JPV-2011-07-0052-R 1 Estimating Uncertainty in the Projected Annual Energy Yield of a Photovoltaic System David F. Parker, Member, IEEE under consideration. Abstract— The first step in the planning of any solarphotovoltaic (PV) system is the solar resource assessment. This II.FACTORS AFFECTING PV ENERGY YIELDassessment is usually performed by an energy analyst andinvolves characterizing the available solar resource and the A.Solar Radiationlocal meteorology. The next step may be to determine what size PV energy yield is directly related to the amount of solarand type PV system to propose based on financial,environmental, and other factors. Producing accurate estimates radiation available at the site. If we ignore local climate for aof the annual energy yield of these systems requires the use of moment one can deduce that there is more annual solarPV simulation tools. This paper examines the uncertainty in the radiation at the earth’s equator than at the poles. Soannual energy yield of a PV system using one of these tools- geographical location has a direct affect on the amount ofSystem Advisor Model (SAM), developed by National solar radiation available at a site. The other factor that affectsRenewable Energy Laboratory. Using published uncertainty solar radiation is climate. A predominantly cloudy locationdata for the submodels used within SAM, the uncertainty of the will have less solar radiation than a location with clear skies.meteorological data, the inter-annual variability ofmeteorological data at the site, and an estimation of the overall In order to estimate the energy yield of a PV system onesystem derate factor error, this report attempts to quantify the must acquire at least one year’s worth of weather data for thetotal uncertainty in annual energy yield. Two case studies where site. However, in order to estimate the effects of inter-annualactual energy yield data is well documented are evaluated. A variability of the solar radiation on energy yield, at least 10method for calculating the exceedance probability-the years worth of data is required . Also, although thelikelihood that the annual energy yield will exceed a given weather data may be defined as a “Typical Meteorologicalprobability- is shown. The purpose of this paper is to give Year,” the data may not represent the mean or average yearenergy analysts a better understanding of the sources ofuncertainty (and their relative magnitude) when using PV in terms of the amount of solar radiation . The simulationsimulation tools to predict the annual energy yield of a PV tool used in this study accepts three types of weather files,system. TMY2, TMY3, and EPW -. Index Terms—Photovoltaic systems, Power systemsimulation, Measurement uncertainty, Solar energy B.PV System Performance Once the amount of solar radiation is determined, the performance of the PV system itself -in terms of energy I.INTRODUCTION conversion efficiency- determines how much energy is supplied to the utility grid. There are numerous parametersI N order to estimate the annual energy yield of a grid-tied photovoltaic (PV) system, the energy analyst needs toknow how much solar radiation is available and what the 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 toolperformance of the system itself is. Unfortunately, there is for the solar module model and the inverter model so thesesignificant uncertainty in both of these areas. These parameters do not need to be estimated. However, there areuncertainties are a major concern of developers of large some parameters, known as “system derate factors” that mustcommercial or utility scale systems. This paper first be estimated by the analyst and may be system dependentexamines the parameters that can affect overall energy yield and/or site dependent . The following is a list of systemof a PV system. It reviews the tool used to simulate two types derate factors found within SAM, the simulation tool used inof PV systems that are later examined in this report. It then this study:describes the two systems and shows what parameters are 1) Mismatch - accounts for manufacturing tolerances thatrelevant for each system. One of the key concepts to learn yield PV modules with slightly different current-voltagefrom this study is that one must consider different value characteristics.simulation parameters for different types of PV systems. 2) Diodes and Connections - accounts for losses fromThese simulation parameters -also known as system derate voltage drops across diodes used to block the reversefactors- will also depend on the site chosen for the PV system flow of current and from resistive losses in electrical connections. Manuscript received June 6, 2011. David F. Parker is the owner of Parker 3) DC Wiring - accounts for resistive losses in the wiringEnergy Solutions, Aromas, CA 95004 USA phone: 831-726-9197; (e-mail:firstname.lastname@example.org). between modules and the wiring connecting the PV array to the inverter.
