1. Theory of I-V Characterization
PV cells can be modeled as a current source in parallel with a diode. When there is no light present to generate any current, the PV cell behaves like a diode. As the intensity of incident light increases, current is generated by the PV cell, as illustrated in Figure 1.
Figure 1 – I-V Curve of PV Cell and Associated Electrical Diagram
In an ideal cell, the total current I is equal to the current Iℓ generated by the photoelectric effect minus the diode current ID, according to the equation:
where I0 is the saturation current of the diode, q is the elementary charge 1.6x10-19 Coulombs, k is a constant of value 1.38x10-23J/K, T is the cell temperature in Kelvin, and V is the measured cell voltage that is either produced (power quadrant) or applied (voltage bias). A more accurate model will include two diode terms, however, we will concentrate on a single diode model in this document.
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 that are described in further detail later in this document:
Figure 2 - Simplified Equivalent Circuit Model for a Photovoltaic Cell
The I-V curve of an illuminated PV cell has the shape shown in Figure 3 as the voltage across the measuring load is swept from zero to VOC, and many performance parameters for the cell can be determined from this data, as described in the sections below.
Figure 3 - Illuminated I-V Sweep Curve
Short Circuit Current (ISC)
The short circuit current ISC corresponds to the short circuit condition when the impedance is low and is calculated when the voltage equals 0.
I (at V=0) = ISC
ISC occurs at the beginning of the forward-bias sweep and is the maximum current value in the power quadrant. For an ideal cell, this maximum current value is the total current produced in the solar cell by photon excitation.
ISC = IMAX = Iℓ for forward-bias power quadrant
Open Circuit Voltage (VOC)
The open circuit voltage (VOC) occurs when there is no current passing through the cell.
V (at I=0) = VOC
VOC is also the maximum voltage difference across the cell for a forward-bias sweep in the power quadrant.
VOC= VMAX for forward-bias power quadrant
Maximum Power (PMAX), Current at PMAX (IMP), Voltage at PMAX (VMP)
The power produced by the cell in Watts can be easily calculated along the I-V sweep by the equation P=IV. At the ISC and VOC points, the power will be zero and the maximum value for power will occur between the two. The voltage and current at this maximum power point are denoted as VMP and IMP respectively.
Figure 4 - Maximum Power for an I-V Sweep
Fill Factor (FF)
The Fill Factor (FF) is essentially a measure of quality of the solar cell. It is calculated by comparing the maximum power to the theoretical power (PT) that would be output at both the open circuit voltage and short circuit current together. FF can also be interpreted graphically as the ratio of the rectangular areas depicted in Figure 5.
Figure 5 - Getting the Fill Factor From the I-V Sweep
A larger fill factor is desirable, and corresponds to an I-V sweep that is more square-like. Typical fill factors range from 0.5 to 0.82. Fill factor is also often represented as a percentage.
Efficiency is the ratio of the electrical power output Pout, compared to the solar power input, Pin, into the PV cell. Pout can be taken to be PMAX since the solar cell can be operated up to its maximum power output to get the maximum efficiency.
Pin is taken as the product of the irradiance of the incident light, measured in W/m2 or in suns (1000 W/m2), with the surface area of the solar cell [m2]. The maximum efficiency (ηMAX) found from a light test is not only an indication of the performance of the device under test, but, like all of the I-V parameters, can also be affected by ambient conditions such as temperature and the intensity and spectrum of the incident light. For this reason, it is recommended to test and compare PV cells using similar lighting and temperature conditions. These standard test conditions are discussed in Part III.
Shunt Resistance (RSH) and Series Resistance (RS)
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), as depicted in Figure 2.
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 further voltage drop before the load.
Decreasing RSH and increasing Rs will decrease the fill factor (FF) and PMAX as shown in Figure 6. If RSH is decreased too much, VOC will drop, while increasing RS excessively can cause ISC to drop instead.
Figure 6 - Effect of Diverging Rs & RSH 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 7.
Figure 7 - Obtaining Resistances from the I-V Curve
If incident light is prevented from exciting the solar cell, the I-V curve shown in Figure 8 can be obtained. This I-V curve is simply a reflection of the “No Light” curve from Figure 1 about the V-axis. The slope of the linear region of the curve in the third quadrant (reverse-bias) is a continuation of the linear region in the first quadrant, which is the same linear region used to calculate RSH in Figure 7. It follows that RSH can be derived from the I-V plot obtained with or without providing light excitation, even when power is sourced to the cell. It is important to note, however, that for real cells, these resistances are often a function of the light level, and can differ in value between the light and dark tests.
Figure 8 - I-V Curve of Solar Cell Without Light Excitation
Temperature Measurement Considerations
The crystals used to make PV cells, like all semiconductors, are sensitive to temperature. Figure 9 depicts the effect of temperature on an I-V curve. When a PV cell is exposed to higher temperatures, ISC increases slightly, while VOC decreases more significantly.
Figure 9 - Temperature Effect on I-V Curve
For a specified set of ambient conditions, higher temperatures result in a decrease in the maximum power output PMAX. Since the I-V curve will vary according to temperature, it is beneficial to record the conditions under which the I-V sweep was conducted. Temperature can be measured using sensors such as RTDs, thermistors or thermocouples.
I-V Curves for Modules
For a module or array of PV 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. When 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, the I-V curve shown in Figure 10 is produced.
2. Toolkit for I-V Analysis with LabVIEW
Using LabVIEW analysis capabilities you can assess the main performance parameters for photovoltaic (PV) cells and modules. In order to facilitate the I-V analysis, National Instruments has created hardware-independent LabVIEW functions to perform the forward-bias I-V characterization analysis.
There are two versions of the toolkit that are available for download: one is hardware independent, and can be used with previously acquired data, while the other can in addition acquire the data using a NI PXI-4130 Power SMU. Both versions will apply the same IV analysis functions to the measured data. Figure 11 shows a screenshot of one of the toolkit’s main VIs that reads data from a file (the sample data is included with the download).
For more information, or to download the toolkit, refer to the following link: Toolkit for I-V Characterization of Photovoltaic Cells.
In this paper, we looked at the theory behind I-V characterization and we also provided a LabVIEW toolkit that is hardware independent to perform the I-V analysis that can be downloaded by researchers and engineers.
In the next section, Part III, we explore an example test system to perform I-V characterization that takes advantage of NI LabVIEW and NI PXI-4130 SMU.
The two other sections that are part of this series are: