# Multicriteria Analysis of a Solar-Assisted Space Heating Unit with a High-Temperature Heat Pump for the Greek Climate Conditions

^{1}

^{2}

^{3}

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## Abstract

**:**

^{2}of solar thermal collectors connected with a storage tank of 2 m

^{3}for facing the total heating demand of 6785 kWh. In this case, the life cycle cost was calculated at 22,694 EUR, the seasonal system coefficient of performance at 2.95 and the mean solar thermal efficiency at 31.60%. On the other hand, the multi-objective optimization indicates the optimum design is the selection of 50 m

^{2}of solar field connected to a thermal tank of 3 m

^{3}. In this scenario, the life cycle cost was calculated at 24,084 EUR, the seasonal system coefficient of performance at 4.07 and the mean solar thermal efficiency at 25.33%.

## 1. Introduction

- An investigation of a high-temperature heat pump and not a conventional one as is usually studied in the literature.
- The use of a detailed model for the heat pump modeling by exploiting the available data from the manufacturers.
- The use of dynamic results for the accurate estimation of the heating loads of the building.
- A multi-objective evaluation of the system with energy and economic criteria aiming to determine a global optimal and sustainable design.
- To provide detailed work about a solar heating system with high efficiency for the Greek climate conditions.

## 2. Materials and Methods

#### 2.1. The Examined Configuration

^{2}K [25]. The solar field collecting area (A

_{col}) and the tank’s volume (V) are design parameters in this work, and they are examined parametrically.

^{2}with a height of 3 m. The south wall includes an opening of an 8 m

^{2}area which is covered with a double-glazed window of U

_{w}= 2.6 W/m

^{2}K [28] and a g-value of 0.75. Each external wall has a U-value of 0.45 W/m

^{2}K, the roof has a U-value of 0.40 W/m

^{2}K and the ground has a U-value of 0.40 W/m

^{2}K [28]. All the external structural components of the building come in contact with the ambient air. The sum of infiltration and natural ventilation rates is equal to one air change per hour, the specific equipment load is chosen at 4 W/m

^{2}and the specific lighting load at 3 W/m

^{2}. The building is a residential one with four occupants with a specific load of 100 W/person [29]. The indoor temperature is properly controlled in order to be over 20 °C during the heating period which starts in November and lasts up to the end of April.

#### 2.2. Mathematical Modeling Part

#### 2.2.1. Solar Field and Storage Tank Modeling

_{col}) is given by the next expression [30]:

_{m}), the ambient temperature (T

_{am}) and the solar irradiation on the collector-tilted plane (G

_{T}) are used in the previous formula.

_{u}) can be calculated as below:

_{sol}) is calculated according to the following formula:

_{out}) is found by the next expression:

_{m}) can be calculated as below:

_{st}) can be expressed by using the tank volume (V), the fluid density (ρ) and the fluid’s specific heat capacity (c

_{p}):

_{loss}) can be calculated by using the thermal loss coefficient (U

_{T}), the tank’s external area (A

_{T}), the tank’s mean temperature (T

_{st}) and the ambient temperature (T

_{am}) [32]:

_{aux}) is activated when the tank’s mean temperature is (T

_{st}< 12 °C) and it tries to make the fluid reach 12 °C with a proper control system. The maximum capacity of the auxiliary system is 5 kW.

_{hp}) is dependent on the heating demand and it can be expressed as below:

_{heat}) was calculated by the simulation in the TRSNSYS tool, while the performance of the heat pump (COP

_{hp}) was calculated by the thermodynamic analysis by the developed code in Engineering Equation Solver.

#### 2.2.2. High-Temperature Heat Pump Modeling

_{hp}) can be written as

_{sh}= 10 K. Moreover, the minimum temperature difference in the evaporator between the two streams is chosen to be at 5 K.

_{heat}):

_{cond}= 70 °C in the present work to be able to feed radiative terminal units for heating.

_{el,com}) can be found below:

_{is}). This parameter is expressed with the next formula:

_{1}with the line of high-pressure p = p

_{h}. More details regarding the modeling of the isentropic efficiency can be found in Ref. [33].

