Abstract

Pumped-thermal energy storage (PTES) systems consume and produce electrical energy using thermal storage media as an intermediate stage. PTES lends itself to long-duration energy storage to facilitate high penetration of intermittent electricity generation. This study presents a model-based comparison of two thermal storage types within a PTES system: a conventional, single-phase, stratified water-glycol sensible storage system (SGS), and an ideal isothermal, two-phase heat exchanger that freezes a water reservoir (isothermal heat exchanger (IHEX)). The SGS thermal storage capacity is based on the liquid’s sensible heat change with temperature, whereas the capacity of the IHEX is based on the latent heat of isothermally freezing and melting water. The idealized IHEX modeled here undergoes steady-state melting and freezing (in contrast to transient rates, as observed with ice-on-coil storage). A computational model of a complete PTES system is presented and used to evaluate the PTES system-level performance with each type of cold storage. Compared to SGS-based PTES, under nominal operating conditions, the IHEX-based PTES increased electrical round-trip efficiency from 61% to 82% and increased energy density from 1.13 to 8.09 kWh/m3 The performance of the PTES configured with IHEX storage was also analyzed under varying operating parameters.

1 Introduction

Electricity consumers expect their demands to be met instantaneously. Nonintermittent power sources such as coal, natural gas, or geothermal electricity production can supply energy in direct response to demand (Fig. 1). Intermittent renewable energy sources (i.e., wind and solar) do not have this luxury [1,2]. Energy storage can act as an intermediary, buffering variable supply to meet consumer demand “just-in-time.” Examples of current storage solutions include pumped hydroelectric storage (PHES) (Fig. 2), compressed air energy storage (CAES) [3], advanced battery energy storage (ABES) [4], and flywheel energy storage [5]. As of 2020, PHES was the most widely used storage system, accounting for 96% of all global energy storage [6].

Fig. 1
Top, Electrical supply in current electrical grid; bottom, a visualization of PTES playing a storage role in an electrical grid with mismatched electrical production and consumption rates
Fig. 1
Top, Electrical supply in current electrical grid; bottom, a visualization of PTES playing a storage role in an electrical grid with mismatched electrical production and consumption rates
Close modal
Fig. 2
Photograph of pumped hydro energy storage facility in southeastern Tennessee (photograph credit: Peter Miklavcic, 2018)
Fig. 2
Photograph of pumped hydro energy storage facility in southeastern Tennessee (photograph credit: Peter Miklavcic, 2018)
Close modal

However, to reach the scale of energy storage necessary to offset renewable’s intermittency, the aforementioned energy storage solutions are not sufficient. In the case of PHES and CAES, there are restrictive geographical and geological limitations. ABES has been successful in short-duration energy storage markets, such as power regulation, but it is not economical for multiple days of storage at large scales.

Bridging the gap of economic viability and scalability, pumped-thermal energy storage (PTES) is one possible energy storage technology that offers a solution to the imminent crisis [7].

During operation, PTES systems consume electrical energy and store it in a thermal form. Then, at a later point, the stored energy is returned in an electrical form. This functionality is achieved with a reversible system that is composed of two subcycles, the heat pump (HP) cycle, and the heat engine cycle, each interacting with the shared thermal storage component. The heat pump cycle consumes electricity and charges the thermal storage component, whereas the heat engine cycle depletes the thermal storage component to generate electricity. PTES systems can incorporate external thermal sources and/or sinks for different stages of the cycle (e.g., using ambient air as a thermal source). Generally speaking, the performance of PTES systems depends on the temperature differential of the high- and low-temperature thermal reservoirs.

In general, PTES performance can be improved in three categories: (1) design of the heat engine and heat pump subcycles, (2) selection of the heat sources/sinks interfacing with the system, and (3) design and cycle location of the thermal storage element.

In one subset of literature, Laughlin [8], McTigue et al. [9], and Farres-Antunez et al. [10] have all presented work on PTES systems based on Brayton cycle designs that use a gaseous working fluid. This article, alternatively, study a PTES system based on a circulating refrigerant.

In a second subset of literature, the thermal sources and sinks with which a system interacts dictate the maximum efficiency said cycle may achieve. Regarding the building sector, Dumont [11,12] examined the use of surplus heat from solar panels to produce electricity via PTES, harnessing energy that would otherwise be lost. Peterson [13] considered the use of ambient air temperature and its regular fluctuation as the thermal source/sink with which the PTES system could interface.

The third category of the PTES design offers the greatest potential for optimization of the PTES system as thermal storage can be configured for the high- or low-temperature side of the system, and the mechanisms for thermal storage can be improved. Robinson [14,15] explored the advantages of ultra-high-temperature thermal energy storage. Davenne et al. [16] compared the performance of packed-bed cold thermal storage and thermocline-based cold thermal storage in the context of a wind-turbine integrated PTES unit. White et al. [17] studied PTES performance with dual sensible heat-based thermal storage elements installed on both high- and low-temperature sides of the cycle.

This work aims to answer the question: How much improvement in PTES performance can be expected from a truly isothermal cold storage? This work is distinguished from prior PTES research because it incorporates two new features into a detailed PTES model: an isothermal ice water heat exchanger as the energy storage unit and the harnessing of waste heat to supplement the system’s electrical production. The isothermal heat exchanger (IHEX) concept is based on current research of ice-shedding heat exchanger prototypes [18] that are outside of the scope of this article but motivate the present work. Henceforth, this heat exchanger and the associated thermal storage reservoir are referred to as the IHEX.

