**3. Model**

The thermodynamic modeling of SASCHCS and model validation are described in this section.

## *3.1. Modeling of SASCHCS*

The off-design model of SASCHCS was built based on the following assumption:


#### 3.1.1. ETC and Storage Tank

The efficiency of ETC is calculated by the following expression [28]:

$$\eta\_{\rm etc,i} = Q\_{\rm etc,i} / Al\_{\rm i} = F\_R \left[ \tau \alpha - lI\_L \left( T\_{\rm etc,i} - T\_{a,i} \right) / I\_{\rm i} \right] \tag{1}$$

where *FR* is the heat removal factor and equal to:

$$F\_R = \frac{mc\_p}{A\_c \mathcal{U}\_L} \left[ 1 - \exp\left(-\frac{\mathcal{U}\_L F' A\_c}{mc\_p}\right) \right] \tag{2}$$

*UL* is the overall heat loss coefficient and can be expressed by:

$$
\mathcal{U}\_L = \mathcal{U}\_t + \mathcal{U}\_t \tag{3}
$$

where *Ue* is header pipe edge loss coefficient and is expressed by:

$$\beta L\_{\rm t} = \frac{2\pi\lambda\_{\rm ins}}{L\_T \ln(D\_{\rm ext}/D\_{\rm int})} \tag{4}$$

*Ut* is the loss coefficient from the absorber tube to the ambient and can be defined as:

$$\mathcal{U}I\_{\mathcal{I}} = \frac{1}{\frac{1}{h\_{\mathcal{K}-a}} + \frac{1}{h\_{\mathcal{P}-\mathcal{G},r} + h\_{\mathcal{P}-\mathcal{G},c}}} \tag{5}$$

The collector efficiency factor, *F*, is derived by [29]:

$$F' = \frac{1/\mathcal{U}\_L}{L\left[\frac{1 + \mathcal{U}\_L/\mathcal{C}\_b}{\mathcal{U}\_L(d + (L - d)F)} + \frac{1}{\mathcal{C}\_B} + \frac{1}{h\_f \tau d}\right]}\tag{6}$$

Furthermore, the thermal e fficiency of collectors based on the operational period is:

$$\eta\_{\rm tct} = \frac{\int\_{\Delta t} Q\_{\rm tct,i} dt}{\int\_{\Delta t} A I\_i dt} \tag{7}$$

The storage tank has three layers, and the energy balance of each layer is calculated below:

$$\frac{1}{3}\rho V\_{\text{st}}c\_p \frac{dT\_{\text{st},i}}{dt} = m\_{\text{c}}c\_p(T\_{\text{st},i-1} - T\_{\text{st},i}) + m\_{\text{g}}c\_p(T\_{\text{st},i+1} - T\_{\text{st},i}) - h\_{\text{st}}A\_{\text{sl}}(T\_{\text{st},i} - T\_{\text{a},i})/3 \tag{8}$$

The initial temperature of storage tank is equal to the surrounding temperature. It is stated that layer 1 donates the top layer of the storage tank and layer three is the bottom layer.

#### 3.1.2. Absorption Subsystem and Compression Subsystem

The o ff-design model of cooling subsystems (the absorption subsystem and the compression one) was developed in our previous study [30]. The model of the absorption subsystem was based on the characteristic equation.

The relationship of the generator heat transfer and the generator hot water flow rate can be expressed as [31]:

$$
\Box LA = \left(\frac{m\_{\mathcal{S}}}{m\_{\mathcal{S}, \text{rated}}}\right)^{0.8} (\Box LA)\_{\text{rated}} \tag{9}
$$

The cooling output of absorption subsystems is expressed as:

$$Q\_{\rm c\beta\varepsilon} = \mathbf{s} \cdot \Delta\Lambda t - \mathbf{a} \cdot Q\_{\rm loss\,\mu\text{s}} = \mathbf{s} \cdot \Delta\Lambda t - \mathbf{s} \cdot \Delta\Lambda t\_{\rm min} \tag{10}$$

The parameter s is related to UA (multiplication of overall heat transfer coe fficient and area in heat exchangers), and ΔΔ*t* is relevant to mean temperature of hot water, cooling water, and chilled water.

