastoral mode does not need to calculate the public grid power gen-eration cost. This paper uses the improved SCA to simulate and calculate the comprehen-sive cost on the Matlab (2018b version) simulation platform, and simulates and compares the optimization scheduling results of microgrids under different algorithms to verify that the improved SCA can optimize the operation cost of microgrids and achieve good results. The typical daily data for 24 h of wind power generation power, photovoltaic power gen-eration power, and load power in towns and farming and pastoral areas in this area are shown in Figures 6 and 7 below: Figure 6. Urban photovoltaic, wind power generation, and user load curves. Figure 7. Photovoltaic, wind power generation, and user load curves in agricultural and pastoral areas. When the system is interconnected and operating, problems such as excessive or in-sufficient power output may occur in microgrids. For these two scenarios, the costs arising from the energy exchange between the microgrid and the utility grid must be fully con-sidered. Therefore, when optimizing the scheduling of interconnected microgrid systems, it is necessary to consider not only the structure and operational characteristics of the mi-crogrid system itself but also factors such as utility grid power and electricity prices. Figure 7. Photovoltaic, wind power generation, and user load curves in agricultural andpastoral areas.When the system is interconnected and operating, problems such as excessive orinsufficient power output may occur in microgrids. For these two scenarios, the costsarising from the energy exchange between the microgrid and the utility grid must befully considered. Therefore, when optimizing the scheduling of interconnected microgridsystems, it is necessary to consider not only the structure and operational characteristics ofthe microgrid system itself but also factors such as utility grid power and electricity prices.In this paper, an improved SCA (sine cosine algorithm) is employed to optimizethe comprehensive cost of microgrids, taking into account the effects of electricity pricefluctuations, environmental costs, and energy storage degradation costs. The improvedoptimal value evolution curves are shown in Figures 8 and 9, where the vertical axisBatteries 2025, 11, 169 17 of 22represents the optimal value of the comprehensive operating cost and the horizontal axisrepresents the number of iterations.Batteries 2025, 11, x FOR PEER REVIEW 17 of 23 In this paper, an improved SCA (sine cosine algorithm) is employed to optimize the comprehensive cost of microgrids, taking into account the effects of electricity price fluc-tuations, environmental costs, and energy storage degradation costs. The improved opti-mal value evolution curves are shown in Figures 8 and 9, where the vertical axis repre-sents the optimal value of the comprehensive operating cost and the horizontal axis rep-resents the number of iterations. Figure 8. Comprehensive cost convergence curve of urban microgrid. Figure 9. Comprehensive cost convergence curve of microgrids in agricultural and pastoral areas. Compared with the SCA and the HHO algorithm [31], the CLACS optimal value curve will not fall into the optimal solution so quickly, and its fitness is also reduced. The comprehensive costs of the SCA and HHO in the urban interconnection mode are 668.4 and 651.1, respectively, and the comprehensive cost of the CLSCA is 629.5. The compre-hensive costs of the SCA and HHO in the independent agricultural and pastoral area mode are 266 and 262.1, respectively, and the comprehensive cost of CLSCA is 253.8. The Figure 8. Comprehensive cost convergence curve of urban microgrid.Batteries 2025, 11, x FOR PEER REVIEW 17 of 23 In this paper, an improved SCA (sine cosine algorithm) is employed to optimize the comprehensive cost of microgrids, taking into account the effects of electricity price fluc-tuations, environmental costs, and energy storage degradation costs. The improved opti-mal value evolution curves are shown in Figures 8 and 9, where the vertical axis repre-sents the optimal value of the comprehensive operating cost and the horizontal axis rep-resents the number of iterations. Figure 8. Comprehensive cost convergence curve of urban microgrid. Figure 9. Comprehensive cost convergence curve of microgrids in agricultural and pastoral areas. Compared with the SCA and the HHO algorithm [31], the CLACS optimal value curve will not fall into the optimal solution so quickly, and its fitness is also reduced. The comprehensive costs of the SCA and HHO in the urban interconnection mode are 668.4 and 651.1, respectively, and the comprehensive cost of the CLSCA is 629.5. The compre-hensive costs of the SCA and HHO in the independent agricultural and pastoral area mode are 266 and 262.1, respectively, and the comprehensive cost of CLSCA is 253.8. The Figure 9. Comprehensive cost convergence curve of