This article quantitatively evaluates the IHEX-configured PTES system in comparison to PTES systems constructed with existing technologies and qualitatively discuss the role of PTES systems as a broad solution to the energy storage crisis brought forth by adoption of renewable energy technology. Data are presented to discuss the attainable efficiencies, scalability, and locational integration of PTES systems.

2 Thermodynamic Layout

2.1 General Design Details.

The PTES system modeled for this research consists of two thermodynamic subcycles that interface with a common thermal storage element. One cycle is designed to consume electricity and “charge” the element, while the other cycle “discharges” the element to produce electricity. The two subcycles are mated together as a single circuit, which reverses the direction of operation depending on charge/discharge action (Fig. 3(a)).

Fig. 3
(a) Component layout of combined HP-HE PTES cycle, (b) component layout of vapor-compression HP, and (c) component layout of organic Rankine cycle HE
Fig. 3
(a) Component layout of combined HP-HE PTES cycle, (b) component layout of vapor-compression HP, and (c) component layout of organic Rankine cycle HE
Close modal

As mentioned in Sec. 1, there are three aspects of the PTES systems that can be managed to adjust performance: (1) design of the heat engine and heat pump subcycles, (2) optimization of the heat sources/sinks interfacing with the system, and (3) design and cycle location of the thermal storage element. The PTES cycle of interest in this paper is now presented in the context of these three points.

The modeled PTES cycle uses R134a refrigerant as the working fluid. Therefore, the electricity-consuming charging subcycle of the PTES is a vapor-compression heat pump and the electricity-producing discharging subcycle is a heat engine, configured as a Rankine cycle.

While this article is based on theory and simulation, the heat sources and sinks the PTES system interacts with have been carefully chosen to reflect real-world conditions. The high-temperature heat sink required for the charging subcycle is plain ambient temperature atmosphere. During the discharging subcycle, the PTES cycle sources heat from low-grade waste heat (sub 80 °C), a massive and untapped potential for energy generation [19,20]. This is especially the case in recent decades, with the wide-spread growth of data centers that discard massive amounts of thermal energy to the atmosphere.

Finally, two options for thermal storage elements are considered. Both are installed on the low-temperature side of the PTES circuit. First, there is the sensible storage system (SGS) unit, which uses sensible heat stratification in a glycol–water reservoir. Second, and of primary interest, the two-phase IHEX thermal storage element is modeled.

2.2 Thermodynamic Component Layout.

The heat pump subcircuit is a vapor-compression heat pump (Fig. 3(b)). In sequence of operation, components include a compressor, condenser, subcooler, expansion valve, and evaporator. The thermal storage component acts as the evaporator of this cycle, with heat being drawn from the thermal media. Given that the objective of this work is to compare sensible and isothermal styles of storage, an ideal HP cycle is assumed here.

The heat engine (HE) circuit is an organic Rankine cycle (ORC) that includes superheating of the working fluid via a sequential boiler and superheater (Fig. 3(c)). Note that the terms HE and ORC are used interchangeably. The order of components of this cycle includes an expander, condenser, subcooler, pump, boiler, and superheater. Within this cycle, the thermal storage component occupies the role of the condenser, with the thermal storage component behaving as a heat sink into which heat flows from the working fluid exiting the expander.

Finally, there are three thermal sources that interface with the PTES cycle. First, for the heat pump subcycle, ambient environment temperature Tambient will provide the high-temperature threshold. Second, the temperature of the cold thermal storage component TCTS will serve as the low-temperature thermal source/sink in both heat pump and heat engine subcycles. Third, industrial waste heat provides the high-temperature source Twaste heat in the heat engine subcycle.

The performance of the heat pump and heat engine subcycles are depicted on the temperature-entropy plots in Fig. 4.

Fig. 4
(a) Model-generated temperature-entropy plot of heat hump and (b) heat engine cycles, overlaid on the characteristic dome for R134a refrigerant
Fig. 4
(a) Model-generated temperature-entropy plot of heat hump and (b) heat engine cycles, overlaid on the characteristic dome for R134a refrigerant
Close modal

3 Numerical Model

The numerical model developed to simulate PTES operation is configured with user-controlled independent variables that are classified into two categories: design variables and operating variables. The design variables include parameters such as the mass flowrates of the system, the isentropic, volumetric, ice-packing, and electrical efficiencies of relevant components, and the reservoir capacities for the thermal storage element. The operating variables consist of the environmental ambient temperatures, waste heat source temperatures, and temperatures of the thermal storage element. As the model runs, data from each cycle are processed to calculate the performance characteristics of the heat engine circuit, heat pump circuit, and holistic PTES system.

The code is written in matlab r2018a [21] and interfaces with the CoolProp database [22] for thermodynamic data on cycle fluids, a design that is precedented in the literature [23,24]. In general, throughout the literature, numerical investigations are used as a tool to improve components of PTES cycles [10].

The model is designed to conduct sensitivity studies of performance on the input variables of the system. Utilizing the model in the parametric study mode will run multiple iterations of the PTES cycle where only one or two independent variables are changed. The performance characteristics for each iteration are stored and plotted at the end of the study.

