Integration of Soiling-Rate Measurements and Cleaning Strategies in Yield Analysis of Parabolic Trough Plants

where Δt is the time difference between measurements. SR is typically a negative value and its absolute value is bigger when soiling occurs faster or soiling load is higher. Positive SR is found due to natural cleaning events such as strong rainfall. Long-term SR measurements for various sites have been reported [2,4–8]. They show high intra-annual variation of SR, which is mostly not bound to seasons. There is a strong dependence on the site of measurement and the conditions of exposure such as inclination angle and orientation of samples [9]. Similar conclusions have been found for photovoltaic modules or cells [10–12].

There exist only few studies investigating the impact of SR and cleaning action on the financial yield of CSP plants. Reference [13] assumes a constant yearly SR in order to determine an optimal target cleanliness value that shall not be underrun during operation. The cost for one complete solar field cleaning in Ref. [12] is taken from Ref. [14] and the solar field size is one of the adjusted variables. They conclude that the optimal results with this cleaning strategy are obtained with a target cleanliness of 0.97–0.98 and a solar field 3–4% larger if cleanliness is assumed as 1.

References [1] and [15] determine an optimal cleaning frequency with only a few assumptions regarding cleaning costs (CC) and financial loss due to reduced reflectance. They use different constant SR to show that the resulting cleaning frequency is highly dependent on SR. They conclude that a constant monitoring of the average solar field cleanliness (ξ_field) is necessary for the best operation of a CSP plant [1].

All the above studies do not take into account the temporal variation of the SR and the cleaning frequency. This causes errors because, e.g., high direct normal irradiance (DNI) days might actually coincide with below average ξ_field. On a day with high DNI, a low cleanliness can reduce power plant output more (in absolute values) than on a cloudy day. The mentioned studies do not simulate plant yield in full detail but assume a linear correlation of plant output and cleanliness. This might cause further errors, for example if overload dumping plays a role. Overload dumping is necessary if the heat that could be provided by the solar field is higher than the heat that can be used by the power block and the storage together. In this case, collectors are defocused. In summer, overload dumping might mean that the same plant yield is obtained for a certain day regardless if cleaning has taken place or not.

To overcome these sources of errors, temporally variable SR and cleaning frequency are used combined with more detailed plant modeling software. The technical and financial output parameters of a CSP project over its lifetime can be calculated using yield analysis software such as greenius [16–18] or the system advisor model (SAM) [19]. Their calculations are based on a time-resolved meteorological dataset, the technical plant layout, and financial input parameters. The above-mentioned software products only offer the possibility to enter a constant yearly cleanliness value for the solar field to quantify soiling-induced losses. CCs are assumed as constant values per unit mirror area.

In the framework of this work, greenius was enhanced with an external software module that allows the treatment of time-resolved SR and cleaning including the corresponding collector outages and cleaning costs. We use this enhanced software to analyze cleaning decisions and its financial consequences in more depth for two parabolic trough plant configurations at two different sites. The following steps outline our approach:

1. (1)

   Apply a one-year SR dataset in daily resolution measured with the tracking cleanliness sensor (TraCS) [9,20,21] at Plataforma Solar de Almería (PSA) in the Tabernas desert in Spain.

2. (2)

   Model the cleanliness of each collector and thus ξ_field(t) using the cleaning action of each cleaning unit (CU).

3. (3)

   ξ_field(t) is used to modify the DNI dataset used as an input to greenius.

4. (4)

   Use realistic cleaning related cost parameters and calculate CC for each service hour and CU.

5. (5)

   Analyze the effects of different cleaning strategies (CS) and cleaning unit availability on plant yield output.

In the second section of this paper, we describe the input parameters for the modeling with a focus on the TraCS cleanliness measurements. Also, the financial and technical parameters used as inputs to greenius and CC calculation are presented. Section 3 describes the CSs and methodology to calculate CC and ξ_field. Section 4 summarizes results; in Sec. 5 a sensitivity analysis is presented, and Sec. 6 contains conclusion.

