Refrigerator
Originally, I expected a fridge's power demand to vary depending on its temperature set point, i.e. the cooler you set the temperature, the more power required to maintain that temperature. In fact, a fridge's cooling motor is only turned on or off according to a thermostat, and as a result always draws the same level of power while it is on, and therefore spends a larger proportion of each day cooling as opposed to idle.
Kettle
Similar to the fridge, I expected the power demand of a kettle to vary depending on the amount of water in the kettle. However, the power demand is always constant while it's boiling, and it's actually the time taken to boil the water which increases with the volume of water.
Oven
Following the same trend, electric ovens are also thermostatically controlled. As a result, they draw the same power irrelevant of the temperature set point. This means the heating element spends more time heating for higher temperatures, and leaves longer gaps between heating periods for lower temperatures.
Others
Spotted the trend yet? Other examples in this category include air conditioners, microwaves, electric hobs and irons. This is in addition the even dumber category of completely manually controlled appliances, such a lamp or fan.
Exceptions
Unfortunately, all appliances aren't this dumb. Some appliances have a power demand that slowly ramps up or down at the start or end of its usage. One appliance which is quite the opposite of those described above is the plasma television. These appliances draw a power demand which is proportional to the brightness of the screen, with a fully white screen requiring the maximum power draw and a black screen requiring the minimum power draw. Such appliances are not only hard to disaggregate, but also significantly complicate the process of disaggregating other simpler appliances.
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