You have three bulbs rated 150W each. That's a load of 450W.
It ran for 7 hours.
That's 7h*450W = 3150Wh (that's watt hours.)
That's approximately how much energy your bulbs consumed.
Your battery had to supply at least 3150Wh to the inverter.
At a nominal 12 volts, 3150Wh is 262 ampere hours. Watts are volts times amperes, so when you divide the Wh by volts, you get ampere hours.
That is only approximate.
- The battery voltage isn't constant while discharging.
- The current isn't constant while discharging.
- The inverter wastes a lot of power, maybe as much as 50 percent.
Given your data, you can't get a better value.
A better value would require measuring the current from the battery, the voltage from the battery, and the time.
You would measure current and voltage periodically. Say, once a second.
For each second, you multiply the volts and the amperes to get watts, then multiply by 1 second to get watt seconds.
When the battery is fully discharged, you sum up all the watt seconds and convert to watt hours.
That result is the energy that your battery had in it. Energy content is the interesting thing.
Most people don't deal with watt hours, though. Batteries are rated in ampere hours, with the assumption of a nominal 12 volts.
You could either divide your watt hours by 12 volts to get an ampere hour rating, or you can sum up the current measurements every second to get ampere seconds then convert to ampere hours.
That will get you a somewhat more accurate measure of the capacity of your battery.
Regardless, you will never get a completely accurate measurement of the capacity.
The measured capacity will vary depending on the load, the temperature, how well charged the battery was, how old the battery is, and probably a bazillion other details.
What matters for hobby use is that you test it under conditions similar to the ones you will use (similar load and temperature) so that you can see how long your device will run using the given battery.
If your battery was rated for 200Ah when new, then you've got something wrong with your setup.
Looking at your discharge curve, I'd say you should have stopped at about 200 minutes. You shouldn't discharge a 12V battery below about 10.5V.
200 minutes is about 3.3 hours. That makes your rating more along the lines of (262Ah * 3.3/7) = 124 Ah.
Your test isn't really comparable to the original rating, and there's no telling what test conditions were used to determine that original rating.
The crazy, squiggly voltage line in the second half of the chart is your poor battery and the inverter doing their best to provide a constant 110VAC to the light bulbs, and failing.
To get the output voltage up, the inverter has to draw more current. Drawing more current makes the voltage drop more, so the inverter draws more current. At some point, the current draw is so high and the battery voltage so low that the inverter gives up and shuts off.
When the inverter shuts off, the battery voltage recovers, and the inverter kicks in again. Keep repeating load, shutoff, recover, load until somebody takes pity on the poor battery and disconnects the inverter.
