•A large synchronous motor with a very low inrush current could have a critical direct-on-line starting: critical starting means that the starting time is higher than the time the rotor can withstand in blocked condition.•It is necessary to assess the actual motor rotation to be sure that the motor is being self-ventilating during its acceleration and can survive the critical starting.•The historical solution of using an under-impedance relay (ANSI code 21) for starting supervision can give some troubles for the correct and safe protection of the starting of the motor due to inherent measuring errors of instrument transformers.•For the aim of starting supervision, the use of a supervision switch relay (ANSI code 14) based on rotor speed measurement is more reliable and safe than using the solution of under-impedance relay (ANSI code 21).•The under-impedance relay (ANSI code 21) can be useful instead for detecting a blocked rotor condition occurring only after each starting while the motor is already running (equivalent to ANSI function 51R – rotor jam during running). Some petrochemical plants (low density polyethylene type) always require the use of big synchronous motors to feed large power compressors (typically from 10 to 30 MW). In certain supply network conditions, it could happen that the motor undergoes a critical starting which takes several tens of seconds to be completed. “Critical” means that the starting time is higher than the time the rotor can withstand in blocked condition: therefore, it is necessary to assess the actual motor rotation to be sure that the motor is being self-ventilating during its acceleration and can survive the critical starting. By means of numerical simulations, it is demonstrated that the solution of using an under-impedance relay (ANSI code 21) for starting supervision, as is proposed in technical literature since many years, gives some troubles for the correct and safe protection of the starting of the motor, with respect to the most common solution of adopting a supervision switch relay (ANSI code 14) based on rotor speed measurement.