Photovoltaic System Yield Uncertainty

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Abstract— The first step in the planning of any solar photovoltaic (PV) system is the solar resource assessment. This assessment is usually performed by an energy analyst and involves characterizing the available solar resource and the local meteorology. The next step may be to determine what size and type PV system to propose based on financial, environmental, and other factors. Producing accurate estimates of the annual energy yield of these systems requires the use of PV simulation tools. This paper examines the uncertainty in the annual energy yield of a PV system using one of these tools-System Advisor Model (SAM), developed by National Renewable Energy Laboratory. Using published uncertainty data for the submodels used within SAM, the uncertainty of the meteorological data, the inter-annual variability of meteorological data at the site, and an estimation of the overall system derate factor error, this report attempts to quantify the total uncertainty in annual energy yield. Two case studies where actual energy yield data is well documented are evaluated. A method for calculating the exceedance probability-the likelihood that the annual energy yield will exceed a given probability- is shown. The purpose of this paper is to give energy analysts a better understanding of the sources of uncertainty (and their relative magnitude) when using PV simulation tools to predict the annual energy yield of a PV system.

Index Terms—Photovoltaic systems, Power system simulation, Measurement uncertainty, Solar energy

I. INTRODUCTION

N order to estimate the annual energy yield of a grid-tied photovoltaic (PV) system, the energy analyst needs to

know how much solar radiation is available and what the performance of the system itself is. Unfortunately, there is significant uncertainty in both of these areas. These uncertainties are a major concern of developers of large commercial or utility scale systems. This paper first examines the parameters that can affect overall energy yield of a PV system. It reviews the tool used to simulate two types of PV systems that are later examined in this report. It then describes the two systems and shows what parameters are relevant for each system. One of the key concepts to learn from this study is that one must consider different value simulation parameters for different types of PV systems. These simulation parameters -also known as system derate factors- will also depend on the site chosen for the PV system under consideration.

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Manuscript received June 6, 2011. David F. Parker is the owner of Parker Energy Solutions, Aromas, CA 95004 USA phone: 831-726-9197; (e-mail: dave@parkerenergysolutions.com).

II. FACTORS AFFECTING PV ENERGY YIELD

A. Solar Radiation

PV energy yield is directly related to the amount of solar radiation available at the site. If we ignore local climate for a moment one can deduce that there is more annual solar radiation at the earth’s equator than at the poles. So geographical location has a direct affect on the amount of solar radiation available at a site. The other factor that affects solar radiation is climate. A predominantly cloudy location will have less solar radiation than a location with clear skies. In order to estimate the energy yield of a PV system one must acquire at least one year’s worth of weather data for the site. However, in order to estimate the effects of inter-annual variability of the solar radiation on energy yield, at least 10 years worth of data is required [1]. Also, although the weather data may be defined as a “Typical Meteorological Year,” the data may not represent the mean or average year in terms of the amount of solar radiation [2]. The simulation tool used in this study accepts three types of weather files, TMY2, TMY3, and EPW [3]-[4].

B. PV System Performance

Once the amount of solar radiation is determined, the performance of the PV system itself -in terms of energy conversion efficiency- determines how much energy is supplied to the utility grid. There are numerous parameters that affect this overall conversion efficiency. Some of these parameters are built into the simulation models. For example, conversion efficiencies are known within the simulation tool for the solar module model and the inverter model so these parameters do not need to be estimated. However, there are some parameters, known as “system derate factors” that must be estimated by the analyst and may be system dependent and/or site dependent [5]. The following is a list of system derate factors found within SAM, the simulation tool used in this study:1) Mismatch - accounts for manufacturing tolerances that

yield PV modules with slightly different current-voltage characteristics.

2) Diodes and Connections - accounts for losses from voltage drops across diodes used to block the reverse flow of current and from resistive losses in electrical connections.

3) DC Wiring - accounts for resistive losses in the wiring between modules and the wiring connecting the PV array to the inverter.

4) Soiling - accounts for dirt, snow, and other foreign matter on the surface of the PV module that prevent solar radiation from reaching the solar cells.

