You can use a wire size table or calculator (such as the one at the bottom of this page
) once you know your wire lengths. You only need the high current wiring between the battery(ies) and the inverter.
The Xantrex XPower 3000 can produce 3000 watts for a maximum of 5 minutes; its continuous rating is for 2500 watts. If we use the 3000 watts to determine wire size, and a nominal 12V as the source voltage, the input current to the inverter will be 3000/12 or 250 amps. If we make the assumption that the total wire length is within the recommended 10', (5' for each wire) and the 3% allowable voltage drop (which is really too high for 12V systems; 3% of 12.6 (a fully charged battery) would leave 12.2 volts at the inverter), a #1 wire would be acceptable.
Unfortunately, it isn't that simple. First, your batteries have internal resistance. If you use a pair of 6V batteries, the internal resistance is in series, which means they add together. Feeding inverters is one of the few places where a pair of 12V batteries with the same amp hour capacity will work better than a pair of 6V because the 12V batteries are wired in parallel, thus halving the internal resistance.
While many devices will work OK at a lower than designed voltage, there is a problem with an inverter. If the voltage feeding the inverter drops, and the load stays the same, the current to the input of the inverter must go up. This results in more voltage drop, both due to the internal resistance of the battery & the loss in the wiring. As the battery supplies current, its voltage drops. The combination of the two can drop the voltage to the inverter to the point where the under voltage buzzer goes off, or even worse, shuts down the inverter (most shut off at 10.5V). You can't do much about the internal resistance of the batteries, but you can produce less across the wiring.
This is why most inverter manufacturers recommend wire sizes in excess of the NEC wire table calculations. For example, Xantrex recommends a minimum of #2/0 wire for a 10' run using the XPower 3000 (PDF Manual
), and states that size wire will not allow the inverter to supply 3000 watts. They recommend using #4/0 for standard installations. Longer runs than a combined 10' require even larger wires.
This is not to say that smaller wiring won't work. As long as you meet the wire size tables, you will have a safe installation (assuming you use a properly rated catastrophic fuse) but you will find the inverter shutting down earlier than it would with the recommended wire, and that it may not operate at all when you battery is not fully charged. Since most users never use the full capacity of their inverters, an undersized installation may never show up, however if at some point down the road you find you need the full capacity, rewiring may be a difficult project.
In my case, I am using Xantrex's recommended #0 wire for a 1000 watt inverter. While making a cup of coffee - a 65 amp draw at the start & with full batteries), I can watch the current increase to 70 amps (and the resulting voltage drop) over the 10 minutes it takes to brew. The voltage recovers quickly after the inverter shuts down, indicating that the drop was caused by resistance, not the 6-8 amp hours supplied to make the coffee.
Sorry to go on so long, but good installations of high powered inverters is a pet peeve of mine - I did a workshop at the last Oregon Gathering on the subject...