0. 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

1. 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)

2. 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)
q is angle between sun and normal to collector
Superscript h indicates values on surface in front of collector; r is estimates reflectivity of surface, ranging from 0.8 for snow to 0.1 for dark shingles

3. 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 and kW

4. 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

5. 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:
Image Source: NYTimes, 4/7/08 5

6. 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:

7. Predicable, but Quite Large Drop-off Later as the Sun Sets
Known as the "Duck Curve"
Image:

8. 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 Decathalon House – 2nd place overall in 2009
"Sojourner" exploring Mars, 1997
Rooftop PV modules on a village health center in West Bengal, India

9. 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:

10. 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 and in it was 15,874 (about 0.4% of total electricity)
Image:

11. PV System Overview Solar cell is a diode Photopower coverted to DC
Shadows & defects convert generating areas to loads
DC is converted to AC by an inverter
Loads are unpredictable
Storage helps match generation to load
Shadows

12. 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

13. What are Solar Cells? Solar cells are diodes
Load -
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 voltage +
n-type
p-type
Open-circuit voltage
Voltage
Current
Maximum Power Point
Short-circuit current

14. Standard Equivalent Circuit Model
Where does the power go?
Series resistance
(minimize)
Photocurrent source
Shunt resistance
Diode
Load
(maximize) 14

15. Photons
Photons are characterized by their wavelength (frequency) and their energy
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
Planck's constant (h) is 10-34 J-s
Velocity of light (c) is 3108 m/s
Above equation for E can be rewritten with E in eV and l in mm

16. 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

17. 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
Band Gap and Cut-off Wavelength Above 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

18. 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

19. 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

20. Solar Cell Efficiency Factors that add to losses
Recombination of electrons/holes
Internal resistance
Photons might not get absorbed, or they may get reflected
Heating
Smaller band gap - easier to excite electrons, so more photons have extra energy
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

21. Maximum Efficiency for Cells
The maximum efficiency of single-junction PV cells for different materials was derived in 1961 by Shockley and Queisser

22. 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

23. 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

24. The p-n Junction Diode
Voltage-Current (VI) characteristics for a diode
k = Boltzmann’s constant x10-23 [J/K]
T = junction temperature [K]
Vd = diode voltage
Id = diode current
q = electron charge 1.602x10-19 C
I0 = reverse saturation current

25. Circuit Models of PV Cells
The simplest model of PV cell is an ideal current source in parallel with a diode
The current provided by the ideal source ISC is proportional to insolation received
If insolation drops by 50%, ISC drops by 50% I I + + Id +
ISC
VLoad Vd
VLoad
PV cell - - -

26. Circuit Models of PV Cells
ISC Id
VLoad + - Vd
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
Setting I to zero, the open circuit voltage is

27. 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)
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

28. PV Cell I-V Curves dark curve
I-V curve for an illuminated cell = “dark” curve + ISC

29. 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 I-V curve, but a collection of them

30. 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)

31. 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

32. PV Equivalent with Parallel Resistor
From KCL, I = ISC - Id – IRP
For any given voltage, the parallel leakage resistance causes load current for the ideal model to be decreased by V/RP
Parallel-Only I
Shunt resistance drops some current (reduces output current)
Photocurrent source RP
Load
(maximize) + + Id
ISC Vd V - -

33. 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
The output voltage V drops by IRS
Photocurrent source
Load Rs
(minimize)
Series-Only I Id + +
Series resistance drops some voltage (reduces output voltage)
ISC Vd V - -

34. General PV Cell Equivalent Circuit
The general equivalent circuit model considers both parallel and series resistance
Photocurrent source RP
Load Rs
(minimize)
(maximize)
Equivalent Circuit I Id + +
ISC Vd V - -

35. Series and Shunt Resistance Effects
Parallel (RP) – current drops by ΔI=V/RP
Series (RS) – voltage drops by ΔV=IRS

36. Fill Factor and Cell Efficiency
area = VOCISC
Fill Factor (FF) =
VR•IR
Isc•Voc
Fill factor is ratio at the ratio at the maximum power point
area = VRIR
Cell Efficiency (h) =
Isc•Voc•FF
Incident Power
Imax•Vmax =

37. Multijunction Cells Load- - -
Problem: Single junction loses all of the photon energy above the gap energy. - + + + +
n-type
p-type
n-type
p-type
n-type
p-type
n-type
p-type
Energy (eV) 20 40 60 80
100
120
140
160
180
300
500
700
900
1100
1300
1500
4.0
3.0
2.5
2.0
1.7
1.5
1.3
1.1
1.0
0.9
Intensity (mW/m2-mm)
Wavelength (nm)
Top Cell (1.9 eV gap)
(1.4 eV gap)
Cell #2
(1.0 eV gap)
Cell #3
(0.6 eV gap)
Cell #4
Solution: Use a series of cells of different gaps.
Each cell captures the light transmitted from above.

38. Record laboratory thin film cell efficiencies