microgrids in agricultural and pastoral areas.Compared with the SCA and the HHO algorithm [31], the CLACS optimal valuecurve will not fall into the optimal solution so quickly, and its fitness is also reduced. Thecomprehensive costs of t SCA and HHO in the rban interconnection mode are 668.4 and651.1, spectively, and the comprehensive cost of the CLSCA is 629.5. The compreh nsivecosts of the SCA and HHO in the independent agricultural and pastoral area mode ar266 and 262.1, respectively, the comprehensive cost of CLSCA is 253.8. The algorithmbefor th improvement in the figure begins to conv rge in the early iteration, while t eimproved algorithm begins to converge after about 60 iterations. This shows that theimproved algorithm has better global exploration capabilities.Batteries 2025, 11, 169 18 of 22Figure 10 depicts the output power of diesel generators, energy storage batteries, andthe utility grid obtained using the CLSCA under the condition of minimizing compre-hensive costs. It can be observed that during the early morning period with the lowestelectricity prices, the utility grid increases its output power while the batteries chargethemselves, thereby achieving energy scheduling during periods of low load and lowelectricity prices. Meanwhile, during the period of 11:00 to 16:00 when the output power ofrenewable energy generation is relatively high, the output power of all three componentsdecreases. This period coincides with the peak wind and sunlight intensity throughout theday. Furthermore, at around 10:00 and 11:00, a portion of the microgrid’s generation is soldback to the utility grid when electricity prices are highest. By selling excess electricity tothe utility grid during peak price periods, the microgrid effectively reduces costs.Batteries 2025, 11, x FOR PEER REVIEW 18 of 23 algorithm before the improvement in the figure begins to converge in the early iteration, while the improved algorithm begins to converge after about 60 iterations. This shows that the improved algorithm has better global exploration capabilities. Figure 10 depicts the output power of diesel generators, energy storage batteries, and the utility grid obtained using the CLSCA under the condition of minimizing comprehen-sive costs. It can be observed that during the early morning period with the lowest elec-tricity prices, the utility grid increases its output power while the batteries charge them-selves, thereby achieving energy scheduling during periods of low load and low electric-ity prices. Meanwhile, during the period of 11:00 to 16:00 when the output power of re-newable energy generation is relatively high, the output power of all three components decreases. This period coincides with the peak wind and sunlight intensity throughout the day. Furthermore, at around 10:00 and 11:00, a portion of the microgrid’s generation is sold back to the utili y grid when electricity prices are highest. By s lling excess elec-tricity to the utility grid during peak price periods, the microgrid effectively reduces costs. After 18:00, as the output power of wind and solar generation reaches its lowest point of the day; both energy storage and the utility grid begin to increase their output power to compensate for th shortfall in renewable energy generation. As the clock approaches midnight, us r loads ter a relatively low lev l, and the utility grid charges based on off-peak electricity prices. This lower electricity price prompts the batteries to start storing energy during the early morning hours. This flexible and dynamic adjustment signifi-cantly reduces the comprehensive operating costs of the microgrid. Figure 10. Urban output power. Figure 11 shows the rated output power of the diesel generator and battery in the independent mode in the agricultural and pastoral areas. It can be seen that the battery is charged during the peak period of photovoltaic and wind power generation, and dis-charged during the low period of renewable energy power generation, which effectively adjusts the peak-to-valley difference of power load and ensures that the microgrid system can provide stable power services when the public network is offline. Figure 10. Urban output power.After 18:00, as the output power of wind and solar generation reaches its lowest pointof the day; both energy storage and the utility grid begin to increase their output powerto compensate for the shortfall in renew ble energy gene ation. As the clock approachesmidnight, user loads enter a relatively low level, and the utility grid charges based onoff-peak electricity prices. This lower electricity price prompts the batteries to start storingenergy during the early morning hours. This flexible and dynamic adjustment significantlyreduces the comprehensive operating costs of the microgrid.Figure 11 shows the rated output power of the diesel generator and battery in theindependent mode in the agricultural and pastoral areas. It