5) Sun Tracking - accounts for losses for one- and two-axis

Estimating Uncertainty in the Projected Annual Energy Yield of a Photovoltaic System

David F. Parker, Member, IEEE

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tracking systems when the tracking mechanisms do not keep the PV arrays at the optimum orientation.

6) Nameplate - accounts for the accuracy of the manufacturer's nameplate rating.

7) AC Wiring - accounts for resistive losses in the wiring between the inverter and the connection to the local utility service.

8) Transformer – accounts for transformer-related losses when a transformer is used.

9) Aging - accounts for performance losses over time because of weathering of the PV modules.

10) Availability - accounts for times when the system is off because of maintenance or inverter or utility outages.

These system derate factors are the same factors used in the popular PVwatts on-line simulation tool [6]. In SAM, these factors are treated as a percent while in PVwatts they are treated as a fraction. Table 1 lists these factors along with their recommended default values.

TABLE ISYSTEM DERATE FACTORS

Factor Default Value (%)System or Site

dependent?Mismatch 98 System Diodes & Connections

99.5 No*

DC wiring 98 SystemSoiling 95 System & SiteSun Tracking** 100 No*Nameplate*** 100 No*AC wiring 99 No*Transformer 100 (no transformer) SystemShading 100 System & SiteAvailability 100 SystemAgeing 0.5/yr System & Site

*In a properly designed and installed system, these values are typical. **For fixed mount systems the default value is 100. Also, for modern tracking systems such as the Case 2 system here, the trackers have a positional accuracy of less than 0.01 ° so tracking accuracy is not an issue [7]. ***The default value in PVwatts is 95. However, in SAM when using either the Sandia or the 5-parameter PV module model the recommended default is 100 because the model takes into account the module nameplate accuracy [8].

What does system or site dependent mean? As an example, if we look at mismatch, this is system dependent because this parameter would be much higher, typically 99.5 % if micro-inverters were used on each module instead of a central inverter [9]. Soiling is dependent on where the system is- a dusty, high traffic area would adversely affect soiling- as well as the type of system. A system on two-axis trackers will have less soiling than a fixed mount system because of the movement and tilt of the array. Shading losses are assumed to be negligible for both PV systems examined. However, in the interest of completeness, shading uncertainty is estimated to be 2%. This value assumes no significant shading between the hours of 9 AM and 3 PM and a shading tool was employed in the site assessment. Shading tool vendors are hesitant to publish uncertainty data for their

products. However, in the author’s experience with these tools, 2% uncertainty seems reasonable.

III.SYSTEM ADVISOR MODEL (SAM)

There are many computer-based tools available for the simulation of PV systems [10]. The tool used in this report is the System Advisor Model, previously known as the Solar Advisor Model [11]. The National Renewable Energy Laboratory (NREL) with Sandia National Laboratories develops this program for the Department of Energy (DOE). This program can be considered a “black box” where one provides inputs such as geographical location, weather data, system costs, components such as solar module quantity, type and model, inverter type and model, and system parameters such as module tilt and orientation. The program then performs an hour-by-hour simulation for a complete year (8760 hours) and outputs system energy yield, levelized cost of energy, peak and annual system efficiency and other performance metrics.

Within SAM, the analyst has a choice of five radiation models, three (PV) module models, and two inverter models. The radiation models can accept the weather solar radiation data as Beam and Diffuse, Total and Beam, or Total and Diffuse. In this context, Beam is also called Direct Normal Irradiance (DNI). This is the amount of radiation received on a plane that is always perpendicular (or facing) the sun. Total is also referred to as Global Horizontal Irradiance (GHI). This is the total amount of radiation received by a horizontal surface. Diffuse is referred to as Diffuse Horizontal Irradiance (DHI). This is the background radiation coming from the sky and surroundings. Fixed panel PV systems rely mostly on GHI, while PV tracking systems use DNI. The weather data file always contains all three solar radiation values, GHI, DNI, and DHI. However, SAM only uses two, as noted above, when passing this data into the radiation model. The radiation model calculates the Plane Of Array (POA) irradiance using two of the three radiation values. The SAM settings used for this study are:

Radiation model inputs are Total and Beam Radiation model is Perez 1990 Module model is Sandia PV Array Performance Model Inverter model is Sandia Performance Model No shadingThe version of SAM used for this study is 2011.5.4.