3.1 Modeling Assumptions.

A fundamental assumption in this numerical model is that of steady-state operation for all components except the thermal storage. This steady-state assumption is justified because the components of a real-world PTES system should usually operate in steady-state conditions outside of start-up, shut-down, and cycle-switch periods: in most cases, the temperatures of the surrounding climate and thermal sources will change on a time scale much longer than the settling time of the system components. While there are several rates that are considered in the model, the magnitudes of these rates do not change as a function of time. When the time required to “charge” or “discharge” the cycle is referenced, these calculations are made based on the steady rate at which the volume of thermal storage media is frozen/cooled or melted/warmed. In this way, an estimate can be made for how long it would take to charge or discharge the cycle while remaining within the steady-state operating assumption.

A second assumption of this model is that heat transfer and work transfer only occur in the components of the cycles. No heat loss or pressure drop occurs in the theoretical sections of the pipe that link components together. In addition, any losses within thermodynamic components are accounted for in the various efficiencies assigned to the part. No further heat losses, such as simple heat conducting out of the compressor or expander through internals, are considered. In some cases, a lumped electrical loss factor is used in the model to observe the impact on performance.

Isentropic efficiencies, ice-packing efficiencies (efficiency of ice to pack into a volume), electrical efficiencies, and volumetric efficiencies are all factored in throughout the model. However, these values are entered by the user and assumed to be constant during model operation. This assumption is reasonable due to the steady-state assumption, but it also means that there is no correlation between model operating parameters and component efficiencies. For instance, the efficiencies of the components of a real PTES cycle are variable dependent on the scale and operating conditions of the system. The model is unable to account for this dependence, which means a prior understanding of the dependence is required to enter a reasonable efficiency for each component.

3.2 Model Structure.

Each thermodynamic component of the IHEX-PTES system is modeled as an input–output matlab function, with the state of the working flow in each modified based on simple thermodynamics and various relevant efficiencies. All component objects are stitched together in sequence to complete the heat pump and heat engine circuits and, ultimately, the full PTES system. Table 1 illustrates the four tiers of hierarchy into which the scripts are arranged: (Tier A) high level user interface, (Tier B) the PTES master file, (Tier C) heat pump and heat engine master files, and (Tier D) the independent component files.

