# Part-Load Energy Performance Assessment of a Pumped Thermal Energy Storage System for an Energy Community

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## Abstract

**:**

## 1. Introduction

- Developing the in- and off-design models to study the performance of a CB.
- Evaluating the CB full-load operation;
- Assessing the performance deterioration of the CB when operating at part load;
- Building the CB characteristic performance curves.

## 2. Methodology

#### 2.1. Preliminary Fluids Selection

#### 2.2. Two-Stage HP Optimization

_{ev}increases and when the ΔT

_{HP}decrease (Figure 6), whilst the ORC efficiency (η

_{cycle}) increases when ΔT

_{ORC}increases and T

_{cond}decreases (Figure 7). Notice that in both Figure 6 and Figure 7, T

_{ev}and ΔT

_{HP}have been used to allow a simultaneous reading of the two figures, T

_{ev}and ΔT

_{HP}of the HP being directly linked to T

_{cond}and ΔT

_{ORC}of the ORC, respectively, through the values of the pinch-points ΔT = 5 °C, as shown in Figure 2a.

_{Loop}have been calculated through Equation (1) for both scenarios (where the storage efficiency η

_{Storage}is considered equal to one), and the results are shown in Figure 8.

_{Loop}= η

_{ORC}·COP

_{HP}·η

_{Storage}

_{loop}appears to be weakly affected by the evaporation temperature T

_{ev}in the considered interval, whilst it increases when ΔT

_{HP}increases, but the increment is sensibly smaller for the higher values of the last parameter. For the working fluid R1233zd(E) (Figure 8b), the maximum values of the η

_{loop}are obtained at the minimum temperature T

_{ev}(about 10 °C or less) and with the temperature increment of the HP in the range ΔT

_{HP}= 75–115 °C. In these conditions, Figure 8b shows η

_{loop}= 0.39–0.40.

## 3. Design Models

#### 3.1. HP Model

_{HP}= 123 °C, while in the second scenario, the HP condenser temperature remains at 130 °C, and the HP evaporator temperature is set at 75 °C, with a ΔT

_{HP}= 55 °C. The first stage considers a 0.8 regenerator efficacy and a compressor efficiency of 0.7, while the second stage has the same compressor efficiency and a 0.3 regenerator efficacy (see Table 6 for all the assumed HP data) to lower the work of the compressor.

_{rig}

_{1}is the regenerator efficacy, h

_{i}is the specific enthalpy of the i-th cycle point, and h

_{2*}is the enthalpy calculated at the saturation temperature of the intermediate pressure (see Equation (8)) and at the evaporation pressure. The efficacy of regenerator 2 of the second stage has been evaluated by changing the subscripts of the cycle points accordingly with Figure 10, considering the cycle point numbers 4 and 5 and the specific enthalpy h

_{5*}calculated at the condensation temperature and at the intermediate pressure (see Equation (8)).

_{3is}is the specific enthalpy of point 3 for an isentropic compression, and the one about the second-stage compressor has been defined by changing the subscript of Equation (3) accordingly with the HP cycle of Figure 10.

_{comp}

_{1}is the work by the compressor of the first stage, ${\dot{m}}_{ev}$ is the mass flow of the working fluid flowing through the HP evaporator, h

_{i}represents the specific enthalpy of the i-th point of the cycle, and η

_{comp}

_{1}is the compression efficiency expressed by Equation (5):

_{comp}

_{2}of the second stage has been modeled through Equation (6):

_{comp_tot}(Equation (7)) and ORC maximum output have been imposed according to Table 7 for the two considered scenarios.

_{cond_hp}= 130 °C and T

_{ev_hp}= 7 °C, while in the second one, they result to be T

_{cond_hp}= 130 °C and T

_{ev_hp}= 75 °C. The intermediate pressure has been evaluated by Equation (9):

#### 3.2. ORC Model

_{ORC}= 96 °C, considering R1336mzz(Z) and R1233zd(E) as the working fluid for both the studied scenarios.

_{i}is the specific enthalpy of the i-th cycle point (as depicted in Figure 11).

_{27*}has been evaluated at the condensation pressure and at the temperature of the pump outlet (point 22 of Figure 11).