_{hp}) for heating production in the heat pump is given according to the next formula:

_{el,aux}). Therefore, the total electricity (P

_{el,tot}) consumption can be written as below:

_{sys}) is given according to the next expression:

#### 2.2.3. Evaluation Metrics

_{heat}) is calculated according to the next expression:

_{el}) is calculated as below:

^{2}[32], of the storage tank at 1000 EUR/m

^{3}[34] and of the heat pump at 750 EUR/kW

_{th}[35] (the maximum thermal load of the building was found at 6 kW according to the simulation in TRNSYS). Moreover, the yearly operation and maintenance cost (O&M) was chosen to be 1% of the investment cost [36]. The investment lifetime was selected at N = 25 years and the discount factor at r = 3%. The electricity was estimated at k

_{el}= 0.22 EUR/kW

_{el}by taking into consideration the new increases in the electricity price.

#### 2.3. Description of the Methodology Path

^{2}floor area is examined and its heating loads were calculated with a model in the TRNSYS tool [22]. A high-temperature heat pump was examined thermodynamically with a created model in Engineering Equation Solver [23]. Data from the Bitzer manufacturer were used to determine the isentropic efficiency of the compressor for the different operating scenarios. It is remarkable that the isentropic efficiency was found to range from 50% to 67%. A comparison of the heat pump COP with the Bitzer data proved a mean deviation of 0.8% which indicates the high accuracy of the developed mode. More details regarding the validity of the present model for the heat pump can be found in Ref. [33]. The next step was the COP approximation with a polynomial in order to develop an accurate formula for further use. Section 3.1 includes the developed formula and its evaluation procedure.

_{col}= 30 m

^{2}and V = 3 m

^{3}. Moreover, the yearly evaluation indexes of the system are given for different combinations of solar field areas and tank volumes. More specifically, the collecting area is varied from 10 to 50 m

^{2}, while the tank volume is from 1 to 5 m

^{3}. The system that leads to the lowest LCC was found to be the most appropriate one. Moreover, an extra multi-objective optimization procedure was applied by using two goals: (i) the minimization of the LCC and the maximization of the SCOP. The global optimum choice was found after using the criterion of the minimum dimensionless geometrical distance between the ideal point and the Pareto Front points. More specifically, the goal of the multi-objective optimization procedure was to minimize the following expression:

## 3. Results

#### 3.1. Heat Pump Investigation

_{hp}increases with the evaporator temperature increase and it also increases with the condenser temperature reduction. The aforementioned behavior is reasonable because the COP

_{hp}of the heat pump increases when there is a lower difference between the temperatures of the condenser and the evaporator devices. For the condenser temperature of 70 °C, the maximum COP

_{hp}is found at 5.087 for T

_{evap}= 35 °C, while the minimum is 1.867 for T

_{evap}= −15 °C.

_{cond}) and the (T

_{evap}) as parameters. The mean deviation of the Equation (25) results and the real calculated values by the code in Engineering Equation Solver were found at 1.21% which is a relatively low value. Thus, Equation (25) can be accepted as a reliable approximation for estimating the heat pump’s efficiency.

_{cond}= 40 °C, the maximum evaporator temperature is T

_{evap,max}= 20 °C, while in the case of T

_{cond}= 50 °C, the maximum evaporator temperature is T

_{evap,max}= 30 °C.

#### 3.2. Dynamic Analysis of the System

_{col}= 30 m

^{2}and V = 3 m

^{3}in order to show how the system behaves during the different heating needs.

^{2}. These results show that in the examined location, (i) there are no extremely low ambient temperature levels, (ii) there are significant heating needs and (iii) there is adequate solar potential for solar thermal technology utilization.

_{sys}be decreased at these periods compared to the COP

_{hp}. In the periods without activation of the electrical resistance, the two indexes (COP

_{sys}and COP

_{hp)}have the same values. The COP

_{hp}ranges between 2.65 and 5.08, with the lowest values obtained when the tank water is relatively cold. The COP

_{sys}ranges from 0.69 to 5.08, with the lowest values obtained when the auxiliary electrical resistance is activated. It is useful to state that the auxiliary system is activated only for 187 h per year which corresponds to 6.2% of the total operating period. Thus, it is clear that for only a few cases the COP

_{sys}takes low values (under 1), and the system is not so efficient. However, the given values of the COP

_{sys}regard the instantaneous efficiency of the unit; this fact indicates that a quantity of the consumed electricity by the auxiliary system can increase the water temperature and assist the system in the near-future time periods, something that indicates that this design is a sustainable one.

