ASME Energy Sustainability 2016

1 Copyright © 2016 by ASME

DRAFT Proceedings of the 10th International Conference on Energy Sustainability

June 26-30, 2016, Charlotte, North Carolina, USA

PowerEnergy2016-59390

MODELS FOR PREDICTION OF SOILING-CAUSED PHOTOVOLTAIC POWER OUTPUT DEGRADATION BASED ON ENVIRONMENTAL VARIABLES IN DOHA,

QATAR

Bing Guo Texas A&M University at Qatar

Doha, Qatar

Wasim Javed Texas A&M University at Qatar

Doha, Qatar

Saadat Khan Texas A&M University at Qatar

Doha, Qatar

Benjamin Figgis Qatar Environment and Energy

Research Institute, HBKU Doha, Qatar

Talha Mirza GreenGulf Inc. QSTP-B at Innovation Centre, QSTP

Doha, Qatar

ABSTRACT Countries in the Middle East and North Africa (MENA)

region have plans to deploy photovoltaic (PV) solar power plants in significant portions of national electricity production capacities. However, high airborne dust concentrations and the arid conditions in the region lead to PV panel soiling that can severely decrease the economic feasibility of PV solar power projects. The ability to accurately calculate PV power output degradation based on available ambient condition data is very important for site selection and maintenance scheduling for solar PV power plants in the MENA region.

In a previous study, using field measurement data from the Qatar Foundation Solar Test Facility, the daily change in Cleanness Index (CI), a measure of PV performance ratio, corrected for temperature and normalized to a clean PV module, was correlated to environmental variables including airborne particulate matter concentration (PM10), wind speed (WS), and relative humidity (RH). A linear empirical equation between daily CI change and the daily average PM10, WS, RH was developed using Microsoft Excel®. However, the model was not extensively evaluated due to the small data set available then.

In this study, a larger data set was used to fit the linear model for daily CI change and daily average values of PM10, WS, and RH. In addition, a semi-physical model was developed to take into account the non-linear mechanics of turbulent deposition, resuspension of deposited dust, and the effect of relative humidity on resuspension. The regression and solver functions of Microsoft Excel® was employed to fit the data. The R-squared values of the linear model and the semi-physical

model are 0.0949 and 0.1774, respectively. The semi-physical model predicts the daily ∆CI slight more accurately than the linear model. However, for prediction of cumulative ∆CI over longer periods of time, the two models perform roughly the same. Overall, both models are able to predict the two-month ∆CI with an uncertainty of less than 16%. The results from this study suggest that it is possible to use mathematical models to calculate PV power output degradation in the Doha, Qatar area. This may be a significant step towards development of models that can be used for economic analysis of PV solar projects and plant maintenance.

NOMENCLATURE CI – Cleanness Index, a measure of relative performance ratio, corrected for solar irradiance and PV model temperature, 24-h mean unless otherwise noted, dimensionless. PM10 – ambient airborne concentration of particulate matter with aerodynamic particle size smaller or equal to 10 µm at the STF, 24-h mean unless otherwise noted, mg/m3. PRT_corr – temperature-corrected performance ratio of a PV, dimensionless. PRT_corr – temperature-corrected performance ratio of the Test PV Array. PRT_corr_clean – temperature-corrected performance ratio of the Clean PV Array. RH – relative humidity of ambient air at the STF, 24-h mean unless otherwise noted, %. STF – Solar Test Facility, a Qatar Foundation research facility located in Doha, Qatar.


– Stokes number based on eddy length scale in a turbulent flow, and the friction velocity, dimensionless.

– gravitational settling velocity of an aerosol particle, m s-1. WD – wind direction at the STF, as the directional angel measured from due north clockwise, daily mean unless otherwise noted, degree. WS – scalar wind speed (m/s) at the STF, 24-h mean unless otherwise noted.

– particle diameter, m.

Fd – flux of dust deposition, kg m-2 s-1.

Fr – flux of dust resuspension, kg m-2 s-1. – gravitational acceleration, m s-2.

– scalar wind speed, m s-1.

