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Thermal energy storage apparatus, controllers and thermal energy storage control methods

Thermal energy storage apparatus, controllers and thermal energy storage control methods are described. According to one aspect, a thermal energy storage apparatus controller includes processing circuitry configured to access first information which is indicative of surpluses and deficiencies of electrical energy upon an electrical power system at a plurality of moments in time, access second information which is indicative of temperature of a thermal energy storage medium at a plurality of moments in time, and use the first and second information to control an amount of electrical energy which is utilized by a heating element to heat the thermal energy storage medium at a plurality of moments in time.

Hammerstrom, Donald J.↗

Technology Strategy Assessment: Findings from Storage Innovations 2030 Thermal Energy Storage

The concept of thermal energy storage (TES) can be traced back to early 19th century, with the invention of the ice box to prevent butter from melting. Modern TES development began with building heating and cooling and concentrated solar thermal technologies for power generation in the early 1900s and late 1970s, respectively. TES systems provide many advantages compared with other long-duration energy storage (LDES) technologies, which include low costs, long operational lives, high energy density, synchronous power generation capability with inertia that inherently stabilizes the grid, and the ability to output both heat and electricity. TES Use Cases TES technologies can couple with most renewable energy systems, including wind, photovoltaic, and concentrated solar thermal energy, and can be used for heat-to-heat, heat-to-electricity, electricity-to-heat, and electricity-to-electricity (bidirectional electricity) applications. The three types of TES that have heat as an input or output are grouped together for the purposes of this report. Retrofitting retired thermal power plants can be a potential cost-effective option for TES with electricity output because they both use a similar thermal-to-electricity type of conversion. Additionally, TES can directly serve heat demand for buildings and industrial processes, displacing fossil fuels to achieve broad decarbonization. Bidirectional Electricity Figure 1 shows a bidirectional electricity TES (ETES) architecture that is emerging as a prime technology for LDES at a grid scale. The ETES technology can utilize existing TES technology infrastructures, has no geological limitations (such as mountains and water for pumped storage hydro, underground natural caverns for compressed-air energy storage, etc.), and is capable of deployment anywhere in the United States and the world for broad uses. Particularly, ETES technology can be placed at retired fossil-fueled thermal power plants to reuse decommissioned assets, protect job security in associated communities, and provide resilient and high-inertia (i.e., spinning) power to the grid. Heat Input and Output There also are many ways to integrate TES within heat-to-electricity, heat-to-heat, and electricity-to-heat applications, such as those used in concentrating solar power (CSP), buildings, district heating, and industry process heat applications. These categories can be further classified for low- and high-temperature applications. High-temperature thermal energy storage (HTTES) heat-to-electricity TES applications are currently associated with CSP deployments for power generation. TES with CSP has been deployed in the Southwestern United States with rich solar resources and has proved its value to the electric grid. Electricity-to-heat and heat-to-heat HTTES applications present great potential for decarbonizing energy-intensive industrial process heat applications [8, 9], such as iron ore processing, iron smelting, cement production, glass manufacturing, mineral processing, and chemical production. Some industrial processes require process heat at temperatures > 1,400°C, so HTTES can be utilized to reduce fuel consumption in those processes through fuel, oxidizer, and process material pre-heating. Thermal energy storage for augmenting existing industrial process heat applications makes a much more attractive economic case because the energy penalty due to thermal-to-electric conversion is eliminated. Co-located applications of power production and heat also can add to the value stacking of integrating utility-scale TES; however, these scenarios are very case specific and not practically possible in many cases. These constraints are primarily attributed to the existing infrastructure being designed, developed, and constructed for many decades around the most economically feasible technologies, such as electricity and a selection of fossil fuels for heat input. Low-temperature TES can be utilized for building and district heating and cooling, as well as some process heat applications in electricity-to-heat and heat-to-heat configurations. Lower temperature TES (LTTES) can be added to heat pump equipment (electric input), either directly interacting with the refrigerant in the condenser or evaporator, or through a secondary heat transfer fluid. It also can be integrated in the building envelope or within the ducts of the heating, ventilation, and air conditioning (HVAC) system. Cost-effective integration of TES into buildings adds significant cost, and it is one of the key barriers preventing the commercialization and deployment of TES. The optimal strategy for integrating TES with buildings has yet to be determined for various applications of TES. Nevertheless, thermal storage materials are far less costly per unit of energy stored than electricity storage materials. This means that thermal storage has the potential to reduce the cost to society of energy storage.

