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EE462L, Spring 2013

PV Arrays (Solar Panels)

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Electrical Properties of a Solar Cell

n-type

p-type

V

+I

Photons

JunctionExternal circuit(e.g., battery,

lights)

IscV

+

I

)1( BVeA

External circuit(e.g., battery,

lights)

)1( BVeA

0

5

0.0 0.6Diode Volts

DiodeA

mps

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

Maximum

power point

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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

I-V Curve

Isc

Voc

I

sc

Pmax at approx. 30V

Pmax 0.7 Voc Isc

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The Maximum Power Point

P=0 at short circuit P=0 at open circuit

Pmax

On a good solar day in Austin, you get about1kWh per square meter of solar panels

(corresponds to about 150W rated)

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Earths Poles

Magnetic poles: Created by Earths magnetic field

Can be located with a compassThey move along Earths surface!

Celestial poles: Created by Earths 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)

Note because of magnetic declination,

a compass in Austin points

approximately 6 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

Jun

Dec

Sep

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Sun Moves From Winter to Summer

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

Austins Latitude: 30o

23.45o

23.45o

30o

Edge ofPV module

Earths surface

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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

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Solar Radiation Monitors

Rotating Shadowband PyranometersMeasure GH and DH

NREL Sci Tec Two-Axis Tracker MeasuresDN, 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 fallson 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

est

DHGH

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 suns rays and a vectornormal to the panel surface (0 means that the suns rays areperpendicular 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% isconverted 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 bysurface area

Est. Watts onpanel 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 atPanels

Voltage atLab Bench

PanelCurrent

Use these two

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Use a Variable Power Resistor to Sweep the

Panel 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 readingwith no load connected

Adjust the power resistor, backingdown in integer volts in two volt steps

(e.g. 38V, 36V, 34V, ) until about25V, while taking the current readings

At about 25V, continue to backdown in integer volts, but in five

volt steps, while taking the currentreadings

Take the short circuit current andpanel voltage reading

Reminder - Hand plot as youtake your data points

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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

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

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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 largedischarged C (like 5 or 10 of the DBR

Cs),

Capture I and V data points on ascope, 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 YEARCOLORKEY per day(kWh/m2-day) (MJ/m2) (quads/100 mi2)

2.3

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Multiply by panelefficiency, e.g. 0.14, toget electrical output

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clock noon

solar noon

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Solar analysis of Sept. 25, 2006. Assume panels are at 30 tilt, 180 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 1kWrated 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, thenthe 3 kW of panels cost about $21K. Consider an average price of electricity for residential users of 11 cents/kWH (TXis about average). So cost of electricity each day is about $2.1. Hence, it will take close to 3 years to pay the solar

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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

Oth f t ff ti PV ff ti d t f i t t

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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 60 tilt,

and 225 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

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Zenith

Incident

GH

DH