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

1. 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 solar
photovoltaic (PV) system is the solar resource assessment. This II.FACTORS AFFECTING PV ENERGY YIELD
assessment is usually performed by an energy analyst and
involves characterizing the available solar resource and the A.Solar Radiation
local meteorology. The next step may be to determine what size PV energy yield is directly related to the amount of solar
and 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 a
of the annual energy yield of these systems requires the use of moment one can deduce that there is more annual solar
PV simulation tools. This paper examines the uncertainty in the radiation at the earth’s equator than at the poles. So
annual energy yield of a PV system using one of these tools- geographical location has a direct affect on the amount of
System Advisor Model (SAM), developed by National solar radiation available at a site. The other factor that affects
Renewable Energy Laboratory. Using published uncertainty solar radiation is climate. A predominantly cloudy location
data 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 of
meteorological data at the site, and an estimation of the overall In order to estimate the energy yield of a PV system one
system derate factor error, this report attempts to quantify the must acquire at least one year’s worth of weather data for the
total uncertainty in annual energy yield. Two case studies where site. However, in order to estimate the effects of inter-annual
actual energy yield data is well documented are evaluated. A variability of the solar radiation on energy yield, at least 10
method for calculating the exceedance probability-the years worth of data is required [1]. Also, although the
likelihood that the annual energy yield will exceed a given weather data may be defined as a “Typical Meteorological
probability- is shown. The purpose of this paper is to give
Year,” the data may not represent the mean or average year
energy analysts a better understanding of the sources of
uncertainty (and their relative magnitude) when using PV in terms of the amount of solar radiation [2]. The simulation
simulation 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 [3]-[4].
Index Terms—Photovoltaic systems, Power system
simulation, 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 parameters
I 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
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
performance of the system itself is. Unfortunately, there is for the solar module model and the inverter model so these
significant uncertainty in both of these areas. These parameters do not need to be estimated. However, there are
uncertainties are a major concern of developers of large some parameters, known as “system derate factors” that must
commercial or utility scale systems. This paper first be estimated by the analyst and may be system dependent
examines the parameters that can affect overall energy yield and/or site dependent [5]. The following is a list of system
of a PV system. It reviews the tool used to simulate two types derate factors found within SAM, the simulation tool used in
of 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 that
relevant for each system. One of the key concepts to learn yield PV modules with slightly different current-voltage
from 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 from
These simulation parameters -also known as system derate voltage drops across diodes used to block the reverse
factors- 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 wiring
Energy Solutions, Aromas, CA 95004 USA phone: 831-726-9197; (e-mail:
dave@parkerenergysolutions.com).
between modules and the wiring connecting the PV array
to the inverter.

2. JPV-2011-07-0052-R 2
4) 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 the
6) Nameplate - accounts for the accuracy of the simulation of PV systems [10]. The tool used in this report is
manufacturer's nameplate rating. the System Advisor Model, previously known as the Solar
7) AC Wiring - accounts for resistive losses in the wiring Advisor Model [11]. 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 parameters
10) 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 cost
the popular PVwatts on-line simulation tool [6]. In SAM, of energy, peak and annual system efficiency and other
these 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 radiation
their 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 on
Mismatch 98 System a plane that is always perpendicular (or facing) the sun. Total
Diodes & 99.5 No* is also referred to as Global Horizontal Irradiance (GHI).
Connections This is the total amount of radiation received by a horizontal
DC wiring 98 System
Soiling 95 System & Site surface. Diffuse is referred to as Diffuse Horizontal
Sun Tracking** 100 No* Irradiance (DHI). This is the background radiation coming
Nameplate*** 100 No* from the sky and surroundings. Fixed panel PV systems rely
AC wiring 99 No*
Transformer 100 (no transformer) System mostly on GHI, while PV tracking systems use DNI. The
Shading 100 System & Site weather data file always contains all three solar radiation
Availability 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 Array
typical. (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 ° 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
• Radiation model inputs are Total and Beam
model the recommended default is 100 because the model
takes into account the module nameplate accuracy [8]. • Radiation model is Perez 1990
What does system or site dependent mean? As an example, • Module model is Sandia PV Array Performance Model
if we look at mismatch, this is system dependent because this • Inverter model is Sandia Performance Model
parameter would be much higher, typically 99.5 % if micro- • No shading
inverters were used on each module instead of a central The version of SAM used for this study is 2011.5.4.
inverter [9]. Soiling is dependent on where the system is- a
dusty, high traffic area would adversely affect soiling- as IV.MEASURES OF UNCERTAINTY
well 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 are
assumed to be negligible for both PV systems examined.
However, in the interest of completeness, shading uncertainty SX
is estimated to be 2%. This value assumes no significant
CV = _
shading between the hours of 9 AM and 3 PM and a shading X
tool was employed in the site assessment. Shading tool