Table 1

File layout of PTES model and input variables used in operation

Tier AUser interface
Tier BPTES master file
Tier CHeat engine master fileHeat pump master file
Tier DExpander modelPump modelIHEX/SGS modelSubcooler modelHeat exchanger modelExpansion valve modelCompressor model 
Input variables
PTES global variablesDesired number of cycles of the standard ETES cycle
Duration of operation for heat pump
Duration of operation for ORC
Type of working fluid (WF) circulating
Thermal storage device to use in PTES system
Mass of thermal storage material at initial time
Isothermal heat exchanger storageVolumetric capacity of the ice storage tank
Heat of fusion for ice formation
Density of ice
Packing efficiency of ice in reservoir
Thickness of material storage tank wall
Conductivity of ice storage tank material
Stratified glycol storageChange in glycol temperature as it interfaces with the main cycle
Specific heat capacity of the propylene glycol
Density of the propylene glycol
Maximum volume capacity of propylene glycol tank for stratified storage
Heat pump variables (charging cycle)Heat pump global operation variablesMass flowrate of working fluid in heat pump
Temperature of the condenser reservoir
Temperature difference between condenser and WF
Temperature of the evaporator source (ice)
Temperature difference between evaporator and WF
Ambient temperature outside of compressor
Compressor-specific variablesUser indication for whether isentropic efficiency or measured work will be entered below
Isentropic efficiency of the compressor
Electrical efficiency of the compressor
Filling factor of the compressor
Ambient heat transfer coefficient (0 for adiabatic)
Swept volume of the compressor
Component volume of the compressor
Condenser-specific variablesType of fluid used for cooling in the condenser
Mass flowrate of cooling fluid
Pressure of the cooling fluid
Mode of operation for heat exchanger regarding main fluid
Subcooler variablesTemperature drop (dT) to be imposed by the subcooler on saturated liquid exiting the condenser
OtherOther practical sources of power consumption not accounted for in this model (to be accounted for in model efficiency calculations)
Heat engine cycle variables (discharging cycle)ORC global operation variablesMass flowrate of the working fluid in the ORC
Temperature of the hot source
Approximate temperature difference between hot source and WF
Heat sink temperature (ice)
Temperature difference between heat sink and WF
Ambient temperature outside of expander
Expander specific variablesUser indication for whether isentropic efficiency or measured work will be entered below
Isentropic efficiency of the expander
Electrical efficiency of the expander
Filling factor of the expander
Ambient heat transfer coefficient (0 for adiabatic)
Swept volume of the expander
Component volume of the expander
Subcooler variablesTemperature drop (dT) to be imposed by the subcooler on saturated liquid exiting the ice heat exchanger
Pump-specific variablesUser indication for whether isentropic efficiency or measured work will be entered below
Isentropic efficiency of the pump
Volumetric efficiency of the pump
Electrical efficiency of the pump
Component display of results (keep at zero)
Swept volume of the pump
Component volume of the pump
Stage I heat exchanger (boiler) variablesType of fluid used for heating in the condenser
Mass flowrate of heating fluid
Pressure of the heating fluid
Mode of operation for heat exchanger regarding main fluid
Stage II heat exchanger (superheater) variablesType of fluid used for heating in the condenser
Mass flowrate of heating fluid
Pressure of the heating fluid
Mode of operation for heat exchanger regarding main fluid
Superheat (dT) to be imposed on working fluid beyond boiling point
OtherOther practical sources of power consumption not accounted for in this model (to be accounted for in model efficiency calculations)
Tier AUser interface
Tier BPTES master file
Tier CHeat engine master fileHeat pump master file
Tier DExpander modelPump modelIHEX/SGS modelSubcooler modelHeat exchanger modelExpansion valve modelCompressor model 
Input variables
PTES global variablesDesired number of cycles of the standard ETES cycle
Duration of operation for heat pump
Duration of operation for ORC
Type of working fluid (WF) circulating
Thermal storage device to use in PTES system
Mass of thermal storage material at initial time
Isothermal heat exchanger storageVolumetric capacity of the ice storage tank
Heat of fusion for ice formation
Density of ice
Packing efficiency of ice in reservoir
Thickness of material storage tank wall
Conductivity of ice storage tank material
Stratified glycol storageChange in glycol temperature as it interfaces with the main cycle
Specific heat capacity of the propylene glycol
Density of the propylene glycol
Maximum volume capacity of propylene glycol tank for stratified storage
Heat pump variables (charging cycle)Heat pump global operation variablesMass flowrate of working fluid in heat pump
Temperature of the condenser reservoir
Temperature difference between condenser and WF
Temperature of the evaporator source (ice)
Temperature difference between evaporator and WF
Ambient temperature outside of compressor
Compressor-specific variablesUser indication for whether isentropic efficiency or measured work will be entered below
Isentropic efficiency of the compressor
Electrical efficiency of the compressor
Filling factor of the compressor
Ambient heat transfer coefficient (0 for adiabatic)
Swept volume of the compressor
Component volume of the compressor
Condenser-specific variablesType of fluid used for cooling in the condenser
Mass flowrate of cooling fluid
Pressure of the cooling fluid
Mode of operation for heat exchanger regarding main fluid
Subcooler variablesTemperature drop (dT) to be imposed by the subcooler on saturated liquid exiting the condenser
OtherOther practical sources of power consumption not accounted for in this model (to be accounted for in model efficiency calculations)
Heat engine cycle variables (discharging cycle)ORC global operation variablesMass flowrate of the working fluid in the ORC
Temperature of the hot source
Approximate temperature difference between hot source and WF
Heat sink temperature (ice)
Temperature difference between heat sink and WF
Ambient temperature outside of expander
Expander specific variablesUser indication for whether isentropic efficiency or measured work will be entered below
Isentropic efficiency of the expander
Electrical efficiency of the expander
Filling factor of the expander
Ambient heat transfer coefficient (0 for adiabatic)
Swept volume of the expander
Component volume of the expander
Subcooler variablesTemperature drop (dT) to be imposed by the subcooler on saturated liquid exiting the ice heat exchanger
Pump-specific variablesUser indication for whether isentropic efficiency or measured work will be entered below
Isentropic efficiency of the pump
Volumetric efficiency of the pump
Electrical efficiency of the pump
Component display of results (keep at zero)
Swept volume of the pump
Component volume of the pump
Stage I heat exchanger (boiler) variablesType of fluid used for heating in the condenser
Mass flowrate of heating fluid
Pressure of the heating fluid
Mode of operation for heat exchanger regarding main fluid
Stage II heat exchanger (superheater) variablesType of fluid used for heating in the condenser
Mass flowrate of heating fluid
Pressure of the heating fluid
Mode of operation for heat exchanger regarding main fluid
Superheat (dT) to be imposed on working fluid beyond boiling point
OtherOther practical sources of power consumption not accounted for in this model (to be accounted for in model efficiency calculations)

During operation, all variables listed in Table 1 are input to Tier A. During model execution, after inputs are passed from Tiers A to D, outputs are passed from Tiers D to A. Performance measurements from individual components are passed to the Tier C heat engine/heat pump master files, where they are factored into cycle performance metrics such as thermal efficiency or coefficient of performance (COP). The Tier D IHEX component also returns data to the Tier C master files about the amounts of ice generated or melted during the cycle completion, and the heat engine master file uses this information to calculate the energy density of the ice. The total electric work input to the heat pump and total electric work output by the heat engine are used to calculate the round-trip efficiency in the PTES master file in Tier B. Finally, all calculated data are passed to code in Tier A for user-friendly output. Sections 3.2.1 and 3.2.2 present the operating principles for the specific operation of the stratified glycol and isothermal energy storage components, respectively.

3.2.1 Cold Storage—Stratified Glycol Thermal Storage.

Figure 5 is a schematic of stratified glycol thermal storage (SGS) tank and the variables associated with its performance are labeled. Reference to the PTES system nodes one and six indicates the location of integration of the SGS component into the PTES circuit in Fig. 3(a).