The yield analysis software greenius requires a meteorological dataset for one year. The first site that is investigated here is PSA in Spain (ES) located at 2.35 deg West, 37.1 deg North and 500 m above mean sea level. The second site is Missour, Morocco (MOR) located at 4.1 deg West, 32.9 deg North and 1107 m above mean sea level where a measurement station is run by IRESEN in cooperation with DLR [22]. The meteorological parameters applied in this study are DNI (direct normal irradiance) measured with pyrheliometers, global and diffuse horizontal irradiance measured with pyranometers, ambient air temperature, relative humidity, atmospheric pressure, wind speed and wind direction. These parameters are saved in 1-min resolution and averaged to hourly resolution. The same time interval from first of May 2013 until the Apr. 30, 2014 was evaluated for both sites. The data were quality checked on a daily basis following Refs. [23] and [24]. The DNI yearly sums for the sites used in the simulations are 2388 kWh/m²/a in ES and 2307 kWh/m²/a in MOR.

Reflectance and SR measurements with handheld devices are time-consuming and the time difference Δt in Eq. (2) between two subsequent measurements is usually in the order of days or weeks. This means that the resulting SR represents only a mean value in the measurement interval and is therefore not suitable for a daily modeling of soiling and cleaning in a solar field. In this study, we employ the TraCS. It is an automatic device that measures cleanliness in 10-min resolution by comparing the directly measured DNI to the DNI reflected by a sample mirror mounted on a solar tracker. The effective acceptance half-angle is 13.6 mrad and similar to a CSP collector [20,21]. The measurement area on the sample mirror is approximately 30 cm² in size. The SR is derived in daily resolution. The one-year SR dataset has been measured with TraCS at PSA. The sample mirror has been cleaned approximately every 2 weeks. In the measurement period, the cleanliness of the sample mirror never dropped below 0.82. The SR dataset is shown in Fig. 1. The average SR is −0.0052/d with a standard deviation of $±$$0.0095/d$ and the highest SR is $−0.089/d$⁠. Positive SR values are due to rain cleaning of the sample mirror and are also considered in the cleaning simulations. SR varies significantly throughout a year. The assumption of a constant SR made in previous studies therefore seems unrealistic.

Two different layouts of parabolic trough power plants are used in this analysis. Their specifications are shown in Table 1. The two layouts are chosen following the power plants “Ibersol Puertollano” (IP) and Andasol I (AS) [25]. They both dispose of a turbine with a nominal electrical output of 49.9 MW_el. AS has a thermal storage capacity of 940 MWh_th, or 7.5 h full load turbine operation while IP has no storage.

The solar fields were scaled linearly such that the product of DNI yearly sums and number of loops is approximately equal for the original (template) and target sites of ES and MOR. The power plants are operated following the strategy “solar only.” This strategy prioritizes the full load operation of the turbine: As long as there is not enough thermal output from the solar field, the missing thermal energy is taken from the storage. If there is more thermal output from the solar field, the excess heat is transferred to the storage in the case of available storage capacity in AS. If storage is fully loaded or absent, the excess heat needs to be discarded (overload dumping). Keeping the storage medium above freezing temperature has priority over electricity generation.

Financial parameters are required by greenius to calculate the financial output of CSP projects and to quantify CC for each CS. The site-specific financial parameters for ES and MOR are listed in Table 2. The parameter “Specific operation costs” does not include CC.

The inflation was set to zero in the greenius calculations. This is an approximation that is assumed to be compensated by the fact that also no cleaning efficiency increase is considered. Such an increase is very likely especially because new and improved vehicles will be bought after the assumed lifetime of the first vehicles of 15 years. It is assumed that this effect counterbalances inflation.

The parameters used as a basis for the CC calculations are shown in Tables 3 and 4. The cleaning unit (CU) specification in Table 3 is used to determine the consumption of fuel, water, and personnel. The parameters cleaning speed and cleanliness after cleaning (ξ₀) have been determined in a field test described in Ref. [34]. ξ₀ is not equal to 1 because cleaning is not perfect in general. It also includes the influence of mirror sections that cannot be reached by the CU. These are left dirty and account for roughly 4% of the mirror surface. The cleaning speed includes the time needed to rank at the collector edges, to refill the water and fuel tank, and to reach the garage and refill stations.

The cost parameters in Table 4 are used to convert the technical parameters to financial values. The yearly salary per person refers to gross costs for the industrial sector. Only those hours spent with cleaning are included in CC calculations. This means that the worker takes on additional tasks in operation and maintenance of the solar field. The wage for short-term workers that can be hired to clean the mirrors manually without the cleaning vehicle is assumed as 150% of the obligatory minimum wage. The depreciation cost of the CU has been calculated as an annuity loan over its assumed lifetime using the countries' interest rates. Annuity loan is characterized by constant down-payments during the amortization period, similar to a leasing model.

