On Sun, 28 Jun 2015 07:14:43 -0400, pete wrote:

I had a recent power outage that lasted for 3 days. Not having a
generator on hand, I decided to try using what I did have for short term
power purposes. The items consisted of the car, 500 watt inverter, and
I had an extra car battery available.

I hooked up the inverter directly to the car battery in the car. With
the car running, I was able to run the 46" LCD TV, and a couple of CFL
lights which was all I really needed to do. However, I ran into some
problems. If the car wasn't running the entire time, the items
connected to the inverter would start flickering on and off after a
period of time. If off of the car battery inside the car, this might be
within an hour, but with the separate battery, maybe 10 minutes unless
it was coupled to the car battery in the car with the car running.

Maybe you overdrew the battery?

A normal car battery has a power of maybe 5kW. It's normally run for a
few seconds which means it normally supplies, let's say, 10kJ of energy.
It's designed to release a few percents of the total energy stored within
itself. Lets say 2%. So a fully charged battery contains about 500kJ of
energy, however only a small percentage of that is repeatedly
recoverable. If we say a car battery can be discharged to 10% repeatedly,
that gives us 50kJ to work with. If we draw that energy at a rate of
200W, it will expire in 500 seconds, which is 8.33 minutes and close to
your measurement of 10 minutes.

The critical question is at what internal charge level does the battery
start dying? If the voltage at the terminals starts dying when the charge
drops to 90%, that explains the performance of the extra battery. If the
charge has to drop to 30% before the battery starts to fail, that
explains the behavior of the in-the-car battery.

Obviously, my calculations assume undamaged batteries. If the batteries
were heavily used and were overdiven previously, that would lower the
total amount of energy present in them and ipso facto lower the amount of
recoverable energy.

I see portable power packs with internal battery and inverter at places
like Walmart. The inverter is usually 400 watts or so, so I know this
method should have worked.

100% certain that the secret is in the battery.

For this scheme to work assuming lead-acid batteries, you want a battery
that can be severely discharged, a so-called "deep cycle battery". These
come in many varieties so shop around if you're interested. You can also
make it work with NiCd batteries. Some have also suggested NiFe batteries
that you can supposedly build yourself.