Transcript Electrical Properties of a Solar Cell

EE462L, Spring 2014
PV Arrays (Solar Panels)
1
Electrical Properties of a Solar Cell
Photons
Junction
n-type
p-type
I
–
V
+
External circuit
(e.g., battery,
lights)
Diode current
5
A(e BV -1)
External circuit
(e.g., battery,
lights)
Diode Amps
Isc
–
V
+
BV
AA((eeBV --11))
I
0
I  I sc - A(e
BV
- 1)
0.0
Diode Volts
0.6
2
I-V Curve
I  I sc - A(e BV - 1) , where A, B, and especially Isc vary with solar insolation
I
Increasing
solar insolation
Isc
Maximum
power point
Im
Pmax  Vm I m
0
V
0
Vm
Voc
3
• 36 Cells in Series Make a 12V-Class Panel (Voc  19V)
9 cells x 4 cells is a
common configuration
• Two 12V-Class Panels in Series Make a 24V-Class Array (Voc  38V)
4
I-V Curve
Isc


I (V )  5.34 - 0.00524 e 0.1777 V - 1
PV Station 13, Bright Sun, Dec. 6, 2002
Isc
6
Pmax at approx. 30V
5
Pmax  0.7 • Voc • Isc
I - amps
4
3
2
1
0
0
5
10
15
20
25
V(panel) - volts
30
35
40
45
Voc
5
The Maximum Power Point
PV Station 13, Bright Sun, Dec. 6, 2002
140.0
Pmax
P(panel) - watts
120.0
100.0
80.0
60.0
40.0
20.0
P=0 at short circuit
P=0 at open circuit
0.0
0
5
10
15
20
25
30
35
40
45
V(panel) - volts
On a good solar day in Austin, you get about
1kWh per square meter of solar panels
(corresponds to about 150W rated)
6
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.
Geological Survey of Canada
They are two imaginary stationary points in the sky.
Important for PV system applications.
7
Where is the Sun?
Up (−z axis)
zenith
 sun
Line perpendicular to
horizontal plane
Horizontal plane
East
(y axis)
azimuth
 sun
North
(x axis)
West
Note – because of magnetic declination,
a compass in Austin points
approximately 6º east of north.
Figure 4. Sun Zenith and Azimuth Angles
Series of equations to get zenith and azimuth angles – see pp. 5-7 in lab doc.
8
Solar Noon
9
Sun Moves Throughout the Year
June 21
December 21
10
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)
Azimuth (South = 180)
0
30
60
90
120
150
180
210
240
270
300
330
360
0
Zenith (Degrees from Vertical)
10
Jun
20
30
Sep
40
50
60
Dec
70
80
90
11
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)
Azimuth (South = 180)
0
0
Zenith (Degrees from Vertical)
10
30
60
90
120
150
180
210
240
270
300
330
360
Jun
20
30
Mar
40
50
60
Dec
70
80
90
12
Panel Orientation is Important
Edge of
PV module
Austin’s Latitude: 30o
30o
Tropic of Cancer
Latitude 23.45o
June 21
23.45o
23.45o
March 21
September 21
Equator
Tropic of Capricorn
Latitude -23.45o
December 21
Earth’s surface
13
Panel Orientation is Important
 tilt
panel
Line perpendicular to horizontal plane
Line perpendicular to panel surface
Edge of panel
 tilt
panel
Horizontal plane
Figure 6. Panel Tilt Angle
• Best all-year tilt = Latitude
• Best winter tilt = Latitude + 15°
• Best summer tilt = Latitude – 15°
14
Solar Radiation Monitors
Rotating Shadowband Pyranometers
Measure 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.
NREL Sci Tec Two-Axis Tracker Measures
DN, GH, and DH
DN (Direct Normal W/m2): Tracking device
points toward sun and sees only the sun disk
15
Keep Solar Radiation Monitor Lenses Clean!
16
Computing Incident Power
GH: Measured sky on horizontal
sensor (includes disk of sun)
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.
(GH − DH): Est. disk of sun
DN est  DH 
(GH - DH )
zenith
cos( sun
)
DH: Measured sky on
shadowed horizontal sensor
(excludes 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
17
Computing Incident Power, cont.
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)
incident
Series of equations to get angle of incidence – see pp. 11-12 in lab doc.
18
Computing Incident Power, cont.
The incident solar radiation, in kW, on a panel surface is approximated by
Measured sky on shadowed
horizontal sensor (excludes
disk of sun)
Est. disk of sun component on
sensor pointed toward sun