#### 3.3. Parametric Analysis and Optimization

^{3}in this figure. A higher collecting area leads to a greater useful heat product from the solar field but with a decreasing rate. The decreasing rate is reasonable because a higher solar field area increases the mean operating temperature in the tank and therefore the solar efficiency is reduced. The increase in useful heat product practically gives the system a higher energy input and makes it possible to reduce the electricity consumption with the collecting area increase. This reduction is more intense in the auxiliary electrical consumption, while the compressor electricity consumption is decreased but not dramatically. More specifically, the auxiliary electrical consumption decreases from 3591 kWh to 210 kWh, while the compressor electricity consumption decreases from 5881 kWh to 1669 kWh.

^{2}in this figure. A larger storage tank’s volume makes the mean temperature of the fluid be reduced and so the thermal performance of the solar system is increased. This fact justifies the increase in the useful heat production of the solar field with the increase in the storage tank volume. Moreover, a higher storage tank capacity leads to smaller electricity consumption, especially by reducing the auxiliary electrical resistance consumption. The compressor consumption shows a very small reduction with the increase in the tank’s volume.

_{col}= 50 m

^{2}and V = 1 m

^{3}) to 64.54% (for A

_{col}= 10 m

^{2}and V = 5 m

^{3}).

_{col}= 50 m

^{2}and V = 5 m

^{3}) to 6112 kWh (for A

_{col}= 10 m

^{2}and V = 1 m

^{3}).

_{col}= 50 m

^{2}and V = 5 m

^{3}) to 62.26% (for A

_{col}= 10 m

^{2}and V = 1 m

^{3}).

^{3}leads to a very small efficiency, while the use of collecting areas up to 20–25 m

^{2}lead also to low performance. The range of the SCOP is found to be from 1.11 (for A

_{col}= 10 m

^{2}and V = 1 m

^{3}) to 4.513 (for A

_{col}= 50 m

^{2}and V = 5 m

^{3}).

^{2}for all the tank volumes. The global minimum LCC is found at 22,694 EUR (for A

_{col}= 35 m

^{2}and V = 2 m

^{3}). So, this design is the optimal configuration according to the financial criterion.

_{col}= 50 m

^{2}and V = 3 m

^{3}) which leads to [SCOP = 4.066, LCC = 24,084 EUR].

_{col}= 35 m

^{2}and V = 2 m

^{3}), while the multi-objective optimization (energy and economic) indicates that the optimum scenario is (A

_{col}= 50 m

^{2}and V = 3 m

^{3}). The ratio of the collectors’ area to the tank’s volume was found at 17.5 m

^{2}/m

^{3}and 16.7 m

^{2}/m

^{3}which are similar values, and this fact indicates that the storage tank volume “follows” the selection of the collecting area value. It is remarkable to state that the optimum collecting area of 35 m

^{2}has a significant difference from that of the value of 50 m

^{2}. This fact indicates that the selection of the optimization criteria plays an important role in the final selection of the installed collecting area. In the case where the economic parameter is the most valuable index, a lower collecting area of 35 m

^{2}has to be selected, while in the case where energy efficiency is important, a higher collecting area of 50 m

^{2}has to be chosen. Practically, a higher collecting area makes the efficiency be enhanced and this fact indicates that in the cases that the efficiency plays a critical role in the decision-making process, then higher collecting areas have to be selected. Table 1 includes the results for the two optimum scenarios.

_{cond}= 70 °C and T

_{evap}= 31 °C in order to reach the value of SCOP = 4.651 approximately. This is an empirical rule which can estimate in a quick way the total SCOP of the system and it can be used for performing quick calculations for the design of future systems. Practically, in future solar-assisted heat pump heating systems, the final optimum SCOP could be calculated by using the inputs (T

_{evap}= 31 °C and T

_{cond}= 70 °C) for having a preliminary reasonable estimation.

