Voltage drop.

[Simon47]

It would need a "constant power" load - but most loads are speed dependent, reducing power when speed reduces.

Most pumps and fans reduce torque considerably with reducing speed. Something like a hoist would take a fixed torque (almost) independent of speed.

The only thing I can think of with a negative speed-torque curve would be a variable output pump or compressor - configured in constant pressure mode. I've an idea some hydrovane compressors are like that, and a variable output hydraulic pump certainly could be. I've a feeling that a refrigeration compressor would also fit the need (assuming constant cooling load) - but that's a complex system to get your head around and I've had a long day
So you've a hydraulic pump or air compressor configured to maintain system pressure by varying pump output (e.g. swashplate hydraulic pump). If the speed drops, then for a given load, the pump will need to pump more fluid per revolution. Shaft power would remain roughly constant, so for a reduced input voltage, the current would increase - slightly more than needed to maintain constant power as there would be more heating in the motor.

 

[Lucien Nunes]

An excellent example there (the variable-displacement pump) of a load with a backward slope, much steeper than that of the motor itself. I don't have much time but I would like to put a selection of squirrel cage motors in real applications on a 3-phase variac and plot a few points. I'm sure I've done it in the lab and seen the current rise with the rotor magnetic load angle on a synchronous motor as the stator volts drop under constant excitation, but not sure if I've done the same with inductions.

What is worth remembering, for the OP, is that in real-life situations the voltage drop on a practical circuit is a small fraction of the supply voltage. Regardless of the exact value of the effective dynamic resistance or load curve, the current variation will also be modest.

 

[Simon47]

Ooh, electrical machines labs - that takes me back ... a loooong time ! I can just about recall doing experiments with a (small) synchronous motor - loading it and watching the pen move on the plotter, until the load goes too high and the pen does abstract artwork all over the sheet as the motor loses sync For some reason, I can't possibly think why, we were never allowed to play on the bigger machines, try syncing a generator with the 3 lamp technique, and stuff like that - done on real LIVE equipment connected to the mains I bet H&S have watered things down a bit since.
But at least we were mostly spared the need to understand the amplidyne and metadyne that were also in the lab. These modern VSDs take so much of the "fun" out of things.
It was also during my time at uni that the lab got rid of the old battery system for DC stuff. Room full of large cells, with a 'kin big switch and plug board that allowed us to pick off anything from (I think) 2V up to 240V from the battery and route it to the terminals on the bench. With directions to check what voltage is there before connecting anything - someone else might have been doing a different experiment. Of ocurse there were temptations to try "unauthorised experiments", but I think our year wasn't all that adventurous compared to some of our predecessors They got rid of that as the cells were failing and it was going to cost a fortune to replace them - so they just got a large transformer/rectifier to run the larger DC machines and bench PSUs for the smaller stuff.

Now I'm getting all nostalgic when I think how much more I'd learn if I could go back and have another go - with the benefit of a bit more knowledge to start with.