I can see that your question is directed at the Alt E Store.
I would like to give my opinion on the subject.
If you take a look at the specifaction chart on the sales page you can see that Trace reccomends 4/0 (pronounced - four ought.) http://shop.altenergystore.com/itemdesc~ic~XANPP-SW5548/D~eq~~Tp~.htm
What I have done in the past is to take the maximum continuous wattage and divde that by the inverters low voltage disconnect set point. which in this case would be 5500/42=131 amps. Now this is where it can get monotonous. Just how much amperage a wire can safely handle (per NEC) depends on several factors. Those being the size and type of wire and its insulation and if it is suspended in free air or in side of conduit and how many current carrying conductors are in that conduit etc. etc. and so on and so forth. I was confused by the statement made in the notes of that "Practical Guide."
"in raceway in freee air"
The first thing to my mind was, which one? In a raceway or in free air? A raceway in free air doesnt make any sense to me. To my mind in a raceway means inside of an enclosure. A box of varible dimensions and or configurations and conduit, and free air to be like but not limited to the grid, from pole to pole. The same size and type of wire can have different amperage ratings in these two scenarios. Alt-E covers themselves nicely though by including the part about refering to the NEC.
That is after all what the inspector is going to use. If the wire size and type is wrong and you tell the inspector "thats what Alt-E said" it will not make any difference.
I know I am probably coming accross as being belligerent but its for a good reason, the NEC falls under the jurisdiction of the NFPA National Fire Protection Association. The key word here being fire. http://www.nfpa.org/index.asp
Back to that figure of mine, 132 amps. I going to give an example. #2AWG CU THHN, uhhm you know what, something just came up so I am going to leave now but I leave you something to research while I am gone. http://www.sandia.gov/pv/docs/John_Wiles_Code_Corner.htm