Fig. 5
The stratified thermal energy storage element using a glycol solution as the thermal storage medium. Indicated nodes 1 and 6 indicate where this element fits into the larger PTES cycle, per Fig. 3.
Fig. 5
The stratified thermal energy storage element using a glycol solution as the thermal storage medium. Indicated nodes 1 and 6 indicate where this element fits into the larger PTES cycle, per Fig. 3.
Close modal
The model that represents the stratified glycol component begins with a desired enthalpic change between PTES system nodes one and six. Using this enthalpic change and the mass flowrate of the working fluid, the total heat transfer to/from the working fluid is expressed in Eq. (1).
Q˙WF=m˙WF(h6h1)
(1)
The user-controlled temperature variation of glycol—alternatively called the “degree of heating/cooling” of the glycol—is indicated by the term ΔTglycol and is the temperature glide of the glycol fluid as it interfaces with the main working fluid circuit. ΔTglycol is given by Eq. (2).
ΔTglycol=|TaTb|
(2)
Since the degree of heating/cooling of the glycol is a fixed input of the model, the required mass flowrate of the circulating glycol required to balance the energy is calculated by Eq. (3).
m˙glycol=Q˙WFCp,glycol×ΔTglycol
(3)

Using this determined mass flowrate, the known storage volume, and levels of warmed and cooled glycol, the runtime of the stratified glycol system before full discharge of its cold glycol supply can be determined.

3.2.2 Cold Storage—Isothermal Heat Exchanger Thermal Storage.

In conventional ice-on-coil storage, ice forms on the surfaces of heat exchanger tubes or coils. During freezing, as the ice layer builds, heat transfer to the surrounding water is reduced by the added thermal resistance of the ice layer. An analogous issue occurs during melting. The novel IHEX overcomes this limitation by preventing the ice formed from sticking to heat exchange surfaces. This means the melting and freezing can occur in one module, while produced ice is stored in another. This allows the IHEX to take advantage of the high enthalpy of phase change while maintaining constant rates of ice generation. Furthermore, this design means the IHEX component is extremely scalable and suitable for large-scale storage applications that may require high volumes of electricity storage for extended periods of time.

The details of the physical IHEX design are not the focus of this article. A simplified depiction of the IHEX is provided in Fig. 6. For purposes of PTES system modeling, the critical distinguishing feature of the IHEX is that it provides constant supply temperature, regardless of the state of charge. This contrasts to conventional ice storage, which requires variable capacity to maintain fixed temperature or variable temperature to maintain fixed capacity.

Fig. 6
Simplified depiction of isothermal heat exchanger applied for cold thermal energy storage in PTES system
Fig. 6
Simplified depiction of isothermal heat exchanger applied for cold thermal energy storage in PTES system
Close modal

Equation (1) applies equally for the SGS and IHEX, where the energy transfer between working fluid and storage medium is governed by an energy balance.

For the isothermal IHEX reservoir, with latent heat of fusion (Lf), Eq. (4) provides the mass rate at which ice forms. Therefore, with the known quantities for packing efficiency and ice reservoir tank volume, the amount of time required to fill a given receptacle volume with ice or fully deplete it can be calculated, and the energy density is determined.
m˙ice=Q˙WFLf
(4)

3.3 Performance Metrics.

A major efficiency metric for a PTES cycle is the round-trip electrical efficiency (RTE), the ratio of electricity out to electricity in. For independent consideration of the heat engine and heat pump performance, the heat engine thermal efficiency (ηth) and heat pump COP are calculated. Another important performance metric is energy density (Ed), which represents the electricity produced during discharge per cubic meter of ice melted in the reservoir (or cubic meter of fluid warmed in the stratified glycol model). These four metrics are defined in Eqs. (5)(8).
RTE=(WnetHE)elec(WnetHP)elec=(WexpanderHEWpumpHE)×tdischargeWcompressorHP×tcharge
(5)
ηth=WoutQinHE
(6)
COP=QinHPWin
(7)
Ed=Welec,netHE|ΔVice|(kWh/m3)
(8)
Component performance metrics include isentropic efficiency of compressor and expander (Eq. (9)), electrical efficiency of generator and pumps (Eq. (10)), and the packing efficiency of thermal storage (Eq. (11)). Note that the electrical efficiency accounts for losses due to friction in the transduction of mechanical work to electrical work, and vice-versa. Packing efficiency is a ratio that considers packing of ice granules in the storage vessel of the IHEX. Because of granular geometry, packing of objects produces a porous structure, which must be accounted for.
ηis=hsuhexhsuhex,is
(9)
ηelec,input=WmechWelecηelec,output=WelecWmech
(10)
ηpack=VICE,magVICE,actual
(11)

3.4 Discussion on Model Repeatability.

The results of Sec. 4 are all sourced from slight variations of the model from a baseline configuration. The baseline efficiencies input to the model are provided in Table 2.

Table 2

Baseline efficiency settings

Isentropic efficiencyElectrical efficiency
Turbine0.900.98
Compressor0.900.98
Pump0.750.98
Isentropic efficiencyElectrical efficiency
Turbine0.900.98
Compressor0.900.98
Pump0.750.98

The other major block of baseline parameters are the thermal reservoirs with which the PTES cycle interacts. For the heat pump cycle, these reservoirs are the ambient environment, the temperature of the thermal storage media, and the pinch temperature in the heat exchanging components. The heat engine interfaces with the external heat source, ambient air, and thermal storage element across pinch temperatures that are modeled into each heat exchanging component. These values used for the baseline configuration are listed in the Table 3 and shown in Fig. 7.

