Vividred Operation

In Oshima the happy, carefree 14-year-old Akane Isshiki lived a poor but well-loved life together with her reliable little sister, Momo, who does all the housework, and her grandfather, Kenjirō, a genius inventor who only created useless devices. When the weather is clear, they can see the artificial island, Blue Island, across the sea. In the center of that island rises the revolutionary Manifestation Engine, a discovery that solved the world's energy problems, and leads to some major problems.

Synopsis from Anime News Network