ΔΔ*t*min is calculated as follows [32]:

$$
\Delta\Delta t\_{\rm min} = 1.9 + 0.1\Delta\Delta t \tag{11}
$$

The COP of absorption subsystems is:

$$\text{COP}\_{\text{dS}} = \frac{\int Q\_{\text{c,as,i}} dt}{\int Q\_{\text{g,i}} dt} \tag{12}$$

The o ff-design model of compressions is based on the lumped parameter method. As a result, the thermodynamic characteristic of its component is controlled by mass and energy conservation:

$$
\sum m\_{\bar{i}} = \sum m\_{o} \tag{13}
$$

$$\mathcal{Q} = \sum m\_i \mathbf{l}\_i - \sum m\_o \mathbf{l}\_o = m \mathbf{c}\_p \Delta T = \mathbf{h} \cdot \mathbf{A} \cdot \text{LMTD} \tag{14}$$

The compressor work consumed by the SASCHCS is calculated by:

$$\mathcal{W} = m\_{\rm Cs} (h\_{\rm dis,s} - h\_{\rm succ}) / \eta\_{\rm s} \tag{15}$$

Compared to the reference case (the cooling load is solely met by the compression subsystem), the energy saving of SASCHCS is:

$$E\_{\text{sart}} = \int\_{\Delta t} (\mathcal{W}\_{ref,i} - \mathcal{W}\_i) dt \tag{16}$$

The COP of compression subsystems is:

$$COP\_{cs} = \frac{\int Q\_{c,cs,i}dt}{\int W\_i dt} \tag{17}$$

#### *3.2. Model Validation and Case Study*

The ETC model was verified through the experimental data of Ghoneim [28]. A good agreemen<sup>t</sup> is displayed in Figure 3. The maximal deviation was 5.9%. In addition, the model validation of absorption subsystems and entire systems was implemented in our previous investigation by experiment [30]. As shown in Figure 4, the deviation regarding the model of absorption subsystems was within 10%. Additionally, it was demonstrated that the maximum relative error with respect to the model of entire systems was 3.58%, as shown in Table 1.

**Figure 3.** Validation of evacuated tube collector (ETC) model.

**Figure 4.** Model validation of absorption subsystem.


**Table 1.** Model validation of compression subsystem.

A case study was performed to assess the relationship of hot water setting temperature and the performance of SASCHCS. A typical high-rise office building located in subtropical Guangzhou was considered. Such buildings consist of ten floors, and the total area of the chosen building is 3840 m<sup>2</sup> (area of each floor is 384 m2). As shown in Figure 5, the length and the width of every floor are 24 m and 16 m, respectively. There are ten rooms (seven offices, one meeting room, one rest room, as well as one machine room) on each story. It is noted that the machine room, the lift, and the staircase are excluded for cooling supply. Corresponding parameters of the above-mentioned building are listed in Table 2. The SASCHCS was employed to fulfill the cooling demand of office buildings. Design and operation parameters of SASCHCS are exhibited in Table 3. It is noted that the ETC was placed in the roof, and its installation area was designed to reasonably prevent the interference of each collector. Similar to the reference [33], parameters of absorption and compression subsystems were proportional to its nominal cooling capacity based on the size of our prototypes [8]. The typical monthly solar irradiance, the surrounding temperature, and the average data of annual measurement in our previous study [34] are exhibited in Figures 6 and 7, respectively. The typical monthly data are the mean of monthly measurement data, i.e., the solar irradiance of 8:00 in August is the average of 8:00 data from 1 to 31 August. Consequently, such typical meteorological data can reflect the solar irradiance and the ambient temperature of the entire month more reasonably. The above-mentioned data were recorded by a small wireless weather station model named DAVIS Vantage Pro 2. Furthermore, the data were verified by the meteorological information center and the maximal deviation was less than 10%. As displayed in Figure 8, the cooling load of buildings was calculated by the software DeST [35] (DeST is the building energy consumption analysis software developed by Tsinghua University). It is the free software package that simulates the building environment and HVAC (heating, ventilation and air conditioning) systems. DeST platform is based on more than 10 years of research data by the Institute of Environment and Equipment, Department of Building Science and Technology, Tsinghua University. The model of entire facilities is solved in the MATLAB environment [36] with 1 min time steps. The thermodynamic property of working fluid and refrigerant was obtained by Refprop 9 [37]. In particular, the cooling demand of high-rise buildings exclusively offered by compression subsystems served as the reference case in the calculation of energy saving regarding the SASCHCS.

