ECE 333
Renewable Energy Systems
Lecture 16: Photovoltaic Materials and
Electrical Characteristics
Prof. Tom Overbye
Dept. of Electrical and Computer Engineering
University of Illinois at Urbana-Champaign
overbye@illinois.edu
Announcements
•
•
•
HW 6 is should be turned in today
HW 7 is 4.2, 4.5, 4.9, 4.13, 5.2; it will be covered by an
in-class quiz on April 2.
Read Chapter 5 (Photovoltaic Materials and Electrical
Characteristics)
1
Total Clear Sky Insolation
•
The total insolation is the sum of the direct beam,
diffuse and reflected
–
Most is direct beam; models for diffuse and reflected are more
approximate (and certainly site dependent)
I C  I BC  I DC  I RC
I BC  I B cos 
 is angle between sun and
normal to collector
I DC  I B C
 360

C  0.096  0.04sin 
( n  100) 
 365

 1  cos  
I RC    I BH  I DH  

2


Superscript h indicates
values on surface in front
of collector;  is estimates
reflectivity of surface,
ranging from 0.8 for snow
to 0.1 for dark shingles
2
Ameren Solar Energy Production
•
•
Many groups publish there actual solar output, so
actual data from a similar facility is often available
A local example is data from Ameren, including from a
variety of different
solar pv technologies on the
roof of their
headquarters in
St. Louis; total for
the mono and poly
ones are 32.56 and
32.76 kW
https://www.ameren.com/missouri/solar/solar-energy-produced
3
California Solar Shade Control Act
•
•
The shading of solar collectors has been an area of legal
and legislative concern (e.g., a neighbor’s tree is blocking
a solar panel)
California has the Solar Shade Control Act (1979) to
address this issue
–
–
–
No new trees and shrubs can be placed on neighboring property
that would cast a shadow greater than 10 percent of a collector
absorption area between the hours of 10 am and 2 pm.
Exceptions are made if the tree is on designated timberland, or
the tree provides passive cooling with net energy savings
exceeding that of the shaded collector
Modified in 2008 to exclude systems designed to offset more
than a building’s electricity demand
4
The Guilty Trees were Subject to
Court Ordered Pruning
This case resulted in 2008 modification to exclude
existing trees (in this case the redwoods were planted
before the panels were installed)
For more information see:
http://www.josre.org/wp-content/uploads/2012/09/California_Solar_Shade_Control_Act-JOSRE_v2-161.pdf
Image Source: NYTimes, 4/7/08
5
Solar PV can be Quite Intermittent
Because of Clouds
Intermittency
can be reduced
some when
PV is
distributed
over a larger
region; key
issue is
correlation
across an area
Image: http://www.megawattsf.com/gridstorage/gridstorage.htm
6
Predicable, but Quite Large Dropoff Later as the Sun Sets
• Known as the "Duck Curve"
Image:http://www.caiso.com/documents/flexibleresourceshelprenewables_fastfacts.pdf
7
Photovoltaics (PV)
Photovoltaic definition- a material or device that is capable
of converting the energy contained in photons of light into an
electrical voltage and current
University of Illinois Solar
nd place
Decathalon
House
–
2
"Sojourner"
overall in 2009
exploring Mars,
1997
Rooftop PV
modules on a
village health
center in West
Bengal, India
http://www1.eere.energy.gov/solar/pv_use.html
http://www.solardecathlon.uiuc.edu/gallery.html#
8
PV History
•
•
•
•
•
•
Edmund Becquerel
(1839)
Adams and Day (1876)
Albert Einstein (1904)
Czochralski (1940s)
Vanguard I satellite
(1958)
Costs have recently
dropped quite
substantially
Image Source:http://pubs.rsc.org/en/Content/ArticleHtml/2013/EE/c3ee40701b
9
US Solar Capacity
•
US solar capacity is growing at close to 100%
yearly, with most of the growth in solar PV (as
opposed to solar thermal)
In 2004 we got 6 GWh
from solar PV; in 2009
it was 735, in 2013
8121 and in
2014 it was 15,874
(about 0.4% of total
electricity)
Image: http://cleantechnica.com/2014/04/24/us-solar-energy-capacity-grew-an-astounding-418-from-2010-2014/
10
PV System Overview
• Solar cell is a diode
• Photopower coverted to DC
Shadows
• Shadows & defects convert
generating areas to loads
• DC is converted to AC by an
inverter
• Loads are unpredictable
• Storage helps match
generation to load
11
Some General Issues in PV
• The device
• Efficiency, cost, manufacturability
automation, testing
• Encapsulation
• Cost, weight, strength,
yellowing, etc.
• Accelerated lifetime testing
• 30 year outdoor test is difficult
• Damp heat, light soak, etc.
• Inverter & system design
• Micro-inverters, blocking diodes, reliability
12
What are Solar Cells?
Load
•
•
current
+
p-type
Solar cells are diodes
Light (photons) generate free
carriers (electrons and holes)
which are collected by the
electric field of the diode
junction
The output current is a fraction
of this photocurrent
The output voltage is a
fraction of the diode built-in
Short-circuit
voltage
Open-circuit
voltage
Voltage
Current
•
•
n-type
-
Maximum
Power Point
13
Standard Equivalent Circuit Model
Where does the power go?
Load
(maximize)
Shunt
resistance
(minimize)
Diode
Photocurrent
source
Series
resistance
14
Photons
•
Photons are characterized by their wavelength
(frequency) and their energy
Planck's constant (h) is
6.626 10-34 J-s
Velocity of light (c) is
3108 m/s
c  v
E  hv 
•
hc

