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Activity : Characteristics of Photovoltaic Solar Cells

Objective:

The objective of this Lab activity is to study and measure the output voltage and current characteristics of a photovoltaic solar panel and develop an equivalent electrical model for use in computer simulation.

Notes:

As in all the ALM labs we use the following terminology when referring to the connections to the M1000 connector and configuring the hardware. The green shaded rectangles indicate connections to the M1000 analog I/O connector. The analog I/O channel pins are referred to as CA and CB. When configured to force voltage / measure current -V is added as in CA-V or when configured to force current / measure voltage -I is added as in CA-I. When a channel is configured in the high impedance mode to only measure voltage -H is added as CA-H.

Scope traces are similarly referred to by channel and voltage / current. Such as CA-V , CB-V for the voltage waveforms and CA-I , CB-I for the current waveforms.

Background:

A solar cell is a semiconductor PN junction diode as shown in figure 1. The large surface area indicated in light blue is exposed to incident light energy. Solar cells are usually coated with anti-reflective materials so that they absorb the maximum amount of light energy. Normally no external bias is applied to the cell. When a photon of light is absorbed near the PN junction a hole / electron pair is produced. This occurs when the energy of the photon is higher than the energy bandgap of the semiconductor. The built in electric field of the junction cause the pair to separate and head toward the respective + and - terminals. The energy from the light causes a current to flow in an external load when the cell is illuminated.

Figure 1 Structure of a basic solar cell.

A typical voltage vs. current characteristic, known as an I/V curve, of a PN diode without illumination is shown in green in figure 2. The applied voltage is in the forward bias direction. The curve shows the turn-on and the buildup of the forward bias current in the diode. Without illumination, no current flows through the diode unless there is external potential applied. With incident sunlight, the I/V curve shifts up showing that there is external current flow from the solar cell to a resistive load as shown with the red curve.

Figure 2 Shift of the solar cell I/V curve with increasing incident light.

Short circuit current, ISC, flows when the external resistance is zero (V = 0) and is the maximum current delivered by the solar cell at a given illumination level. The short circuit current is a function of the PN junction area collecting the light. Similarly, the open circuit voltage, VOC, is the potential that develops across the terminals of the solar cell when the external load resistance is very large, RLOAD = 8. For silicon based cells a single PN junction produces a voltage near 0.5V. Multiple PN junctions are connected in series in a larger solar panel to produce higher voltages. Photovoltaic cells can be arranged in a series configuration to form small modules, and modules can then be connected in parallel-series configurations to form larger arrays. When connecting cells or modules in series to produce higher output voltages, they must have the same current rating ( if not the cell with the lowest current specification will limit the ultimate current of the module ), and similarly, modules must have the same voltage specification when connected in parallel to generate larger currents.

The power delivered to the load is of course zero at both extremes of the I/V curve and reaches a maximum (PMAX) at a single load resistance value. In figure 3, PMAX is shown as the area of the shaded rectangle.

Figure 3 The maximum power delivered by a solar cell, PMAX, is the area of the largest rectangle under the I/V curve.

A commonly used parameter that characterizes a solar cell is the fill factor, FF, which is defined as the ratio of PMAX to the area of the rectangle formed by VOC and ISC.

The efficiency of a solar cell is the ratio of the electrical power it delivers to the load, to the optical power incident on the cell. Maximum efficiency is when power delivered to the load is PMAX. Incident optical power is normally specified as the power from sunlight on the surface of the earth which is approximately 1mW/mm2. Spectral distribution of sunlight is close to a blackbody spectrum at 6000º C minus the atmospheric absorption spectrum.

The maximum efficiency ηMAX may be written as:

For a cell of a certain size, ISC is directly proportional to the incident optical power PIN. However, VOC increases logarithmically with the incident power. So, we would expect the overall efficiency of the solar cell to also increase logarithmically with incident power. However, thermal effects at high sunlight concentrations and electrical losses in the series resistance of the solar cell limit the enhancement in efficiency that can be achieved. So the efficiency of practical solar cells peaks at some finite light concentration level.

