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FIRST, I AM NOT AN ELECTRICIAN SO BEFORE YOU DO ANY OF THIS CHECK WITH A LICENSED ELECTRICIAN WHO HAS THE LIABILITY INSURANCE TO OFFER ADVICE.
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I talked to a few electricians I know about generator grounding and travel trailers. Here is a condensed version of what they told me.
According to NEC trailers do not require ground because they are a
separately derived system. A separately derived system is essentially a system that has an isolated source. Assuming your trailer has one electrical source. That is one of the reasons why a trailer mounted generator does not require a ground rod to be driven into the ground. The same applies to a portable generator connected to a trailer.
NOW THE BIGGIE AND IMPORTAN ITEM
The generator must be bonded to trailer ground. That is the ground lug of the generator must be connected to trailer ground. A trailer mounted generator will have this done at the factory when the generator was installed. Likewise, with a portable generator you should (or as NEC would say "SHALL") do the same.
So what does bonding do? I have a ground installed in my power cable; doesn't that do the same thing?
The answer is yes,
but for safety sake, bonding is a better way to go. For example, just suppose the ground wire came loose in the cable from the connector you would now have an ungrounded trailer. Not a safe thing to happen.
The solution is rather simple, ground the generator's ground lug to the trailer ground on a separate cable. As long as either ground (power main or the grounding bond) stays intact, the generator stays grounded with respect to the trailer.
This only applies to separately derived systems (trailers, for example). Houses are a different story, since they are typically not separately derived and usually require ground rods.