Storage Capacity Research Articles

Availability, storage capacity, and diffusion: Stationary states of an asymmetric exclusion process connected to two reservoirs

Availability, storage capacity, and diffusion: Stationary states of an asymmetric exclusion process connected to two reservoirs

Flexible Bridged Thermoelectric Device with an Optimized Heatsink for Personal Thermal Management.

A wearable thermoelectric cooler (TEC) for personal thermal management exhibits significant growth in numerous applications in personal thermal comfort and saving the energy consumed by space cooling. Most TECs provide a large cooling performance with the assistance of rigid heatsinks and electrodes, limiting wearability and practical implementation. Here, we design and propose a flexible bridged personal TEC with a high thermal management heatsink and spray-printed liquid metal electrodes. The system combines a bendable heatsink, a thermally insulative TE layer, and a bottom thermally conductive layer. Especially, the flexible heatsink composed of metal foam, phase change material, and fin structure greatly enhances the thermal conduction, storage, and diffusion capacities. Our TEC exhibits the desired comfortability and obtains an ideal temperature drop of 3 °C on human skin. Also, it could work as a self-generator providing 45 mV with a ΔT of 5 °C, which improves the generation efficiency by more than 3 times due to the stable temperature difference between the two sides. This work provides an effective way to develop wearable TEC devices and paves the way for achieving practical, personalized cooling applications.

Comprehensive analysis of the synthesized Zinc-doped yttrium titanate pyrochlore solid solution: Structural, vibrational, and electrochemical insights

A novel Zinc-doped Yttrium Titanate (YTZ) solid solution with a pyrochlore structure, synthesized via a solid-state route, was investigated for its potential in hydrogen storage applications. Comprehensive characterization using various techniques confirmed the formation of a cubic crystal structure with the Fd-3m space group for compositions within the ZnO content range from x = 0 to 0.30. A subtle increase in the lattice parameter (a) was observed with increasing substitution levels (x). This increase is attributed to the substitution of Zn2+ on Ti4+ sites and the concomitant creation of vacancies in both the anionic and cationic sublattices, as revealed by quantitative Rietveld analysis. The YTZ solid solution exhibits semiconducting behavior with a band gap ranging from 3.10 to 3.25 eV that may contribute to its hydrogen storage properties. Notably, the YTZ0.25 composition displayed a remarkable hydrogen storage capacity of 1200 mAh/g. This can be attributed to the presence of active redox species, favorable morphology, and the structural vacancies introduced by Zn2+ substitution, which facilitate hydrogen interaction. These findings position YTZ solid solution as a promising candidate for clean energy technologies, particularly in the realm of hydrogen storage.

Effect of CNF ratio and pressure on structural and electrochemical performance of hybrid hydrogel for flexible free-standing electrode and sensors

A 2D flexible hydrogel (GO/CNFn) with layered structure and superhydrophilic is synthesized via cross-linking and self-assembling of graphene oxide (GO) with cellulose nanofiber (CNF) through microwave-assisted hydrothermal. CNF acts as “dispersant” and “spacer”, making GO nanosheets uniformly disperse on their surface with less agglomerations. The carboxyl groups and hydrophilicity of CNF effectively improve the charge storage capacity of carbon materials through interactions. When the mass ratio of GO to CNF is 3:1, the GO/CNF1 exhibits an excellent comprehensive electrochemical performance as free-standing electrodes, with the specific capacitance reaching 295 F/g at 0.5 A/g in three-electrode system. The influence of press pressure on GO/CNFn reveals that increasing the pressure improves the hydrophilicity of the electrode, favoring their wettability to aqueous electrolyte. GO/CNF1–6 possesses the highest degree of graphitization, and delivers a highest mass specific capacitance up to 493 F/g at 0.5 A/g. Flexible solid-state symmetric supercapacitor with GO/CNF1–6 as electrodes exhibits an energy density of 20.6 Wh/kg at a power density of 250 W/kg. The good flexibility and biocompatibility of the devices show sensitive current response to biological signals, endowing them potential application prospect in wearable portable electronics and human motion detections.

