A new approach for modeling the global distribution of ionospheric electric potentials utilizing high-precision maps of field-aligned currents (FACs) derived from measurements by the Ørsted and Magsat satellites as input to a comprehensive numerical scheme is presented. We simulate the universal time (UT) effect in convection patterns caused by variation of solar luminosity and its effect on ionospheric conductivity. A rather complicated dependence of the convection patterns on the combination of UT and IMF clock angle is found. We consider different seasons and IMF conditions and find an increase of the daily variation in the cross-polar potential drop (U_PC) at the equinoxes and a decrease at the solstices. Under equinoctial and zero IMF conditions the U_PC can vary by a factor of two, while the convection cells keep their shape. The model predicts that the summer U_PC can be smaller or larger than the winter U_PC depending on the combination of UT and IMF clock angle. If a UT control of the FAC is introduced to the model, the U_PC does not vary more than 10% over the course of the day.