– friction velocity, m s-1. u*,th,0 – threshold friction velocity in the dust resuspension model, m s-1. ∆CI – change in CI, daily change unless otherwise noted, dimensionless. α0 – parameter in Semi-Physical Model, controlling the turbulence effect in aerosol deposition velocity, dimensionless. α1 – parameter in Semi-Physical Model, proportionality between scalar wind speed and friction velocity, dimensionless. β1 – parameter in Semi-Physical Model, controlling the contribution of relative humidity to the threshold friction velocity for resuspension, m s-1 %-1. β2 – parameter in the Semi-Physical Model, relating friction velocity and flux of resuspension, kg s2 m-5. γ – parameter in the Semi-Physical Model, proportionality between mass accumulation of dust on a PV module and the change in Cleanness Index, m2 kg-1.

– function of the eddy Stokes number of a particle, dimensionless. deposition velocity due to the turbulent-inertial effect, m s-1.

– dynamic viscosity of air, Pa s. – kinematic viscosity of air, m2 s-1. – density of an aerosol particle; is the dynamic

viscosity of air. ϕ0 , ϕ1 , ϕ2 , ϕ3 – parameters of the Linear Model.

INTRODUCTION In the Middle East and North Africa (MENA) region,

there is a strong push to deploy photovoltaic (PV) solar power generation. There is abundant solar irradiation in the MENA region. However, this region also sees high concentrations of airborne dust. Dust deposition causes soiling of the PV panels, which can severely reduce the PV power output and hence

decrease the economic value of a PV solar power generation project [1, 2].

Understanding soiling-caused PV performance degradation as a function of environmental variables is necessary for assessing the economic impact of PV soiling, selecting PV solar power plant sites, devising cleaning strategies, and developing new soiling mitigation techniques. A number of researchers have investigated the effect of environmental variables on PV soiling. For example, Tahboub identified dust concentration, wind speed, wind direction and relative humidity as variables that affect PV soiling. He used visibility data to infer dust concentration, and reported a peak daily mean dust concentration of about 3.5 mg m-3 for February 2008. He used the energy output difference between a soiled PV array and a clean PV array to quantify soiling. He recognized that the net dust accumulation on a PV array could be positive or negative in an individual 24-h day, because deposition of airborne dust and resuspension of deposited dust could take place at the same time [3]. Tahboub also included humidity as an important factor for PV soiling, but did not give specific results on the effect of humidity, partially due to the belief that using daily average relative humidity would limit one’s ability to study its effect [3]. In their review paper on PV soiling, Sayyah et al. give a literature survey of the effect of relative humidity [2]. The studies cited draw correlations between air humidity, solar irradiance, biological growth, and PV performance, but they do not necessarily address the effect of relative humidity on PV soiling. However, relative humidity does affect the threshold wind speed for resuspension of deposited dust particles [4]. Therefore higher relative humidity would lead to greater rate of PV soiling, when other environmental variables are kept constant. Such an effect of relative humidity on PV soiling has been confirm in our previous study [1].

Previously, we measured the PV power output degradation as a function of environmental variables (dust concentration, wind speed, and relative humidity) in Doha, Qatar. A “cleanness index” (CI) was used to quantify the DC power output of a soiled PV array relative to a clean array operating under the same solar irradiation. CI is a relative performance ratio, corrected for the solar irradiation and temperature effect, which reflects the effect of PV soiling, similar to what other researchers refer to as “soiling ratio”. It is based on maximum PV power output, rather than short-circuit current, as PV soiling is typically non-uniform, which should be described with power-based measurement [5]. The difference in mean CI between two consecutive 24-h days (daily ∆CI) is considered the DC power output change in a 24-h day. Without rain or cleaning events, there is long-term decrease in CI due to dust deposition on the PV panels. However, on individual days, daily ∆CI could be positive, due to resuspension of deposited dust from PV panels and a net reduction in PV soiling [1]. A linear correlation was developed using data collect in a period of seven months in our previous study.

The focus of our previous study was to collect PV soiling data through field measurements and to determine the correlation between daily ∆CI and the daily mean of the

Stke

Vg

dp

guscu*

ηdI

µνρp µ


environmental variables including PM10, WS, and RH. A linear regression was carried out to correlate the daily ∆CI and the environmental variables, but no attempt was made to evaluate the accuracy and usefulness of the model.

