Geometry effects on luminescence solar concentrator efficiency: analytical treatment

Area of Science:

• Materials Science
• Renewable Energy
• Optoelectronics

Background:

• Luminescence solar concentrators (LSCs) are semitransparent photovoltaic cells suitable for urban environments.
• Optimizing LSC design is crucial for enhancing solar energy harvesting efficiency.

Purpose of the Study:

• To analytically derive efficiency expressions for LSCs with various regular unit shapes.
• To investigate the impact of shape and size on LSC device performance.
• To determine the critical size of LSC units beyond which inner regions become inactive.

Main Methods:

• Analytical derivation of integral-free efficiency expressions for different regular unit shapes.
• Analysis of optical path distribution to understand shape effects.
• Formulation of critical size equations based on matrix absorption coefficients.

Main Results:

• All regular shapes exhibit similar efficiencies, irrespective of perimeter length, based on optical path distribution.
• Rectangular LSC units demonstrate higher efficiency than other shapes of equivalent area due to reduced average optical path.
• An explicit formula for critical LSC unit size (∼2.7/α for squares) was derived, indicating inactivity in larger units (70-90 cm for common polymers).

Conclusions:

• LSC efficiency is influenced by shape, with rectangles offering advantages.
• Understanding critical size is essential for designing effective LSC units and large-area tiling.
• The derived formulas provide a basis for optimizing LSC design for urban solar energy applications.