There are two simple examples of constant power loads.
One is a motor which is mechanically loaded at anything up to its full load power.
If you reduce the voltage the motor's speed will decrease slightly (more slip) and the current being drawn will increase to provide the same torque and power which was being produced at the higher voltage.
You can look at it this way:
If the motor is to continue to produce the same power (turn at roughly the same speed), the small decrease in speed resulting from the voltage drop will reduce the back EMF of the motor, which will in turn cause more current to be drawn.
With the exception of a several percent factor related to slip, the motor will continue to drive its full mechanical load and consume nearly constant power (as measured by a wattmeter) from the AC source.
A second common constant power load is the regulated driver to an LED lamp. The driver tries to deliver the same DC power to the LED array independent of the incoming voltage. Whether the driver tries to maintain constant power or tries to sense the voltage and/or duty cycle of the AC source determines whether or not that driver allows the lamp to be dimmed by control of the incoming line voltage.
The constant power driver will draw more current from the source to keep the internal capacitor charged as the input voltage decreases.
Constant current loads include the airport and some street lighting described in an earlier post. But keep in mind that it is the system of transformer and lamps that is constant current, not the lamps themselves. The lamps are designed to operate at a constant current, but do nothing by themselves to regulate that current.
A simple constant voltage load is a zener diode. It will conduct as the applied voltage exceeds the zener voltage and as the voltage rises slightly it will consume much more current so that the internal resistance times the current makes up the difference between the applied voltage and the zener voltage. If the source voltage is stiff, this will at some point destroy the diode.
An electric resistance heater is a constant impedance load (the typical nichrome wire has a very low temperature coefficient of resistance, unlike an incandescent light bulb.)