25 ENERGY STORAGE↗

Salt Hydrate Eutectic Thermal Energy Storage for Building Thermal Regulation (Final Technical Report)

Thermal energy storage is anticipated to play an important role in developing the power grid of the future - a power grid that meets increasing demands of users, is resistant to disruptions, but also allows for greater penetration of renewable resources. Specifically, thermal energy storage materials can be integrated into HVAC systems and building envelopes, where they can be used to shift power demands for building climate control from periods of peak demand to periods of low demand. Phase change materials (PCMs) are compelling as low-cost, high energy density thermal energy storage materials for building thermal management. However, there is a lack of high performance low-cost PCMs within the specific temperature ranges which would most effectively allow for power load shifting. Inorganic salt hydrates represent a promising class of PCMs, but their inherent limitations cause them to be currently unavailable for reliable building applications. The overarching goals of this research effort are to: 1) Discover low-cost, high volumetric density salt hydrate eutectic PCMs to store low-quality heat (10 to 40 °C); 2) Introduce a high thermal conductivity matrix to reduce the time constant for energy storage to ~0.1 to 1 hr, incorporate nucleation catalysts to decrease undercooling, and utilize microencapsulation and shape stabilization approaches, minimizing moisture loss/gain, mitigating phase separation, and maintaining stable melting behavior over the lifetime of the compounds; 3) Evaluate the impact these systems have on peak load shifting, and the potential for overall energy savings under different climatic scenarios and building configurations. These goals will be achieved by an integrated research program consisting of six cohesive research subtasks: 1) Materials discovery of eutectic salt hydrate PCMs by using computationally predicted thermodynamic equilibria, coupled with high-throughput experimental validation, 2) Rapid experimental screening of nucleation catalysts identified through robust computational databases, 3) Embedding salt hydrate PCM into a low cost and scalable high conductivity matrix, 4) Microencapsulation of salt hydrate microspheres using hybrid inorganic-polymer microencapsulation approach, 5) Shape stabilization by thermoreversible salt hydrate salogels, and 6) Analysis of end-use using thermal simulations, and characterization of mock-up energy storage finished components.

25 ENERGY STORAGE↗

Performance evaluation of a dynamic wall integrated with active insulation and thermal energy storage systems

Thermal energy storage systems in buildings can store cooling/heating energy during non-peak load hours or when renewable energy sources are available for later use when demanded. Using the building envelope as a thermal battery can help to shave the peak load, reduce the burden in electric grids, and enhance the occupant's thermal comfort. Sensible energy storage on wall systems such as thermally activated building systems can provide an active thermal storage strategy. However, most of the stored energy is used through passive means directed by the thermal lag, which can impede the on-demand release of the stored energy. Integrating active insulation systems with building thermal storage systems can increase the flexibility of charging and discharging time and duration. In this study, a wall system equipped with an active insulation system and thermally activated storage system was designed, and its performance on active cooling energy contribution was studied. The performances of energy storage (charging), release (discharging) of the thermal energy storage energy, and the active insulation system were studied separately and together as an integrated system. Results showed that the thermal properties of the thermal energy storage core material and the pipe spacing of both embedded pipes in the thermal energy storage and hydronic pipes used in the active insulation system affected the wall performance the most out of all the tested wall system parameters. During discharging, the heat flux into the wall was as high as 81.92 W/m 2 . This active insulation system's dynamic R-value varied between less than 1ft 2 •°F•h/BTU (0.18 m 2 •K/W) to 98% of the equally thick foam insulation's R-value.

25 ENERGY STORAGE↗

On the operational characteristics and economic value of pumped thermal energy storage