In this context energy is often expressed in
electronvolts (eV), which is defined as 1.6 10-19 J
–
This is the amount of energy gained by a single electron
moving across a voltage difference of one volt
Above equation for E can be
rewritten with E in eV and  in m
E
hc

, EEV 
1.242
 m
15
Band-Gap Energy
•
•
Electrical conduction is caused by free electrons
(electrons in conduction band)
At absolute zero temperature metals have free electrons
available and hence are good conductors
–
•
Metal conductivity decreases
with increasing temperature
Semi-conductors, such as
silicon, have no free
electrons at absolute zero
and hence are good
insulators
16
Band-Gap Energy, cont.
•
•
Silicon conductivity increases with increasing
temperature; at room temperature they only have
about 1 in 1010 electrons in the conduction band
Band gap energy is the energy an electron must
acquire to jump into the conduction band
1.242
EEV 
Band Gap and Cut-off Wavelength Above
 m
Which Electron Excitation Doesn’t Occur
Quantity
Si
GaAs
CdTe
InP
Band gap (eV)
1.12
1.42
1.5
1.35
Cut-off wavelength (μm)
1.11
0.87
0.83
0.92
17
Silicon Solar Cell Max Efficiency
•
•
Wavelengths above cutoff have no impact
This gives an upper bound on the efficiency of a
silicon solar cell:
–
•
•
Band gap: 1.12 eV,
Wavelength: 1.11 μm
This means that photons with wavelengths longer
than 1.11 μm cannot send an electron into the
conduction band.
Photons with a shorter wavelength but more energy
than 1.12 eV dissipate the extra energy as heat
18
Silicon Solar Cell Max Efficiency
•
•
For an Air Mass
Ratio of 1.5,
49.6% is the
maximum
possible fraction
of the sun’s energy
that can be
collected with a
silicon solar cell
Efficiencies of
real cells are in the
~20-25% range
19
Solar Cell Efficiency
•
Factors that add to losses
–
–
–
–
•
Smaller band gap - easier to excite electrons, so more
photons have extra energy
–
•
•
Recombination of electrons/holes
Internal resistance
Photons might not get absorbed, or they may get reflected
Heating
Results in higher current, lower voltage
High band gap – opposite problem
There must be some middle ground since P=VI (DC),
this is usually between 1.2 and 1.8 eV
20
Maximum Efficiency for Cells
•
The maximum efficiency of single-junction PV
cells for different materials was derived in 1961 by
Shockley and Queisser
21
Review of Diodes
•
•
Two regions: “n-type” which donate
electrons and “p-type” which accept
electrons
p-n junction- diffusion of electrons
and holes, current will flow readily in
one direction (forward biased) but not
in the other (reverse biased), this is
the diode
http://en.wikipedia.org/wiki/File
:Pn-junction-equilibrium.png 22
The p-n Junction Diode
•
Can apply a voltage Vd and get a current Id in one
direction, but if you try to reverse the voltage
polarity, you’ll get only a very small reverse
saturation current, I0
•
Diode voltage drop
is about 0.6 V
when conducting
23
The p-n Junction Diode
Voltage-Current (VI) characteristics for a diode
I d  I 0 (e qVd / kT -1)
I d  I 0 (e
38.9Vd
-1)
(at 25C)
k = Boltzmann’s constant
1.381x10-23 [J/K]
T = junction temperature [K]
Vd = diode voltage
Id = diode current
q = electron charge 1.602x10-19 C
I0 = reverse saturation current
24
Circuit Models of PV Cells
•
The simplest model of PV cell is an ideal current
source in parallel with a diode
I
I
+
PV
cell
•
•
VLoad
+
ISC
Id +
Vd
VLoad
-
The current provided by the ideal source ISC is
proportional to insolation received
If insolation drops by 50%, ISC drops by 50%
25
Circuit Models of PV Cells
ISC
Id +
Vd
-
+
I
VLoad
The subscript SC
is for short circuit
-
•
From KCL, ISC = Id + I, and the current going to the
load is the short-circuit current minus diode current
I  I SC  I 0 (e qV / kT -1)
•
Setting I to zero, the open circuit voltage is