Since the publication of our previous study, additional data of PV soiling and environmental variables have been collected at the STF. In this study, the objective is to determine the accuracy of a linear multivariate regression model and a semi-physical model for the prediction of daily ∆CI and cumulative ∆CI based on environmental variables. Herein we describe the approach, the results, and the conclusions of this study.

APPROACH PV soiling, in terms of CI and daily ∆CI, was

calculated based on field measurement at the STF. Environmental variables were measured at the STF. The data were processed to understand the effect of daily means of environmental variables. Three different models were used to relate the daily ∆CI with the daily means of the environmental variables. The accuracy of the model predictions was evaluated. The methods are described in the following sections.

PV and Ambient Environmental Data Collection Data collection took place at the Qatar Foundation STF

located in Doha, Qatar. The methods of data collection have been described in our previous study [1]. Briefly, two identical PV arrays were used in this study, each comprising eight 220 Wp polysilicon PV modules, tilted at 22° and facing due south, in a single string connected to identical grid-tied inverters. The arrays’ DC electrical parameters and module back surface temperatures were measured at maximum power point condition once per minute. DC power, voltage and current were measured via transducers with +/- 0.5% accuracy. Module temperatures were measured via permanently attached thermocouples, with unspecified accuracy. One array was cleaned every week, hereafter referred to as the Clean PV Array, one every second month, hereafter referred to as the Test PV Array. Both the Clean PV Array and the Test PV Array were typically down wind of several rows of PV arrays, as the prevailing wind was from the northwest. PM10 was measured using a TSI 8533EP DustTrak® DRX Aerosol Monitor (TSI Inc., Shoreview, MN, USA). Weather conditions were monitored at one-minute intervals. The 24-h arithmetic mean values were calculated for PM10, WS and RH. The 24-h mean of WD was computed by treating all angular measurements as point on the unit circle and computing the resultant vector of the unit vectors determined by data points [6]. During the test period (from May 29, 2014 to September 29, 2015), there were a few significant rain events and dust storms. Also, some data were missing on a few occasions, due to instrument outage.

The cleanness index of the Test PV Array is defined the same as in our previous study [1].

CI = PRT _ corrPRT _ corr _ clean

(1)

The CI of a clean PV array is by definition equal to 1. As the level of soiling increases, CI decreases.

Dust Accumulation Measurement The development of a semi-physical model requires

knowledge of the quantitative relation between the daily quantity of dust accumulation on PV panels and the daily change in CI. For that purpose, dust accumulation was measured on two PV panels, hereafter referred to as Dust Accumulation PV Panels. The Dust Accumulation PV Panels were of the same type as the Clean PV Array and the Test PY Array, which were frameless, 1.2 m in width and 0.6 m in height, with inclination angle of 22˚, facing due south. Dust samples were collected fro the Dust Accumulation PV Panels every 24 hours, from 11 January 2015 to 20 February 2015, and from 1 June 2015 to 15 July 2015. The collected dust samples were weighed to determine the mass of accumulated dust in each 24-hour period. In other words, the Dust Accumulation PV Panels were reset to the clean state at the beginning of each 24-h period. In contrast, the Test PV Array had continuous dust accumulation for periods much longer than 24 hours. Therefore, the dust accumulation in a 24-hour period on the Dust Accumulation PV Panels could be different than that on, due to the difference in PV surface conditions. However, this was the best method available for estimating the mass of dust accumulation on the Test PV Array in each 24-h period. Knowing how much dust has accumulated on the Test PV Array in a 24-h period, and the ∆CI in the same period, we were able to estimate the relationship between ∆CI and mass of dust accumulation on the per unit area basis.

Linear Model This model was used in the previous study and fitted with a

smaller data set [1]. In this model, the daily ∆CI is simply expressed as a linear combination of WS, PM10 and RH:

∆CI =ϕ0 +ϕ1PM10 +ϕ2WS +ϕ3RH (2)

where ϕ0 , ϕ1 , ϕ2 , and ϕ3 are model parameters. Microsoft Excel® was used to fit the linear model with the data obtained in this study. RH enters the model in the decimal format, e.g., 50% would enter the model as 0.50.