Fig. 7
Visualization of heat and work flow throughout PTES sequence and charge–discharge temperature levels
Fig. 7
Visualization of heat and work flow throughout PTES sequence and charge–discharge temperature levels
Close modal
Table 3

Baseline temperature settings

Heat pump cycle baseline temperaturesHeat engine cycle baseline temperatures
Condensing temperature (Tcond)293 KHeat source (Thigh)333 K
Condenser pinch (ΔTcond)8 KHeat source pinch (ΔThigh)10 K
Evaporator temperature (Tevap)273 KIHEX temperature (Tlow)273 K
Evaporator pinch (ΔTevap)4 KIHEX pinch (ΔTlow)3 K
Degree of superheat (ΔTsuperheat)10 K
Heat pump cycle baseline temperaturesHeat engine cycle baseline temperatures
Condensing temperature (Tcond)293 KHeat source (Thigh)333 K
Condenser pinch (ΔTcond)8 KHeat source pinch (ΔThigh)10 K
Evaporator temperature (Tevap)273 KIHEX temperature (Tlow)273 K
Evaporator pinch (ΔTevap)4 KIHEX pinch (ΔTlow)3 K
Degree of superheat (ΔTsuperheat)10 K

4 Results

The first set of cases (Sec. 4.1) presents a performance comparison between the IHEX-fitted PTES and the SGS-fitted PTES. Efficiencies achieved by each system are presented as well as practical aspects of the design.

The second set of cases (Sec. 4.2) studies exclusively the IHEX-fitted PTES performance response to variances in a single input parameter, for instance, dependency of round-trip efficiency to changes in component isentropic efficiency, electrical efficiency, and the like.

Finally, the third batch of cases (Sec. 4.3) considers the dependency of the IHEX-fitted PTES system on both external heat source and environmental temperatures. Data from these studies provide insight on installation of PTES systems and the impact of local ambient temperatures and waste heat temperatures on overall RTE performance.

4.1 IHEX-Fitted PTES Comparison Against Stratified Glycol Thermal Storage-Fitted PTES.

SGS-fitted PTES uses the energy requirement of heating/cooling glycol fluid as the thermal mechanism for storing electricity. Similarly, IHEX-fitted PTES uses the energy requirement of freezing/melting ice as the thermal mechanism. Considering these facts, since the IHEX system entails a phase change event, the capacity for energy storage of the IHEX system is predictably much greater than that of SGS. These differences in storage capacity suggest that for an SGS system to perform with the same energy storage capacity, it will require a significantly larger volume of glycol than the IHEX system will require of ice.

Five cases were run for a PTES cycle configured on the settings from Tables 2 and 3. For cases 1–4, the SGS component was installed and various degrees of glycol temperature glide were prescribed. Case 5 was the baseline configured IHEX model. The major performance metrics from each of these cases is presented in Table 4.

Table 4

Performance results for SGS- and IHEX-configured PTES systems

Stratified glycol storage componentIHEX storage component
ΔT = 10 KΔT = 20 KΔT = 40 KΔT = 60 K
Round-trip efficiency0.6050.4500.2430.1180.816
ORC thermal efficiency (ηth)0.0960.0850.0630.0410.106
HP coefficient of performance5.504.653.452.656.62
Energy density (Ed)1.13kWhm31.99kWhm32.90kWhm32.74kWhm38.09kWhm3
Stratified glycol storage componentIHEX storage component
ΔT = 10 KΔT = 20 KΔT = 40 KΔT = 60 K
Round-trip efficiency0.6050.4500.2430.1180.816
ORC thermal efficiency (ηth)0.0960.0850.0630.0410.106
HP coefficient of performance5.504.653.452.656.62
Energy density (Ed)1.13kWhm31.99kWhm32.90kWhm32.74kWhm38.09kWhm3

Observing the results, one notes the difference in energy density and RTE across the cases. The SGS cases produce energy densities ranging from 1.13 kWh/m3 at an RTE of 0.605 for a glycol temperature glide of 10 K to 2.74 kWh/m3 at an RTE of 0.118 for a glycol temperature glide of 60 K. In comparison, for the IHEX, an energy density of 8.09 kWh/m3 is calculated at an RTE of 0.816. For the 10 K differential SGS component, this translates to a 34% gain in RTE and a greater than 700% gain in energy density, respectively.

For further consideration, both cases presented use a storage volume of 1 m3. Due to the factor-of-seven difference in energy densities, there is a corresponding disparity in the operating time of each cycle. Although the IHEX-configured model consumes the 1 m3 of ice (not considering packing efficiency) in 1.44 h, the SGS configured model at a temperature variation of 60 K (best energy density) warms its 1 m3 of chilled glycol solution in just 0.321 h. Therefore, to modify the SGS-fitted PTES to operate for a similar runtime as its IHEX counterpart, a glycol storage tank of almost 4.5 m3 would be required. This is about a third the volume of a large passenger car. Maintaining such a large storage volume carries with it such problems as a large physical footprint and insulation challenges. These challenges would also scale with the size of the storage system, drastically affecting viability. In addition, the SGS system would still only achieve a fraction of the RTE, COP, and thermal efficiency of the IHEX system.

