IRRADIANCE MODELING VARIANCE ON VERTICAL PLANE OF ARRAY
SURFACES
Scott Burger
Dept. of Energy & Mineral Engineering
The Pennsylvania State University
263 MRL Building
scottburger1090@gmail.com
Lucas Witmer
Dept. of Energy & Mineral Engineering
The Pennsylvania State University
263 MRL Building
LWitmer@psu.edu
Jeffrey R. S. Brownson*
Dept. of Energy & Mineral Engineering
The Pennsylvania State University
265 MRL Building
University Park, PA 16802
solarpower@psu.edu
ABSTRACT
1. INTRODUCTION
Significant radiative transfer occurs outside of
buildings, yet energy control systems are typically
signaled by internal air temperature thermostats. As
façades essentially behave as flat plate solar thermal
collectors, while windows permit rooms to behave as
cavity collectors, we propose that buildings may
perform at higher economic efficiency with external
signals. An analysis of measured irradiation for plane of
array (POA) vertical surfaces was compared to modeled
irradiance data (TRNSYS) to evaluate differences in
error. The measured POA irradiation data integrates
all irradiation components for a given orientation,
collected on minute intervals for half of the year
between the months of July and December. The data
were available for the East, West, and North surfaces of
the Energy Efficient Buildings Hub’s Building 101 in
the Philadelphia Navy Yard. Modeled data was
generated from global horizontal irradiation from a
meteorological station in Avondale, Pennsylvania,
located thirty three miles from the Philadelphia Navy
Yard. Comparative analyses between irradiation data
averaged over each hour and irradiance collected from
Avondale, PA resulted in a weighted mean error of 36
W/m2 or 26%. Results align with findings of
Gueymard (2010), particularly at minute interval time
steps that are necessary for building controls.
Accurate Plane of Array (POA) irradiance
measurements collected by sensors are valuable in the
solar resource evaluation of a given site. Sometimes it
can be advantageous to mount sensors along the plane
of array (at an angle or vertically), and roofs or vertical
walls have slopes which require sensor mounting at
angles far from horizontal. We propose that the
information a set of POA sensors provides is useful for
efficient building controls responding to changes in the
outside environment.
Fig. 1: Image of Building 101 and its East wall .[1]
Component-based irradiance data, such as beam and
diffuse radiation, can be collected by a pyrheliometer or
a shadowband radiometer, but this data is relatively
expensive and not readily available for most
locations.[2] Global irradiance data is more widely
available and can be used to calculate the irradiation
components (beam and diffuse) by various methods
1
such as the Perez Model.[3] However, these correlation
models are subject to errors from the spread in the
data. When examining a diffuse fraction versus
clearness index plot of real data, the potential for error
is evident. The accuracy of the correlation declines as
the data time step decreases as well.[2] The team of
Orehounig, Dervishi, and Mahdavi at the University of
Vienna in Austria found these errors to be on the order
of about ±20% in the best of conditions.[4] The
Transient System Simulation tool (TRNSYS) is used to
process the solar irradiation onto surfaces by the Perez
model. The results are then output in parallel with the
measured POA data.[5]
The locale of data collection is within the Philadelphia
Naval Yard, where the current research operations for
the US Dept. of Energy’s supported Energy Efficient
Buildings Hub (EEB Hub) is located, lead by the
Pennsylvania State University. The EEB Hub is a
catalyst for improving building energy efficiency with
the goal of reducing commercial building energy use by
20% by 2020. It also promotes economic growth and
job creation in the Navy Yard.
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the North, East, and West vertical walls. Figure 2
shows the orientation of the building along a
North-South axis. Remote shortwave irradiation data
was collected from a meteorological station
approximately 33 miles west of the Navy Yard.
2. METHODS
2.1 Data Processing and TRNSYS
The remote data source for correlation analysis was
collected from the National Oceanic and Atmospheric
Administration (NOAA) meteorological station in
Avondale, PA, located approximately 33 miles west of
the Philadelphia Navy Yard. The data was adjusted for
this geographic difference, but short term differences
created by scattered clouds or microclimatic difference
are not accounted for. Over time steps of one hour, the
impact of these differences is assumed to be small.
Global horizontal shortwave irradiation data (GHI) was
downloaded from the Avondale weather station for use
with model correlations as a comma-separated values
(CSV) file.[6] Due to the large quantity of irradiation
data, each month of the year was downloaded
separately rather than as one large data set for the
entire year.
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Fig. 3: TRNSYS screen shot of the simulation studio for
the Avondale and Building 101 data
The measured POA (vertical) data from Building 101
must also be downloaded. The irradiance values
incident on the East, West, and North walls on minute
intervals of Building 101 were downloaded from the
EEB Hub’s website.[1] The irradiance data from the
EEB Hub sensors are in units of W/m2 .