Semi-Physical Model In the semi-physical model, the daily change in a PV

panel’s cleanness index is proportional to the daily average dust deposition flux minus the daily average dust resuspension flux. The dust deposition flux is proportional to the ambient dust concentration and the deposition velocity, the latter being a function of wind speed. The dust resuspension flux is a function of wind speed and relative humidity. In this model, we assume that the density, shape and size distribution of the depositing and resuspension particles are constant.

Dust deposition flux onto the PV panel may be expressed as the product of ambient dust concentration and the dust deposition velocity [7]. Dust particles are polydisperse. For simplicity of the model, we assume that the dust particle size


distribution is constant, and hence there is an representative particle size to be used in the analysis and calculation.

The aerosol deposition velocity is a combination of gravitational settling and turbulent deposition. We adopt the dry deposition model by Kim and Larson [8]. In comparison to other dry deposition models [9], this model is better suited for larger particles, which are the primary concern for PV soiling in this study.

(3)

The gravitational settling velocity of aerosol particles, Vg, may be calculated using the following equation.

(4)

Through data regression, Kim and Larson finds the following relationship between and the friction velocity

[8]:

(5)

The eddy Stokes number is a function of particle size and the friction velocity. It is a Stokes number assessed using the friction velocity and the eddy length scale [7, 10].

(6)

Note that is the kinematic viscosity of air, and the quantity

represents the eddy time scale.

In our PV soiling problem, the relationship between

and the friction velocity may be expected to follow the same functional relationship, but with a parameter in the exponent to be determined through regression.

(7)

The friction velocity can be experimentally determined through measurement of air velocity fluctuation [8]. There is not a universally accepted definition for the friction velocity, and the various definitions have considerable differences [11]. The definition using by Kim and Larson is equivalent to the “B” type definition in Weber [11]. Weber gives a convenient linear relationship between the “A” type friction velocity and the scalar wind speed. Here we assume that the same linear relationship exists between the friction velocity and the scalar wind speed in general [11].

(8)

where is the scalar wind speed. It should be noted that the relation above is for friction velocity and scalar wind speed at

the same location. One would need to consider the elevation difference, if the friction velocity and the scalar wind speed are assessed for different locations.

In our study, the relationship between the friction velocity and the scalar wind speed should be expected to differ from that reported in the literature, because our “terrain” (the PV panels) is different from that used in atmospheric boundary layer studies.

(8a)

where is a parameter to be determined through regression, which may be assigned an initial value of 0.15 considering Eqn. (8).

Therefore, we can express the deposition velocity in terms of the scalar wind speed.

(9)

where and . Then the dust deposition flux may be expressed as the product of deposition velocity and the nominal dust concentration PM10:

(10)

Because the PV panels are elevated above the ground, it appears appropriate to assume that dust resuspension from the PV panels should not involve saltation. Loosemore and Hunt obtained an empirical equation that relates resuspension flux and the friction velocity [12]:

Fr = βu*2 u* −u*,th( ) (11)

where u*,th is a threshold friction velocity; β is a coefficient. Humidity has been reported to affect the threshold friction

velocity for dust resuspension, in a roughly linear manner. One study reports that the threshold friction velocity increases from 0.24 m s-1 to about 0.31 m s-1, as the relative humidity increases from 0 to approximately 90% [4]. We choose to use the following equation for modeling the resuspension, taking into consideration relative humidity and the threshold friction velocity:

Fr =β2 u* − u*,th,0 +β1RH( )!" #$u*

2

exp −100 u* − u*,th,0 +β1RH( )!" #${ } (12)

where u*,th,0 is the threshold friction velocity at zero relative

Vd = u*ηdI +Vg

Vg =ρpgdp18µ

ηdI

u*

ηdI =10−2.8Stke

Stke

Stke =Vgu*

2

gνν

νu*2

ηdI

u*

ηdI = exp−α0gνVgu*

2

"

#$$

%

&''

u*

u* = 0.15uscusc

u* =α1uscα1

Vd =α1usc exp−α0gνVgα1

2usc2

"

