There was a good research project on this by the EPRI. It is called "The Effects of Reduced Voltage on the Operation and Efficiency of Electric Systems" EPRI EL-3591 in 1984. The report has excellent data on residential and industrial equipment showing the voltage, torque (if applicable), VAR's, I, V, etc. It almost suggests the wattage generally goes down on most equipment with reduced voltage, which would benefit the residential customer. It also suggests that smaller motors operated at nameplate torque also show an decrease in VARs, the extent depends on the load on the motor; light load - more decrease in VARs and W, while a fully loaded motor shows some decrease but not much.
Check it out, the results of the research are very interesting and might surprise you.