I imagine from the questions that you have asked that you are planning some project that may require a high capacity lithium iron phosphate battery that you would like to build yourself.
The only large capacity battery pack in high numbers production that uses a number of cells in parallel vs only a couple of large cells in parallel is the Tesla. All of the other EV seem to go with the large capacity pouch cells and then only use a couple in parallel. The advantage to the Tesla is that their power to weight ratio is almost double that of everyone else.
The disadvantage has to be safety. Tesla has 104 patents on its battery pack and most of them have to do with safety. Specifically with how to deal with single cells that short or go into thermal runaway. FYI the Tesla S battery pack uses 74 cells in parallel and then 96 in series.
I have read through their patents and none of them deal with any sort of system to repair or remove damaged individual cells. They just make sure that on the rare occasion that a cell does short or heat up, start fire etc., that it is contained to that cell. They do this by separating each cell by a certain distance, using active and passive cooling, using a fuse at each cell etc.
Tesla brags that they can replace an entire battery pack out of a Tesla S in only 90 seconds, but they make no claims about repairing that battery pack. In fact because of all of the safety features like fire proof foam, it takes a couple of hours for a person to get access to the individual cells of the Tesla battery pack and by that time you have ruined the structure of the battery, so it is no longer useable to the car even if you did replace the destroyed individual cell.
So to answer your question, it appears that they put a lot of effort into preventing a shorted cell from destroying the rest of the pack, but otherwise they leave it there and let the rest of the cells in that parallel group take over.
Remember that the Tesla is demanding a very heavy load from its battery, not only pushing the cells to their limits to get a further distance out of the pack (some owners report cell voltages that dip below 3.0 volts) they also demand a high current for the crazy acceleration the Tesla gets.
From reading their patents, Tesla believes that over charging is much more dangerous than over discharging (this is from tests they have done in their labs). Over charging leads to fires and explosions while over discharging tends to speed up capacity loss.
Good luck in your project. Using lithium iron phosphate cells you are already a magnitude safer.
First things first. In your previous post, you stated that your source would not provide any certification about actual battery capacity. Unless you can get some sort of guarantee, drop the whole idea. At claimed capacity and price, this http://www.ebay.com/gds/18650-Battery-Buying-Guide-test-on-all-from-eBay-below-3-/10000000178020340/g.html is likely what you will get. If you insist on dealing with these bozos, arrange for your total order to be shipped in smaller (say, 100 cells ea) with sufficient time between lots to allow for testing. Structure the order so that if a certain percentage (a few per cent or less) fails test, the entire order is cancelled. If they won't do it, don't buy from them. And good luck getting your money back if they ship you crap.
Second. If you are going to build up blocks, you're going about it backwards. Start with strings of 13 in series, with a PCM. Due to the variations between cells, you MUST not connect many cells in parallel. 2 is generally OK, and some manufacturers are OK with 4, but connecting 12 is a fabulous way to destroy your cells. The problem is that the weakest cell determines the cutoff voltage for the entire block, and it also hogs the entire charge current at the start of charge, resulting in high charge currents and battery temperature problems.
Third. You need a BMS for each string.
Fourth. For your application, you need a different package than 18650s. If you're willing to take chances, you can buy or build a spot welder and put tabs on the cells, then solder your strings. If you're thinking of using standard cell holders, forget it. Over long periods of disuse, corrosion at the contact points will be a killer.
Fifth. You need to rethink your cooling setup. The cell assemblies must be physically separated to allow airflow, and you'll need a powerful fan. If you don't know how much fan you'll need, you're in trouble. And you need a mechanism to allow the temperature sensor to disable charging as appropriate if the fan is not adequate.'
Sixth. Your calculations are off somewhere. Even allowing for the fact that you don't seem to know the difference between power and energy, the calculations for your battery array are straightforward. 3.7 volts x 4.9 Ah x 3744 equals about 86 kWh. If you want this to last "several days" (let's say two), then the allowable power is about 2800 kW, not 30kW. 30 kW / 3744 is 8 watt per cell, or about 2 amps. While this is not, by itself, an unreasonable number, it makes no sense given your stated battery capacity. You'd expect a lithium ion cell to handle at least a 1C rate, or 5 amps. If 2 amps is the number given by your prospective supplier, it indicates that he's not being honest (although the price/capacity/documentation issues pretty well establish that).
7th. Oh, feh. Enough of this. Try another approach. Do a lot more research, and start experimenting. Start small, and get experience with progressively larger arrays. Trying to jump in at the scale you're proposing is just not a good idea.
First the bucket, then the pail,
Then the laboratory scale.
Ever bigger, ever faster;
Faster, faster, then - disaster.
Best Answer
Advice: 1) Your battery bank should be 48V (otherwise wire diameters will become unreasonable). Run through the calculations and you will see what I mean. For example, if you need, even momentarily, 50 Amps of 120V AC, that would be over 500 Amps at 12V.
2) Your charge controller must be designed for lithium batteries (or be programmable). Lithium batteries cannot be safely floated. You must stop charging them once charge is complete.
3) Investigate any building code issues prior to purchasing anything. If you are going to pull permits to do this, you will need approved plans. An inspector might not allow you to put in a large lithium ion battery pack without UL approvals or some such. If you live in the US you should be concerned about this. If you are outside the US, you are outside my experience.
4) When you put all those batteries together and charge or discharge them rapidly, the batteries in the middle will be unable to dissipate heat effectively. I don't know how big a problem this is but I would be very worried about it. I think you will need a thermal sensor near the middle of the pack to make sure the batteries do not overheat.
5) You cannot put the batteries in parallel without some type of over-current protection. It could be as simple as a fuse or PTC. The reason is, you don't want one bad cell (imagine it failing short circuit) to become a sink for all the other cells in parallel. This could make a bad situation much worse.
That is all I can think of at the moment. I can tell you right now that I would not do this. I would use AGM lead acid batteries. If you provide individual over voltage protection for each cell, that might help prevent the dangers of imbalance. When one cell in a series string stops accepting current, the whole series string stops. So the string would only be as good as the weakest cell.