# Performance Analysis of a Combined Solar-Assisted Heat Pump Heating System in Xi’an, China

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## Abstract

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## 1. Introduction

## 2. Methodology

#### 2.1. System Descriptions

^{7}kJ. The proposed combined SAHP system could be switched between the serial and parallel modes conveniently. It was mainly composed of a solar collector, a heat storage water tank (HSWT), a WSHP, an ASHP and a consumer side water tank (CSWT), as shown in Figure 2. For the serial mode, the water stored in the HSWT was heated by the solar collector, which served as an evaporation heat source for the WSHP, finally, the water in the CSWT was heated by the WSHP until reaching the required temperature; for the parallel mode, the solar collector and the ASHP heated the water in the CSWT simultaneously. The system could achieve a steady and efficient operation throughout the whole year without electric auxiliary heat source.

#### 2.2. Design Parameters of the Serial Mode

^{−2}·d

^{−1}according to the meteorological parameters of typical years in Xi’an, with a southern direction and a tilt angle of 59° [42]. According to the results found in previous research [43,44], the collector efficiency was 75%, and the heat coefficient of the heat pump was 2.8 [45,46]. Thus, if the daily heating load of the system (10

^{7}kJ) was needed, the daily heat-collecting capacity of the solar collector should be 6.42 × 10

^{6}kJ·d

^{−1}. The area of the solar collector could be obtained using the following Equation [47]:

_{u}’ is the daily heat collection capacity of the solar collector, kJ·d

^{−1}; I

_{c}is the daily average solar radiation in the coldest month, kJ·m

^{−2}·d

^{−1}; and η

_{c}is the collector efficiency.

^{2}by using Equation (1). The collector consisted of 60 sets of evacuated collectors of MK-58 × 1800-50-2 × 1-83-20, as shown in Figure 3. In view of the low-temperature environment, the antifreeze fluid mixed by alcohol and water (volume ratio of 1:2, freezing point of −14.2 °C) was used as the heating medium [48].

_{s}’ is the daily heat storage capacity, kJ·d

^{−1}; (ρc)

_{w}is the volumetric heat capacity of the heating medium, kJ·m

^{−3}·°C

^{−1}; Δt is the temperature difference of the heating medium, °C; and η

_{s}is the heat loss rate of heating medium.

^{6}kJ·d

^{−1}with consideration of an extra coefficient of 20%. Generally, the temperature difference of the heating medium was 10–15 °C [48], and it was supposed to be 12 °C in this study. Furthermore, the heat loss rate of the heating medium was generally 20%–40% [52], and it was supposed to be 20% due to the low working temperature of the HSWT in the serial mode. Finally, using Equation (2) the volume of the HSWT was found to be 55 m

^{3}. Considering the economy and durability of the tank, the main structure of the tank was welded with a 3-mm-thick steel plate; the shell of the tank was composed of a 1.2 mm thick steel plate; and the whole water tank was thickened with a 200 mm insulation layer.

^{7}kJ and a running period of 10 h. Therefore, the heating power of the WSHP was 278 kW. According to the capacity of the heat pump and the working range of the evaporation, two RW210-F WSHPs were adopted, each with an input power of 48 kW and a circulating water flow of 20 T·h

^{−1}.

#### 2.3. Design Parameters of Parallel Mode

^{−1}, as shown in Figure 4.

^{−2}·d

^{−1}[42], consequently, the collector area was 1025 m

^{2}using Equation (1). However, the serial and parallel modes shared the same solar collector, given the investment [14], and the collector area was designed to be 860 m

^{2}in this experiment.

#### 2.4. Measurement Instrumentation

^{−1}·m

^{−2}, a response time of less than 30 s, and a measurement range of 0~2000 W·m

^{−2}. The installation angle of the pyranometer was consistent with the angle of the solar collector. Moreover, two layers of quartz glass cover made by optical cold processing were employed to reduce the influence of environmental changes on equipment performance. The water flow rate was measured by the YB-70H hand-held ultrasonic flowmeter. The measurement range for velocity was 0–30 m·s

^{−1}and the applicable diameter range was 10–6000 mm. The real-time experimental data was recorded by a HP34970A data collector. The measuring instruments are shown in Figure 5. During the experimental process, the accuracy of measuring instruments was the main factor that caused system error [54,55]. In this study, the uncertainty analysis method put forward by Moffat was adopted [56]. Assuming the variant R, which is calculated from a set of independent variants X