3. 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 silicon
is the mean [12]. For example, the uncertainty in the annual Modules per string 13
GHI of a site over a 10 year period would be the standard Strings in parallel 18
Array peak power 35.1 kW
deviation 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/A
expressed in percentages. Uncertainties are added by the System physical location Lat: 39.14 °
Long: -77.22°
Root Sum Square (RSS) method [13]. 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 monthly
uncertainty values because these are readily available and
B.CASE 1-System Derate Factors
because the author is hesitant to extrapolate from monthly to
yearly 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 Uncertainty
system 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 0.5
axis trackers. In each case a complete system description is DC wiring 98 1
given first. For the uncertainty analysis in each case, we Soiling 92* 4
review: 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 [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
Fig. 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%. [8]. These values are based on using the
This grid-tied PV system is located on the roof of the submodels specified previously and the PV module
National Institute of Standards and Technology campus in technology (single-crystal or multi-crystalline). Other
Gaithersburg, MD. The system annual energy data used for technologies such as amorphous thin-film may have higher
this study was recorded from Nov. 2001 until Oct. 2002 [14]. uncertainty and/or should be modeled with a different
The 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-often
Inverter Trace/Xantrex Model PV-30208 used weather data available to the energy analyst is data

4. JPV-2011-07-0052-R 4
estimated from satellite-derived models. The data used for E.CASE 1-Total Uncertainty and Exceedance Probability
Case 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. An
2005. The station used is a class 1, # 724060, Baltimore explanation of the module ageing parameter is in order. If
Washington International Airport station [18]. This is we assume a degradation rate of 0.5% per year with an
approximately 28 miles from the physical location of the PV uncertainty of 0.25% per year, then after 9 years the modules
system. 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 [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 TABLE 5
TMY3 data for the site. The results are shown in Figure 2. CASE 1 PV SYSTEM (35 KWP FIXED ARRAY ) UNCERTAINTIES
Table 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 4.9
Fig. 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 Result
Mean 33941 kWh 0 2 4 6 8 10 12 14
Standard Deviation 1773 kWh (5.2%)
%
TMY2 Prediction 35057 kWh
TMY3 Prediction 35576 kWh Fig. 3. Case 1 PV System- Uncertainties
Actual Yield 2002* 35676 kWh
Modeled Yield 2002 35370 kWh As can be seen by Figure 3, the solar radiation and climate
Model Error -0.9%
uncertainties are the largest contributors to the system total
*Nov. 2001-Oct. 2002 uncertainty. It should be noted that, even though some
Using the previously discussed system derate factors the components of the uncertainties are not linear, the radiation
model error for year 2002 is quite small, -0.9%. In other model in this case, and some components may not have a
words, 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 valid
annual yields are much higher than the mean for this data. method to estimate the total uncertainty. Reference [13]
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%) in
reasons. One is to find the true mean or average annual yield. this case? If we take the mean value of the annual energy
The other is to find the standard deviation in the data in order yield from table 4 and subtract the module degradation loss
to determine the inter-annual variability. The inter-annual due to ageing (-0.5% per year for 9 years or -4.5% of 33941
variability (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

5. JPV-2011-07-0052-R 5
12.5% of 32413 kWh from this value we get 28361 kWh. F.CASE 2-System Description
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 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 kWh
P90 (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
[21]. 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 [21].
kWh
G.CASE 2-System Derate Factors
Fig. 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.

6. JPV-2011-07-0052-R 6
**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 Fig. 5. Case 2 PV System- CDF of Yield calculated over 10 years
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 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 kWh
NSRDB ±8.6% ±15% Standard Deviation 8599 kWh (3.4%)
NASA SSE ±8.7% ±20.93% TMY2 Prediction 252502 kWh
WA ±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 (for
performed 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 higher
The results are shown in Figure 5. Table 10 summarizes the than the mean for this data. The inter-annual variability (or
key 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%

7. 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 300000
Fig. 6. Case 2 PV System- Uncertainties kWh
Fig. 7. Case 2 PV System- Exceedance Probability
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. VI.CONCLUSION
There is more variation due to climate in both GHI and DNI This paper shows how one can estimate the uncertainty in
for coastal and mountain locations than in central plain the annual energy production of a grid-tied PV system. One
locations 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 system
probability for this case we need to first estimate the mean derate factors. The fact that this choice is subjective is
annual energy yield for year 3 (2011). If we assume the same problematic. In a blind study done in 2010, 20 energy
module degradation rate (0.5%/yr) then after 2 years of analysts using 7 models analyzed a given PV system. This
operation, our new mean will be 249646 kWh- 1% or 247150 resulted in 20 different estimates for the annual energy yield
kWh. This value will be our P50 value for this system for
[27]. This can lead to a lack of credibility on the part of
2011-see Table 12. With an uncertainty of 17.6%, the P90
investors and other decision makers when deciding on
value will be 191297 kWh. A graph of exceedance
probability for this system is shown in Figure 7 along with funding a large PV system. As energy analysts, we need to
the 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 statistical
P50 (2011) 247150 kWh
P90 (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

