1. The document discusses photovoltaic (solar) panels, including their electrical properties, I-V curves, how multiple cells are connected in series or parallel arrays, and factors that affect panel output like orientation, tilt angle, and solar insolation. 2. Key specifications of solar panels like open circuit voltage (Voc) and short circuit current (Isc) are defined, and equations are provided to calculate the maximum power point based on the I-V curve. 3. Important variables for solar energy production are discussed, including direct normal irradiance, global horizontal irradiance, diffuse horizontal irradiance, zenith angle, and angle of incidence on the panel surface.

1. 1
EE462L, Spring 2014
PV Arrays (Solar Panels)

2. 2
Electrical Properties of a Solar Cell
n-type
p-type
–
V
+
I
Photons
Junction
External circuit
(e.g., battery,
lights)
Isc
–
V
+
I
)1( −BV
eA
External circuit
(e.g., battery,
lights)
)1( −BV
eA
0
5
0.0 0.6Diode Volts
DiodeAmps
Diode current
)1( −BV
eA
)1( −−= BV
sc eAII

3. 3
I-V Curve
V
I
Isc
Voc
Im
Vm
, where A, B, and especially Isc vary with solar insolation
0
0
Increasing
solar insolation
Maximum
power point

4. 4
• 36 Cells in Series Make a 12V-Class Panel (Voc ≈ 19V)
• Two 12V-Class Panels in Series Make a 24V-Class Array (Voc ≈ 38V)
9 cells x 4 cells is a
common configuration

5. 5
( )100524.034.5)( 1777.0
−−= V
eVI
I-V Curve
Isc
Voc
Isc
Pmax at approx. 30V
Pmax ≈ 0.7 • Voc • Isc

6. 6
The Maximum Power Point
P=0 at short circuit P=0 at open circuit
Pmax
On a good solar day in Austin, you get about
1kWh per square meter of solar panels
(corresponds to about 150W rated)

7. 7
Earth’s Poles
• Magnetic poles: Created by Earth’s magnetic field
Can be located with a compass
They move along Earth’s surface!
• Celestial poles: Created by Earth’s rotation.
They are two imaginary stationary points in the sky.
Important for PV system applications.
Geological Survey of Canada

8. 8
Where is the Sun?
Figure 4. Sun Zenith and Azimuth Angles
West
North
(x axis)
Line perpendicular to
horizontal plane
East
(y axis)
Horizontal plane
Up (−z axis)
Note – because of magnetic declination,
a compass in Austin points
approximately 6º east of north.
Series of equations to get zenith and azimuth angles – see pp. 5-7 in lab doc.

9. 9
Solar Noon

10. 10
Sun Moves Throughout the Year
June 21
December 21

11. 11
Sun Moves from Summer to Winter
Jun
Dec
Sep

12. 12
Sun Moves From Winter to Summer
Dec
Jun
Mar

13. 13
Panel Orientation is Important
June 21
December 21
March 21
September 21
Equator
Tropic of Cancer
Latitude 23.45o
Tropic of Capricorn
Latitude -23.45o
Austin’s Latitude: 30o
23.45o
23.45o
30o
Edge of
PV module
Earth’s surface

14. 14
Panel Orientation is Important
Line perpendicular to horizontal plane
Horizontal plane
Figure 6. Panel Tilt Angle
Line perpendicular to panel surface
Edge of panel
• Best all-year tilt = Latitude
• Best winter tilt = Latitude + 15°
• Best summer tilt = Latitude – 15°

15. 15
Solar Radiation Monitors
Rotating Shadowband Pyranometers
Measure GH and DH
NREL Sci Tec Two-Axis Tracker Measures
DN, GH, and DH
GH (Global Horizontal W/m2
): Sensor points
straight up, sees entire sky, including sun disk
DH (Diffuse Horizontal W/m2
): Once per
minute, band quickly swings over, shadow falls
on sensor. Then, sensor sees entire sky, less
sun disk.
DN (Direct Normal W/m2
): Tracking device
points toward sun and sees only the sun disk

16. 16
Keep Solar Radiation Monitor Lenses Clean!

17. 17
Computing Incident Power
)cos(
)(
zenith
sun
est
DHGH
DHDN
θ
−
+=
Direct normal (DN), global horizontal (GH), and diffuse horizontal (DH), all
in W/m2
, are the three important components of solar radiation. DN can be
estimated from GH and DH.
DH: Measured sky on
shadowed horizontal sensor
(excludes disk of sun)
GH: Measured sky on horizontal
sensor (includes disk of sun)
(GH − DH): Est. disk of sun
component on horizontal
sensor
Est. disk of sun component on
sensor pointed toward sun
DN: Est. total sky on
sensor pointed
toward sun

18. 18
Computing Incident Power, cont.
incidentβ
The angle of incidence is the angle between the sun’s rays and a vector
normal to the panel surface (0° means that the sun’s rays are
perpendicular to the panel surface)
Series of equations to get angle of incidence – see pp. 11-12 in lab doc.

