In my opinion we have to consider that motor try to maintain the nominal revolution.
And the all machine load the motor the constant mechanical power. If we lower the voltage motor try still maintain the mechanical power and the current has to rise and vice versa.
It is connected with E inducted in the motor in opposite to the U supply voltage.
It is most observed when the motor starts, current is the biggest. I=(U-E)/R, R is summary windings and line supply.
Sorry for my language, I am Polish.
