The Lyon- Fedder- Mobarry global magnetohydrodynamic simulation code is used to examine a period of steady magnetospheric convection driven by a moderately southward IMF and a steady and quite low solar wind speed. Two other runs were performed to test the effects of increasing solar wind driving: one with 50% increase in the IMF magnitude and one with 50% increase in the solar wind speed. Larger IMF magnitude leads to nightside reconnection closer to the Earth but the steady state of the magnetotail is not changed. On the other hand, higher solar wind speed enhances Earthward mass and Poynting flux transport as well as their variability. The increase in the solar wind E-Y is the same for both runs, but the EY in the magnetosheath is larger in the run in which the speed is enhanced, which is associated with the higher magnetotail activity in that simulation.