_{gross_exp}and W

_{net_exp}are the gross and net work done by the ORC, respectively, and ${\dot{m}}_{orc}$ is the working fluid mass flow into the ORC.

#### 3.3. High-Temperature Thermal Storage Hypothesis

_{3}/NaNO

_{3}/KNO

_{3}, as a PCM and water as a medium to exchange heat with the HP condenser and the ORC evaporator. The latent heat material has been selected considering the PCM temperature, as stated in Table 9, after a search in the literature.

#### 3.4. District Heating Network Thermal Storage Hypothesis

#### 3.5. Cold Thermal Storage Hypothesis

#### 3.6. Heat Exchangers Sizing

_{j}of the j-th HEX has been divided by the overall heat exchange coefficient U

_{j}, which in turn has been approximated with Equation (17), which does not take into account the thickness of the tubes:

_{t}and h

_{s}are the convective heat transfer coefficients of the fluid on the tube side and on the shell side, respectively. The latter coefficients have been computed using the Nusselt number definition and other correlations described in the following subsections. The values of the overall conductance, UA

_{j}, have been obtained through the logarithmic mean temperature difference (LMTD) as described in Section 3.6.2.

#### 3.6.1. Regenerator Models

#### 3.6.2. Evaporators Models

_{ev_hp}and Q

_{ev_orc}, have been assessed through the Equations (20) and (21), accordingly with Figure 10 and Figure 11:

_{ev_hp}and UA

_{ev_orc}with the help of Equation (22), the LMTD has been defined accordingly with Equation (23) and Figure 10, Figure 11 and Figure 12:

_{ml}is the LMTD of the evaporator, depicted in Figure 12a,b for the HP and the ORC, respectively; MM is the molar mass of the fluid flowing in the shell side of the HEX; and P

_{R}is the reduced pressure of the working fluid defined by Equation (28):

_{sat_eva}and P

_{CR}are the saturation and the critical pressure of the working fluid into the evaporator.

_{o}is the outer tube’s diameter, C

_{1}is a geometrical factor based on the triangular pitch P

_{t}of the tube bundle, and D

_{b}is the tube bundle diameter described by Equation (30):

_{p}of the HEX. All these factors are as follows [36]:

- P
_{t}= 1.25 d_{o}(chosen by authors); - N
_{p}= 1 (chosen by authors); - C
_{1}= 0.866; - K = 0.319;
- n = 2.142.

#### 3.6.3. Condenser Models

_{cond_hp}and Q

_{cond_orc}, described by Equations (31) and (32), accordingly with Figure 10 and Figure 11,

- k
_{l}is the liquid working fluid heat conductivity; - ρ
_{l}is the liquid working fluid density; - ρ
_{v}is the vapor working fluid density; - g is the gravity acceleration;
- μ
_{l}is the liquid working fluid dynamic viscosity; - d
_{o}is the tube’s outer diameter; - T
_{sat}is the saturation temperature of the working fluid; - T
_{w}should be the tube outer wall temperature, but since we have disregarded the wall thickness, we have used the temperature of the water flowing inside the tubes evaluated as a mean between the inlet and outlet condenser water temperatures; - λ′ is the heat defined as follows, by Equation (36) from Serth and Lestina [36]:

#### 3.6.4. ORC Economizer Model

_{eco_orc}, through the Equation (37), accordingly with Figure 11:

#### 3.6.5. Heat Exchanger Calculated Areas

## 4. Off-Design Models

#### 4.1. Part-Load Mass Flows and Machine Efficiencies

_{v}, is described by Liu et al. [38] as shown by Equation (44):

_{v_fl}at different pressure ratios. In this work, these two coefficients are

- a = 0.893768
- b = 0

#### 4.2. Heat Exchanger Part-Load Operation

## 5. Results and Discussion

#### 5.1. The Round-Trip Efficiency of the Carnot Battery

_{Loop}= 0.80. The simulation performed with the same temperatures and pinch-point temperature differences, using the R1336mzz(Z) instead of toluene as the working fluid in the 2sHP, shows that the round-trip efficiency at full load resulted to be about η

_{Loop}= 0.72, a lower value with respect to the case with toluene, consistent with the preliminary analysis.

