Solar Cells 1

This is the first of a series of posts I wish to make about solar cells. I am particularly interested in the diode models which are used to calculate the I-V characteristic curve of a solar cell. These models have an implicit equation relating current I and voltage V, and that implicit equation can be solved to give voltage as an explicit function of current, for instance. The solution uses the Lambert W function, which is what first led me to the topic of solar cell models.

The calculation of V = f(I) for a solar cell, using the exact formula, can be difficult using computer hardware arithmetic, such as in Fortran or C. Overflow of the arithmetic hardware may occur, because some intermediate numbers in the calculation are extraordinarily large. That poses a problem, since for many applications, such as load balancing of solar cell array panels, it is desirable to be able to perform solar cell calculations on inexpensive computer hardware, such as micro-controllers.

That situation led me in Spring 2015 to write a brief note (Arxiv 1504.01964) suggesting that a variant function y = g(x) = log(W(exp(x))), where W() is the principal branch of the Lambert W function, might be a better way to perform solar cell calculations. That article, though correct, was perhaps a bit terse. Recently S. R. Valluri and I have prepared a working paper which sets out the solar cell application of the y = g(x) function in detail, with example calculations for two actual silicon solar cells (one-diode model) and one actual organic solar cell (two-diode model).

Our working paper is now available on Researchgate at
https://www.researchgate.net/publication/287195509

My intent is, via a sequence of posts in this blog, to walk through that working paper. It may be enjoyable (for me, at least) to go through the material gradually, perhaps explaining some of the details which had to be condensed for the working paper itself.

Best wishes,
Ken Roberts
16-Dec-2015