  We propose a new linearizable model for the nonlinear photocurrent-voltage
characteristics of nanocrystalline TiO$_2$ dye sensitized solar cells based on
first principles and report predicted values for fill factors. Upon
renormalization diverse experimental photocurrent-voltage data collapse onto a
single universal function. These advances allow the estimation of the complete
current-voltage curve and the fill factor from any three experimental data
points, e.g., the open circuit voltage, the short circuit current and one
intermediate measurement. The theoretical underpinning provides insight into
the physical mechanisms responsible for the remarkably large fill factors as
well as their known dependence on the open circuit voltage.