_{Storage}= 0.9 has been introduced, as in Frate’s work. Results are reported in the following Table 16, where the results for the CB with a 2sHP and an ORC condenser temperature of 17 °C are also shown.

#### 5.2. Conclusions and Perspectives

- The round-trip efficiencies of a CB realized as in the case one has to be regarded as too poor (even if toluene were used the round-trip efficiency would not be greater than 0.37).
- A CB, as in case two, could be a good device in order to store and release energy when desired. In fact, a design round-trip efficiency of about 80% is a high value, justifying the hypothesis of performance in line with the better thermo-mechanical energy storages also for the real device, where some penalization is expected because of pressure losses.
- The round-trip efficiencies depend on the part-load operation so that a proper optimal choice of the CB size appears mandatory for taking advantage of the good design round-trip efficiency values.
- When the minimum temperature of the HP evaporator is greater than about 65 °C, toluene shows acceptable saturation pressure, so it can be used in order to obtain a better HP COP.
- When the minimum temperature of the HP evaporator or of the ORC condenser is low (in the cases considered 7 °C and 15 °C, respectively), toluene cannot be adopted because of its too low saturation pressure. In this case, both R1233zd(E) and R1336mzz(Z) seem to be good. So, R1336mzz(Z) could be preferred because it has a slightly better performance in the off-design operation, while, if a higher minimum pressure in both cycles were needed, then R1233zd(E) could be the proper choice.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

2sHP | Two-stages heat pump |

a | Slope of a straight line |

b | Intercept of a straight line |

C_{1} | HEX geometrical factor |

CB | Carnot Battery |

COP | Coefficient of performance |

C_{p,v} | Specific heat at constant pressure of the vapor fluid phase, kJ/kg K |

CStor | Cold thermal energy storage |

D_{b} | Tube bundle diameter, m |

DHN | District Heating Network |

d_{i} | Inner tube diameter, m |

d_{o} | Outer tube diameter, m |

DS | Energy Community Distribution Substation |

EC | Energy Community |

Fb | Factor for the calculation of the convective heat transfer coefficient on the evaporator shell side |

g | Gravity acceleration, m/s^{2} |

h | Specific enthalpy, kJ/kg |

HEX | Heat exchanger |

HP | Heat pump |

h_{s} | HEX convective heat transfer coefficient on the shell side, kW/m^{2} K |

h_{t} | HEX convective heat transfer coefficient on the tubes side, kW/m^{2} K |

HTHStor | High-temperature heat storage |

ICE | Internal combustion engine |

K | A HEX factor |

k_{l} | Thermal conductivity of the liquid fluid phase, kW/m K |

LMTD | Logarithmic mean temperature difference, °C |

$\dot{m}$ | Mass flow, kg/s |

${\dot{m}}_{\mathit{cond}}$ | HP condenser mass flow, kg/s |

${\dot{m}}_{\mathit{ev}}$ | HP evaporator mass flow, kg/s |

MGT | Micro gas turbine |

MILP | Mixed-Integer Linear Programming |

MM | Molar mass, kg/kmol |

${\dot{m}}_{\mathit{orc}\_\mathit{pl}}$ | ORC mass flow, kg/s |

n | A HEX factor |

N_{p} | HEX number of passages |

N_{t} | Number of tubes in the HEX |

Nu | Nusselt number |

ORC | Organic Rankine cycle |

PCM | Phase change material |

P_{Cr} | Critical pressure, bar |

P_{int} | HP intermediate pressure, bar |

Pr | Prandtl number |

PR | Pressure ratio |

P_{t} | Pitch of the tube bundle |

PTES | Pumped thermal energy storage |

PVp | Photovoltaic panel |

Q | Heat flow, kW |

Re | Reynolds number |

RES | Renewable energy sources |

RE | Renewable energy |

STP | Solar thermal panel |

T_{cond} | Condensation temperature, °C |

T_{ev} | Evaporation temperature, °C |

TStor | Hot thermal energy storage |

T_{w} | Temperature of the HEX water inside the tubes, °C |

U | Overall heat transfer coefficient, kW/m^{2} K |

UA | Overall conductance, kW/K |

W_{comp} | HP compressor work, kW |

W_{gross_exp} | ORC expander gross work, kW |

W_{net_exp} | ORC expander net work, kW |

W_{pump} | ORC pump work, kW |

α | Part load factor |

α_{nb} | Factor for the calculation of the convective heat transfer coefficient on the evaporator shell side |