IV.MEASURES OF UNCERTAINTY

For this study, the key measure of uncertainty (or variability) is the Coefficient of Variation or CV. The CV is defined as:

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where is the standard deviation of the sample and

is the mean [12]. For example, the uncertainty in the annual GHI of a site over a 10 year period would be the standard deviation of the 10 annual GHI values divided by the mean of the 10 GHI values. All the uncertainties in this report are expressed in percentages. Uncertainties are added by the Root Sum Square (RSS) method [13]. In terms of solar radiation, uncertainty may be expressed in hourly, daily, monthly, or annual intervals. In this study we use monthly uncertainty values because these are readily available and because the author is hesitant to extrapolate from monthly to yearly values because of seasonal bias differences.

V.CASE STUDIES

In this study we review two grid-tied PV systems. One system is a fixed roof mounted commercial size system and the other is a small utility scale system mounted on five two-axis trackers. In each case a complete system description is given first. For the uncertainty analysis in each case, we review: The values chosen for the system derate factors and the

uncertainty in those factors. Uncertainty in the simulation model. The solar resource, both in terms of annual climate

variability and in terms of the estimation of the resource itself.

Calculation of the total uncertainty and exceedance probability.

A. CASE 1-System description

Fig. 1. Part of the NIST PV System in Gaithersburg, MD. (CASE 1)

This grid-tied PV system is located on the roof of the National Institute of Standards and Technology campus in Gaithersburg, MD. The system annual energy data used for this study was recorded from Nov. 2001 until Oct. 2002 [14]. The components of the system are listed in Table 2.

TABLE 235 KWP FIXED ARRAY COMPONENT LIST (CASE 1)

Component Type

Inverter Trace/Xantrex Model PV-30208 Inverter size 30 kWTransformer 208V delta-480V wye (30 KVA)PV Modules Siemens SP150Module Technology single-crystal siliconModules per string 13Strings in parallel 18Array peak power 35.1 kWTilt 0 degrees (horizontal)Azimuth N/ASystem physical location Lat: 39.14 °

Long: -77.22°Weather data location Lat: 39.167 °

Long: -76.683°

B. CASE 1-System Derate Factors

For Case 1, the estimated system derate factors and the uncertainty in those factors are shown in table 3 below.

TABLE 3CASE 1 SYSTEM DERATE FACTORS

Factor Estimated Value (%)Estimated Uncertainty

(%)Mismatch 98 1Diodes & Connections 99.5 0.5DC wiring 98 1Soiling 92* 4Sun Tracking 100 0Nameplate 100 0AC wiring 99 0.5Transformer 98* 0.5Shading 100 2Availability 100 1Ageing** 0.5/yr 0.25/yrTotal Derate Factor Uncertainty (RSS)

4.9

* These values are different than the recommended default.**Ageing is considered separately later in this analysis and is NOT included in the Total Derate Factor Uncertainty.

A value of 92% was chosen for the soiling derate factor because the modules are mounted horizontally and the system relies on natural precipitation for module cleaning [15-16]. A value of 98% was used for the transformer derate factor because a 30 KVA distribution transformer is being used. A value of 0.5% per year for age degradation appears to be representative for both single-crystal and multi-crystalline PV modules [17]. The estimated uncertainty in the system derate factors appears reasonable based on the acceptable range of values and on the author’s own experience.

C. CASE 1-Simulation Model Uncertainties

In addition to the uncertainties in the solar resource and in the PV system performance, the uncertainties in the simulation model need to be estimated. For SAM, the estimated uncertainty in the combined Radiation model and PV module model is estimated to be 5%. The inverter model uncertainty is 1%. [8]. These values are based on using the submodels specified previously and the PV module technology (single-crystal or multi-crystalline). Other technologies such as amorphous thin-film may have higher uncertainty and/or should be modeled with a different submodel in SAM.

