Thermodynamic Analysis of Thermal Efficiency and Entropy Production in Distributed Energy Storage Systems within Power Distribution Networks

In the domain of power distribution networks, the energy storage modules within DESS typically utilize highly efficient energy storage media, coupled with advanced thermal management techniques, to ensure effective energy storage and release. These modules predominantly comprise Phase Change Materials (PCM) as the energy storage medium, characterized by their ability to oscillate between solid and liquid states while absorbing or releasing heat, effectuating high-density energy storage and stable thermal output. Encircling the PCM, heat transfer fluid channels, strategically designed, facilitate the conversion of surplus electrical energy from the grid into thermal energy. This thermal energy is transferred to the PCM via mediums like water or air, or conversely, the stored thermal energy is swiftly converted back to electrical energy as necessitated. The exterior of the storage module is enveloped in an insulation material with low thermal conductivity to reduce thermal losses and prevent ineffective thermal energy leakage due to external environmental fluctuations, thereby preserving the overall thermal efficiency of the system.

In these networks, the DESS energy storage module is the central component for energy regulation and storage. Its heat transfer mechanism is critical to the thermal efficiency and energy management performance of the system. This study is dedicated to a detailed analysis of the heat transfer mechanism in the storage module, aiming to optimize its thermal efficiency and minimize entropy production. This analysis encompasses three key aspects:

· Heat exchange between the heat transfer fluid and the PCM surface: This process significantly influences the thermal efficiency of the storage module. The fluid, as it traverses the channels, engages in heat transfer with the PCM through convection. The efficiency of this interaction is contingent upon factors such as the fluid's flow velocity, the nature of contact between the fluid and PCM surface, the fluid's temperature, and the PCM's thermal conductivity. Optimizing the fluid's flow dynamics and surface properties enhances the heat exchange efficiency at this interface.

· Internal heat transfer within PCM: This involves both thermal conduction and phase change heat transfer mechanisms. Thermal conduction within the PCM pertains to heat propagation through molecular or lattice vibrations in its solid state. Phase change heat transfer pertains to the absorption or release of heat during the PCM's phase transition. The latent heat associated with PCM phase changes is substantial, making the efficiency of heat storage or release during these transitions vital to the overall module performance. Enhancing internal heat transfer efficiency in the PCM can be achieved by incorporating high thermal conductivity fillers or utilizing metallic framework structures to amplify internal heat conduction.

· Thermal exchange between the system and its environment: Operational storage modules inevitably engage in thermal exchange with their surroundings, often resulting in thermal energy losses and affecting the system's thermal efficiency. To mitigate undesired thermal exchange, the storage module is designed with insulation layers that limit heat transfer to the environment through radiation, convection, and conduction. The insulating performance, and thus the system's energy retention capability and stability, are influenced by the material choice and structural design of these insulation layers.

In the arena of power distribution networks, computational models for thermal analysis of DESS predominantly focus on accurately delineating the thermal response of storage materials and the system’s thermal management behavior. These models extensively use complex partial differential equations for characterizing heat conduction, convection, and phase transitions, enabling the simulation of temperature distribution within storage materials and its temporal alterations. Integration of porous media models in some instances allows for considering the percolation effects of heat transfer fluids within the storage medium. Distinguished by their capacity to manage intricate boundary conditions, time-dependent heat sources, and the temperature-dependent non-linearity of material properties, these models are instrumental in design and optimization phases. They facilitate engineers in assessing thermal efficiency and thermal load response across varied design scenarios and support the development of operational strategies by simulating the system's thermal behavior under diverse operating conditions. Figure 1 depicts a schematic of the numerical computation for the energy storage module in DESS.

