6/17/2015
Lesson 24: Photocell Electrical
Characteristic and Circuit Model
ET 332a
Dc Motors, Generators and Energy Conversion Devices
1
Lesson 24 332a.pptx
Learning Objectives
After this presentation you will be able to:
Identify and interpret a photocell electrical
characteristic
 Find the maximum power output from a photocell
 Calculate a photocell’s efficiency
 Determine circuit model parameters for a photocell
given its characteristic curve
 Perform a calculation using the circuit model of a
photocell.

2
Lesson 24 332a.pptx
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6/17/2015
Photocell Characteristic Curve
Pm = Maximum cell power
IC
Max Power Pt.
(Vm, Im)
ISC
Fill Factor = FF
PM
IM VM
FF
Pm
ISC VOC
0
0
VOC
Cell Efficiency
0.7 <FF<0.85 Typical FF range
V
C
PC
PI
3
PI = incident solar power
Lesson 24 332a.pptx
Solar Cell Characteristics Example (1)
Example: A photocell has a saturation current of 2.5 x 10-12 A
and a short circuit current of 35 mA. It has an area of 1.5 cm2.
The incident solar power is 1000 W/m2. Assume that the cell
operates at room temperature. Find Voc, Pm, Fill Factor and
conversion efficiency.
Is
4
2.5 10
12
VT
0.026 V
VOC
VT ln 1
A
Isc
IL
IL
Is
0.035 A
Isc
VOC
0.607
V
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Solar Cell Characteristics Example (2)
Find Pm graphically
Create function for plotting
Ic ( V)
Calculate power as
function of V
P ( V)
5
Is e
1
0.0 0.02 0.62
V
Define plot range
IL
V
VT
V
Ic ( V) V W
Lesson 24 332a.pptx
Solar Cell Characteristics Example (3)
Cell Characteristic
Cell Current (A), Cell Power (W)
0.04
I sc
0.03
Vm
0.02
Im
0.5360 V
Ic Vm
Im
0.0177 W
Pm
0.0328 A
Find the Fill Factor (FF)
0.01
FF
0
0
0.1
0.2
0.3
0.4
Cell Voltage (V)
Cell Current
Cell Power
6
0.5
0.6
Pm
VOC Isc
FF
0.8
0.7
V
OC
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Solar Cell Characteristics Example (4)
Find the cell efficiency at maximum power output
Find the incident power, PI
I
Am
PI
1000
A
W
2
m
A
1 m2
10000 cm2
Am I
PI
Pm
C
1.5 cm2
PI
C
1.5 10
Am
0.2 W
0.1
Pm
4
m
2
0.0177 W
Cell efficiency is 10%
7
Lesson 24 332a.pptx
Circuit Model of Solar Cell
+
D
IL
+
Rs
VOC Rsh
RL
Vc
-
Cell Characteristic
0.04
sh
0.02
1/Rs
Values determined by cell construction
1/R
0.03
Cell Current (A)
Rs slope of characteristic near Voc
Rsh slope of characteristic near Isc
0.01
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Cell Voltage (V)
8
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Solar Cell Circuit Model Parameters
Finding Model Parameters, Rsh and Rs
Cell Characteristic
Pick points on characteristic plot and compute slope.
For Rs use points 1 and 2.
1/R
0.04
sh
4
1.)
V1s
0.5781 V
I1s
0.02395 A
2.)
V2s
0.6058 V
I2s
3.9 10
3
Gs
0.02
2
1/Rs
Cell Current (A)
0.03
I2s
I1s
V2s
V1s
A
Conductance is 1/Rs
1
Gs 0.8505
Gs
For Rsh use points 3 and 4
Rs
0.01
4
S
Rs
1.176
1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Cell Voltage (V)
3.)
V1sh
0.512
4.)
V2sh
0.550
I2sh
V2sh
Gsh
9
V
I1sh
Gsh
Gsh
I1sh
0.0343 A
I2sh
0.0311 A
Conductance is 1/Rsh
V1sh
1
Rsh
V
0.0842
S
Rsh
11.875
Lesson 24 332a.pptx
Solar Cell Circuit Model Example (1)
IRL
+
ID
VOC Rsh
Ish
D
RL
-
Vc
-
IL
R sh
100 mA
VOC
11.875
Rs
By KCL
+
R eq
D
VOC Req
Rs
Rs
ID
I eq
R L R sh
RL
ID
IL
I eq
0.71 volt
1.176
I eq
ID
RL
30
0
R eq
R sh
Parallel circuit so.....
-
10
IL
Ieq
100 mA
IL
ID
IL
+
Rs
Example: Find the power delivered to a 30 ohm resistive load
by the solar cell with a light current of 100 mA and model
parameters of R s =1.176
and R sh of 11.875
. Determine
the cell load voltage for this load resistance.
8.599
VOC
R eq
I eq
82.6 mA
17.4 mA
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Solar Cell Model Example (2)
IRL
Ish
+
-
Ish
Rsh
VOC
+
Rs
RL
Use Current Divider rule to find IRL
Vc
-
IRL
PL
Ieq
Rsh
Rsh RL
IRL
2
Find VC from KVL
RL
PL
VC
VC
11
IRL
Rs
22.77 mA
15.6 mW
VOC
IRL Rs
0.683 V
Lesson 24 332a.pptx
Solar Cell Efficiency

AM1.5 Solar Intensity (Incident power density) 1000 W/m2 or
100 W/cm2
 Losses





Photon Energy -47% of photons have eV<1.1, 30% goes to heat
Voltage factor – ratio of energy given to energy required to produce
electron 0.65
Recombination – electron/holes that recombine 10%
Reflection – reduced to 4%
Overall Efficiency c = (0.47)(0.65)(.10)(.96)=.26

12
26% Maximum efficiency using current technologies
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End Lesson 24
ET 332a
Dc Motors, Generators and Energy Conversion Devices
13
Lesson 24 332a.pptx
7