JPV-2011-07-0052-R 24) Soiling - accounts for dirt, snow, and other foreign vendors are hesitant to publish uncertainty data for their matter on the surface of the PV module that prevent products. However, in the author’s experience with these solar radiation from reaching the solar cells. tools, 2% uncertainty seems reasonable.5) Sun Tracking - accounts for losses for one- and two-axis tracking systems when the tracking mechanisms do not III.SYSTEM ADVISOR MODEL (SAM) keep the PV arrays at the optimum orientation. There are many computer-based tools available for the6) Nameplate - accounts for the accuracy of the simulation of PV systems . The tool used in this report is manufacturers nameplate rating. the System Advisor Model, previously known as the Solar7) AC Wiring - accounts for resistive losses in the wiring Advisor Model . The National Renewable Energy between the inverter and the connection to the local Laboratory (NREL) with Sandia National Laboratories utility service. develops this program for the Department of Energy (DOE).8) Transformer – accounts for transformer-related losses This program can be considered a “black box” where one when a transformer is used. provides inputs such as geographical location, weather data,9) Aging - accounts for performance losses over time system costs, components such as solar module quantity, type because of weathering of the PV modules. and model, inverter type and model, and system parameters10) Availability - accounts for times when the system is off such as module tilt and orientation. The program then because of maintenance or inverter or utility outages. performs an hour-by-hour simulation for a complete year These system derate factors are the same factors used in (8760 hours) and outputs system energy yield, levelized costthe popular PVwatts on-line simulation tool . In SAM, of energy, peak and annual system efficiency and otherthese factors are treated as a percent while in PVwatts they performance metrics.are treated as a fraction. Table 1 lists these factors along with Within SAM, the analyst has a choice of five radiationtheir recommended default values. models, three (PV) module models, and two inverter models. The radiation models can accept the weather solar radiation TABLE I data as Beam and Diffuse, Total and Beam, or Total and SYSTEM DERATE FACTORS Diffuse. In this context, Beam is also called Direct Normal System or Site Factor Default Value (%) dependent? Irradiance (DNI). This is the amount of radiation received onMismatch 98 System a plane that is always perpendicular (or facing) the sun. TotalDiodes & 99.5 No* is also referred to as Global Horizontal Irradiance (GHI).Connections This is the total amount of radiation received by a horizontalDC wiring 98 SystemSoiling 95 System & Site surface. Diffuse is referred to as Diffuse HorizontalSun Tracking** 100 No* Irradiance (DHI). This is the background radiation comingNameplate*** 100 No* from the sky and surroundings. Fixed panel PV systems relyAC wiring 99 No*Transformer 100 (no transformer) System mostly on GHI, while PV tracking systems use DNI. TheShading 100 System & Site weather data file always contains all three solar radiationAvailability 100 System values, GHI, DNI, and DHI. However, SAM only uses two,Ageing 0.5/yr System & Site as noted above, when passing this data into the radiation*In a properly designed and installed system, these values are model. The radiation model calculates the Plane Of Arraytypical. (POA) irradiance using two of the three radiation values. The **For fixed mount systems the default value is 100. Also, SAM settings used for this study are:for modern tracking systems such as the Case 2 system here,the trackers have a positional accuracy of less than 0.01 ° sotracking accuracy is not an issue .