**Figure 5.** Layout and orientation of building.

**Table 2.** Load simulation assumptions and schedules for the case study.



**Table 3.** Operation parameters of SASCHCS.

**Figure 6.** Solar radiation.

## **4. Results and Discussion**

This section includes two topics: (1) the impact of hot water setting temperature and (2) the optimization of set point temperature in two hot water cycles based on the annual period by the genetic algorithm. It is noteworthy that the analysis of hot water setting temperature was based on the August data. Furthermore, the influence of set point temperature in hot water cycles was analyzed step by step to show the exact relationship between hot water setting temperature and facility performance. Firstly, the quasi-steady variation of hot water temperature and flow rate for two set point temperatures of hot water was analyzed. Secondly, the useful heat of collectors, COP, and cooling output of absorption subsystems for different hot water setting temperatures was illustrated. Thirdly, the monthly energy savings of SASCHCS for different set point temperatures of hot water cycles was elucidated.

#### *4.1. E*ff*ect of Hot Water Setting Temperature*

The variation of hot water temperature and flow rate with two set point temperatures of collector outlet is demonstrated in Figure 9. It is noteworthy that the setting inlet temperature of generator hot water was 70 ◦C. For the case in which the set point temperature of the collector outlet was 75 ◦C, it was observed that the collector flow rate went up gradually and maintained the nominal one from 11:05 to 14:45. Subsequently, the collector flow rate came down gradually and maintained the minimal one owing to the drop of solar irradiance. It was seen that the collector pump stopped at 16:57 because the collector outlet temperature was less than the bottom temperature of the storage tanks. Simultaneously, the collector outlet temperature kept the setting one with a 2 ◦C increase from 9:33 to 16:02. It dropped to 58 ◦C quickly in the end of the operation. Additionally, the generator pump was activated at 11:07, and the flow rate of generator hot water kept the rated one until 15:27. Subsequently, the flow rate of generator hot water went down quickly to the lowest one, and the generator pump was switched off at 16:37 since the hot water temperature of the generator outlet was less than 55 ◦C. Moreover, the hot water temperature of the generator inlet remained at 75 ◦C until 14:35 and reduced to 64 ◦C gradually in the end of the operation. For the case in which the set point temperature of the collector outlet was 105 ◦C, the collector flow rate nearly held the minimal one during the entire period. Besides, the collector outlet temperature attained the set point one in midday. It was found that the duration that the collector outlet temperature maintained the setting one reduced by 57% compared to the case in which the set point temperature of the collector outlet was 75 ◦C. The trend of collector outlet temperature for two setting temperatures overlapped after 16:00. Furthermore, the generator pump was activated 39 min earlier due to the faster improvement of top layer temperature in the storage tank. The sudden fall of generator hot water flow rate at the start of the generator pump was mainly attributed to the insufficient heat of the storage tank. Subsequently, the flow rate of generator hot water gradually approached the rated one at 14:00 and then decreased quickly to the lowest one. Furthermore, the generator inlet temperature almost held the set point one until 15:10. The generator pump was turned off at 16:19, which was 18 min earlier than the case in which the set point temperature of the collector outlet was 75 ◦C.