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Figure 1. Schematic diagram of numerical computation for energy storage module in DESS

Current simulation models predominantly utilize a single-phase flow approach, presuming a consistent phase state during heat transfer processes, or a more elaborate two-phase flow paradigm. Despite their detail, these models incur high computational demands and necessitate precise parameterization, which may impede swift application in practical engineering settings. To more effectively capture heat conduction and convective heat transfer phenomena during phase changes, while circumventing the computational intensity of tracking phase interfaces in complete two-phase flow models, this study adopts a two-phase continuum model. Based on the local non-thermal equilibrium theory in porous media, a simplified transient flow and heat transfer model is established. Figure 2 presents the numerical calculation flowchart for the energy storage module in DESS.

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Figure 2. Numerical calculation flowchart for energy storage module in DESS

In the energy storage modules of DESS within power distribution networks, the formulation of conservation equations for mass, momentum, and energy in relation to the heat transfer fluid is imperative. Accurate modeling and resolution of these conservation equations are foundational for optimizing thermal management, enhancing the efficiency of energy storage, reducing energy losses, and augmenting the system’s thermal stability.

The mass conservation principle dictates that the total mass within a specified control volume remains unchanged in the absence of material ingress or egress. For the heat transfer fluid within the energy storage module, this necessitates a balance between the inflow and outflow masses at any point, thereby ensuring no unaccounted disappearance or creation of the fluid. In developing the mass conservation equation, considerations include the fluid’s velocity distribution across various directions and the fluid density fluctuations. Key parameters include the module’s porosity (γ), the heat transfer fluid's density (ϑ_d), its constant pressure heat capacity (v_o,d), the fluid’s velocity vector (i^→), pressure (o), gravitational constant vector (h^→), fluid's dynamic viscosity (ω), viscous resistance coefficient (J), inertial resistance coefficient (V_D), width per unit of PCM (f_o), convective heat transfer coefficient (g_c) between PCM and fluid, and effective thermal conductivity (j_EFF). The mass conservation equation for the heat transfer fluid is expressed as follows:

$\frac{\partial \left( \gamma {{\vartheta }_{d}} \right)}{\partial y}+\nabla \cdot \left( {{\vartheta }_{d}}\vec{i} \right)=0$          (1)

Regarding momentum conservation within the energy storage module, it encompasses the fluid particles' velocity alterations due to internal friction, interaction with conduit walls, fluid mass changes, and external pressure gradients. The momentum conservation equation is established to ensure equilibrium between all forces exerted on a fluid element and its momentum change rate. The equation is articulated as follows:

$\begin{align}  & \frac{\partial \left( {{\vartheta }_{d}}\vec{i} \right)}{\partial y}+\nabla \cdot \left( {{\vartheta }_{d}}\frac{\vec{i}\vec{i}}{\gamma } \right)=-\gamma \nabla o+\nabla \cdot \left( \vec{i}\nabla \vec{i} \right)+\gamma {{\vartheta }_{d}}\vec{h} \\ & +\gamma \left( \frac{\omega }{J}+\frac{{{V}_{D}}}{\sqrt{J}}{{\vartheta }_{d}}\left| {\vec{i}} \right| \right)\vec{i} \\\end{align}$            (2)

${{V}_{D}}=\frac{1.75}{\sqrt{150{{\gamma }^{3}}}}$             (3)

$J=\frac{f_{o}^{2}{{\gamma }^{3}}}{150{{\left( 1-\gamma  \right)}^{2}}}$           (4)

The energy conservation equation in the module captures the internal energy variations attributable to temperature changes in the heat transfer fluid and energy transfers due to the working substance's flow. In framing this equation, a balance is maintained between the energy absorbed, stored, converted, and lost by a fluid element at any moment. The energy conservation equation for the heat transfer fluid is formulated as follows:

$\begin{align}  & \frac{\partial \left[ {{\left( \gamma \vartheta {{v}_{o}} \right)}_{d}}{{Y}_{d}} \right]}{\partial y}+\nabla \cdot \left[ {{\left( \vartheta {{v}_{o}} \right)}_{d}}{{Y}_{d}}{{{\vec{i}}}_{d}} \right]= \\ & \nabla \cdot \left( {{j}_{EFF}}\nabla {{Y}_{d}} \right)+{{g}_{c}}\left( {{Y}_{a}}-{{Y}_{d}} \right) \\\end{align}$              (5)