#$$

%

&''+Vg

g = 9.81 m s−2 ν =1.5×10−5 m2 s−1

Fd = PM10 α1usc exp−α0gνVgα1

2usc2

"

#$$

%

&''+Vg

(

)**

+

,--

TABLE I STATISTICS OF AMBIENT CONDITION VARIABLES

Variable Mean Standard Deviation

Daily ∆CI -0.0051 0.0097 PM10 (mg m-3) 0.112 0.047

WS (m s-3) 2.0 0.9 RH 48% 14%


humidity, with a unit of m s-1. The parameter should be in the range of 0.0004 – 0.0016 m s-1 %-1 according to Neuman and Sanderson [4]. Applying the relation between friction velocity and scalar wind speed, we have:

Fr =β2 α1usc − u*,th,0 +β1RH( )!" #$α1

2usc

2

exp −100 α1usc − u*,th,0 +β1RH( )!" #${ } (12a)

Eqns. (12) has the correct asymptotes that closely resemble the piecewise function used by Neuman and Sanderson [4].

The difference between dust deposition flux and dust resuspension flux is the net dust deposition flux. Therefore, we may have a semi-physical model relating the ∆CI for a 24-h period and the 24-h means of the environmental variables:

∆CI = 8.64×104 s( )γβ2 α1WS − u*,th,0 +β1RH( )#$ %&α1

2WS2

1+ exp −100 α1WS − u*,th,0 +β1RH( )#$ %&{ }−PM10 α1WS exp −α0gν

Vgα12WS2

'

())

*

+,,+Vg

#

$--

%

&..

/01

21

341

51

(13)

where γ is the proportionality between ∆CI and change in dust loading on the PV surface. Microsoft Excel® was used to determine the parameters of the semi-physical model. RH enters the model in the percentage format. That is, for relative humidity of 50%, the value of RH would be 50 in this model.

RESULTS AND DISCUSSION The statistics of daily ∆CI, PM10, WS and RH are shown

in Table I. The values are similar to that of the previous study [1].

Daily Dust Accumulation Rate Daily dust accumulation rate was measured for Jan-Feb

2015 and Jun-Jul 2015. The results are shown in Figure 1. It can be seen that in the winter months the daily dust accumulation rate was higher than in the summer months. Correspondingly, the daily ∆CI in the winter months was more negative than in the summer months. Using data from both Jan-Feb and Jun-Jul 2015, the coefficient relating daily ∆CI and daily dust accumulation rate is approximately 5×10-5 m2 mg-1, or 50 m2 kg-1. Using this coefficient and the average daily ∆CI found in Table I, one may infer that that the rate of dust accumulation on the PV panels is approximately 100 mg m-2 d-

1.

(a)

(b)

Figure 1. Daily dust accumulation on PV panels and daily ∆CI in (a) Jan-Feb 2015 and (b) Jun-Jul 2015

Model Parameters The parameters of the linear regression model was

determined using Microsoft Excel®, and are shown in Table II. It can be seen that the model parameters obtained in this study are similar to that from the previous study. The parameter for PM10 is almost identical between the two studies. The other parameters differ no more than a factor of two. The difference in the regression parameters may be attributed to the temporal variation in environmental variables and consequently the shift in soiling mechanisms. The previous study covered the last seven months of 2014. Whereas this study includes the data used in the previous study, plus the data from the first ten months of 2015.

β1

TABLE II LINEAR REGRESSION MODEL PARAMETERS

Coefficient This Study Previous Study [1]

5.22×10-4 2.3×10-4

-5.67×10-2 m3 mg-1 -5.7×10-2 m3 mg-1 2.80×10-3 s m-1 3.5×10-3 s m-1 -1.06×10-2 -2.0×10-2

R2 = 0.0949 (451 data points)


The parameters of the Semi-Physical Model were obtained through the solver function of Microsoft Excel®, by minimizing the sum of squared errors of model-predicted daily ∆CI. The parameters are shown in Table III. The values of the model parameters are in good agreement with the literature or the physical conditions of the dust deposition process. Such agreement gives confidence that the Semi-Physical Model does capture the physics involved in the dust soiling process.

