This paper studies the problem of robustly optimal operation control of microgrids with a high share of renewable energy sources. The main goal is to ensure optimal operation under a wide range of circumstances, given the highly intermittent and uncertain nature of renewable sources and load demand. We formally state this problem, and, in order to solve it, we make effective use of the hierarchical power system control approach. We consider an enhanced primary control layer including droop control and autonomous limitation of power and energy. We prove that this enables the use of constant power setpoints to achieve optimal operation under certain conditions. In order to relax these conditions, the approach is combined with an energy management system, which solves a robust unit commitment problem within a model predictive control framework. Finally, a case study demonstrates the viability of the control design.