Multi-objective planning of distribution network based on distributionally robust model predictive control

The uncoordinated integration of numerous distributed resources poses significant challenges to the safe and stable operation of distribution networks. To address the uncertainties associated with the intermittent output of distributed power sources, we propose a multi-objective planning strategy for distribution networks based on distributionally robust model predictive control (MPC). Initially, an error fuzzy set is established on a Wasserstein sphere using historical data to enhance out-of-sample performance. Next, a multi-objective optimization framework is constructed, balancing returns and risks, and is subsequently converted into a single-objective solution using value-at-risk conditions. This is followed by the implementation of multi-step rolling optimization within the model predictive control framework. We have linearized the proposed model using the linearized power flow method and conducted a thorough validation on an enhanced IEEE 37-node test system. Distributionally robust optimization (DRO) has been shown to reduce costs by a significant 29.16% when compared to an RO method. Moreover, the energy storage capacity required has been notably reduced by 33.33% on the 29-node system and by 20% on the 35-node system. These quantified results not only demonstrate the substantial economic efficiency gains but also the enhanced robustness of our proposed planning under the uncertainties associated with renewable energy integration.

Theoretical assessment of a novel NaXH3 and KXH3 (X = Tc, Ru and Rh) perovskite hydrides for hydrogen storage

Utilizing the Cambridge Serial Total Energy Package (CASTEP), we examined various properties of the compounds NaXH3 and KXH3 (where X represents Tc, Ru and Rh). These properties include structural, thermodynamic, hydrogen storage, optical, mechanical, and electronic. The studied compounds exhibit stables cubic crystal structures with lattice constants between 3.53 Å and 3.77 Å. Their mechanical and thermodynamic stability is confirmed by their elastic constants, phonon dispersion, and negative formation energies. The gravimetric hydrogen storage capacities are 2.44, 2.38, 2.35, 2.16, 2.11 and 2.08 wt percent for NaTcH3, NaRuH3, NaRhH3, KTcH3, KRuH3 and KRhH3, respectively. Notably, KTcH3 has the most practical hydrogen desorption temperature of 365 K. Electronic properties reveal a consistent metallic behavior across all compounds, opening possibilities for applications beyond hydrogen storage. Their calculated optical properties, including conductivity, absorption, and refractive index, suggest that KTcH3 may be suitable for use in optoelectronic devices and solar cells. Mechanical analysis highlights NaRuH3 as the hardest material, based on the investigated elastic moduli. These findings underscore the potential of sodium- and potassium-based perovskite hydrides not only for hydrogen storage but also for advanced energy systems, electronics, and optics.

Copper based high temperature heat storage macrocapsules with optimized inner cavity

The development of practical high temperature metallic phase change macrocapsules still faces difficulties, because metallic phase change materials undergo volume expansion during phase transformations, which can lead to outer shell rupture. When a core made of stacked metal powders is used, a cavity is eventually formed inside the capsule that acts as a cushion for volume expansion, thus reducing the risk of capsule rupture. However, the cavity will weaken the thermal storage capacity of the capsule, and in order to obtain a capsule with good thermal storage capacity and long-time cycling stability, it is necessary to find a suitable cavity volume of the capsule. In this paper, Cu powders are used as the core raw material, which are spherelized into millimeter level spheres, and the Cu powder spheres are isostatically pressed using an isostatic presser under different pressures to achieve the optimization of the cavity volume by reducing the gap between the powders. The high strength α-Al2O3 is selected as the shell, and sintering additives MgO and SiO2 are doped into the raw material, and the Cu@MgO-SiO2/Al2O3 capsules are prepared after two-step sintering treatment. The material properties and thermal storage properties of the capsules are investigated in detail, which have strong thermal storage properties, for example, in the temperature interval of 1000–1100 ℃, capsules with a core-shell structure (named as 9@1.5–100 MPa, prepared with initial diameter of Cu core of 9 mm, shell thickness of 1.5 mm, and isostatic pressing under 100 MPa to the core precursor) exhibit a high heat storage density of 222 J/g and 841 MJ/m³. In addition, we conduct melting-solidification cycle tests, which confirms the excellent durability of the capsules. The comprehensive results show that the Cu@MgO-SiO2/Al2O3 macrocapsules possess strong thermal storage capacity and can be used as effective thermal storage materials, especially in advanced high temperature thermal storage systems.

Intermetallic Compounds for Hydrogen Storage: Current Status and Future Perspectives.