_{1}, X

_{2}, …, X

_{n}, that is to say R = R(X

_{1}, X

_{2}, …, X

_{n}), the uncertainty of the variant R can be determined by combining the uncertainties of individual terms and can be expressed as follows:

## 3. Modelling

#### 3.1. Models of the Two Modes

#### 3.2. Model Validation

## 4. Results and Discussions

#### 4.1. Switching Analysis

_{m}) was 3070 kJ·m

^{−2}·h

^{−1}, and the maximum ambient temperature (T

_{m}) was above 14 °C. In this case, the COP of the parallel mode was 8.84, while that of the serial mode was 4.06. However, as the solar radiation decreases, the efficiency of the collector will decrease dramatically, which led to the decline of COP in parallel mode. For March 21, when I

_{m}was 1756 kJ·m

^{−2}·h

^{−1}and Tm was 13 °C, the COPs of the serial and parallel modes were 3.99 and 4.32, respectively; for March 1, when I

_{m}was 2056 kJ·m

^{−2}·h

^{−1}and T

_{m}was 11 °C, the COP of the serial mode was 3.94 and that of the parallel mode was 3.86. From these two results, it could be seen that the COPs of the two modes were simultaneously influenced by the solar radiation and ambient temperature. In addition, it was found that in the winter condition (January 11), the serial mode had a better performance than the parallel mode; with the increased ambient temperature and solar radiation, the parallel mode exhibited a performance advantage in transition season (March 21 and April 1). The comparison results fully illustrated the rationality and necessity of the mode switching during a day. However, to obtain the reasonable optimization method as well as the accurate results, the mode switching condition needed to be further analyzed by establishing heat balance equations of the SAHP system, which are detailed and discussed in Section 4.2, Section 4.3 and Section 4.4 in this manuscript.

#### 4.2. Heat Balance Equations of the SAHP System

- (1)
- Stable operation of the system.
- (2)
- Linear distribution of the temperatures in the solar collector and the heat exchanger.
- (3)
- Negligible heat loss of pipes and valves.

_{p}is the heat capacity of the heating medium, kJ·°C

^{−1}·s

^{−1}; T

_{co}is the outlet temperature of the collector, °C; T

_{ci}is the inlet temperature of the collector, °C; T

_{ca}is the average temperature of the collector, °C; F

_{r}is the heat removal factor; A

_{c}is the solar collector area, m

^{2}; I is the solar radiation, kJ·m

^{−2}·h

^{−1}; τα is the product of the transmittance and absorption rates of the plate; K

_{1}is the heat transfer coefficient of the plate to environment, kW·m

^{−2}·°C

^{−1}; and T

_{a}is the ambient temperature, °C.

_{u}is the heat collection capacity of the solar collector, kw.

_{s}is the heating capacity of the HSWT, kw; Q

_{c}is the heat transfer rate of the WSHP evaporator, kw; K

_{s}is the heat transfer coefficient of the HSWT, kW·m

^{−2}·°C

^{−1}; A

_{s}is the heat exchange area of the HSWT, m

^{2}; T

_{sm}is the average water temperature in the HSWT, °C; (mC

_{p})

_{s}is the heat capacity of water, kJ·°C

^{−1}·s

^{−1}; $\delta {T}_{s}/\delta \tau $ is the water temperature change rate, °C.

_{k}is the heat transfer rate of the WSHP condenser, kw; COP

_{s}is the COP of the WSHP; W is the compressor power consumption of the WSHP, kw.

- (1)
- The compressor power consumption under the two modes was equal, which was described as follows:$$W=\overline{W}.$$
- (2)
- The condensation temperatures of the ASHP and WSHP were approximately the same at the mode switching timing, thus it was supposed that the COPs of the heat pump systems were only influenced by the evaporation temperature.
- (3)
- The HSWT was insulated, thus the heat loss of the HSWT, e.g., K
_{s}A_{s}(T_{sm}− T_{a}) could be ignored.

_{s}is the water temperature in the HSWT, °C.

_{r}, τα, and K

_{1}in Equations (3) and (6) were 0.6, 0.76, and 0.001, respectively, in this study. The constraint condition for mode switching was:

_{s}) as well as the ambient temperature (T

_{a}) and the solar radiation (I). The relationship between the water temperature in the HSWT and system running time can be illustrated by Equation (17).