β | Pressure ratio |

ΔT | Temperature difference, °C |

ΔT_{app} | Approach-point temperature difference, °C |

ΔT_{pp} | Pinch-point temperature difference, °C |

ε | Regenerator efficacy |

η_{el} | Electric efficiency |

η_{is} | Isentropic efficiency |

η_{loop} | Round-trip efficiency |

η_{mec} | Mechanical efficiency |

η_{n} | Leakage efficiency |

η_{orc} | ORC efficiency |

η_{storage} | Thermal storage efficiency |

η_{v} | Volumetric efficiency |

λ | Latent heat of condensation, kJ/kg |

λ′ | $\mathrm{Modified}\text{}\mathrm{latent}\text{}\mathrm{heat}\text{}\mathrm{of}\text{}\mathrm{condensation},\text{}{\lambda}^{\prime}=\lambda +{C}_{P,\text{}V}\cdot \left({T}_{V}-{T}_{sat}\right)$, kJ/kg |

μ_{l} | Dynamic viscosity of the liquid fluid phase, N/m^{2} s |

ρ_{l} | Density of the liquid fluid phase, kg/m^{3} |

ρ_{v} | Density of the vapor fluid phase, kg/m^{3} |

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**Figure 1.**The Carnot Battery installed at the Energy Community: (

**a**) scenario one, the HP takes the heat from the ground (latent heat thermal storage); (

**b**) scenario two, the HP takes the heat from the central unit thermal storage (sensible heat thermal storage).

**Figure 2.**The Carnot Battery temperature diagram: (

**a**) scenario one, the HP and the ORC work between the same storages; (

**b**) scenario two, the devices work between different storages.

**Figure 3.**The operation diagram of the cycles of the CB for both scenarios. It is worth noting that in the first scenario, both 2sHP and ORC are connected to the ground storage CStor, while in the second scenario, the 2sHP is connected to the storage TStor feed by the EC DHN.

**Figure 4.**The COP performance of the single-stage HP working at a ΔT

_{HP}= 75 °C for several fluids. It is possible to observe that the best performances are those of toluene and isopentane.

**Figure 5.**The efficiency of the ORC working at a ΔT

_{ORC}= 55 °C for several fluids. It is possible to observe that the best performances are those of toluene and isopentane.

**Figure 6.**Two-stage HP optimized COP for toluene taking into account different cycle temperature differences.

**Figure 8.**Round-trip efficiency at the cycle temperature difference considered: (

**a**) for toluene; (

**b**) for R1233zd(E).

**Figure 9.**The saturation pressures for the best-performing fluids analyzed. Please note how the toluene has a very low saturation pressure value compared with those of the other fluids.

**Figure 10.**(

**a**) The HP cycle in scenario one with R1336mzz(Z) as the working fluid; (

**b**) The HP cycle in scenario two with toluene as working fluid. Point 14 represents the separation of the two fluid phases at the intermediate exchangers. The working temperature profiles for the thermal storages are shown in red and blue, for high and low temperatures, respectively.

**Figure 11.**The ORC cycle for both scenarios with R1336mzz(Z) as the working fluid. Point 124 represents the economizer outlet. The working temperature profiles for the thermal storages are shown in red and blue, for high and low temperatures, respectively.

**Figure 12.**The evaporator pinch-point representation: (

**a**) for the HP; (

**b**) for the ORC. The ORC economizer approach-point is depicted as well.

**Figure 14.**The performance of the four best working fluids for both scenarios: (

**a**) about the ORC; (

**b**) about the 2sHP.

**Figure 15.**The round-trip efficiencies of the four best working fluids: (

**a**) about the first scenarios; (

**b**) about scenario two B.

**Figure 16.**The two-stage HP characteristic curves: (

**a**) about the first scenario for R1336mzz(Z) and R1233zd(E); (

**b**) about the second scenario for toluene. Characteristic curves are in green, COPs in red and fuchsia.

**Figure 17.**The ORC characteristic curve for both scenarios with R1336mzz(Z) and R1233zd(E) as the working fluid. Characteristic curves are in green, COPs in red and fuchsia.