kT  I SC
VOC 
ln 
 1
q  I0

26
PV Cell I-V Characteristic
•
For any value of ISC , we can calculate the
relationship between cell terminal voltage and
current (the I-V characteristics)
I  I SC  I 0 (e qV / kT -1)= f(ISC ,V)
•
•
Thus, the I-V characteristic for a PV cell is the
diode I-V characteristic turned upside-down and
shifted by ISC (because I = ISC – Id)
The curve intersects the x-axis at VOC and the y-axis
is ISC
27
PV Cell I-V Curves
dark curve
•
I-V curve for an illuminated cell = “dark” curve + ISC
28
PV Cell I-V Curves
•
•
More light effectively shifts the curve up in I, but
VOC does not change much
By varying the insolation, we obtain not a single IV curve, but a collection of them
29
Need for a More Accurate Model
•
•
The previous circuit is not realistic for analyzing
shading effects (we’ll talk more about shading later)
Using this model, absolutely NO current can pass
when one cell is shaded (I = 0)
30
PV Equivalent Circuit
•
•
•
•
•
It is true that shading has a big impact on solar cell
power output, but it is not as dramatic as this
suggests! Otherwise, a single shaded cell would
make the entire module’s output zero.
A more accurate model includes a leakage
resistance RP in parallel with the current source and
the diode
RP is large, ~RP > 100VOC/ISC
A resistance RS in series accounts for the fact that
the output voltage V is not exactly the diode voltage
RS is small, ~RS < 0.01VOC/ISC
31
PV Equivalent with Parallel Resistor
From KCL, I = ISC - Id – IRP
•
+
Vd
-
I
+
V
Load
ISC
Id
(maximize)
Shunt resistance drops
some current (reduces
output current)
Parallel-Only
RP
I  ( I SC
V
 Id ) 
RP
Photocurrent
source
•
-
For any given voltage, the parallel leakage
resistance causes load current for the ideal model to
be decreased by V/RP
32
PV Equivalent with Series Resistor
•
•
Add impact of series resistance RS (we want RS to
be small) due to contact between cell and wires and
some from resistance of the semiconductor
From KVL
Series-Only
Vd  V  I  RS
I
R
•
ISC
Id
+
(minimize)
+
Vd
V
-
-
Load
Series resistance drops
some voltage (reduces
output voltage)
Photocurrent
source
s
The output voltage V drops by IRS
33
General PV Cell Equivalent Circuit
The general equivalent circuit model considers both
parallel and series resistance
Equivalent Circuit
Vd
I  ( I SC  I d ) 
RP
Vd
I  ( I SC  I 0 (e
+
V
Load
+
(maximize)
Id
ISC
q / kT V  RS I 
I
(minimize)
RP
V  Vd  I  RS
Rs
Photocurrent
source
•
-
V  RS I
-1)) 
RP
34
Series and Shunt Resistance Effects
•
Parallel (RP) –
current drops by
ΔI=V/RP
•
Series (RS) –
voltage drops by
ΔV=IRS
35
Fill Factor and Cell Efficiency
Fill Factor
(FF) =
VR•IR
Isc•Voc
Fill factor is ratio at the ratio at
the maximum power point
Cell
Efficiency
(h) =
area = VOCISC
area = VRIR
Imax•Vmax
Isc•Voc•FF
Incident = Incident
Power
Power
36
Multijunction Cells
Load
+
n-type
-
p-type
+
p-type
n-type
n-type
p-type
n-type
Problem: Single junction loses
all of the photon energy above
the gap energy.
+
1.1
1.0
+
p-type
-
-
Energy (eV)
180
4.0
3.0
2.5
2.0
1.7
1.5
1.3
0.9
160
140
Intensity (mW/m2-m)
80
60
40
20
0
300
500
700
900
1100
Wavelength (nm)
Cell #4
(0.6 eV gap)
Each cell captures the light
transmitted from above.
Cell #3
(1.0 eV gap)
100
Cell #2
(1.4 eV gap)
120
Top Cell (1.9 eV gap)
Solution: Use a series of cells
of different gaps.
1300
1500
37
Record laboratory thin film cell
efficiencies
38