Intermetallic compounds are an emerging class of materials with intriguing hydrogen activation and storage capabilities garnering attention for their application in low-temperature hydrogen storage and metal hydride batteries. However, none of the existing intermetallic compounds have met the gravimetric hydrogen storage capacity target of 5.5wt.%. Some A2B-type intermetallic compounds, like Mg2Ni, Mg2Co, and Mg2Fe, approach this target but require high temperatures for hydrogen desorption limiting their use in low-temperature hydrogen storage and automotive applications. Conversely, some intermetallic compounds like ZrV2 and LaNi5, exhibit hydrogen desorption at ambient conditions but with comparatively lower hydrogen storage capacities. This review article provides a comprehensive account of the different types of intermetallic compounds, their synthesis using different solidification-based and solid-state diffusion-based approaches, and their metallurgical and structural properties. It examines the complex interdependencies between the structural parameters of intermetallic compounds and hydrogen storage performance. A definitive but non-linear correlation is identified between void volume and gravimetric hydrogen storage capacities while lattice structure, evolution of lattice structure with hydrogen absorption, enthalpy of hydride formation, and hydrogen activation reactivities of intermetallic compounds are identified as critical parameters governing hydrogen storage performance.

Performance evaluation of nano-enhanced phase change materials for thermal energy storage: An experimental study

In rapidly developing economies, the increasing energy demand and fossil fuel consumption have made the need for renewable energy sources and efficient thermal energy storage (TES) solutions more urgent than ever. This study focuses on enhancing the thermal energy storage capabilities of paraffin-based phase change materials (PCMs) by incorporating Al2O3, MgO, and CuO nanoparticles. The evaluation of nano-enhanced PCMs focused on their melting temperatures, thermal storage capacities, thermal conductivities, and charge/discharge times. The experimental results revealed significant changes in the thermal properties of the nano-enhanced PCMs compared to pure paraffin. The melting temperature was raised by 2 °C due to Al2O3 nanoparticles, whereas CuO and MgO nanoparticles decreased it by 1.7 °C and 1.8 °C, respectively. Compared to pure paraffin, Al2O3-PW, MgO-PW, and CuO-PW exhibited improvements of 13 %, 39 %, and 48 % in thermal conductivities, respectively. CuO-doped paraffin showed an 11.8 % decrease in discharge time, suggesting its suitability for rapid heat transfer applications like defrosting systems or thermal management in electronics. On the other hand, paraffin doped with MgO showed a minimal 2.24 % reduction in discharge time, indicating its effectiveness in applications requiring heat retention, particularly for improved thermal insulation in building materials. The results highlighted the potential of nano-enhanced PCMs in energy storage and construction is underlined, offering a sustainable approach to improving energy efficiency in various sectors.

Optimized Dehydrogenation of Magnesium Hydride with Fe and Cu Additives

Solid state hydrogen storage with the use of MgH2 has gained widespread attention because of its good reversible storage capacity. This metal hydride however slowly releases hydrogen at high temperatures ranging between 325 – 375 oC. An important feature required of MgH2 is its ability to commence hydrogen release at a fast rate and reduced temperature. Transition metal-containing alloys/compounds having either Fe or Cu as the principal element have been used to improve the dissociation of hydrogen from MgH2. Studies involving the use of each metal in its elemental form as an additive are minimal. This study investigated the catalytic effects of elemental Fe and Cu on the hydrogen release performance of MgH2 for potential applications in transportation and power generation. It was observed that MgH2/Fe had a better dehydrogenation performance; the temperature of onset of MgH2/Fe and MgH2/Cu dehydrogenation were 205, and 215 oC which were 98 and 88 oC lower than that for as-received MgH2. The highest amount, 1.9 wt. % H2 was released by MgH2/Fe while 1.44 wt. % H2 was released by MgH2/Cu. The activation energy for dehydrogenation was reduced from 150.5 kJ/mol for as-received MgH2 to 89.8 and 79.8 kJ/mol in MgH2/Cu and MgH2/Fe respectively. It took 18.8 min for as-received MgH2 to commence dehydrogenation while that for MgH2/Fe and MgH2/Cu composites started from 12.2 and 13.4 min respectively. The in-situ formed Fe and Cu in MgH2 after milling acted as active catalytic sites for its improved dehydrogenation with MgH2/Fe behaving better.

