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2018 Forester XT Limited CVT
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I have just completed an extensive search for an inverter to use my other car's (Nissan Leaf) battery as backup power for the infamous California blackouts and have the following advice:
1. Stick with pure sine wave units. They are more efficient and your electronics will thank you.
2. If you are going to do a permanent installation, such as 110VAC outlets in the back of the console, you will need a compact unit that can fit in a small, well ventilated space.
a. keep at or below 300W due to cooling requirements. Consider mimicking the Subaru option. You can probably do it cheaper and better anyway.
3. For occasional use as a direct battery hookup, go big, like up to 3,000W constant power. This will run tools and appliances that have heavy starting loads. No need to be too compact here. spend money on the guts, not a fancy case.
a. consider using a 50A quick disconnect (Anderson connector) permanently wired to the battery.

Happy inverting!

GD
1. Pure sinewave is preferable, however they are not more efficient. The pure sinewave will cause fewer problems with your electrical loads though.
2. The most important installation issue is the voltage drop along the dc cables between the battery and the inverter. Voltage drop along these cables will cause the inverter to enter low-voltage shutdown during non-insignificant current draw. As an example, if you are going to run a 300 W ac load, you're going to draw approx 30 A from the battery.
3. You're not going to put a 3,000 W inverter in a Forester (3,000 W = 300 A dc draw). A 50 A switch is not going to cut it for more than a 500 W inverter.

For a Forester or similar vehicle, you won't be doing more than charging your phone or running a laptop or similar load, and I'd recommend you have the engine running since the vehicle battery is a starting battery and not a deep-cycle battery.

Find the power draw of the loads you want to run, and then see if the dc socket in the car can supply the current (at a decent voltage). If the socket can't supply the power, you're looking at direct connection to the battery. Remember to size the wire appropriately -- calculate the dc current required, calculate the voltage drop through copper, look up the wire gauge needed to provide the needed (or less) voltage drop, and as close to the battery as possible, install your overcurrent protection, sized for the gauge of wire installed.
 

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The DC plugs in the car (at least my 2016) share a 20A fuse, and are individually rated to 10A, which is somewhat confusing. A 150W inverter should work fine in either DC plug, if the device you want to power pulls more than that, hardwire it to the battery with big wires. Your mileage will vary with loads surging over 150W, but continuous shouldn't be a problem at that level.
Without breaking out the calculator, you can just divide by 10. A 150 W inverter will draw approx 15 A from a 12 V vehicle system. There is a bit of fudge in this approximation to account for efficiency and voltage drop. Using the sockets will incur additional voltage drop at the contact resistance (between socket and plug).

Also look at the inverter ratings. Some ratings are "surge" ratings, power that the inverter can supply for a short time, limited by the physical electronics and connections, and some are "continuous" ratings, power that the inverter can supply indefinitely given appropriate input, at a given ambient temperature.
 

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Power inverters are very good noisemakers, but then so is a gasoline engine's ignition system. The charging system might not be that quiet either.
 

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Years back, an inverter would not run a 110V refrigerator, the specs specifically said they would not power anything with a compressor. Things might have changed since then.
Inverters come in different sizes and capabilities. A passenger car may struggle with or be incapable of running an inverter of the required size.
 

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All you need to do is make sure the inverter can meet or exceed the locked-rotor current for the compressor you are using. Many people aren't going to install additional batteries in their vehicles. (I used to do tech support for a power conversion company.)
 
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