Why do I need to use a stepper motor supply voltage higher than the rated phase voltage?

Stepper motors have a rated phase voltage and rated phase current. A typical stepper motor might have a rated voltage of 2.5 Volts and a maximum current of 2.8 Amps, for example. This means if you hook it up to 2.5 Volts it will draw 2.8 Amps. If you try to run it at a higher voltage it will draw more current and get excessively hot. But stepper motors are usually not hooked up straight to a voltage source. Instead, a stepper driver circuit is used that regulates the current. If you hook it up to 24V, for example, the motor would try to draw more current, but the stepper motor driver will not allow that to happen. That's because driver circuit uses its high frequency PWM and comparator algorithm to limit the average current to the desired maximum value, which is typically configurable. Stepper motors are designed to work this way and it is safe to run the motors at up to 20 times the rated voltage. You will actually get much better performance (max speed and dynamic behavior) by running at a higher voltage than the rated voltage.