4.2 IHEX-Fitted PTES Performance Dependence on Individual Parameters.

This set of cases studies the impact of individual parameters on IHEX-fitted PTES performance. Here, data are shown in tornado plots, with the spread of the dependent variable shown for some indicated range of the independent variable. It should be noted that these tornado plots are not direct outputs from the model but are compiled exclusively with the data produced by the model. As an example, consider the top bar of Fig. 8(a). These data indicate that for a heat pump condensing temperature ranging from 283 K to 303 K, the PTES round-trip efficiency (RTE) ranges from ∼ 22% below to ∼ 43% above the baseline RTE of 0.816 for a condensing temperature 293 K. This means that the condensing temperature of the heat pump side of the PTES plays a major role in the total RTE of the system, with higher condensing temperatures being detrimental to performance.

Fig. 8
(a) Tornado plot of round-trip efficiency parametric dependence, (b) Tornado plot of ORC thermal efficiency parametric dependence, (c) Tornado plot of HP coefficient of performance parametric dependence, and (d) Tornado plot of IHEX energy density parametric dependence
Fig. 8
(a) Tornado plot of round-trip efficiency parametric dependence, (b) Tornado plot of ORC thermal efficiency parametric dependence, (c) Tornado plot of HP coefficient of performance parametric dependence, and (d) Tornado plot of IHEX energy density parametric dependence
Close modal

In addition to RTE, the variances of the three other performance metrics—heat engine thermal efficiency, heat pump COP, and energy density—are also presented in following plots. System parameters that are tested include temperature of the heat source, heat pump condensing temperature, compressor and turbine isentropic efficiencies, and system electrical efficiency (efficiency by which electrical work is converted to mechanical work and vice-versa).

The tornado plot in Fig. 8(b) shows the sensitivity of the heat engine’s thermal efficiency to variances in the design and operating variables that play a role in the heat engine discharging cycle. Considering this plot, it is shown that the thermal efficiency is most dependent on the waste heat source. For a thermal source temperature of +10 K over the baseline, a thermal efficiency is shown to increase by 1.49% from the baseline efficiency of 0.106. For a drop of the source temperature by −10 K from the baseline, a 1.72% loss in the thermal efficiency is caused.

Figure 8(c) provides information about the sensitivity of the heat pump’s coefficient of performance to relevant design and operating variables. Here, the condensing temperature that interacts with the heat pump circuit on the high-pressure side is the most significant. The impact of this thermal source relates inversely with the resulting COP, with lower temperatures drastically increasing the COP. For a decrease of the condensing temperature of −10 K, a 52.88% gain is experienced in the COP. Alternatively, increasing the condensing temperature from the baseline by +10 K causes a drop of 28.18% in coefficient of performance.

Finally, the parametric sensitivity of the discharging cycle’s energy density is portrayed in Fig. 8(d). As was the case for thermal efficiency, the temperature of the hot thermal source is the most impactful factor in the energy density metric. Increasing the waste heat source temperature by +10 K leads to a 15.93% gain in energy density, whereas a likewise decrease in the temperature causes a 17.79% loss in reported energy density.

The parametric sensitivity analyses clarify what aspects of the PTES system should be targeted for performance optimization. This information can be used when deciding how to configure and install a PTES unit to gain the best performance possible for its given locale and fixed operating conditions.

4.3 IHEX-PTES Performance Dependence on Thermal Sources.

In this battery of simulations, a range is input for two parameters of the model. From these two ranges, a matrix of possible combinations is generated, and the PTES model is run for each combination.

The results presented here study the impact on the system RTE due to variations in the ORC heat source temperature and the HP condensing temperature. For the former, values range from 318 K to 348 K in 0.5 K increments. The condensing temperature varies from 278 K to 308 K, also in 0.5 K increments. The matrix of possible temperature cases to run contains 3600 elements, meaning that the plot displayed below is the aggregate of 3600 individual runs of the model. Since there are two independent variables (IV) being studied, the dependent variable collected (RTE) adds a third dimension to the data. Therefore, the data are presented in the form of a contour plot, with contours colored based on the indicated magnitude of the RTE.

Interpretation of Fig. 9 informs on how thermal sources can be configured to majorly optimize the round-trip efficiency of a PTES unit. Fundamentally, for extremely low condensation temperatures and high waste heat temperatures, the RTE value can approach 1.4. Practically, this depicts a PTES system installed in a cold climate (approximately, 0 °C) with access to a waste heat source approaching 70 °C. Under these conditions, the electricity returned by the PTES in discharging mode is effectively supplemented by the high temperature of the waste heat source, meaning RTE values greater than unity can occur.

Fig. 9
Contour plot of RTE dependence on PTES thermal reservoir temperature
Fig. 9
Contour plot of RTE dependence on PTES thermal reservoir temperature
Close modal

These contour plots highlight the extreme impact that the PTES’ thermal source/sink temperatures have on system overall performance. Realization of this dependence is critical for considering the large-scale implementation of IHEX-PTES systems. For instance, the condensing temperature of the heat pump is simply the ambient temperature of the location where the PTES system is installed. As seen with these results and in the tornado plot above, higher condensing temperatures negatively impact round-trip efficiency. Therefore, it can be estimated that a PTES system installed in a cool climate will perform better than one installed in a hot climate if ambient air is selected as the heat sink. Alternatively integrating water-cooling or similar methods may mitigate this issue. This is an example of just one conclusion that can be drawn about the IHEX-fitted PTES system from the data presented.