This section describes the method to trace the CU movement throughout the year following several sets of rules called CS and the procedure to calculate the resulting CC and daily ξ_field.

We define two different types of CS: two different threshold-based CSs, where the cleaning intensity is adapted to the current ξ_field and constant CSs where cleaning occurs at a fixed frequency. The motivation for the threshold-based CSs is to reduce CC whenever ξ_field is sufficiently high.

A summary of the CSs is given in Table 5. The following assumptions apply:

1. (1)

   One cleaning shift (day or night) lasts 8 h.

2. (2)

   Cleaning during the day implicates defocusing of the currently cleaned loops resulting in lower solar field availability

3. (3)

   If more than one CU is used, each pair of two CUs cleans the same loop simultaneously to maximize availability.

4. (4)

   The labor for measuring ξ_field is not accounted for in CC calculation. This is part of the specific operation costs in greenius.

5. (5)

   In the strategies “Threshold” and “Assisted,” either all or none of the CUs take up cleaning if ξ_field is below the threshold ξ_lim. If ξ_field falls below ξ_lim,as < ξ_lim, additional four cleaning teams of short-term workers for manual cleaning are hired in the CS Assisted.

Each cleaning team consists of four additional workers that use manual wipers to clean the mirrors. The investment cost for the additional cleaning teams' gear is neglected. The cleaning speed of each additional team is half the speed of a CU consuming half the amount of water per loop as a CU and negligible amounts of fuel. The external workers are employed in two daily shifts until ξ_field> ξ_lim− 0.01.

The following parameters are varied within the limits given below:

1. (1)

   Number of available CUs in the solar field (N_CU) from 1 to 6.

2. (2)

   ξ_lim for the strategies Threshold and assisted from 0.96 to 0.99.

3. (3)

   Power plant type IP/AS.

4. (4)

   Location ES/MOR.

For each combination of parameters, a simulation run for one-year power plant operation is performed. To keep the results manageable, only ξ_{lim, as} = 0.9 is used for the second threshold in the CS Assisted in this study. This choice follows the recommendation to keep ξ_field constantly above this value [4]. Also, we only model a fixed number of four external cleaning teams that assist the CUs of the power plant in case that ξ_field < ξ_{lim, as}.

$KL$ is the yearly cost of a solar field worker according to Table 4. The conversion from person-year to costs per hour is obtained assuming 250 work days of 8 h in a person-year.

where $td$ represents the day of the year, d is the time unit day, and $ξi$ refers to the cleanliness of loop number i. Each CU takes up cleaning at the beginning of one shift where it stopped at the end of the last shift. This way, the loops that have been exposed longest to soiling are cleaned first. The loops of the solar field are cleaned in the same order. Once a CU has reached the end of the field, it starts from the first loop again. External cleaning teams follow the same order. They are distributed in a way that the number of loops separating the cleaning vehicles and teams is as homogeneous as possible.

where t represents time in hourly resolution and $td$ the day of the year. This equation applies to all days $td$ of a year.

The hourly one-year modified DNI time series (⁠$DNImod)$ is then passed as an input to greenius instead of the original DNI measurement data. A reduction of DNI is assumed to have the same effect on solar field thermal output as a reduction of mirror cleanliness. The parameter $ξfield$ in greenius is not used, i.e., it is set to 1 in all our simulation runs.

This study focuses on comparing different CSs among each other. Therefore, a reference CS is chosen as “Constant dn” using one CU during one daily and one nightly shift. The financial performance of any candidate CS is compared to the performance of this reference CS.

Some of the financial output parameters for the reference strategy (Constant dn, with one CU) and the strategy “Threshold n” with three CUs are given in Fig. 2 for AS in ES. The difference in the total revenues and profit of the project show small relative differences. The higher cleaning intensity in Threshold n increases the CC by a factor of 2 and $ξfield$ by 1%. Water costs are displayed on a scale of factor 100 smaller than the other parameters that contribute to CC.