Based on its physical meaning, γ was assigned an initial value of 50 m2 kg-1, as determined through the daily dust accumulation rate and daily ∆CI measurement. The final value of γ is 30.6 m2 kg-1. The slight difference between these two values may be may be attributed to the fact that the experimental measurement was only able to determine daily dust accumulation rate on PV panels that were cleaned every 24 hours, but the cleaning cycles of the test PV arrays were much longer. The daily dust accumulation rate on PV panels could be significantly dependent on the length of the cleaning cycle.

In the semi-physical model, the parameter α0 controls the effect of turbulence on dust deposition velocity. The final value obtained in this study is much larger than what would be derived from the literature [8]. This may be explained by the difference in experimental conditions used in this study and that of the other studies. The larger value of α0 seems to suggest that the turbulence effect on dust deposition is relatively weak in this study. However, due to the numerical nature of the parameterization process, we probably should not over-interpret the significance of this parameter.

The parameter α1 is an empirical coefficient that relates the scalar wind speed to the friction velocity, which is involved in the calculation of both dust deposition and resuspension. The final value 0.375 is quite close to the literature value of 0.15. The difference may well be attributed to the difference in experimental conditions between different studies.

The parameters β1 and u*,th,0 control the effect of relative humidity on dust resuspension. It is interesting that the final value of u*,th,0 is zero, consistent with the resuspension model without saltation [12] – when relative humidity is zero. However, the non-zero parameter β1 leads to an effective threshold friction velocity, below which there will be no

resuspension. The proportionality parameter β1 is about one order of magnitude greater than the values reported in the literature [12]. The difference could be due to experimental uncertainty as well as the empirical nature of the resuspension model.

In the Semi-Physical Model, the parameter is the gravitational settling velocity of the hypothetical dust particle that has the “representative” size. This representative particle size obviously should be a function of dust particle size distribution. The aerodynamic diameter corresponding to gravitational settling velocity of 0.0199 m s-1 is roughly 26 µm. This is consistent with the fact that a large fraction of the dust particles is larger than 10 µm in aerodynamics diameter.

Model Predictions of Daily ∆CI Figure 2 shows the Linear Model predictions of daily ∆CI

results compared against the measurement data. Of the 451 data points utilized in the fitting, 124 Linear Model predictions deviate from the measurement data by more than one standard deviation of the measurement data.

Figure 3 shows the Semi-Physical Model predictions of daily ∆CI results compared against the measurement data. Of the 451 data points utilized in the fitting, 111 Semi-Physical Model predictions deviate from the measurement data by more than one standard deviation of the measurement data. Due to the limitations of the Microsoft Excel® solver, it is possible that the Semi-Physical Model could be further improved by finding a set of global optimal parameters.

Figure 2. Linear Model predictions in comparison with

measured daily ∆CI, dashed lines representing vertical offset by one standard deviation of the measurement data

Vg

TABLE III SEMI-PHYSICAL MODEL PARAMETERS

Coefficient Value and Unit

30.6 m2 kg-1

1.71×103 0.375 1.95×10-2 m s-1 %-1 3.00×10-9

kg s2 m-5 0 m s -1

0.0199 m s-1 R2 = 0.1774 (451 data points)


Figure 3. Semi-physical model prediction in comparison with

measured daily ∆CI, dashed lines representing vertical offset by one standard deviation of the measurement data

Model Predictions of Cumulative ∆CI In reality, a model would only be useful if it can accurately

predict the Cleanness Index of PV arrays over longer periods of time, so that such a model may be used for estimating

electricity output of a PV solar power project and assessing its financial return. Therefore, it is necessary to evaluate a model’s accuracy in predicting cumulative ∆CI. The model performance of cumulative ∆CI prediction is shown in Figure 4 and summarized in Table IV. From Figure 4, it can be seen that cumulative ∆CI prediction from both Linear Model and Semi-Physical Model agree well with the measurement data. The Semi-Physical Model often over-predicts the cumulative ∆CI, which the Linear Model often under-predicts. In this study, the longest contiguous period of comparison is two months. (The test PV panel was cleaned every two months.) The models’ prediction of cumulative ∆CI is accurate within 0.08 over periods of up to two months. To put it in perspective, the Cleanness Index of a PV array could drop by more than 0.5 over a period of two months. In other words, the current models can predict the power degradation due to dust soiling with an uncertainty of less than 16%.

