One main advantage is that it is easier, cheaper, and more efficient to battery back the system. -48V DC can be made simply of 4 12V batteries (think giant car batteries) in series. The string looks like this:
AC POWER --> RECTIFIER --> BATTERIES --> DC LOAD
To battery back an AC system you have this string.
AC POWER --> RECTIFIER --> BATTERIES --> INVERTER --> AC LOAD (which is usually converted back to DC by the equipment's power supply to run the electronics).
No step in this process is 100% efficient, and every part costs $$. DC eliminates a lot of these steps.
This is not to say that everything in a Central Office is DC powered -- they still have Air Conditioning, Lights, convenience outlets, etc -- but if you're ever in a Central Office when the power goes out, those things turn off until the generator kicks on and the transfer switch swings.
Also -- doing things with Low Voltage (-48V) does have some EXPENSIVE costs associated with it. COPPER power runs are very expensive because of the low voltage used (-48VDC) -- it takes more than twice as much copper to feed the same Wattage/Amperage as a 120V supply.
A=V*W
W=V/A
V=W/A
The simplest rating on a wire is how many A it can draw for how many feet (there are other ratings, such as maximum voltage, but most of these approach 600V, so don't apply to this comparison).
Most of these additional costs are one-time costs and therefore are justifiable.
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