(GH - DH )
Pincident   DH 
 cos(  incident )  A panel
zenith
cos( sun )


About 14% is
converted to
electricity
Est. disk of sun component
on panel surface
Est. Watts on
panel surface
Multiply by
surface area
19
Panels Atop ENS
85W each
Area of this
Area of each
Station 19
2
2
panel is 0.54m panel is 1.04m
BP
Disconnected
Area of each
panel is 0.52m2
Area of each
panel is 0.60m2
Station 17
BP
Station 21
Photowatt
Station 20
BP
Station 19
BP
Station 17
BP
Station 16
Solarex
Station 15
Solarex
Station 21
Photowatt
150W
Station 18
BP
Station 18
BP
Station 16
Solarex
Station 15
Solarex
80W each
All panels atop ENS have azimuth angle = 190o
85W each
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)
20
Weather Forecast
http://www.nws.noaa.gov/forecasts/graphical/sectors/southplains.php#tabs
21
Panel Pairs Connected to Power Lab
Voltage at
Panels
Voltage at
Lab Bench
Panel
Current
Use these two
22
Use a Variable Power Resistor to Sweep the
Panel I-V Curve
23
Record, Plot, and Visually Inspect the IV 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
Reminder - Hand plot as you
take your data points
• 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
24
Use the Excel Solver to Curve Fit Your Measurements
PV Station
Vpanel
Vload
I
39
35
30
25
20
4
0
2.65
4.3
4.95
5.15
5.3
I equation
-1.818E-02
2.710E+00
4.262E+00
4.899E+00
5.162E+00
5.334E+00
Isc=
5.340E+00
A=
5.241E-03
B=
1.777E-01
(I error)^2 Ppanel = VI P equation
0.00033
0.0
-0.7
0.003654
92.8
94.9
0.00148
129.0
127.8
0.002558
123.8
122.5
0.000138
103.0
103.2
0.001178
21.2
21.3
0.009338
I = Isc − A(exp(BVpanel) − 1)
di/dv
R(v)
equation equation
-9.31E-04
1073.6
-9.31E-04
1073.6
-9.31E-04
1073.6
-9.31E-04
1073.6
-9.31E-04
1073.6
-9.31E-04
1073.6
PV Station, Bright Sun
6
5
I - amps
4
3
2
1
0
0
5
10
15
20
25
V(panel) - volts
30
35
40
45
28
27
26
25
24
23
22
21
20
19
18
17
16
15
14
25
40
Automated way to get I-V curve:
35
• Suddenly connect panel to large
discharged C (like 5 or 10 of the DBR
C’s),
30
25
Voltage
20
Current
15
• Capture I and V data points on a
scope, save to a floppy, and read the
file with Excel,
10
5
0
0
0.5
1
1.5
2
Seconds
• Replot I versus V,
• Replot P versus time to get max P
I-V
Power
6
140
5
120
4
100
3
80
60
2
40
1
20
0
0
0
10
20
30
40
0
0.5
1
1.5
2
Seconds
26
Solar Radiation in Texas
AVERAGE DIRECT NORMAL INSOLATION MAP LEGEND
COLOR
KEY
per YEAR
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
27
28
Multiply by panel
efficiency, e.g. 0.14, to
get electrical output
29
clock noon
solar noon
30
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
31
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
In recent years, financial incentives have acted
like catalysts to increase PV power penetration
and to bring solar panels costs down
32
• 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)
33
Practice Problem
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,


(GH - DH )
Pincident   DH 
 cos(  incident )W / m 2 ,
zenith
cos( sun
)


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.
34
Sun Zenith Angle (Top Curve), and Incident Angle on Panel (Bottom Curve), for Dec. 16
(Panel Tilt and Azim uth = 60 and 225 Degrees, Respectively)
90
85
Zenith
80
75
70
65
60
Degrees
55
50
45
40
35
30
Incident
25
20
15
10
5
0
11
11.5
12
12.5
13
13.5
14
14.5
15
15.5
16
16.5
17
Hour of Day
Global Horizontal (Top Curve), and Diffuse Horizontal (Bottom Curve), for Dec. 16
650
600
550
500
Watts Per Square Meter
450
400
350
300
GH
250
200
150
100
DH
50
35
0
11
11.5
12
12.5
13
13.5
14
Hour of Day
14.5
15
15.5
16
16.5
17