In the DESS energy storage modules of power distribution networks, formulating energy conservation equations for PCM and their insulation layers is crucial. The equation for PCM delineates the dynamics of energy storage and release during heating and cooling processes, incorporating latent heat absorption and release during phase transitions. This aspect is critical for optimizing PCM's energy storage capacity, response rate, and overall thermal efficiency. For the insulation layer and system's external walls, the energy conservation equation is pivotal in minimizing energy loss to the external environment through radiation, convection, and conduction during operation, thereby elevating the system's energy utilization rate and stability. Precise formulation of these equations facilitates comprehensive control over intricate thermal transfer processes within the storage module, offering a robust foundation for enhancing system performance and understanding thermal management mechanisms.

The construction of PCM's energy conservation equation revolves around balancing energy changes during the material's phase transitions. In the heating phase, PCM transforms from solid to liquid, retaining a constant temperature while storing substantial latent heat. Conversely, during cooling, PCM reverts to solid, releasing stored latent heat. The equation is formulated to encapsulate this phase transition energy exchange and thermal interactions with the environment. The equation for PCM's energy conservation is formulated as:

$\frac{\partial \left\{ {{\left[ \left( 1-\gamma  \right)\vartheta {{v}_{o}} \right]}_{a}}{{Y}_{a}} \right\}}{\partial y}=\nabla \cdot \left( {{j}_{a}}\nabla {{Y}_{a}} \right)-{{g}_{a}}\left( {{Y}_{a}}-{{Y}_{d}} \right)$       (6)

For the insulation layer and system's external walls, the energy conservation equation aims to bolster thermal stability and efficiency. The insulation layer plays a vital role in impeding the thermal energy stored internally from dissipating to the outside environment, a crucial aspect when external temperature differences are significant. This equation factors in the insulation layer's thermal conductivity and potential convective and radiative heat losses from external walls, aiding in simulating and assessing the insulation layer's effectiveness. The energy conservation equation for the insulation layer and external walls is articulated as:

$\frac{\partial \left[ {{\left( \vartheta {{v}_{o}} \right)}_{INS}}{{Y}_{INS}} \right]}{\partial y}=\nabla \cdot \left( {{j}_{INS}}\nabla {{Y}_{INS}} \right)$               (7)

In DESS modules, the efficient thermal exchange between heat transfer fluid and PCM is instrumental for system performance optimization. Precise calculation of the convective heat transfer coefficient is essential for ensuring effective heat transfer to or from PCM as the fluid flows through. This coefficient influences the PCM's energy absorption and release rates, impacting the module's response time and energy density. Likewise, determining the effective thermal conductivity of the heat transfer fluid is crucial, influencing the fluid's internal thermal energy transfer capability, an integral parameter for designing fluid channels and evaluating the system's overall thermal performance. Computing the natural convective heat transfer coefficient on external vertical walls is also vital, as it governs the thermal exchange rate between the module and the environment. In scenarios lacking forced convection, natural convection dominates module cooling, with its efficiency directly affecting the system's thermal stability and energy retention.

In this study, the focus on calculating the convective heat transfer coefficient between the heat transfer fluid and PCM in DESS energy storage modules reveals how fluid dynamics facilitate thermal exchange at the fluid-solid interface. This coefficient's value is influenced by the fluid's inherent properties, its flow behavior, and the characteristics of the solid surface. The principle underlying this calculation is the assessment of heat transfer efficiency from areas of higher temperature to lower temperature, propelled by the movement of the fluid under specific conditions. Variables considered include the Reynolds number (Er_o), the Prandtl number (Oe), thermal conductivity (j_d) of the heat transfer fluid, constant pressure heat capacity (v_o,a) of PCM, PCM temperature (Y_A), thermal conductivity (j_a) of PCM, constant pressure heat capacity (v_o,INS) of insulation material, insulation material temperature (Y_INS), and thermal conductivity (j_INS) of insulation material. The equation calculating the convective heat transfer coefficient g_c is presented as:

