NikolaTesla, If the power supplies are redundant hot swap power supplies, then you can remove and replace PS1 while the server is online. I would also suggest, at your earliest convenience, to schedule downtime to update the server to current.  I see you are a few updates back on the BIOS, iDrac, as well as the Lifecycle Controller. Now with the BIOS and iDrac being 4 updates back, I would suggest clicking on "Other Versions" on those pages and walk the updates up to current.   Let me know if this helps.
System Model PowerEdge R720 System Revision IBIOS Version 1.6.0Firmware Version 1.40.40 (Build 17)Lifecycle Controller Firmware 1.1.5.165IDSDM Firmware Version N/A     IDRAC LOG The system board PS1 PG Fail voltage is outside of range. The temperature for power supply 1 is outside of range.Power Supply 1: Status = 0x200c, IOUT = 0x0, VOUT= 0x0, TEMP= 0xc0, FAN = 0x0, INPUT= 0x30Power supply 1 is operating normally. Voltages System Board PS1 PG Fail power configuration , Reduncancy Not Redundant Hot spare Enable Primary PSU1 So, - 7/24 working server, Can I solve this w/o shutdown. - Can I change PSU while power on? What have to be redundancy setting ? Regards.   
The system board PS1 PG Fail voltage is outside of range