# Photovoltaic Cleaning Optimization: A Simplified Theoretical Approach for Air to Water Generator (AWG) System Employment

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Water From Air Supplied by AWG Systems: Highlights and AWG Technology Choice for Panel Washing

- Coolant evaporation in a heat exchanger of a reverse cycle;
- Enhancement of vapour content in the airflow that is obtained with desiccant employment, in particular some type of metal organic framework (MOF), and subsequently air free-cooling due to natural temperature daily variation (L. Gordeeva et al. [29]);
- Thermoelectric coolers (TEC) employment (D. Milani et al. [30]).

^{3}of water for each kW peak of installed power (0.5 dm

^{3}/m

^{2}) [25]. At any rate, the cleaning time optimization method and the system selection and size determination method that are proposed here can be applied to any kind of AWGs.

#### 2.2. Soiling Related Efficiency Reduction Prediction Model Using the DIrt Method

_{soiled}is the solar radiation power reaching the soiled panel (kW); P

_{clean}is the solar radiation power reaching the clean panel (kW); D is the dust attenuation coefficient (absorptivity) due to particle type and size (m

^{2}/g); l is the optical path length (dust thickness, in m); and c is the dust density (g/m

^{3}).

^{2}), and therefore Equation (1) can be written as:

^{2})); and R is the soiling reduction rate coefficient (1/s), which represents natural effects that remove dust from the panel (i.e., gravity, rebound, wind effect, etc.). The actual reduction rate is proportional to such a coefficient and to the dust layer thickness.

_{0}(t) is the energy production (kJ or kWh) of the perfectly clean solar field at time t.

_{0}(t) can be estimated in two ways: (1) it can be set equal to the expected theoretical production, considering clean panels, as noted by N.W. Alnaser et al. [37]; (2) it can be evaluated by means of a control set, composed of one or more panels that are maintained constantly cleaned, as noted by M.M. Fraga et al. [38].

- (i).
- If the measure is carried out in a brief period of time, for example within a month, the term en
_{0}(t) can be, at first approximation, maintained constant and equal to the value measured at the beginning of the test, en_{0}, in cleaned conditions. - (ii).
- If the entire year’s theoretical expected production in cleaned conditions is available, another possible approximation is to set the parameter equal to the average daily expected production. In this last case, en
_{0}(t) is set a constant, i.e., en_{0}.

_{dirty}is the energy measured when panels reach the maximum efficiency degradation due to dirt (when, from experimental measure, the ratio between en(t) and en

_{0}(t) reaches a constant value).

_{1}> t

_{0}, where t

_{0}is the measure starting point. Combining Equation (11) with Equation (8), it comes:

#### 2.3. Cleaning Period Optimization Method

- 1.
- Calculate the water needed for one field cleaning, W [kg], considering the specific water quantity that is required by the intended cleaning method (e.g., cleaning robots or manual brushing require 3.2 kg/kW i.e., 0.5 kg/m
^{2}, as given in [25], assuming the constant density for water ρ = 1000 kg/m^{3}) and the solar field installed power or the solar field panels surface. - 2.
- Gather weather data about the solar field location that describe the entire year on the basis of statistical data; a hourly sampling frequency is recommend, taking into account previous work performed in the AWG field [21].
- 3.
- Determine the behaviour of the AWG machine, on the basis of collected hourly weather data, in terms of the produced water and related energy consumption, taking into account the entire energy cost of each item involved in the water extraction from air, in liquid phase, apart from any sanification/filtration system, as described in [21]. Such a step is mandatory because AWG systems change behaviour depending upon inlet air conditions. In the case of AWGs employed for panel cleaning, it is a reasonable assumption to take into account only those AWG machines that treat external air.
- 4.
- Define solar field electrical losses due to the dirt accumulation as described in Section 2.2 by means of the DIrt function.
- 5.
- Calculate the average energy required by the AWG for water production, i.e., en
_{w}(kJ/kg or kWh/kg), taking into account the data from Step 3. - 6.
- Determine the cleaning operation costs (c.o.c.) and translate them into equivalent energy by means of the electrical energy selling price (e.s.p.) granted to the photovoltaic field, where c.o.c. is the cleaning operation costs (currency), and en
_{eq}is the equivalent electrical energy (kJ or kWh):$$\frac{c.o.c.}{e.s.p.}=e{n}_{eq}$$ - 7.
- Determine Ce, which is the whole energy cost due to cleaning (kJ or kWh), as:$$Ce=e{n}_{w}\cdot W+e{n}_{eq}$$
- 8.
- Define the daily average energy loss due to the combination between the panel soiling and cleaning costs as:$$AEL\left({t}_{c}\right)=\frac{{{\displaystyle \int}}_{0}^{tc}EL\left(t\right)dt+Ce}{{t}_{c}}$$
_{c}) is the daily average energy loss (kJ or kWh), and t_{c}is the cleaning time interval (days). - 9.
- Calculate t
_{1}, the cleaning optimal time interval (days), which minimizes Equation (21). An integration step of one day was chosen in compliance with the proposal given in Equation (22).$$\mathrm{min}\text{}\frac{{{\displaystyle \int}}_{0}^{t1}EL\left(t\right)dt+Ce}{{t}_{1}}$$

