I am trying to calculate how long I can run a given load (a sound system and laptop charger) from a 55 Ah 12 V battery using a pure sine wave inverter (specifically, this one). Though, at the end of the day, I'm mostly interested in figuring out "can this battery run the system for the duration of an event".
I used a Kill-a-Watt to measure the power used to run the system for a 4-hour event, and at the end it read 0.28 kWh.
I've calculated the capacity of my battery in watt-hours, including a factor for inverter inefficiencies (which admittedly, I just pulled out of the internet, if this looks wrong feel free to point me in the right direction!)
12 V * 55 Ah * 90% efficiency = 594 watt-hours. 594 is less than 280, so yes, the battery has the capacity to run my system for the duration I'm interested in (with plenty of wiggle room).
However, I noticed that the Kill-a-Watt reported a power factor fluctuating around 0.65-0.67.
I have heard (somewhere online, though I couldn't find it when I tried searching) that there's a difference between "apparent power" and "actual power". I can't find the reference for this claim, but I have heard that power factor is a concern in large industrial plants because "the power plant has to do the work to generate the whole sine wave, even if the load only uses part of it", and the power company measures the power factor for these industrial plants and charges them for the "apparent power", or "the entire sine wave".
Question #1: Is that understanding of power factor correct?
Question #2: Does this mean that I have to take power factor into consideration when calculating how long my battery can run my system? If my inverter needs to generate the "entire sine wave" but my load only uses 60% of it, where does that other 40% of the power go? Dissipated somewhere as heat?