A system for reducing evaporation of slow moving water in a water conveyance structure, such as an aqueduct or canal, which includes a series of floating membrane sheets, where each sheet has a leading edge attached to a cable anchored at each end to the water conveyance structure across the water and a trailing edge that underlies the leading edge of the adjacent sheet and that floats on the surface of the water, with the membrane sheets carrying a solar energy system for the production of electrical energy.