Fluid | Critic Temperature [°C] | Saturation Temperature at P = 1 atm [°C] |
---|---|---|

Toluene | 318.6 | 109.9 |

Isopentane | 187.2 | 27.48 |

R600 | 152 | −0.87 |

R600a | 134.7 | −12.01 |

R1224yd(Z) | 155.5 | 14.27 |

R1233zd(E) | 165.6 | 17.98 |

R1234ze(E) | 109.4 | −19.58 |

R1234ze(Z) | 150.1 | 9.39 |

R1336mzz(Z) | 171.3 | 33.12 |

Machine | Compressor/Expander Efficiency | HP/ORC Regenerator Efficacy |
---|---|---|

One-Stage HP | 0.7 | 0.8 |

ORC | 0.88 | 0.8 |

Two-stage HP ^{a,1} | 0.7 | 0.8 |

Two-stage HP ^{a,2} | 0.7 | 0.3 |

^{a}Values for the two-stage HP used in the second part of the preliminary analysis.

^{1}HP first stage;

^{2}HP second stage.

Machine | ΔT_{1} = T_{H} − T_{L} [°C] | ΔT_{2} [°C] | ΔT_{3} [°C] | ΔT_{4} [°C] |
---|---|---|---|---|

ORC | 55 | 75 | 95 | 115 |

One-Stage HP | 75 | 95 | 115 | 135 |

Fluid | COP at ΔT_{1} | COP at ΔT_{2} | COP at ΔT_{3} | COP at ΔT_{4} |
---|---|---|---|---|

Toluene | 3.597 | 2.832 | 2.341 | 2.003 |

Isopentane | 3.300 | 2.612 | 2.175 | 1.876 |

R1336mzz(Z) | 3.224 | 2.546 | 2.116 | 1.823 |

R1233zd(E) | 3.171 | 2.517 | 2.100 | 1.814 |

R1224yd(Z) | 3.071 | 2.444 | 2.045 | 1.772 |

Fluid | η_{cycle} at ΔT_{1} | η_{cycle} at ΔT_{2} | η_{cycle} at ΔT_{3} | η_{cycle} at ΔT_{4} |
---|---|---|---|---|

Toluene | 0.1161 | 0.1534 | 0.1902 | 0.2252 |

Isopentane | 0.1107 | 0.1479 | 0.1844 | 0.2206 |

R1336mzz(Z) | 0.1089 | 0.1456 | 0.1812 | 0.2163 |

R1233zd(E) | 0.1071 | 0.1434 | 0.1769 | 0.2105 |

R1224yd(Z) | 0.1057 | 0.1410 | 0.1756 | 0.2098 |

**Table 6.**Compressor efficiencies and regenerators efficacies assumed for the two-stage HP at full load.

Case | HP Stage | Regenerator Efficacy ε_{rig} | Isentropic Efficiency η_{is} | Electrical Efficiency η_{el} | Mechanical Efficiency η_{mec} |
---|---|---|---|---|---|

1 and 2 | 1 | 0.8 | 0.82 | 0.97 | 0.94 |

2 | 0.3 | 0.82 | 097 | 0.94 |

Scenario | HP Total Input Power [kW] | ORC Net Output Power [kW] |
---|---|---|

1 | 200 | 70 |

2 | 85 | 70 |

Device | Regenerator Efficacy ε_{rig} | Isentropic Efficiency η_{is} | Electrical Efficiency η_{el} | Mechanical Efficiency η_{mec} |
---|---|---|---|---|

Expander | - | 0.82 | 0.97 | 0.94 |

Pump | - | 0.85 | 0.97 | 0.70 |

Regenerator | 0.80 | - | - | - |

Compound | Melting Temperature [°C] | Heat of Fusion [kJ/kg] | Source |
---|---|---|---|