The CC account for 6.6% of the running costs and 12.5% of the operation and maintenance (O&M) costs (both including CC) in the example CS (Threshold n). Approximately, half as high values are found for the reference CS. The CC corresponds to 1–3% on the annual profits of the project. The 1.3% increase to 3262 turbine full load hours causes an increase of 0.18% of O & M costs. The example CS results in an RPI of 0.76% and an API of 122 kEUR/a with D_y being 16.1 MEUR/a. The power plant produces 1.7 GWh_el/a or 1.2% more electrical energy if the example CS is applied in comparison to the reference CS. Total revenues differ by the same percentage or 463,000 EUR/a. The project amortizes economically 2.3 months earlier. The LCOE (levelized costs of electricity) is 0.1806 EUR/kWh_el for the reference CS and 0.1790 EUR/kWh_el for the example CS. CC have not been accounted for in the LCOE.

The RPI is calculated for the four combinations of countries (ES and MOR) and power plant layouts (AS and IP). The RPIs are plotted in Fig. 3 against N_CU for both modes n and dn. In Figure 3 left, results for AS are shown and results for IP are shown on the right. The maximum RPI of 1.35% is reached for AS in MOR with N_CU = 2 and mode dn. This CS results in an API of 141 kEUR/a. The occurrence of the maximum for AS, MOR, and this CS can be explained by the fact that the availability of the solar field is the same as in the reference CS because of the pairing of even numbers of CUs. Cleaning intensity, i.e., the number of loops being cleaned per day, is doubled at the same time with only one more CU in service. Larger steps occur when going from even to uneven N_CU. This effect is attributed to the unsteady decrease of the availability S that is not present when going from uneven to even N_CU because of pairwise cleaning with two CUs of one loop. In comparison to the mode n with three CUs, S is smaller but one CU more has to be financed, resulting in higher CC. The difference to the maximum RPI in MOR and cleaning mode n is relatively small: RPI is 1.26% with 3 CUs compared to 1.35% for the maximum for MOR found with Constant n.

For ES, the maximum RPI is 0.53% and API is 84.3 kEUR/a deploying 3 CUs that operate in nightly shifts. D_y in this case is 16.1 MEUR/a. The CS Constant tn peaks at an RPI of 0.12% or an API of 18.5 kEUR/a when employing two CUs.

In the power plant IP (Fig. 3, right), the following observations are made: The maximum RPI occurs for both countries for the cleaning mode n with two CUs. The maximum RPI is 0.91% in ES and 0.82% in MOR. The cleaning intensity for this CS is the same as in the reference CS (Constant dn, 1 CU). The positive RPI is caused by the higher availability S that overcompensates for the higher CU depreciation cost.

The cleaning mode tn does not result in a positive RPI in IP. The reference CS with one CU is the best configuration for this cleaning mode. For greater N_CU, the RPI in IP decreases faster than in the left graph (AS). This behavior can be explained by the smaller solar field in IP where S assumes lower values for same N_CU than in AS.

Labor costs for night shifts are assumed to be the same as for day shifts in this study. An increase of 25% on costs for night labor as is recommended for Germany [42] would still lead to the finding that the highest RPI are reached with nightly cleaning. As there is no reliable information available on the implementation of such an increased night shift salary for countries like Morocco, the comparability of the two sites would be compromised and therefore an increased night salary is omitted.

In summary, nightly cleaning is more profitable than cleaning in day and night shifts. The profit of a project can be increased by up to 1.35% if the optimum number of CUs and constant nightly cleaning is selected.

The defocusing of a part of the solar field when thermal output exceeds the capabilities of the power block and the storage is called dumping. A higher ξ_field increases the optical efficiency and thus the thermal energy produced in the solar field which in turn increases dumping.

The thermal energy that is not collected due to dumping is called Q_dump. In Fig. 4, the ratio of Q_dump and the total thermal energy if no dumping would be required (Q_tot) is plotted against N_CU for the CS Constant in all countries and power plants. With increasing N_CU, ξ_field increases. Therefore, Q_dump also increases steadily for the cleaning mode n because the threshold for dumping of the thermal solar field output is reached more frequently than with a lower ξ_field. Because Q_tot also depends on ξ_field, this increase is not linear. Q_dump/Q_tot behaves differently in the cleaning mode tn due to the properties of the solar field availability S that can also be seen in Fig. 3.