An Overview of the R&D of Flywheel Energy Storage Technologies in China

The literature written in Chinese mainly and in English with a small amount is reviewed to obtain the overall status of flywheel energy storage technologies in China. The theoretical exploration of flywheel energy storage (FES) started in the 1980s in China. The experimental FES system and its components, such as the flywheel, motor/generator, bearing, and power electronic devices, were researched around thirty years ago. About twenty organizations devote themselves to the R&D of FES technology, which is developing from theoretical and laboratory research to the stage of engineering demonstration and commercial application. After the research and accumulation in the past 30 years, the initial FES products were developed by some companies around 10 years ago. Today, the overall technical level of China’s flywheel energy storage is no longer lagging behind that of Western advanced countries that started FES R&D in the 1970s. The reported maximum tip speed of the new 2D woven fabric composite flywheel arrived at 900 m/s in the spin test. A steel alloy flywheel with an energy storage capacity of 125 kWh and a composite flywheel with an energy storage capacity of 10 kWh have been successfully developed. Permanent magnet (PM) motors with power of 250–1000 kW were designed, manufactured, and tested in many FES assemblies. The lower loss is carried out through innovative stator and rotor configuration, optimizing magnetic flux and winding arrangement for harmonic magnetic field suppression. Permanent magnetic bearings with high load ability up to 50–100 kN were developed both for a 1000 kW/16.7 kWh flywheel used for the drilling practice application in hybrid power of an oil well drilling rig and for 630 kW/125 kWh flywheels used in the 22 MW flywheel array applied to the flywheel and thermal power joint frequency modulation demonstration project. It is expected that the FES demonstration application power stations with a total cumulative capacity of 300 MW will be built in the next five years.

Energy Management System for Polygeneration Microgrids, Including Battery Degradation and Curtailment Costs.

Recent advancements in sensor technologies have significantly improved the monitoring and control of various energy parameters, enabling more precise and adaptive management strategies for smart microgrids. This work presents a novel model of an energy management system (EMS) for grid-connected polygeneration microgrids that allows optimizing the management of electrical storage systems, electric vehicles, and other deferrable loads such as heat pumps. The main novelty of this model is that it incorporates both climate comfort variables and the consideration of the degradation of the energy storage capacity in the control strategy, as well as a penalty for the dumping of surpluses. The model has been applied to a smart, sustainable building as a case study. The results show that the proposed model is highly adaptable to diverse weather conditions, minimizing renewable energy losses while satisfying the energy demand and providing comfort to the building's users. The study shows (i) that EVs' dynamic charging schedules play a crucial role, (ii) that it is possible to minimize a battery's degradation by optimizing its cycling, averaging one cycle per day, and (iii) the critical impact of seasonal weather patterns on microgrid energy management and the strategic role of EVs and storage systems in maintaining energy balance and efficiency.

Optimizing CLM4.5 simulations of the active layer: The role of gravel in Tibetan Plateau permafrost

Gravel is widely distributed in soils of the Tibetan Plateau (TP), where permafrost also occurs over approximately half of the total area. Gravel has different thermal and hydrological properties to those of fine-grained soils, which may have a considerable impact on hydrothermal transport within TP soils. However, few land models consider gravel. Here, we incorporated the thermal and hydraulic properties of gravel into the Community Land Model and explored the effect of differing gravel contents on land surface processes. We found that all parameters affecting soil hydrothermal transport were sensitive to gravel content. Soil thermal and hydraulic conductivities increased with increasing gravel content, ultimately leading to variations in soil temperature, soil water content, and radiation fluxes with changing gravel content. Soil containing gravel exhibited higher infiltration and greater total water storage capacities. We also compared different model schemes in an attempt to improve the simulation of active layers in permafrost regions with high gravel content on the TP. The scheme in which both gravel and freeze–thaw parameterizations were applied (i.e., SP3) improved both the latent heat flux and ground heat flux transfer. The SP3 scheme performed best in terms of soil temperature and soil moisture simulations at both the Nagqu and Madoi field stations, demonstrating a particular ability to better characterize soil moisture processes as a function of temperature during soil freezing and thawing.

