The current ideas to power the single strand tether climber center around beaming the power from a ground station to the climber. The most commonly suggested method uses lasers or other high power light sources to transmit the energy, and solar panels to collect this energy at the climber. Probably the biggest issue with this approach is that currently available solar cells are rather inefficient and there will be a significant loss in the energy conversion process. Additionally there are issues with this form of transmission due to atmospheric interference with the light transmission. Clouds, pollution, and movement of the air all have negative effects on the efficiency of such power transmision methods.
The Better Space Elevator solves this problem by eliminating the power beaming system entirely. Using a continuous loop of tether material allows the tether itself to be driven, and therefore act as the power transmission system to the load. This system provides a near lossless transmission of the energy applied to the tether.