Pumped thermal energy storage (PTES) systems use an electrically-driven heat pump to store electricity in the form of thermal energy, and subsequently dispatch the stored thermal energy to generate electricity using a thermodynamic heat engine. Optimal day-ahead operational scheduling and annual value of a PTES system based on Joule-Brayton thermodynamic cycles and two-tank molten salt hot thermal storage is evaluated in this work. Production cost models, which simultaneously optimize commitment and dispatch schedules for an entire set of generators to minimize the cost of satisfying electricity demand, are employed to determine system-optimal operation and day-ahead energy value of the PTES system within each of six hypothetical near-future grid scenarios intended to approximately represent the U.S. Western Interconnection or the Texas Interconnection. Sensitivity to grid scenario (including the contribution of variable renewable energy sources), thermal storage capacity, relative heat pump and heat engine capacities, and startup/shutdown cycling costs are evaluated. PTES energy value and heat engine annual capacity factor increase strongly as the contribution of variable renewable resources increases, heat pump capacity increases relative to heat engine capacity, or PTES cycling costs decrease. Grid scenarios in which the contribution of variable renewable energy is dominated by solar photovoltaics (PV) vs. wind produce inherently different PTES operational patterns. Annual PTES energy value within PV-dominated scenarios increased with storage capacity only up to approximately seven hours of full-load discharge capacity, whereas that within wind-dominated scenarios exhibited a continual increase with storage duration up to at least 16 hours.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Techno-Economic Analysis and Market Potential of Geological Thermal Energy Storage (GeoTES) Charged With Solar Thermal and Heat Pumps into Depleted Oil/Gas Reservoirs and Shallow Reservoirs: A Technology Overview: Preprint

Depleted oil/gas reservoirs represent a waste of underground resources and investments of drilling, and also a potential risk to the earth's environment. Geologic thermal energy storage (GeoTES) is proposed as a solution to convert depleted oil/gas reservoirs into long-term seasonal energy storage. GeoTES can be hybridized with other techniques for viable commercial deployment, such as 1) concentrating solar power (CSP) collectors and 2) heat pumps with excess renewable energy. Here, a technology overview is given on the two GeoTES technologies, which includes system overview, techno-economic models, and case study. Both GeoTES technologies show great potential in the economics of individual project deployment and applicability across the US.

concentrating solar power↗

Coupling thermal energy storage with a thermally anisotropic building envelope for building demand-side management across various US climate conditions

Here, the thermally anisotropic building envelope (TABE) is a novel active building envelope that enhances energy efficiency and thermal comfort in buildings by transferring heat and cold between building envelopes and hydronic loops. When coupled with thermal energy storage (TES) units, the TABE + TES enables the storage of both heat and cold energy captured by the TABE roof or exterior walls. This stored energy can be later released by the TABE floor for indoor heating and cooling, benefiting both the grid and the end user. This paper evaluates the merits of TABE + TES for building demand-side management across various US climate conditions, focusing on peak load shaving, annual energy savings, and cost savings under time-of-use (TOU) electric rate schedules. Simulations were conducted by integrating time-of-day–informed, rule-based control strategies in MATLAB, TABE components and TES units in COMSOL Multiphysics, and whole-building energy analysis in EnergyPlus. A case study using the US Department of Energy’s prototype single-family detached house model in Birmingham, Alabama; Los Angeles, California; Oak Ridge, Tennessee; and Denver, Colorado, showed that the TABE + TES system achieved (1) 70 % peak load shaving in Los Angeles and Denver and 20 % in Birmingham and Oak Ridge; (2) significant peak electricity savings of 351–497 kWh, reducing peak energy consumption by 38 %–78 %; and (3) annual heating cost savings of 0.79 $\$$/m2–1.17 $\$$/m 2 and cooling cost savings of 0.60 $\$$/m 2 –1.17 $\$$/m 2 using a normal utility rate or low-TOU rate. The benefits of employing the TABE + TES system are even more significant under high TOU rates.

25 ENERGY STORAGE↗

Geological Thermal Energy Storage Using Solar Thermal and Carnot Batteries: Techno-Economic Analysis: Preprint

Energy storage is increasingly necessary as Variable Renewable Energy (VRE) technologies are deployed. Seasonal energy storage can shift energy generation from the summer to the winter, but these technologies must have extremely large energy capacities and low costs. Geological Thermal energy storage (GeoTES) is proposed as a solution for long-term energy storage. Excess thermal energy can be stored in permeable reservoirs such as aquifers and depleted hydrocarbon reservoirs for several months. In this article, we describe a techno-economic model that has been developed to evaluate GeoTES systems. The models are developed by combining the output of specialist models which enables the performance and cost of both the subsurface and surface systems to be captured. Off-design models are developed so that the performance can be evaluated at each hour of the year. GeoTES can be charged with two different energy sources: (1) concentrating solar thermal and (2) renewable electricity using heat pumps (henceforth known as a "Carnot Battery"). The stored thermal energy can be used to generate electricity and - uniquely - also directly produce heat that can be used by industrial processes. Furthermore, Carnot-Battery-GeoTES can also be used to form a cold storage reservoir. Preliminary results that quantify the technical and economic performance of these two GeoTES systems are presented.