can be seen that the battery ischarged during the peak period of photovoltaic and wind power generation, and dischargedduring the low period of renewable energy power generation, which effectively adjusts thepeak-to-valley difference of power load and ensures that the microgrid system can providestable power services when the public network is offline.The following Figure 12 illustrates the output power and degradation cost of thebattery. It can be observed that when the charging and discharging depths of the batteryare relatively large, the degradation cost of the battery also increases accordingly. Therefore,adjusting the output power of energy storage reasonably can effectively reduce the degra-dation cost of the battery, thereby lowering the overall operating costs of the microgrid.The same applies to agricultural and pastoral areas.The predicted power balance diagrams obtained through the experiment are as follows,namely, Figure 13, the urban power balance diagram, and Figure 14, the agricultural andpastoral power balance diagram. The curves in the figure represent the changes in powerload during the day. In the case of multiple limiting factors in renewable energy powergeneration, the output power of multiple power generation ends is adjusted in variousBatteries 2025, 11, 169 19 of 22ways to ensure the smooth operation of the load end of the microgrid system at a lowoperating cost.Batteries 2025, 11, x FOR PEER REVIEW 19 of 23 Figure 11. Output power in agricultural and pastoral areas. The following Figure 12 illustrates the output power and degradation cost of the bat-tery. It can be observed that when the charging and discharging depths of the battery are relatively large, the degradation cost of the battery also increases accordingly. Therefore, adjusting the output power of energy storage reasonably can effectively reduce the deg-radation cost of the battery, thereby lowering the overall operating costs of the microgrid. The same applies to agricultural and pastoral areas. Figure 12. Battery output power and degradation cost. The predicted power balance diagrams obtained through the experiment are as fol-lows, namely, Figure 13, the urban power balance diagram, and Figure 14, the agricultural and pastoral power balance diagram. The curves in the figure represent the changes in power load during the day. In the case of multiple limiting factors in renewable energy power generation, the output power of multiple power generation ends is adjusted in various ways to ensure the smooth operation of the load end of the microgrid system at a low operating cost. Fig re 11. t t o er in agric lt ral an astoral areas.Batteries 2025, 11, x FOR PEER REVIEW 19 of 23 Figure 11. Output power in agricultural and pastoral areas. The following Figure 12 illustrates the output power and degradation cost of the bat-tery. It can be observed that when the charging and discharging depths of the battery are relatively large, the degradation cost of the battery also increases accordingly. Therefore, adjusting the output power of energy storage reasonably can effectively reduce the deg-radation cost of the battery, thereby lowering the overall operating costs of the microgrid. The same applies to agricultural and pastoral areas. Figure 12. Battery output power and degradation cost. The predicted power balance diagrams obtained through the experiment are as fol-lows, namely, Figure 13, the urban power balance diagram, and Figure 14, the agricultural and pastoral power balance diagram. The curves in the figure represent the changes in power load during the day. In the case of multiple limiting factors in renewable energy power generation, the output power of multiple power generation ends is adjusted in various ways to ensure the smooth operation of the load end of the microgrid system at a low operating cost. Figure 12. Battery output power and degradation cost.Batteries 2025, 11, x FOR PEER REVIEW 20 of 23 Figure 13. Urban power balance diagram. Figure 14. Power balance diagram for agricultural and pastoral areas. 7. Conclusions Microgrids, as flexible and organized electrical power systems, effectively integrates various generation sources and loads to meet regional electricity demands. The dynamic optimization of multiple distributed energy resources ensures the stability of the entire system, achieving efficient and reliable power supply. This paper analyzes the operational characteristics of distributed energy resources in microgrid systems, establishes mathe-matical models for wind power generation, photovoltaic generation, diesel generator gen-eration, and battery energy storage, and clarifies their constraints. Based on this, a daily operational model for microgrids is constructed to reduce the overall operating costs of microgrid systems. Unlike previous studies that only consider economic costs and envi-ronmental management costs in microgrid operating costs, this paper incorporates battery degradation costs as an important influencing factor in comprehensive cost analysis of the Figure 13. Urban power balance diagram.Batteries 2025, 11, 169 20 of 22Batteries 2025, 11, x FOR PEER REVIEW 20 of 23 Figure 13. Urban power balance diagram. Figure 14. Power balance diagram for agricultural and pastoral areas. 