Shunt Resistance (Rsh) and Series Resistance (Rs)

Photovoltaic cells can be modeled as a current source in parallel with a diode as depicted in figure 4. When there is no light present to generate any current, the cell behaves like a diode. As the intensity of incident light increases, current is generated by the PV cell.

In an ideal cell, where RSH is infinite and RS is zero, the load current I is equal to the current Il generated by the photoelectric effect minus the diode current ID, according to the equation:

Where IS is the saturation current of the diode, q is the charge on an electron, 1.6×10-19 Coulombs, k is Boltzmann's constant, 1.38×10-23 J/K, T is the cell temperature in degrees Kelvin, and V is the measured cell voltage that is either produced (power quadrant) or applied (voltage bias). A more accurate model would include two diode terms, however, we will limit the model to a single diode for this discussion.

Expanding the equation gives the simplified circuit model shown below and the following associated equation, where n is the diode ideality factor (typically between 1 and 2), and RS and RSH represents the series and shunt resistances.

Figure 4 Electrical model of solar cell

During operation, the efficiency of solar cells is reduced by the dissipation of power across internal resistances. These parasitic resistances can be modeled as a parallel shunt resistance (RSH) and series resistance (RS). For an ideal cell, RSH would be infinite and would not provide an alternate path for current to flow, while RS would be zero, resulting in no voltage drop and power loss before the load. Decreasing RSH and increasing Rs will decrease the fill factor (FF) and PMAX as shown in figure 5. If RSH is decreased too much, VOC will drop, while increasing RS excessively can cause ISC to drop instead.

Figure 5 - Effect of changing RSH & RS from ideality

It is possible to approximate the series and shunt resistances, RS and RSH, from the slopes of the I/V curve at VOC and ISC, respectively. The resistance at VOC, however, is at best proportional to the series resistance but it is larger than the series resistance. RSH is represented by the slope at ISC. Typically, the resistances at ISC and at VOC will be measured and noted, as shown in figure 6.

Figure 6 - Obtaining values for RS and RSH from the I/V curve

I-V Curves for Modules

For a module or array of solar cells, the shape of the I/V curve does not change. However, it is scaled based on the number of cells connected in series and in parallel. If n is the number of cells connected in series and m is the number of cells connected in parallel and ISC and VOC are values for individual cells, then the short circuit current for the array is nISC and the open circuit voltage is mVOC. An example I/V curve is shown in figure 8 with an overall ISC of about 80mA and a VOC of about 4.2V and PMAX is slightly higher than 160mW.

Figure 8, example solar panel I/V and power curves

Materials:

ADALM1000 hardware module
Solder-less breadboard, and jumper wire kit
1 or more Solar Panels (see appendix for suggested types)
Light source, preferably full sunlight

Directions:

The 0 to 5 volt analog output waveform generators in the ALM1000 hardware can source / sink up to only 200 mA. Small to medium size solar panels can generally supply less current than that.

On your solder-less breadboard construct the circuit shown in figure 9. This measurement setup will work for solar panels with open circuit voltages less than 5 volts. It will force a variable voltage, provided by the channel A voltage generator CA-V, across the solar panel. The channel A current trace (CA-I) is used to measure the current flowing out of the solar panel ( red arrow in figure ). The solar panel current flows from the + terminal through the channel A generator back to the negative terminal.

Figure 9, solar panel measurement circuit

The channel A voltage trace measures the solar panel voltage.

The configuration shown in figure 9 can measure only part of the I/V curve for panels with VOC greater than about 5V. It can be used to measure ISCfor any panel and the current for voltages up to 5V. To measure the rest of the I/V curve for panels with higher VOC voltages the circuit can be modified as shown in figure 10. A “shunt regulator” is connected in series with the solar panel to effectively induce a more negative voltage with respect to ground at the negative terminal. More on how to build a shunt regulator in the appendix at the end of this Lab. The shunt regulator is “powered” from the solar panel current ( red arrows in figure ). The waveform generator in the M1000 can swing a maximum of 5 Volts (0 to +5) so that will be the ultimate limit of the total voltage range of any I/V measurements that can be produced using these setups.