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D. CASE 1-Solar Resource Uncertainties

As noted before, solar resource uncertainty involves both uncertainty due to climate-year to year variability-and uncertainty in the weather database used. The most-often used weather data available to the energy analyst is data estimated from satellite-derived models. The data used for Case 1 is from the National Solar Radiation Database (NSRDB) and includes 15 years of hourly data from 1991 to 2005. The station used is a class 1, # 724060, Baltimore Washington International Airport station [18]. This is approximately 28 miles from the physical location of the PV system. A study in 2005 reported the uncertainty in the NSRDB as ±8.6% for GHI and ±15% for DNI [19]. For the Case 1 system we will use the GHI uncertainty since this is a fixed mount array.

In order to estimate the effects of climate variability, we performed a parametric simulation in SAM using the 15 years of NSRDB data. We also looked at TMY2 data and TMY3 data for the site. The results are shown in Figure 2. Table 4 summarizes the key findings.

Fig. 2. Case 1 PV System- CDF of Yield calculated over 15 yearsTABLE 4

CASE 1 PV SYSTEM (35 KWP FIXED ARRAY ) CLIMATE SIMULATION RESULTS

Parameter Result

Mean 33941 kWh Standard Deviation 1773 kWh (5.2%)TMY2 Prediction 35057 kWhTMY3 Prediction 35576 kWhActual Yield 2002* 35676 kWhModeled Yield 2002 35370 kWhModel Error -0.9%

*Nov. 2001-Oct. 2002

Using the previously discussed system derate factors the model error for year 2002 is quite small, -0.9%. In other words, the simulation predicts a slightly lower annual yield than what was measured. The TMY2 and TMY3 predicted annual yields are much higher than the mean for this data. This data shows that the energy analyst must use at least 10 years of Actual Meteorological Year (AMY) data for two

reasons. One is to find the true mean or average annual yield. The other is to find the standard deviation in the data in order to determine the inter-annual variability. The inter-annual variability (or climate uncertainty) for this system is 5.2%.

E. CASE 1-Total Uncertainty and Exceedance Probability

The Case 1 system uncertainties are shown in Table 5 below. This data is shown in a bar graph in Figure 3. An explanation of the module ageing parameter is in order. If we assume a degradation rate of 0.5% per year with an uncertainty of 0.25% per year, then after 9 years the modules have degraded 4.5% ±2.25%.

TABLE 5CASE 1 PV SYSTEM (35 KWP FIXED ARRAY ) UNCERTAINTIES

Parameter Uncertainty

Solar Radiation (GHI) 8.6%Climate 5.2%Radiation and PV Module Submodels (SAM)

5.0 %

Inverter submodel (SAM) 1.0%Module Aging (9 years) 2.25%System Derate Factor (total)

4.9%

Total Uncertainty (RSS) 12.5%

Fig. 3. Case 1 PV System- Uncertainties

As can be seen by Figure 3, the solar radiation and climate uncertainties are the largest contributors to the system total uncertainty. It should be noted that, even though some components of the uncertainties are not linear, the radiation model in this case, and some components may not have a normal distribution, such as solar radiation, the Root-Sum-Square method (RSS) of adding these uncertainties is a valid

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method to estimate the total uncertainty. Reference [13] demonstrates this.

What is the meaning of the total uncertainty (12.5%) in this case? If we take the mean value of the annual energy yield from table 4 and subtract the module degradation loss due to ageing (-0.5% per year for 9 years or -4.5% of 33941 kWh), we get 32413 kWh. This is the mean value for this PV system after 9 years of operation. (The system was commissioned in September 2001). If we add 12.5% of 32413 kWh to this value we get 36465 kWh. If we subtract 12.5% of 32413 kWh from this value we get 28361 kWh. Recall that this 12.5% represents one standard deviation. So there is a 66% likelihood that this year (Year 2011), this system will generate between 28361 kWh and 36413 kWh.

In terms of exceedance probability, the mean (32413 kWh) is referred to as the P50 value-see Table 6. The probability of reaching a higher or lower annual energy production is 50:50. The P90 value is that annual energy yield value where the risk of NOT reaching it is 10% [20]. For this PV system, for year 2011, the P90 value is 27228 kWh. A graph of exceedance probability for this system is shown in Figure 4 below. The P50 and P90 values are shown. Notice that this graph is a mirror image of the cumulative distribution function (CDF) because, for exceedance probability, one subtracts the cumulative probability from one in order to get the exceedance probability.