${{g}_{c}}=\frac{6\left( 1-\gamma  \right){{j}_{d}}\left[ 2+1.1E{{r}_{o}}^{0.6}O{{e}^{{}^{1}/{}_{3}}} \right]}{f_{o}^{2}}$              (8)

$E{{r}_{o}}=\frac{{{\vartheta }_{d}}{{f}_{o}}\left| \overset{\to }{\mathop{i}}\, \right|}{{{\omega }_{d}}}$         (9)

$Oe=\frac{{{V}_{o,d}}{{\omega }_{d}}}{{{j}_{d}}}$          (10)

Determining the effective thermal conductivity of the heat transfer fluid centers on assessing the fluid's capability to disseminate internal thermal energy via molecular motion and collisions in the absence of substantial flow. This coefficient reflects the intrinsic thermal conduction attributes within the fluid, dependent on the fluid type, temperature, and pressure. The formula for calculating the effective thermal conductivity is:

${{j}_{EFF}}=\left\{ \begin{align}  & 0.7\gamma {{j}_{d}},E{{r}_{o}}<0.8 \\ & 0.5OeE{{r}_{o}}{{j}_{d}},E{{r}_{o}}>0.8 \\\end{align} \right.$                (11)

The computation of the natural convective heat transfer coefficient on external vertical walls is based on the buoyancy effect caused by density variations in the fluid due to temperature differences. Heat transfer in this context relies on internal temperature differentials and subsequent density shifts, rather than external forces inducing fluid movement. The fluid's expansion upon heating and contraction upon cooling establish a natural convective cycle, driving heat transfer. The calculation factors in wall characteristics, fluid thermal properties, and the temperature gradient. Variables include the Nusselt number (B_i), Rayleigh number (Es), Prandtl number (Oe), fluid's volumetric thermal expansion coefficient (α), and kinematic viscosity (c). The natural convective heat transfer coefficient g_OUT on external vertical walls is calculated as follows:

${{g}_{OUT}}=\frac{B{{i}_{OUT}}{{j}_{INS}}}{G}=\frac{{{\left[ 0.825+0.387{{\left( Es\cdot d\left( Oe \right) \right)}^{{}^{1}/{}_{6}}} \right]}^{2}}{{j}_{INS}}}{G}$            (12)

$d\left( Oe \right)={{\left[ 1+{{\left( {}^{0.492}/{}_{Oe} \right)}^{{}^{9}/{}_{16}}} \right]}^{{}^{16}/{}_{9}}}$              (13)

$Es=HeOe$             (14)

$He={}^{h\alpha \Delta Y{{G}^{3}}}/{}_{{{c}^{2}}}$          (15)

A significant pressure drop can escalate energy consumption and potentially result in non-uniform fluid flow. This non-uniformity can adversely affect the consistency of thermal exchange and the response of PCMs. Furthermore, the precise assessment of pressure drop is paramount for the reliability analysis of the system. Improper pressure distribution may induce fatigue in the equipment, consequently diminishing its operational lifespan. Therefore, the calculation of pressure drop within the energy storage units of DESS in power distribution networks holds critical significance. In determining the pressure drop, factors such as the fluid's density and viscosity, flow rate, as well as the conduits' length, diameter, and surface roughness are imperative. These elements collectively influence the magnitude of frictional forces encountered by the fluid in motion. Additionally, the specific geometric characteristics of each channel within the energy storage unit, along with the nature of fluid flow, substantially impact the overall pressure drop. An elaborate equation is formulated for the calculation of this pressure drop, encompassing these diverse parameters.

