PermalinkSubmitted by jmwagner on Wed, 02/15/2023 - 09:41

You state: "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."

I agree, and I would like to point out a relevant consequence: When the operating point of the diodes is kept constant and not-too-large variations in current and voltage are considered, an equivalent circuit could still be obtained by linearizing the behavior of the diode(s). The most simple case to which this approach can be applied is the lumped equivalent circuit, containing only one (or two) diode(s).

Then, for the chosen operating point, any nonlinear circuit element can be replaced by a linear resistor, the value of the latter obviously depending on the operating point. In this way, we have found a significantly improved version of the lumped equivalent circuit where the current dependence of the lumped series resistance is taken into account explicitly (at least in linear order) [1]. Comparing this approach with experiment, we find excellent qualitative agreement [2]; achieving quantitative agreement is the subject of ongoing work.

Experimentally, however, we already found that the standard notion of the series resistance under illumination (Rs,light) being different from that in the dark (Rs,dark), as concluded in the paper by Pysch, Mette, and Glunz (2007), is based on a misinterpretation of the experimental results [3]. Instead, when the concept of an operation-point-dependent Rs is consequently applied, one finds that for normal operation conditions, there is no difference between Rs,light and Rs,dark -- in full agreement with the lumped equivalent circuit [1, 2].

Dr. Jan-Martin Wagner, University of Kiel, Germany

[1] J.-M. Wagner, J. Carstensen, and R. Adelung, "Fundamental Aspects Concerning the Validity of the Standard Equivalent Circuit for Large-Area Silicon Solar Cells" (Editor's Choice), Physica Status Solidi A 217, 1900612 (2020); DOI: 10.1002/pssa.201900612

[2] J.-M. Wagner, A. Schütt, J. Carstensen, and R. Adelung, "Linear-response description of the series resistance of large-area silicon solar cells: Resolving the difference between dark and illuminated behavior", Energy Procedia 92, 255 (2016); DOI: 10.1016/j.egypro.2016.07.072

[3] J.-M. Wagner, K. Upadhyayula, J. Carstensen, and R. Adelung, "A critical review and discussion of different methods to determine the series resistance of solar cells: Rs,dark vs. Rs,light?", AIP Conference Proceedings 1999, 020022 (2018); DOI: 10.1063/1.5049261

## Comments

## Equivalent circuit

You state: "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."

I agree, and I would like to point out a relevant consequence: When the operating point of the diodes is kept constant and not-too-large variations in current and voltage are considered, an equivalent circuit could still be obtained by linearizing the behavior of the diode(s). The most simple case to which this approach can be applied is the lumped equivalent circuit, containing only one (or two) diode(s).

Then, for the chosen operating point, any nonlinear circuit element can be replaced by a linear resistor, the value of the latter obviously depending on the operating point. In this way, we have found a significantly improved version of the lumped equivalent circuit where the current dependence of the lumped series resistance is taken into account explicitly (at least in linear order) [1]. Comparing this approach with experiment, we find excellent qualitative agreement [2]; achieving quantitative agreement is the subject of ongoing work.

Experimentally, however, we already found that the standard notion of the series resistance under illumination (Rs,light) being different from that in the dark (Rs,dark), as concluded in the paper by Pysch, Mette, and Glunz (2007), is based on a misinterpretation of the experimental results [3]. Instead, when the concept of an operation-point-dependent Rs is consequently applied, one finds that for normal operation conditions, there is no difference between Rs,light and Rs,dark -- in full agreement with the lumped equivalent circuit [1, 2].

Dr. Jan-Martin Wagner, University of Kiel, Germany

[1] J.-M. Wagner, J. Carstensen, and R. Adelung, "Fundamental Aspects Concerning the Validity of the Standard Equivalent Circuit for Large-Area Silicon Solar Cells" (Editor's Choice), Physica Status Solidi A 217, 1900612 (2020); DOI: 10.1002/pssa.201900612

[2] J.-M. Wagner, A. Schütt, J. Carstensen, and R. Adelung, "Linear-response description of the series resistance of large-area silicon solar cells: Resolving the difference between dark and illuminated behavior", Energy Procedia 92, 255 (2016); DOI: 10.1016/j.egypro.2016.07.072

[3] J.-M. Wagner, K. Upadhyayula, J. Carstensen, and R. Adelung, "A critical review and discussion of different methods to determine the series resistance of solar cells: Rs,dark vs. Rs,light?", AIP Conference Proceedings 1999, 020022 (2018); DOI: 10.1063/1.5049261