carnot battery↗

Geological Thermal Energy Storage Using Solar Thermal and Carnot Batteries: Techno-Economic Analysis

Energy storage is increasingly necessary as variable renewable energy technologies are deployed. Seasonal energy storage can shift energy generation from the summer to the winter, but these technologies must have extremely large energy capacities and low costs. Geological thermal energy storage (GeoTES) is proposed as a solution for long-term energy storage. Excess thermal energy can be stored in permeable reservoirs such as aquifers and depleted hydrocarbon reservoirs for several months. In this article, we describe a techno-economic model that has been developed to evaluate GeoTES systems. The models are developed by combining the output of specialist models, which enables the performance and cost of both the subsurface and surface systems to be captured. Off-design models are developed so that the performance can be evaluated at each hour of the year. GeoTES can be charged with two different energy sources: (1) concentrating solar thermal and (2) renewable electricity using heat pumps (henceforth known as a "Carnot Battery"). The stored thermal energy can be used to generate electricity and, uniquely, also directly produce heat that can be used by industrial processes. Furthermore, Carnot Battery GeoTES can also be used to form a cold storage reservoir. Preliminary results that quantify the technical and economic performance of these two GeoTES systems are presented.

carnot battery↗

System and component development for long-duration energy storage using particle thermal energy storage

Energy storage, at various scales, will be required to maintain reliable power supply from variable renewable resources, and improve grid resilience. Long-duration energy storage (10-100 h) can substitute baseload coal power generation and increase levels of renewable power supply. Thermal energy storage (TES) has siting flexibility and the ability to store a large capacity of energy, and thus it has the potential to meet the needs of long-duration energy storage. Here, a novel TES system was developed by using solid particles as storage media and charging/discharging electricity from renewable power connected via the electric grid. The particle TES uses low-cost silica sand at 30-40$/Ton that is stable at high temperatures of >1,000 degrees C. Thus, the particle TES system has an overall low storage cost and high thermal-power efficiency. Key components of the system were conceptually designed and modeled for their performance. Conversion of electricity to thermal energy using electric heating can achieve a >98% charging efficiency, and the conversion of thermal energy back to electricity uses an air-Brayton combined power cycle with >52% thermal-to-electricity efficiency at >1,170 degrees C to achieve a >50% roundtrip efficiency after subtracting estimated plant parasitic losses. Laboratory-scale prototypes were fabricated and tested to verify their design approaches and operations relevant to product-scale components.

25 ENERGY STORAGE↗

A Demonstration System for Geological Thermal Energy Storage of Concentrating Solar Thermal

Energy storage is increasingly necessary as variable energy technologies are deployed. Seasonal energy storage can shift energy generation from the summer to the winter, but these technologies must have extremely large energy capacities and low costs. Geological Thermal Energy Storage (GeoTES) is proposed as a solution for long-term energy storage [1]. Excess thermal energy can be stored in permeable reservoirs such as aquifers and depleted hydrocarbon reservoirs for several months. The energy capacity cost of GeoTES is very low which makes it suitable for both daily- and seasonal storage of Concentrating Solar Thermal (CST) energy, thus enabling CST to provide value to electricity markets and thermal energy off-takers. A CST-GeoTES demonstration system has been funded by the U.S. Department of Energy, Solar Energy Technology Office. In this article, we will describe this demonstration system and progress that has been made in its development. The demonstration system will comprise a 2 MWth parabolic trough with an 8m aperture developed by Gossamer Space Frames, seven wells, and a 100 kWe power cycle. The demonstration system will be deployed in Kern County, California by Premier Resource Management. A techno-economic model for CST-GeoTES systems has also been developed [3] and is applied to the demonstration system and its planned future expansion. The model integrates the output of specialist models of each subsystem, which enables the performance and cost of both the subsurface and surface systems to be captured. Off-design models enable the performance to be evaluated at each hour of the year, before being aggregated to evaluate the economic potential of CST-GeoTES. Initial analysis indicates that CST-GeoTES can provide long duration energy storage capabilities with low marginal costs of energy capacity - leading to a low value of Levelized Cost of Storage (LCOS) compared to alternative technologies, see Figure 2. In this article, we investigate the cost and performance of the specific demonstration site being developed by PRM and explore a range of operational profiles that can deliver different value streams, such as daily and seasonal storage, capacity, and resiliancy.