#### 3.4. Discussion and Future Steps

## 4. Conclusions

- -
- It was found that an increase in the solar field area and of the thermal tank volume leads to higher useful heat produced by the exploitation of the sun and consequently to a greater performance in the system.
- -
- The auxiliary heater aids the mean tank temperature to be kept at the desired levels and it is activated only for a small time period which is only 6.2% of the heating time.
- -
- According to the results, the economic optimization indicates that the optimal design includes 35 m
^{2}of solar thermal collectors connected to a storage tank of 2 m^{3}for facing the total heating demand of 6785 kWh. In this case, the life cycle cost was calculated at 22,694 EUR, the seasonal system coefficient of performance at 2.947 and the mean solar thermal efficiency at 31.60%. - -
- The multi-objective optimization with both energetic and economic criteria indicates that the optimum design is the selection of 50 m
^{2}of solar thermal collectors connected to a storage tank of 3 m^{3}. In this case, the life cycle cost was calculated at 24,084 EUR, the seasonal system coefficient of performance at 4.066 and the mean solar thermal efficiency at 25.33%. - -
- It can be concluded that the rise in the solar field area leads to significant enhancements to the system performance by leading to electricity savings, while the additional cost is reasonable, according to the life cycle cost analysis.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

A_{col} | Solar field area, m^{2} |

c_{p} | Specific heat capacity, kJ/kgK |

CC | Investment cost, EUR |

h | Specific enthalpy, kJ/kg |

F | Dimensionless geometrical distance from the ideal design |

G_{T} | Solar irradiation on the tilted surface, W/m^{2} |

k_{el} | Electricity cost, EUR/kWh_{el} |

LCC | Life cycle cost, EUR |

m | Mass flow rate, kg/s |

N | Lifetime of the project, years |

p | Pressure, bar |

P_{el} | Electricity demand on the compressor, kW |

Q_{aux} | Auxiliary electricity power, kW |

Q_{heat} | Heating demand, kW |

Q_{hp} | Heat input from the ambient to the heat pump, kW |

Q_{loss} | Thermal losses in the tank, kW |

Q_{st} | Stored energy rate in the tank, kW |

Q_{u} | Useful heat production, kW |

Q_{sol} | Solar energy, kW |

r | Discount factor, % |

s | Specific entropy, kJ/kgK |

T | Temperature, °C |

U | Thermal transmittance, W/m^{2}K |

V | Storage tank volume, m^{3} |

(O&M) | Operation and maintenance cost, EUR |

Greek Symbols | |

ΔΤ_{sh} | Superheating in the evaporator outlet, K |

η_{col} | Collector thermal efficiency |

η_{is} | Isentropic efficiency |

ρ | Density, kg/m^{3} |

Subscripts | |

aux | Auxiliary |

am | Ambient |

b | Boiler |

col | Collector |

com | Compressor |

cond | Condenser |

evap | Evaporator |

hp | Heat pump |

in | Inlet |

is | Isentropic |

m | Mean |

max | Maximum |

min | Minimum |

sys | System |

tot | Total |

out | Outlet |

w | Window |

Abbreviations | |

ASHP | Air-source heat pump |

COP | Coefficient of performance |

ETC | Evacuated tube collector |

FPC | Flat-plate collector |

GWP | Global warming potential |

ODP | Ozone depletion potential |

SAHP | Solar-assisted heat pump |

SCOP | Seasonal coefficient of performance |

## References

- European Commission. Communication from the Commission to the European Parliament, the Council, the European Economic and Social Committee and the Committee of the Regions a Renovation Wave for Europe—Greening our Buildings, Creating Jobs, Improving Lives; European Commission: Brussels, Belgium, 2020.
- Hielscher, S.; Wittmayer, J.M.; Dańkowska, A. Social movements in energy transitions: The politics of fossil fuel energy pathways in the United Kingdom, the Netherlands and Poland. Extr. Ind. Soc.
