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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

13

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

0

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