Solar Energy

Bifacial production formula

The science of today is the technology of tomorrow – Edward Teller


A new thermodynamic formula reveals that the bifacial cells making up double-sided panels generate, on average, 15% to 20% more sunlight to electricity than the mono facial cells of today’s one-sided solar panels. The formula considers different terrain, such as grass, sand, concrete, and dirt. The formula, developed by two Purdue University physicists, can be used for calculating in minutes the most electricity that bifacial solar cells could generate in a variety of environments, as defined by a thermodynamic limit.

“The formula involves just a simple triangle, but distilling the extremely complicated physics problem to this elegantly simple formulation required years of modeling and research. This triangle will help companies make better decisions on investments in next-generation solar cells and figure out how to design them to be more efficient,” said Muhammad “Ashraf” Alam, Purdue’s Jai N. Gupta Professor of Electrical and Computer Engineering.




The formula can calculate the thermodynamic limits of all solar cells developed in the last 50 years. These results can be generalized to technology likely to be developed over the next 20 to 30 years. The formula shows that the efficiency gain of bifacial solar cells increases with light reflected from a surface. Significantly more power converted from light reflected off of concrete, for example, compared to a surface with vegetation.




The powerful graphical approach called the normalized “Shockley–Queisser (S-Q) triangle” (i.e., imp=1−vmpimp=1−vmp) is sufficient to calculate the bandgap sequence and efficiency limits of arbitrarily complex photovoltaic (PV) topologies. There is validated results against a wide variety of specialized cases reported in the literature and are accurate within a few percent. We anticipate that the widespread use of the S-Q triangle will illuminate the deeper physical principles and design trade-offs involved in the design of bifacial tandem solar cells under arbitrary concentration and series resistance. Over the next decade by year 2030, the expectation is that 50% of all module production will be with bifacial cells.

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