Why bother with an advanced energy storage system at all? It would have to be capable of a MINIMUM of 32KWh just to deal with the ~354-hour Lunar night, assuming 90W average draw. That's pretty big, even at 500Wh/kg, considering we'd have to launch that mass from Earth's surface, when instead it could be made lighter *or* carry more useful instruments, more powerful motors, or whatever. It would be a minimum of 64kg of battery (assuming 100% DOD!), and that does not include support systems necessary to charge that battery at a high enough rate so that it would fill up the battery with available (solar?) incoming power during the ~354-hour Lunar day.
Personally I'd assume 50% DOD, so we could be sure that degradation over time would still leave it with enough capacity to always last the night cycle even as it ages, and also have no worries about damaging the battery by overdischarge. That means at least 128kg of battery.
Since they want *3 Lunar cycles* (presumably 3 synodic periods, or 2125 hours and some change) worth of battery, that's at least 384kg of battery. During Apollo, we barely brought back that much mass *from* the moon, AFAIK. :lol:
That is almost 850 pounds of batteries! Even if you had a battery that could deal with 100% DOD and thus could use half of that, 425 pounds of batteries is a whole lot of weight and size that you don't really need, because there is a better way.
EDIT: I messed up the above 3-cycle calculation. It is actually TWICE that, since 3-cycles includes daytime running as well (although it would need only about 8/9 of the power during the day since it doesn't have to run heaters, presumably). So that is 768kg of battery, for 50% DOD, or 1700lbs of batteries. The 384kg/850lbs is only for 100% DOD!
AFAICS, there is no way to actually achieve what they want unless the energy density is much higher than 500Wh/kg. They want 100kg or less pack, but capable of at least 192KWh (for 3 full day/night cycles). That is close to 2000Wh/kg unless I messed up the math badly. :? And that's assuming 100% DOD!
Hopefully I messed up somewhere else, too because these numbers seem pretty impossible to get around. 
That's assuming 500Wh/kg. You can do the math if that can't be reached, for the other power densities. And for what mass battery you would need if you used existing proven technology.
Oh--one more thing: Whatever is used needs to be "safe" in the case of system or power failure that causes heating or cooling problems. It gets nice and toasty in the day, and danged cold at night, and each of those stay that way for most of their respective cycle halves, of 354 hours.
At the equator, that could be below -279F, or above 242F!
And 500Wh/kg (and especially 2000Wh/kg!) is probably unattainable right now, anyway, or if it is attainable will cost WAY too much money. Even for NASA. :lol:
For that money, I would bet you could stick a solar powered microwave station in both Lunar L4 and L5, and install a rectenna system on the many rovers, bases, orbital spacecraft, etc. that they can power.
No atmosphere to spread the beams or lose power, so if they can be focused well enough you could beam a lot of power to any of these things.
If there are areas to be explored that could be out of LOS of a station's orbital loop, "mirror" stations could be placed in Lunar orbit so that periodically they would overfly the area with an intersection path; if the mirror cannot be done directly it could be done with a receiver/retransmitter. Such stations could also have radio relays on them for data streams, as well as other instrumentation packages for use when they are not receiving a microwave beam (I assume that would interfere with various RF-based instruments and communications, at those power levels).
Tracking the beams to the rovers with the time-delay of light at that distance might be an issue, but not unsolveable, since we would easily be able to predict or program the path of the rovers. Manned craft on the surface might be less predictable if manually controlled, but orbital craft would all be perfectly predictable in all normal circumstances.
I don't know if it is more or less efficient to convert from solar to microwave, receive microwave and convert to electrical energy, use it as it's received, and also store some of it as needed to top off batteries, than it would be to have the solar directly on the rover to charge the batteries, and to carry enough battery to last *at least* two weeks at 90W average draw. But I expect teh rectennas and smaller batteries would enable a smaller rover or at least a lighter one, making it easier for it to traverse rougher terrain (of which there is a lot!
) and to go up hills and thru that fine dust with less power usage.
Dunno what they use for storage on things like the Mars rovers, but that could be used as backup storage on the Lunar rovers, for times when they might go out of LOS of a station or "mirror" station, or the short periods when the L4/5 stations are in Lunar or Earth shadow, unable to provide power.
Doesn't help with this actual challenge, but that's what I would probably do to help power Lunar exploration/exploitation missions, becuase these stations would be permanent installations, and able to beam power anywhere in the Earth/Luna system other than the opposite sides of either body from the stations. A station at Lunar L3 would fix the Earth shadow, and L2 the narrow Farside shadow zone. Not sure what to fix polar shadow zones with, other than polar-orbiting "mirror" units.
... If yer always in shadow, that's one-half of the thermal flux to have to deal with. The spec says "Rover", but what's to prevent the rover from fueling up?