14 SOLAR ENERGY↗

Numerical Evaluation of Effective Thermal Conductivity of PCM with Metal Foam Incorporating Buoyancy Effects for Thermal Energy Storage

The thermal energy storage (TES) system has the capability to efficiently preserve thermal energy directly derived from the energy source, minimizing any conversion losses. Especially latent heat storage offers distinct advantages, including a substantial increase in energy storage density and minimization of temperature fluctuations within the plants. However, the phase change material (PCM) employed in latent heat storage has low thermal conductivity. Consequently, various studies are being conducted to enhance heat transfer. One approach to enhance heat transfer involves utilizing metal foam to maximize the heat transfer area. However, modeling metal foam with its intricate structure is a challenging task in numerical analysis. For this reason, ongoing research focuses on simplifying the modeling of metal foam. Nevertheless, fully encompassing all the characteristics of actual metal foam proves to be a challenging task for the simplified analytical model. The objective of this paper is to interpret the simple lattice metal foam analysis model from the perspective of behavior induced by buoyancy. When comparing the analysis results of solid PCM and liquid PCM with the same thermal conductivity under changes in porosity and gravity direction, we conducted an analysis to discern the trends in effective thermal conductivity that are overestimated due to convection. In the analysis, a constant heat flux of 10 kW and a constant surface boundary condition of 350 K were applied, and a sensitivity study regarding the mesh was conducted. The results indicate that, from the perspective of gravity in the simple lattice model, the solid analysis yields an effective thermal conductivity 29-47% higher compared to the liquid analysis. Additionally, as porosity increases, there is an observed increase of 24-33% in effective thermal conductivity.

25 ENERGY STORAGE↗

Pumped Thermal Energy Storage With Liquid Storage

Pumped Thermal Energy Storage (PTES) uses electricity to power a heat pump; transferring heat from a cold space to a hot space forms a hot and a cold thermal reservoir, thereby storing energy. To discharge, the temperature difference between the two stores is used to drive a heat engine which generates electricity. In this chapter, PTES systems which store energy in liquids will be described. The chapter will concentrate on Joule-Brayton power cycles with molten salt storage. Part-load operation of Joule-Brayton PTES with liquid storage can be managed with "inventory control," and it is demonstrated that this control method leads to relatively good performance over a range of operating points.

Carnot batteries↗

Thermal Modeling and Simulation of the Packed-bed Thermal Energy Storage Combined with INL Thermal Energy Distribution System

Dynamic Energy Transport and Integration Lab (DETAIL) at Idaho National Laboratory is to support experimental demonstration and validation research on Nuclear-Renewable Hybrid Energy System [1]. The Thermal Energy Distribution System (TEDS) is a thermal-hydraulic flow loop in DETAIL with its own dedicated control system to support the integration of co-located multiple experimental systems, where a packed-bed thermal energy storage (TES) is installed as a thermal buffer and storage unit. Among various TES options, the packed-bed TES is adopted in TEDS because it offers a low-cost single-tank thermal storage option compared to the traditional two-tank TES. However, since the TES tank is filled with granular fillers having different thermophysical properties from those of TES tank wall, there is a potential thermo-mechanical issue to be carefully addressed like thermal ratcheting which may pose a significant design concern for the packed-bed TES tank. Thermal ratcheting is a thermomechanical process caused by the repeated rearrangement of granular filler inside a TES tank during continuous thermal cycling operation of the packed-bed TES system. If the thermally induced stress exceeds the yield strength of a TES tank wall, catastrophic consequences may happen like rupture of the TES tank. Thus, it is important to understand the phenomenon to ensure the robust operation of the packed-bed TES tank. Given that thermal ratcheting is caused by complex interaction of thermal transport in the porous bed and solid mechanics, the accurate prediction of transient thermal behavior of the packed-bed TES tank, which is the focus of this paper, is critical to the reliable thermal ratcheting analysis. This paper discusses the numerical modeling, simulation, and validation studies that are ongoing at INL to investigate the transient thermal behavior of the packed-bed TES. Of particular concern is the transient thermal process occurring in the packed-bed TES unit that is operated in conjunction with the INL TEDS. The main goal of this research is three-fold: (i) provide preliminary insights into the transient thermal behavior of the TEDS TES tank, (ii) support the thermal measurement and validation plan for TEDS experiment, and (iii) provide transient thermal boundary conditions to support the reliable thermal ratcheting analysis of the TEDS TES tank. For the transient thermal modeling and analysis, a CFD model was developed, and the validity of the modeling approach was examined via comparing the numerical simulation results with the experimental data obtained from various design characteristics of packed-bed TES tanks. Then, the present modeling method was applied for the transient thermal analysis of the TEDS TES tank, and the results are discussed along with the potential improvement of data acquisition strategy for the future TEDS experiments for more precise validation study.

