# Pumped Thermal Energy Storage System for Trigeneration: The Concept of Power to XYZ

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Material and Methods

#### 2.1. The Concept of the Pumped Thermal Energy Storage Unit for Trigeneration

_{low}), which is 5 K lower than cold storage; the (T

_{in-am}), which is 5 K greater than the ambient temperature; the (T

_{heat}

_{,m}), which is 5 K greater than the medium storage temperature; and the (T

_{heat}

_{,h}), which is 5 K greater than the high thermal storage temperature. These temperature differences of 5 K are selected as typical values for efficient and proper heat transfer.

#### 2.2. Mathematical Formulation Part

#### 2.2.1. Heat Pump Modeling

_{cool}) can be written as:

_{in}) can be written as:

_{heat}

_{,m}) can be written as:

_{heat}

_{,h}) can be expressed as:

_{el}

_{,in}) in the trigeneration scenario is:

_{el}

_{,a}) is set to zero.

_{f}) as:

#### 2.2.2. Organic Rankine Cycle Modeling

_{el}

_{,out}) is calculated by using the produced electricity from the generator minus the electricity consumption from the organic fluid pump and can be written as:

_{is}

_{,pump}) can be written as:

_{is}

_{,tur}) can be written as:

_{out}) can be written as:

_{orc}) is given as:

#### 2.2.3. Evaluation Indexes

_{en}

_{,sys}) is defined as:

_{ex}

_{,sys}) is defined as:

#### 2.3. Simulation Methodology

_{heat}

_{,h}) which is a crucial design parameter, as well as for different ambient temperatures. It is worth noting that for ambient temperature levels lower than 20 °C, it is assumed to have a cogeneration system, while for temperature levels above 20 °C the trigeneration operation is selected. This is a simple and practical technique in order to separate the two examined scenarios. Moreover, different values of the loads (Q

_{cool}, Q

_{heat}

_{,m}and Q

_{heat}

_{,h}) are examined. In the last step of this investigation, the operating margins of the unit are defined in order to map the possible operating conditions. Practically, the ambient heat input is a critical parameter that can be used to counterbalance and cover the needed loads.

## 3. Results

#### 3.1. The Influence of High Heating Temperature on the Results

_{am}= 10 °C). It is worthwhile mentioning that when the high heating temperature increases from 80 °C to 200 °C, the ORC efficiency increases from 7.47% to 21.90% for the trigeneration scenario and from 10.46% to 23.99% for the cogeneration scenario.

_{heat}

_{,h}= 115 °C at 45.28%, while for the cogeneration scenario, it is maximized for T

_{heat}

_{,h}= 125 °C at 45.17%. The global maximum exergy performance of the trigeneration scenario is greater than the respective value of the cogeneration because there is better exploitation of the input electricity when there are three useful outputs. Moreover, it can be said that for temperature levels up to 135 °C, trigeneration has higher exergy efficiency, but after this limit, the cogeneration scenario is more efficient.

#### 3.2. The Influence of Ambient Temperature Level on the Results

_{heat}

_{,h}= 115 °C), which is a reasonable value according to the Section 3.1 analysis.

#### 3.3. The Influence of Loads on the Results

_{heat}

_{,h}) is optimized in order to maximize the system exergy efficiency. This simple optimization is conducted with the EES by using the “Golden Section Research” method which is supported by the same software. The relative tolerance was chosen at 10

^{−6}and the maximum function calls at 1000.

_{heat}

_{,h}= 50 kW and at 133.5 °C for Q

_{heat}

_{,h}= 200 kW. Figure 19 indicates that both energy and exergy efficiencies have a decreasing rate when higher amounts of heating are stored at the high-temperature level. This shows the need to store only the redundant quantities of energy in the high-temperature levels and not to design the high storage temperature level in high capacity. Specifically, the energy efficiency ranged between 204.39% and 456.95%, while the exergy efficiency ranged between 42.34% and 48.98%.

#### 3.4. Operating Limits of the Examined System

_{in}) cannot be negative and this is a restriction of the present design.

_{am}= 25 °C and T

_{heat}

_{,h}= 115 °C, with this combination used in the majority of cases of this work.