#### 4.3. Switching Conditions

^{2}, the compressor power was about 100 kW, and the volume of HSWT was 55 m

^{3}. In addition, at the moment of mode switch, substituting the values of these parameters into Equation (16), it can be simplified as follows:

_{s}was variable, the combined SAHP should be started in the serial mode for conveniently monitoring the value of T

_{s}in real-time. As the ambient temperature and solar radiation were increasing gradually after 8:00 AM, the system would switch from the serial mode to the parallel mode at a proper time. Similarly, the parallel mode should be switched to the serial when its performance was worse than the serial system. The logic diagram of the mode switching is shown in Figure 10. The system loaded the real time values of T

_{a}, I and T

_{s}at first and transmitted them to Equation (19) to determine whether to switch to the parallel mode. According to the above analyses, it was obvious that the parallel mode would performance better if Equation (19) is below or equal to zero. However, the monitoring was still continuing. When the ambient temperature and solar radiation reduced to a certain extent, it would result in a low evaporation temperature of ASHPs and a limited solar heat output for the parallel system. In this case, the serial mode might perform better than the parallel mode, thus the system should be switched back to the serial mode. Therefore, the mode switching is a continuous cycle until 18:00 PM in each day.

#### 4.4. Annual Performance Analysis

^{3}GJ, which was obviously lower than those of the serial and the parallel systems, with values of 1.17 × 10

^{3}GJ and 0.87 × 10

^{3}GJ, respectively, indicating the good energy efficiency of the combined SAHP system.

#### 4.5. System Benefit Analysis

^{2}; J

_{t}is the annual solar radiation projecting onto the surface of the solar collector, MJ/m

^{2}; η

_{cd}is the heat loss rate of the pipeline and water tank; η

_{c}is the collector efficiency. In this study, the solar collector area was 860 m

^{2}. According to GB 50495-2009 [63], the J

_{t}in Xi’an region was 2752 MJ/m

^{2}, η

_{cd}and η

_{c}were 25% and 75%, respectively. Thus, the annual energy-saving amount of the proposed combined SAHP system was 1,318,218 MJ by Equation (20).

_{i}is the annual cost-saving amount, CNY; C

_{i}is the heat pricing of the conventional energy, CNY/MJ, which is expressed as:

_{i}’ is the conventional energy price, CNY/kg; q is the calorific value of the conventional energy, MJ/kg; Eff is the heating efficiency of the devices with conventional energy. Generally, the coal price in China was about 450 CNY/ton and the calorific value of the standard coal was 29.308 MJ/kg. The thermal efficiency of boilers was 75%. Thus, the value of C

_{i}could be obtained by Equation (22), which is 0.02 CNY/MJ. Consequently, the value of M

_{i}could be obtained by Equation (21), which is 26,363 CNY.

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

ASHP | air source heat pump |

CSWT | consumer side water tank |

HSWT | heat storage water tank |

SAHP | solar assisted heat pump |

WSHP | water source heat pump |

A_{c} | area of the solar collector, m^{2} |

A_{s} | heat exchange area of HSWT, m^{2} |

A_{w} | surface area of the exterior wall, m^{2} |

C_{i} | conventional energy heating price in the year of system design, CNY/MJ |

C_{i}’ | systematic assessment of conventional energy prices, CNY/kg |

COP_{a} | COP of ASHP |

COP_{s} | COP of WSHP |

Eff | efficiency of conventional energy heating devices |

F_{r} | heat removal factor |

I | solar radiation, kJ·m^{−2}·h^{−1} |

I_{c} | average daily solar radiation in the coldest month, kJ·m^{−2}·d^{−1} |

J_{t} | annual solar radiation on the surface of solar collector, MJ/m^{2} |

K_{1} | heat transfer coefficient of the plate to environment, kW·m^{−2}·°C^{−1} |