25 ENERGY STORAGE↗

Iso-cost-performance of thermal energy storage

As thermal energy storage (TES) systems gain increasing recognition as next-generation energy storage solutions, evaluating their techno-economic performance is crucial. This perspective analyzes the cost-performance of latent heat-based TES systems and introduces the concept of iso-cost-performance—maintaining a constant cost per unit energy ($\$$/kWh) despite material degradation. Using an empirical degradation model, we show that after 1200 thermal cycles, the thermal conductivity and volumetric energy density of a paraffin-based phase change material (PCM) decreased by 36.0% and 26.1%, respectively, resulting in a 31.2% reduction in the figure of merit (FOM) and, consequently, the system cost-performance. However, by introducing thermally conductive additives to enhance effective thermal conductivity, the TES system can recover its initial FOM, achieving iso-cost-performance operation. This framework quantitatively demonstrates how degradation-mitigation strategies—such as improving thermal conductivity—can offset material degradations and maintain long-term cost-effectiveness. Beyond PCM-based TES, the proposed FOM-based approach provides a generalized pathway for cost-performance optimization across various TES technologies.

25 ENERGY STORAGE↗

Experimental investigation on phase change material–based finned tube heat exchanger for thermal energy storage and building envelope thermal management

Phase change materials (PCMs) are attractive solutions for thermal energy storage (TES) applications by absorbing and releasing large amounts of latent heat during solid–liquid phase transitions. However, their relatively low thermal conductivity requires novel heat exchanger–based solutions to improve the power density and overall energy storage efficiency of the TES system. This work presents the design and experimental results of a finned tube heat exchanger to store collected natural thermal energy from a building envelope in a latent-based TES and to release it later for building heating/cooling applications. We experimentally evaluate the finned tube heat exchanger and evaluate the performance of TES in reducing building heating and cooling loads over 3–4 h of desired time of operation (e.g., peak load). The optimized design allows for maximum energy density by minimizing the heat exchanger volume, and the system is evaluated experimentally using commercially available heat exchanger materials and an organic PCM. Here, the experimental results reveal that the TES system is able to charge and discharge stored latent energy within 3–4 h, matching peak building electricity demand duration under an average fluid flow rate of 0.136 kg/s and temperature difference of 5.55 °C. Importantly, such optimized designs illuminate a path toward TES designs that are low-cost, scalable, and optimized for thermal energy and power availability under the desired time of operation.

25 ENERGY STORAGE↗

Reduced-Order Modeling Method for Phase-Change Thermal Energy Storage Heat Exchangers

Thermal energy storage can facilitate the effective utilization of renewable energy. To speed up the design process of thermal energy storage devices, it is critical to develop fast and accurate modeling methods for phase change material embedded heat exchangers (PCM HXs). This study developed and compared two approximation-assisted reduced-order PCM HX models for the simulation of thermal storage components and systems, which were verified against a validated finite-volume model. They are a pure black-box model, and a grey-box model based on the Number of Transfer Units (or effectiveness-NTU) approach. We used the reduced-order models to predict the performance of standalone PCM HX for 1000 cases with different fluid inlet conditions and HX designs. We also integrated the models with a vapor compression system to predict the compressor energy consumption and total charging time under various conditions. The results show that overall, the black-box model gave more accurate results than the grey-box model. On average, the mean absolute deviation in the PCM HX fluid outlet temperature was 0.05 K and 0.1 K for the black-box model and grey-box model, respectively. The grey-box model gave larger temperature deviation toward the end of the phase change process, due to the simplified two-node PCM representation. On the system level, the mean absolute deviation in compressor energy consumption was 0.2% and 0.3% for the black-box model and grey-box model, respectively. Their mean absolute deviation in total charging time was 1.1% and 2.6%, respectively. In terms of computation efficiency, the system simulation speedup ratio gained by using the reduced-order models was 11 to 57. System simulation time was decreased from an average of 1465 s to an average of 59 s. This shows that the proposed reduced-order modeling methods can be used to predict system performance of PCM HXs with less than 3% accuracy penalty, and 25 times less computational time than finite-volume models, enabling faster design and evaluation of PCM thermal storage devices.

25 ENERGY STORAGE↗