***The default value in PVwatts is 95. However, in SAMwhen using either the Sandia or the 5-parameter PV module • Radiation model inputs are Total and Beammodel the recommended default is 100 because the modeltakes into account the module nameplate accuracy . • Radiation model is Perez 1990 What does system or site dependent mean? As an example, • Module model is Sandia PV Array Performance Modelif we look at mismatch, this is system dependent because this • Inverter model is Sandia Performance Modelparameter would be much higher, typically 99.5 % if micro- • No shadinginverters were used on each module instead of a central The version of SAM used for this study is 2011.5.4.inverter . Soiling is dependent on where the system is- adusty, high traffic area would adversely affect soiling- as IV.MEASURES OF UNCERTAINTYwell as the type of system. A system on two-axis trackers For this study, the key measure of uncertainty (or variability)will have less soiling than a fixed mount system because of is the Coefficient of Variation or CV. The CV is defined as:the movement and tilt of the array. Shading losses areassumed to be negligible for both PV systems examined.However, in the interest of completeness, shading uncertainty SXis estimated to be 2%. This value assumes no significant CV = _shading between the hours of 9 AM and 3 PM and a shading Xtool was employed in the site assessment. Shading tool
JPV-2011-07-0052-R 3 Inverter size 30 kW _ Transformer 208V delta-480V wye (30 KVA) where SX is the standard deviation of the sample and X PV Modules Siemens SP150 Module Technology single-crystal siliconis the mean . For example, the uncertainty in the annual Modules per string 13GHI of a site over a 10 year period would be the standard Strings in parallel 18 Array peak power 35.1 kWdeviation of the 10 annual GHI values divided by the mean Tilt 0 degrees (horizontal)of the 10 GHI values. All the uncertainties in this report are Azimuth N/Aexpressed in percentages. Uncertainties are added by the System physical location Lat: 39.14 ° Long: -77.22°Root Sum Square (RSS) method . In terms of solar Weather data location Lat: 39.167 °radiation, uncertainty may be expressed in hourly, daily, Long: -76.683°monthly, or annual intervals. In this study we use monthlyuncertainty values because these are readily available and B.CASE 1-System Derate Factorsbecause the author is hesitant to extrapolate from monthly toyearly values because of seasonal bias differences. For Case 1, the estimated system derate factors and the uncertainty in those factors are shown in table 3 below. TABLE 3 V.CASE STUDIES CASE 1 SYSTEM DERATE FACTORS In this study we review two grid-tied PV systems. One Factor Estimated Value (%) Estimated Uncertaintysystem is a fixed roof mounted commercial size system and (%)the other is a small utility scale system mounted on five two- Mismatch 98 1 Diodes & Connections 99.5 0.5axis trackers. In each case a complete system description is DC wiring 98 1given first. For the uncertainty analysis in each case, we Soiling 92* 4review: Sun Tracking 100 0 Nameplate 100 0• The values chosen for the system derate factors and the AC wiring 99 0.5 uncertainty in those factors. Transformer 98* 0.5• Uncertainty in the simulation model. Shading 100 2 Availability 100 1• The solar resource, both in terms of annual climate Ageing** 0.5/yr 0.25/yr variability and in terms of the estimation of the resource Total Derate Factor 4.9 itself. Uncertainty (RSS) * These values are different than the recommended default.• Calculation of the total uncertainty and exceedance **Ageing is considered separately later in this analysis and is NOT included probability. in the Total Derate Factor Uncertainty. A value of 92% was chosen for the soiling derate factor A.CASE 1-System description 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 . 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 andFig. 