19. 19
Computing Incident Power, cont.
panelincidentzenith
sun
incident A
DHGH
DHP •








•
−
+= )cos(
)cos(
)(
β
θ
The incident solar radiation, in kW, on a panel surface is approximated by
About 14% is
converted to
electricity
Est. disk of sun component on
sensor pointed toward sun
Measured sky on shadowed
horizontal sensor (excludes
disk of sun)
Est. disk of sun component
on panel surface
Multiply by
surface area
Est. Watts on
panel surface

20. 20
Panels Atop ENS
All panels atop ENS have azimuth angle = 190o
View Facing Front of ENS Panels (i.e., looking toward north)
(Note – areas shown are for individual panels, so for a pair, double the values shown)
Station 18
BP
Station 19
BP
Station 18
BP
Station 17
BP
Station 16
Solarex
Station 16
Solarex
Station 19
BP
Station 17
BP
Station 15
Solarex
Station 15
Solarex
Station 21
Photowatt
Station 21
Photowatt
Area of each
panel is 0.54m2
Area of each
panel is 0.52m2
Area of each
panel is 0.60m2
Station 20
BP
Area of this
panel is 1.04m2
80W each
150W
85W each
85W each
Disconnected

21. 21
Weather Forecast
http://www.nws.noaa.gov/forecasts/graphical/sectors/southplains.php#tabs

22. 22
Panel Pairs Connected to Power Lab
Voltage at
Panels
Voltage at
Lab Bench
Panel
Current
Use these two

23. 23
Use a Variable Power Resistor to Sweep the
Panel I-V Curve

24. 24
Record, Plot, and Visually Inspect the
I-V Data Points as You Take Them
•Take the open circuit voltage reading
with no load connected
•Adjust the power resistor, backing
down in integer volts in two volt steps
(e.g. 38V, 36V, 34V, … ) until about
25V, while taking the current readings
•At about 25V, continue to back
down in integer volts, but in five
volt steps, while taking the current
readings
•Take the short circuit current and
panel voltage reading
Reminder - Hand plot as you
take your data points

25. 25
PV Station Isc= 5.340E+00 I = Isc − A(exp(BVpanel) − 1)
A= 5.241E-03
B= 1.777E-01 di/dv R(v)
Vpanel Vload I I equation (I error)^2 Ppanel = VI P equation equation equation
39 0 -1.818E-02 0.00033 0.0 -0.7 -9.31E-04 1073.6
35 2.65 2.710E+00 0.003654 92.8 94.9 -9.31E-04 1073.6
30 4.3 4.262E+00 0.00148 129.0 127.8 -9.31E-04 1073.6
25 4.95 4.899E+00 0.002558 123.8 122.5 -9.31E-04 1073.6
20 5.15 5.162E+00 0.000138 103.0 103.2 -9.31E-04 1073.6
4 5.3 5.334E+00 0.001178 21.2 21.3 -9.31E-04 1073.6
0.009338
28
27
26
25
24
23
22
21
20
19
18
17
16
15
14
PV Station, Bright Sun
0
1
2
3
4
5
6
0 5 10 15 20 25 30 35 40 45
V(panel) - volts
I-amps
Use the Excel Solver to Curve Fit Your Measurements

26. 26
0
5
10
15
20
25
30
35
40
0 0.5 1 1.5 2
Seconds
Voltage
Current
I - V
0
1
2
3
4
5
6
0 10 20 30 40
Power
0
20
40
60
80
100
120
140
0 0.5 1 1.5 2
Seconds
Automated way to get I-V curve:
• Suddenly connect panel to large
discharged C (like 5 or 10 of the DBR
C’s),
• Capture I and V data points on a
scope, save to a floppy, and read the
file with Excel,
• Replot I versus V,
• Replot P versus time to get max P

27. 27
Solar Radiation in Texas
AVERAGE DIRECT NORMAL INSOLATION MAP LEGEND
per YEARCOLOR
KEY
per day
(kWh/m2
-day) (MJ/m2) (quads/100 mi2
)
<3.0 <3,940 <1.0
3.0 - 3.5 3,940 - 4,600 1.0 - 1.1
3.5 - 4.0 4,600 - 5,260 1.1 - 1.3
4.0 - 4.5 5,260 - 5,910 1.3 - 1.5
4.5 - 5.0 5,910 - 6,570 1.5 - 1.6
5.0 - 5.5 6,570 - 7,230 1.6 - 1.8
5.5 - 6.0 7,230 - 7,880 1.8 - 1.9
6.0 - 6.5 7,880 - 8,540 1.9 - 2.1
6.5 - 7.0 8,540 - 9,200 2.1 - 2.3
>7.0 >9,200 >2.3

28. 28

29. 29
Multiply by panel
efficiency, e.g. 0.14, to
get electrical output

30. 30
clock noon
solar noon

31. 31
Solar analysis of Sept. 25, 2006. Assume panels are at 30º tilt, 180º azimuth. Incident kWH on 1m2
panel (approx.
150W rated) is 7.02kWH. Multiplying by 0.14 efficiency yields 0.98 kWH. That corresponds to about 6.6kWH per 1kW
rated of solar panels (1000*0.98/150). Thus, if a (non-air conditioned) house consumes 20 kWH per day, then about
3kW of panels are needed. Using $2.5 per W, which inflates to about $7.0 per W with mounting and electronics, then
the 3 kW of panels cost about $21K. Consider an average price of electricity for residential users of 11 cents/kWH (TX
is about average). So cost of electricity each day is about $2.1. Hence, it will take close to 3 years to pay the solar

32. 32
In recent years, financial incentives have acted
like catalysts to increase PV power penetration
and to bring solar panels costs down

33. 33
• Other factors affecting PV use effectiveness and return of investment:
- Air conditioner impact
- PV panel orientation (SW is better during the summer because it
tends to maximize generation when air conditioner consumption is
maximum)

34. 34
December 16 was a brilliant solar day here in Austin. Consider a PV installation that has 60º tilt,
and 225º azimuth (i.e., facing southwest). Use the following equation,
,
and the graphs on the following page to estimate
5a. the maximum incident solar power density on the panels (in W/m2), and
5b. the time at which the maximum occurs.
Practice Problem

35. 35
Zenith
Incident
GH
DH