TABLE 6CASE 1 PV SYSTEM EXCEEDANCE PROBABILITY , UNCERTAINTY 12.5%

Parameter Annual Energy Yield

P50 (2011) 32413 kWhP90 (2011) 27228 kWh

Fig. 4. Case 1 PV System- Exceedance Probability

F. CASE 2-System Description

Fig. 5. This photo is of a two-axis tracker of a similar system to the five-tracker system in Toledo, Spain (CASE 2)

This two-axis tracker PV system is located approximately 40 miles south of Madrid. The system annual energy data used for this study was recorded from Oct. 2008 until Sept. 2009 [21]. The components of the system are listed in Table 7.

TABLE 7112 KWP TWO-AXIS TRACKER ARRAY COMPONENT LIST (CASE 2)

Component Type

Inverter INGETEAM INGECON SUN 100 Inverter size 100 kWTransformer N/APV Modules* Kyocera 190-GHT-2Module Technology multi-crystalline siliconModules per string** 19Strings in parallel 31Array peak power 111.9Tilt dual-axis trackersAzimuth dual-axis trackersSystem physical location Lat: 39.98 °

Long: -4.29°Weather data location Lat: 39.806 °

Long: -4.063°

*In SAM, the PV module modeled is an Evergreen ES-190.** In SAM, the total number of modules is 589. The system production document specified 590 modules [21].

G. CASE 2-System Derate Factors

For Case 2, the estimated system derate factors and the uncertainty in those factors are shown in Table 8 below.

TABLE 8CASE 2 SYSTEM DERATE FACTORS

Factor Estimated Value (%)Estimated Uncertainty

(%)Mismatch 98 1Diodes & Connections 99.5 0.5DC wiring 98 1Soiling 95 4Sun Tracking 100 0Nameplate 100 0AC wiring 99 0.5Transformer 100 0Shading 100 2Availability 99* 1Ageing** 0.5/yr 0.25/yrTotal Derate Factor 4.8

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Uncertainty (RSS)

* These values are different than the recommended default.**Ageing is considered separately later in this analysis and is NOT included in the Total Derate Factor Uncertainty.

The availability value (99%) was chosen based on the additional maintenance time required for the two-axis trackers. A value of 95% (the default) was chosen for the soiling derate factor because, although the modules are mounted on dual-axis trackers, the system relies on natural precipitation for module cleaning [22]. Note that for this system there is no distribution transformer.

H. CASE 2-Simulation Model Uncertainties

The simulation model uncertainties are the same as in Case 1, above. The combined Radiation model and PV module model uncertainty is estimated to be 5%. The inverter model uncertainty is 1%.

I. CASE 2-Solar Resource

Weather Analytics (WA) provided 10 years (2000-2009) of AMY data for the Toledo, Spain site, ID # 579220 [23]. Weather Analytics also included a TMY file for the site. This data is derived from the National Oceanic and Atmospheric Administration/ National Centers for Environmental Prediction/ Climate Forecast System Reanalysis data sets (NOAA/NCEP/CFSR) [24]. This solar radiation data has an uncertainty of ±4.8% for GHI and ±15.8% for DNI [25]. This amount of uncertainty is consistent with the published uncertainty of other satellite-derived modeled data such as the National Aeronautics and Space Administration Surface meteorology and Solar Energy (NASA SSE) data set. See Table 9 for a comparison of the different data sets.

TABLE 9SATELLITE DERIVED RADIATION DATA UNCERTAINTIES (MONTHLY)

Data set GHI (%) DNI (%)

NSRDB ±8.6% ±15%NASA SSE ±8.7% ±20.93%WA ±4.8% ±15.8%

For the Case 2 system we will use the DNI uncertainty, (±15.8%), since this is a two-axis tracker mounted array.

In order to estimate the effects of climate variability, we performed a parametric simulation in SAM using the 10 years of WA data. We also looked at TMY2 data for the site. The results are shown in Figure 5. Table 10 summarizes the key findings.

