## 5 Cleaning of the PV System
### Optimal Cleaning Frequency  
In this section, the optimum cleaning frequency of the PV system under study is obtained. The optimum cleaning frequency is the cleaning activity period carried out for the PV system under \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Model**} & **Average** & **Energy** & **Energy** & **Economic** & **Economic** & **Average** \\  & **Efficiency Drop** & **Loss** & **Loss** & **Loss** & **Loss** & **Economic Loss** \\  & **(\%/day)** & **(kWh/m\({}^{2}\))** & **(kWh)** & **(US$/m\({}^{2}\))** & **(US$)** & **(US$/day)** \\ \hline MLR & 0.768 & 10.282 & 504.445 & 3.76 & 184.627 & 1.03 \\ \hline Two hidden layer ANN & 0.607 & 8.140 & 399.342 & 2.98 & 146.159 & 0.82 \\ \hline
**Optimized ANN** & **0.593** & **7.862** & **385.711** & **2.877** & **141.170** & **0.789** \\ \hline
**Optimized ELM** & **0.615** & **8.329** & **408.652** & **3.049** & **149.567** & **0.836** \\ \hline \end{tabular}
\end{table} 
Table 2: Losses and dust effect using all investigated prediction models for the whole study period (\(n=179\) days). Figure 7: Measured and predicted values of the PV daily system conversion efficiency obtained by the prediction models for the whole study period, without the dust effect. which the two opposing effects of cleaning are minimized, the cleaning cost of the PV system panels and the dust loss that decreases the system efficiency for a given cleaning period calculated for the study period using the prediction models. To this end, we consider reasonable and acceptable values of cleaning costs (0.212 US$/kWp) and the electricity tariff (0.366 US$/kWh) in Jordan during the study period [54]. Firstly, the average daily expenses incurred by cleaning is computed for different cleaning periods that span the interval from 1-30 days. If the PV system is cleaned daily, then the average daily cleaning cost is 0.212 US$/kWp, whereas if the PV system is cleaned every 2 days, then the average daily cleaning cost will be 0.212/2 = 0.106 US$/kWp, leading to an inversely proportional relationship between the average daily leaning cost and period of cleaning activity. Secondly, if the PV system is cleaned daily, then the system efficiency decrease due to dust accumulation equals the average efficiency drop calculated in Table 2 using the prediction models, whereas if the PV system is cleaned every 2 days, then the system efficiency decrease equals the average efficiency drop calculated in Table 2 multiplied by 2, leading to a linear relationship between efficiency loss and cleaning periods. This decrease in the system efficiency is, then, converted into energy loss using Equation (1) and economic loss by considering the electricity tariff of 0.366 US$/kWh in Jordan. For clarity purposes, Figure 8 shows the average daily cleaning cost (inversely proportional curve) and losses due to dust accumulation (linear curves) obtained by the four prediction models with respect to the different cleaning periods, from 1 to 30 days. To identify the optimum cleaning frequency from Figure 8, the average daily losses due to cleaning cost (inversely proportional curve) and losses due to dust accumulation (linear curves) obtained by the four prediction models. To identify the optimum cleaning frequency from Figure 8, the average daily losses due to cleaning cost (inversely proportional curve) and losses due to dust accumulation (linear curves) obtained by the four prediction models are combined as depicted in Figure 9. The optimum cleaning frequencies (i.e., the intersections of the inversely proportional linear curves of Figure 8) obtained by the MLR (13 days), two hidden layer ANN (15 days), the proposed optimized single hidden layer ANN (15 days) and ELM (14 days) models are also indicated in Figure 9, with the best optimum cleaning frequency of 14 days provided by the optimized ELM model as the best prediction model among the others (Table 1).