Technically yes.
Probably yes.
Possibly no.
Hard interconnection: The supplies will have diodes in the output so connecting foreign external voltage may be OK when it is operating and might be OK when it transitions from off to running. There is a possibility that the regulation / feedback does not like to see 19V on the output when it has not provided power and may not start.
Similarly, if one supply is set at say 19.1V out and the other at 18.9 V out,
Best case: the 18.9V supply sees 19.1V so concludes tha all is well so lays low. The 19.1V supply cannot supply the load and 'ags' until the 18.9V supply cuts in to take up the excess.
Worst case: The two supplies play 'pass the parcel' in some manner. the hv version is overloaded and start to shut down or completely shuts down. The LV version leaps in and is in turn overloaded. It shuts down and ...
But, it MAY "just work"
Series output isolating diodes: A Schottky diode or FET super-diode is connected externally to each of the supplies and the two diodes are commoned. Having a shared capacitor at the common point probably helps. I'd expect this to work well, but nothing is 100% when two control systems interact and each is not 'aware' that the other is there. Size of cap may make a difference. Larger reduces swings when serttling down. Too large may inhibit startup.
Adding a diode with say 0.5V drop loses 0.5/19 ~~= 3% = tolerable. The Gigabyte 19V input supply can almost certaionly to;lerate lower voltages than this.
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.
Best Answer
Something like this should work.
Comparators are usually slightly biased (biasing not shown - could perhaps just be drop across wiring with proper design) such that when fuses are not blown comparator outputs are high and LED not lit.
If say battery B12 blows fuse 4 then B12 voltage rises under sudden no load.
Comparator 2 in- rises above its in+ and comparator output goes LOW and lights LED D2.
simulate this circuit – Schematic created using CircuitLab
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WINDOW COMPARATOR MONITORING OF BLOWN BALANCING FUSE.
Here is a conceptual window comparator system that lights an LED if a balance fuse is high or low.
I'm not convinced that this is useful - but, it may be.
I expect that being able to monitor whole string current contribution would tell you if a string was bad - but with a lot less work.
However:
CP is the common point for all 3 cells B4 B5 B6.
Say F3 blows.
CP is now the common +ve voltage of BAT4 and BAT5 but NOT BAT6.
CMP1_+ is slightly above CP due to R3/R1. If BAT6 +ve is still AT CP or below it then CMP1 output will be high.
If BAT6 output rises slightly above CP then CMP1 output will go low signalling a fault.
Similarly
CMP2_- (opposite of for CMP1) is slightly above CP due to R3/R1. If BAT6 +ve is still AT CP or ABOVE it then CMP1 output will be high.
If BAT6 output falls slightly below CP then CMP2 output will go low signalling a fault.
So, CMP1 + CMP2 form a window comparator so that if BAT6 with blown F3 remains very close to CP then no alarm is given. BUT if BAT6 Vout deviates more than very slightly from Cp an alarm will be given.
You need two comparators and 4 resistors per battery.
Comparators can be very low cost. I've assumed an open collector output (eg ye olde LM339, LM393 etc).
BUT - is this really meeting your need? It MAY be.
If
simulate this circuit