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EE462L, Spring 2014PV Arrays (Solar Panels)
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Electrical Properties of a Solar Cell
n-type
p-type
– V +
I
Photons
Junction
External circuit (e.g., battery,
lights)
Isc – V +
I
)1( BVeA
External circuit (e.g., battery,
lights)
)1( BVeA
0
5
0.0 0.6Diode VoltsD
iode
Am
ps
Diode current
)1( BVeA
)1( BVsc eAII
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I-V Curve
V
I
Isc
Voc
Im
Vm
, where A, B, and especially Isc vary with solar insolation
0
0
Increasing solar insolation
mm IVP max
Maximum power point
)1( BVsc eAII
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• 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 acommon configuration
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100524.034.5)( 1777.0 VeVI
PV Station 13, Bright Sun, Dec. 6, 2002
0
1
2
3
4
5
6
0 5 10 15 20 25 30 35 40 45
V(panel) - volts
I - a
mp
s
I-V Curve
Isc
Voc
Isc
Pmax at approx. 30V
Pmax 0.7 • Voc • Isc
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The Maximum Power Point
PV Station 13, Bright Sun, Dec. 6, 2002
0.0
20.0
40.0
60.0
80.0
100.0
120.0
140.0
0 5 10 15 20 25 30 35 40 45
V(panel) - volts
P(p
an
el)
- w
att
s
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)
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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
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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)
zenithsun
azimuthsun
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.
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Solar Noon
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Sun Moves Throughout the Year
June 21
December 21
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Sun Moves from Summer to Winter
Solar Zenith versus Azimuth at Austin
22nd Day of Jun, Jly, Aug, Sep, Oct, Nov, Dec(Sun hrs/day. Jun=13.9,Jly=13.6,Aug=12.8,Sep=12.0,Oct=11.0,Nov=10.3,Dec=10.0)
0
10
20
30
40
50
60
70
80
90
0 30 60 90 120 150 180 210 240 270 300 330 360
Azimuth (South = 180)
Ze
nit
h (
De
gre
es
fro
m V
ert
ica
l)
Jun
Dec
Sep
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Sun Moves From Winter to Summer
Solar Zenith versus Azimuth at Austin
22nd Day of Dec, Jan, Feb, Mar, Apr, May, Jun(Sun hrs/day. Dec=10.0,Jan=10.3,Feb=11.0,Mar=12.0,Apr=12.8,May=13.6,Jun=13.9)
0
10
20
30
40
50
60
70
80
90
0 30 60 90 120 150 180 210 240 270 300 330 360
Azimuth (South = 180)
Ze
nit
h (
De
gre
es
fro
m V
ert
ica
l)
Dec
Jun
Mar
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Panel Orientation is Important
June 21
December 21
March 21September 21
Equator
Tropic of CancerLatitude 23.45o
Tropic of CapricornLatitude -23.45o
Austin’s Latitude: 30o
23.45o
23.45o
30o
Edge of PV module
Earth’s surface
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Panel Orientation is Important
tiltpanel
Line perpendicular to horizontal plane
tiltpanel
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°
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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
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Keep Solar Radiation Monitor Lenses Clean!
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Computing Incident Power
)cos(
)(zenithsun
estDHGH
DHDN
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
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Computing Incident Power, cont.
incident
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.
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Computing Incident Power, cont.
panelincidentzenithsun
incident ADHGH
DHP
)cos(
)cos(
)(
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
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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
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Weather Forecast
http://www.nws.noaa.gov/forecasts/graphical/sectors/southplains.php#tabs
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Panel Pairs Connected to Power Lab
Voltage at Panels
Voltage at Lab Bench
Panel Current
Use these two
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Use a Variable Power Resistor to Sweep thePanel I-V Curve
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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
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PV Station Isc= 5.340E+00 I = Isc − A(exp(BVpanel) − 1)A= 5.241E-03B= 1.777E-01 di/dv R(v)
Vpanel Vload I I equation (I error)^2 Ppanel = VI P equation equation equation39 0 -1.818E-02 0.00033 0.0 -0.7 -9.31E-04 1073.635 2.65 2.710E+00 0.003654 92.8 94.9 -9.31E-04 1073.630 4.3 4.262E+00 0.00148 129.0 127.8 -9.31E-04 1073.625 4.95 4.899E+00 0.002558 123.8 122.5 -9.31E-04 1073.620 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 1073.60.009338
282726252423222120191817161514
PV Station, Bright Sun
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1
2
3
4
5
6
0 5 10 15 20 25 30 35 40 45
V(panel) - volts
I -
am
ps
Use the Excel Solver to Curve Fit Your Measurements
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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
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Solar Radiation in Texas
AVERAGE DIRECT NORMAL INSOLATION MAP LEGEND
per YEAR COLOR 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
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Multiply by panel efficiency, e.g. 0.14, to get electrical output
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clock noon
solar noon
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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 panels
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In recent years, financial incentives have acted like catalysts to increase PV power penetration
and to bring solar panels costs down
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• 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)
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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,
2/)cos()cos(
)(mW
DHGHDHP incidentzenith
sunincident
,
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
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Sun Zenith Angle (Top Curve), and Incident Angle on Panel (Bottom Curve), for Dec. 16
(Panel Tilt and Azimuth = 60 and 225 Degrees, Respectively)
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5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
11 11.5 12 12.5 13 13.5 14 14.5 15 15.5 16 16.5 17
Hour of Day
Deg
rees
Global Horizontal (Top Curve), and Diffuse Horizontal (Bottom Curve), for Dec. 16
0
50
100
150
200
250
300
350
400
450
500
550
600
650
11 11.5 12 12.5 13 13.5 14 14.5 15 15.5 16 16.5 17
Hour of Day
Wat
ts P
er S
qu
are
Met
er
Zenith
Incident
GH
DH