The document discusses a solar resource lab where students learn to: 1. Forecast seasonal and daily solar insolation levels using clear-sky models and validate with measurements. 2. Estimate errors in their models by comparing to pyrheliometer and pyranometer readings. 3. Identify sources of error and derive optimal parameter estimates to improve their models.

1. Solar Resource Lab
Learning Goal
• Students will be able to understand sources of
variation in insolation, construct insolation
forecasting models, validate these models with solar
radiation measurements, and gain an appreciation
for solar forecasting as an intriguing challenge for the
design of renewable energy systems.
Learning Outcome
• Forecast seasonal and daily variation in insolation on
a collector surface using clear-sky insolation theory.
• Estimate model error using pyrheliometer and
pyranometer measurements.
• Propose plausible sources of error in model and
derive optimal parameter estimates.
• Predict the quantity and timing of insolation losses
due to obstructions using site maps and sun-path
diagrams.

2. P1) The component of insolation that
has the most insolation during clear-
sky conditions is
1. Diffuse
2. Direct-beam
3. Reflected

3. P2) Solar altitude angle is
1. The angle between the incoming direct sunlight and
a plane normal to the earth’s surface.
2. The angle between the incoming direct sunlight and
the equator.
3. The angle between due south and the location of an
obstruction to a solar collector.

4. P3) Applying clear-sky insolation
theory during cloudy conditions
1. may underestimate optical depth and result in an
overestimate of direct insolation.
2. may underestimate the sky diffuse factor and result
in an underestimate of diffuse insolation.
3. may overestimate the air mass ratio and result in
an underestimate of direct insolation.
4. Both 1 and 2.

5. P4) The pyrheliometer measurements (blue line)
represent what component(s) of insolation ?
1. Direct
2. Diffuse
3. Direct + Diffuse + Reflected

6. Clear-Sky Insolation Theory

9. PyranometerPyrheliometer

10. PyranometerPyrheliometer
kW/m2

13. Lat/Lon = 37.414319/-122.057944
http://maps.google.com/?ie=UTF8&ll=37.414319,-122.057944&spn=0.000392,0.000603&t=h&z=21

14. Tools and Data
• Clear-sky insolation theory (Masters, 2004)
• Google maps : 37.414319,-122.0579 Lat / Lon
http://maps.google.com/?ie=UTF8&ll=37.414319,-122.057944&spn=0.000392,0.000603&t=h&z=21
• Sun path diagram (Appendix B)
• UCSC Tracker
– Online tracker controller (Use from my computer)
– Archived daily insolation (10/15/10, 10/17/10)

15. 1. Compare the archived insolation data on 10/15/2010 with your
prediction based on clear-sky insolation calculations. Complete the
table below (each team pick a different time) and discuss the
differences.
2. Discuss which parameters could be adjusted to improve the fit of the
model. Adjust these parameters in your model for solar noon to
improve fit to the data and report the optimal adjustment.
3. Compare the observations and calculations from #1 with expected
values based on insolation data in the appendix of Masters (2004).
Quantity Symbol
Day Number n
Latitude, deg. L
Collector azimuth, deg φc
Collector tilt Σ
Solar time, 24 hr ST
Hour angle H
Declination,deg δ
Altitude angle β
Solar azimuth φs
Air mass ratio m
Appar.ET fluxW/m2 A
Optical depth k
Beam radiation, W/m2 IB
Incidence angle cos(θ)
Beam on collector, W/m2 IBC
Sky diffuse factor C
Diffuse rad on collector, W/m2 IDC
Adding Reflected
Reflectance ρ
Reflec. Rad on collector W/m2 IRC
Total I (IBC+IDC+IRC) W/m2 IC

16. 4. Use Google maps and a sun-path diagram to estimate the timing of
obstructions in the afternoon.
5. Does your sun-path diagram analysis agree with the measured data?
6. What percent of the potentially collected energy is lost during January,
June and October in the afternoon?

17. 1. Compare the archived insolation data on 10/15/2010 with what insolation
values you would predict from calculations by completing the following
table.

18. Measured vs. Predicted
• Total insolation is similar between measurements and predictions
• However the model does a poor job of predicting the partitioning to direct and
diffuse insolation
0
200
400
600
800
1000
6 7 8 9 10 11 12 13 14 15 16 17 18
Appendix
Simulated Direct
Simulated Total
Class - Total
Class - Direct

19. 2. Comment on the reason for the difference and on what parameter
adjustments might be required to obtain a better match.
1. Larger optical depth (k) to get less direct.
2. Larger sky diffuse factor (C) to get more diffuse
0
200
400
600
800
1000
1200
Measured Model (k = 0.171, C = 0.092) Model (k = 0.45, C = 0.75)
Insolation(W/m^2)
Total
Direct
Diffuse

20. 3. Compare the observations and calculations from #1 with expected values
based on Appendix of your text book. 996 kW/m2 (Appendix C: Hourly
clear-sky Insolation Tables).
0
200
400
600
800
1000
6 7 8 9 10 11 12 13 14 15 16 17 18
Appendix
Simulated Direct
Simulated Total

21. 4. Use Google maps and a sun-path diagram to estimate the timing of
obstructions in the afternoon.
Azimuth of obstruction (φ): Altitude angle of obstruction (β):
φ = -tan-1(Y/X) = -58°
φX
Y
Z
Height (H) roughly 9 meters
β = tan-1(H/Z) = 72°

22. 4. Use Google maps and a sun-path diagram to estimate the timing of
obstructions in the afternoon.
5. Does your sun-path diagram analysis agree with the measured data?

23. 6. What percent of the potentially collected energy is lost during October
and June due to obstructions in the afternoon?
October: 10% loss in daily energy due to afternoon obstructions
June: 45% loss in daily energy due to afternoon obstructions

24. The component of insolation that has
the most insolation during clear-sky
conditions is
1. Diffuse
2. Direct-beam
3. Reflected

25. Solar altitude angle is
1. The angle between the incoming direct sunlight and
a plane normal to the earth’s surface.
2. The angle between the incoming direct sunlight and
the equator.
3. The angle between due south and the location of an
obstruction to a solar collector.

26. Applying clear-sky insolation theory
during cloudy conditions
1. may underestimate optical depth and result in an
overestimate of direct insolation.
2. may underestimate the sky diffuse factor and result
in an underestimate of diffuse insolation.
3. may overestimate the air mass ratio and result in
an underestimate of direct insolation.
4. Both 1 and 2.

27. The pyrheliometer measurements (blue line)
represent what component(s) of insolation ?
1. Direct
2. Diffuse
3. Direct + Diffuse + Reflected

28. Anonymous Survey
http://www.surveymonkey.com/s/R6WT33Z