The effect of cleaning on Q_dump/Q_tot raises the question if it could be incorporated into cleaning decision-making. In theory, it would be better to omit cleaning some days before a period with excess solar insolation in order to save running cleaning costs. From a practical point of view, this would require a reliable forecast of the irradiance and the soiling rate for the next days, because ξ_field cannot be altered instantaneously, i.e., it takes several days to clean a solar field completely. While DNI forecasts are available, the soiling rate is currently not forecasted. Persistence forecast could be applied in combination with rain and dust storm forecasts, but this is not considered in this study.

The CS Threshold is similar to the CS Constant with the difference that if ξ_field is greater than a threshold value ξ_lim, the CUs stop cleaning in order to reduce CC. In the following, N_CU and ξ_field are varied. Only nightly cleaning is considered, because it showed better performance in the constant cleaning strategies.

The resulting RPIs are displayed in a color-coded 2D plot shown in Fig. 5. The location of the maximum RPI is marked by an “X” with the value displayed next to it.

The RPIs shown in the uppermost row of each graph correspond to the RPIs shown in Fig. 3 for CS Constant n and same combinations of power plant, country, and N_CU. The reason is that ξ_lim is greater than the cleanliness after cleaning ξ₀ = 0.986 there. This causes the CUs to clean the solar field every night. If an RPI at ξ_lim< ξ₀ is greater than the RPI in the uppermost row, the application of CS Threshold can increase the profit of the project for same N_CU.

In power plant AS in MOR, the highest RPI of 1.36% is found for ξ_lim = 0.99. Hence, no increase of RPI is achieved by application of the CS Threshold in comparison to CS Constant. For IP in MOR, the maximum RPI can be increased by 0.16% to 0.98% for N_CU = 2. Here and in the following, the percentage values used for comparing RPIs are to be understood as absolute increases. In IP in ES, the CS Threshold leads to an increase in maximum RPI of 0.36% to 1.27%. Generally, the difference between the CSs Threshold and Constant are greater for the power plant IP due to the higher effect of CC on net profit.

In ES, the possible CC reduction due to the application of CS Threshold is higher compared to MOR, because of higher personnel rates and material costs. The increase of maximum RPI with CS Threshold is 0.23% compared to CS Constant in ES. The running cleaning costs are more than 65 kEUR/a or 16% lower compared to CS Constant.

The gradient of the RPI in the proximity of the maximum RPI is smaller in AS compared to IP. One of the reasons is the higher N_CU at the peak RPI in AS: A difference of one vehicle causes less relative difference in CC and cleaning intensity. In MOR, the gradients are higher than in ES due to the higher ratio CC/D_y. This implies that a change in CC has more effect on the projects' net profit. The same changes in CC thus have more effect on RPI in MOR than on the RPI in ES.

It can be concluded that the application of the CS Threshold can increase the RPI by up to 0.36% relative to the CS Constant. It is therefore attractive for power plant operators to monitor ξ_field and base their cleaning decisions upon it.

The resulting maximum RPIs for the CS Assisted and the soiling rate time series used so far are identical to those for CS Threshold. Therefore, the RPIs are not shown here for the application of the CS Assisted. The reason is that ξ_field never falls below the second threshold value $ξlimas=0.9$ at the points where the maximum RPI is reached. In this case, no external personnel are hired resulting in the same cleaning action for both CS. For combinations of $ξlim$and N_CU for which RPIs below the maximum RPI are reached, the external personnel play a role. The effect of the CS Assisted is found in the significantly lower gradients when moving away from the point of maximum RPI in direction of N_CU and/or ξ_lim. Thus, the CS Assisted is more robust to wrong cleaning decisions even if no increase of the maximum RPI is achieved.

In order to investigate the effects of different CSs at a site subjected to more severe soiling conditions, the SR dataset measured at PSA is altered by the introduction of five heavy soiling events as could be caused by sand storms or aerosol wet deposition events. The SR values and days are created randomly to −0.21, −0.10, −0.15, −0.11, and −0.22 per day for the days of the year 31, 49, 158, 166, and 302.

The results of the simulation runs for the CS Threshold and Assisted for this altered soiling rate time series are shown for the power plant AS in Fig. 6. The maximum RPIs roughly double for both CS compared to the results for the original soiling rate data set. The maximum RPIs for CS Threshold are achieved with one more CU compared to the original SR dataset. This can be explained by the fact that the higher SRs cause lower power output for the cleaning intensity applied in the reference CS. Employing more CUs can compensate better for the soiling induced losses.

