OSHA requires arc fault study?

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Yes, OSHA requires a hazard and risk assessment for all electrical hazards including arc flash. This may require a determination of the incident energy for utilities and industry. OSHA 1910.269 requires "reasonable" assessment of arc flash hazards and PPE to match the potential hazard.
In addition, NFPA 70E - 2015, which is a consensus standard - and used by OSHA for abatements - stipulates that an arc flash study be performed unless the arc flash look-up tables apply. All references do allow you to use tables in the NFPA 70E, NESC and OSHA - however, these tables are intended to provide a wide and conservative value whereas an arc flash study generally models the arc flash energy more accurately. We don't want to overprotect; neither do we want to under-protect. Performing an arc flash study generally pays for itself in identifying system errors (like fuse ratings and protection setting anomalies) and provides savings by procuring the correct level of arc rated PPE.