## 1 Introduction  
During the last decades, the energy demand required to activate the conventional air-conditioning systems has increased due to the growing population. The countries with warm conditions need to use air-conditioning systems to achieve comfortable conditions [1]. In the case of Mexico, this country has four climatic regions: arid, dry tropic, mild weather and humid tropic [2]. In Mexico, 5.2 million air-conditioning units were installed in the Mexican households in 2011 [3]. Thus, conditioned households were calculated to be 19.5% of the total, however, if it is considered the annual growing rate as 7.5% [4], in 2015, the average number of households with air-conditioning devices was determined at 6.9 million. Therefore, the electricity demand estimated for air-conditioning was 11.8 TW/h in 2015, increased 2.9 TW/h with respect at 8.9 TW/h calculated in 2011 [5]. This fact means that we must find an alternative option for mitigating the energy demand. Solar energy is an alternative option because it is the most abundant energy source on earth. Thanks to its favorable geographic location, Mexico can use solar technologies [6]. As a very convenient option. To take advance of solar energy, a wide range of solar collectors can be used, however, one of the more advanced technology is the parabolic trough collector (PTC) [7]. Several authors have reported the performance of several air-conditioning systems driven by solar technologies, such as [PERSON] et al. [8], who reported about the performance of LiBr-H\({}_{2}\)O absorption chiller of 4.7 kW cooling capacity for a traditional and partitioned storage tank. The system was installed at the University of Hong Kong and employed a set of flat-plate collectors covering an area equivalent to 38 m\({}^{2}\) and a storage tank with a volume of 2.73 m\({}^{3}\). The results calculated COP was 0.07 (15% higher than traditional tank mode). [PERSON] et al. [9] evaluated a LiBr-H\({}_{2}\)O absorption air-conditioning unit (35 kW) and 49.9 m\({}^{2}\) flat-plates collectors designed for cooling for a typical Spanish house. The results show the cooling effect was provided by 8.6 h, the maximum cooling capacity was 7.5 kW. The average COP was 0.6 during the period. [PERSON] et al. [10] analyzed an experimental solar absorption cooling system installed at the University Carlos III in Madrid. The system consists of 50 m\({}^{2}\) flat plate solar collectors model Vitosol 100 coupled to a Yazaki absorption machine, it uses LiBr-H\({}_{2}\)O. According to the results, the average cooling capacity was 3 kW during the summer season, the cooling period was 6.5 h, and the COP was 0.7. The collectors' field can supply 56% of cooling demand. [PERSON] and [PERSON] [11] studied the behavior of a solar air-conditioning system in Almeria in the south of Spain. The cooling system consists of a Yazaki absorption chiller with a capacity of 70 kW, which uses LiBr-H\({}_{2}\)O. Single-glazed flat plate collectors with 160 m\({}^{2}\) area were coupled to the absorption machine. The evaluation showed that a generation temperature under 84 \({}^{\circ}\)C, the chilled water achieved is in a range from 10 to 13 \({}^{\circ}\)C and the cooling water temperature was 27-28 \({}^{\circ}\)C, with these conditions, they obtained a cooling capacity at 40 kW and a COP of 0.6. [PERSON] et al. [12] studied an experimental solar absorption cooling system installed in Saint Pierre in Reunion Island. The solar field consists of 36 double-glazed flat plate solar collectors (90 m\({}^{2}\) area) coupled to single-effect absorption chiller that uses LiBr-H\({}_{2}\)O as working fluid with cooling capacity at 30 kW. The maximum electrical coefficient of performance was 1.65. The temperatures for the absorption system are as follows: generator, absorber and evaporator were 90 \({}^{\circ}\)C, 30 \({}^{\circ}\)C and 11 \({}^{\circ}\)C respectively. [PERSON] et al.