# Measurement of Series Resistance

The series resistance of a solar cell dominates fill factor losses, especially in large area commercial solar cells, so an accurate measurement is vital in quantifying losses. There are several methods to measure series resistance and the comparisons of the accuracy for specific cell types.12

### Curve Fitting

The simplest way to measure series resistance is to fit the illuminated IV curve with either the ideal diode equation or the double diode equation. While this is conceptually very simple there are often problems in practice. One of the biggest problems is that the cell series resistance is a lumped parameter composed of many resistances within the device. A solar cell is a three dimensional device and can be thought of as a network of resistors and diodes. As the level of current changes so does the apparent series resistance. A Thévenin or Norton equivalent circuit can only be constructed in the absence of non-linear elements such as diodes. The blue points are measured data and the blue line is a double diode fit. Curve fitting only works so long as the externally seen Rs is constant, which is rarely the case in practice.

### Effect of Rs on Only Part of the Cell

The simplest way to demonstrate the problems caused by the deviations from the one dimensional model is with the model shown below3. Here only part of the cell is affected by a series resistance as shown in the figure below: Solar cell in which only part of the cell is affected by series resistance.

With only part of the cell affected by Rs a variety of curves are produced. In the simulation below try setting the fraction to 1 (i.e. the simple case where Rs affects the whole cell) and adjusting the internal Rs. It sill follows the simple one dimensional case. The try setting the fraction to 0.5, it produces a rounding around the maximum power point similar to a high J02. In the final case try setting the fraction of the cell affected by Rs to 0.1. In this case the IV curve looks very similar to a cell with a low Rshunt.

### PartialRs

X
020
X
01

Model of a solar cell where only part of the cell is affected by series resistance

Due to the practical limitations of curve fitting extra measurements need to be taken to measure series resistance.