Another issue has to do with of the grounding of the secondary circuit. Section 630.15 says "the secondary circuit conductors of an arc welder, consisting of the electrode conductor and the work conductor, shall not be considered as premises wiring for the purpose of applying Article 250."

Since they are not considered premises wiring, the secondary circuit is not required to be grounded. The explanation given in the informational note under Section 630.15 is that connecting welder secondary circuits to grounded objects can create parallel paths and can cause objectionable current over the grounding conductors.

The secondary side for the electrode conductor is very commonly connected to something grounded like a steel structure or a steel building, so that welding can be done on the structure.  This incidental grounding of the secondary circuit is not prohibited, but it can cause problems if the point of grounding for a specific weld is not well chosen.