**2022**, 10, 101073. [Google Scholar] [CrossRef] - Chomać-Pierzecka, E.; Kokiel, A.; Rogozińska-Mitrut, J.; Sobczak, A.; Soboń, D.; Stasiak, J. Analysis and Evaluation of the Photovoltaic Market in Poland and the Baltic States. Energies
**2022**, 15, 669. [Google Scholar] [CrossRef] - Wang, Z.; Li, G.; Wang, F.; Zhang, Y. Performance investigation of a transcritical CO
_{2}heat pump combined with the terminal of radiator and floor radiant coil for space heating in different climates, China. J. Build. Eng.**2021**, 44, 102927. [Google Scholar] [CrossRef] - Jiang, J.; Hu, B.; Wang, R.Z.; Deng, N.; Cao, F.; Wang, C.-C. A review and perspective on industry high-temperature heat pumps. Renew. Sustain. Energy Rev.
**2022**, 161, 112106. [Google Scholar] [CrossRef] - Bellos, E.; Tzivanidis, C. Energetic and financial sustainability of solar assisted heat pump heating systems in Europe. Sustain. Cities Soc.
**2017**, 33, 70–84. [Google Scholar] [CrossRef] - Kong, X.; Yan, X.; Yue, Z.; Zhang, P.; Li, Y. Influence of refrigerant charge and condenser area on direct-expansion solar-assisted heat pump system for radiant floor heating. Sol. Energy
**2022**, 247, 499–509. [Google Scholar] [CrossRef] - Hu, Z.; Gao, Z.; Xu, X.; Fang, S.; Zhou, L.; Ji, D.; Li, F.; Feng, J.; Wang, M. Suitability zoning of buried pipe ground source heat pump and shallow geothermal resource evaluation of Linqu County, Shandong Province, China. Renew. Energy
**2022**, 198, 1430–1439. [Google Scholar] [CrossRef] - Deng, J.; Ma, M.; Wei, Q.; Liu, J.; Zhang, H.; Li, M. A specially-designed test platform and method to study the operation performance of medium-depth geothermal heat pump systems (MD-GHPs) in newly-constructed project. Energy Build.
**2022**, 272, 112369. [Google Scholar] [CrossRef] - Lyakhomskii, A.; Petrochenkov, A.; Romodin, A.; Perfil’eva, E.; Mishurinskikh, S.; Kokorev, A.; Kokorev, A.; Zuev, S. Assessment of the Harmonics Influence on the Power Consumption of an Electric Submersible Pump Installation. Energies
**2022**, 15, 2409. [Google Scholar] [CrossRef] - Souhail, W.; Alsharif, S.; Ahmed, I.; Khammari, H. Optimal Tradeoff between MPP and Stability of a PV-Based Pumping System. Energies
**2022**, 15, 1106. [Google Scholar] [CrossRef] - Nandhini, R.; Sivaprakash, B.; Rajamohan, N. Waste heat recovery at low temperature from heat pumps, power cycles and integrated systems—Review on system performance and environmental perspectives. Sustain. Energy Technol. Assess.
**2022**, 52, 102214. [Google Scholar] [CrossRef] - Li, J.; Qu, C.; Li, C.; Liu, X.; Novakovic, V. Technical and economic performance analysis of large flat plate solar collector coupled air source heat pump heating system. Energy Build.
**2022**, 277, 112564. [Google Scholar] [CrossRef] - Gaonwe, T.P.; Hohne, P.A.; Kusakana, K. Optimal energy management of a solar-assisted heat pump water heating system with a storage system. J. Energy Storage
**2022**, 56, 105885. [Google Scholar] [CrossRef] - Li, J.; Wei, S.; Dong, Y.; Liu, X.; Novakovic, V. Technical and economic performance study on winter heating system of air source heat pump assisted solar evacuated tube water heater. Appl. Therm. Eng.
**2023**, 221, 119851. [Google Scholar] [CrossRef] - Jiang, Y.; Zhang, H.; Wang, Y.; Wang, Y.; Liu, M.; You, S.; Wu, Z.; Fan, M.; Wei, S. Research on the operation strategies of the solar assisted heat pump with triangular solar air collector. Energy
**2022**, 246, 123398. [Google Scholar] [CrossRef] - Leonforte, F.; Miglioli, A.; Del Pero, C.; Aste, N.; Cristiani, N.; Croci, L.; Besagni, G. Design and performance monitoring of a novel photovoltaic-thermal solar-assisted heat pump system for residential applications. Appl. Therm. Eng.
**2022**, 210, 118304. [Google Scholar] [CrossRef] - Yang, L.W.; Xu, R.J.; Zhou, W.B.; Li, Y.; Yang, T.; Wang, H.S. Investigation of solar assisted air source heat pump heating system integrating compound parabolic concentrator-capillary tube solar collectors. Energy Convers. Manag.
**2023**, 277, 116607. [Google Scholar] [CrossRef] - Bellos, E.; Tzivanidis, C.; Moschos, K.; Antonopoulos, K.A. Energetic and financial evaluation of solar assisted heat pump space heating systems. Energy Convers. Manag.
**2016**, 120, 306–319. [Google Scholar] [CrossRef] - Plytaria, M.T.; Bellos, E.; Tzivanidis, C.; Antonopoulos, K.A. Financial and energetic evaluation of solar-assisted heat pump underfloor heating systems with phase change materials. Appl. Therm. Eng.
**2019**, 149, 548–564. [Google Scholar] [CrossRef] - Bellos, E.; Tzivanidis, C.; Nikolaou, N. Investigation and optimization of a solar assisted heat pump driven by nanofluid-based hybrid PV. Energy Convers. Manag.
**2019**, 198, 111831. [Google Scholar] [CrossRef] - Welcome TRNSYS: Transient System Simulation Tool. Available online: https://www.trnsys.com/ (accessed on 17 December 2022).
- EES: Engineering Equation Solver F-Chart Software: Engineering Software. Available online: https://fchartsoftware.com/ees/ (accessed on 17 December 2022).
- Mota-Babiloni, A.; Navarro-Esbrí, J.; Molés, F.; Cervera, Á.B.; Peris, B.; Verdú, G. A review of refrigerant R1234ze(E) recent investigations. Appl. Therm. Eng.
**2016**, 95, 211–222. [Google Scholar] [CrossRef] - Bellos, E.; Tzivanidis, C.; Belessiotis, V. Daily performance of parabolic trough solar collectors. Sol. Energy
**2017**, 158, 663–678. [Google Scholar] [CrossRef] - Welcome to BITZER. Available online: https://www.bitzer.de/gr/en/ (accessed on 17 December 2022).
- BITZER Software. Available online: https://www.bitzer.de/websoftware/Default.aspx (accessed on 17 December 2022).
- Available online: http://portal.tee.gr/portal/page/portal/SCIENTIFIC_WORK/GR_ENERGEIAS/kenak/files/TOTEE_20701-1_2017_TEE_1st_Edition.pdf (accessed on 17 December 2022).
- ISO 7730:2005. Available online: https://www.iso.org/standard/39155.html (accessed on 17 December 2022).
- Solar Collector Calpak M4. Available online: https://calpak.gr/el/products/iliakoi-sullektes-boilers/33/210 (accessed on 6 January 2023).
- Solar Engineering of Thermal Processes, 4th Edition Wiley. Available online: https://www.wiley.com/en-us/Solar+Engineering+of+Thermal+Processes%2C+4th+Edition-p-9780470873663 (accessed on 6 January 2023).
- Bellos, E.; Tzivanidis, C.; Antonopoulos, K.A. Exergetic, energetic and financial evaluation of a solar driven absorption cooling system with various collector types. Appl. Therm. Eng.
**2016**, 102, 749–759. [Google Scholar] [CrossRef] - Bellos, E.; Tsimpoukis, D.; Lykas, P.; Kitsopoulou, A.; Korres, D.N.; Vrachopoulos, M.G.; Tzivanidis, C. Investigation of a High-Temperature Heat Pump for Heating Purposes. Appl. Sci.
**2023**, 13, 2072. [Google Scholar] [CrossRef] - Bellos, E.; Tzivanidis, C.; Symeou, C.; Antonopoulos, K.A. Energetic, exergetic and financial evaluation of a solar driven absorption chiller—A dynamic approach. Energy Convers. Manag.
**2017**, 137, 34–48. [Google Scholar] [CrossRef] - Heat Pumps YDOR. Available online: https://www.ydor.com.gr/antlies-thermotitas/?gclid=CjwKCAiAp7GcBhA0EiwA9U0mtkyRiiUfH5m8RsWav7hpm85YOuhnNqXMx851rw63fKlo_KWaUNVcxRoCgzwQAvD_BwE&f2--=6-kw&page=2 (accessed on 17 December 2022).
- Bellos, E.; Sarakatsanis, I.; Tzivanidis, C. Investigation of Different Storage Systems for Solar-Driven Organic Rankine Cycle. Appl. Syst. Innov.
**2020**, 3, 52. [Google Scholar] [CrossRef]