In all cases, the here applied CSs perform better than the CS Constant. The CS Assisted reaches very similar maximum RPIs with the difference that one CU less is employed. Due to the labor costs, CS Assisted reaches slightly lower RPIs in ES than in MOR. The gradients of RPI are less pronounced in the CS Assisted qualifying this strategy are more robust against an imperfect choice of N_CU or ξ_lim. The CS Assisted can also help to avoid losses in years when untypically high soiling rates occur, for which the number of CUs present in the power plant are not sufficient. For example, if a lower number of three CUs and a ξ_lim of 0.987 are applied in AS in MOR, an RPI of 1.87% is achieved with CS Threshold compared to a RPI of 2.10% with the CS Assisted. Similar differences are found for most other points in the graphs.

In the following, it is investigated how accurate simulations with the assumption of constant soiling rates or even cleanliness are. Such approximations simplify the modeling. Furthermore, it must be considered that soiling rate time series are currently not available for most sites and the estimation of an average soiling rate is easier to obtain than time series.

In the following, the CS Threshold is applied to a scenario of a constant SR equal to the mean value of the PSA data set of −0.0052 per day. The reference CS yield was also calculated for this constant SR. Figure 7 shows that the maximum RPI is 0.21% smaller for this scenario compared to the original SR dataset (see Fig. 5). The CS Threshold cannot increase profits in comparison to SR Constant for this scenario.

If the SR of a site is approximated by one constant value for all days of the year, the best number of CUs and cleaning mode can be determined sufficiently for the CS Constant in this case. A potentially higher RPI for fluctuating SR and advanced CSs cannot be detected. For the best planning of cleaning action and the best estimation of financial project outputs, time-resolved SR measurements are therefore recommended.

In many existing studies, a constant ξ_field of 0.95 is assumed [43–46]. The average value of ξ_field resulting from the application of the reference CS to the original SR dataset is 0.965 with a standard deviation of 0.013. The reference CS (calculated with the original SR dataset) achieves a profit that is 2.2% higher than the one achieved with ξ_field = 0.95 even if CC are set to 0 for the constant cleanliness scenario. If the CC for the case of a constant ξ_field is set to the same value as resulting from the reference CS, the difference in profits is 9.4%. The assumption of a constant ξ_field can thus cause significant errors.

If the average cleanliness for the reference CS and the soiling time series (0.965) is set as the constant ξ_field and the same CC as in the reference CS are used, the constant scenario results in a profit that is 0.58% higher than the one obtained with the original SR and reference CS. This difference is caused by the variation of ξ_field, the solar position-dependent plant efficiency and DNI variation in the course of the year. Therefore, different ξ_field values are weighted differently by the plant efficiency and DNI occurring at different days. This means that in the reference case, ξ_field on average was lower on days with higher used DNI. Thus, if a constant ξ_field is applied and is estimated in the best possible way for yield analysis, the remaining uncertainty will be in the range of 0.58%.

The influence of the input parameters on the RPI is investigated in the following. The parameters from Table 4 as well as the lifetime of the CUs, the feed-in tariff, and the mean SR are varied while keeping the rest of the inputs at their original values. The effects on the RPI obtained with the SR Threshold with N_CU = 3 and ξ_lim = 0.977 in AS in ES are shown in Fig. 8. The average of the SR dataset is the most influential of the parameters if varied from 50% to 150% of their initial values. The SR was varied by simple multiplication of each daily value with a constant factor.

The feed-in tariff has the greatest influence on the RPI among the financial input parameters followed by the prices applied in the calculation of CC. The influence of the latter roughly corresponds to their share in the CC. The results of this study are found to be quite robust against small changes of the input parameters.

Cleaning action in a solar field has a significant effect on the profits of a CSP project over its lifetime. Cleaning costs (CC) correspond to 1–3% of the profits, which in turn highly depend on the efficiency of the solar field. Constant cleaning strategies (CS) can increase profits by up to 1.35% relative to a reference cleaning strategy where one cleaning unit (CU) cleans the solar field in one night and one day shift (dn). Nightly cleaning (n) achieves better results in most cases than day and night cleaning. The resulting higher investment costs for more CUs in n are overcompensated by the higher availability of the solar field. The CS Threshold reduces CC when solar field cleanliness (ξ_field) is sufficiently high. It can increase the RPI by 0.36% relative to the CS Constant, although in some cases, the benefit is negligible. The CS Assisted does not result in higher maximum RPIs compared to the CS Threshold for the soiling rates measured at PSA, but it is advantageous in cases with occasional high SRs for which not enough CUs are present. The latter can be shown in a scenario where five artificial intense soiling events are introduced to the SR dataset resulting in higher RPIs for CS Assisted compared to CS Threshold.