$\Delta O=150G\frac{{{\left( 1-\gamma  \right)}^{2}}}{{{\gamma }^{2}}}\frac{{{\omega }_{d}}{{i}_{d}}}{f_{o}^{2}}+1.7G\left( 1-\gamma  \right)\frac{{{\vartheta }_{d}}i_{d}^{2}}{{{f}_{o}}}$            (16)

Figure 4 depicts the variation in energy storage efficiency of DESS within power distribution networks, contrasting scenarios with and without insulation layers across multiple operational cycles. It was observed that, in the absence of an insulation layer, energy storage efficiency initiates at 57% and exhibits a gradual increase, achieving stability at 61% by the fourth cycle. This trend indicates an initial phase of substantial thermal losses due to significant temperature gradients, followed by the system attaining a more stable state characterized by reduced thermal losses and consistent energy storage efficiency. In contrast, the presence of an insulation layer results in a notable initial efficiency of 62.5%. This efficiency escalates rapidly with each cycle, stabilizing at 69.8% by the fourth cycle. Such findings underscore the efficacy of the insulation layer in diminishing thermal losses, thus facilitating a swifter attainment and maintenance of elevated energy storage efficiency.

Figure 5 illustrates the relationship between the pressure drops in DESS energy storage units and the corresponding energy storage efficiency across a range of temperatures (250K to 500K) over successive cycles. This analysis contributes to comprehending the impact of temperature and pressure drop on the efficiency of energy storage units. Data reveal that under all examined temperatures, an initial increase followed by a decrease in pressure drop is noted with each cycle. This pattern implies an association between pressure drop and the thermal balancing process within the energy storage unit. During the phase of increasing pressure drop, a reduction in energy storage efficiency occurs, attributed to the escalated energy loss inferred from the augmented pressure drop. Conversely, as pressure drop attains its maximum and subsequently decreases, an enhancement in energy storage efficiency is noted, attributed to the reduction in the system's internal resistance. At lower temperatures (250K and 300K), the system begins with a lower initial pressure drop; however, with temperature elevation, the initial pressure drop escalates due to the diminished fluid density and augmented flow resistance at elevated temperatures. Conversely, at higher temperatures (450K and 500K), not only does the peak pressure drop intensify with each cycle, but the post-decline stabilized pressure drop is also lower. This indicates that energy storage units more effectively achieve thermal equilibrium at higher temperatures, resulting in diminished energy losses during later cycles. Thus, it is deduced that the temperature-dependent characteristics of pressure drop in energy storage units significantly influence their efficiency. In designing and operating DESS within power distribution networks, the effect of temperature on pressure drop and energy storage efficiency warrants consideration. The design objective should encompass minimization of energy loss, involving thermal management and fluid dynamics optimization within energy storage units to achieve reduced pressure drops and augmented energy storage efficiency across varying temperatures.

Figure 6 elucidates the interplay between system efficiency and convective heat transfer temperature differences under varied pressure drops in energy storage modules of DESS within power distribution networks. The data enable an understanding of how operational pressure and temperature differentials impact the efficiency of energy storage systems. It has been discerned that at a constant convective heat transfer temperature difference, an increase in operating pressure corresponds to a gradual decrease in system efficiency. This phenomenon is attributable to augmented flow resistance at elevated pressures, thereby diminishing the efficacy of thermal transfer. Furthermore, at a given operating pressure, an escalation in the convective heat transfer temperature difference leads to a decrement in system efficiency, suggesting that augmented temperature differentials elevate thermal resistance, consequently impairing heat exchange efficiency. A consistent trend is noted: irrespective of the operating pressure, a negative correlation exists between convective heat transfer temperature difference and system efficiency, indicating that greater temperature differences result in lower efficiencies. The inference is that variations in operating pressures and convective heat transfer temperature differences substantially influence the efficiency of energy storage modules in DESS. Design and operational considerations of these systems should include the selection of suitable operating pressures and minimization of convective heat transfer temperature differences to enhance heat exchange efficiency. An optimal operational scenario is characterized by lower pressure and minimal temperature differences, thereby optimizing the system's overall thermal efficiency.