1T′-MoSP monolayer as an anode material for sodium-ion batteries with ultrahigh storage capacity and ultralow diffusion barrier

Sodium-ion batteries (SIBs) have gained significant attention due to the abundant availability and low cost of sodium. However, the search for high-performance anode materials remains a critical challenge in advancing SIB technology. Based on first-principles swarm-intelligence structure calculations, we propose a metallic 1T′-MoSP monolayer as an anode material that offers a remarkably high storage capacity of 1011 mA h g−1, an ultralow barrier energy of 0.04 eV, and an optimal open-circuit voltage of 0.29 V, ensuring high rate performance and safety. Additionally, the monolayer presents favorable wettability with commonly used SIB electrolytes. Even after adsorbing three-layer Na atoms, the 1T′-MoSP monolayer retains its metallic nature, ensuring excellent electrical conductivity during the battery cycle. These desirable properties make the 1T′-MoSP monolayer a promising anode material for SIBs.

Energy enhancement of Nd,Sc:YAG crystal in passively Q-switched lasers.

We report on the laser performance of Nd,Sc:YAG (yttrium aluminum garnet), for the first time, to our knowledge. In this study, 10 at.% Sc3+ ions were doped into the Nd:YAG crystal to form the Nd,Sc:YAG crystal, which improves the saturation flux while nearly maintaining the excellent properties of the Nd:YAG crystal. The continuous-wave (CW) and passively Q-switched (PQS) laser performances of the Nd,Sc:YAG crystal at 1064 nm were investigated. The CW output power reached 4.5 W at the absorbed pump power of 8.07 W, with a slope efficiency of 63.1% and an optical-to-optical efficiency of 55.7%. A stable PQS laser was achieved employing Cr4+:YAG as a saturable absorber (SA). The maximum average output power attained was 1.84 W, with a slope of 23.5%. The pulse width, pulse energy, and frequency were 17.0 ns, 69.2 µJ, and 26.6 kHz, respectively. Compared to the Nd:YAG crystal, the pulse energy of the Nd,Sc:YAG crystal was enhanced by approximately 1.7 times. These results show that the Nd,Sc:YAG crystal is a promising laser material with larger energy storage capacities, making it suitable for the application of high-energy lasers (HELs) with high repetition rate.

Hybrid Renewable Systems for Small Energy Communities: What Is the Best Solution?

This research developed smart integrated hybrid renewable systems for small energy communities and applied them to a real system to achieve energy self-sufficiency and promote sustainable decentralized energy generation. It compares stand-alone (SA) and grid-connected (GC) configurations using a developed optimized mathematical model and data-driven optimization, with economic analysis of various renewable combinations (PV, Wind, PHS, BESS, and Grid) to search for the optimal solution. Four cases were developed: two stand-alone (SA1: PV + Wind + PHS, SA2: PV + Wind + PHS + BESS) and two grid-connected (GC1: PV + PHS + Grid, GC2: Wind + PHS + Grid). GC2 shows the most economical with stable cash flow (−€123.2 annually), low CO2 costs (€367.2), and 91.7% of grid independence, requiring 125 kW of installed power. While GC options had lower initial investments (between €157k to €205k), the SA configurations provided lower levelized costs of energy (LCOE) ranging from €0.039 to €0.044/kWh. The integration of pumped hydropower storage enhances energy independence, supporting peak loads for up to two days with a storage capacity of 2.17 MWh.

Electrochemical Performance of MoB/Si3N4 Heterojunction as a Potential Anode Material for Li Ion Batteries.

In response to the current policy of high storage capacity, two-dimensional (2D) materials have revealed promising prospects as high-performance electrode materials. MoB, as a type of such material, is widely regarded as an anode candidate for Li-ion batteries due to its large specific surface area and abundant ion diffusion channels; the long-term cycling stability, however, is poor owing to material pulverization during the cycle. Therefore, MoB/Si3N4 heterojunction in this work is proposed as an anode material, with Si3N4 acting as a skeleton, maintaining the stability of the structure, while retaining the high energy storage properties of MoB as well. In addition, a certain built-in electric field is formed between them, which can play a role in regulating charge transfer, improving the ion transport channel, and accelerating the migration rate. Herein, the structural, electronic, and electrochemical properties are systematically investigated by first-principles calculations; the final results indicate that the heterojunction anode material does indeed have built-in electric fields, which promote the anode material to possess excellent electrical conductivity and outstanding electrochemical property. Meanwhile, the introduction of vacancy defects can bolster the diffusion kinetic performance of ion transport and greatly reduce the diffusion energy barrier of Li ions, which is conducive to the realization of rapid charge and discharge for the Li ion battery. Based on the synergistic effect of two single-component materials, the synthesized anode material displays a high theoretical capacity of 461 mAh/g, and the calculated open-circuit voltage is 0.66 V, within the range of the negative electrode criterion of 0-1 V, which can effectively play a role in preventing the formation of Li dendrites; these properties are comparable to other 2D anode materials as well. Given these intriguing properties, the MoB/Si3N4 heterojunction is an exceptional candidate for advanced LIB high-performance anode materials.