K_{s} | heat transfer coefficient of HSWT, kW·m^{−2}·°C^{−1} |

(mC_{p})_{s} | heat capacity of water, kJ·°C^{−1}·s^{−1} |

mC_{p} | heat capacity of the heating medium, kJ·°C^{−1}·s^{−1} |

M_{i} | simple annual energy saving cost, CNY |

q | calorific value of conventional energy, MJ/kg |

Q | heating capacity of CSWT for serial mode, kW |

$\overline{Q}$ | heating capacity of CSWT for parallel mode, kW |

Q_{C} | heat transfer rate of WSHP evaporator, kW |

$\overline{{Q}_{c}}$ | heat transfer rate of ASHP evaporator, kW |

Q_{k} | heat transfer rate of WSHP condenser, kW |

$\overline{{Q}_{k}}$ | heat transfer capacity of ASHP condenser, kW |

Q_{s} | daily heat capacity, kW |

Q_{u} | heat collection the solar collector, kW |

$\overline{{Q}_{u}}$ | collecting heat of the solar collector, kW |

ΔQ | annual energy-saving amount, MJ |

T_{a} | ambient temperature, °C |

T_{ca} | average water temperature of the solar collector, °C |

T_{ci} | inlet water temperature of the collector, °C |

T_{co} | outlet water temperature of the solar collector, °C |

T_{sm} | average water temperature in HSWT, °C |

V | volume of the HSWT, m^{3} |

W | compressor power of WSHP, kW |

$\overline{W}$ | compressor power of ASHP, kW |

(ρc)_{w} | volumetric heat capacity of the heating medium, kJ·m^{−3}·°C^{−1} |

τα | product of the transmittance and absorption rates of the plate |

η_{c} | collector efficiency |

η_{cd} | heat loss rate of pipeline and water tank |

η_{s} | heat loss rate of heating medium |

Δt | temperature difference, °C |

δT_{s}/δτ | water temperature change rate, °C |

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**Figure 1.**Sketch of the indirect-expansion solar-assisted heat pump (IDX-SAHP) system. (

**a**) Serial system; (

**b**) parallel system; (

**c**) complex system.

**Figure 5.**Measuring instruments. (

**A**) HP34970A data collector; (

**B**) TBQ-2 pyranometer; (

**C**) YB-70H hand-held ultrasonic flowmeter; (

**D**) DF-type centralized electric energy meter.

**Figure 7.**Water temperature changes; (

**a**) validation of the evacuated collector; (

**b**) validation of the water source heat pump (WSHP); (

**c**) validation of the air source heat pump (ASHP).

**Figure 9.**Performance curves of the heat pumps. (

**a**) Performance curve of the ASHP; (

**b**) performance curves of the WSHP.

Component | TRNSYS Type |
---|---|

Weather data reader | 109 |

Evacuated collector | 538 |

Controller | 2 |

HSWT | 4 |

CSWT | 4 |

WSHP | 668 |

Water pump | 114 |

Load profile | 14 |

Results | 24 |

Printer | 25 |

Graphic plotter | 65 |

ASHP | 941 |

Mixer | 11 |

Performance Parameters | Jan 11 | Mar 1 | Mar 21 | Apr 1 | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

S Mode | S + P Mode | S Mode | S + P Mode | S Mode | S + P Mode | S Mode | S + P Mode | |||||

C | A | C | A | C | A | C | A | |||||

Heating capacity/10^{6} kJ (C&A) | 4.08 | 1.55 | 2.70 | 5.22 | 2.14 | 3.17 | 5.34 | 2.36 | 3.71 | 5.46 | 4.45 | 1.93 |

Energy consumption/10^{6} kJ | 1.26 | 1.35 | 1.32 | 1.38 | 1.34 | 1.40 | 1.35 | 0.72 | ||||

COP | 3.24 | 3.15 | 3.94 | 3.86 | 3.99 | 4.32 | 4.06 | 8.84 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Huan, C.; Li, S.; Wang, F.; Liu, L.; Zhao, Y.; Wang, Z.; Tao, P.
Performance Analysis of a Combined Solar-Assisted Heat Pump Heating System in Xi’an, China. *Energies* **2019**, *12*, 2515.
https://doi.org/10.3390/en12132515

**AMA Style**

Huan C, Li S, Wang F, Liu L, Zhao Y, Wang Z, Tao P.
Performance Analysis of a Combined Solar-Assisted Heat Pump Heating System in Xi’an, China. *Energies*. 2019; 12(13):2515.
https://doi.org/10.3390/en12132515

**Chicago/Turabian Style**

Huan, Chao, Shengteng Li, Fenghao Wang, Lang Liu, Yujiao Zhao, Zhihua Wang, and Pengfei Tao.
2019. "Performance Analysis of a Combined Solar-Assisted Heat Pump Heating System in Xi’an, China" *Energies* 12, no. 13: 2515.
https://doi.org/10.3390/en12132515