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Figure 4. Variation in energy storage efficiency of DESS with and without insulation layers across multiple operational cycles

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Figure 5. Relationship curves between the pressure drops in DESS energy storage units and the corresponding energy storage efficiency across a range of temperatures

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Figure 6. System efficiency curves corresponding to convective heat transfer temperature differences under different energy storage unit pressure drops

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Figure 7. Exergy loss rates of different components in DESS for power distribution networks

Table 1. Experimental results of system performance indices for different DESS configurations in power distribution networks

Table 2. Comparison of energy storage density and power density for different energy storage solutions

Table 1 presents the experimental results for various system performance indices of different DESS configurations within power distribution networks. The table compares the performance of systems utilizing paraffin and fatty acid as PCM against a reference system. The data indicate that the system in this study, when employing paraffin as PCM, exhibits a significant energy storage efficiency (114.2%) compared to the reference system (88.9%), suggesting the adoption of more effective thermal management strategies or advanced technologies that surpass conventional performance limits. Conversely, when fatty acid is used as PCM, the energy storage efficiency (87.9%) is marginally lower than that of the reference system, indicating that fatty acids may be less effective in this particular system configuration. Regardless of the PCM used, the round-trip efficiency of this study's system surpasses the reference system's 56.8%, with values of 67.8% and 62.3% respectively. This indicates that the system in this study incurs fewer losses during energy storage and release processes, effectively preserving the input energy. When utilizing paraffin, the system's exergy efficiency reaches 77.5%, and with fatty acid, it is 67.8%, both higher than the reference system's 68.8%. This demonstrates that the system in this study experiences lesser irreversible losses during energy conversion, leading to more efficient energy utilization. Consequently, the system in this study, particularly with paraffin as PCM, outperforms the reference system in terms of energy storage efficiency, round-trip efficiency, and exergy efficiency, while with fatty acid, despite a slight decrease in energy storage efficiency, round-trip efficiency and exergy efficiency still surpass the reference system. This signifies that the system proposed in this study has distinct advantages in design and performance, enabling more effective energy storage and conversion.

Table 2 offers a comparative analysis of energy storage density and power density across four distinct energy storage solutions within power distribution networks. These solutions incorporate either paraffin or fatty acid as PCMs, combined with either air or water as heat transfer fluids. The data illustrate that Solution 4, employing paraffin and water, demonstrates superior energy storage density, whereas Solution 2, combining fatty acid and water, excels in power density. The selection of an appropriate solution is contingent upon specific application requirements. For scenarios demanding high energy storage density, such as long-duration stable energy supply, Solution 4 emerges as the preferable choice. Conversely, for applications necessitating rapid response and high power output, Solution 2 is more apt. Solutions 1 and 3 present competitive alternatives for applications with intermediate performance demands. This underscores the pivotal role of selecting the appropriate PCM and heat transfer fluid in optimizing the performance of energy storage systems.

Figure 7 shows the exergy loss rates of different components in DESS for power distribution networks. The exergy loss rates, indicative of irreversibility and efficiency loss in each component during the energy conversion process, are critically examined. The analysis elucidates that batteries exhibit the highest exergy loss rate, quantified at 0.325. This significant loss rate is primarily due to internal resistance and the irreversibility inherent in electrochemical reactions during the charging and discharging cycles. This finding underscores that batteries are the predominant source of energy loss within the system, highlighting the necessity for advancements in battery technology to enhance overall system efficiency. In contrast, inverters and transformers demonstrate comparably substantial exergy loss rates, recorded at 0.23 and 0.228, respectively. These values suggest notable efficiency losses during the conversion of electrical energy, which are ascribed to electromagnetic and thermal losses, among other factors. PCM and heat transfer fluids, with exergy loss rates of 0.05 and 0.0498, respectively, show relatively higher efficiency in energy storage and thermal management processes. Nonetheless, these components still present opportunities for further efficiency improvements. Additionally, heat exchangers and pumps, with exergy loss rates of 0.045 and 0.04, benefit from relatively optimized designs, yet they still require enhancements in efficiency. Fans and voltage regulators, on the other hand, register the lowest exergy loss rates in the system, at 0.02 and 0.01, respectively. This indicates minimal energy loss in comparison to other components, attributed to their simpler operational principles and lower levels of irreversibility. Thus, within DESS for power distribution networks, batteries, inverters, and transformers emerge as principal contributors to exergy loss and demand focused attention for efficiency improvement. While PCMs and heat transfer fluids exhibit lower loss rates, indicating higher efficiency, there is still scope for further optimization. Fans and voltage regulators operate with the highest relative efficiency under the existing system configuration.

