## 1 Introduction
Moreover, it was shown that when particle sizes of 150-300 mm are dominant, the deviation in the optimal tilt angle is 8\({}^{\circ}\) from the clean module angle. Artificial soiling experiments to investigate the relationship between irradiance, tilt angle and power output with soil particle deposition were conducted by [PERSON] et al. [PERSON] et al. (2018): they introduced a correction factor as a function of the particle size in the regression model, and by doing so, a much better efficiency prediction is achieved. The effects of local environmental conditions in Surabaya, Indonesia on the reduction in PV power output were investigated by [PERSON] et al. (2018); their results illustrate that the dust accumulation after two weeks' exposure in a dry season resulted in a 10.8% reduction in PV output power. Additionally, it was shown in the work presented in [PERSON] et al. (2018) that out of more than 17 pollutants, six had a significant effect on PV performance. A mathematical formulation for the optimum cleaning interval depending on the dust accumulation and the cost of cleaning operation in central Saudi Arabia was presented in [PERSON] et al. (2018): they concluded that the highest loss rates occur in the spring season due to the dust storms. The authors emphasize that this conclusion is exclusive for this site and corrections to the model should be taken into consideration for other geographical and climatic conditions. An experimental study in Chang'an District, Xi'an, China, to investigate the impact of dust deposition on the module temperature, transmittance and output power of the PV module was carried out by [PERSON] et al. (2018). They derived a linear model to predict the output power as a function of the deposition density, and they showed that as the deposition density increases, the relative transmittance and output power drop compared to clean modules. Also, an experimental study to investigate the effect of normal dust, clay and ash on PV performance is illustrated in [PERSON] et al. (2018): they showed that the maximum power loss was 36.7% at 258 W/m\({}^{2}\) and was mainly because of the carbonaceous ash and clay. To solve the problem of dust accumulation and reduction in the output power generated from the PV modules, cleaning is a key feature from an economic as well as performance standpoint [PERSON] et al. (2018). Consequently, a weekly or bi-weekly cleaning cycle for PV systems installed in the MENA region is recommended [PERSON] et al. (2018). Many experiments that tackle the effect of the cleaning cycle on the PV performance have been conducted in the last few decades. For instance, an experiment in the west of Saudi Arabia was conducted, where the performances of different modules were monitored, as well as two sand abrasion methods investigated, based on the transmittance and reflectance of PV modules [PERSON] et al. (2018). It was concluded that significant dust deposition and lack of rainfall led to a loss in the daily average performance. Moreover, much higher losses were recorded during dust storms. Another experiment was conducted in Egypt in Egypt in (2018) to investigate the effect of daily cleaning for 45 consecutive days on the performance of the PV system. It was shown that a non-pressurized water system will not clean the panels properly, while pressurized water will but with a penalty of an increase in the running cost. In another experimental study in Egypt [20], it was demonstrated that dust has an important effect on the short-circuit current and less effect on the open-circuit voltage. Moreover, it was recommended to clean the panels once every four days. A comparison between nano-coated self-cleaning panels to untreated panels was executed experimentally in Algeria [37]. It was shown that nano-coated panels have better performance with a lower cleaning cost compared to conventional methods. In their work, [PERSON] et al.