8. JPV-2011-07-0052-R 8
Toledo, Spain PV system. Charles Khuen at Weather Analyses,” presented at American Solar Energy Society Conference,
May 17-20, 2011, Raleigh, North Carolina, USA.
Analytics provided the solar radiation weather data for the
[26] D. Renné, R. George, S. Wilcox, T. Stoffel, D. Myers, and D. Heimiller,
Toledo, Spain site. “Solar Resource Assessment,” National Renewable Energy Laboratory,
Golden, CO NREL/TP-581-42301 February 2008.
REFERENCES [27] J.S. Stein, “Design of PV Systems: Model Accuracy and Limitations,”
presented at a Utility/Lab workshop on PV Technology and Systems,
[1] S. Wilcox and C.A. Gueymard, “Spatial and Temporal Variability of the Nov. 8-9, 2010, Tempe, Arizona.
Solar Resource in the United States,” presented at American Solar
Energy Society Conference, May 15-22, 2010, Phoenix, Arizona, USA ,
Paper ASES-47760.
[2] S.R. Dean, “Quantifying the Variability of Solar PV Productions
Forecasts,” presented at American Solar Energy Society Conference,
May 15-22, 2010, Phoenix, Arizona, USA , Paper ASES-045
[3] W. Marion and K. Urban, “User’s Manual for TMY2s,” National
Renewable Energy Laboratory, Golden, CO June 1995.
[4] S. Wilcox and W. Marion, “User’s Manual for TMY3 datasets,”
National Renewable Energy Laboratory, Golden, CO
NREL/TP-581-43156 May 2008.
[5] M.A. Abella and F. Chaunlo, “Estimación de la Energía Generada por
un Sistema Fotovoltaico conectado a red,” Centro de Investigaciones
Energéticas, Medioambientales y Técnicas, (CIEMAT), Laboratorio de
Sistemas Fotovoltaicos, Madrid, Spain, 2006.
[6] PVwatts changing parameters:
(http://www.nrel.gov/rredc/pvwatts/changing_parameters.html)
[7] Titantracker two-axis solar trackers:
(http://www.titantracker.com/v_portal/apartados/apartado.asp?te=58)
[8] C.P. Cameron, W.E. Boyson and D.M. Riley, “Comparison of PV
System Performance-Model Predictions with Measured PV System
Performance,” Sandia National Laboratories, Albuquerque, NM 2008.
[9] PV Watts Calculation Values for an Enphase Micro-inverter System,
Application Note, Enphase Energy, Petaluma, CA, 2008.
[10] G.T. Klise and J.S. Stein, “Models Used to Assess the Performance of
Photovoltaic Systems,” Sandia National Laboratories, Albuquerque,
NM Rep SAND2009-8258, Dec. 2009.
[11] System Advisor Model:
(https://www.nrel.gov/analysis/sam/)
[12] R.M. Bethea, B.S. Duran and T.L. Boullion, Statistical Methods for
Engineers and Scientists, New York, NY: Marcel Dekker, 1985, pp.
105-106.
[13] D. Thevenard, “Uncertainty in Long-Term Photovoltaic Yield
Predictions,” presented to Natural Resources Canada, Varennes, QC
March 2010.
[14] A.H. Fanney, K.R. Henderson and E.R. Weise, “Measured Performance
of a 35kW Roof Top Photovoltaic System,” presented at International
Solar Energy Conference, March 15-18, 2003, Hawaii, USA , Paper
ISEC2003-44230.
[15] M. Garcia, L. Marroyo, E. Lorenzo, and M. Pérez, “Soiling and other
optical losses in solar tracking PV plants in Navarra,” Progress in
Photovoltaics:Research and Applications, vol. 19, issue 2, pp 211-217,
Jul. 2010.
[16] B. Dougherty, National Institute of Standards and Technology (NIST),
Gaithersburg, MD, private communication, May 2011.
[17] C.R. Osterwald, J. Adelstein, J.A. del Cueto, B. Kroposki, D. Trudell,
and T. Moriarty, “Comparison of Degradation Rates of Individual
Modules held at Maximum Power,” National Renewable Energy
Laboratory (NREL), Golden, CO 2006.
[18] S. Wilcox, et al, “National Solar Radiation Database 1991-2005 Update:
User’s Manual,” National Renewable Energy Laboratory, Golden, CO
NREL/TP-581-41364 April 2007.
[19] D.R. Meyers, S. Wilcox, W. Marion, R. George, and M. Anderberg,
“Broadband Model Performance for an Updated National Solar
Radiation Database in the United States of America,” National
Renewable Energy
[20] H. Klug, “What does Exceedance Probabilities P90-P75-P50 Mean?”,
DEWI Magazin Nr 28, Feb. 2006.
[21] C. Garcia, “Informe de Producción Planta Torrijos-I Seguimiento a dos
ejes,” unpublished.
[22] C. Garcia, Titan Tracker, Toledo, Spain, private communication, May
2011.
[23] Weather Analytics: (http://weatheranalytics.com/company.html)
[24] S. Saha et al, “The NCEP Climate Forecast System Reanalysis”:
(http://cfs.ncep.noaa.gov/cfsr/docs/)
[25] J. Keller, C. Khuen and C.A. Gueymard, “A New Web-Based Data
Delivery System to Provide Global Support for Solar Site Selection