Figure 8 demonstrates the influence of ambient temperature on key performance indices in DESS within power distribution networks, encompassing energy storage efficiency, round-trip efficiency, exergy efficiency, and energy storage density. It is observed that as ambient temperature rises, a reduction in energy storage efficiency occurs, declining from 1.21 to 1.11. This pattern suggests enhanced energy storage capability at lower temperatures, whereas at elevated temperatures, efficiency suffers due to augmented thermal losses. Round-trip efficiency exhibits a decreasing trend with rising ambient temperature, moving from 0.76 to 0.6. This trend implies increased energy losses in both energy storage and release processes at higher temperatures, likely owing to heightened challenges in thermal management. Energy storage density displays a non-linear response to temperature changes, initially increasing, peaking at approximately 30°C, and subsequently decreasing. This behavior reflects the complexities in the performance of PCMs or storage media as a function of temperature. Exergy efficiency experiences a marginal decrease with increasing ambient temperature, shifting from 0.78 to 0.764. The decline in exergy efficiency signifies an escalation in irreversibility within energy conversion processes, attributed to intensified thermal stress and losses in system components under high-temperature scenarios. In conclusion, escalating ambient temperatures adversely affect the performance metrics of DESS in power distribution networks. The observed decrease in energy storage and round-trip efficiencies underscores the necessity for integrating effective thermal management strategies, such as utilizing superior insulation materials or refining cooling methodologies. These strategies aim to alleviate the impact of ambient temperature on system performance. A more nuanced analysis is warranted to elucidate the non-linear behavior of energy storage density and to guide the strategic selection and optimization of storage substances. Moreover, the slight reduction in exergy efficiency points to opportunities for augmenting the overall efficiency of energy conversion within the system, particularly in high-temperature environments.

Figure 9 elucidates the impact of the inlet temperature of the heat transfer fluid on several critical performance indices of DESS within power distribution networks. These indices include energy storage efficiency, round-trip efficiency, and exergy efficiency. The analysis indicates a progressive increase in energy storage efficiency, ascending from 1.05 to 1.17, as the inlet temperature rises from 490K to 550K. This elevation in efficiency is attributable to the enhanced thermal absorption promoted by the increased temperature differential at higher inlet temperatures. Conversely, the round-trip efficiency exhibits a declining trend with an elevation in inlet temperature, diminishing from 0.73 to 0.67. This pattern suggests an escalation in overall energy loss during the processes of storage and release, likely due to amplified internal or external thermal losses at elevated temperatures. Similarly, exergy efficiency undergoes a slight reduction as the inlet temperature increases, descending from 0.78 to 0.768. The decrease in exergy efficiency reflects an augmentation in the irreversibility of the energy conversion process at higher inlet temperatures. The data thus infer that the elevation of the inlet temperature of the heat transfer fluid profoundly influences the performance of DESS. Although higher inlet temperatures are associated with improved energy storage efficiency, they concurrently induce an increase in total energy losses, resulting in diminished round-trip and exergy efficiencies. This phenomenon is primarily due to the intensification of thermal losses within the system at higher temperatures, coupled with the potential degradation in the performance of materials and components under extreme temperature conditions. These findings underscore the need for meticulous design and operational strategies in DESS, especially considering the thermal dynamics influenced by inlet temperature variations.

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Figure 8. Impact of ambient temperature on performance indices of DESS in power distribution networks

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Figure 9. Influence of inlet temperature of the heat transfer fluid on performance indices of DESS in power distribution networks