**Figure 9.** Hot water temperature and flow rate for different *Tc*, *<sup>o</sup>*,*set*.

The variation of hot water temperature and flow rate with two set point temperatures of generator inlet is displayed in Figure 10. It is noteworthy that the setting temperature of the collector outlet was 95 ◦C. It was seen that collector flow rates for two setting temperatures of the generator inlet nearly overlapped except for the midday. The collector flow rate corresponding to 90 ◦C of *Tg*, *i*,*set* became quadratic in this period owing to the strong solar irradiance and generator consumption. The collector outlet temperatures for two set point temperatures of the generator inlet were extremely similar except the duration when the collector outlet temperature kept the setting one for 90 ◦C of *Tg*, *i*,*set* and extended 15 min. The flow rate of generator hot water for 90 ◦C of *Tg*, *i*,*set* came down quickly after the activation of the generator pump. Similarly, its generator inlet temperature just maintained the set point one for 51 min, and the corresponding period was 20% of the one for 70 ◦C of *Tg*, *i*,*set*. In addition, it was shown that the activation and the stop of the generator pump were delayed by 127 min and 46 min, respectively, for the case in which the setting temperature of the generator inlet was 90 ◦C.

**Figure 10.** Hot water temperature and flow rate for different *Tg*, *i*,*set*.

The impact of collector setting temperature with 70 ◦C set temperature of generator hot water is demonstrated in Figure 11. It was shown that trends of monthly useful heat in collectors and cooling capacity of absorption subsystems were similar. Both grew slightly as the set point temperature of the collector rose to 80 ◦C at first. It is known that the improvement of collector setting temperature decreases the collector flow rate so that the consequent drop in collector inlet temperature is favorable compared to the lower heat loss of collectors. Nevertheless, the excessive increase of collector setting temperature seriously deteriorated the performance, i.e., the monthly useful heat of collectors and the cooling capacity of absorption subsystems came down by 9.3% and 11.6%, respectively, if the collector set point temperature went up from 80 ◦C to 105 ◦C. The significant decrease of heat transfer coefficient caused by the excessive drop of collector flow rate led to the above-mentioned phenomenon. In addition, the COP of absorption subsystems with the set point temperature of collectors was quadratic as well. It enhanced by 1.8% when the collector setting temperature grew from 80 ◦C to 105 ◦C, which was led by the increased operation period of absorption subsystems. In general, the enhancement of the absorption subsystem COP was offset by the reduction of collector useful heat so that the excessive improvement of collector set point temperature was adverse for the solar cooling.

**Figure 11.** Impact of setting temperature of collector outlet.

The effect of generator setting temperature with 95 ◦C collector set point temperature is displayed in Figure 12. It was seen that the rise of generator set point temperature decreased the solar heat, i.e., useful heat of the collector went down by 11.8% as the setting temperature of the generators went up by 30 ◦C. This was attributed to the enhanced generator set point temperature increasing the bottom layer temperature of the storage tanks. Thereby, the rise of collector inlet temperature lowered the amount of solar heat. However, the COP of absorption subsystem grew with the enhancement of generator setting temperature except when the set point temperature of the generator exceeded 85 ◦C. It was shown that the COP of the absorption subsystem rose by 10.1% as the generator setting temperature went up from 60 ◦C to 85 ◦C. The above-mentioned phenomenon was attributed to the influence of increased generator hot water temperature surpassing the one of decreased flow rate. Accordingly, there was an optimal setting temperature of the generator that maximized the cooling power of absorption subsystems. It was derived that the optimal generator set point temperature was 75 ◦C when the setting temperature of the collector outlet was 95 ◦C. Additionally, the cooling output of absorption subsystems with 75 ◦C generator setting temperature was 13.6% more than that in the 60 ◦C one. In general, appropriate improvement of generator set point temperature was beneficial for the solar cooling though the amount of solar heat went down slightly.

**Figure 12.** Impact of set point temperature of generator inlet.

The monthly energy savings of SASCHCS for different setting temperatures of the collector outlet are shown in Figure 13. It was noted that the set point temperature of the generator was 70 ◦C. As expected, it was observed that the higher the cooling capacity of absorption subsystems was, the higher the energy saving of hybrid systems became from the August data. It was demonstrated that qualitative trends of energy saving with collector set point temperature based on different monthly data were similar. Furthermore, the energy saving trends were independent from the set point temperature of the collector as the collector setting temperature was higher than 85 ◦C for April, May, and June (months with low and moderate solar irradiance). This was illustrated by the fact that the hot water could not be heated to such excessively high temperatures by the weak solar irradiance, and even its flow rate was reduced to the minimal one. This also implied that the set point temperature of the collector outlet below 85 ◦C was effective for the hot water control from April to June. Moreover, the excessive enhancement of the collector setting temperature lowered the performance of SASCHCS, i.e., the monthly energy savings of May and June only fell by 7.6% and 7.9%, respectively. The above-mentioned effect became notable for the months with strong solar irradiance. For example, the monthly energy savings of July, August, September, and October came down by 15%, 10.7%, 10.1%, and 11%, respectively, if the collector setting temperature grew from 80 ◦C to 105 ◦C.

