We develop a comprehensive rate equations model for semiconductor quantum dot solar cells (QDSCs). The model is based on the continuity equations with a proper account for quantum dots (QDs). A general analytical expression for the total current density is obtained, and the currentvoltage characteristic is studied for several specific situations. The degradation in the open circuit voltage of the QDSC is shown to be due to strong spontaneous radiative recombination in QDs. Due to small absorption coefficient of the QD ensemble, the improvement in the short circuit current density is negligible if only one QD layer is used. If spontaneous radiative recombination would be suppressed in QDs, a QDSC with multiple QD layers would have significantly higher short circuit current density and power conversion efficiency than its conventional counterpart. The effects of photoexcitation of carriers from discrete-energy states in QDs to continuum-energy states are discussed. An extended model, which includes excited states in QDs, is also introduced.