5 Future Work

As is the nature of modeling work, there is room for refinement of modeling techniques and advancing algorithms to add value to results. Future iterations of the model may account for more real-world thermodynamic factors such as heat loss and pressure drop through pipes as well as transient states of operation of the entire system or even specific components. A more involved analysis of the use of low-grade waste heat could open doors to massive and untapped energy resources. An incorporation of geothermal elements could further boost system efficiencies. Inclusion of these types of factors, and so much more would increase the value of the modeling results and help to uncover countless new angles for optimization in PTES design.

6 Conclusions

A thermodynamic numerical model has been created to study the steady-state performance of a pumped-thermal energy storage system equipped with an isothermal heat exchanger. The modular design of this model and its direct correspondence to the physical layout of the PTES system was discussed, along with the driving assumptions of a steady-state system, user dictated isentropic/electrical/packing efficiencies, and zero heat losses or pressure drops in piping between cycle components.

Using the model, a comparison of the IHEX-fitted PTES system was made against an SGS-fitted PTES. It was shown that the PTES cycle equipped with the IHEX achieves an energy density of its storage material that is several times greater than the stratified glycol PTES.

In further analysis, various configurations of the model were run to present further data on the IHEX-fitted PTES system. The variation of system performance resulting from tweaks of one or two model inputs was studied for a specified baseline configuration. For a single input tweak, it was revealed that the round-trip efficiency of the PTES is heavily affected by the condensing temperature; a ±10 K variation in condensing temperature reflected a −22% and +43% variation in the RTE, respectively. Similarly, thermal efficiency of the heat engine and the energy density was shown to be most sensitive to change in the waste heat temperature source. The heat pump’s coefficient of performance was most dependent on the condensing temperature, practically the ambient temperature of the location where the PTES is installed.

Finally, cases were run for a combination matrix of heat pump condensing temperatures and heat engine waste heat temperatures. Results showed that a PTES operating with lower ambient condensing temperatures and higher temperature waste heat achieved extremely high RTE performance due to supplementary effects in the heat engine design. However, it is also understood from this finding that there are significant climactic factors to be considered when installing a PTES system that uses ambient air as the heat sink: since condensing temperature is effectively the ambient temperature of the environment, PTES systems will theoretically perform better when installed in cold regions. Regardless, PTES systems still lend themselves to installation in any environment and optimization can be achieved by managing the condensing temperature and other factors of the system.

In summation, a numerical model has been presented that emulates the thermodynamic circuitry of the PTES system. The modular code design has been motivated with reference to the would-be physical layout, and the potential analysis capabilities of this numerical model are presented in Sec. 4. Using this tool, the case has been made for IHEX-equipped PTES as the next electrical energy storage platform with massive potential for large-scale use and installation in virtually any climate. The construction of the PTES unit is conventional yet when paired with the IHEX component, its performance outpaces sensible heat-based counterparts and offers scalability where ice-on-coil designs cannot.

Footnote

Acknowledgment

This work was sponsored by the U.S. Department of Energy’s Building Technologies Office under Contract No. DE-AC05-00OR22725 with UT-Battelle, LLC. The authors would like to acknowledge Mr. Antonio Bouza, Technology Manager—HVAC&R, Water Heating, and Appliance, U.S. Department of Energy Building Technologies Office. The Department of Energy will provide Public Access to these results of Federally Sponsored Research in Accordance with the DOE Public Access Plan.2 We would like to thank Oak Ridge National Laboratory’s Innovation Crossroads Program, sponsored by the U.S. Department of Energy’s Advanced Manufacturing Office and Tennessee Valley Authority, for their support. The authors would also like to acknowledge Olivier Dumont from University of Liège for contributions during the development process of the model, and Viral Patel for review of the paper.

Conflict of Interest

There are no conflicts of interest.

Data Availability Statement

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request. The authors attest that all data for this study are included in the paper.

Nomenclature

     
  • m =

    mass (with overdot denotes mass flowrate)

  •  
  • x =

    vapor/liquid quality (100% liquid, x = 0.0; 100% vapor, x = 1.0)

  •  
  • A =

    area (m2)

  •  
  • Q =

    heat (with overdot denotes heat flowrate)

  •  
  • T =

    temperature

  •  
  • W =

    work

  •  
  • ΔT =

    temperature differential

  •  
  • ΔV =

    volume change

  •  
  • Ed =

    energy density (xx/m3)

Greek Symbols

     
  • Δ =

    gradient

  •  
  • ηth =

    thermal efficiency

  •  
  • η__ =

    efficiency pertaining to subscript

  •  
  • ω =

    humidity ratio (kgw/kgda)

Subscripts and Superscripts

     
  • cond =

    pertaining to condenser

  •  
  • elec =

    electrical

  •  
  • evap =

    pertaining to evaporator

  •  
  • high =

    relatively high quantity

  •  
  • in =

    influx

  •  
  • low =

    relatively low quantity

  •  
  • net =

    net quantity

  •  
  • 0 =

    initial

  •  
  • 1, 2, 3, 4, 5, or 6 =

    nodal indices as referenced from Fig. 3 

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