Is it possible to set PBZ series to maintain the current limit without turning off the output?

You can use the overcurrent protection function of the I.LIM (current limit), which limits the output current from exceeding the set point.
When this protection is activated, the panel shows “+I.LIM” with a beep sound.
For the details, read the user’s manual – chapter of Basic Features – Protection Features and Alarms – Protection Feature Types.