KCl/LiNO_{3} | 165.6 | 201.7 | S. A. Mohamed [32] |

A164 * | 164 | 306 | H. Ge et al. [33] |

NaNO_{3}/KNO_{3}/NaNO_{2} | 142 | - | S. A. Mohamed [32] |

Bi_{58}Sn_{42} | 138 | 44.8 | H. Ge et al. [33] |

LiNO_{3}/NaNO_{3}/KNO_{3} | 121 | - | S. A. Mohamed [32] |

MgCl_{2}·6H_{2}O | 117 | 168.6 | M. M. Farid et al. [34] |

Bi_{52}Pb_{30}Sn_{18} | 96 | 44.8 | S. A. Mohamed [32] |

(NH_{4})Al(SO_{4})_{2}·12H_{2}O | 95 | 269 | S. A. Mohamed [32] |

E89 * | 89 | 163 | H. Ge et al. [33] |

E83 * | 83 | 152 | H. Ge et al. [33] |

**Table 10.**HP heat exchanger areas for the two considered scenarios using R1336zz(Z) (scenario 1) and toluene (scenario two).

HP HEX | Scenario | Area [m^{2}] |
---|---|---|

Condenser | 1 | 340.0 |

2 | 175.8 | |

Regenerator 1 | 1 | 85.7 |

2 | 66.8 | |

Regenerator 2 | 1 | 2.2 |

2 | 1.6 | |

Evaporator | 1 | 593.4 |

2 | 201.1 |

ORC HEX | Area [m^{2}] |
---|---|

Condenser | 457.1 |

Regenerator | 148.8 |

Economizer | 7.4 |

Evaporator | 50.2 |

Scenario | ΔT_{pp_ev_hp} ^{1} | ΔT_{pp_cond_hp} ^{1} | ΔT_{pp_ev_orc} ^{1} | ΔT_{pp_cond_orc} ^{1} | ΔT_{app_eco_orc} ^{1} |
---|---|---|---|---|---|

1 and 2 | 2 | 4 | 3 | 2 | 6 |

**All the temperature differences are in degrees Celsius.**

^{1}**Table 13.**Round-trip efficiency values obtained for maximum and minimum values of the part-load factor α.

Scenario | Fluid | α | HP COP | ORC η_{cycle} | η_{loop} |
---|---|---|---|---|---|

1 | Toluene | 1 | 2.248 | 0.164 | 0.369 |

0.175 * | 1.834 | 0.125 | 0.230 | ||

1 | Isopentane | 1 | 2.012 | 0.157 | 0.315 |

0.275 * | 1.750 | 0.126 | 0.212 | ||

1 | R1336mzz(Z) | 1 | 1.955 | 0.154 | 0.300 |

0.25 * | 1.698 | 0.122 | 0.206 | ||

1 | R1233zd(E) | 1 | 2.009 | 0.149 | 0.300 |

0.3 * | 1.750 | 0.120 | 0.210 | ||

2 | Toluene | 1 | 5.223 | 0.164 | 0.857 |

0.175 * | 4.008 | 0.125 | 0.503 | ||

2 | Isopentane | 1 | 4.774 | 0.157 | 0.748 |

0.275 * | 3.879 | 0.126 | 0.487 | ||

2 | R1336mzz(Z) | 1 | 4.712 | 0.154 | 0.724 |

0.25 * | 3.795 | 0.122 | 0.462 | ||

2 | R1233zd(E) | 1 | 4.666 | 0.149 | 0.697 |

0.3 * | 3.822 | 0.120 | 0.459 |

Scenario | α | HP COP | ORC η_{cycle} | η_{loop} |
---|---|---|---|---|

1 | 1 | 1.955 | 0.154 | 0.300 |

0.25 * | 1.698 | 0.122 | 0.206 | |

2 | 1 | 5.223 | 0.154 | 0.802 |

0.25 * | 4.162 | 0.122 | 0.506 |

Authors | Fluids | Maximum Temp [°C] | Minimum Temp [°C] | Intermediate Temp [°C] | Scenario | Round-Trip Efficiency |
---|---|---|---|---|---|---|

