I have a 3kw pure sine wave inverter with 1/0 cable connected to two group 31 AGM batteries and I wouldn't run a 13k btu A/C off of it. Even with AGM batteries the peukert effect would quickly drain the batteries. Very few alternators can keep up with a 150a continuous draw. This isn't to mention the 300+ amps of start surge load. Keep in mind that you must recalculate the current draw for any change in voltage. For example 1200 watt constant load at 120 V is only 10 amps but at 12 V it is 100 amps. This does not account for losses in the inversion process or capacitive start loads.