Part II – Photovoltaic Cell I-V Characterization Theory and LabVIEW Analysis Code

This article is the second in a series of 3 tutorials on assessing the performance of photovoltaic cells through I-V characterization. This series includes an overview of PV cells, and describes the theory behind I-V characterization. The tutorials also include an example setup using National Instruments hardware and a free downloadable library of LabVIEW code for performing the I-V analysis. The other two articles in this series are:

• Part I – Photovoltaic Cell Overview
• Part III – I-V Characterization of Photovoltaic Cells using PXI

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 I_ℓ generated by the photoelectric effect minus the diode current I_D, 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 voltage produced by the cell.

The I-V curve of an illuminated PV cell has the shape shown in Figure 2 as the voltage across the measuring load is swept from zero to V_OC, and many performance parameters for the cell can be determined from this data, as described in the sections below.

Figure 2 - Illuminated I-V Sweep Curve

Short Circuit Current (I_SC)

I_SC represents to the maximum current that passes through the cell that corresponds to the short circuit condition when the impedance is low.  It occurs at the beginning of the sweep when the voltage is zero.  In an ideal cell, this maximum current value is the total current produced in the solar cell by photon excitation.

I_SC = I_MAX  at V=0

Open Circuit Voltage (V_OC)

The open circuit voltage is the maximum voltage difference across the cell, and it occurs when there is no current passing through the cell. 

V_OC =V_MAX  at I=0

Maximum Power (P_MAX), Current at P_MAX (I_MP), Voltage at P_MAX (V_MP)

The power produced by the cell in Watts can be easily calculated along the I-V sweep by the equation P=IV.   At the I_SC and V_OC 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 V_MP and I_MP respectively.

Figure 3 - 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 (P_T) 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 4.

Figure 4 - 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.

Efficiency (η)

Efficiency is the ratio of the electrical power output P_out, compared to the solar power input, P_in, into the PV cell.  P_out can be taken to be P_MAX since the solar cell can be operated up to its maximum power output to get the maximum efficiency.

P_in 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 (η_MAX) 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 (R_SH) and Series Resistance (R_S)

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 (R_SH) and series resistance (R_S), as depicted in Figure 5.

Figure 5 - Simplified Equivalent Circuit Model for a Photovoltaic Cell

For an ideal cell, R_SH would be infinite and would not provide an alternate path for current to flow, while R_S would be zero, resulting in no further voltage drop before the load.

Decreasing R_SH and increasing R_s will decrease the fill factor (FF) and P_MAX as shown in Figure 6.  If R_SH is decreased too much, V_OC will drop, while increasing R_S excessively can cause I_SC to drop instead.

Figure 6 - Effect of Diverging R_s & R_SH From Ideality

The series and shunt resistances, R_S and R_SH, can be approximated from the I-V curve as shown in Figure 7.

Figure 7 - Obtaining the Shunt and Series 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 R_SH in Figure 7.  It follows that R_SH can be derived from the I-V plot obtained with or without providing light excitation, even when power is sourced to the cell.

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, I_SC increases slightly, while V_OC 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 P_MAX.  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 I_SC and V_OC are values for individual cells, the I-V curve shown in Figure 10 is produced. 

Figure 10 - I-V Curve for Modules and Arrays

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 a hardware-independent LabVIEW toolkit to perform the I-V characterization analysis. Figure 11 shows a screenshot of the toolkit’s main VI.

Figure 11 - LabVIEW VI for Solar Cell Characterization

The code consists of three parts: the code that controls the PXI-4130, data that has been collected; not on standard condition, from a poly-crystal solar module for simulation purposes, and the code for analysis. To use the toolkit you have two options you can either open the project and run the simulated examples or you can build your code from scratch using the I-V modeling functions.

Figure 12 - LabVIEW VI for Solar Cell Characterization

Some consideration to take into account are that the code was develop in LabVIEW 8.5 and that you will need to have the math analysis menu on your “functions palette”, since some of the calculation use the “Linear Fit.vi”.

All the calculations are based on the article: Part II – Photovoltaic Cell I-V Characterization Theory and LabVIEW Analysis Code.

The downloadable toolkit contains two sets of code for I-V characterization from forward-bias tests:

• One set to read and analyze data that was previously acquired and saved in LVM format 
• The second set can be run with National Instruments hardware, as described in Part III of this series.  It acquires, analyzes, and presents the results of the I-V characterization.

The toolkit can be downloaded here: Toolkit for I-V Characterization of Photovoltaic Cells.

Summary

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:

• Part I – Photovoltaic Cell Overview
• Part III – I-V Characterization of Photovoltaic Cells using PXI

 

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