^{2}= 1. The next step is the development of an overall equation for determining the system operating limits. This equation is:

^{2}= 0.9999 and a mean absolute deviation error of 0.02%; thus, it is a very accurate formula. The equation has been developed for zero ambient source heat input. Therefore, it is a low limit because higher ambient heat input gives a greater possibility for heating production.

## 4. Conclusions

- -
- The exergy efficiency of the trigeneration scenario was maximized for T
_{heat}_{,h}= 115 °C at 45.28%, while for the cogeneration scenario it was maximized for T_{heat}_{,h}= 125 °C at 45.17%. - -
- The energy efficiency ranged from 242.58% to 378.29% for the trigeneration case, while it varied from 146.72% to 213.09% for the cogeneration case.
- -
- The increase of the ambient temperature reduced the system exergy efficiency while leading to higher system energy efficiency.
- -
- The increase of the cooling load and of the space heat load led to higher energy and exergy efficiencies. However, the augmentation of the high heating temperature reduced both energy and exergy efficiencies.
- -
- It was found that the high heating temperature storage must exceed a minimum limit and it is preferable, thermodynamically, for it not to be designed in a very high capacity in order to have high energy and exergy efficiency rates.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

h | Fluid specific enthalpy, kJ/kg |

m | Fluid mass flow rate, kg/s |

P_{el} | Electric power, kW |

P_{el,in} | Input electric power in the system, kW |

P_{el,out} | Output electric power from the organic Rankine cycle, kW |

PP | Pinch point, K |

Q | Heat rate, kW |

Q_{in} | Input heat rate in the unit from the ambient, kW |

T | Temperature, °C |

X | Useful energy quantity from electricity conversion, kW |

Y | Useful energy quantity from electricity conversion, kW |

Z | Useful energy quantity from electricity conversion, kW |

Greek Symbols | |

ΔΤ | Temperature difference, K |

η_{en,sys} | Energy efficiency of the unit |

η_{ex,sys} | Exergy efficiency of the unit |

η_{is} | Isentropic efficiency of the compressor |

η_{is,p} | Organic fluid pump isentropic efficiency |

η_{is,t} | Isentropic efficiency of the turbine |

η_{m} | Mechanical efficiency |

η_{mg} | Electromechanical efficiency |

η_{motor} | Motor-pump efficiency |

η_{orc} | Thermodynamic efficiency of the organic Rankine cycle |

Subscripts and Superscripts | |

a | Compressor (a) |

am | Ambient |

b | Compressor (b) |

c | Compressor (c) |

cool | Cooling |

is | Isentropic |

in-am | Inside ambient |

low | Low |

HEX | Heat exchanger |

heat | Heating |

heat, h | Heating at high-temperature level |

heat, m | Heating at medium temperature level |

HRS | Heat recovery system |

high | High |

opt | Optimum |

orc | Organic Rankine cycle |

rec | Recuperator |

sat | Saturation |

Abbreviations | |

EES | Engineering Equation Solver |

HEX | Heat Exchanger |

HP | Heat Pump |

HRS | Heat Recovery System |

ORC | Organic Rankine Cycle |

PCM | Phase Change Material |

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**Figure 2.**Detailed description of the examined configuration of the pumped thermal energy storage system for trigeneration.

**Figure 4.**The impact of high heating temperature on ORC electricity production for both trigeneration and cogeneration scenarios.

**Figure 5.**The impact of high heating temperature on ORC efficiency for both trigeneration and cogeneration scenarios.

**Figure 6.**The impact of high heating temperature on system exergy efficiency for both trigeneration and cogeneration scenarios.

**Figure 7.**The impact of high heating temperature on system energy efficiency for both trigeneration and cogeneration scenarios.

**Figure 8.**The impact of high heating temperature on energy input from the ambient for both trigeneration and cogeneration scenarios.

**Figure 9.**The impact of ambient temperature on ORC electricity production for both trigeneration and cogeneration scenarios.

**Figure 10.**The impact of ambient temperature on ORC efficiency for both trigeneration and cogeneration scenarios.

**Figure 11.**The impact of ambient temperature on system exergy efficiency for both trigeneration and cogeneration scenarios.

**Figure 12.**The impact of ambient temperature on system energy efficiency for both trigeneration and cogeneration scenarios.

**Figure 13.**The impact of ambient temperature on energy input from the ambient for both trigeneration and cogeneration scenarios.

Parameters | Scenarios | |
---|---|---|

Trigeneration | Cogeneration | |

Q_{cool} (kW) | 100 | 0 |

Q_{heat}_{,m} (kW) | 100 | 150 |

Q_{heat}_{,h} (kW) | 100 | 150 |

T_{am} (°C) | 25 | 10 |

Parameter | Symbol | Value |
---|---|---|

Heat Pump | ||

Compressor’s isentropic efficiency | η_{is}_{,C} | 80% |

Temperature difference on the HEX | ΔΤ_{HEX} | 5 K |

Temperature difference | ΔΤ | 5 Κ |

Shaft mechanical efficiency | η_{m} | 99% |

Low temperature | T_{low} | −5 °C |

Input temperature from ambient | T_{in-am} | Tam + ΔΤ = 20 °C |

Medium temperature | T_{med} | 55 °C |

High temperature | T_{high} | 120 °C |

Storage Systems | ||

Cooling stored temperature | T_{cool} | T_{low} − ΔΤ = 0 °C |

Medium stored temperature | T_{heat}_{,m} | T_{med} − ΔΤ = 50 °C |

High stored temperature | T_{heat}_{,h} | T_{high} − ΔΤ = 115 °C |

ORC | ||

Superheating | ΔΤ_{sh} | 5 K |

Turbine isentropic efficiency | η_{is}_{,T} | 80% |

Pinch point | PP | 5 K |

Pump isentropic efficiency | η_{is}_{,P} | 85% |

Saturation temperature | T_{sat} | (T_{heat}_{,h}-ΔΤ_{sh}-PP) °C |

Electromechanical efficiency | η_{mg} | 97% |

Recuperator temperature difference | ΔΤ_{rec} | 5 K |

Motor-pump efficiency | η_{motor} | 80% |

**Table 3.**Summary of the optimum designs for the examined scenarios according to the criterion of exergy efficiency maximization.

Parameters | Scenarios | |
---|---|---|

Trigeneration | Cogeneration | |

Q_{cool} (kW) | 100 | 0 |

Q_{heat}_{,m} (kW) | 100 | 150 |

Q_{heat}_{,h} (kW) | 100 | 150 |

T_{am} (°C) | 25 | 10 |

T_{heat}_{,h-opt} (°C) | 115 | 125 |

P_{el}_{,in} (kW) | 66.13 | 97.22 |

P_{el}_{,out} (kW) | 13.05 | 25.34 |

Q_{in} (kW) | 34.53 | 203.8 |

η_{en}_{,sys} | 322.16% | 180.35% |

η_{ex}_{,sys} | 45.28% | 45.17% |

η_{orc} | 13.05% | 16.89% |

m_{a} (kg/s) | 0.342 | 0 |

m_{b} (kg/s) | 0.4503 | 0.6797 |

m_{c} (kg/s) | 0.2308 | 0.3397 |

m_{d} (kg/s) | 0.1083 | 0.6797 |

m_{e} (kg/s) | 0.2195 | 0.34 |

m_{f} (kg/s) | 0.4503 | 0.6797 |

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**MDPI and ACS Style**

Bellos, E.; Lykas, P.; Tzivanidis, C.
Pumped Thermal Energy Storage System for Trigeneration: The Concept of Power to XYZ. *Appl. Sci.* **2022**, *12*, 970.
https://doi.org/10.3390/app12030970

**AMA Style**

Bellos E, Lykas P, Tzivanidis C.
Pumped Thermal Energy Storage System for Trigeneration: The Concept of Power to XYZ. *Applied Sciences*. 2022; 12(3):970.
https://doi.org/10.3390/app12030970

**Chicago/Turabian Style**

Bellos, Evangelos, Panagiotis Lykas, and Christos Tzivanidis.
2022. "Pumped Thermal Energy Storage System for Trigeneration: The Concept of Power to XYZ" *Applied Sciences* 12, no. 3: 970.
https://doi.org/10.3390/app12030970