Just a couple of notes:

1. The diagram of the warp field from Star Trek is unclear whether the grid shows spacetime from the reference frame of the ship or an observer.
2. For the Casimir effect the plates need to be conductive but not conducting. Power is not used however the charges from the virtual particles need to be able to flow within regions of the conductor in order that their outward force be effectively negated, however overall there will be no resulting current or work done.