Mo‐Doped Perovskite Cathode Enables High‐Performance Cycling‐Stable Zinc‐Ion Batteries

AbstractManganese compounds have emerged as promising cathode materials for aqueous zinc‐ion batteries (AZIBs). But their broader applications are impeded by such cathodes' poor structure stability and sluggish ion transportation. Herein, these limitations are addressed by proposing high‐valence Mo doping regnant LaMnO3 perovskite oxide cathodes to develop high‐performance rate stable AZIBs. The optimized doped cathode contributes a highest specific capacity of 445 mAh g−1 at the current density of 0.5 A g−1, which maintains 206 mAh g−1 at 2 A g−1 and accompanies with a remarkable capacity retention of 114% beyond 1000 cycles for continuous charge/discharge process. The doping of multivalent Mo is revealed to boost the energy storage capacity and stabilize the electrode structure via various ex situ characterization and theoretical calculations. Importantly, the incorporation of Mo facilitates the acceleration of reaction kinetics and sufficient charge transfer with H+ and Zn2+ as dual charge carriers, where H+ plays a dominant role. This work provides a new perspective on developing innovative perovskite oxide cathodes with high‐valence metal doping for AZIBs.

Distribution of phosphorus forms in soil amended with poultry litter of different ages and application rates: Agronomic and environmental perspectives

AbstractPoultry litter (PL) can be used as a viable alternative to phosphate fertilizers. However, there is a lack of information about phosphorus (P) distribution in inorganic (Pi) and organic (Po) forms and its transformation in soils amended with PL of varying age (based on litter clean‐out frequency) and application rate. This study aimed to determine the effect of PL age and application rate on soil P forms and their bioavailability. Soils were amended with 5 and 10 Mg ha−1 PL using 6‐, 18‐, and 30‐month‐old litter and incubated for 6 months. Soil P fractionation was performed following the Hedley protocol. Soil P availability and soil P storage capacity (SPSC) were determined using Mehlich 3 (M3) extraction. Results indicated that P transformation from labile to stable P forms occurred over 150‐day incubation. Litter age had no significant effect on the distribution of soil P forms. However, the highly reactive Pi (HRPi) form was higher for treatments with 10 Mg ha−1 PL on Day 0, indicating a risk for P loss, which was also revealed by negative SPSC for those treatments. At Day 0, M3‐P was positively correlated to HRPi. However, from Day 30 to 150, M3‐P was strongly correlated to both HRPi and moderately reactive Pi (MRPi) forms, indicating MRPi contribution to soil P availability. The negative relationship between HRPi and SPSC further confirms that high HRPi on Day 0 may be an environmental concern.

Capacity Optimization of Wind–Solar–Storage Multi-Power Microgrid Based on Two-Layer Model and an Improved Snake Optimization Algorithm

A two-layer optimization model and an improved snake optimization algorithm (ISOA) are proposed to solve the capacity optimization problem of wind–solar–storage multi-power microgrids in the whole life cycle. In the upper optimization model, the wind–solar–storage capacity optimization model is established. It takes wind–solar power supply and storage capacity as decision variables and the construction cost of the whole life cycle as the objective function. At the lower level, the optimal scheduling model is established, considering the output characteristics of various types of power supplies and energy storage, microgrid sales, and purchases of power as constraints. At the same time, the model considers constraints, such as the power balance, the operating state of the energy storage system, the power sales and purchases, and the network fluctuations, to ensure the system operates efficiently. Taking a microgrid in South China as an application scenario, the model is solved and the optimal capacity allocation scheme of the microgrid is obtained. Meanwhile, the demand response mechanism and the influence of planning years are introduced to further optimize the configuration scheme, and the impact of different rigid–flexible load ratios and various planning horizons on microgrid capacity optimization is analyzed, respectively, by a numerical example. The comparison shows that the ISOA has better optimization performance in solving the proposed two-layer model.