Power plants with storage tend to tolerate wrong cleaning decisions better than those without storage. In Morocco, where labor costs are low, a higher cleaning frequency pays off better than in Spain despite the higher Spanish feed-in tariff. Constant, daily cleaning strategies result in higher profit in Morocco as compared to Spain.

If a constant SR or constant ξ_field is assumed, significant errors were found by comparison to the time-resolved simulations of this work. If the constant SR is set to the mean of the reference SR-dataset, the potential increase of 0.22% on profits for the CS Threshold is not detected. If ξ_field is set to the mean ξ_field obtained with the reference CS, the profits differ by 0.58% from that with a time-resolved ξ_field. This represents the accuracy increase achieved with the time-resolved simulation of cleaning and soiling for the investigated case. Therefore, the here presented method increases the accuracy of yield analysis studies.

The CSs, cost parameters, and power plant layouts investigated in this study are to be understood as examples. The presented method allows for the simulation of more elaborate or custom CSs that can be investigated in future publications and that can serve as a basis for optimizing the cleaning strategies in commercial power plants.

• European Union's Horizon 2020 research and innovation program (Grant No. 654479) (WASCOP).

• Helmholtz Gemeinschaft and NREL Solar Energy Initiative (HNSEI) (SO 075).

a =

year

d =

day

dn =

cleaning action performed in one daily and one nightly shift

D_y =

mean annual net dividends

D_y,ref =

mean annual net dividends for the reference cleaning strategy

$Dwocl$ =

dividends without considering cleaning costs

IP =

power plant layout following the template “Ibersol Puertollano” plant

K_CU =

cost for one cleaning unit

K_L =

salary for one person year of solar field labor

$KLas$ =

wage for short term contract solar field labor

n =

cleaning action only performed in one night shift

N_CU =

number of cleaning units

N_loops =

number of collector loops in a solar field

$Nl,cl$ =

number of loops cleaned with cleaning units

$Nl.clas$ =

number of loops cleaned by additional cleaning teams

P_F =

cost of fuel for cleaning one collector loop

$PLas$ =

cost of short term contract labor for the cleaning of one loop

P_W =

cost of water for cleaning one collector loop

Q_dump =

dumped thermal energy

Q_tot =

total thermal energy from solar field

S =

availability vector for the solar field

S_i =

availability of loop i

t =

time

t_d =

day of the year

t_n =

cleaning action is performed in one night and one day shift

T_d =

length of the solar day t_d

T_lt =

total lifetime of a power plant

ξ =

cleanliness

ξ_i =

cleanliness of loop i

ξ_field =

average solar field cleanliness

ξ_lim =

threshold for ξ_field in CS threshold

ξ_lim,as =

threshold for ξ_field in CS assisted determining when external personnel is employed additional to CUs

ξ₀ =

average mirror cleanliness after the passage of a CU

ρ =

specular reflectance

Abbreviations

API =

absolute net profit increase. Difference between the profits obtained with a candidate CS and the reference CS in EUR

AS =

power plant layout similar to “Andasol I” plant

CC =

cleaning costs

CS =

cleaning strategy, a set of rules defining when and how cleaning is performed

CSP =

concentrating solar power

CU =

cleaning unit, the entity of a cleaning vehicle and operating personnel

DLR =

Deutsches Zentrum für Luft- und Raumfahrt, German Aerospace Center

DNI =

direct normal irradiance

ES =

Spain

IP =

power plant layout similar to “Ibersol Puertollano” plant

LCOE =

levelized cost of electricity

MOR =

Morocco

O&M =

operation and maintenance

PSA =

Plataforma Solar de Almería

RPI =

relative profit increase of a candidate CS compared to the reference CS for same power plant layout and site

SR =

soiling rate

TraCS =

tracking cleanliness sensor for soiling rate measurement