7. Conclusions Microgrids, as flexible and organized electrical power systems, effectively integrates various generation sources and loads to meet regional electricity demands. The dynamic optimization of multiple distributed energy resources ensures the stability of the entire system, achieving efficient and reliable power supply. This paper analyzes the operational characteristics of distributed energy resources in microgrid systems, establishes mathe-matical models for wind power generation, photovoltaic generation, diesel generator gen-eration, and battery energy storage, and clarifies their constraints. Based on this, a daily operational model for microgrids is constructed to reduce the overall operating costs of microgrid systems. Unlike previous studies that only consider economic costs and envi-ronmental management costs in microgrid operating costs, this paper incorporates battery degradation costs as an important influencing factor in comprehensive cost analysis of the Figure 14. Power balance diagram for agricultural and pastoral areas.7. ConclusionsMicrogrids, as flexible and organized electrical power systems, effectively integratesvarious generation sources and loads to meet regional electricity demands. The dynamicoptimization of multiple distributed energy resources ensures the stability of the entiresystem, achieving efficient and reliable power supply. This paper analyzes the operationalcharacteristics of distributed energy resources in microgrid systems, establishes math-ematical models for wind power generation, photovoltaic generation, diesel generatorgeneration, and battery energy storage, and clarifies their constraints. Based on this, a dailyoperational model for microgrids is constructed to reduce the overall operating costs ofmicrogrid systems. Unlike previous studies that only consider economic costs and envi-ronmental management costs in microgrid operating costs, this paper incorporates batterydegradation costs as an important influencing factor in comprehensive cost analysis of thesystem. The aim is to ensure the lowest operating costs of the microgrid while mitigatingbattery degradation through dynamic adjustments.Energy management and cost planning in microgrids pose a complex nonlinear prob-lem. Traditional methods are limited by dimensionality and data volume, making itchallenging to solve such problems effectively. Therefore, this paper employs the SCA, ametaheuristic algorithm, to address this issue. The SCA offers advantages such as a simplestructure and fast convergence. To achieve better optimization results, this study improvesthe SCA using two strategies: circle chaotic mapping and Levy flight. The effectiveness ofthe improved algorithm is validated through testing functions.By applying the SCA and CLSCA to optimize the operating costs of the same mi-crogrid system, this research provides a more comprehensive and accurate assessment ofcomprehensive costs. Finally, by comparing the application effects of the SCA and CLSCA,the superiority and reliability of the CLSCA in microgrid system optimization are verified.The results demonstrate that the model effectively reduces the comprehensive operatingcosts of microgrids, promoting their optimized operation.Author Contributions: Methodology, Y.Z.; Validation, H.L.; Resources, B.C.; Writing—review & edit-ing, C.W., D.D. and B.C. All authors have read and agreed to the published version of the manuscript.Funding: This research received no external funding.Batteries 2025, 11, 169 21 of 22Data Availability Statement: The original contributions presented in this study are included in thearticle. Further inquiries can be directed to the corresponding author.Conflicts of Interest: Author Yiming Zhao was employed by the company Inner Mongolia ElectricPower (Group) Co., Ltd. Author Dong Du was employed by the company Inner Mongolia ElectricPower Group Mengdian Information and Communication Industry Co., Ltd. The remaining authorsdeclare that the research was conducted in the absence of any commercial or financial relationshipsthat could be construed as a potential conflict of interest.References1. Thirunavukkarasu, G.S.; Seyedmahmoudian, M.; Jamei, E.; Horan, B.; Mekhilef, S.; Stojcevski, A. Role of optimization techniquesin microgrid energy management systems—A review. Energy Strategy Rev. 2022, 43, 100899. 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microgrid
optimal scheduling
renewable energy sources
degradation costs
Microgrid Energy Management Considering Energy Storage Degradation Cost
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