Fig. 2: Plan view of Building 101 with sensor locations
in blue. Google Earth Imagery
The measured on-site POA data was acquired from
Building 101 (B101) in the Navy Yard. Figure 1 shows
a bird’s-eye view of B101 in the Navy Yard from the
East. On the second floor of B101, LI-COR LI200X-L
silicon photodiode pyranometers have been mounted on
With the data in tabulated files, Microsoft Excel
macros were developed to process the data for easy
import into TRNSYS. Both data sets were reviewed for
gaps and corrected by interpolation, typically occurring
during the nights. The TRNSYS model employed two
data readers (Type 9c), a radiation processor (Type
16a), a unit conversion routine, and an output
component. Figure 3 displays the TRNSYS simulation
studio layout with the combined functions for Avondale
and Building 101.
2
GHI
Irradiance and Errors - Week of July 12, 2012 - [W/m^2]
1000
800
600
400
200
0
East Error
400
200
0
-200
-400
West Error
400
200
0
-200
-400
North Error
400
200
0
-200
-400
7/12/12
7/13/12
7/14/12
7/15/12
7/16/12
7/17/12
7/18/12
Fig. 4: Building 101 errors assess for GHI and POA during the week of July 12-July 18, 2012
2.2 Error Calculation and Graphical Approach
3. RESULTS
The output from the TRNSYS model yields tabulated
measured irradiance data from Building 101 and
modeled data from Avondale, where the vertical surface
irradiance is estimated by component derivation from
Avondale GHI. The differential irradiance and error
between the measured and modeled data for each wall
was calculated using Equations 1 and 2, respectively.
Using the difference in irradiance, percent error, and
global horizontal irradiance for each month, data for
each wall was combined into a single tabulated file.
From that set, the lower quartile, minimum, median,
upper quartile, maximum, and mean at each hour for
each wall was evaluated, as well as GHI. Using
Equation 3, weighted averages were calculated for each
wall, where x is the data set and w the weighted value.
Diff = Measured − Modeled
Measured − Modeled
Modeled
Pn
xi wi
x̄ = Pi=1
n
i=1 wi
%Error =
(1)
(2)
(3)
With the weighted averages for each wall, the mean
irradiance was estimated on each wall and summed.
Using Equation 3 again, the weighted mean error and
the weighted mean percent error was also calculated.
Box and whisker plots were generated for each wall to
show the error values, or residuals, during each hour of
the day for each month analyzed, offering a new
perspective on the hourly distributions of error.
Figure 4 demonstrates the daily residual errors between
the modeled values and the measured POA data. The
top line of daily GHI is the source data from Avondale
during a select clear sky week. The residual differences
between measured and modeled vertical surface
irradiance for the East, West, and North façades are
represented below that primary GHI set. Repetitive
errors of a sinusoidal over/under prediction can be
observed each morning in the East, each afternoon for
the West, and for both periods to the North.
From detailed single-day inspections, the modeled
vertical surface irradiation for Avondale was found to
be similar yet not equivalent to the measured Building
101 data. Figure 6 shows a day’s comparison between
measured POA data and modeled data from Avondale,
using the example of a sunny day in July. Figure 7
displays an example of an alternate cloudy day in July.
Of the three sensors on Building 101, the West sensor
was found to be partially shaded at times in November
and December from nearby deciduous trees. The North
sensor was also within close proximity to a large
decidous tree located to the Northeast of the sensor,
while the East sensor was located in a transition shade
region by building wing-wall interference located
Southeast of the pyranometer (see Figure 2). Figure 5
shows the transition time in October where the East
sensor starts in full sun all morning and ends the month
shaded by a building wing during most of the morning.
Hence, the East sensor is completely shaded for the
month of December and half of January, but is not
shaded by the building wing-wall from the beginning of
March through early October. Phenomena such as this
were delivered strong biases and skewing of the error
3
Building 101 Measured Data - East Wall
Irradiance (W/m^2)
800
700
600
500
400
300
200
100
0
Oct 1
Oct 4
Oct 5
Oct 11
Oct 22
Fig. 5: Building 101 East sensor data for select clear days during the month of October, showing a transition from
fully exposed to partially shaded.
data analyses for different months and times of the day.
1000
900
B101 Vertical Surface Irradiance Data vs. Modeled
(one July day, modeled data are dashed lines)
North (B101 Data)
Solar Irradiance [W/m^2]
800
North (Modeled)
East (B101 Data)
700
East (Modeled)
West (B101 Data)
600
West (Modeled)
500
400
300
200
increase in the morning in both magnitude and skew as
time progresses from July to December. This is due to
the significant shading that obscures the East sensor
during the 10am hour in October and most of the day
in both November and December. The positive
residuals earlier in the day in July and August followed
by negative residuals approaching noon show a trend
that could be due to surrounding objects that may
reflect or absorb more or less irradiance than is
predicted by the correlation model.
