A new design concept, called one axis three positions sun-tracking polar-axis aligned CPCs (3P-CPCs, in short), was proposed and theoretically studied in this work for photovoltaic applications. The proposed trough-like CPC is oriented in the polar-axis direction, and the aperture is daily adjusted eastward, southward, and westward in the morning, noon and afternoon, respectively, by rotating the CPC trough, to ensure efficient collection of beam radiation nearly all day. To investigate the optical performance of such CPCs, an analytical mathematical procedure is developed to estimate daily and annual solar gain captured by such CPCs based on extraterrestrial radiation and monthly horizontal radiation. Results show that the acceptance half-angle of 3P-CPCs is a unique parameter to determine their optical performance according to extraterrestrial radiation, and the annual solar gain stays constant if the acceptance half-angle, theta(a) is less than one third of omega(0,min), the sunset hour angle in the winter solstice, otherwise decreases with the increase of theta(a). For 3P-CPCs used in China, the annual solar gain, depending on the climatic conditions in site, decreased with the acceptance half-angle, but such decrease was slow for the case of theta(a) <= omega(0,min)/3, indicating that the acceptance half-angle should be less than one third of omega(0.min) for maximizing annual energy collection. Compared to fixed east west aligned CPCs (EW-CPCs) with a yearly optimal acceptance half-angle, the fixed south-facing polar-axis aligned CPCs (1P-CPCs) with the same acceptance half-angle as the EW-CPCs annually collected about 65-74% of that EW-CPCs did, whereas 3P-CPCs annually collected 1.26-1.45 times of that EW-CPCs collected, indicating that 3P-CPCs were more efficient for concentrating solar radiation onto their coupling solar cells. (C) 2010 Elsevier Ltd. All rights reserved.