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Vertical space bears great potential of solar energy especially for congested urban areas, where photovoltaic (PV) windows in high-rise buildings can contribute to both power generation and daylight harvest. Previous studies on sun-tracking PV windows strayed into the trade-off between tracking performance and mutual shading, failing to achieve the maximum energy generation. Here we first build integrated models which couple the performance of sun-tracking PV windows to the rotation angles. Secondly, one-degree-of-freedom (DOF) and two-DOF sun tracking are mathematically proven to be not able to gain either maximum power generation or non-glare daylighting under reasonable assumptions. Then we derive the optimum rotation angles of the variable-pivot-three-degree-of-freedom (VP-3-DOF) sun-tracking elements and demonstrate that the optimum VP-3-DOF sun tracking can achieve the …