Abstract
We introduce a problem of control for power grids with the microgrid architecture. Microgrid is a novel architecture of power grid in which a cluster of distributed energy resources is locally and consistently operated. The objective of the control problem is to determine a controller that keeps the load-generation balance in a power grid and regulates the grid's behavior to satisfy safety specifications. We use a combination of continuous and discrete controllers in order to archive the objective for a rudimentary microgrid. The result is a hybrid controller for the continuous-time nonlinear model and is correct for the microgrid with a realistic setting of parameters.