Fig. 5. Case 2 PV System- CDF of Yield calculated over 10 years

TABLE 10CASE 2 PV SYSTEM (112 KWP TWO-AXIS TRACKER ARRAY) CLIMATE

SIMULATION RESULTS

Parameter Result

Mean 249646 kWh Standard Deviation 8599 kWh (3.4%)TMY2 Prediction 252502 kWhActual Yield 2009* 257088 kWhModeled Yield 2009 249308 kWhModel Error -3.0%

*Oct. 2008-Sep. 2009

Using the previously discussed system derate factors (for Case 2) the model error for year 2009 is relatively small, -3.0%. The TMY2 predicted annual yield is slightly higher than the mean for this data. The inter-annual variability (or climate uncertainty) for this system is 3.4%.

J. CASE 2-Total Uncertainty and Exceedance Probability

The Case 2 system uncertainties are shown in Table 11 below. This data is shown in a bar graph in Figure 6.

TABLE 11CASE 2 PV SYSTEM (112 KWP TWO-AXIS TRACKER ARRAY) UNCERTAINTIES

Parameter Uncertainty

Solar Radiation (DNI) 15.8%Climate 3.4%Radiation and PV Module Submodels (SAM)

5.0 %

Inverter submodel (SAM) 1.0%Module Aging (2 years) 0.5%System Derate Factor 4.8%

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(total)Total Uncertainty (RSS) 17.6%

Fig. 6. Case 2 PV System- Uncertainties

The solar radiation (DNI) has the largest uncertainty. One of the biggest challenges for energy analysts is in finding more accurate DNI data for a specific site [26]. The uncertainty due to climate in this case is relatively small. There is more variation due to climate in both GHI and DNI for coastal and mountain locations than in central plain locations similar to this site in Toledo, Spain.

In order to estimate the P50 and P90 exceedance probability for this case we need to first estimate the mean annual energy yield for year 3 (2011). If we assume the same module degradation rate (0.5%/yr) then after 2 years of operation, our new mean will be 249646 kWh- 1% or 247150 kWh. This value will be our P50 value for this system for 2011-see Table 12. With an uncertainty of 17.6%, the P90 value will be 191297 kWh. A graph of exceedance probability for this system is shown in Figure 7 along with the P50 and P90 values.

TABLE 12CASE 2 PV SYSTEM EXCEEDANCE PROBABILITY , UNCERTAINTY 17.6%

Parameter Annual Energy Yield

P50 (2011) 247150 kWhP90 (2011) 191297 kWh

Fig. 7. Case 2 PV System- Exceedance Probability

VI. CONCLUSION

This paper shows how one can estimate the uncertainty in the annual energy production of a grid-tied PV system. One of the key elements in this estimation is what values the energy analyst decides to employ for the different system derate factors. The fact that this choice is subjective is problematic. In a blind study done in 2010, 20 energy analysts using 7 models analyzed a given PV system. This resulted in 20 different estimates for the annual energy yield [27]. This can lead to a lack of credibility on the part of investors and other decision makers when deciding on funding a large PV system. As energy analysts, we need to develop better guidelines on what values to use for the system derate factors. We could gather data, based on the actual performance of different PV systems in different locations, to determine what values to use. Ideally, this database of actual systems could be used to define the system derate factors in PV simulation tools, using statistical methods. This would reduce the uncertainty in the estimated yield from different analysts and modelers.

Another area of concern is the uncertainty in the estimation of the solar resource. DNI uncertainty can be 20% or more. Some modelers use several sources of DNI data and take a weighted average in an attempt to minimize this uncertainty. We need access to more accurate data on the solar resource if we are to reduce the uncertainty in the projected energy performance of a PV system.

ACKNOWLEDGMENT

The author would like to thank the following people for their help in completing this study. Paul Gilman at NREL helped my understanding in the use of SAM. Didier Thevenard at Numerical Logics provided the SAM file he used for performing Monte Carlo uncertainty simulations of a PV system. Brian Dougherty and Matthew Boyd at NIST provided key information on the NIST PV system. Carlos

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Garcia at Titan Tracker provided utility bill data on the Toledo, Spain PV system. Charles Khuen at Weather Analytics provided the solar radiation weather data for the Toledo, Spain site.

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