The Optimal Tilt Angle of Monofacial and Bifacial Modules on Single-Axis Trackers
Keith R. McIntosh, Malcolm Abbott, Benjamin A. Sudbury
Abstract
The optimal tilt <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">β</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">opt</sub> of the modules in a single-axis tracker is often determined by assuming all sunlight is direct and ground reflectance is zero. Prior works, however, have demonstrated that <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">β</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">opt</sub> is smaller when diffuse light is significant. In this article, we determine how <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">β</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">opt</sub> decreases as the conditions change from clear sky to overcast, accounting for many complicated effects like row-to-row shading of diffuse light, ground reflection, structural shading, cell-to-cell mismatch, and angular and spectral dependencies. We find that when compared to monofacial systems, bifacial systems tend to have a higher <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">β</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">opt</sub> when it is cloudier and a lower <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">β</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">opt</sub> when it is sunnier. We also quantify the increase in annual yield that arises when accounting for indirect light at three example sites with different climates, finding it to be ∼30% lower for a bifacial system than a monofacial system; the gain was 0.8%–1.5% for bifacial systems and 1.1%–2.1% for monofacial systems, where the highest gain was attained in the cloudiest climate.