_{1}, can be written in the following way:

_{0}is the energy production of the clean panel (kJ or kWh), which is considered to be constant during the calculation period, whose approximation was already discussed.

_{1}that minimizes the whole energy loss:

_{1}is the same for each month of the year. Such a simplification is acceptable not only when the production curve of the AWG during the year is almost flat but also when it is possible to provide the site with water storages, which is currently a very common solution that is already adopted in many cases, for example when the rainfall is collected.

#### 2.4. Method for Selecting the AWG Machine and Determining System Size

_{c}). In order to achieve such a target, the authors propose the following simplified procedure:

- 1.
- Carry out the actions described in Steps 1 and 2 of the cleaning period optimization method (in Section 2.3).
- 2.
- Consider the existing AWGs and choose a possible group of them on the basis of their working range, expressed in temperature and relative humidity of the air, which must be compatible with environmental conditions of the solar field site.
- 3.
- Carry out the actions in Step 3 of the cleaning period optimization method.
- 4.
- Transform machine cost in equivalent energy by means of the electrical energy selling price of the photovoltaic field production, where m.c. is the machine cost (currency); e.s.p. is the electrical energy selling price (currency/kJ or currency/kWh); and en’
_{eq}is the equivalent energy machine cost (kJ or kWh):$$en{\prime}_{eq}=\frac{m.c.}{e.s.p.}$$ - 5.
- On the basis of the expected life of the considered AWGs, determine the entire expected water production, i.e., e.w.p., that each machine can provide during its lifetime.
- 6.
- Divide each machine equivalent energy (en’
_{eq}as calculated at Step 4) by its expected entire production of water during its lifetime (calculated at Step 5), in order to find the additional equivalent energy cost for mass of produced water, where e.w.p. is the machine expected entire water production during its lifetime (kg), en’_{w}is the equivalent energy cost for mass of produced water (kJ/kg or kWh/kg):$$en{\prime}_{w}=\frac{en{\prime}_{eq}}{e.w.p.}$$ - 7.
- Calculate Ce for each considered AWG:$$Ce=W\left(e{n}_{w}+e{{n}^{\prime}}_{w}\right)+e{n}_{eq}$$
- 8.
- Choose the model that gives the lowest Ce value.
- 9.
- Carry out the actions described in Steps 8 and 9 of the cleaning period optimization method.
- 10.
- Determine the yearly water requirements for the optimum cleaning W
_{y}(kg):$${W}_{y}=W\frac{365}{{t}_{1}}$$ - 11.
- Divide the chosen AWG water yearly productions by W
_{y}and determine the number of machines, N_{AWG}, that are required to satisfy the cleaning needs.

## 3. Case Study: Methodology Application

^{3}/kW for the required water and a water density of 1000 kg/m

^{3}, it is possible to calculate the entire water mass required to clean the whole solar field:

## 4. Results

_{w}and thus Ce, in combining Equations (24) and (25) and applying Equation (26). Results are reported in Table 4.

_{0}was considered constant and equal to the average daily production, calculated simply as:

_{1}), remembering that t

_{1}= 25, applying Equation (21) is:

## 5. Discussion and Further Developments

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

Acronyms | |

AWG | Air to water generator |

MOF | Metal organic framework |

TEC | Thermoelectric coolers |

UV | Ultraviolet |

Symbols | |

AEL(t_{c}) | Daily average energy loss (kJ or kWh) |

c | Dust density (g/m^{3)} |

Ce | Energy cost due to cleaning (kJ or kWh) |

c. o. c. | Cleaning operation costs (currency) |

D | Dust attenuation coefficient (absorptivity) due to particle type (m^{2}/g) |

EL(t) | Solar field energy loss due to soiling (kJ or kWh) |

ELR | Energy loss ratio (-)en0 = is the energy production of the clean panel, considered constant during the calculation period (kJ) or (kWh) |

en(t) | Energy production of the solar field at time t (kJ or kWh) |

en_{0}(t) | Energy production of the perfectly clean solar field at time t (kJ or kWh) |

en_{eq} | Equivalent electrical energy (kJ or kWh) |

en’_{eq} | Equivalent energy machine cost (kJ or kWh) |

en’_{w} | equivalent energy cost for mass of produced water (kJ/kg or kWh/kg) |

e.w.p. | Expected entire water production (kg) |

e.s.p. | Electrical energy selling price (currency/kJ or currency/kWh) |

I | Panel inclination form-factor (ratio of dust actually accumulated and not falling apart) |

