I don't know if anyone mentioned this in all of these messages (nor do I know for sure if anyone really cares) but when the power drops dramatically - but is still measurable - I believe that this is what is called a "brown-out". This is opposed to what we call a "black-out". A black-out is where all power has ceased to be delivered.
When either of these things happen to me I realize how incredibly spoiled and "civilized" I am. I am so very used to being able to just go and plug in virtually anything in an electrical outlet and the device will properly operate. My air conditioner, my fans, my television, etc. I feel particularly stripped-down when I cannot do any of these things.
If anyone would like to comment on this one particular point I would very much appreciate it. I too live in an area where the power has failed me. And when this happens one generally does not know how long this condition is going to last. And getting a good answer from the electricity company is often, if not always, impossible.
I also have battery back-up systems. What I have concluded is that what my tank would need more than anything else is oxygen and water movement. I have noted fish stressing from what I assume is oxygen depletion (gasping at the surface) in a very short amount of time.
My theory is this: To get the maximum amount of life-sustaining operation from a device (the most efficient method coupled with the least draw on the back-up battery - meaning the longest possible period that the battery will power the life-sustaining device) would be to simply have an air pump with an air stone. The air pump will circulate the water to some degree for filtration with the live rock and at the same time provide oxygen for the animals.
If temperature is an issue and you want to use a back-up power supply, such as a chiller, the high wattage necessary to run one of those things will greatly reduce the power - and hence, the longevity - of the battery in no time as compared with just an air pump)
It is all in the wattage! Sure the battery back-up system will perhaps power everything for a limited amount of time. And even if your battery is new (older batteries do not perform like newer ones), I would think that due to the unknown variable of how long the power is going to be out, preparing for a worst case scenario is the way to go.
In the colder months one also has to be concerned with temperature too. But then, at least you can always build a fire underneath the tank (although I am being factitious here, I recently read somewhere, that this is what they did in the "old days" in an attempt to maintain a practical temperature. UPDATE: I could't find the reference. Perhaps I dreamt it.)