| Summary: | In this article, the performance of an inclined north-south axis (INSA) multiple positions sun-tracked V-trough with restricted reflections for photovoltaic applications (MP-VPVs) is investigated theoretically based on the imaging principle of mirrors, solar geometry, vector algebra and three-dimensional radiation transfer. For such a V-trough photovoltaic module, all incident radiation within the angle <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>θ</mi> <mi>a</mi> </msub> </mrow> </semantics> </math> </inline-formula> arrives on solar cells after less than <i>k</i> reflections, and the azimuth angle of V-trough is daily adjusted <i>M</i> times about INSA to ensure incident solar rays always within <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>θ</mi> <mi>a</mi> </msub> </mrow> </semantics> </math> </inline-formula> in a day. Calculations and analysis show that two-dimensional sky diffuse radiation can’t reasonably estimate sky diffuse radiation collected by fixed inclined north-south V-trough, but can for MP-VPVs. Results indicate that, the annual power output (<i>P<sub>a</sub></i>) of MP-VPVs in a site is sensitive to the geometry of V-trough and wall reflectivity (<i>ρ</i>), hence given <i>M</i>, <i>k</i> and <i>ρ</i>, a set of optimal <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>θ</mi> <mi>a</mi> </msub> </mrow> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mi>φ</mi> </semantics> </math> </inline-formula>, the opening angle of V-trough, for maximizing <i>P<sub>a</sub></i> can be found. Calculation results show that the optimal <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>θ</mi> <mi>a</mi> </msub> </mrow> </semantics> </math> </inline-formula> is about 21°, 13.5° and 10° for 3P-, 5P- and 7P-VPV-<i>k</i>/<inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>θ</mi> <mi>a</mi> </msub> </mrow> </semantics> </math> </inline-formula> (<i>k</i> = 1 and 2), respectively, and the optimal <inline-formula> <math display="inline"> <semantics> <mi>φ</mi> </semantics> </math> </inline-formula> for maximizing <i>P<sub>a</sub></i> is about 30° for <i>k</i> = 1 and 21° for <i>k</i> = 2when <i>ρ</i> > 0.8. As compared to similar fixed south-facing PV panels, the increase of annual electricity from MP-VPVs is even larger than the geometric concentration of V-trough for <i>ρ</i> > 0.8 in sites with abundant solar resources, thus attractive for water pumping due to stable power output in a day.
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