Figure 10, solar panel measurement circuit, VOC > 5 V

For panels with high VOC is will be necessary to take data in each configuration to obtain data for both ISC and VOC. The data from the two configurations can be combined to get a complete I/V curve. For more on how to make voltage measurements beyond 0 to 5 V with the ALM1000 refer to the this document on the analog inputs.

Hardware Setup:

Set the voltage vertical scale of scope channel A to 0.5V/div. The current vertical scale of channel A will depend on the maximum current your panel can generate.

Set the frequency of waveform generator A to 100 Hz, and the horizontal time base so that at least one full 0 to VOC sweep is displayed. With the channel A generator disabled, first measure the open circuit voltage produced by the panel when in full sun light. Set the Max voltage of waveform generator A to the open circuit voltage you just measured. Set the Min voltage of waveform generator A to 0. Now enable the channel A generator to force voltage.

Procedure:

Measure the dimensions of the panel or cell to determine the area in mm2that collects light. You will need this to estimate the amount of input power from the sunlight.

Turn on the XY display mode.

Ideally you should take data outside under constant temperature and sunlight conditions - i.e. no clouds. This may not always be practical depending on the computer used with the M1000 hardware. A sun facing window would work but it would be best to open the window and remove any shades or screens that might reduce the amount of sunlight. You should also make your measurements quickly to avoid the heating of the panel from the direct sunlight that may then change the characteristics during the data-collection. Make sure that you don't cast any shadows or reflections over the panel during the experiment. Once you have fixed the position of the panel with relation to the sun it is NOT TO BE MOVED DURING THE EXPERIMENT.

Once you have obtained an I/V plot using the Waveforms software, export a data file in .csv format. Load the .csv data file into a data analysis software program like MatLab or a spreadsheet (Excel). You should have adjusted the horizontal time base of the scope to display a little more than one sweep of the voltage ramp. Your output data file will probably contain more than one set of voltage and current values from 0 to VOC. You should remove this extra data before generating a plot of your data. You should also calculate the power ( I*V ) for each data point. From your I/V curves calculate values for the fill factor, FF, PMAX, maximum efficiency ηMAX (based on approximately 1mW/mm2for the incident light power) RS and RSH.

Repeat taking data for other positions where the panel faces away from the sun.

Questions:

In your lab report, compare the voltage (V) vs current (A) graphs for each panel position and note any differences.

Compare the different maximum powers, voltages, currents and external resistances for the different panel positions and comment on their comparison. Comment on how power output is affected by the external resistance connected to a photovoltaic panel.

Calculate the maximum output efficiency for each part as follows:

Maximum efficiency (%) = (PMAX/PIN) x 100

Comment on the significance of the size of the efficiency.

Extra Questions:

Measure the amount of current flowing through, and power output of your photovoltaic panel over time. Based on the size of your panel determine how large of a PV system you need to supply all the daily energy needs for a typical household.

Each solar Photovoltaic panel produced has certain specifications related to its power output and current flow. Your solar panel is rated at how many Watts of power at how many milliamperes of current. In this lab you should measure the current flow of this panel over a 20 minute period. You should also calculate its power output and energy production over time. You can then calculate how large of an array (panels wired together in parallel / series) you would need to completely supply the energy needed for a typical residence.

Can you determine the relationship between the peak power output of the solar panel and thickness of experimental “clouds”?

Additional Materials: a few sheets of 8“ X 11” white translucent paper ( wax paper may be a good choice ) , radiation lamp with 150W bulb, meter stick, ring stand with clamps. This part of the lab will simulate how the solar panel is affected by varying amounts of cloud cover using sheets of somewhat transparent or translucent paper to simulate cloud thickness. You will be looking to see if there is a mathematical relationship between cloud thickness and voltage x current output of the panel. The voltage produced is not the true measure of energy being collected in this situation, current and peak power will better show the relationship we are looking for.

Determine if changing the angle of your panel over time to follow the Sun would add up to substantial savings in your energy bill?

You will need a protractor or clinometer to measure the angle of the panel to the incident sunlight.