1. Part of the NIST PV System in Gaithersburg, MD. (CASE 1) PV module model is estimated to be 5%. The inverter model uncertainty is 1%. . These values are based on using theThis grid-tied PV system is located on the roof of the submodels specified previously and the PV moduleNational Institute of Standards and Technology campus in technology (single-crystal or multi-crystalline). OtherGaithersburg, MD. The system annual energy data used for technologies such as amorphous thin-film may have higherthis study was recorded from Nov. 2001 until Oct. 2002 . uncertainty and/or should be modeled with a differentThe components of the system are listed in Table 2. submodel in SAM. D.CASE 1-Solar Resource Uncertainties TABLE 2 35 KWP FIXED ARRAY COMPONENT LIST (CASE 1) As noted before, solar resource uncertainty involves both Component Type uncertainty due to climate-year to year variability-and uncertainty in the weather database used. The most-oftenInverter Trace/Xantrex Model PV-30208 used weather data available to the energy analyst is data
JPV-2011-07-0052-R 4estimated from satellite-derived models. The data used for E.CASE 1-Total Uncertainty and Exceedance ProbabilityCase 1 is from the National Solar Radiation Database The Case 1 system uncertainties are shown in Table 5(NSRDB) and includes 15 years of hourly data from 1991 to below. This data is shown in a bar graph in Figure 3. An2005. The station used is a class 1, # 724060, Baltimore explanation of the module ageing parameter is in order. IfWashington International Airport station . This is we assume a degradation rate of 0.5% per year with anapproximately 28 miles from the physical location of the PV uncertainty of 0.25% per year, then after 9 years the modulessystem. A study in 2005 reported the uncertainty in the have degraded 4.5% ±2.25%.NSRDB as ±8.6% for GHI and ±15% for DNI . For theCase 1 system we will use the GHI uncertainty since this is afixed mount array. In order to estimate the effects of climate variability, weperformed a parametric simulation in SAM using the 15years of NSRDB data. We also looked at TMY2 data and TABLE 5TMY3 data for the site. The results are shown in Figure 2. CASE 1 PV SYSTEM (35 KWP FIXED ARRAY ) UNCERTAINTIESTable 4 summarizes the key findings. Parameter Uncertainty Solar Radiation (GHI) 8.6% Climate 5.2% Radiation and PV Module 5.0 % Submodels (SAM) Inverter submodel (SAM) 1.0% Module Aging (9 years) 2.25% System Derate Factor (total) 4.9% Total Uncertainty (RSS) 12.5% Uncertainties- 35kW Fixed Solar Radiation (GHI) 8.6 climate 5.2 Radiation & Module 5 Models Inverter Model 1 Ageing (Year 10) 2.25 System Derate total 4.9Fig. 2. Case 1 PV System- CDF of Yield calculated over 15 years TABLE 4 CASE 1 PV SYSTEM (35 KWP FIXED ARRAY ) CLIMATE SIMULATION RESULTS Total uncertainty 12.5 Parameter ResultMean 33941 kWh 0 2 4 6 8 10 12 14Standard Deviation 1773 kWh (5.2%) %TMY2 Prediction 35057 kWhTMY3 Prediction 35576 kWh Fig. 3. Case 1 PV System- UncertaintiesActual Yield 2002* 35676 kWhModeled Yield 2002 35370 kWh As can be seen by Figure 3, the solar radiation and climateModel Error -0.9% uncertainties are the largest contributors to the system total*Nov. 2001-Oct. 2002 uncertainty. It should be noted that, even though someUsing the previously discussed system derate factors the components of the uncertainties are not linear, the radiationmodel error for year 2002 is quite small, -0.9%. In other model in this case, and some components may not have awords, the simulation predicts a slightly lower annual yield normal distribution, such as solar radiation, the Root-Sum-than what was measured. The TMY2 and TMY3 predicted Square method (RSS) of adding these uncertainties is a validannual yields are much higher than the mean for this data. method to estimate the total uncertainty. Reference This data shows that the energy analyst must use at least 10 demonstrates this.years of Actual Meteorological Year (AMY) data for two What is the meaning of the total uncertainty (12.5%) inreasons. One is to find the true mean or average annual yield. this case? If we take the mean value of the annual energyThe other is to find the standard deviation in the data in order yield from table 4 and subtract the module degradation lossto determine the inter-annual variability. The inter-annual due to ageing (-0.5% per year for 9 years or -4.5% of 33941variability (or climate uncertainty) for this system is 5.2%. 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
