Microgrids that are able to work both in grid-connected and islanded modes need a hierarchical structure based on tertiary, secondary and primary controllers, which are fundamental for the maintenance of frequency and stability. In this paper, two types of controllers are formalized and solved as optimal control problems: tertiary and secondary controls. For secondary control two different scaled single-phase models are used for the microgrid: one merely electric and the other one based on the synchronous machine. The approach is applied to a real test-bed facility: the University of Genova Smart Polygeneration Microgrid (SPM). Specifically, a portion of the microgrid is selected to study the behavior in islanded mode. The considered grid is characterized by: a diesel engine connected to an electrically excited synchronous generator, a photovoltaic plant and an electric storage (these last two are respectively connected to a couple of inverters set as current source generator (CSI)).