Extension Cord Useage - Guage

You don't want solid wire (not sure they even sell them). You want "stranded" copper wire. Romex in houses is solid wire (ie: 1 strand). In a house, it's OK because once installed, it rarely if ever is moved. An extension cord is constantly being bent and unbent. The outer layer of a very thick strand is stressed more than the outer layer of a thin strand. Eventually, that outer layer "work hardens" and becomes brittle and can break or worse, the poor connection around the break point can overheat. The thinner strands of stranded wire experience less strain so they hold up longer.

Of course, it really depends on how long the wiring run is and how many amps you are drawing. If you are just running the fridge and a few lights (maybe 3-5amps), a little 15amp cord from home depot is generally going to be fine. Once you want to run the air/con and everything else (15-24amps), even 10ga may be marginal if you have  the standard 50ft cord with a 100ft extension.

Regardless, it's a good idea to keep a voltage meter plugged in where you can see it or have a surge protector that also checks for low voltage and will cut power if it gets too low. We have a meter that stays plugged in near the door and if we see it get down around 108v or lower, we shut down and switch to generator power.