JPV-2011-07-0052-R 512.5% of 32413 kWh from this value we get 28361 kWh. F.CASE 2-System DescriptionRecall that this 12.5% represents one standard deviation. Sothere is a 66% likelihood that this year (Year 2011), thissystem 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 ofreaching a higher or lower annual energy production is 50:50.The P90 value is that annual energy yield value where therisk of NOT reaching it is 10% . For this PV system, foryear 2011, the P90 value is 27228 kWh. A graph ofexceedance probability for this system is shown in Figure 4below. The P50 and P90 values are shown. Notice that thisgraph is a mirror image of the cumulative distributionfunction (CDF) because, for exceedance probability, onesubtracts the cumulative probability from one in order to getthe exceedance probability. TABLE 6 CASE 1 PV SYSTEM EXCEEDANCE PROBABILITY , UNCERTAINTY 12.5% Fig. 5. This photo is of a two-axis tracker of a similar system to the five- Parameter Annual Energy Yield tracker system in Toledo, Spain (CASE 2)P50 (2011) 32413 kWhP90 (2011) 27228 kWh 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 . The components of the system are listed in Table 7. TABLE 7 Exceedance Probability of Annual Energy Yield (2011) 112 KWP TWO-AXIS TRACKER ARRAY COMPONENT LIST (CASE 2) P90 P50 100% Component Type 90% Inverter INGETEAM INGECON SUN 100 Inverter size 100 kW 80% Transformer N/A Exceedance Probability 70% PV Modules* Kyocera 190-GHT-2 Module Technology multi-crystalline silicon 60% Modules per string** 19 Strings in parallel 31 50% Array peak power 111.9 40% Tilt dual-axis trackers Azimuth dual-axis trackers 30% System physical location Lat: 39.98 ° 20% Long: -4.29° Weather data location Lat: 39.806 ° 10% Long: -4.063° *In SAM, the PV module modeled is an Evergreen ES-190. 0% 26000 28000 30000 32000 34000 36000 38000 ** In SAM, the total number of modules is 589. The system production document specified 590 modules . kWh G.CASE 2-System Derate FactorsFig. 4. Case 1 PV System- Exceedance Probability For Case 2, the estimated system derate factors and the uncertainty in those factors are shown in Table 8 below. TABLE 8 CASE 2 SYSTEM DERATE FACTORS Estimated Uncertainty Factor Estimated Value (%) (%) Mismatch 98 1 Diodes & Connections 99.5 0.5 DC wiring 98 1 Soiling 95 4 Sun Tracking 100 0 Nameplate 100 0 AC wiring 99 0.5 Transformer 100 0 Shading 100 2 Availability 99* 1 Ageing** 0.5/yr 0.25/yr Total Derate Factor 4.8 Uncertainty (RSS) * These values are different than the recommended default.
JPV-2011-07-0052-R 6**Ageing is considered separately later in this analysis and is NOT includedin the Total Derate Factor Uncertainty. The availability value (99%) was chosen based on theadditional maintenance time required for the two-axistrackers. A value of 95% (the default) was chosen for thesoiling derate factor because, although the modules aremounted on dual-axis trackers, the system relies on naturalprecipitation for module cleaning . Note that for thissystem there is no distribution transformer. H.CASE 2-Simulation Model Uncertainties The simulation model uncertainties are the same as in Case1, above. The combined Radiation model and PV modulemodel uncertainty is estimated to be 5%. The inverter modeluncertainty is 1%. I.CASE 2-Solar Resource Weather Analytics (WA) provided 10 years (2000-2009) ofAMY data for the Toledo, Spain site, ID # 579220 .Weather Analytics also included a TMY file for the site. Thisdata is derived from the National Oceanic and AtmosphericAdministration/ National Centers for EnvironmentalPrediction/ Climate Forecast System Reanalysis data sets(NOAA/NCEP/CFSR) . This solar radiation data has an Fig. 5. Case 2 PV System- CDF of Yield calculated over 10 yearsuncertainty of ±4.8% for GHI and ±15.8% for DNI . Thisamount of uncertainty is consistent with the publisheduncertainty of other satellite-derived modeled data such asthe National Aeronautics and Space Administration Surfacemeteorology and Solar Energy (NASA SSE) data set. SeeTable 9 for a comparison of the different