Chapter 4
Modeling and Thevenin Equivalency
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CHAPTER 4. MODELING AND THEVENIN EQUIVALENCY
4.1 Section Overview
In this section a solar cell is examined. A solar cell is a non-ideal voltage and current source that can be modeled as
a Thevenin equivalent circuit. Solar cells are an interesting class of energy sources because they do not produce
energy in a linear fashion over all current and voltages. Instead every solar cell has a ‘sweet spot’ that gives the most
power (remember power is voltage times current, P = V ∗ I)
4.2 Preparation
In preparation for this lab, review the concept of the Thevenin equivalent model.
4.3 Procedure
In this section, the following items will be covered.
1. Differential Measurements
2. Taking Measurements
3. Graphing Non-ideal Energy Sources
4.3.1
Differential Measurements
To be able to plot power supplied by the solar cell, the current sourced by the cell must be determined. The
DataLogger can only measure voltage, but current through an element is proportional to the voltage dropped across
it. By using a fixed value resistor in the circuit and Ohm’s law, current can be found. To take measurements of the
solar cell, begin by constructing the circuit in Figure 4.1. Do not connect the DataLogger to the circuit until it has
been verified. The solar cell can supply enough energy to damage the DataLogger if it is not properly connected.
Pay special attention to the orientation of power and ground pins!
Figure 4.1: This circuit is used to characterize a solar cell
Solar Cell Background
The power generated by a solar cell is proportional the amount and type of light it is exposed to . In commercial solar
cell production, a characterization process is conducted on every cell using a specific calibrated light source that
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4.3. PROCEDURE
closely matches the sun in spectrum and has a fixed intensity per unit area. These calibrated light sources can be
very expensive but a basic understanding of the cells can be found using other light sources.
For this experiment a traditional tungsten filament incandescent light bulb will be used. This light source is
inexpensive and available but has more yellow and red in its spectrum compared to sun light. This change will result
in a deviation from the specification of the solar cell from its manufacturer.
The intensity of light striking a solar cell correlates to the voltage of the solar cell while unloaded. This means that a
solar cell without much resistance attached to it will increase its output voltage when exposed to more light. Solar
cells are designed with an upper voltage range and the voltage will not increase past this amount. This is important
to note since the DataLoggers can only measure voltages of up to 3.3 volts approximately and could be damaged by
too much voltage! Set the solar cell under the source so that the intensity of the light can be adjusted as in Figure 4.2.
Figure 4.2: This setup is used to test the solar cell
1. With the DataLogger disconnected from the circuit and the potentiometer adjusted to 5K ohms, adjust the
height of the light source so that there approximately 3.3V observed at the point ‘Input 1’ in Figure 4.1.
2. Once the solar cell is calibrated, vary the resistance of the potentiometer in the circuit to reduce its resistance.
This reduction will cause more current to flow and the power supplied by the cell to change. Use caution,
increasing the resistance at ‘Input 1’ could increase the supplied voltage and damage the DataLogger. Be sure
to know which way to turn the potentiometer!
4.3.2
Taking Measurements
1. Configure the DataLogger to take 10 measurements per second (or more). Enable logging on both channels.
2. Connect the DataLogger to the circuit as shown in Figure 4.1. Switch the switch to run and begin sampling.
3. Reduce the resistance of the potentiometer slowly (taking approximately 10 seconds). The DataLogger will
record these samples. Dump the data to a file and open it in Excel for inspection.
4.3.3
Graphing Non-ideal Energy Sources
In order to analyze how the solar cell supplies energy, it is important to apply Ohm’s law and the equation for power
before examining the results numerically and graphically. Include the following graphs for a thorough analysis:
VIN P U T 1 , VIN P U T 2 vs. time
ILOOP vs. RLOAD (RP OT + RF IXED )
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VIN P U T 1 vs. RLOAD (RP OT + RF IXED )
VIN P U T 1 vs. RLOAD (RP OT + RF IXED )
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CHAPTER 4. MODELING AND THEVENIN EQUIVALENCY
The final outcome of this data manipulation should be the graph of load resistance on the x-axis, and power supplied
on the y-axis. This includes using the compiled information to determine at what load resistance, optimal power is
supplied.
P = VSOLAR ∗ ILOOP
(4.1)
VP OT = VIN P U T 1 − VIN P U T 2
(4.2)
ILOOP =
VIN P U T 2
R2
(4.3)
(4.4)
VSOLAR = VIN P U T 1
Look at the scales of the graphs to ensure that the values are correct. The graphs should indicate that when power
(P ) vs. either ILOOP or VSOLAR that there is a local maxima or minima that shows the sweet spot for using the solar
cell. If this is not present, redo the experiment ensuring that the potentiometer is varied properly and that the same
light is supplied to the solar cell during the entire test.
4.4 Lab Report
Write a clear and concise report. Turn in the typed report following the second week of this lab.
The report should include the following:
1. The type of data collected, where it was collected, and any conclusions that can be drawn from the data.
2. As mentioned previously include the following graphs:
VIN P U T 1 , VIN P U T 2 vs. time
ILOOP vs. RLOAD (RP OT + RF IXED )
VIN P U T 1 vs. RLOAD (RP OT + RF IXED )
VIN P U T 1 vs. RLOAD (RP OT + RF IXED )
3. Any graphs that might help to display changes in measurements.
4. A schematic drawing of the sensor circuit used (using LTSpice or a similar program).
5. A simulation output showing the output voltage of Input1 , Input2 , and the power supplied by the source. Use
the ‘Simulating a non-ideal voltage source’ tutorial found on the lab website as a reference.
6. A diiscussion of the differences between a linear and non-linear source.
7. Properly labeled graphs with titles, correct axes and correct scale.
8. A written explanation of the graphs and the data received (along with equations that were used to calculate
final and intermediate values). Be aware that there is some error in the DataLogger measurements.
Current guidelines and an example lab report are available on the lab website.
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