**Figure 1.**The examined system with a solar-assisted heating unit which includes a solar field, a thermal storage tank with auxiliary electrical resistance and a high-temperature heat pump.

**Figure 5.**Heating load and cumulative heating demand for the examined building (1 October to 30 April).

**Figure 6.**Mean water temperature in the storage tank for the case with 30 m

^{2}collecting area and 3 m

^{3}tank volume (1 October to 30 April).

**Figure 7.**Electricity demand for the compressor and the auxiliary electrical resistance in the tank for the case with 30 m

^{2}collecting area and 3 m

^{3}tank volume (1 October to 30 April).

**Figure 8.**COP for the system and the heat pump for the case with a 30 m

^{2}collecting area and 3 m

^{3}tank volume (1 October to 30 April).

**Figure 9.**Variation in energy quantities for different collecting areas with the storage tank volume at 3 m

^{3}.

**Figure 10.**Variation in energy quantities for different storage tank volumes with the collecting area at 30 m

^{2}.

**Figure 11.**Mean yearly solar thermal efficiency of the collectors for different combinations of (A

_{col}) and (V).

**Figure 12.**Total electricity demand (compressor and auxiliary electrical resistance) for different combinations of (A

_{col}) and (V).

**Figure 13.**Percentage of the auxiliary electricity compared to the total electricity demand for different combinations of (A

_{col}) and (V).

**Figure 16.**Illustration of the multi-objective optimization process of the system aiming for the maximization of the system SCOP and the minimization of the LCC.

Parameter | Economic Optimization (LCC Minimization) | Multi-Objective Optimization |
---|---|---|

Optimum collecting area | 35 m^{2} | 50 m^{2} |

Optimum storage tank volume | 2 m^{3} | 3 m^{3} |

Yearly solar thermal efficiency | 31.60% | 25.33% |

System SCOP | 2.947 | 4.066 |

Heat pump SCOP | 4.125 | 4.651 |

LCC | 22,694 EUR | 24,084 EUR |

Heating demand | 6785 kWh | 6785 kWh |

Total electricity demand | 2302 kWh | 1669 kWh |

Compressor electricity demand | 1645 kWh | 1459 kWh |

Auxiliary electricity demand | 657 kWh | 210 kWh |

Percentage of auxiliary demand | 28.55% | 12.59% |

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## Share and Cite

**MDPI and ACS Style**

Bellos, E.; Lykas, P.; Tsimpoukis, D.; Korres, D.N.; Kitsopoulou, A.; Vrachopoulos, M.G.; Tzivanidis, C.
Multicriteria Analysis of a Solar-Assisted Space Heating Unit with a High-Temperature Heat Pump for the Greek Climate Conditions. *Appl. Sci.* **2023**, *13*, 4066.
https://doi.org/10.3390/app13064066

**AMA Style**

Bellos E, Lykas P, Tsimpoukis D, Korres DN, Kitsopoulou A, Vrachopoulos MG, Tzivanidis C.
Multicriteria Analysis of a Solar-Assisted Space Heating Unit with a High-Temperature Heat Pump for the Greek Climate Conditions. *Applied Sciences*. 2023; 13(6):4066.
https://doi.org/10.3390/app13064066

**Chicago/Turabian Style**

Bellos, Evangelos, Panagiotis Lykas, Dimitrios Tsimpoukis, Dimitrios N. Korres, Angeliki Kitsopoulou, Michail Gr. Vrachopoulos, and Christos Tzivanidis.
2023. "Multicriteria Analysis of a Solar-Assisted Space Heating Unit with a High-Temperature Heat Pump for the Greek Climate Conditions" *Applied Sciences* 13, no. 6: 4066.
https://doi.org/10.3390/app13064066