data sets. TABLE 10 CASE 2 PV SYSTEM (112 KWP TWO-AXIS TRACKER ARRAY) CLIMATE SIMULATION TABLE 9 RESULTS SATELLITE DERIVED RADIATION DATA UNCERTAINTIES (MONTHLY) Parameter Result Data set GHI (%) DNI (%) Mean 249646 kWhNSRDB ±8.6% ±15% Standard Deviation 8599 kWh (3.4%)NASA SSE ±8.7% ±20.93% TMY2 Prediction 252502 kWhWA ±4.8% ±15.8% Actual Yield 2009* 257088 kWh Modeled Yield 2009 249308 kWh Model Error -3.0% For the Case 2 system we will use the DNI uncertainty,(±15.8%), since this is a two-axis tracker mounted array. *Oct. 2008-Sep. 2009 In order to estimate the effects of climate variability, we Using the previously discussed system derate factors (forperformed a parametric simulation in SAM using the 10 Case 2) the model error for year 2009 is relatively small,years of WA data. We also looked at TMY2 data for the site. -3.0%. The TMY2 predicted annual yield is slightly higherThe results are shown in Figure 5. Table 10 summarizes the than the mean for this data. The inter-annual variability (orkey findings. 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 11 CASE 2 PV SYSTEM (112 KWP TWO-AXIS TRACKER ARRAY) UNCERTAINTIES Parameter Uncertainty Solar Radiation (DNI) 15.8% Climate 3.4% Radiation and PV Module 5.0 % Submodels (SAM) Inverter submodel (SAM) 1.0% Module Aging (2 years) 0.5% System Derate Factor (total) 4.8% Total Uncertainty (RSS) 17.6%
JPV-2011-07-0052-R 7 Exceedance Probability of Annual Energy Yield (Year 3- P90 2011) P50 Uncertainties- 112kW Tracker 100% 90% Solar Radiation (DNI) 15.8 80% climate 3.4 Exceedance probability 70% Radiation & Module Models 5 60% Inverter Model 1 50% Ageing (Year 3) 0.5 40% System Derate total 4.8 30% 20% Total uncertainty 17.6 10% 0 5 10 15 20 0% % 180000 200000 220000 240000 260000 280000 300000Fig. 6. Case 2 PV System- Uncertainties kWh Fig. 7. Case 2 PV System- Exceedance Probability The solar radiation (DNI) has the largest uncertainty. Oneof the biggest challenges for energy analysts is in findingmore accurate DNI data for a specific site . Theuncertainty due to climate in this case is relatively small. VI.CONCLUSIONThere is more variation due to climate in both GHI and DNI This paper shows how one can estimate the uncertainty infor coastal and mountain locations than in central plain the annual energy production of a grid-tied PV system. Onelocations similar to this site in Toledo, Spain. of the key elements in this estimation is what values the In order to estimate the P50 and P90 exceedance energy analyst decides to employ for the different systemprobability for this case we need to first estimate the mean derate factors. The fact that this choice is subjective isannual energy yield for year 3 (2011). If we assume the same problematic. In a blind study done in 2010, 20 energymodule degradation rate (0.5%/yr) then after 2 years of analysts using 7 models analyzed a given PV system. Thisoperation, our new mean will be 249646 kWh- 1% or 247150 resulted in 20 different estimates for the annual energy yieldkWh. This value will be our P50 value for this system for . This can lead to a lack of credibility on the part of2011-see Table 12. With an uncertainty of 17.6%, the P90 investors and other decision makers when deciding onvalue will be 191297 kWh. A graph of exceedanceprobability for this system is shown in Figure 7 along with funding a large PV system. As energy analysts, we need tothe P50 and P90 values. develop better guidelines on what values to use for the system derate factors. We could gather data, based on the TABLE 12 actual performance of different PV systems in different CASE 2 PV SYSTEM EXCEEDANCE PROBABILITY , UNCERTAINTY 17.6% locations, to determine what values to use. Ideally, this Parameter Annual Energy Yield database of actual systems could be used to define the system derate factors in PV simulation tools, using statisticalP50 (2011) 247150 kWhP90 (2011) 191297 kWh 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 Garcia at Titan Tracker provided utility bill data on the
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