Eppinger et al. [30] | R1233zd(E) | 120 | 30 | 75 | 2 | 0.52 |

Frate et al. [19] | R1233zd(E) | 130 | 35 | 80 | 2 | 0.75 |

Fan et al. [39] | R1336mzz(Z) | 130 | 35 | - | 1 | 0.27 |

Frate et al. [19] | Toluene | 130 | 35 | 80 | 2 | 0.58 |

Dumont et al. [18] | R1233zd(E) | 78 | 20 | 75 | 2 | 0.82 |

Frate et al. [21] | R1233zd(E) | 100–170 | 17 | 75 | 2 | 1.02 |

Frate et al. [21] | R1336mzz(Z) | 100–170 | 17 | 75 | 2 | 1.03 |

Fluid | Paper | DHN Storage Temp [°C] | PCM Storage Temp [°C] | ORC Condenser Temp [°C] | HP Stages | Round-Trip Efficiency | Delta |
---|---|---|---|---|---|---|---|

Toluene | Frate et al. [19] | 80 | 120 | 35 | 1 | 0.58 | |

Present work | 80 | 121 | 35 | 1 | 0.53 | −0.05 | |

Present work | 80 | 121 | 17 | 2 | 0.77 | ||

R1233zd(E) | Frate et al. [19] | 80 | 120 | 35 | 1 | 0.41 | |

Present work | 80 | 121 | 35 | 1 | 0.43 | +0.02 | |

Present work | 80 | 121 | 17 | 2 | 0.63 | ||

n-Pentane | Frate et al. [19] | 80 | 120 | 35 | 1 | 0.44 | |

Present work | 80 | 121 | 35 | 1 | 0.48 | +0.04 | |

Present work | 80 | 121 | 17 | 2 | 0.69 | ||

Isopentane | Frate et al. [19] | 80 | 120 | 35 | 1 | 0.41 | |

Present work | 80 | 121 | 35 | 1 | 0.47 | +0.06 | |

Present work | 80 | 121 | 17 | 2 | 0.67 | ||

R245fa | Frate et al. [19] | 80 | 120 | 35 | 1 | 0.37 | |

Present work | 80 | 121 | 35 | 1 | 0.41 | +0.04 | |

Present work | 80 | 121 | 17 | 2 | 0.59 | ||

Isobutane | Frate et al. [19] | 80 | 120 | 35 | 1 | 0.28 | |

Present work | 80 | 121 | 35 | 1 | 0.32 | +0.04 | |

Present work | 80 | 121 | 17 | 2 | 0.46 | ||

Cyclopentane | Frate et al. [19] | 80 | 120 | 35 | 1 | 0.52 | |

Present work | 80 | 121 | 35 | 1 | 0.52 | +0.00 | |

Present work | 80 | 121 | 17 | 2 | 0.73 | ||

Benzene | Frate et al. [19] | 80 | 120 | 35 | 1 | 0.56 | |

Present work | 80 | 121 | 35 | 1 | 0.52 | −0.04 | |

Present work | 80 | 121 | 17 | 2 | 0.75 | ||

Cyclohexane | Frate et al. [19] | 80 | 120 | 35 | 1 | 0.52 | |

Present work | 80 | 121 | 35 | 1 | 0.53 | +0.01 | |

Present work | 80 | 121 | 17 | 2 | 0.76 |

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## Share and Cite

**MDPI and ACS Style**

Nadalon, E.; De Souza, R.; Casisi, M.; Reini, M.
Part-Load Energy Performance Assessment of a Pumped Thermal Energy Storage System for an Energy Community. *Energies* **2023**, *16*, 5720.
https://doi.org/10.3390/en16155720

**AMA Style**

Nadalon E, De Souza R, Casisi M, Reini M.
Part-Load Energy Performance Assessment of a Pumped Thermal Energy Storage System for an Energy Community. *Energies*. 2023; 16(15):5720.
https://doi.org/10.3390/en16155720

**Chicago/Turabian Style**

Nadalon, Emanuele, Ronelly De Souza, Melchiorre Casisi, and Mauro Reini.
2023. "Part-Load Energy Performance Assessment of a Pumped Thermal Energy Storage System for an Energy Community" *Energies* 16, no. 15: 5720.
https://doi.org/10.3390/en16155720