Power supply over-current protection mode: constant current
If you set your power supply to constant current mode, the voltage will change depending on the load. Pure Ohms law V = IR. If I is constant and you change R, V must change. 

Obviously within the limits of how much V is available.

So when you set your current limit on the supply and watch the meters while you increase the load, at first V will be constant and the current needle will ramp up to the limit. After that the current needle will stay put and the voltage needle will drop.