Another correction, since it's come up several times.
Increases in current due to reduced voltage only happens with induction motors, since the connected (driven) load is essentially constant-torque and speed (and therefore, constant power). I = P / V applies, if you ignore efficiency and power factor (or just assume they're constant). Air conditioning and refrigeration compressor motors will, therefore, draw more current as the voltage is decreased.
Purely resistive loads, like water heaters, hair dryers, and space heaters, will draw less current as the voltage decreases, since the impedance is essentially fixed. For those, I = V / R does apply (R is essentially a constant, so as V goes down, I goes down). A 1500W heater is only 1500W at the rated voltage (usually 120V in North America), and will draw less current and produce less heat at lower voltages.