Much is made of the amount of energy lost by fixed Photovoltaic systems because they don't always point with the optimal angle of the sun. In this lab you should investigate how changing the angle of your panel varies the amount of current produced by the panel, and how that would relate to a typical energy bill. You will need to perform this lab at a time when sky cover is very consistent. It is preferable to have sunny skies, but a uniform cloud cover will work.

For Further Reading:

http://en.wikipedia.org/wiki/Solar_cell
http://en.wikipedia.org/wiki/Theory_of_solar_cells
http://en.wikipedia.org/wiki/Maximum_power_point_tracking
http://pveducation.org/pvcdrom/characterisation/introduction
http://users.df.uba.ar/sgil/physics_paper_doc/papers_phys/e&m/I-V_measure_solar_cell.pdf
Mathworks Solar Cell model
http://www.mathworks.com/help/physmod/elec/ref/solarcell.html?searchHighlight=solar+cell
Solar Cell Spice model: http://www.intusoft.com/nlhtm/nl78.htm

Appendix: Sources of Solar Panels

Solar panels come in many sizes with various voltage and current specifications and various prices. Just about any panel or combination of panels that provide between 5V and 9 V and current up to 150 mA will work for these lab ( and related ) activities. The following are a few sources for solar panels.

Sun Power panels are made of Copper Indium Diselenide. They are 60mm (2-3/8“) square, with nominal 4.5 VOC and 90mA ISC in full sunlight.

60mm square solar panel

Suppliers:

http://www.bgmicro.com/PWR1241.aspx
http://www.jameco.com/webapp/wcs/stores/servlet/Product_10001_10001_1928142_-1

OSEPP SC10072 Monocrystalline Solar Cell - Barrel Plug Termination, 100mA ISC, 7.2 VOC. This one comes prewired with a power plug. A matching jack would be needed to connect the panel to your experiments.

Supplier: http://www.tigerdirect.com/applications/SearchTools/item-details.asp?EdpNo=4368549&csid=_61

A low cost and generally available option is the remove the solar panel from something like either of these solar powered LED Lamps sold at dollar stores:

Solar Desk Lamp

Solar Garden Light

Some disassembly and un-soldering is required and then soldering longer wires to panel. A side benefit is that you also get one or more white LEDs, a 1.2 V rechargeable AAA battery with holder, and a DC-DC boost converter circuit. These extra components can be used in other ALM Lab activities.

Appendix: Shunt Regulators:

There are a number of possible shunt regulator circuits that might be used in this application. Some as simple as a reversed biased power zener diode or series stack of multiple forward biased normal diodes. These do not actually regulate. Regulation generally means the circuit contains an amplifier gain stage and negative feedback.

The three transistor band-gap shunt regulator from this Lab Activity is one example of a shunt regulator. If such a circuit design were to be used here the resistor values would likely need to be recalculated for a higher output voltage of between 3 and 5 volts and to be able to sink between 100 mA and 200 mA, the limit of a 2N3904 or 2N3906 transistor.

Another simple shunt regulator circuit suitable for use in this solar panel test application is shown in figure A2. Two complementary versions are shown. The one on the left used a PNP (2N3906) as the output device to carry the large sink current. The one on the right used an NPN (2N3904) as the output device to carry the large sink current.

The regulated output voltage will be equal to the VBE of transistor Q1 plus the forward drop of LED1. The current in the LED is set by the value of R1 and the VBE. A range of output voltages are possible by choosing different color LEDs. The forward voltage drop can range from around 2 V for red and up to 3 V for blue or white. Even more output voltage values can be made by inserting the forward voltage drop of one or more standard Si diodes in series with the LED.

Looking at the version on the left, NPN transistor Q1 and collector resistor R2 form a common emitter amplifier stage. PNP transistor Q2 provides current gain. As soon as enough current is flowing through the LED and R1 such that the voltage across R1 is large enough to turn on Q1 the circuit starts to regulate. Beyond the initial startup current in the LED, the majority of the current through the shunt regulator flows through Q2. The above explanation similarly holds for the complementary version on the right.

Figure A2 Shunt Regulator with negative feedback

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