Figure 4. Model prediction of cumulative ∆CI in comparison

with measurement, discontinuity due to missing data points or resetting due to cleaning or rain events

CONCLUSIONS In this study, we fitted field measurement data to a linear

model from predicting daily ∆CI using 24-h mean values of environmental variables. Also, we developed a semi-physical model and determined its parameters using the measurement data. Both models show similar accuracy in daily ∆CI prediction and cumulative ∆CI prediction. The models are sufficiently accurate, with a less than 16% relative uncertainty for predicting two-month cumulative ∆CI. Such models may become useful for PV solar power plant site selection, mitigation technology development, and maintenance scheduling. It is conceivable that, with these models and a database of environmental conditions (ambient dust concentration, wind speed, relative humidity, etc.), it will be possible to quantitatively assess the impact of dust soiling on the economics of PV solar generation for any given site.

The parameters obtained for the semi-physical model are in general agreement with literature values and are consistent with the physical meanings of these quantities. It may be possible to improve the semi-physical model to more accurately reflect the physics involved in PV soiling due to dust deposition, so as to increase the accuracy and robustness of the model.

ACKNOWLEDGMENTS Financial support from Qatar National Research Fund

through the National Priority Research Program (NPRP07-987-2-372) is gratefully acknowledged,

REFERENCES

[1] Guo, B., Javed, W., Figgis, B. W., and Mirza, T., "Effect of dust and weather conditions on photovoltaic performance in Doha, Qatar," Proc. Smart Grid and Renewable Energy (SGRE), 2015 First Workshop on, pp. 1-6. [2] Sayyah, A., Horenstein, M. N., and Mazumder, M. K., 2014, "Energy yield loss caused by dust deposition on photovoltaic panels," Solar Energy, 107, pp. 576-604.

TABLE IV CUMULATIVE ∆CI PREDICTION STATISTICS

Deviation from Measurement Data Linear Model Semi-Physical

Model Mean -0.01 0.01

Std. Dev. 0.02 0.02 Max. 0.07 0.08 Min. -0.07 -0.06

Longest contiguous period: 60 days


[3] Tahboub, Z., 2011, "Understanding the Factors that Affect the Utilization of Photovoltaics in High Atmospheric Dust Concentration Regions," MS, Masdar Institute. [4] Neuman, C. M., and Sanderson, S., 2008, "Humidity control of particle emissions in aeolian systems," Journal of Geophysical Research: Earth Surface, 113(F2), pp. n/a-n/a. [5] Gostein, M., and Stueve, B., 2015, "Accurately Measuring PV Soiling Losses Using Module Power Measurements," http://www.nrel.gov/pv/performance_reliability/pdfs/2015_pvmrw_31_gostein.pdf. [6] Jammalamadaka, S., and Lund, U., 2006, "The effect of wind direction on ozone levels: a case study," Environ Ecol Stat, 13(3), pp. 287-298. [7] Hinds, W. C., 1999, Aerosol Technology: Properties, Behavior, and Measurement of Airborne Particles, John Wiley & Sons, Inc., New York.

[8] Kim, E., Kalman, D., and Larson, T., 2000, "Dry deposition of large, airborne particles onto a surrogate surface," Atmospheric Environment, 34(15), pp. 2387-2397. [9] Pleim, J., and Ran, L., 2011, "Surface Flux Modeling for Air Quality Applications," Atmosphere, 2(3), p. 271. [10] Kulkarni, P., Baron, P. A., and Willeke, K., 2011, "Aerosol Measurement: Principles, Techniques, and Applications," John Wiley & Sons, Inc., Hoboken, New Jersey. [11] Weber, R. O., 1999, "Remarks on the definition and estimation of friction velocity," Boundary-Layer Meteorology, 93(2), pp. 197-209. [12] Loosmore, G. A., and Hunt, J. R., 2000, "Dust resuspension without saltation," Journal of geophysical research, 105(D16), pp. 20663-20672.

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