**Figure 13.** Energy saving for different collector setting temperatures.

The monthly energy savings of SASCHCS for di fferent setting temperatures of the generator inlet are exhibited in Figure 14. It is noteworthy that the collector set point temperature was 95 ◦C. The energy savings with set point temperature of the generator were quadratic in the entire period. In addition, it was found that the optimal setting temperature of generators was around 70–75 ◦C. The e ffect of the generator set point temperature on the performance was stronger for the months with weak and moderate solar irradiance, i.e., the monthly energy savings of April, May, June, July, August, September, and October rose by 123.7%, 38.7%, 38.2%, 25%, 12.3%, 8.8%, and 10.6%, respectively, when the setting temperature of generators went up from 60 ◦C to the optimal one. This was attributed to the rise of absorption subsystem COP by the increased generator hot water temperature dominating the performance of SASCHCS in April to June. In particular, the excessively high setting temperature of the generator deteriorated the solar cooling dramatically in April to June. The reason was that such a relatively high set point temperature of the generator was extremely di fficult to reach by the weak solar irradiance, thus the duration of absorption subsystems went down dramatically.

**Figure 14.** Energy saving for di fferent generator setting temperatures.

.

The optimal collector setting temperature for di fferent set point temperatures of the generator is listed at Table 4. It was shown that the optimal collector setting temperature associated with the certain set point temperature of generators was same regardless of month. Therefore, it can be said that the optimal setting temperature of the collector outlet was independent from the meteorological data. Furthermore, the optimal collector set point temperature strongly relied on the setting temperature of the generator, i.e., it was around 8–10 ◦C above the generator set point temperature. This was explained by the fact that the stratification of storage tanks, the critical factor of solar cooling, was kept by the synchronized growth of collector setting temperature. It should be noted that the amount of useful heat in collectors was subjected to remarkable reduction through the excessive rise of collector set point temperature.


**Table 4.** Optimal *Tc*,*o*,*set* for di fferent *Tg*,*i*,*set*.

#### *4.2. Global Optimization of Setting Temperature in Two Hot Water Cycles*

According to the analysis of Section 4.1, it is known that the appropriate increase of generator setting temperature is favorable for the COP of absorption subsystems. However, the improvement of generator set point temperature depends on the rise of collector setting temperature leading to the decrease of solar heat. Consequently, the global optimization of hot water set point temperature is extremely essential. Moreover, because the optimal setting temperature of hot water was shown to be independent from the meteorological data, the result of global optimization is convenient for the operation. Such optimization was done by the genetic algorithm function in the MATLAB environment. The maximum generation number and the population number were set as 50 and 20, respectively. The ranges of the collector and the generator setting temperature were 70–105 ◦C and 60–90 ◦C, respectively. Additionally, the maximal annual energy savings was employed as the objective function.

The annual performance of SASCHCS in the optimal case is shown in Table 5. It was shown that 71.6 ◦C of the collector setting temperature with 64.5 ◦C of the generator one was optimal for the annual operation of SASCHCS. The corresponding peak energy savings of SASCHCS were 8841.3 kWh/year, which was equivalent to 32.75 kWh/m<sup>2</sup> of a specific one. Additionally, the annual collector e fficiencies, the COP of absorption and compression subsystems, were 0.39, 0.63, and 4.86, respectively, in the optimal case. It was derived that the COP of compression subsystems enhanced by 14.1% due to the solar cooling compared to its nominal COP.

**Table 5.** Annual performance of SASCHCS in the optimal case.

