**3. Performance Analysis**

## *3.1. Solar Fraction*

.

.

The SACS performance can be evaluated using solar fraction (solar coverage). This factor demonstrates the solar energy contribution in chilled water production [37]; the following equation enables the calculation of the solar fraction.

$$SF = \frac{\dot{Q}\_s}{\dot{Q}\_S + \dot{Q}\_{aux}}\tag{18}$$

where *Qs* solar gained energy and *Qaux* is energy from the auxiliary heater. *Qs* can be calculated by:

$$
\dot{Q}\_{\text{s}} = \dot{Q}\_{\text{c}} - \sum Q\_{\text{loss}} \tag{19}
$$

where *Qc* is useful collectors' energy and *Qloss* is the system losses energy.

.

.

#### *3.2. Primary Energy Saving*

The primary energy (PE) savings is the saved primary energy, electric, and fossil. These values are mathematically described below, in order to evaluate the primary energy consumption of a solar system and a conventional one:

$$PE\_{\text{surve}} = \Delta PE\_{foss\text{ill}} + \Delta PE\_{\text{electricity}} \tag{20}$$

Δ*PEf ossil* = -*Qheat f ossil*,*re f* − *Qaux*,*total* η*boiler*·*Ccon*, *f ossil* (21)

$$
\Delta PE\_{\rm elc} = \left(\frac{P\_{\rm el,ref,tot} - P\_{\rm el,sc,tot}}{C\_{\rm con,cloc}}\right) \tag{22}
$$

$$Relative\ PE\_{\text{surv}} = \frac{PE\_{\text{surv}}}{PE\_{ref}}\tag{23}$$

$$PE\_{ref} = \frac{Q\_{\text{heatfossill},ref}}{\eta\_{\text{bviler}} \cdot \mathbb{C}\_{con,fossill}} + \frac{P\_{el,ref,tot}}{\mathbb{C}\_{con,clle}} \tag{24}$$

where:

η*boiler* is the efficiency of auxiliary boiler 0.9;

*Qheat f ossil*,*re f* is required heat for both space heating and DHW (Domestic Hot Water) in the conventional system (kWh).

*Qaux*,*total* is the produced energy by auxiliary heater (kWh).

*Ccon*, *f ossil*, *Ccon*,*ele* are the primary energy conversion factors for heat and electricity from fossil fuel, 0.95 kWhheat,fossil/kWhPE and 0.5 kWhelec,fossil/kWhPE.

#### *3.3. Electric E*ffi*ciency of the Total System*

The electric efficiency is the relationship of the total heating and cooling energy generation to the required electricity for this production. The total system electrical efficiency η*ele*,*tot* is given by:

$$\eta\_{\rm elc,tot} = \frac{(Q\_{\rm cold})}{\left(P\_{\rm c} + P\_{\rm c\nu} + P\_{\rm el,chiller} + P\_{\rm el,CT} + P\_{\rm el,PS} + P\_{\rm el,bvir}\right)}\tag{25}$$

where:

*Pc* is the consumed electricity by a pump that feeds the chiller (kWh). *Pcw* is the consumed electricity by cooling water loop pump (kWh). *Pel*,*chiller* is the consumed electricity by the chiller (kWh). *Pel*,*CT*istheelectricaloffancoolingtower(kWh).

 power *Pel*,*PS*istheconsumedelectricitybysolarloopspumps(kWh).

*Pel*,*boiler*is the consumed electricity by boiler (kWh).

#### **4. Results and Discussion**

#### *4.1. House Energy Balance Analysis*

In this section, the thermal energy balance of SACS for the house under study was established through the evaluation of harvested solar energy, the delivered energy from a hot solar tank, the energy from the auxiliary boiler, and the necessary energy to satisfy the load. Table 5 shows the important and vital information efficiency parameters (result of SACS) for the summer season.


**Table 5.** Most relevant data and results for the cooling season operation (kWh).

Figures 6 and 7 show, respectively, the energy contribution of the integrated gas boiler and solar field during the cooling season. The analyses results show that the useful energy of the solar field was 34,730 kWh and the energy delivered by the boiler was 26,025 kWh, indicating that the total season solar fraction (also called solar coverage) to the load was about 58% (see Figure 7). It is clearly seen that the system operating in May had the highest average solar fraction (a value of about 65%) due to the higher value of captured energy and the lower cooling load. Contrarily, the system presenting the lowest average value of solar fraction (45%) operated under October weather conditions. This is because of the lower energy supplied by the storage tank and lower harvested energy by ETC collectors (see Table 5). This outcome reflects the effect of solar irradiation on the energy performance of SACS.

**Figure 6.** Energy contribution of integration gas boiler and solar field.

It is also clear that there is a significant impact on the solar fraction from the weather data each month, particularly, solar irradiation that has a direct influence on the energy generated by the ETC field. It is possible to observe this by referring to Equation (18).

Figure 8 shows the energy contribution of solar irradiation, energy from solar collectors, and solar tank. The average monthly values of incident solar radiation energy on the solar collectors was 178,023 kWh, while the total captured solar energy was 96,073 kWh, and the energy from the solar tank was 34,730 kWh, which implies that the efficiency of ETC collectors during the cooling season was about 54% (see Table 5).

**Figure 7.** Solar coverage during cooling season.

**Energy from Solar Tank [kWh]**

**Figure 8.** Energy contribution of solar field and solar tank.

Table 5 outlines the evaluation of the COP over six months, indicating that the average COP of SACS ranges between 0.39 and 0.52. It was also found that the system, operating in July and August, has the best average COP (a value of 0.51 and 0.52), respectively, due to a large amount of captured energy by ETC and a large cooling load that is led to higher solar coverage. Moreover, the lowest average COP (0.39) was recorded in April. Based on Equation (17), we can conclude that the variation in COP (see Table 5) through the six months is directly reported to the thermal energy at the input and output of the generator, and evaporator of the absorption chiller. The COP strongly depends on the flows of energy in these two parts. In general, the generator is influenced by the solar radiation of each month, while the evaporator is affected by building a cooling load, which depends on the ambient outdoor temperature of each month.

#### *4.2. Primary Energy Analysis*

The target of this analysis is to find the configuration that optimizes the system performance. Sensitivity analysis is presented under a di fferent number of collectors (areas) and solar tank sizing. The number of collectors, and storage size, in the base case is 12 (30 m2) and 50 <sup>L</sup>/m<sup>2</sup> (1500 L), respectively, compared with the base case. The sensitivity analysis includes changing the surface collector area from 25 m<sup>2</sup> to 35 m2; the solar tank volume varied from 1000 l to 2000 l. The results are displayed in Table 6.


**Table 6.** Primary energy performance for various collector areas and solar tank volume.

It is shown that, with a greater collector area, the best results were obtained. A 16.6% increase in collector surface area is followed by an increase in the solar fraction and relative PE saved, 12.6% and 48.3%, respectively. Regarding solar tank volume, it is clearly seen that variation of tank volume does not present a significant influence on solar fraction, electrical e fficiency, and PE relative; a solar tank volume increasing of 33.3% reflects on increasing in a solar fraction of about 2.5%, and PE relative around 10.3%. From the previous results, it can be recommended to use a collector area of 35 m<sup>2</sup> and a storage tank volume of 2000 L in order to achieve better performance than that reached in the base case.