L | Optical path length (dust thickness, in m) |

m | Dust density per area unit (g/m^{2}) |

m.c. | Machine cost (currency) |

P_{clean} | Solar radiation power reaching the clean panel (kW) |

P_{soiled} | Solar radiation power reaching the soiled panel (kW) |

r | Soiling deposition rating on a perfectly flat (horizontal) surface (g/(s m^{2}) |

t_{c} | Cleaning time interval (days) |

t_{1} | Cleaning optimal time interval (days) |

W | Water needed for one field cleaning (kg) |

W_{y} | Yearly water requirements for the optimum cleaning (kg) |

Greek Letters | |

η | Ratio between soiled panel efficiency and clean Panel efficiency |

ρ | Density (kg/m^{3}) |

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**Figure 1.**Average daily water production of (

**a**) Machine 1 and (

**b**) Machine 2; average specific electricity consumption of (

**c**) Machine 1 and (

**d**) Machine 2. Avg = average.

Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Average daily temperature (°C) | 9.6 | 12.4 | 16.1 | 19.3 | 22.3 | 23.9 | 23.5 | 23.2 | 22.5 | 19.1 | 14.3 | 10.4 |

Average daily humidity (%) | 72 | 69 | 65 | 60 | 64 | 73 | 82 | 84 | 81 | 77 | 75 | 75 |

AWG Machines | Price (EUR) | Expected Lifetime (Years) | Machine Intended for | Working Temperature (°C) and Relative Humidity (%) Ranges |
---|---|---|---|---|

Machine 1 | 22,000 | 20 | Outdoor | From 5 °C and 90% to 50 °C and 30% |

Machine 2 | 6200 | 10 | Outdoor | From 5 °C and 99% to 50 °C and 30% |

AWG Machines | Yearly Expected Production (kg) | Expected Lifetime (Years) | Expected Water Production during Lifetime (kg) | Average Daily Production (kg/day) | Average Electricity Specific Consumption (kWh/kg) |
---|---|---|---|---|---|

Machine 1 | 48,115 | 20 | 962,308 | 131.8 | 0.351 |

Machine 2 | 24,195 | 10 | 241,948 | 66.3 | 0.431 |

AWG Machines | en’_{w} | Ce |
---|---|---|

Machine 1 | $\frac{22,000\text{}\mathrm{EUR}}{0.07\frac{\mathrm{EUR}}{\mathrm{kWh}}\cdot 962,308\text{}\mathrm{kg}}=0.327\text{}\mathrm{kWh}/\mathrm{kg}$ | $\left(0.351+0.327\right)\frac{\mathrm{kWh}}{\mathrm{kg}}\cdot 3200\text{}\mathrm{kg}=2170\text{}\mathrm{kWh}\text{}$ |

Machine 2 | $\frac{6200\text{}\mathrm{EUR}}{0.07\frac{\mathrm{EUR}}{\mathrm{kWh}}\cdot 241,948\text{}\mathrm{kg}}=0.366\text{}\mathrm{kWh}/\mathrm{kg}$ | $\left(0.431+0.366\right)\frac{\mathrm{kWh}}{\mathrm{kg}}\cdot 3200\text{}\mathrm{kg}=2550\text{}\mathrm{kWh}$ |

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**MDPI and ACS Style**

Cattani, L.; Cattani, P.; Magrini, A.
Photovoltaic Cleaning Optimization: A Simplified Theoretical Approach for Air to Water Generator (AWG) System Employment. *Energies* **2021**, *14*, 4271.
https://doi.org/10.3390/en14144271

**AMA Style**

Cattani L, Cattani P, Magrini A.
Photovoltaic Cleaning Optimization: A Simplified Theoretical Approach for Air to Water Generator (AWG) System Employment. *Energies*. 2021; 14(14):4271.
https://doi.org/10.3390/en14144271

**Chicago/Turabian Style**

Cattani, Lucia, Paolo Cattani, and Anna Magrini.
2021. "Photovoltaic Cleaning Optimization: A Simplified Theoretical Approach for Air to Water Generator (AWG) System Employment" *Energies* 14, no. 14: 4271.
https://doi.org/10.3390/en14144271