100
0
4920
4926
4932
4938
4944
Hour of the year
Fig. 6: A sunny day on July 6, modeled data is dashed,
measured data is solid.
1000
900
B101 Vertical Surface Irradiance Data vs. Modeled
(one cloudy July day, modeled data are dashed lines)
North (B101 Data)
Solar Irradiance [W/m^2]
800
North (Modeled)
East (B101 Data)
700
East (Modeled)
West (B101 Data)
600
West (Modeled)
500
400
300
200
100
0
4776
4782
4788
4794
4800
Hour of the year
Fig. 7: An cloudy day on July 20, modeled data is
dashed, measured data is solid.
Figures 8, 9, and 10 provide a detailed and highly
informative perspective on the evolution of hourly error
among each of the three Building 101 vertical surfaces.
The box and whisker plots show the hourly spread of
data for each month analyzed, from July 2012 through
December 2012. In certain cases the maximum
observed point was outside the bounds of the
standardized plots–the values were then labelled on the
graphs.
Figure 9 shows residuals from the West sensor that are
larger in the afternoon at specific times (August) and
seem to shift from positive to negative at different
times throughout the year without much of a trend.
This is likely due to a large deciduous tree located to
the West of the building that obscures the West sensor
at certain times of the day for different months.
Additionally, as the leaves fall off in the Autumn
months and are not present in November and
December, the magnitude of the residuals is decreased.
Figure 10 shows residuals from the North sensor with a
trend in July and August where the residuals are
negative in the morning and positive in the afternoon.
Here, there is a tree located near the North East corner
of the building that sometimes obscures the North
sensor. Due to the rotation of the building of 6 degrees
West of North, in July and August the correlation
model anticipates the sensor to see some beam
irradiation in the morning and be shaded in the
afternoon. However, because of the tree, the sensor is
in shade in the morning, and sees some reflection off of
the tree in the afternoon. In the later months, August
through December, the residuals are negative showing
that the tree is simply making it even darker on the
North side than the model is anticipating.
Figure 8 shows residuals from the East sensor that
4
July West Wall
July East Wall
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November East Wall
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December East Wall
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Fig. 8: Monthly box and whisker plots of the residuals
of hourly irradiance on the east sensor on Building 101.
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Fig. 9: Monthly box and whisker plots of the residuals
of hourly irradiance on the west sensor on Building 101.
5
July North Wall
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Residual (W/m²)
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4. CONCLUSION
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Measured irradiance on the plane of array for building
surfaces offers different results than are obtained by
modeled correlations from global horizontal irradiance.
Trends and biases in the errors show certain objects
near to the building that both increase and decrease
incident irradiance depending on the time of year and
the time of day. Some of the more significant errors can
be accounted for in future work through more accurate
modeling that includes the surrounding objects (e.g.
trees) and their material properties. However, without
an advanced energy model accounting for accurate
surroundings, errors on the order of hundreds of watts
per meter squared were observed.
Such detailed energy models are atypical, far outside of
the normal commissioning, operation, and maintenance
of a commercial building due to expense. Use of local
sensors that report actual shading conditions upon a
building are actually more useful in this case, as a
shaded region will lead to a reduced energy gains for
entire zones of the building, and require control
response to maintain a comfortable indoor
environment. Solar irradiation varies significantly on a
building’s many surfaces based on the environment and
surrounding objects. This case study shows how local
plane of array irradiance data can be informative to a
building control system.
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November North Wall
The Energy Efficient Buildings HUB of the Greater
Philadelphia Innovation Cluster at the Philadelphia
Navy Yard, a U.S. Department of Energy Innovation
Hub.
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5. ACKNOWLEDGMENTS
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The Pennsylvania State University, the College of Earth
and Mineral Sciences, and the John and Willie Leone
Family Department of Energy and Mineral Engineering.
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6. REFERENCES
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Fig. 10: Monthly box and whisker plots of the residuals
of hourly irradiance on the north sensor on Building 101.
(1) Energy Efficient Building Hub (2012), URL
http://cloud.cdhenergy.com/bldg101/ (2)
Gueymard, C. A. (2009) “Direct and indirect
uncertainties in the prediction of tilted irradiance for
solar engineering applications, Solar Energy, 83, pp.
432444 (3) Duffie, J. A. and W. A. Beckman (2006)
Solar Engineering of Thermal Processes, 3rd ed., John
Wiley and Sons, Inc. (4) Orehounig, K., S. Dervishi,
and A. Mahdavi (2011) “Comparison of Computed and
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Measured Irradiance on Building Surfaces, Proceedings
of Building Simulation 2011: 12th Conference of
International Building Performance Simulation
Association, Sydney, 14-16 November (5) The Transient
System Simulation Tool (2013), URL
http://www.trnsys.com/ (6) NOAA US Climate
Reference Network (2012), URL
http://www.ncdc.noaa.gov/crn/report
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