First let's adjust the battery pack voltage to 165.6V or 46 cells, because the peak voltage of the AC signal is \$\sqrt { 2 } * 117 = 165.46V\$. Then rectify the voltage, so we aren't reverse biasing the battery pack:
Now apply that AC voltage to the battery pack when it is fully discharged to 92V (2V per cell) and the only time a charge current will flow is when the AC line voltage exceeds the battery pack voltage.
In this graph, V(n001) is the AC voltage. V(n002) is the voltage on the battery's positive terminal. I(V2) is the current into the battery, assuming a 10\$\Omega\$ internal resistance, which is a value I randomly selected.
This has 2 potential problems:
I don't think this is a major issue, as the current may be low and the effects negligible, but it's not good to have all the current in the system flow at only one point of the wave form. This is an example of non-linear/non-sinusoidal distortion power factor. (As opposed to displacement power factor, which is linear about out of phase.) This is similar to a basic switched mode power supply, which only draws power when the rectified AC voltage exceeds the storage capacitor voltage. From wikipedia:
the input current of such basic switched mode power
supplies has high harmonic content and relatively low power factor.
This creates extra load on utility lines, increases heating of
building wiring, the utility transformers, and standard AC electric
motors, and may cause stability problems in some applications such as
in emergency generator systems 3
How does this cause heating of the building wiring and utility transformers? Here is one way to think about it: a circuit could draw a steady sinusoidal 5A at 60Hz, or it might draw 20A spikes at 60Hz. Heat created by current passing through a wire goes up with the square of the current and the decrease in time during which the current is flowing does not compensate. (\$P={ i }^{ 2 }Rt\$) I've had personal experience with this when trying to maximize efficiency with a bicycle hub dynamo. No current would flow until the voltage exceeded the storage capacitors, then the hub was practically shorted and a large portion of the power was lost to heating up the dynamo.
(If you prefer printed books, another good discussion of this is in Electromagnetic Compatibility Engineering by Henry W. Ott, chapter 13 section 9. 5)
This is essentially a constant voltage across the battery, which increases to the maximum battery voltage. This can cause cell balancing issues and excessive current, which can damage the LiFePO4 batteries.
Controlling the current through the batteries and limiting the power factor distortion can both be solved with, for example, a Buck-boost Converter 4 using a current controlled feedback loop or another switched converter topology and specifically designed charge controller IC.
At this point, the charger is just as complex as the original system that had a lower battery voltage. It may be that requiring a smaller voltage step down could improve system efficiency, but I believe this would depend on the overall design and component selection.
Another interesting thing to point out here, is that the current would be delivered in pulses. I have seen some comments that pulsed current charging is safe for LiFePO4 batteries, but I haven't conducted or read any research regarding this, and would recommend further investigation.
Schematic and graph were generated by LTSpice. 6